Design of a Planetary Explorer
Third Year Project
Jack Andrews (ChCh) Aamir Aziz (New) Nicholas Baker (SJC) Alexander Chadwick (SJC) James Coates (BNC) Oliver Cohen (LMH) Liam Donovan (Hert) Hugo Grimmett (BNC) James Hawkes (Keb) Michael May (Worc) Joshua McFarlane (SJC)
2009-2010 Contents
1 Introduction 13
1.1 Mission to Titan ...... 13
1.2 Titan’s Characteristics ...... 13
1.3 Mission Components ...... 14
2 Delivery of the Orbiter 15
2.1 Introduction ...... 15
2.2 Orbital Mechanics ...... 15
2.2.1 Kepler’s Laws ...... 15
2.2.2 Energy Considerations ...... 17
2.2.3 Characterising Orbits ...... 18
2.3 Transfer Orbits ...... 20
2.4 The N-Body Problem ...... 20
2.4.1 A Computational Model ...... 20
2.4.2 Sourcing Planetary Data ...... 21
2.5 Simulating the Problem in Matlab ...... 22
2.6 Fly-by Manoeuvres ...... 22
2.6.1 The Origin of Gravity-Assist Velocity Increase ...... 22
1 CONTENTS
2.6.2 Calculating the Velocity Increase ...... 23
2.7 The Oberth Effect ...... 23
2.8 Time-to-Intercept & Mean Anomaly ...... 23
2.9 Targetting Manoeuvres ...... 24
2.10 Planning out the route to Titan ...... 26
2.11 Launch ...... 26
2.11.1 Calculating the Relative Launch Velocity ...... 28
2.11.2 Optimal Launch Window ...... 29
2.12 The Control System ...... 31
2.12.1 Implementing the Control System in Matlab ...... 31
2.13 The Simulation ...... 32
2.14 Conclusions ...... 35
3 Attitude Control System 36
3.1 Introduction ...... 36
3.1.1 Purpose ...... 36
3.1.2 Control Goal ...... 37
3.1.3 System Overview ...... 37
3.1.4 Aim ...... 38
3.2 Mathematical model of the orbiter dynamics ...... 38
3.2.1 Reference Frames ...... 38
3.2.2 Rigid body Dynamics ...... 39
3.2.3 Attitude Kinematics ...... 40
3.2.4 Actuator Dynamics ...... 40
3.2.5 Gravity Gradient Torque ...... 41
2 CONTENTS
3.2.6 Linearisation of the model ...... 42
3.3 Continuous-time Controller ...... 43
3.3.1 Plant Model ...... 43
3.3.2 Design Specifications ...... 44
3.3.3 PID Control ...... 45
3.3.4 Optimal Control ...... 47
3.4 Discrete-time Controller ...... 50
3.4.1 Discrete Plant Model ...... 50
3.4.2 Design by Emulation ...... 51
3.4.3 Estimator Design ...... 51
3.4.4 Regulator Design ...... 53
3.5 Conclusions ...... 54
4 Landing the Probe 56
4.1 Introduction ...... 56
4.2 Gathering Data ...... 56
4.2.1 Wind Speed ...... 57
4.2.2 Pressure and Density ...... 59
4.3 Simulation Engine ...... 60
4.3.1 Gravity ...... 60
4.3.2 Drag ...... 60
4.3.3 First Simulation ...... 61
4.3.4 Drift ...... 62
4.4 A Safe Landing ...... 62
4.4.1 Parachutes/Thrusters ...... 62
3 CONTENTS
4.4.2 Simulating Parachutes ...... 63
4.4.3 Test Data ...... 63
4.5 Analysis ...... 66
4.5.1 Test Plan ...... 66
4.5.2 The Need For Analysis ...... 67
4.5.3 Analysis Example - Drift ...... 68
4.5.4 Parameter Weighting ...... 70
4.5.5 Result Weighting ...... 72
4.5.6 Finding the Optimal Area ...... 72
4.6 Final Design ...... 75
4.6.1 Results ...... 76
4.7 Errors ...... 78
4.7.1 Systematic Errors ...... 78
4.7.2 Theoretical Wind Model ...... 80
4.8 Predicted Landing Zone ...... 81
5 Problems Faced by the Explorer During its Voyage Through Space 83
5.1 Introduction ...... 83
5.2 Problems ...... 83
5.2.1 Problems Encountered on Earth ...... 84
5.2.2 Problems Encountered whilst en Route to Titan ...... 84
5.2.3 Problems Encountered whilst in Orbit around Titan ...... 85
5.3 Effects ...... 87
5.3.1 Heating Effects ...... 87
5.3.2 Radiation Effects ...... 88
4 CONTENTS
5.3.3 Power Requirement Effects ...... 90
5.4 Solutions ...... 91
5.4.1 Solving the Heating Problem ...... 91
5.4.2 Solving the Radiation Problem ...... 94
5.4.3 Solving the Electrostatic Discharge Problem ...... 97
5.4.4 Solving the Power Demand Problem ...... 99
5.4.5 Solving the Environmental Hazard Problem ...... 101
5.5 Conclusion ...... 103
6 Lander Power Systems 104
6.1 Introduction ...... 104
6.1.1 Lander Power Specifications ...... 104
6.1.2 Design Parameters ...... 105
6.2 Power System Options ...... 105
6.2.1 Solar ...... 105
6.2.2 Radioisotope Thermoelectric Generators ...... 106
6.2.3 Wind ...... 107
6.2.4 Tidal ...... 108
6.2.5 Batteries ...... 108
6.2.6 Selection ...... 109
6.3 Wind Power ...... 110
6.3.1 Feasibility ...... 110
6.3.2 Implementation ...... 112
6.3.3 Deployment and Operation ...... 115
6.3.4 Voltage rectification ...... 116
5 CONTENTS
6.3.5 Conclusions ...... 118
6.4 Secondary Batteries ...... 119
6.4.1 Chemistry ...... 119
6.4.2 Transit to Titan ...... 122
6.4.3 Charging ...... 123
6.4.4 Conclusions ...... 125
6.5 Power Usage Routine ...... 127
6.6 Lander Heating ...... 127
7 UAV Design and Power 128
7.1 Introduction ...... 128
7.2 Operational Conditions on Titan ...... 129
7.2.1 Location ...... 129
7.2.2 Atmosphere and Terrain ...... 129
7.2.3 Meteorological activity ...... 130
7.3 Design Decisions ...... 131
7.3.1 Heavier or Lighter than Air flight? ...... 131
7.3.2 Balloon Type ...... 132
7.3.3 Propulsion ...... 134
7.3.4 Operating Height ...... 135
7.3.5 Materials ...... 136
7.4 Power Decisions ...... 136
7.4.1 Batteries ...... 137
7.4.2 Solar Power ...... 137
7.4.3 RTGs ...... 138
6 CONTENTS
7.4.4 Other options ...... 139
7.4.5 RHUs ...... 139
7.5 Balloon Thermodynamics ...... 140
7.6 Conclusion ...... 140
8 UAV Control 141
8.1 Introduction ...... 141
8.1.1 Nomenclature ...... 141
8.2 Hot Air Balloon Dynamics ...... 142
8.2.1 Atmospheric properties ...... 142
8.2.2 Balloon Equations of Motion ...... 143
8.2.3 Linearisation ...... 145
8.2.4 Numerical Parameters ...... 146
8.3 Modelling ...... 147
8.3.1 Linear Model ...... 147
8.3.2 Non-Linear Model ...... 148
8.3.3 Comparison of Models ...... 148
8.4 Thermodynamics ...... 151
8.4.1 Thermodynamic Model ...... 152
8.5 Titanic ballooning ...... 153
8.5.1 A More Refined Atmospheric Model ...... 154
8.5.2 Valving ...... 155
8.5.3 Building a Controller ...... 157
8.6 Testing the Controller ...... 158
8.6.1 Sinusoidal Demand ...... 158
7 CONTENTS
8.6.2 Entry Scenario ...... 158
8.6.3 Landing ...... 161
8.6.4 Disturbance Rejection ...... 163
8.7 Horizontal Control ...... 163
8.7.1 Wind Data ...... 163
8.7.2 Horizontal Dynamics ...... 165
8.7.3 The Horizontal Controller ...... 165
8.8 Conclusion ...... 169
9 Remote Sensing 171
9.1 Introduction ...... 171
9.2 Information to Sense ...... 171
9.2.1 Temperature ...... 172
9.2.2 Chemical ...... 173
9.2.3 Life ...... 175
9.2.4 Light ...... 176
9.2.5 Sound ...... 177
9.2.6 Acceleration ...... 177
9.2.7 Wind Speed ...... 179
9.3 Communications ...... 181
9.3.1 Radiation Hardening Chips ...... 181
9.3.2 Wired Communication ...... 182
9.3.3 Light Communication ...... 183
9.3.4 Wireless Protocols ...... 183
9.3.5 Localisation ...... 185
8 CONTENTS
9.4 Module Design ...... 186
9.4.1 Antenna Design ...... 186
9.4.2 Landing Protection ...... 188
9.4.3 Flotation ...... 190
9.4.4 Storage and Deployment ...... 191
9.5 Conclusion ...... 193
10 Deep space communications 194
10.1 Introduction ...... 194
10.1.1 Challenges and Requirements ...... 194
10.2 Link Budget and Signal to Noise Ratio ...... 195
10.2.1 Frequency selection ...... 198
10.2.2 Path loss ...... 200
10.2.3 Orbiter antenna ...... 200
10.2.4 Earth antenna ...... 201
10.2.5 Conclusion ...... 201
10.3 Modulation scheme ...... 201
10.3.1 Appropriate schemes ...... 202
10.3.2 Spectral efficiency ...... 204
10.3.3 Pulse shaping ...... 206
10.3.4 Bit error rate and noise rejection ...... 207
10.3.5 Microwave mixing ...... 209
10.4 Simulation of modulator/transmitter and receiver/demodulator ...... 209
10.4.1 Transmitter design ...... 209
10.4.2 Receiver design ...... 210
9 CONTENTS
10.4.3 Demodulation ...... 210
10.5 Hardware and software implementation ...... 214
10.5.1 Implementation of the digital stages ...... 214
10.5.2 Mixers ...... 216
10.5.3 Amplification ...... 216
10.5.4 Conclusion ...... 216
10.6 Internal communications ...... 217
10.6.1 Internal Protocol ...... 217
11 Navigation Systems 219
11.1 Introduction ...... 219
11.2 Coordinate Systems ...... 220
11.3 Orbiter Navigation ...... 221
11.3.1 Potential Methods and Analysis ...... 222
11.3.2 Software ...... 225
11.3.3 Hardware ...... 227
11.4 UAV and Lander Navigation ...... 228
11.4.1 Potential Methods and Analysis ...... 228
11.4.2 Conclusions ...... 233
12 Titanic Communication Systems 234
12.1 Overview of UAV, Lander and Orbiter Communication ...... 234
12.2 Antennas ...... 234
12.3 Amplifiers ...... 236
12.4 Noise ...... 236
10 CONTENTS
12.5 Range of Transmission ...... 237
12.6 Conclusions ...... 240
13 Imaging Systems 241
13.1 Introduction ...... 241
13.2 Systems Overview ...... 241
13.2.1 The Three Imaging Systems ...... 241
13.2.2 System Specialisations ...... 242
13.3 Base Imaging System ...... 242
13.3.1 CCD Sensor ...... 243
13.3.2 Computer Hardware ...... 243
13.3.3 Operating System ...... 244
13.3.4 Image Compression ...... 245
13.3.5 Image Storage ...... 248
13.3.6 Hierarchy of Transmission ...... 248
13.4 Lander Imaging System ...... 249
13.4.1 Camera Mounting ...... 249
13.4.2 Lamp ...... 249
13.4.3 Autofocusing Method ...... 250
13.4.4 Autofocus Noise Rejection ...... 251
13.4.5 Focus Window ...... 252
13.4.6 Climbing Search Algorithm ...... 253
13.5 Orbiter Imaging System ...... 253
13.5.1 Lens Filter ...... 254
13.5.2 Infinity Focus ...... 255
11 CONTENTS
13.5.3 Mapping Algorithm ...... 255
13.5.4 Modeling the Orbit ...... 256
13.5.5 Locating previous photos which have captured portions of the current view . . 257
13.5.6 Determining the useful region of a photo ...... 258
13.5.7 The complete Simulation ...... 261
13.5.8 Optimisation and Implementation ...... 263
13.5.9 Choosing parameters based on simulation ...... 263
13.6 UAV Imaging System ...... 266
13.6.1 Infinity Focus ...... 266
13.6.2 Lens Filter ...... 267
13.7 Conclusion ...... 267
Appendices 268
A Calculating Launch Windows In Matlab 269
B The PD Controller in Matlab 272
C Optimal Control: LQR Controller in Matlab 273
D Estimator Design in Matlab 275
E Orbiter Navigation Simulation in MATLAB 277
Bibliography 280
12 CHAPTER 1 - Hugo Grimmett
Introduction
1.1 Mission to Titan
This document details the technical specifications of a mission to explore the moon Saturn VI, more commonly known as Titan. The mission is to send various autonomous units to the distant moon in order to learn more about it. Having arrived at their destination, these units are to take detailed photographs of the surface, take measurements of radiation levels, temperature, wind speed and direction, and any seasonal change over the mission duration, which is estimated to be greater than
365 days.
1.2 Titan’s Characteristics
Titan is interesting because it is a very large body with a dense nitrogen-based atmosphere (with radius 0.404 times that of Earth’s [154]). This makes it difficult to take accurate readings (such as those mentioned above) from Earth using telescopes, and so a closer encounter is required. A previous mission which took readings on Titan, the Huygens probe from the Cassini orbiter, found methane lakes and methane clouds, but as of yet there has been no mission dedicated to learning more about this seemingly impenetrable moon. Very little is known about the composition of the core, although various hypotheses about layers of ice and ammonia-rich water exist [213]. However, it is certain that there is no metallic core, and hence no magnetic field.
13 Chapter 1. Introduction Hugo Grimmett
1.3 Mission Components
There are three units or parts to the mission apparatus: an orbiter, a lander, and a hot air balloon
(or Unmanned Aerial Vehicle, UAV). Once in a stable orbit, the orbiter will drop the lander near the Northern pole of Titan, which in turn will release the UAV during its descent. The lander will establish a permanent position, and the UAV will circle the moon at an altitude of approximately
10km. The orbiter will gather the data accumulated by its two counterparts and relay them back to
Earth.
There are eleven members working on this project, and they have been split into groups of three or four to work on specific domains. The domains are as follows:
• Deployment. This group is responsible for getting the orbiter to Titan, and making sure the
lander and orbiter are released correctly. Getting the lander to the correct landing velocity
requires carefully-timed parachute releases, which if performed incorrectly, could result in a
crash. This group is also responsible for analysing the wind characteristics on the moon and
modelling how the UAV will move over time.
• Power. The three units will require various power sources for electricity and heat, and all have
different requirements for duration, intensity and mass. The electrical systems used for sensing,
processing and communication will need to be kept above certain minimum temperatures in
order to function correctly.
• Navigation, communication and sensing. This involves the data gathered by the three units, and
how each datum is “titan-tagged”, or linked to a precise time and location on Titan corresponding
to when and where it was taken. These data need to be passed between the unit which gathered
them, combined with the time and location information which may reside on another unit, and
transmitted back to Earth via the orbiter.
This report has been compiled and formatted by James Coates.
14 CHAPTER 2 - Joshua McFarlane
Delivery of the Orbiter
2.1 Introduction
To achieve the successful delivery of the probe into an orbit around Titan the route from earth needs careful planning and simulation. In order to orbit around Titan the probe must gain energy to climb out of the Sun’s gravity well to the orbit radius of Saturn. Then it must shed energy to enter an orbit around Saturn at the same orbit radius as Titan; finally an orbit around Titan will be established by further shedding potential energy and becoming trapped in Titan’s gravity well. In order to devise a plan to achieve this the orbital mechanics of the solar system were carefully considered.
With the route planned, it will be implemented on the probe while in space using an on-board con- troller. To test the operation of this controller and the feasibility of the route a simulation was written in Matlab and the results analysed to assess possible improvements to the controller and route.
2.2 Orbital Mechanics
2.2.1 Kepler’s Laws
The trajectory of a body in free orbit around a much more massive body is determined by Keper’s laws of planetary motion: [95]
l r = (2.1) 1 + e cos ν
15 Chapter 2. Delivery of the Orbiter Joshua McFarlane
( ) d 1 r2 ν˙ = 0 (2.2) dt 2
4π2a3 P 2 = (2.3) GM
Where:
• r = the orbital radius
• l = the semi-latus rectum1 (see figure 2.1)
• e = the eccentricity of the orbit
• ν = the true anomaly - the angle through which the body has travelled since passing the
periapsis2 (see figure 2.1)
• P = the orbital period
• a = the semi-major axis3 (see figure 2.1)
• G = the universal gravitational constant (∼ 6.67 × 10−11 m3 kg−1 s−1)
• M = the mass of the central body
These equations are simplified from their original form with the assumption that one of the bodies has a much larger mass than the other and so the centre of mass of the system can be assumed to be coincident with that of the largest body.
The first equation states that orbits follow eliptical paths with the central, massive body at one of the focii. The second equation states that a line drawn between the body in orbit and the body which it is orbiting will sweep out equal areas in equal times (see figure 2.2.) The third equation states that the orbital period squared is proportional to the semi-major axis of the orbit cubed.
1 π The semi-latus rectum is the orbital radius of the body in consideration when ν = 2 2The periapsis is the point at which the orbiting body is closest to the central body 3The semi-major axis is the arithmetic mean of the apoapsis radius and the periapsis radius
16 Chapter 2. Delivery of the Orbiter Joshua McFarlane
Orbiting body Semi-latus rectum
Second focus Central body
2
Figure 2.1: Illustration of some of the properties of an ellipse.
Figure 2.2: Illustration of Kepler’s second law. [44] Areas A1 & A2 are equal and the difference between times t1 & t2 is equal to that between times t3 & t4
Using these as a starting point many more useful relationships between orbital parameters can be determined.
2.2.2 Energy Considerations
By applying conservation of energy it can be stated that in any unpowered orbit the relationship between orbital radius and velocity between any two points in the orbit is given by:
17 Chapter 2. Delivery of the Orbiter Joshua McFarlane
1 2 GMm 1 2 GMm mv1 − = mv2 − (2.4) 2 r1 2 r2
Or equivalently:
( ) 2 2 1 1 v2 − v1 = 2GM − (2.5) r2 r1
2.2.3 Characterising Orbits
A corollary of Kepler’s second law (equation 2.2) is, for any two points 1 & 2 during an orbit:
ωr2 = const (2.6)
Considering two separate points on an orbit, the angle between the velocity and position vectors ‘γ’ can be related to the angular velocity: (see figure 2.3)
v sin γ = ωr (2.7)
Figure 2.3: Illustration of the angle ‘γ’ [27]
Mostly the orbits cosidered were elliptical and they will be initiated at either the apoapsis or the periapsis to make the most efficient use of fuel (see section 2.3.) Using the relationships established in
18 Chapter 2. Delivery of the Orbiter Joshua McFarlane equations 2.5 & 2.7, and taking the two reference points to be the apoapsis and periapsis, the velocities at these points can be determines in terms of the altitudes.
r1v1 sin γ1 = r2v2 sin γ2 (2.8) π ↓ Taking reference points r & r where γ = γ = a p r p 2
rpvp = rava (2.9)
This is substituted into equation 2.5 to give:
( ) 2 2 1 1 vp − va = 2GM − (2.10) rp ra r ↓ v = p v a r p ( ) (a ) 2 2 rp 1 1 vp − vp = 2GM − (2.11) ra rp ra ( ( ) ) ( ) 2 − 2 rp ra rp vp 1 − = 2GM (2.12) ra rarp ( ) ( ) r 2 − r 2 r − r v 2 a p = 2GM a p (2.13) p r 2 r r a ( a p )( ) r − r r 2 v 2 = 2GM a p a (2.14) p r r (r + r )(r − r ) ( a p )a p a p 2 ra vp = 2GM (2.15) rp (ra + rp)
The perapsis velocity is therefore calculated as:
√ 2GMra vp = (2.16) rp(ra + rp)
The apoapsisl velocity is, similarly:
√ 2GMrp va = (2.17) ra(ra + rp)
19 Chapter 2. Delivery of the Orbiter Joshua McFarlane
2.3 Transfer Orbits
When adjusting the orbital radius of the probe, the best orbit to use is a Hohmann transfer orbit.
This is because it requires the lest fuel overall for the transfer. [105]
Figure 2.4: Illustration of a Hohmann Transfer Orbit
2.4 The N-Body Problem
All the equations considered so far are only concerned with the interaction between two bodies. To derive equations describing the behaviour of a system with three or more bodies is more complicated and are not discussed here. This is because the 2-body approximation turns out to be a useful simplification which results in an imperceptable error (discussed further in subsection 2.4.1)
2.4.1 A Computational Model
Because of its complexity it is best to solve the N-body problem using a computational model. Using a pre-written simulation of the computational solution of the N-body problem [161] the fidelity of the 2-body equations were tested using the planets in our own solar system. The differences in the predicted trajectories of the 2-body model, the computational model, and the actual values (source discussed in subsection 2.4.2) were insignificant - proving the assumptions made do not affect the
20 Chapter 2. Delivery of the Orbiter Joshua McFarlane
fidelity of the results. The differences between the trajectories predicted by the computational model and those from NASA can be seen in figure 2.5.
Figure 2.5: Differences in trajectories predicted using different methods
2.4.2 Sourcing Planetary Data
While the simulation used here calculated the trajectories of all the planets based on a set of initial conditions it is clear that computing the motion of the planets during each simulation is unnecessary as any changes we make to the trajectory of the probe will not alter the trajectories of the planets perceptibly. The improved simulation function drew the data for the future co-ordinates of the planets from a NASA model [112] rather than calculating them internally using the computational N-body simulator.
21 Chapter 2. Delivery of the Orbiter Joshua McFarlane
2.5 Simulating the Problem in Matlab
Using the data obtained from the NASA website it was then possible to run the simulation of the solar system with a set of initial conditions for the probe and plot the trajectory the probe would take under ’free-fall’ (i.e. with no thrusters active on the probe.) By adjusting the initial position and velocity of the probe the simulation was tested to ensure the output trajectory matched that predicted by classical mechanics.
2.6 Fly-by Manoeuvres
2.6.1 The Origin of Gravity-Assist Velocity Increase
The means by which the probe can gain energy through gravitational interaction during a fly-by can be explained through the use of a velocity diagram. Considering the motion of the probe relative to the planet in figure 2.6, the probe follows a hyperbolic trajectory and the magnitudes of the incoming velocity and the final velocity are equal and assumed to be vinf for this hyperbolic orbit.
Figure 2.6: Trajectory of the probe relative to the planet during a fly-by compared with trajectory relative to the sun [13]
22 Chapter 2. Delivery of the Orbiter Joshua McFarlane
Comparing this to the motion of the probe in the frame of reference of the Sun with the planet moving to the left in figure 2.6 is is clear that the deflection of the probe’s velocity relavive to the planet has given rise to an overall increase in the velocity of the probe relative to the Sun.
2.6.2 Calculating the Velocity Increase
To look quantitatively at the effects of fly-by manoeuvres in increasing the orbit velocity of the probe it is necessary to consider computational solutions to the restricted three-body problem. [56] The restricted three-body problem is a simplified version of the standard three-body problem with the assumption that one of the bodies has negligable mass compared to the other two.
2.7 The Oberth Effect
By using the thrusters at the periapsis of a hyperbolic fly-by it is possible to gain a greater benefit from the same amount of fuel. [47] [196] This is why the probe will fire the thrusters to initiate the transfer orbit over the closest point of approach during a fly-by.
2.8 Time-to-Intercept & Mean Anomaly
In order to ensure fly-by manoeuvres are executed correctly the probe will need to know how long it will take to intercept the orbit of the planet it is targetting. This can be calculated using a parameter called the mean anomaly. The mean anomaly is defined as the time elapsed since the periapsis as a proportion of the total orbital period expressed as an angle in radians. It is given the symbol M.
t M = 2π × (2.18) p
Since the period of the orbit is known from Kepler’s third law (equation 2.3) this can be rewritten as:
√ GM M = t sun (2.19) a3
In order to relate this to the true anomaly – ν – which is the angle between the current position in the orbit and the position at the periapsis as measured at the body round which the probe is orbiting,
23 Chapter 2. Delivery of the Orbiter Joshua McFarlane the intermediate variable E, the eccentric anomaly must be defined. E is related to ν by: [27]
e + cos ν cos E = (2.20) 1 + e cos ν and in turn the eccentric anomaly is related to the mean anomaly by: [27]
M = E − e sin E (2.21)
Remembering theat the true anomaly is related to the orbit radius by the equation of an ellipse in polar co-ordinates:
a(1 − e2) r = (2.22) 1 + cos ν
The time until the probe will be at the same orbit radius as the target planet can be calculated.
2.9 Targetting Manoeuvres
If the calculation of time-to-intercept reveals that the probe will be in position slightly ahead of or behind the target planet it will be necessary to adjust the trajectory such that the two come sufficiently close to interact in the desired manner and the probe recieves a gravity boost.
For example, if the probe is on such a trajectory as to result in the probe arriving ahead of the planet at the intersection of the orbitt it will adjust the trajectory acordingly (see figure 2.7.)
24 Chapter 2. Delivery of the Orbiter Joshua McFarlane
Trajectory of orbiter
Trajectory of planet Position of planet at time of intersection Position of orbiter at time of intersection
(a) The orbiter will arrive at the intersection point ahead of the planet.
Original orbiter Altered position trajectory of orbiter at time of intersection Altered trajectory of orbiter
Trajectory of planet Altered position of planet at time of intersection
(b) The periapsis of the transfer orbit is reduced to move the intersection point.
Figure 2.7: Altering the trajectory of the probe to ensure gravitational interaction during fly-bys. The closest point of approach is reduced.
25 Chapter 2. Delivery of the Orbiter Joshua McFarlane
2.10 Planning out the route to Titan
In deciding on the optimum route to Titan, the best use of gravity assist will need to be made in order to reduce the fuel requirements while still keeping the journey time low. Kepler’s third law
(equation 2.3) states that the orbital period of a body in free-fall is proportional the the semi-major axis of the orbit raised to the power of 3/2. It would therefore be best to first perform a fly-by of a planet with a smaller orbit radis than earth to keep the semi-major axis of the orbit of the probe small while allowing it to gain enough kinetic energy to carry it out of the sun’s gravity well to the orbit radius of Saturn.
This makes Venus an ideal candidate for the first fly-by. Mars was considered as an alternative candidate for the first fly-by as the probe is required to shed total orbital energy at launch in order to intercept Venus (at a lower orbit radius than Earth.) Initiating a Hohmann transfer orbit to Mars, however, would mean that the probe was travelling at a lower velocity than Mars at intercept; it would therefore receive a reduction in velocity from the interaction during the fly-by rather than an increase.
Furthermore, the mass of Mars is smaller than that of Venus4 so the magnitude of the gravity assist obtainable from Venus is greater that from Mars.
After the first fly-by of Venus the orbiter will orbit the Sun once before passing Venus again for a second fly-by. During this fly-by the thrusters on the probe will fire and increase the velocity so as to initiate a Hohmann transfer orbit to Saturn. At the apoapsis of the transfer orbit the probe will be pulled into Saturn’s gravity well and, by performing another manoeuvre, a circular orbit around
Saturn will be initiated. From this orbit another Hohmann transfer will be made to intersect with
Titan and another orbit insertion will result in the probe having a stable orbit around Titan.
2.11 Launch
The launch of the probe from Earth is not considered in the simulation. This is because a time-step of one hour is used; this is insufficient to simulate the conditions at launch as the force acting on the orbiter due to the gravity of the Earth will change significantly over one time-period. An initial velocity was assumed, determined by calulations resulting in the ideal inital trajectory (this is discussed further in section 2.11.2.) An initial height of 9.27 × 105km was chosen as the starting altitude during the simulation as this was determined to be the edge of the Earth’s sphere of gravitational influence using
4The mass of Mars is 6.42 × 1023kg while that of Venus is 4.87 × 1024kg. The mass of the Earth is 5.97 × 1024kg.[123]
26 Chapter 2. Delivery of the Orbiter Joshua McFarlane
Earth
Venus
Saturn Orbiter
Insertion into orbit around Saturn
Figure 2.8: Orbiter path to Saturn
an equation derived by Laplace: [25]
[ ] 2 MP 5 rP = DSP (2.23) MSun
Where:
• DSP = the distance between the Sun and the planet (the Earth)
• MP = mass of the planet
• MSun = mass of the Sun
The origin of this equation is the assumption that the ‘sphere of influence’ is the volume in which the gravitational force from the Earth which acts on a body in space is stronger than the gravitational force from the Sun. In reality this does not produce a perfect sphere but this simplifying assumption can be made based on the fact that the distance between the Earth and the Sun will be much greater than the radius of the sphere of influence.
27 Chapter 2. Delivery of the Orbiter Joshua McFarlane
2.11.1 Calculating the Relative Launch Velocity
Ignoring the rotation of the surface of the Earth, the required relative velocity between the probe and the Earth can be calculated by summing the vectors corresponding to:
• The required final velocity for the desired orbit trajectory taken relative to the sun;
• The velocity of the Earth relative to the Sun;
• The required additional velocity required to overcome the gravitational pull from the Earth.
Figure 2.9: Required relative velocitiy at the initiation of a Hohmann transfer orbit.
So overall:
vlaunch = vesc + vEarth − vHohmann (2.24) √ √ √ 2GMEarth GMSun 2GMSun vlaunch = + − (2.25) REarth rEarth rEarth (rV enus + rEarth)
Where:
6 • REarth = the distance between the launch site and the centre of the Earth (∼ 6.4 × 10 m)
11 • rEarth = the orbital radius of the Earth (∼ 1.9 × 10 m)
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2.11.2 Optimal Launch Window
In order for the probe to target Venus for a fly-by manoeuvre, the desired point at which to launch the probe was calculated assuming the initial orbit will be a Hohmann transfer orbit to minimise the fuel consumption required for launch. The apoapsis radius will be the orbit radius of the Earth and the periapsis radius will be the orbit radius of Venus (assuming the planets follow circular orbits here.)
The semi-major axis a of the transfer orbit was calculated:
r + r r + r a = p a = venus earth (2.26) 2 2
Next the time it will take for the probe to travel from the apoapsis of the orbit to the periapsis was calculated. This was made simpler by the fact that it is exactly half the orbit period (by symmetry.)
So:
√ P 1 a3 tintersect = = (2.27) 2 2 GMsun
By assuming circular motion for Venus, its angular velocity was calculated as:
√ GMsun ω = 3 (2.28) rvenus
This indicates that during the transfer of the probe Venus will advance through an angle ‘β’ given by:
√ ω a3 β = ωt = (2.29) 2 GMsun
Since the periapsis occurs π radians after the apoapsis, the angle between the Earth and Venus as seen by the Sun must be β − π = δ at the launch of the probe.
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Figure 2.10: Required relative position of Venus at the initiation of a Hohmann transfer orbit.
This defines the transfer window and using the data from NASA the appropriate times for launch were found to occur at:
• 1st August 2010 at 16:00
• 13th March 2012 at 7:00
• 12th October 2013 at 5:00
• 22nd May 2015 at 21:00
• 26th December 2016 at 13:00
• 30th July 2018 at 8:00
Since the duration of the next stage was known to be double the orbital period of Venus, the times at which it will be possible to initiate the Hohmann transfer orbit to Saturn were calculated. These times were then compared against the times at which a transfer orbit from Venus to Saturn can be initiated to ensure that the orbiter intercepts Saturn at the apoapsis of the orbit. The two possible times with the smallest possible difference were chosen and this resulted in a launch date of 1st August 2010 at
16:00. The difference in times turned out to be 13 days, 4 hours. This represents 6% of the orbital period of Venus so an angle of 21◦. This can be corrected for in the initiation of the transfer orbit by the thrusters. The program used to determine the appropriate launch dates is given in Appendix A.
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2.12 The Control System
In reality it will be insufficient to assume that the values calculated for position, velocity and time at launch will produce the required trajectory to perform a successful fly-by. The probe’s trajectory will need to be adjusted to compensate for various sources of error which could cause the probe to be imperfectly positioned at the time of the fly-by. Some of these sources of error include:
• Errors in the inital values of velocity and position
• Collisions with small objects in space
• Gravitational effects from other bodies neglected in calculations
• Perturbations from solar radiation
2.12.1 Implementing the Control System in Matlab
In the Matlab simulation used to plan the trjectory of the probe on its journey to Titan, the function to control the desired thrust acting on the probe at each time interval consists of several stages:
1. The Idle Stage: This forces the probe to wait for the appropriate launch time before initiating
the first transfer.
2. The Launch Stage: This activates the thrusters if the probe calculates it has insufficient kinetic
energy to escape from Earth’s gravity well.
3. Venus Targetting: Here the probe predicts the interaction with Venus based ont the unimpeded
current trajectory and makes adjustments to the transfer orbit to ensure the desired interaction
at the intercept of Venus’s orbit is achieved.
4. Venus Oberth: A controlled burn is executed over the periapsis of the hyperbolic fly-by around
Venus to initiate the correct orbit for the next fly-by.
5. Venus Targetting #2: The second fly-by of Venus is assessed to ensure that the probe will leave
the manoeuvre on a Hohmann transfer trajectory to intercept Saturn.
6. Venus Oberth #2: The execution of the second Oberth manoeuvre.
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7. Saturn Targetting: Analysis of the current trajectory to calculate the optimum point at which
to perform the Saturn orbit insertion.
8. Saturn Orbit Insertion: Manoeuvre to put the probe in orbit around Saturn.
9. Titan Launch Window Analysis: Analysis to determine the optimal point at which to initiate
the Hohmann transfer orbit to intercept Titan.
10. Titan Transfer Execution.
11. Titan Orbit Insertion: Analysis and execution of final orbit around Titan at the point of closest
approach resulting from the Hohmann transfer orbit.
2.13 The Simulation
The Matlab final simulation incorporates the n-body simulation and the probe control system. The
final trajectory of the probe on its voyage to Titan is shown in figure 2.11.
Figure 2.11: Output of the simulation showing the route of the probe on its way to Titan
The first two fly-bys of venus can be seen more clearly in figure 2.12.
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Figure 2.12: Closeup of the trajectory around Venus
The trajectory of the probe relative to Saturn is shown in figure 2.13. The pink crosses mark the points at which a manoeuvre is made to adjust the trajectory and the numbers correspond to the stages in the numbered list in section 2.12.1.
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Figure 2.13: The trajectory of the orbiter relative to Saturn
The energy of the probe throughout the voyage is plotted in figure 2.14. In this graph the conversion of kinetic to potential energy around the orbit can be seen along with the increases in total energy which arise as a result of the Oberth manoeuvres.
Figure 2.14: Energy of the orbiter during the first two fly-bys of Venus.
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2.14 Conclusions
In this chapter the proposed route of the probe from Earth to Titan has been discussed. The imple- mentation of this route through the use of a control system for the probe’s thrusters has also been discussed and a simulation of our solar system has shown the successful delivery of the probe to a stable orbit around Titan.
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Attitude Control System
3.1 Introduction
In mathematical terms attitude is a coordinate transformation. This means that for a spacecraft, its attitude is the orientation of the spacecraft main axes with respect to a reference system (see section
3.2.1). Put simply, attitude is the pointing- direction of the satellite. This chapter will investigate the design and digital implementation of an attitude control system for the orbiter of the planetary explorer mission to Titan. In this chapter the terms orbiter, satellite and spacecraft will be used interchangeably as will attitude, orientation and pointing-direction.
3.1.1 Purpose
Throughout the mission the spacecraft will be subjected to external forces such as drag, gravity from nearby bodies, solar winds and more, which can change it’s orientation in space. In order to maintain a desired pointing direction, a control system is needed that with monitor the orientation of the spacecraft and ensure that it does not deviate from this state resulting in proper pointing of communications equipment for data transfer to Earth, optical equipment that will image the Titan surface during orbit, as well as thruster pointing throughout the mission. If a suitable attitude control system was not in place the other equipment would become useless and the spacecraft would not even reach its destination.
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3.1.2 Control Goal
As suggested in Dorf and Bishop [55] the control goal of the attitude control system is to maintain a steady Titan-pointing attitude when in orbit, by minimising the roll, yaw and pitch angles in the presence of persistent external disturbances while simultaneously minimising the control moment gyro momentum.
This means that we will be able to specify the desired pointing direction of the satellite and the control system will ensure that the attitude is changed to this state and will remain fixed despite external disturbances. It will also minimise the use of the Control Moment Gyros (CMG) which are the actuators of the system and need to be managed effectively(see section 3.2.4) .
3.1.3 System Overview
Before designing the system it is important to get an overview of the main sub-systems that will combine to accomplish our goal. As shown in figure 3.1 the attitude control system is dependent upon the attitude determination system which continually computes the orientation on the orbiter and feeds this information to the controller in order for it to apply the necessary control signals to the actuators.
Figure 3.1: An overview of how the attitude control and attitude determination systems work together
A more detailed look at the attitude control system is shown in figure 3.2 which gives the general form of the control system.
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Figure 3.2: The control loop of the attitude control system
3.1.4 Aim
The aim of this chapter is to design and digitally implement an attitude control system. First, a math- ematical model of the spacecraft dynamics will be constructed in order to apply control theory analysis and determine the best controller to meet requirements. The controller will initially be designed in continuous-time and then in discrete-time which will allow for the controller to be implemented dig- itally. The digital controller will be designed and tested using Matlab. The attitude determination system will be assumed to be present for the purposes of attitude feedback in the system and will not be discussed.
3.2 Mathematical model of the orbiter dynamics
In order to design an attitude controller for the spacecraft, a mathematical model must be developed which fully describes the motion of the satellite in space. It is desirable to construct as simple a model as possible while including all the essential characteristics of the system. When creating the model there are three main aspects which must be analysed and then combined to produce the governing equations.
3.2.1 Reference Frames
To model the system, reference frames for the different bodies must be specified. As discussed in
Dahleh and Richards [45], three coordinate systems will be used to completely specify the position and orientation of the satellite around Titan. First is the body frame, which is aligned with the prin- cipal axis of the orbiter and is used when looking at quantities associated with the spacecraft itself such as the CMG Torques.
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Secondly, there is the local vertical local horizontal (LVLH) frame, which is referenced to Titan and the satellite orbit. The line from the center of Titan through the orbiter defines one axis with the line perpendicular to this in the direction of the orbit defining another, the third completes a right-handed coordinate system.
The final frame is the inertial frame, which is fixed in space and is necessary as a fixed reference for the body and LVLH frames which a dependent on orbital position. The inertial frame is usually
fixed as being coincidental with the LVLH frame at some initial time To. The LVLH frame then rotates at orbital frequency with respect to the inertial frame.
3.2.2 Rigid body Dynamics
A rigid body is a body in which the relative position of all its points is constant. Rigid body dynamics can be used to define how the spacecraft will respond to a set of forces and torques that will act on it. The basic equations for the satellite rigid body dynamics [98] [138] are Eqns. 3.1 and 3.2 where L is the angular momentum of the orbiter, I is the inertia tensor, and ⃗ω is the angular velocity of the craft.
L = I⃗ω (3.1) ∑ ˙ ˙ L = I⃗ω + ⃗ω × I⃗ω = Texternal (3.2)
Equation 3.2 states that the rate of change of angular momentum of the craft is equal to the sum of the external torques (Texternal) acting on the system. Texternal is expanded in equation 3.3, where
TCMG is the reaction torque of the CMG on board the spacecraft, Tgg is the gravity gradient torque, and Tdisturbance is the disturbance torque which includes all other external torques that may act.
∑ Texternal = TCMG + Tgg + Tdisturbance (3.3)
Equations 3.2 and 3.3, fully describe the rotational motion of the spacecraft but cannot be used on their own for the purpose of attitude control.
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3.2.3 Attitude Kinematics
Kinematics is the method of describing the orientation of a body that is in rotational motion without direct reference to the forces acting upon it. The orientation of a rigid body in three-dimensional space can be defined by use of Euler Angles. Euler angles describe a sequence of three rotations about different axes in order to align one set of coordinate axes with another. Therefore, the three elemental rotations can be combined to produce the overall rotation matrix for relating the axes of the spacecraft with its inertial axes or with the Titan fixed axes set.
As in Dorf and Bishop [55] and Wie [228] the kinematics of the spacecraft can be represented using the relationship between the Euler angles, denoted θi and the angular velocity vector ⃗ω
θ˙ = R˜ω + n (3.4) where n is the orbital angular velocity. Representing equation 3.4 in matrix form gives:
˙ θ1 cos θ3 − cos θ1 sin θ3 sin θ1 sin θ3 ω1 0 1 θ˙2 = 0 cos θ1 − sin θ1 ω2 + n (3.5) cos θ3
θ˙3 0 sin θ1 cos θ3 cos θ1 cos θ3 ω3 0
where θ1, θ2, θ3 are the roll, pitch and yaw angles respectively. These are the angles of the satellite axes with respect to an inertial reference which must not have an angular acceleration.
3.2.4 Actuator Dynamics
Many space vehicles use control moment gyros (CMGs) as primary actuating devices during normal
flight mode. A CMG consists of a large wheel rotating at a constant speed and producing a an angular momentum about its spin axis. This rotating wheel is mounted in a two-degree-of-freedom gimbal system that can point the spin axis (momentum) vector of the wheel in any direction. The CMG generates an output reaction torque that is applied to the orbiter by inertially changing the direction of its wheel momentum (spin axis).
CMGs are momentum exchange devices and so external torques such as reaction jets and gravity
40 Chapter 3. Attitude Control System Aamir Aziz gradient torques, must be used to de-saturate the CMGs. One way to approach the CMG momentum management is to combine it with the attitude control design. In this design it is necessary to reach a compromise between spacecraft pointing and CMG momentum management.
CMGs are advantageous as they do not consume any fuel or propellant, however, one CMG is unable to provide the three-axis torque needed to control the attitude, so at least two are required.
Making the assumption that the CMGs are ideal torquers and can produce precise torque without delay and combining all CMGs together to view them as a single source of torque, the CMG momentum dynamics as shown in Dorf and Bishop [55] and Wie [228] are:
h˙ = −ω˜ × h + u (3.6) where u is the CMG input torque. Representing equation 3.6 in matrix form gives:
˙ h1 0 −ω3 ω2 h1 u1 h˙ = − ω 0 −ω h + u (3.7) 2 3 1 2 2
h˙3 −ω2 ω1 0 h3 u3
3.2.5 Gravity Gradient Torque
Gravity Gradient torques arise from the slightly different attraction of gravity across the satellite, and will cause the spacecraft to rotate and deviate from the desired orientation if unaccounted for by the attitude control system. Wie [228] shows that the gravity gradient torque acting on the spacecraft is given by:
2 Tgg = 3 n c × I c (3.8)
Where n is the orbital angular velocity, I is the moment of Inertia matrix and c is a transformation matrix.
A small satellite such as ours, in a high orbit is almost a perfect, torque-free system. This means
41 Chapter 3. Attitude Control System Aamir Aziz that the difference in gravity gradient torques across the satellite is negligible and the model can be simplified by omitting this external torque, without damaging the model or altering its results.
This can be confirmed by using the Cassini-Huygens dimensions [225] to estimate the gravity gradient torque across the orbiter.
3.2.6 Linearisation of the model
The purpose of linearisation is to simplify the high-order non-linear model while retaining the impor- tant system characteristics. This will enable easier analysis and controller design.
As in Dorf and Bishop [55], linearisation of the non-linear mathematical model developed, is accom- plished by use of a Taylor series approximation. For the purposes of linearisation, it is assumed that the spacecraft has zero products of inertia. This means that the inertia tensor, I, is a diagonal matrix such that I = diag{I1,I2,I3}. Also, aerodynamic disturbances such as atmospheric drag, are negligi- ble. This is justified by the high orbit altitude of the satellite, which will not be close to the edge of the atmosphere.
The equilibrium state that the model will be linearised about is:
0 θ⃗ = 0, ⃗ω = −n , h = 0 (3.9) 0
Applying a Taylor series expansion about the equilibrium state, yields the linear model, which also decouples the pitch axis from the roll and yaw axes. This is an important result and means that the dynamics and controller for the pitch axis can be considered without any effect from the roll or yaw axes. Therefore the linearised pitch equations are:
θ˙2 = ω2 + n (3.10)
I2ω˙2 = Tcmg + Tdisturbance (3.11)
h˙2 = u2 (3.12)
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Similar equations can be found in Wie [228] for the coupled roll and yaw axes.
3.3 Continuous-time Controller
3.3.1 Plant Model
From the mathematical model of the system, equation 3.11, which is uncoupled from the raw and yaw equations, is used as a base for pitch control analysis and design. Substituting equation 3.10 into 3.11 and letting u2 = Tcmg/I2 and d2 = Tgg/I2 gives
θ¨2 = u2 + d2 (3.13)
Taking Laplace transforms for the case of no disturbances (d2 = 0), and in reference to figure 3.2 gives the approximate transfer function of the system as
θ2 1 G3(s) = (s) = 2 (3.14) U2 s
Equation 3.14 is known as a double integrator and will be used as the plant model for which the pitch attitude controller will be designed. Transforming equation 3.14 to its state-space form yields
0 1 0 ˙ θ2 = θ2 + u ; y = (1 0) θ2 (3.15) 0 0 1
Open-loop Response
Before designing a controller for the system, it is important to observe the characteristics of the system as it is, in order to identify which elements of the system need improvement. This is known as the open-loop response. Matlab can be used to simulate the double-integrator plant and plot the open-loop dynamics as given by figure 3.3
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Figure 3.3: A plot of the open-loop step response of the system
As seen in figure 3.3 the open-loop step response of the system is unstable. This means that for a change in desired pointing direction, the system does not converge to the new desired orientation.
Clearly, this is the main aim of the control system and so a controller must be designed that ensures the system converges to the new desired attitude as quickly and efficiently as possible and maintains that state in the presence of external disturbances.
To solve this problem, a feedback controller will be added to improve the system performance. This is shown in figure 3.4 below.
Figure 3.4: a) open-loop plant (b)feedback control system
3.3.2 Design Specifications
In order to judge whether a controller performs as required and is adequate for use, a design criteria that involves certain requirements associated with the time response of the system must be specified.
For a step-response, (which simulates a change in desired pointing-direction) the criteria is composed of elements shown in figure 3.5. As discussed in Franklin et al. [77]
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• Rise time, is the time taken for the system to go from 10% to 90% of the desired value.
• Settling time, is the time taken for the system transient to decay to within a certain percentage
error of the demand
• Overshoot, is the maximum value the system goes above the demand, divided by the demand,
as is given as a percentage
• Steady-state error, is the difference between the demand and final value once the system has
settled
Figure 3.5: characteristics of the step response plot
For the pitch attitude control system, the requirements have been chosen as:
• Rise time ≤ 1 second
• Settling time (to within ±1%) ≤ 3.5 seconds
• Overshoot ≤ 5%
• Steady-state error = 0
3.3.3 PID Control
For the purpose of designing the attitude control system and gaining a better understanding of the orientation of the satellite as a whole, and not weighing the problem down with precise management of the CMGs, the reaction wheel dynamics will be ignored. In other words, in figure 3.2 G2 = 1, which is equivalent to treating the reaction wheel input voltage as u.
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By implementing a proportional-integral-derivative (PID) controller in the forward path where C(s) is given by equation 3.16, the input to the pitch plant model is given by differential equation 3.17 and the system model is shown diagrammatically in figure 3.6
k C(s) = k + i + k s (3.16) p s d
∫ ˙ − u = kp θ + kd θ + ki θ dθ (3.17)
Figure 3.6: PID controller with feedback control
Applying the feedback law, the closed-loop transfer function of the system is given by equation 3.18.
2 kds + kps + ki Gcl = 3 2 (3.18) s + kds + kps + ki
In order to procede with a direct design of the controller, where the system characteristic equation
(denominator of equation 3.18) is matched with the standard form of the characteristic equation
(s2 + 2ζωs + ω2) and thus allows simple calculation of the damping ratio ζ and the natural frequency
ω, the integral action of the PID controller must be set to zero. This results in the closed-loop transfer function
kds + kp Gcl = 2 (3.19) s + kds + kp
√ √kd from which it can be seen that ω = kp and ζ = . 2 kp
Simulating the PD controller in Matlab (see appendix B) it is possible to test different values of proportional and derivative gain in order to achieve a step response that is acceptable according to the design specifications. Tuning the PD controller by human trial and error, the values kp = 5.5 and
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kd = 9.5 give a system performance that satisfies the design criteria and the step response as shown in figure 3.7.
Figure 3.7: Step Response of the tuned PD controller
3.3.4 Optimal Control
Feedback can be used to improve the open-loop dynamic behaviour of the system. In order to optimise the feedback, u(t) is chosen so that the system performs in a desirable manner. One measure of
”desirability” is that of the regulator problem, which is concerned with minimising deviation of the desired state (pitch attitude of the satellite) from its equilibrium state, while minimising the control effort. This desirability is written as a regulator cost with weightings Q and R, that penalise deviation from equilibrium and control input respectively.
∫ T T |min{z} J = (x Qx + u Ru)dt s.t x˙ = Ax + Bu (3.20) x,u
If the system is at equilibrium (and this state is taken as a datum) then x(t) and u(t) are 0. If an external disturbance causes the state to assume some other value, then the regulator problem addressed by the minimisation of the cost J, considers control laws that would return the system to equilibrium as quickly and with as little effort as possible. It does this by penalising deviations from equilibrium. Given the linear dynamics of the system and quadratic nature of the cost, the ”control” is known as linear-quadratic regulator (LQR) control [29].
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Solution to the LQR problem
To derive the optimal LQR control law, classical (static) optimisation is used. The key result [29] is that constrained problems can be transformed, and then solved in the same way that unconstrained problems are solved. This can be achieved with Lagrange multipliers.
′ |min{z} L(x, u) s.t f(x, u) ⇔ |min{z} L (x, u, p) (3.21) x,u x,u,p
Optimal State-Feedback Control Law
Applying equation 3.21 to the constrained regulator cost function given by equation 3.20 produces the unconstrained cost as,
∫ ′ T T T |min{z} J = [(x Qx + u Ru) + p (Ax + Bu − x˙ )] dt (3.22) x,u,p
Solving equation 3.22 results in the optimal control law as,
u = −Kopt x (3.23)
−1 T Kopt = R B P (3.24)
Where R is the penalty on control effort, B is defined in the state-space model of the system and P is the solution to the matrix Riccati equation.
This is a remarkably simple and powerful solution to a complex problem. Equation 3.23 states that to optimise the closed-loop system, all that needs to be done is to pass the state vector (x) through a constant gain (Kopt) and use the output as the input to the system. In other words, the optimal feedback control law is given by simple state feedback, with a constant feedback controller Kopt. This is shown in figure 3.8.
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Figure 3.8: Optimal feedback control
Optimal Controller
In order for Kopt to be calculable, the system must be both controllable and observable. If the controller is not controllable, then there exist certain modes that cannot be influenced by the control input. Similarly, a system is completely observable if a change in state or input will always result in some change in the output. As shown in Franklin et al. [77] the system model described by equation
3.15 is completely controllable and observable, thus the optimal gain Kopt can be analytically found using equation 3.24 as suggested in Bryson and Ho [29] to be
√ √ 1 Kopt = [ p 2p 4 ] (3.25) where p is defined by the tracking weight Q = p(CT C). R is chosen by looking at the eigenvalues of the Hamiltonian matrix and ensuring that these are not too fast. It can be shown [29] [55] that the damping ratio (ζ = √1 ) of the optimal controller is critically damped, which gives the best trade-off 2 1 between rise-time and overshoot, and the natural frequency ω is p 4 .
Simulating the LQR controller in Matlab (see appendix C) gives Kopt = [7.07 3.76] and a step response as shown in figure 3.9 satisfies all design specifications. Poles are s = −1.88 ± 1.88i
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Figure 3.9: Closed-loop step response (left) and Root locus (right): LQR controller
3.4 Discrete-time Controller
In reality, continuous controllers are built using analogue electronics such as resistors, capacitors and transistors, and are increasingly being replaced by equivalent discrete controllers that can be developed as software and implemented by digital computers. This gives discrete control many advantages such as the ability to handle increased complexity, flexibility of design and redesign, increased reliability, and reduced cost.
3.4.1 Discrete Plant Model
1 Discrete transfer function of a s2 plant preceded by a zero-order-hold (zoh).
T 2(z + 1) G(z) = (3.26) 2 (z − 1)2
Discrete state-space model of the system as described by equation 3.15 preceded by a zoh is given by
T equation 3.27, where θ(k) = (θ2,1 θ2,2) , θ2,1 is the position of the pitch axis of the satellite and θ2,2 its velocity. T is the sampling period.
2 1 T T θ(k + 1) = θ(k) + 2 u(k); y(k) = (1 0) θ(k) (3.27) 0 1 T
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3.4.2 Design by Emulation
Design by emulation is a two stage process where, after selecting a sample period, a continuous control design (section 3.3) is converted to its discrete equivalent and used in place of the continuous controller.
There are different ways in which to compute the equivalent discrete controller, two of which include
• converting the continuous transfer function to its discrete equivalent
• mapping the poles of the control system from the continuous s-plane to the discrete z-plane
Mapping s-plane poles to the z-plane
In order to compute a discrete controller that produces the same response in discrete-time as the optimal controller (section 3.3.4) did in continuous-time, the poles must be mapped from the s-plane to the equivalent location on the z-plane.
Using a sampling time of T = 0.06sec so that the sample rate is at least 30 times faster than the bandwidth of the system to give adequate performance [77], the poles shown in the root locus plot in
figure 3.9 are mapped to the z-plane using equation 3.28
z = eT s (3.28)
z = 0.888 ± 0.09716 i (3.29)
3.4.3 Estimator Design
So far, it has been assumed that the state vector can be measured perfectly and the actual values are available for the feedback control law. However, in reality this is not the case and a state estimator
(also known as a state observer) must be used in place of measured values. For pitch attitude control, the position θ2,1 is measured and therefore available to be fed back. However, the velocity θ2,2 cannot be easily measured and differentiating the position is not advisable as it may be a noisy signal (ripply) and differentiating it would introduce large errors into θ2,2. Hence, θ2,2 must be reconstructed in order to be fed back and used for the control law. In order to do this an estimated state vector θb(k) of the
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actual state vector θ2 will be obtained given an initial measurement of the position and a knowledge of the system dynamics [77]. There are two basic types of estimator:
• Current estimator - θb(k) is based on measurements up to and including current output y(k)
• Predictor estimator - θb(k) is based on measurements up to and including previous output y(k-1)
As claimed by Franklin et al. [77], the current estimator is a better choice than the predictive estima- tor, because it provides the fastest response to unknown disturbances or measurement error and thus better regulation of the desired output. There are also other variations on the current or predictor estimators. One such design is the reduced-order estimator. While predictor and current estimators are designed to reconstruct the entire state vector, given an initial state, the reduced-order estimator only reconstructs the unmeasured state elements and combines these with the measured elements to produce the full state vector [77].
This is advantageous as it saves time, memory and computing power as the known state elements are not reconstructed but used directly. However, as suggested in Franklin et al. [77], when there is significant noise on the measurements, the estimator for the full state vector provides smoothing of the measured elements which does not occur with the reduced-order observer.
Simulating both the current estimator and reduced-order estimator in Matlab (see appendix D), allows for a comparison of the two designs. Figure 3.10 shows the time-history of the estimator error of the current and reduced-order estimators with an initial (velocity) estimate error of 1 rad/sec. The figure shows very similar results for the velocity element estimate. There is no position estimate for the reduced-order observer which uses the measurement directly without smoothing[77].
52 Chapter 3. Attitude Control System Aamir Aziz
Figure 3.10: Time history of current and reduced-order estimators error
3.4.4 Regulator Design
Combining the control law (section 3.3.4) and the estimator design (section 3.4.3) results in a full pitch attitude control system as shown in figure 3.11. Analysing this system, it can be shown [29] that the use of an estimated state vector instead of the actual state vector does not change the dynamics of the system. The poles of the system consisting of the estimator and control law, are the same as if the actual states had been used.
Figure 3.11: Estimator and controller mechanization
53 Chapter 3. Attitude Control System Aamir Aziz
Compensator based on the Reduced-Order Estimator
As shown in Franklin et al. [77] the compensation equations consist of difference equations of the estimator and control law. Using values of K = [7.0711 3.7606] and Lr = 5 the compensator transfer function is given by equation 3.30.
(z − 0.9180) D (z) = −25.87 (3.30) r (z − 0.5082)
This compensation is exactly like classic lead compensation and is the type that would typically be used for the double-integrator plant. The step response of the system and root locus is shown in figure
3.12. The step response satisfies the design criteria. For this design a gain of 25.85 is now the gain variable on the root locus plot. The closed-loop root locations corresponding to this gain lie on the two control roots at z = 0.9 ± 0.356i and on the estimator root at z = 0.6 as they should [77].
Figure 3.12: Closed-loop step response (left) and Root locus (right): lead compensator
3.5 Conclusions
This section has considered the design of a compensator based on the LQR optimal control law and reduced-order estimator, in order to allow control of the pitch attitude of a small satellite. The case has been considered where there are no external disturbances and the system is responding only to changes in desired pointing-direction. This was the necessary prerequisite to design of a control system capable of disturbance rejection, which is a logical extension of the analysis done in this chapter. Optimal control theory was chosen as it gave the best possible trade-off between tracking the desired pitch
54 Chapter 3. Attitude Control System Aamir Aziz attitude, minimising the control effort required and speed of response of the system. This was in the form of the linear-quadratic regulator problem and allowed analytic calculation of the optimal gain. Design of the optimal control law was initially considered in the continuous-time domain and then by emulation in the discrete-time domain to allow for digital implementation with the use of a state-observer, needed to reconstruct the state-vector which has elements that are unmeasurable and others that are noisy. The control law and estimator are then combined to produce a compensator and complete the system design.
Limitations
The plant model of the satellite pitch attitude is an approximate model as it was linearised. The actual system is non-linear and the three axis are indeed coupled, so the pitch attitude cannot be completely considered on its own. The purpose of this chapter was to give an insight into the problem of attitude control and a possible method for its solution.
55 CHAPTER 4 - Nicholas Baker
Landing the Probe
4.1 Introduction
Once the orbiter is in a controlled orbit around Titan the next stage of the mission is to release a probe that will land safely on the surface. This chapter will consider how to create the optimal method for landing the probe. As the probe will comprise the majority of the mission it is essential that the landing system is safe and robust. The probe should also be able to make measurements of
Titan’s atmosphere; the descent must be controlled in order for these measurements to be as accurate as possible. The effect that wind will have on the probe’s trajectory will also be taken into account, and an attempt to minimise lateral drift will be made.
The chapter will be split into separate parts. The first will discuss the data acquisition and building of a climate model and simulator. The second part will describe the test program and the results obtained. The final design will be covered and the errors involved will be looked at.
4.2 Gathering Data
In December 2004 the Huygens probe detached from the Cassini spacecraft and began its descent onto the surface of Titan[7]. As the probe was falling through the atmosphere it made measurements of temperature, pressure and wind speed which were recorded and transmitted back to Earth. The data from Huygens is freely available and so was used as the basis for creating an atmospheric model of Titan[219]. It should be mentioned that Titan’s atmosphere is sufficiently dense to cause drag up to 900km above the surface, though for the purposes of landing the probe only the ionospheric layer
56 Chapter 4. Landing the Probe Nicholas Baker
(extending up to around 140km altitude) will be necessary to use in calculations. This is because the drag experienced above this layer is negligible when the probe is in free-fall, and any attempt to slow the probe down above this layer would result in excessive errors and drift. For these reasons all graphs and data presented in this chapter will refer to the atmosphere between the top of the ionosphere and ground level.
4.2.1 Wind Speed
One of the biggest considerations associated with landing the probe is how far it will drift due to atmospheric winds. The graph below shows the wind speed as measured by the Huygens probe:
Titan’s Atmospheric Wind Speed 150
100 Altitude (km)
50
Gaps in Data
0 −20 0 20 40 60 80 100 120 Wind Speed (m/s) Figure 4.1: Wind speed with altitude as measured by the Huygens Probe
The measured wind speed is fairly noisy as can be seen in figure 4.1. It is not sensible to use this model directly in the simulation as the real wind speed will not behave exactly the same as it did for the Huygens probe. A filter was therefore designed to remove some of the noise; the wind speed was averaged over a number of data points in order to filter the signal to a smoother form. As the wind speed was sampled at regular time intervals there is a greater density of data points where the probe was travelling slower. This corresponds to a greater data density at lower altitudes. For this reason
57 Chapter 4. Landing the Probe Nicholas Baker the filter was split into three stages comprising the upper atmosphere (140km to 65km), the middle
(65km to 30km) and the bottom (30km to ground). The filter algorithm is shown below:
for k = 1:5
i = 1;
while alt(i) > 65;
for j = 0:(n-1);
windv_avg(i) = windv_avg(i)+windv(i+j);
end
windv_avg(i) = windv_avg(i)/n;
altnew(i) = alt(i);
i = i + 1;
end
end
The algorithm works by averaging over n data points and rolling over the signal. This is iterated k times to alter the weights that each point is given. For example, if n = 3, the first loop would compute
n−1 + n0 + n+1 3 and the second loop would compute
n−2 + 2n−1 + 3n0 + 2n+1 + n+2 9
Through a system of trial and error, the best values for n and k were found for each stage. These are shown in the table below
Range (km) n k
140-65 50 5
65-30 100 5
30-0 40 2
The data used also had gaps that lasted for up to 7km. These arose from where Huygens deployed
58 Chapter 4. Landing the Probe Nicholas Baker its parachutes and so could not collect meaningful data. A simple linear interpolation was used to
fill in these blanks before the filter was applied. By interpolating before the filter it was possible for the algorithm to smooth the straight lines into curves to match the data. The result of the 3 stage
filtering and interpolation is shown below
Titan’s Atmospheric Wind Speed 150
100 Altitude (km)
50
0 −20 0 20 40 60 80 100 120 Wind Speed (m/s)
Figure 4.2: Wind speed with altitude after processing
4.2.2 Pressure and Density
The Huygens probe measured the pressure of Titan’s atmosphere as it fell. However, for drag equations it is density that is required rather than pressure. Titan’s atmosphere is 98.4% Nitrogen; this was approximated to 100% and the Compressibility Factor (Z) was studied:
pV Z = m RT
Where p is pressure, T is temperature, Vm is molar volume and R is the gas constant.
The Ideal Gas Law assumes a value of Z = 1. Therefore this is a suitable approximation to make if
59 Chapter 4. Landing the Probe Nicholas Baker
Z ≈ 1[136]. The calculation is shown below
3 −3 3 p = 147 × 10 Pa,T = 94K,Vm = 5.01 × 10 m /mol,R = 8.314
Z = 0.94
This value is close enough to 1 for the approximation to be within 1% of the true value.
4.3 Simulation Engine
The processed data was used to create a climate model of Titan’s atmosphere from ground level to
140km altitude. Using this model a simulation engine was created that would plot the trajectory of the probe as it fell. This engine would provide the basis for testing multiple descents onto the surface.
4.3.1 Gravity
The radius of Titan is ≈2600km[6]. The simulation runs from 140km above the surface, representing a 5% change in radius. Using the following equation it was possible to find the change in gravitational force that the probe would experience during the descent
Gm m F g = 1 2 (r + h)2
2 2 Using h1 = 140000, h2 = 0 gives g1 = 1.217m/s , g2 = 1.350m/s , or a 10% change. This was large enough to require inclusion into the engine and the above equation was implemented.
4.3.2 Drag
The biggest factor affecting the probe’s descent is the atmospheric drag it will experience. The drag equation is well known and is shown below
1 F = ρv2C A 2 d
where ρ is density, v is the probe’s velocity, Cd is the drag coefficient and A is the effective area.
The only difficulty with using this equation is defining the drag coefficient. As the probe has not been built and therefore the coefficient cannot be determined experimentally, a value of 0.9 was assumed.
60 Chapter 4. Landing the Probe Nicholas Baker
This assumption was based on the fact that the shape is likely to have various protruding instruments and a flat base for the landing, so Cd is presumed to be fairly high.
4.3.3 First Simulation
The results of the first simulation are shown in figure 4.3. The graphs show height above the surface of Titan as well as velocity and acceleration of the probe.
4 x 10 First Simulation Results 15
10
Height (m) 5
0 0 500 1000 1500 2000 2500 3000 3500 4000 Time (s)
300
250
200
150
100 Velocity (m/s)
50
0 0 500 1000 1500 2000 2500 3000 3500 4000 Time (s)
0.5 ) 2 0
−0.5 Acceleration (m/s
−1 0 500 1000 1500 2000 2500 3000 3500 4000 Time (s) Figure 4.3: First simulation of a descent showing height, velocity and acceleration of the probe
The graphs are as expected, with the terminal velocity of the probe decreasing as it descends and the atmosphere becomes more dense. The acceleration graph shows negative acceleration spikes; this is due to the fact that the atmosphere was sampled by the Huygens probe every 2km. By interpolating the density data this should become a more accurate curve.
61 Chapter 4. Landing the Probe Nicholas Baker
4.3.4 Drift
One of the main objectives is to minimise lateral drift of the probe as it falls, this requires a simulation of the horizontal motion of the probe to be built. Using the climate model above an adaptation of the drag equation allowed the simulation to be completed. The equation for the horizontal drag needed to take into account the fact that there are components of wind and probe velocities. This was not the case for the vertical simulation as the atmosphere can be assumed to be static in the vertical direction.
Taking the wind velocity and the probe velocity to be defined in the same direction, the equation is
1 F = ρ(v − v )2C A 2 w p d
4.4 A Safe Landing
4.4.1 Parachutes/Thrusters
There are two options for slowing the probe down as it falls. One is to use rocket thrusters that have the option of being multi-directional while the other is to use one or more parachutes of different sizes.
The table below compares the two methods in a decision matrix
Factor Weighting Parachutes Thruster
Weight 3 4 1
Safety 5 5 3
Controllability 2 2 5
Complexity 1 4 1
Total 45 29
This analysis showed that parachutes would be the better option. The largest benefit to using parachutes is the safety aspect. Parachutes can be deployed with a simple mechanism whereas thrusters are much more susceptible to failure, either through electronics or through mechanics, as there is a greater complexity to them. Thrusters would also add a lot more weight to the probe and therefore adversely affect the project in terms of both cost and complexity. Therefore a parachute system was chosen as the descent mechanism.
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4.4.2 Simulating Parachutes
The simulation engine needed to take account of the fact that there could be multiple parachutes being opened and detached at different altitudes. This was implemented by storing the altitudes of release and detachment, the frontal areas, and the drag coefficients of the parachutes in a matrix.
When a parachute is open, the stored parameters would be used in the drag equations as opposed to the parameters for the probe only. When a parachute is detached the values for area and Cd are reset to the original values. For horizontal drag the frontal area was halved as the parachutes are assumed to be dome shaped.
4.4.3 Test Data
Once the simulation was set up and could handle multiple parachute releases, a test plan was required in order to optimise the descent. By studying the wind velocity in figure 4.1 it became clear that a two parachute system would give the best results as there is a small range of altitudes where the wind velocity is negative. Using two parachutes would allow a main parachute to be opened to slow the probe for the majority of the descent and a landing parachute opened later to slow the probe to a safe landing velocity. By using this method a smaller parachute could be used for higher altitudes where the wind speed (and therefore drift) is higher, and a larger parachute could be used where the wind speed is much lower. A stabilising parachute would also be used prior to main parachute deployment in order to orientate the probe correctly.
Given that two main parachutes would be used, there were five parameters that could be adjusted.
These were the area, the deployment and detachment altitudes of the main parachute, and the area and deployment altitude of the landing parachute (the detachment being at ground level). It was then necessary to find an upper and lower bound for each of the parameters. The values for canopy area were chosen by considering space limitations on the probe. The altitudes were chosen to maximise safety and to include as large a range as possible. The values are summarised in the table below.
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Parachute Parameter Values
Stabilising Chute Area 1m2
Deployment alt. 130km
Detachment alt. 125km
Main Chute Area 0 - 20m2
Deployment alt. 120 - 40km
Detachment alt. 110 - 20km
Landing Chute Area 0 - 20m2
Deployment alt. 100 - 5km
Detachment alt. 0km
To check that the upper bounds were sensible, a descent simulation was run using these values, i.e. both areas set to 20m2, main parachute open between 120km and 20km, landing parachute open between 19km and ground level. The results are shown in the vertical profile below
64 Chapter 4. Landing the Probe Nicholas Baker
4 x 10 Descent Using Upper Bound Data 14
12
10
8
6 Height (m) 4
2
0 0 5000 10000 15000 Time (s)
300
200
100 Velocity (m/s) 0
−100 0 5000 10000 15000 Time (s)
10
) 0 2
−10
−20
Acceleration (m/s −30
−40 0 5000 10000 15000 Time (s)
Figure 4.4: Descent simulation using upper bound values
The graphs show that the probe experiences a large deceleration when the main parachute is opened and the velocity is reduced rapidly from 300m/s to just 50m/s. The length of time to touch down is
14500s, or 4 hours. This length of time is excessively long and would give rise to a very large drift.
The probe would also be more susceptible to variations in wind speed and so the expected landing area would be much larger. These reasons suggest that the set of values chosen are acceptable as upper bounds for the test procedure as it is very unlikely these values will be reached.
In order to analyse the data some of the parameters needed to be temporarily fixed while others were investigated. By using 3D plots it was possible to invesigate how one result changed with respect to two parameters. Therefore in each test three parameters were fixed. This process was made simpler by coupling two parameters together; for example, deployment altitude and detachment altitude were combined to give a ’range’ parameter. This was then studied against both area and deployment altitude. It was also considered acceptable to study one parachute at a time and keep the other
65 Chapter 4. Landing the Probe Nicholas Baker constant as they do not have a large impact on each other. The following table gives details of the test plan implemented
Parameter 1 Range n Parameter 2 Range n Total
Main Deploy 120-40 9 Main Range 100-10 10 90
Main Deploy1 120-40 9 Main Area 20-0 20 180
Main Range 100-10 10 Main Area 20-0 20 200
Landing Deploy 100-5 10 Landing Area 20-0 20 200
In the table, the column ’n’ shows how many data points were considered for each parameter, and
’total’ shows the number of simulations that needed to be run. Each line in the table represents three series of tests, with the outputs being the final amount of drift the probe will experience, the average velocity over the descent and the time to land.
4.5 Analysis
4.5.1 Test Plan
The aim of the tests were to determine the optimal set of parameters that would satisfy the following conditions as far as possible
• Minimise drift
• Maintain a vertical velocity below 50 m/s for as long as possible
• Land within a time range of 1.5 to 3 hours to allow for detailed measurements
• Land at a safe speed of below 6m/s
For each of the tests given in table 4.4.3 the optimum value was determined graphically through analysis of the plots. This gave a basis for calculating the efficacy of all other values for each parameter tested. For example, for one test the optimal area of the main parachute was found to be 7m2 to minimise drift. From this all other areas were graded by how close a value they achieved to this
1This test was conducted twice, once with the detachment altitude fixed and once with the range fixed
66 Chapter 4. Landing the Probe Nicholas Baker optimum drift level. Once the weighted matrices were set up, a further cost matrix was derived to calculate the best set of parameters based on all the tests conducted.
4.5.2 The Need For Analysis
For many of the conducted tests the results were obvious. For example, consider looking at how average velocity changes with deployment height and canopy area. It is clear that for a larger canopy the velocity should decrease, and the higher up the parachute is released the slower the average velocity should be. The graph below confirms this and is typical of many of the graphs produced.
Test Results Showing Average Velocity
35
30
25
20 Average Velocity (m/s) 4 15 0 6
5 8 4 10 x 10 2 10 Area (m ) 15 20 12 Deployment Altitude (m)
Figure 4.5: Average velocity of the probe shown over many simulated descents
Although this result was easily predictable, others were not so simple. The next graph shows how the probe’s drift changes with the deployment altitude and area of the main canopy. This test assumed a constant altitude range for which the parachute was in use and fixed values for the landing parachute.
67 Chapter 4. Landing the Probe Nicholas Baker
4 Test Results Showing Drift x 10 8
7
6
5 Drift (m)
4
3 20
15
10 Area (m2) 5 12 8 10 0 6 4 2 4 x 10 Deployment Altitude (m) Figure 4.6: Drift of the probe shown over many simulated descents
The double peak in the graph above arises from the fact that the wind speed over the atmosphere has two minima. Therefore if the main parachute is released at the first minimum point then the drift will be reduced. This graph demonstrates why such an extensive analysis is required for the descent trajectories.
4.5.3 Analysis Example - Drift
This section will explain in detail the analysis procedure for lateral drift. Although the analysis is demonstrated for only one variable and one result here, the procedure used was similar for all other entities.
Using Figure 4.6 the values that minimise drift were selected. In this case it was found to be an area of 2m2 and a deployment altitude of 20km (ignoring the trivial results for a 0m2 parachute). These values correspond to a value of 31.2km drift. This process was repeated for the maximum amount of drift. The values were found to be an area of 20m2 at an altitude of 70km, giving a drift of 76.2km.
Using these values the results matrix was normalised to between 0 and 1. This then acted as a cost
68 Chapter 4. Landing the Probe Nicholas Baker matrix for the area and deployment altitude of the main parachute.
This process was repeated for the other tests concerning drift and a series of cost matrices were derived.
These matrices had the same number of elements as there were tests conducted; a typical cost matrix for one of the tests described in Table 4.4.3 had dimensions of 20x10. Once the matrices had been derived they were grouped by parameter. For example, using drift as the studied result one would be able to extract three cost matrices for the effect of main parachute area. By looking again at Table
4.4.3 this is confirmed as there were only three tests that involve the area of the main parachute.
In this example there are now three cost matrices. One shows how area and deployment altitude affect drift, another shows how area and detachment altitude affect drift and the last shows how area and range affect drift. These matrices were aligned with respect to area (i.e. setting the columns to have constant area values) a column-average will then give a cost vector for the area. As a low value of drift is required, a lower value in the cost vector indicates a more desirable value of area. To illustrate this a portion of a cost matrix, and the subsequent vector obtained from it, are shown below
Area (m2)
1 2 3 4 5 6
0.0090 0.0090 0.0215 0.0425 0.0648 0.0874
0.0126 0.0126 0.0297 0.0571 0.0846 0.1114
0.0135 0.0135 0.0329 0.0628 0.0910 0.1159
0.0152 0.0152 0.0380 0.0710 0.1004 0.1258
0.0286 0.0286 0.0637 0.1107 0.1521 0.1888
The rows in this case correspond to different values of range. Carrying out a column average produced the following cost vector
Area (m2)
1 2 3 4 5 6
0.0261 0.0261 0.0676 0.1232 0.1726 0.2169
There were two other similar cost vectors that related the area parameter to drift. Therefore by aligning similar values for area and then combining the three vectors by multiplication a single cost vector was found that gave the cost of differing area values when looking at drift. This was normalised to give a cost vector between zero and one, a portion of which is shown here
69 Chapter 4. Landing the Probe Nicholas Baker
Area (m2)
1 2 3 4 5 6
0.0000 0.0001 0.0012 0.0073 0.0205 0.0404
This final cost vector shows the desirability of different values of the area of the main parachute with regards to final probe drift. Here low numbers are defined as being more desirable, and as expected a smaller canopy area leads to a smaller amount of drift. It should be noted that the above process looked at how area interacts with all other parameters (deployment altitude, range etc) to produce a
final vector that has this information incorporated into it.
This process was repeated for all the parameters and results in order to include all the known informa- tion. This meant that area was also related to minimum acceleration, and to time to land. Deployment altitude, detachment altitude, range and the two parameters for the landing parachute also needed to be compared to the three result variables as well. There were therefore six test parameters each with three results, giving eighteen cost vectors that were all normalised between zero and one. All cost vectors were defined as a low cost being more desirable.
4.5.4 Parameter Weighting
The cost vectors for deployment altitude against drift are shown below for the three tests. The final cost vector is displayed at the bottom
Deployment Altitude (km)
40 50 60 70 80 90 100 110 120
0.1020 0.1442 0.3251 0.5426 0.6422 0.6830 0.8219 0.9623 0.9924
0.3101 0.5321 0.8712 0.9103 0.5701 0.2815 0.3286 0.7731 0.8487
0.1354 0.3762 0.7644 0.7719 0.6891 0.6276 0.7120 0.8295 0.8462
0.0000 0.0347 0.2995 0.5321 0.3501 0.1643 0.2654 0.8651 1.0000
Table 4.1: Cost vectors for deployment against drift.
In this table the first three rows show the individual cost vectors for the tests conducted using area and range while the final row shows the overall cost vector for deployment altitude against drift.
70 Chapter 4. Landing the Probe Nicholas Baker
In order to find the optimum set of parameters to minimise drift the cost vectors from all the individual parameters were combined. However they do not all cause the same degree of drift as might be suggested by the normalised vectors. This is easy to see by extrapolating the test data. If for example the test included all canopy areas up to 30m2 one would expect that the worst value to use would be 30m2 and so in the cost vector this would be represented by a 1. In the test set used here the worst area to use is 20m2 and the cost vector has a 1 in the relevant position. A normalised vector is therefore only useful when put in context with the results. For this reason the cost vectors were associated with a weighting matrix that describes the degree of cost.
In table 4.1 the bottom row shows that the amount of drift is proportional to the height that the main parachute is released. The cost vector for area also shows that the amount of drift is proportional to the area of the main parachute, but neither vector gives an insight into the degree that each parameter affects drift. The procedure for determining the relative degrees of each parameter is to compare the results that combine these two. This graph is shown below
Test Results Showing Drift
5 x 10
2
1.5
1 Drift (m) 0.5
0 20 15 12 10 10 8 4 5 6 x 10 2 0 4 Area (m ) Deployment Altitude (m)
Figure 4.7: Drift of the probe shown over many simulated descents
By looking at the graph it is not immediately clear whether area or altitude affects drift more. To determine this the average gradient for drift was studied for area and for altitude. The result was that
71 Chapter 4. Landing the Probe Nicholas Baker area causes a mean change in drift of 37km across the measured range, and that deployment altitude
63 causes a mean change of 63km. Therefore the weight applied to deployment altitude was 37 or 1.7 times greater than that applied to area.
4.5.5 Result Weighting
As well as applying a weighting factor to the different parameters it was also necessary to weight the results to achieve the desired descent. However, this procedure was different to the one described above as the weighting was not determined analytically from the results. The goal here was to find a set of weights for the three result variables (drift, time to land and minimum acceleration) that would give the best descent trajectory. The absolute values of the weights is not important, it is the relative values that determine the outcome.
The result weights were decided by considering the effect that each result would have on the project as a whole. For example, it is important to minimise drift so that the communications can work effectively between the lander and the orbiter. Although the weights applied are somewhat arbitrary, they provide a means to model the desires of the Titan mission.
Result Weight
Lateral Drift 2
Time to Land 1
Minimum Acceleration 1.5
These values imply that it is considered twice as important to minimise the amount of drift than to spend a longer time in the atmosphere.
4.5.6 Finding the Optimal Area
In section 4.5.4 the cost vector for area with respect to drift was calculated. In this section the example will be continued to demonstrate how the weights are used and a preliminary value will be calculated for the area of the main parachute.
Firstly the cost vectors for area with respect to minimum acceleration and to ’time to land’ were required to complete the analysis. Using the process described in section 4.5.3 these were found and
72 Chapter 4. Landing the Probe Nicholas Baker are shown below (note that due to space limitations only the first six elements are shown). In the full analysis the cost vectors for area were twenty elements long. In the tables, the first column denotes which test the cost vector refers to.
Parameter 2 Area Cost Vector for Maximising Time to land
Deployment Altitude 1.0000 0.9458 0.8375 0.7562 0.6750 0.6208
Detachment Altitude 1.0000 0.9498 0.8997 0.8245 0.7492 0.6991
Range 1.0000 0.9643 0.9142 0.8642 0.7892 0.7142
Parameter 2 Area Cost Vector for Minimising Deceleration
Deployment Altitude 0.0000 0.0503 0.1006 0.1509 0.2012 0.2515
Detachment Altitude 0.0000 0.0250 0.0500 0.0750 0.1000 0.1750
Range 0.0000 0.0526 0.1053 0.1579 0.2105 0.2632
Once the three cost vectors for each result were found, they had to be multiplied element-wise and normalised to give a vector that related area to the result. This is shown below
Result Area Cost Vector
Drift 0.0000 0.0001 0.0012 0.0073 0.0205 0.0404
Time to Land 0.1000 0.8413 0.6612 0.4921 0.3612 0.2883
Min. Deceleration 0.0000 0.0001 0.0005 0.0018 0.0042 0.0116
The next step was to use the procedure defined in section 4.5.4 to find the parameter weights for each of the above cost vectors. From section 4.5.4 it was found that for drift, the area vector should be 1.7 times smaller than that for deployment altitude. This process was repeated for range and detachment altitude. Having done this the weights were defined with the smallest weighting being 1.
The calculated weights are shown here
73 Chapter 4. Landing the Probe Nicholas Baker
Result Area:Deploy Area:Detach Area:Range
Drift 1:1.7 1:2.3 1.3:1
Time to Land 1:1.9 1:1.8 1:1.9
Min. Deceleration 5.3:1 3:1 8.1:1
Setting the smallest weight in each row to 1 gives the final weight set for area
Result Area Deploy Detach Range
Drift 1.3 2.2 3 1
Time to Land 1 1.9 1.8 1.9
Min. Deceleration 8.1 1.5 2.7 1
The cost vectors for each result then needed to be multiplied by their relevant weight from the table above - the vector for minimising drift needed to be multiplied by 1.3 etc. Once this was done the resulting vectors needed to be multiplied by the result weights as given in section 4.5.5. The final vectors are
Result Area Cost Vector
Drift 0.0003 0.0032 0.0191 0.0536 0.1052 0.1766
Time to Land 0.9642 0.8213 0.6512 0.4921 0.3612 0.2883
Min. Deceleration 0 0.0008 0.0064 0.0217 0.0515 0.1407
These three vectors were summed and normalised to give an overall cost vector for the parameter area across all results. This is shown in the table below and plotted on a graph in figure 4.8
Area (m2)
1 2 3 4 5 6 ... 17 18 19 20
0.0654 0.0560 0.0459 0.0385 0.0351 0.0411 ... 0.6753 0.7852 0.8757 1.0000
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Cost Associated With Area of Parachute 1
0.9
0.8
0.7
0.6
0.5 Cost 0.4
0.3
0.2
0.1
0 0 5 10 15 20 Area (m2)
Figure 4.8: The cost of using different canopy areas for the main parachute
The table and graph show that the best canopy area for the main parachute is 5m2 as this has the lowest cost associated with it. They also show that there is relatively little variation for areas up to
10m2, therefore there is some flexibility in the final design for areas within this range.
4.6 Final Design
Repeating the analysis procedures outlined in section 4.5 gave the optimum values for all the parame- ters involved in the simulation (the full derivation is not shown here due to space limitations). These values are shown below
75 Chapter 4. Landing the Probe Nicholas Baker
Parameter Value
Main Area (m2) 5
Deployment Altitude (km) 100
Detachment Altitude (km) 50
Landing Area (m2) 12
Deployment Altitude 20
4.6.1 Results
Using the values found from the analysis the trajectories were plotted using the simulator. The vertical and horizontal descent profiles are shown overleaf
76 Chapter 4. Landing the Probe Nicholas Baker 8000 8000 8000 7000 7000 7000 6000 6000 6000 5000 5000 5000 4000 4000 4000 Time (s) Time (s) Time (s) Horizontal Descent Profile 3000 3000 3000 Landing Open Landing Open Landing Open ← ← ← 2000 2000 2000 Main Close Main Close Main Close ← ← ← 1000 1000 1000 4 Main Open Main Open Main Open ← ← ← x 10
0 0 0
6 5 4 3 2 1 0 0 0 Drift (m) Drift 40 30 20 10 0.1
−10
0.15 0.05 −0.1
Velocity (m/s) Velocity −0.05
) (m/s Acceleration 2 8000 8000 8000 7000 7000 7000 6000 6000 6000 5000 5000 5000 4000 4000 4000 Time (s) Time (s) Time (s) Vertical Descent Profile 3000 3000 3000 Landing Open Landing Open Landing Open ← ← ← 2000 2000 2000 Main Close Main Close Main Close ← ← ← 1000 1000 1000 4 Main Open Main Open Main Open ← ← ← x 10 0 0 0
8 6 4 2 0 0 5 0
14 12 10 50 −5
Height (m) Height 300 250 200 150 100 −10 −15
Velocity (m/s) Velocity ) (m/s Acceleration 2 Figure 4.9: Descent profiles using calculated values
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In the vertical profile the maximum deceleration experienced by the probe is 13m/s2. The landing velocity is 3.3m/s or 11.9kph, which is an acceptable landing velocity (the Huygens probe landed at 4.5m/s or 16kph). It can also be seen that despite a large time gap between releasing the main parachute and deploying the landing parachute, the probe is sufficiently low in the atmosphere that the higher density prevents it from reaching speeds of greater than 50m/s. At this speed the probe is still within an acceptable range for taking detailed measurements as the slowest sampling rate is assumed to be 2s. These values give the resolution to be within 100m. The expected drift the probe will experience is about 60km, and it will take just over two hours to land after entering the lower ionosphere.
4.7 Errors
Throughout the analysis above the data used for the simulator was experimentally gathered from the Huygens probe that landed on the surface of Titan in a NASA mission. However, the results gathered by Huygens differed from expectations in that there was a local minimum in the lateral wind velocity at about 70km altitude. There has also only ever been one descent onto Titan’s surface, and so there are no repeat measurements of density, temperature, wind speed etc. It is important to run simulations for differing levels of error on the original data in order to calculate an expected landing zone. It is essential to have an estimate for the landing zone for two reasons; firstly so that antennae can be directed correcty for communications, and secondly so that a region of scientific interest can be selected. Titan has liquid methane lakes and seas so being able to choose a landing zone is important if the mission is to succeed.
4.7.1 Systematic Errors
The simulator was edited to output results for differing levels of error on the wind speed and atmo- spheric density data. Levels of plus and minus 2.5%, 5% and 10% were used for each. As a final test the simulator loaded the theoretical wind speed model and ran a simulation to see how the results differed. The results of these tests are given in the tables below
Wind Speed Error -2.5% +2.5% -5% +5% -10% +10%
Drift (km) 54.9 57.9 53.4 59.4 50.4 62.4
Percentage Difference -2.7% +2.7% -5.3% +5.3% -10.6% +10.6%
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Atmospheric Density Error -2.5% +2.5% -5% +5% -10% +10%
Time (s) 7653 7849 7552 7943 7348 8133
Landing Velocity (m/s) 3.26 3.18 3.30 3.14 3.39 3.07
Drift (km) 55.5 57.3 54.7 58.1 52.8 59.8
Percentage Difference
Time -1.3% +1.3% -2.6% +2.5% -5.2% +4.9%
Landing Velocity +1.2% -1.2% +2.5% -2.5% +5.3% -4.7%
Drift -1.6% +1.6% -3.0% +3.0% -6.4% +6.0%
These results show that the percentage change in the chosen variable (landing velocity, time etc) are closely correlated to the percentage error in the unknown (wind speed or density). Therefore for the time to land and the landing velocity this does not pose a big problem. The probe should be able to safely land at a velocity up to 5m/s and the difference in time taken to land will have almost zero effect on the measurements taken during the descent. The result that is affected most is drift. This does not present too much of a problem as the predicted landing zone will be given regions of confidence for each of the error levels.
The errors also needed to be tested in parallel. As the purpose of these tests is to investigate the maximum deviation, wind speed and density errors will be tested either both in the positive or both in the negative direction.
Wind Speed/Density Error -2.5% +2.5% -5% +5% -10% +10%
Time (s) 7653 7849 7552 7943 7348 8133
Landing Velocity (m/s) 3.26 3.18 3.30 3.14 3.39 3.07
Drift (km) 54.0 58.8 51.8 61.2 47.2 66.1
Percentage Difference (Drift) -4.3% +4.3% -8.2% +8.5% -16.3% +17.2%
The table shows again that the landing velocity and time to land are largely unaffected. The percentage difference row only gives values for drift as the other two parameters can be found from table 4.7.1.
Here the change in drift varies considerably more than above as the two factors, wind speed and density, are both taken to their extremes. This level of error is unlikely to occur but will be considered when calculating the landing zone.
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4.7.2 Theoretical Wind Model
As the Huygens probe recorded a wind profile that was not predicted by theoretical models it was considered important to make an estimate of the probe’s descent trajectory based on the theory. By doing this an absolute upper bound can be placed on where the probe will land which will be important when deciding where the probe should enter the atmosphere. Using the Flasar et al. wind model[75]
(shown below) the same landing parameters were used to simulate a descent. The horizontal profile is also given below
Measured and Theoretical Wind Profiles 150
100
Measured Theoretical Altitude (km) 50
0 −20 0 20 40 60 80 100 120 Wind Speed (m/s) Figure 4.10: Wind profile over the lower ionosphere as predicted by Flasar et al. and as measured by the Huygens Probe
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4 x 10 Horizontal Descent Profile for Theoretical Wind Model 14
12
10
8
6 Drift (m) 4
2
0 0 1000 2000 3000 4000 5000 6000 7000 8000 Time (s)
50
40
30
20 Velocity (m/s)
10
0 0 1000 2000 3000 4000 5000 6000 7000 8000 Time (s)
0.3
) 0.2 2
0.1
0
Acceleration (m/s −0.1
−0.2 0 1000 2000 3000 4000 5000 6000 7000 8000 Time (s)
Figure 4.11: Horizontal descent profile calculated using a theoretical wind model
The graph shows that with the theoretical wind model the drift experienced by the probe is about
140km. The velocity profile shows a much smoother curve with just one maximum that is higher than in previous simulations. As the wind velocity is higher on average this is to be expected and explains why the drift is higher.
4.8 Predicted Landing Zone
Using the Huygens Probe data, the expected drift is 56km. The wind direction is predominantly West to East - the direction that Titan rotates, and so the predicted landing zone forms an ellipse about this expected drift value. For a 10% change in density and wind speed the drift value can be expected to change by ±17% giving values of between 47km and 66km. However, if the Huygens Probe recorded anomalous data during its descent and the theoretical model is accurate then the probe drift could be
81 Chapter 4. Landing the Probe Nicholas Baker as much as 140km from its entry point.
The full surface of Titan has not been mapped out yet, so choosing a landing site at this stage is inadvisable. The satellite that will orbit Titan will contain imaging cameras that should be able to provide much more information about Titan’s surface (see 13.5). Most importantly it should be able to interpret where the ground is solid, and where methane lakes and seas exist. The best landing site will be decided once the surface mapping has been completed by the orbiter. In this way every effort can be made to avoid the probe from landing in liquid methane which would drastically reduce the lifetime of the exploration. Based on analysis of the theoretical wind model, an ellipse with a major axis of 140km and minor axis of 60km should be used as an outer bound for the landing zone. If a land mass can be found that can accomodate this size landing area then that should be selected as the desired landing zone. If such a land mass cannot be found, the theoretical model will be ignored and the landing zone can be reduced to a major axis of 70km and a minor axis of 60km.
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Problems Faced by the Explorer During its Voyage Through Space
5.1 Introduction
Our project is to send an unmanned planetary explorer to Saturn’s moon Titan to further explore a relatively unknown environment by mapping, roving, and conducting experiments. The Lander,
Orbiter, and UAV of our explorer must first reach Titan in order to conduct experiments. In order to do this the modular components will travel together as a whole in the delivery module. This modular spacecraft will face challenges at every stage of its lifetime due to the hostile environments through which it will travel. What problems is the explorer likely to encounter, and can these problems be prevented? If they cannot, can their negative effects on the explorer be ignored or minimised, and if so how? Below we explore some of the main problems our craft may face, and how we can begin to defend our craft from their effects.
5.2 Problems
Outer space is a hostile environment. Earth’s atmosphere defends us from many harmful forms of cosmic radiation, but any craft outside the protection of the Earth’s atmosphere is exposed to many different kinds of emissions from the cosmos. The temperatures and environment of space is very different to that of Earth and that of other planets. In moving through these different environments our craft will encounter problems which may well affect the ability of its equipment to function properly.
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5.2.1 Problems Encountered on Earth
In preparing our craft to deal with the environment of space and Titan, where it will spend the majority of its lifetime, we may affect its ability to survive on Earth. Whilst still on Earth, one of the problems the craft may face is overheating. To keep the craft at an operational temperature in space it will need to be heated in some manner. There are several systems for heating a spacecraft, but most have a potential problem in that they can cause the craft and its systems to overheat when in the temperatures found on Earth’s surface. Once the craft has been completely assembled it will remain on the surface of the Earth in its ready state whilst it waits to be launched. The upper temperature limit or ‘survival temperature’ of some particle detectors and sensors can be as low as 35℃[170] which is a temperature not uncommon on the surface of the Earth. If we were to launch our craft in a hot enough season there is a danger that the onboard heating systems will overheat the craft.
5.2.2 Problems Encountered whilst en Route to Titan
One of the largest problems the craft will face whilst in transit between Earth and Titan is radiation.
On Earth, most of the dangerous solar and cosmic radiation is stopped by the Earth’s atmosphere and the magnetosphere[88]. However the effect of Earth’s magnetosphere on charged particles ceases at around 104 nautical miles[88]. After this the craft will be completely exposed to the full radiation emitted by the sun and the cosmos which could damage the equipment on the craft.
A further problem the craft may face is that of Electro-Static Discharge (ESD). This is caused by the different parts of the craft charging to different potentials. Once a high enough potential has been reached to break down the resistance between the different regions on the craft, the potential will discharge as a current across these regions. If these potential gaps occur, they could damage or destroy the instruments and electronics onboard the craft.
On Earth the craft faces the problem of overheating. Conversely, once it has left the relatively warm Earth there becomes a danger of the craft being underheated. If the craft becomes too cold the electronics, instruments and batteries may cease to function correctly. Space sits at an average temperature of 3 Kelvin[135], but the temperature of the craft would change depending on how much radiation is incident upon the craft at any time. When designing the operational temperature range for a craft which has batteries on board, the general aim is to keep it roughly that which a human could cope with[116], and 3K much colder than 293K.
84 Chapter 5. Problems Faced by the Explorer During its Voyage Through Space James Hawkes
Figure 5.1: Magnetosphere around Titan [212]
To prevent the problem of underheating we will be using some manner of heating system on our craft.
Whilst this will prevent underheating, if the system is uncontrollable or overzealous we could, once again, bring the problem of overheating back. Clearly we need to look carefully at the options we have for heating, and also at how tolerant our equipment will be.
5.2.3 Problems Encountered whilst in Orbit around Titan
Once the craft has traversed hostile space and is finally in orbit around Titan, there will still be problems to be faced.
Again the problems of overheating and underheating will be present. As discussed in chapter 13 of this project the craft will be orbiting at around 2000km above the surface of Titan, and this sits within the outer layer of Titan’s atmosphere, the exosphere[46], which extends up to 50, 000km. This means that the craft will be experiencing a different environment to that on Earth or in space, so we will have to implement a good control system for the onboard heating.
There will be a potential problem from ESD once again. Differential charging is a problem for any orbiting satellite[178] due to different parts of the craft being exposed or shadowed by the body they orbit and we have the added problem in that Titan is inside Saturn’s magnetosphere[73][188]. There is a plasma build-up in the magnetosphere near Titan [118], see fig 5.1, and this can contribute to charging the craft, which can lead to a potential ESD problem.
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Another problem of a different nature is a lack of power required for transmissions back to Earth. If the communications systems require more power than the onboard generating equipment can provide, then a suitable work around must be made.
Originally we had feared that there might have been a problem of charging when the craft started to enter Saturn’s magnetosphere, as it would have been cutting flux. However, after doing some basic calculations it turns out that this will not a problem;
Assuming the magnetosphere of Saturn decays like the field of a magnetic dipole, i.e. proportionally to 1 (5.1) r3 where r is the radius from the centre of Saturn, we can calculate a value for the magnetic field strength of the magnetosphere at Titan. Taking the magnetic field strength at the surface of Saturn to be
−5 Bs = 2 × 10 T (5.2)
and then considering that its magnetosphere is twenty-five Saturn radii (Rs) away[73] from Saturn, and Titan is twenty Rs away[188] from Saturn, where Rs
Rs = 60, 268, 000 m (5.3) we can see that the magnetic field strength at Titan
2 × 10−5 B = T (5.4) t (60268000 × 20)3 and the magnetic field strength at the edge of the magnetosphere is
2 × 10−5 B = T (5.5) p (60268000 × 25)3 which gives us
∆B = 5.55 × 10−33T (5.6)
The EMF generated in a loop is given by the rate of change of magnetic flux:
−dΦ ε = m (5.7) dt
86 Chapter 5. Problems Faced by the Explorer During its Voyage Through Space James Hawkes where magnetic flux is given by
Φm = ∆BA (5.8) where A is the cross sectional area of flux being cut. It is not uncommon for orbiting satellites to be sitting at a potential of around -19,000 volts[232], and our craft could feasibly be at this potential too.
Thus we would need our spacecraft to be either of the order of 1035m2 in area, or travelling many times the speed of light to generate a problematic loop EMF. It can be dismissed as a problem.
Solar radiation is not going to be a problem once we have reached Titan, as the craft will be too far away from the sun. For the sake of comparison, let us look at the amount of solar radiation incident at the top of a planet’s atmosphere; Earth receives 1100 cal cm−2day−1[121] whereas Saturn receives 6 calcm−2(Saturnday)−1[121]. The radiation received on Saturn is 183 times smaller than that received by the Earth.
5.3 Effects
As seen in the sections above, the craft will face many potential problems on its voyage to Titan. We now need to consider what effects these problems will have on our craft, and how severe they will be so we can decide how to deal with the problems.
5.3.1 Heating Effects
The effects associated with the problem of overheating or underheating could be many. For instance, different materials will expand by a different amount due to the same change in temperature[96].
There is little we can do to analyse some of the mechanical effects of the heating problems as we are not designing the physical structure of the craft in great detail. However, we can analyse how some of the equipment we will be taking on the craft will behave.
Overheating can have a negative effect on batteries and circuitry on board the craft. The standard batteries for use in space, Lithium-Ion batteries, may discharge slowly even when not connected to a circuit, but even so their temperature can affect how quickly they discharge. At high temperatures the batteries will lose their charge and their permanent ability to store charge faster[34]. See figure 5.2
The electronic circuitry on board the craft can also be damaged by overheating. The same problems one might face in electronics on Earth, overheating laptops and computers for example, can happen in
87 Chapter 5. Problems Faced by the Explorer During its Voyage Through Space James Hawkes
Figure 5.2: Battery Degradation [34] space. Short circuits can form where circuits melt and solder breaks, which could potentially render the circuitry inoperable.
Underheating can pose just as bad a set of effects. For example, if the batteries are too cold they will cease to function normally. They can discharge more quickly and may not be chargeable at low temperatures [32], and this could have a knock-on effect on systems which rely on battery power.
5.3.2 Radiation Effects
Radiation in outer space can come from several places including deep space, planets, and the sun.
See figure 5.3. It is common knowledge that radiation is harmful to humans, but it can be as equally harmful to electronics as well. Radiation can affect the batteries and cause battery degradation, it can cause errors in computer circuits, and it can cause charging on the structure of the spacecraft, leading to ESD situations.
Radiation can damage both solar cells and batteries[170], however as we are not using solar cells we at least do not have this to worry about. A study was done to see how gamma radiation would affect lithium ion cells[53]. The study found that after being bombarded with 100 Grays/minute for 24 hours there was a 20% decrease in capacity of a lithium ion cell. This is a very large amount of radiation by background measures, however the study does highlight the fact that radiation will affect the lifetime and serviceability of the batteries onboard a craft travelling through space for seven years.
In circuitry, ionising radiation can cause damage to hardware or can cause errors in programmes running on the onboard computers. In the long term, ionising radiation can degrade and destroy dielectrics in semiconductors and capacitors, and can even degrade the insulation on normal wiring to the extent that it becomes electrically leaky[195]. See figure 5.4. In the short term, ionising radiation can damage RAM modules and flip-flops, latches and transistors[195]. The devices can be stuck in a particular state and be unable to change back, rendering them useless as storage devices.
88 Chapter 5. Problems Faced by the Explorer During its Voyage Through Space James Hawkes
Figure 5.3: Radiation in Space [181]
High energy radiation, such as cosmic radiation, can cause Single Event Upsets (SEUs) which will also affect programmes and hardware. Cosmic rays can pass through semiconductor devices, leaving a brief ionised trail which will allow current to flow[195]. This can change the value in a RAM memory, or on some other semiconductor hardware such as a transistor. As these errors are random, i.e. they cannot be predicted as they only happen when a cosmic ray penetrates a semiconductor on the craft, they are hard to deal with, and well designed pieces of software which work perfectly on Earth may fail once they face the challenge of radiation.
Radiation can also have a charging effect on a craft in space, which will then lead to an ESD situation.
ESD can also be caused by solar radiation and charged particles, which often build up in the form of charged plasma in magnetospheres.[232] ESD becomes a bigger problem around dielectric materials, where a larger potential difference can build up over a piece of equipment before it discharges across delicate circuits. This can permanently damage the equipment, which could have severe consequences were it part of a vital system.
It is also worth remembering that we may get problems from some of the equipment we are using on the spacecraft. All the Radioisotope Thermoelectric Generators (RTGs) and Radioisotope Heater
Units (RHUs) we will be using contain a radioactive fuel, and if the units are poorly designed they could potentially leak radiation onto the craft, having the effects outlined above.
89 Chapter 5. Problems Faced by the Explorer During its Voyage Through Space James Hawkes
Figure 5.4: Semiconductor degredation due to radiation [210]
Another effect from these radioactive units can come from their fuel source, which is plutonium.
Plutonium is a poisonous element. This may not be a problem with direct effects on the craft itself but it could have severe effects on any people involved with it. For example, if the spacecraft were to crash back to Earth during the initial takeoff period, it could pose a serious environmental hazard[120] for people on Earth. This would be hard to control as crashes and accidents by their very nature are unpredictable. The craft could crash into any number of places were an accident to happen on takeoff.
5.3.3 Power Requirement Effects
Power requirement may be an unusual thing to count as a problem with effects, but it can be helpful to think of it in this way. The spacecraft will require power at all stages once it has left the launchpad.
Guidance systems and sensors will require power during the flight to operate, as will some commu- nications equipment. Once the spacecraft has reached Titan, the Orbiter unit will then require more power for communications as it will be transmitting to Earth and down to the planet to talk to the
UAV and Lander units. If there is not enough power being provided, the Orbiter will not be able to communicate thus rendering it effectively useless. This is unlikely to be a constant problem, but there is a chance that at a “peak time”of all our sensors, navigation units, downlinks, uplinks and
Earth communications systems operating concurrently we may lack the right amount of power. These situations are best visualised as problems with effects, as it is all very well shielding a craft from environmental hazards only to have it fail from lack of basic power. It is thus pivotal to the mission that we check we have suitable power sources and redundant systems so our craft can deal with these
90 Chapter 5. Problems Faced by the Explorer During its Voyage Through Space James Hawkes
Figure 5.5: RHU [168] peak loads.
5.4 Solutions
Space technology is becoming more mature as the years go on, and space agencies are constantly growing in knowledge and experience. Many of the problems we are likely to encounter have been encountered by professional space agencies before us, and they have a wealth of information we can learn from. As different agencies have overcome problems in different manners, there are often sev- eral solutions to a particular problem, and sometimes no perfect solution. We can use this pool of experience to our advantage in combatting the problems our spacecraft may encounter, using proven solutions, and when none is possible in using a robust work-around.
5.4.1 Solving the Heating Problem
The heating problems described above are a fairly fundamental but basic problem. To solve the problem of the craft being too cold, most current missions use a Radioisotope Heater Unit (RHU) to keep the craft warm (see fig 5.5). This device is a small (3.2cm long, 2.6cm diameter, 40g net weight) capsule containing 2.7g of Plutonium Oxide fuel. It has no moving parts, is not powered by electricity and generates around 1 Watt of thermal power[51].
The RHU works by directly transferring thermal energy from the natural decay of plutonium to the craft. This has an advantage of electrical heaters in that it doesn’t require power and thus doesn’t add to electromagnetic interference. It also means that it is very low maintenance, which is ideal for a long space journey prior to experimentation beginning.
91 Chapter 5. Problems Faced by the Explorer During its Voyage Through Space James Hawkes
To calculate a rough figure for how many of these we would need to keep our craft at around 0◦C,I modelled the thermal power radiated by the craft when it was at 0◦C. Using the Stefan Boltzmann law equation
P = ϵσA∆T 4 (5.9) where ϵ is the emissivity factor of a material, σ is the Stefan Boltzmann constant, A the area of the spacecraft, and ∆T the temperature change, I then substituted in the values we need.
The emissivity factor of aluminium[67];
ϵ = 0.09 (5.10)
The Stefan-Boltzmann constant;
σ = 5.670400 × 10−8W m−2K−4 (5.11)
The change in temperature, which is 0◦C - temperature of space[135];
∆T = (273 − 2.725) = 270.3K (5.12)
The area of the Cassini - Huygens craft[72];
A = 6.7 × 4 = 26.8m2 (5.13)
Our craft will be a similar size to the Cassini - Huygens craft, and as we are not designing the physical shape and layout of our craft it gives me a realistic set of dimensions to use. I used aluminium as the material as a large part of the Cassini - Huygens craft was aluminium[93]. Once all these values have been substituted into the equation, we find that the power emitted by the spacecraft is;
P = 730W (5.14) which means using 730 RHUs. The Cassini - Huygens craft used 35 on the probe [90], and Cassini used 157[111]. However, my model is fairly basic - it assumes that the craft is a regular solid cuboid in shape, and that all parts of the craft needs heating. In reality the craft will not be a regular shape and not all of it will need heating - structural components will not need to be kept warm, neither will the RTGs and RHUs themselves as they produce heat. In this way, with more knowledge about the
92 Chapter 5. Problems Faced by the Explorer During its Voyage Through Space James Hawkes physical layout of the spacecraft we could decide how many RHUs would be necessary, and compute the optimum layout for them.
Using RHUs however does constitute a problem in that they cannot be switched off. RHUs will constantly generate power until the plutonium fuel has completely decayed away - something which will not happen for tens of years. RHUs could solve the problem of underheating, but in so doing cause a further problem of overheating.
Fortunately this new problem of overheating by RHUs has been discovered by the agencies already operating in a space environment, and they have developed a device called a Variable Radioisotope
Heater Unit (VRHU). This has been developed by NASA’s Jet Propulsion Labs (JPL). This is a device which contains up to 3 standard RHUs, but it can rotate inside a holder (see figure 5.6) by means of a bi-metallic spring, which rotates at a given threshold temperature. A holder is attached to this spring, and this contains the RHUs. Half of this holder is thermally insulated to prevent heat from the RHU from passing through it, and the other half is not. When the craft is too cold, the VRHU rotates so that no insulation is between the RHUs and the craft, allowing it to be heated. When it is too hot the VRHU rotates the other way so the insulated side faces the spacecraft, and most of the heat generated goes out into space. Depending on what metals are used in the spring, different threshold temperatures can be set. The VRHU system requires no electricity, so does not compromise the low power and lack of interference qualities of a standard RHU, whilst solving the overheating problem[129].
This system is very similar to another system used - using louvres on space radiators to emit heat into space. Louvres are low emissivity surfaces that can rotate, once again on a bi-metallic spring, to either completely bare or obscure a radiating surface[170]. This works only to combat overheating, as the louvres themselves cannot heat the craft, only prevent it from losing further heat. With this system used in conjunction with VRHUs and standard RHUs, vital components beneath the surface of the craft can be judiciously heated - VRHUs dealing with surface components, RHUs preventing underheating beneath the surface, and the louvres combatting a related overheating problem from the
RHUs.
For our planetary explorer it is likely that we will use a combination of the above methods. VRHUs are a very attractive method for heating a craft thanks to their ability to effectively switch off. Using a mix of these and deeper RHUs deep under the surface to heat internal components we can maintain a workable temperature for our craft. Louvres will help to keep the craft cool as we are using internal
RHUs.
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Figure 5.6: VRHU [129]
5.4.2 Solving the Radiation Problem
There are many different ways of shielding equipment from radiation. One school of thought is to use existing parts of the spacecraft that are robust, or not affected by radiation, to shield those which are more fragile. For example, in some manned spacecraft they are using the water tanks[9], which will be already present to support human life, to shield astronauts from severe radiation from solar flares.
This saves on space and weight as well as being effective.
Aluminium is the standard choice for shielding, with about 2cm required to stop ionising radiation[232] but other materials with a high hydrogen content seem to show potential. [153] Polyethelyne is such a material, and is being looked into as it is lighter than aluminium and it is both a good thermal and electrical insulator. Using a material shield such as aluminium or polyethelyne could cause problems when shielding sensor equipment - for example it would be pointless to shield a camera from the front with 2cm of aluminium. A more novel way of shielding radiation is being researched at the moment - a ‘force field’[134]. It is technically called a Multipole Electrostatic Radiation Shield (MERS). Several configuration options are being considered for different applications, but the general principle is to have one powerful positively charged monopole with two or more weaker negative monopoles placed some distance apart. For spacecraft, these monopoles could be relatively near, as a higher voltage would be required to create current arcs in a vacuum, whereas a smaller voltage would be require on a planet with an atmosphere[139]. The MERS works by repulsion. Ionising radiation is either
Alpha radiation, which is a positive nucleus, or Beta radiation, which is a negative electron. The
94 Chapter 5. Problems Faced by the Explorer During its Voyage Through Space James Hawkes
Figure 5.7: Lunar MERS System [35] positive monopoles will repel the Alpha radiation, and the negative monopoles will repel the Beta radiation. However, as the MERS relies upon an electrostatic charge, it will require a large amount of power to run. The advantage of a material shield, such as aluminium or polyethylene, is that is can work with no power, and draws no power. So far, research into MERS has suggested that incredibly high voltages will be required to make the system work[18], which could confound our power supply problems further. Where we could save weight in using a non-material shield, we may well gain weight in providing the power for it. However, it could be switched on at critical times, and off at less critical times to save power. The whole MERS project is still in the early research stage. See fig 5.7 for an artist’s impression of how a MERS system could look on a moonbase - a configuration not dissimilar to that necessary on a spacecraft.
Earlier in this chapter I mentioned that some problems would not have a solution. Radiation falls into this category as it is incredibly difficult to the point of being impossible to fully prevent rays from penetrating into our circuitry, thus we have to find a good work-around.
Radiation’s effect on programmes and electronic circuitry can be attenuated by the use of hardware and software ‘radiation hardening’. This can be done with standard shielding, which would limit the amount of ionising radiation reaching components, or by physically changing the actual hardware.
Changing the hardware can be done by adding redundancies to circuits, so if a part fails the rest will work, or by changing the strength of the circuit. Semiconductor junctions are susceptible to radiation causing Single Event Upsets (SEUs), which is when a logic gate changes state and creating an error.
95 Chapter 5. Problems Faced by the Explorer During its Voyage Through Space James Hawkes
Figure 5.8: Silicon-on-Sapphire hardening [211]
Figure 5.9: Comparison of Radiation Hardened and COTS Processors [137]
This can also cause ‘latchups’, which is when a short circuit is formed in a MOSFET transistor. A way of dealing with this is to insulate the transistors from other around it, so as to minimise damage to the entire circuit. Isolation can prevent latchup and minimise the risk of SEUs[211]. Isolation can be done in several ways, with Silicon-on-Insulator and Silicon-on-Sapphire being two of the most common methods. The way these methods work is by changing the way the transistor is made. The transistor is grown on top of an insulator, such as sapphire, creating an island for the transistor to sit on. Sapphire is known for having a high radiation tolerance, and insulating all the components prevents leakage currents. See fig 5.8.
As well as using hardware techniques, we can also create more robust software to deal with the occurrence of SEUs. An advantage of software hardening is that it is cheaper than hardware, and imposes much smaller penalties on power and speed than hardware radiation hardening[137] which can significantly reduce the speed of a circuit. Radiation hardened processors are much more expensive and much slower than conventional off the shelf (COTS) processors. See fig 5.9. Using robust software radiation hardening means we can use faster and more economic hardware. Software hardening can be used to correct errors, or to reset a computer if it becomes corrupted - some SEUs can cause a Single
Event Function Interrupt (SEFI), where the device goes into an unknown state and must therefore be reset[137].
We can write software which checks for errors which have occured. Memory scrubbers are software programmes which scan the memory and check for errors, using parity bits and check data to work out if the data stored in a memory location is a true value or a value caused by an SEU. If they find an error, they can often repair it using the check codes[137]. It is important that the scrubber checks frequently enough so that there is little accumulation of errors. Multi bit errors are sometimes uncorrectable,
96 Chapter 5. Problems Faced by the Explorer During its Voyage Through Space James Hawkes and a reset would be required. Generally a memory scrubber is a standalone programme, and it will compete for CPU time with other programmes. This means that there is a level of optimisation to be done in deciding how frequently the scrubber should check the memory. Another way of increasing the reliability of the scrubber is to increase the amount of check data. Once again a degree of optimisation would have to go into this, as we don’t want to waste valuable RAM or ROM space on what could be an over generous amount of check data. One compromise would be to only increase the amount of check data and parity bits used for each memory entry during periods of high incident radiation.
This would free the CPU up to process standard programmes during low risk periods.
The use of a watchdog timer could also contribute to a functional work around. A watchdog timer is a robust programme which will hard reset the system unless it receives a particular signal which tells it that the system is working properly - rather like a dead man’s handle on a train. A watchdog timer doesn’t so much solve the problem of radiation damage, but will help the system recover from a blow which may make it come to a standstill.
The most economical way to solve the problem of radiation damaging our craft and its software is to use a mixture of prevention methods. It makes sense to shield the important semiconductors on our craft with a material shield, either aluminium or polyethylene depending on whether it is more useful to have a thermal insulator or conductor in a particular area. Though a MERS is a theoretically good system, the high voltage requirements and physical arrangement are not suited to the nature of our craft. It would have to carry more power generating equipment to cope with the demand, making it heavier and more expensive than simply cladding it in a material shield would. As for radiation hardening, a mix of both hardware and software would be the best method. Rather than using the most expensive radiation hardened chips, more economical COTS hardware could be used and combined with robust software to give us the advantage of low power consumption and fast processors. This would be especially important for parts of the craft deployed on the surface of Titan, as they may not have access to as sturdy a power supply as an RTG.
5.4.3 Solving the Electrostatic Discharge Problem
Electrostatic discharge has been a problem in the space industry for a while. As mentioned before, satellites orbiting Earth can sit at potentials around −19, 000V [232]. One might think that preventing the spacecraft from charging would be the best way of preventing charging problems, but this is hard to do, given that there are so many charged particles coming from Cosmic Background Radiation, and from the Sun. It is also worth remembering that it is the differential charging of a spacecraft which
97 Chapter 5. Problems Faced by the Explorer During its Voyage Through Space James Hawkes
Figure 5.10: Electron Penetration ( 1 mil = 0.0254mm) [82] causes the main problems. We must look at the different forms of charging that occur on a spacecraft and decide how best to deal with them.
The two principal kinds of charging of a spacecraft are surface charging and internal charging[82].
Surface charging is generally from lower energy electrons striking the surface of a spacecraft and charging it. Internal charging is from electrons with a higher energy, which have the ability to penetrate deeper into the craft. See fig 5.10. Deep dielectric charging is a problem caused by internal charging.
It might not be possible to ground dielectric materials, as they may be being used in a circuit which requires a potential voltage, and there may be some isolated conductors which are required to be isolated and thus can’t be grounded. There is also the problem that when a dielectric becomes charged but cannot discharge as fast as it is being charged. This presents a problem even if it is grounded, as the very physical properties of the material cause this[150]. Parts of the craft can be insulated to prevent surface charging, but it is unreasonable to try and shield against any electrons with a high energy (> 1MeV )[232] as it would require too thick a shield to be economical. Another technique is to rigorously ground as much of the spacecraft to itself as possible, including the structural and internal parts[232], which will prevent differential charging.
Our best approach to preventing damaging effects from ESD situations is to rigorously ground as much of the craft as possible, and to use a level of redundancy in our equipment. The grounding will prevent the problems associated with surface charging, and the redundancy will reduce the danger of deep
98 Chapter 5. Problems Faced by the Explorer During its Voyage Through Space James Hawkes dielectric charging causing errors in an entire system. Either software redundancies in programmes running on sensitive equipment should be used, or several of the same circuits if it is economical and possible so to do.
5.4.4 Solving the Power Demand Problem
Lacking sufficient power whilst on the mission could jeopardise the entire mission. If there is not enough power to run the navigational computers the craft may not even reach Titan, if there is not enough power to process data it is useless, and if there is not enough power to communicate back with Earth it is equally useless. To prevent this problem we have compared several different powering options to get the best configuration. I considered five devices in considering what to use, and also considered a combination. Firstly, there is the Radioisotope Thermoelectric Generator (RTG), secondly there are cells, thirdly capacitors, fourthly fuel cells, and finally a new device still in its research stage.
There are several different kinds of RTGs in use, and the technology on which they are based is very mature. The details on the different kinds is discussed in chapter 7 of this report, however they all work on the principle of using the heat from radioactive decay and some thermocouples to generate electric current[141]. The output is related to the half life of the fuel used, and is constant over the short term. For example, the RTGs sent with Cassini started their life producing 125W and 14 years later were producing 100W . Cassini used three of these[108] and its requirements were similar to ours.
Cells come as either primary or secondary, and with many different kinds of material in them. A primary cell is one designed not to be recharged, and a secondary is one which is designed to be repeatedly charged and discharged[170]. The advantages of using cells are that they can be repeatedly charged using other power sources so they can provide a constant power later on. For example, if a system needed more power than a particular source gave, a cell could be charged over a certain period, and discharged over a shorter period to provide the power required[31]. This provides us with some
flexibility when choosing the best options - we can offset a more economic but less powerful generator with some cells. Primary cells may give a better energy density than secondary cells[33], and energy density is an important consideration for space applications, but primary cells will not provide power long enough for our requirement of several years. If we are to use secondary cells then we must take a power source as well to charge them. The next question would be what kind of cell to take. This is discussed in detail elsewhere in the report.
Capacitors could potentially be used in place of secondary cells. If we need to store charge to use
99 Chapter 5. Problems Faced by the Explorer During its Voyage Through Space James Hawkes
Figure 5.11: Acid Fuel Cell Reactions [115] in a high demand situation, perhaps a capacitor would be useful. Capacitors tend to have a much larger life cycle than cells, and can be charged to very high voltages very quickly[63]. However, despite their advantages they have a low energy density, and are not capable of providing power for very long[234]. They are also susceptible to radiation damage, as mentioned earlier in this chapter. These disadvantages will likely outweigh the advantages when compared to secondary batteries.
Fuel cells are another option. They take hydrogen and oxygen as fuel and convert it to electrical energy. For instance, in an acid fuel cell hydrogen ionises, releasing electrons. Equation 14 is the reaction at the anode, and equation 15 is that at the cathode. See fig 5.11. A similar reaction happens at the electrodes in an alkali fuel cell[115].
+ − 2H2 → 4H + 4e (5.15)
− + O2 + 4e + 4H → 2H2O (5.16)
Fuel cells have a higher power density than most batteries, but unlike RTGs they do require a fuel.
They will also require heating, whereas an RTG won’t. Some of the Apollo missions used Alkaline Fuel
Cells[40] so they are not unknown to space applications. How they would cope, and how much fuel would be required, for a longer mission such as ours is another question. The Apollo mission which used fuel cells used three hydrogen-oxygen fuel cells, each of which weighed 113kg and produced between 500 − 1500W [36]. Compare that with the three GPHS-RTGs used by Cassini which weighed
55.5kg and carried 7kg of fuel[103]. We also then have the added danger of carrying hydrogen as a fuel.
Were the craft to crash before leaving Earth’s atmosphere the fuel it was carrying could contribute to a large explosion.
100 Chapter 5. Problems Faced by the Explorer During its Voyage Through Space James Hawkes
For our purposes the orbiter need only have RTGs. Looking at power demands from the Cassini mission and from our designs for the navigation and data collection systems, we would not need more than three standard RTGs to provide sufficient power even at peak load times. The orbiter will have no need for batteries or capacitors to supplement its power generation. Fuel cells are an interesting technology, but they are not as weight efficient as RTGs, nor as safe in a crash circumstance. We must however have a level of redundancy in providing power. Were one of our RTGs to fail, we would need to be able to provide sufficient power for all of our systems from the remaining two, and perhaps too have a priority system if the power supply falls below the maximum peak value requirements.
5.4.5 Solving the Environmental Hazard Problem
Plutonium is a very poisonous material[171]. It is not as toxic as many have made out, but there is still a severe threat from inhaling the material[171]. Our RTGs and RHUs all contain plutonium in one form or another [141][103]. Were the craft to crash to Earth on takeoff it could present an environmental hazard. Clouds of plutonium dust could be thrown into the atmosphere, which could be inhaled by people and animals, or the craft could disintegrate and crash into the sea where the plutonium could poison the environment there.
As it happens, were plutonium to be ejected into the sea only about 0.001% of the plutonium would become dissolved and thus be dangerous [8]. The effect of it crashing and dispersing on land would be different - inhalation poses a serious threat, as does panic from the public perception of the danger of plutonium[59].
One of the designs used to prevent poisoning from plutonium is to make sure the plutonium fuel will burn up in the atmosphere during a re-entry.The satellite Transit 5-BN-3 reentered the atmosphere, and all of the fuel from its Systems Nuclear Auxiliary Power Program (SNAP) RTG was burnt up in the upper atmosphere[131]. Another design is to ensure that the RTG and RHU are shielded well enough to withstand impact from a crash. The Apollo 13 craft contained another SNAP RTG, which remained intact during reentry. The RTG fell into the sea and currently resides at the bottom of a trench[131]. Testing has been done to ensure that its RTGs will not leak in sea water, and also testing to see how RTGs will react to an impact[183]. The results showed that the shielding could take an impact of 57m/s before the crash caused serious damage to the inner RTG working. For comparison, the average terminal velocity of a person is 55m/s[64]. Another test looked at how an RTG could survive damage from objects hitting it once it had crashed itself - this would be a real problem as chances are the launch vehicle would crash down with the spacecraft, increasing the likelihood of debris
101 Chapter 5. Problems Faced by the Explorer During its Voyage Through Space James Hawkes
Figure 5.12: Consequences of Impact on an RTG [144] hitting it[144]. See fig 5.12. 30 years of experience have led NASA to have a very good safety record with RTGs. One of their safety developments is that the fuel used is now a ceramic fuel[152]. This means that it tends to break into large pieces, rather than become a dust. The ceramic is also highly insoluble and unreactive[152]. They also use a large amount of shielding on each part of the fuel, and separate the fuel into separate pieces. This means that if any damage does come about it affects only a small part of the fuel. See fig 5.13.
Figure 5.13: RTG and Shielding [152]
The vast experience of space agencies who have been tackling this problem for many years suggests
102 Chapter 5. Problems Faced by the Explorer During its Voyage Through Space James Hawkes that if we choose our equipment carefully there should be no extraordinary environmental threat from our craft. Both the RHU systems and the RTG systems we will be using are very safe, and have good records in crashes were that to happen. Opting to not use fuel cells also reduces the danger from a crash.
5.5 Conclusion
This chapter has explored some of the main problems our explorer may face, the effects thereof, and how to defend against them. The experience of the major space agencies across the globe shows us how possible it is to deal with these problems, and has shown some of the better ways of so doing. Our craft, as its emphasis is on experimenting and exploring upon its arrival years after leaving Earth, will have an interesting set of constraints on it. Once the craft has left the Earth we are unable to maintain it, so all of the solutions to our problems must be long term, reliable, and redundant. Redundancy and compromise are the key terms in such a project, and we must ensure, using the techniques outlined above, that our craft can continue to function in harsh environments with no intervention.
103 CHAPTER 6 - Oliver Cohen
Lander Power Systems
6.1 Introduction
In this chapter we will examine the power systems that will be in use on board the Titan lander. Our
first task is to analyse the available options for powering the lander and when we have selected the optimum solution we will design power units specific to the lander. We will then briefly consider further issues related to the powering of the lander: power usage, and the heating of lander components.
6.1.1 Lander Power Specifications
In order for us to make our analysis we need to know the precise electrical design requirements, so we can compare the power output from a potential generation system to the required power consumption.
We are still unable to finalise this requirement as we have not been able to complete a full design of the lander, with precise details regarding many components not fully characterised. The exact specifications of our lander are thus impossible to currently determine; however, educated guesses may be made by assessing our designs is against a set of typical figures for a similar lander.
Over recent years there have been many proposals and studies by national space agencies into missions to Titan (for example the Titan Saturn System Mission [184]), as well as one probe which has already been sent (Cassini-Huygens). We will use estimated values from these missions as the basis of our lander design. These are as follows:
• Power budget: 65W [164]
• Bus Voltage: 28V [43]
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6.1.2 Design Parameters
The lander is designed to operate for at least one Earth year on the surface of Titan, and its primary functions are conducting scientific experiments and communicating the results of these experiments back to the orbiter for onward transmission to Earth. Any power system must be designed with these objectives in mind. These objectives lead to a number of implications that will be the focus of the following section, in which we select options for powering the lander.
6.2 Power System Options
There are many available alternatives for powering a lander on Titan; some are conventional and proven technologies, others are untried possibilities. We have tried to consider as broad a range of solutions as possible and we will select which to use based on the previously outlined specifications and parameters. There will be advantages and drawbacks to each of them, and no single solution can meet all of the lander’s needs, so the final selection will be a combination of power systems.
6.2.1 Solar
Solar power has been used successfully for powering numerous satellites and probes. It is a locally sourced form of energy and can generate electricity for a long period of time by converting sunlight into electricity via photoelectric cells, but only when light is available at the necessary intensity. When light is not incident on the panels, such as over the Titan winter, solar systems typically rely on batteries until light intensity increases.
Utilising advanced photovoltaic cells, a Titan orbiter would need 160m2 solar panels to generate 377W
[22], therefore a lander needing only 35W would need 15m2, assuming identical light conditions to the surrounding space. In practice however, atmospheric conditions on Titan would severely restrict light reaching the surface — in particular there is thick, permanent, high level haze that is highly opaque to visible light. Intensity is related to opacity by the Beer-Lambert law:
−κν ρx I(x) = I0e (6.1)
where I0 is intensity prior to entering the opaque substance, κν is the opacity and ρ is the density of the substance.
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Figure 6.1: Haze opacity at ground level on Titan [162]
Figure 6.2: Spectrum of total downward solar flux [215]
As shown in Figure 6.1, the opacity is least at -30◦ latitude, so if we were to use solar power, this would be the optimal location to ensure maximum solar power. However, Figure 6.2 shows that intensity is reduced by about 1/4 relative to the top of the atmosphere (at the most penetrating wavelengths), so this confirms that even at this latitude solar power generation is not really a viable option for the surface of Titan as ambient light levels are so low that the required power output is extrememly difficult to attain.
6.2.2 Radioisotope Thermoelectric Generators
Radioisotope Thermoelectric Generators (RTGs) are a second technology that has been tried and tested in space. The details of their operation are contained within a separate chapter, but in summary, they convert the heat from a decaying radioactive material to generate electricity. This has the advantage for the lander that the power source is self contained rather than relying on an external source. In addition, the power output of the RTG is regular (though slowly decaying) so can be
106 Chapter 6. Lander Power Systems Oliver Cohen predicted very reliably, thus removing the need for a power supply backup in the form of batteries.
Because the RTG is a single unit, there is also no risk of a failed deployment, only the risk of damage during flight.
The most significant penalty of using an RTG is its weight; the Multi-Mission RTG that is currently under development by NASA for use in such misssions weighs 43kg [1]. This mass must both be launched from Earth and, more difficultly, be decelerated to land on Titan, creating a significant technological hurdle if this technology is to be used, as adding mass to a lander has a snowball effect on the total mass (as extra mass requires extra propulsion, and extra propulsion requires extra power, requiring extra mass). There is also the added concern that, should there be a rocket failure on take- off, there is potential to spread highly radioactive material over a large area. Modern RTGs address this through heavy reinforcement of the RTG casing.
6.2.3 Wind
Extra-terrestrial wind has never been used as a mechanism for power generation in space, but it has great potential to be harnessed on Titan [117]. Drift over ground of the Huygens probe has allowed surface winds on Titan to be estimated to have a magnitude of about 1ms−1 [69] [68]. These winds are caused by the tidal forces of Saturn interacting with the rotation of Titan, and at surface level run from the equator to the poles.
One advantage of using the wind on Titan is that due to its tidal source, the winds are fairly constant, though seasonal variation is to be expected and a study shoud be undertaken to determine when in
Titan’s orbit of Saturn is likely to lead to the fastest surface winds.
A significant disadvantage of wind, in common with almost all systems using a local power source, is that if deployment of the turbine fails then the lander is effectively useless. The turbine would have to open fully for operation, unlike a solar power system, where a partial opening generates partial power. Another disadvantage is that a wind turbine needs a stable base to deploy and operate from, so a landing on an uneven surface would make successful operation unlikely.
An off-Earth wind turbine is totally untested, and would require significant design investment, and its operation could not be guaranteed. In this respect, using a reliable technology such as an RTG would be better.
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6.2.4 Tidal
The surface of Titan is, over a small fraction of its surface area, now known to be covered in lakes of methane [71]. It has been postulated that due to the forces of Saturn on these liquid bodies there are likely to be tidal [191]. Extraction of this energy has potential as a power source, but there would be some significant design hurdles to overcome if it were to be used; it is almost impossibly complex.
Firstly, the landing site must be carefully chosen to ensure the lander is in a sea, otherwise the generator is useluess. Since detailed maps of the surface are not available, a prior surveying mission would therefore be a pre-requisite. We must also therefore have a landing system able to place the lander on the surface with accuaracy, in addition to the lander itself being impermeable.
Fundamentally, we must also have a mechanism of turning the motion of the liquid into useful energy
— this has yet to be perfected on Earth, much less on an extra-terrestrial body. To prevent the lander drifting, we would need to anchor it, so in turn would need to know the depth of the sea (this ties in to having accurate surveys of the planet). Some kind of underwater turbine could then harness the power of the methane flowing past the stationary lander. In common with wind power, this turbine must deploy successfully for any power generation.
6.2.5 Batteries
Batteries come in two categories, primary or secondary - single use or rechargeable respectively. Which type we use is dependent on the function we wish them to perform.
As stated in the design parameters, we wish for our lander to operate for a year or more. To load up the lander with enough primary batteries to last this long is not a practical propostition. If we assume that the lander operates at maximum load (65W) for just 3 hours a day, energy requirement is 71175Wh. A typical Lithium/Carbon Monofluoride (CFx) chemistry battery has an energy density of 590Wh/kg [19], so 120kg of batteries would be needed for this energy requirement. We must also consider the impact of self discharge on the number of batteries requires, at 0.5% per year [19]. This leads to a 4% reduction in capacity over a 7 year flight and a 1 year mission, therefore actual intial energy stored should be 74kWh, and leading to a revised total of 125kg of batteries.
The alternative option is to use secondary batteries as a temporary power storage solution in conjunc- tion with a previously mentioned method; they cannot function as a sole power supply in themselves.
In this case, only enough batteries to store energy until use would be required. A set of secondary batteries are likely to be a prerequesite to any power generation system that uses the local environment as a power source, as the source will probably be too unpredictable, weak or subject to seasonal/time
108 Chapter 6. Lander Power Systems Oliver Cohen variation to be used directly to power the lander.
Batteries, whether primary or secondary, could also function as the backup power supply on the lander as they are a reliable and quantifiable source of power.
6.2.6 Selection
The following qualitative measures will be used in a weighted analysis of the designs, to make our
final selection for more detailed analysis:
• Cost (where a low score indicates high cost)
• Effectiveness of supply (to what extent are the power needs of the lander met?)
• Effectiveness over time (how long will the supply last for?)
• Originality
• Safety (on take off)
• Achieveability (will the idea actually work?)
• Deployability (how easy is it to set up once landed in Titan?)
By asigning ratings out of 10 to these measures (high values indicated improved performance, so a high total is desirable), and weightings based on the objectives of this project, a cost-benefit analysis produced the results shown in the Table 6.1.
Table 6.1: Results of power system selection analysis
Criteria Supply Time Cost Originality Safety Achieveability Deployability Effectiveness Effectiveness Weighting 0.2 0.9 0.9 0.8 0.5 0.7 0.5 Total Solar 3 5 8 5 8 4 5 25.6 RTGs 5 9 7 4 5 7 10 31 Wind 2 6 8 10 10 5 3 31 Tidal 1 2 8 10 10 1 1 24.3 Method Primary 6 8 4 4 8 5 10 27.7 Batteries
Solar and Tidal have the 2 lowest scores, so are not worth further consideration with regard to powering the lander. A battery system based on single-use batteries is possible though undesirable when compared to the two equal highest-scoring solutions - RTGs and Wind. Chapter 5 and Chapter
7 of this report conclude to use RTGs on board the orbiter and the balloon, so in this chapter we
109 Chapter 6. Lander Power Systems Oliver Cohen will focus on wind power as the chosen system for the lander, as the research into RTG use on those platforms can be applied to the lander if necessary, but Wind may only be used on the surface. We will also therefore need a secondary battery system to accompany it, as discussed in Section 6.2.5.
6.3 Wind Power
6.3.1 Feasibility
We must know how much power we can expect to harvest from the winds on Titan. Total power (P ) available in a moving body of air of cross-sectional area A and density ρ, is proportional to velocity
(V ) cubed, and given by [62]: 1 P = ρAV 3 (6.2) 2
We cannot expect our turbine to be 100% efficient — there will be losses associated with turbulence over the turbine blades, generator losses, gearbox loses and other miscellaneous sources of of ineffi- ciency. We should therefore include an extra term to scale down the power generated — the coefficient of performance, Cp. 1 P = ρAV 3C (6.3) 2 p
We will now work out the values of the terms in this equation.
Coeffficient of performance
Betz’z law [230] allows us to show that
( ( ) ( ) ) 2 3 dE 1 3 − v2 v2 − v2 = ρAv1 1 + (6.4) dt 4 v1 v1 v1
dE where v1 and v2 represent the wind velocities before and after the turbine respectively, and dt is the power. By differentiating again, but with respect to v2 , we see a maximum at v2 = 1 , which v1 v1 3 corresponds to a maximum efficiency at ideal conditions of 59.3%.
On Earth, the best turbines approach 70% of this limit, at wind speeds several times those found on
Titan. On Titan, we cannot approach this level of efficiency as our turbine design will be compromised by the necessities of space travel to make it light and deployable. The low wind speeds also will make
110 Chapter 6. Lander Power Systems Oliver Cohen high efficiency difficult to attain.
Generator efficiency should be high and comparable to what can be achieved on earth. Gearbox efficiency should also be comparable, as the low gravity environment will make the turbine sit less heavily on its bearings so less energy is lost to friction.
Overall, a coefficient of performance of 30% is not an unreasonable ballpark figure.
Density
On Titan, the atmosphere is primarily made up of nitrogen with a small amount of methane and other gases [122]. Using the ideal gas law in the form (where p=pressure, ρ=density, R0=universal gas constant, M=molecular mass and T =temperature in Kelvin)
R p = ρ 0 T (6.5) M and approximating the atmosphere to pure nitrogen with a molecular mass of 28 kg kmol−1 we can determine the density of the atmosphere at surface level. Voyager 1 measured, with good confidence levels, the surface temperature at 94K, and pressure at 1496 mbar [122]. Substituting these, with the appropriate unit conversions, we find that the density is 5.36 kg/m3.
Wind Speed
As previously discussed, the wind speed on Titan is expected to be around 1ms−1.
Turbine Area
This is the factor within the equation which we have the most power to influence with our design.
Table 6.2 shows, using the above values, how much power can be produced with turbines of differing areas. Table 6.2: Power generated by a turbine of a given area
Area (m2) Power (W) 1 0.80 4 3.22 6 4.82 10 8.04
This shows that even with a large turbine, we could not extract enough power from the wind to
111 Chapter 6. Lander Power Systems Oliver Cohen continuously power all systems. This does not, however, make wind power an unfeasible option; if the turbine can store energy in batteries for most of a charging cycle, then the batteries can discharge in short bursts. With a turbine with an area of 6m2, it takes just under 14 hours of charging to provide the energy for one hour of continuous full power (65W) operation. In practice, a small amount of power is always used to run essential systems, but wind remains a feasible option.
6.3.2 Implementation
A ‘wind turbine’ is a very general name for a device that extracts electrical power from the movement of air, but there are several different ways in which a turbine can be designed.
Horizontal Axis Wind Turbine
Figure 6.3: A typical Earth-based HAWT
A horizontal axis wind turbine (HAWT) is the design exhibited by most large wind turbines on Earth, shown in Figure 6.3. The generator is mounted at the top of a tower, at the centre of the blades. The head is rotated by a motor to face into the prevailing wind.
Swept area (A) is given by:
A = πr2 (6.6) where r is the radius of the turbine blades. Therefore, the minimum height of the tower is r, though actual height would be r + ϵ, where ϵ is some margin to reach clear air.
Vertical Axis Wind Turbine
There are several variations of the vertical axis wind turbine (VAWT), but all have the generator at the base of the tower and the blades rotate around a vertical axis. The form that is most common is
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Figure 6.4: A Darreius VAWT the Darreius-type VAWT (see Figure 6.4).
The area of such a turbine may be approximated by the area of two triangles, bases together. Terms are as shown in Figure 6.5.
Figure 6.5: A simplified drawing of a Darreius VAWT
1 A = width. height (6.7) 2
It is worth pointing out that the standard wind power equation applies to both vertical and horizontal axis turbines [74].
An advantage of using a VAWT over a HAWT is that the VAWT generator is mounted on the lander, so it is much less complicated to deploy, as with a HAWT the generator must be raised to the top of the tower. Also, a VAWT does not need to be pointed in the direction of the wind.
VAWTs are less favoured on Earth compared to HAWTs due to the high cyclic stresses that their frame undergoes, as blades only generate lift, and therefore power, when pointing into the wind, and on Titan this is also a concern with this option.
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Multiple Smaller Turbines
Instead of having one large turbine, one turbine solution would be to have multiple smaller turbines spaced over the lander. The area presented in total by these would be:
A = n(πr2) (6.8) where r is the radius of each turbine and n is the number of turbines.
Having multiple turbines is an attractive idea for the redundancy it provides. If one turbine fails to deploy, only a fraction of the generation capacity is compromised, whereas if we are relying on a single turbine solution and that turbine fails to deploy then the whole lander is useless.
Materials
Whichever type of turbine is used, one key aspect of implementation is the material of which the structure is made. The blades must have a specific shape in order to function, so our material must be rigid, though not necessarily strong, and also very light, both to reduce the cost of transport to
Titan, and to minimise intertia of the blades. Furthermore, an insulated build up of charge through interaction with molecules in the atmosphere or cosmic radiation could lead to an uncontrolled dis- charge, which could in turn damage the electronics on board the lander. As it will be difficult to have an effective earth to a rotating turbine, the material should also be conducting.
Figure 6.6: Materials selection chart showing the relationship between density and Young’s Modulus for various classes of materials [11]
From examination of Figure 6.6, the three most suitable categories of materials in terms of low density
114 Chapter 6. Lander Power Systems Oliver Cohen and high Young’s modulus are composites, ceramics and the less dense metals, such as aluminium.
Ceramics, though strong, are also brittle, so if they sustained an impact during the landing they could break. Neither ceramics or composites conduct, which leaves low density metals as the option of choice.
6.3.3 Deployment and Operation
HAWT
One of the previously identified disadvantages of an HAWT is the need to face it into the wind. In addition, having the generator at the top of the pole has the potential to make it top heavy and possibly blow over in a low gravity environment.
Figure 6.7: Possible operation solution for a HAWT
Figure 6.7 shows a solution to these issues, which is to mount the turbine on the outer circumference of a platform, with a strut crossing the diameter of the platform to a point directly opposite of the the turbine, connecting it to a motor. This motor sits on a toothed track, and works as a rack and pinion gearing to move the turbine around to face into the wind. The turbine also sits on the track and therefore rotates around the outer edge of the platform. The dual function of this setup is that the motor acts as a counterweight/support to the turbine against the wind force to prevent it blowing over.
A problem with this implementation is that having a strut sweeping over the platform restricts how the deck of the lander can be used. This could be solved by using the platform itself as the connecting arm, and rotating the whole platform, though this would take a lot of energy. Alternatively, we could have a lower instruments deck beneath the turbine base level; this would also enable the turbine level to be used for turbine storage during the flight, leading to a less complicated deployment.
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VAWT
A VAWT has the generator at the base, and does not need to face into wind, but has the problem that it is a much more complicated and intricate structure, therefore not as easy to transport and deploy.
Figure 6.8: A VAWT folded for transportation
A method of achieving this, shown in Figure 6.8, would be to have a telescopic central support which rises either hydralically or with a spring. The former option requires machinery, while a spring is would require no external energy to effect the deployment. Using a spring, the support could be held withdrawn by wires which are then cut with pyrotechnics to release it. A redundant second set of pyrotechnics would be included to be used in the event of a failure.
Attached to the top of the support would be the two aerofoil shaped blades. These would be hinged in the centre to allow them to fold down.
The central crossbrace support would attach to each blade at a hinge in the middle with an elastic strap leading into a rigid section which connects to a ring to slide up the telescopic main support as it rises. When fully deployed, the blades will be flush with the the rigid part of the crossbrace and the elastic will be fully retracted.
6.3.4 Voltage rectification
Both forms of turbine generate alternating current electricity (AC). However, battery charging needs to be done with a steady direct current (DC) supply. The process for converting AC to DC is rectification.
A simple rectification scheme is a half-wave rectifier, where a diode cuts out the negative part of the supply. However, this leads to half of the generated voltage being lost, which is a significant reduction in efficiency. Since we are already operating in an environment where energy is at a premium, this would be an unnecessarily wasteful method of rectification.
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A more sophisticated scheme is a full-wave rectifier, where 4 diodes are connected in such a way that the negative part of the AC cycle is reversed in polarity while the positive part is unaffected. This is an improvement, but voltages still fluctuate from zero up to the the maximum every half cycle, which is unacceptable for the purposes of battery charging (see Section 6.4.3).
Figure 6.9: Full wave rectifier circuit with smoothing capacitor
Figure 6.10: Load voltage against time for the full wave rectifier with smoothing capacitor
To improve on this we can add a ‘smoothing capacitor’ in parallel with the load (see Figure 6.9), which stores energy when the voltage is high and discharges it when the supply voltage drops, smoothing the gaps between the peaks; this can be seen in Figure 6.10.
The magnitude of the ripple voltage that occurs between peaks must be known so we can design the circuit to meet the charging supply specifications.
From point A to point B on Figure 6.10:
V dV L + C L = 0 (6.9) RL dt
− t ( R C ) VL = Vmaxe L (6.10)
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where Vmax is the voltage at points A and C, and t is the time between A and B, which is a fraction of the time period.
From point B to point C:
− t ( R C ) VL = Vmaxe L (6.11) t ≈ Vmax(1 − ) (6.12) RLC Vmaxt ∴ VL = Vmax − (6.13) RLC
Therefore the ripple voltage ∆VL is given by
Vmaxt ∆VL = (6.14) RLC
To confirm this conclusion, we used Microcap to simulate a rectifier circuit using a supply of frequency
5Hz and magnitude 6V, a load of 100Ω, and a smoothing capacitor of 10mF. The signal across the load had a Vmax of 4.119V, and t was 76.8ms. Our theory therefore indicates
4.119 × 76.8 × 10−3 ∆V = = 0.32V (6.15) L 100 × 10 × 10−3
Our simulation returned a ripple voltage of 0.29V, confirming our theory, the difference being due to the exponential approximation.
In reality, there will be further considerations we must account for in our system, as it is likely that the effective resistance of the batteries will vary while charging, and t may vary as wind speed changes the generator frequency. This could require us to have some kind of variable capacitance, or a selection of available capacitors. This will be examined further in the Section 6.4 which discusses batteries and charging in more detail.
6.3.5 Conclusions
Based on the respective advantages and disadvantages of the various turbine solutions, we would recommend a VAWT as the optimal wind turbine design. The need to have a turbine which produces as much power as possible needs to be balanced against the need to save weight both to keep costs down, and to ensure the turbine operates in the light winds on Titan. Therefore a turbine with an area of 6m2 is recommended. For a VAWT, this would equate to a total height of 6m, with an apex width of 2m.
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Our detailed examination of the use of a turbine has shown that despite its equality with an RTG in the earlier cost-benefit analysis in section 6.2.6, with this extra data we would adjust the supply effectiveness and the acheivability scores downwards, making RTGs the best solution. We will continue with an analysis of secondary batteries to support a turbine, on the principle that with further research and a more advanced design a turbine is still a potential solution for providing power on Titan.
6.4 Secondary Batteries
6.4.1 Chemistry
We must select a battery chemistry that fulfils the demands of the lander; this is a prerequisite to any further investigation as different types require different charging schemes and come with different drawbacks to overcome. The criteria we must consider are:
• Cycles (how many times the battery may be charged and discharged over the course of its life)
• Operating temperature
• Radiation resistance
• Energy Density (we want this to be high so the batteries weigh as little as possible)
• Internal resistance (we don’t want to waste too much energy internally)
• Self-discharge (the amount of energy lost while in open circuit)
Battery voltage is also relevant, as we need to know how many batteries in series will be required to acheive the bus voltage, though it is not a consideration that affects which chemistry we choose. Table
6.3 summarises the quantifiable characteristics of some typical chemistries:
Table 6.3: A comparison of common secondary batteries [30]
NiCd NiMH Lead Acid Li-ion Li-ion polymer Reusable Alkaline Energy 45-80 60-120 30-50 110-160 100-130 80 Density (Wh/kg) Internal 100-200 200-300 <100 150-250 200-300 200-2000 Resistance (mW) (6V pack) (6V pack) (12V pack) (7.2V pack) (7.2V pack) (6V pack) Cycles 1500 300-500 200-300 500-1000 300-500 50 Self-discharge 20% 30% 5% 10% ∼ 10% 0.3% per month Cell Voltage (V) 1.25 1.25 2 3.6 3.6 1.5 Operating ◦ -40 to 60 -20 to 60 -20 to 60 -20 to 60 0 to 60 0 to 65 Temperature ( C)
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Cycles
The aim of the lander is to function on Titan for an Earth year; with the power output of the turbine, we expect to achieve about 2 charge/discharge cycles a day, so our batteries must last for 730 cycles.
This might imply that we automatically restrict ourselves to Li-ion and Nickel Cadmium batteries, but in practice we will need to carry redundant batteries as back-up for battery failures, so all we need are batteries with high cycle capability to minimise the amount of redundant batteries that we need. Therefore the only two battery classes we rule out on application of this criterion are Alkaline and possibly Lead Acid.
Operating temperature
The higher the required operating temperature of a battery, the more heating apparatus must be carried, which adds to lander weight. The precise mechanism of heating is dealt with in Section 6.6, but it will be important that design ensures that the batteries are not overheated while waiting to launch, as this will reduce their capacity. Most batteries appear to have similar operating ranges, though Nickel Cadmium batteries have the widest range of temperatures. Overall, it is unlikely this criterion will impact on our final selection.
Radiation resistance
Ionising cosmic radiation could interfere with battery operation, so the selected chemistry should be reistant to such effects. A method of tackling this problem would be to ensure the specific selected battery is intended for use beyond Low Earth Orbit (where it becomes exposed to radiation).
Energy Density
The battery types with the highest energy density by far are the Li-ion based cells, the standard type in particular (as opposed to Li-ion polymer). If we require our battery set to hold 200Wh, enough to power the lander at full power for 3 hours, and 40 hours of solid charging based on our turbine calculations, a Li-ion set fulfilling this will only weigh
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Energy stored Mass = (6.16) Energy density 200 = (6.17) 100 = 2kg (6.18)
at most, or just
200 Mass = = 1.25kg (6.19) 160 at best. Extra redundancy on top of this would be needed, but this is an excellent preliminary result.
The next best option based on energy density behind Li-ion would be NiMH, which also has a high energy density associated with it.
2 The worst performing battery in this respect is Lead Acid, which would weigh 4 to 6 3 kg, significantly heavier than Li-ion. Couple this with its poor cycle performance which would mean that even more than this mass would need to be carried, and Lead Acid seems an unwise choice, so we will discount it.
Internal resistance
The data on internal resistance has been provided relative to different sized packs; for it to be mean- ingful we should consider how much energy will be lost when enough batteries are connected to run the bus at 28V. This is shown in Table 6.4. Table 6.4: Internal energy lost operating at 28V
Chemistry: NiCd NiMH Lead Acid Li-ion Li-ion polymer Reusable Alkaline Energy Lost (W) 0.47-0.93 0.93-1.40 <0.23 0.58-0.97 0.78-1.17 0.93-9.33
It is now clear that Lead Acid performs best, but we have already discounted this for other reasons.
Alkaline fails this criterion, and also has already been ruled out. All other battery types asssesed show similar acceptable energy losses, though Li-ion polymer perform slightly worse than the rest.
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Self-discharge
This will be examined in more detail in the next Section 6.4.2, but of the batteries left in contention, it is Li-ion chemistry batteries that have the lowest self-discharge. This means that once a Li-ion cell is charged and waiting to be used much less of the energy that has been stored in it leaks out through chemical processes than if a less well performing chemistry was used.
Selection
Based on the above examination, the battery chenistry that appears best suited to our requirements on the lander is Li-ion. Both forms (standard Li-ion and Li-ion polymer) are quite similar, but on balance, standard has overall better ratings.
Li-ion is also a proven space-capable technology, having been used on the Mars Spirit and Opportunity rovers where Li-ion batteries performed a similar function of storing locally sourced energy (in these cases solar) for release later overnight [49]. This has parallels with what we are trying to achieve on
Titan.
6.4.2 Transit to Titan
The transit to Titan will take a number of years - the flight of the previous probe to be sent, Cassini-
Huygens, lasted almost 7 years [54]. For the landing on Titan, we wish to have the batteries initially fully charged. However, at a 10% self-discharge rate per month for Li-ion batteries (which will always occur, even with an open circuit), if we started holding 200Wh of energy, by the end of the flight only
(Self-discharge rate per month)Flight months × Initial energy = Remaining energy (6.20)
(0.90)12×7 × 200 = 20mW h (6.21) remain. In practice, self-discharge rate is related to total charge, so the 10% rate of self-discharge reduces as charge is depleted. It is also reduced by cold temperatures, so this too would slow the effect. However, even then there would be almost no energy left in the cells by the end of the journey.
There are several options to address this. Firstly, we could reduce the self-discharge somehow by a clever chemistry or by holding the battery at low temperatures. However, temperature control is difficult to achieve on the lander as the heating is fixed (see Section 6.6). Therefore reducing self- discharge is not an option.
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Alternatively, the initial battery load could be increased, so remaining charge at the end of the flight is increased. This too is unfeasible as it would require an increase in mass carried of almost 4 orders of magnitude.
A third option is to decrease flight time and/or final energy requirements. Again, this is not a practical option as even after a year only 56Wh remain from 200Wh, and this timescale cannot be achieved with current rocket technology (we use gravity assist flybys to attain the required speed to reach Saturn).
Our final option is to link the lander batteries to the power supply on the orbiter by an umbilical power cable and charge them from the power provided by the orbiter’s RTG on the final approach to
Titan, leaving the batteries uncharged for most of the flight. A minor disadvantage of this method is that it either requires a battery charging system on the orbiter, or the lander charging system to be adapted to take power from two sources. We must also consider how to cut this umbilical wire to allow the lander to separate from the orbiter for Titan entry. This has been previously acheived on the Galilleo mission to Jupiter using a pyro-driven guillotine blade [151], which should be doubly redundant in case of a pyro failure, and there is no reason why this method cannot be used again.
6.4.3 Charging
Charging Scheme
Lithium ion batteries have a very specific way in which they must be charged, shown in Figure 6.11.
Figure 6.11: Lithium ion battery charging scheme [30]
The first stage is at constant current to restore charge to deeply depleted cells, and continues until the cell reaches its voltage limit at 4.2V. This stage only needs to be done if the cell has been depleted so
123 Chapter 6. Lander Power Systems Oliver Cohen far that its output voltage has dropped below nominal (3.6V).
The second stage is at constant voltage, 4.2V for a Li-ion cell, until charging current is reduced to about 3% of rated current. Control of the voltage during this stage is critical as it must not vary by more than ±1% to ensure cell capacity is maintained. Current sensing is equally important as if the cell becomes overcharged, lithium ions can become lithium metal and plate onto the electrodes leading to instability and potential failure [48].
Charging Control
Figure 6.12: Lithium ion battery equivalent circuit [81]
In order to design a charging control system we must know the transfer function of a Li-ion battery.
We can derive this from the circuit shown in Figure 6.12 [218], where terms correspond to those shown in the figure:
1 V (s) = (C2//R2)I(s) + (R1 + )I(s) (6.22) sC1 V (s) 1 1 = 1 + R1 + (6.23) I(s) sC + sC1 2 R2 C2R2 1 R2 + sC2R2R1 + + R1 + = C1 sC1 (6.24) 1 + sC2R2 C C R R s2 + (R C + R C + R C )s + 1 = 1 2 1 2 2 1 2 2 1 1 (6.25) C1(1 + sC2R2)s
We could charge by having two separate controllers, one at constant current, the other at constant voltage, and sense when to switch regimes. Alternatively, we could use a proportional controller to- gether with a current limiter in the form of a saturation element designed to operate linearly once the battery is within 0.1V of its maximum voltage, therefore requiring only one controller and the only sensing mechanism necessary is to determine when to stop charging and move on to the next cell. The
124 Chapter 6. Lander Power Systems Oliver Cohen block diagram for this is Figure 6.13.
Using typical Li-ion battery parameters [218] of R1=0.15Ω, R2=0.44Ω, C1=7200F, C2=170F, Imax=1.1A and Vref (the charging voltage in stage 2 of the charging scheme)=4.2V, and setting the gain of our proportional controller to 11 (i.e. the current will drop into the linear region of the current limiter when the cell voltage is 0.1V away from Vref ), we can simulate this system using Simulink. The results are shown in Figures 6.14 and 6.15.
We can see that these closely resemble the desired scheme earlier described. Note that most power used while charging a single battery is used at the transition between the two charging stages, and is
P = IV (6.26)
= Maximum charging current × Maximum charging voltage (6.27)
= 4.2 × 1.1 (6.28)
P = 4.62W (6.29) which is comparable to the power being generated by the turbine.
To terminate charging at when current is at 3% of Imax, we can have an ammeter connected, via an analogue-to-digital converter, to a microprocessor containing containing a multiplexer that selects which battery to charge next.
6.4.4 Conclusions
We have selected Li-ion batteries to store power produced by the VAWT, and shown that they have the capability to perform this function. We have also designed and simulated the appropriate charging system.
One specific Li-ion battery we have found that would be appropriate to use is the Saft VES 100
(Figure 6.16), a space-proven cell [189]. The data sheet [190] shows that is has typical Li-ion electrical characteristics. Charging method corresponds to the constant-current/constant-voltage scheme that we have investigated, with a maximum charging voltage of 4.1V. It can be stored between -40◦C to
+65◦C, so should not be affected by any overheating at launch. Finally, it is rated for an 18 year life and recommmended for use on probes, so seems a an appropriate choice.
To achieve a bus voltage as specified of 28V, we will need 8 × 3.6V cells, and would use 10 for redundancy. At 0.81kg per cell, this is a total of 8.1kg.
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Figure 6.13: Proportional controller with current limiter
Figure 6.14: Cell voltage over time using proportional control with current limiter
Figure 6.15: Charging current over time using proportional control with current limiter
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Figure 6.16: Saft VES 100 Li-ion battery
6.5 Power Usage Routine
Initially, when the lander touches down on the surface of Titan the batteries should be fully charged, and this energy will be used for erecting the turbine, initial recordings of the descent and environment and communication with the orbiter.
As calculated in Section 6.3.1, it will take 14 hours for a full charge, but it is not as simple as charging fully then discharging fully on a regular basis. Communication with the orbiter should be made at every available opportunity, even if early in a charge cycle, with two exceptions:
• When no new data has been gathered since the previous report
• When power reserves are very low and must be conserved for vital lander functions
Experiments may be conducted/instruments should used in the gaps between orbiter communications, and ideally only when charge level is high, though this condition may be relaxed if it is important to get readings at even time intervals.
Most importantly, no non-essential system shall be switched on once the charge level drops below
15%, arbitarily chosen as the level at which the lander moves from an active mode to ‘survival’ mode where every scrap of power is conserved to keep power collection systems running so a safe and useful charge level may be re-attained.
6.6 Lander Heating
Lander heating will be accomplished via the firmly established technology of Radioisotope Heater
Units (RHUs) [51]. These are analysed and explained in Chapter 5, so we will not examine them here, beyond stating that they will be used for this purpose.
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UAV Design and Power
7.1 Introduction
Titan’s thick methane clouds and largely opaque atmosphere (especially a layer of orange haze let very little light through either way; trying to get images or readings of its surface from orbit around it means light reaching the camera has had to pass through the atmosphere twice. In 2005, the Huygens probe (and its partner Cassini, which was an orbiter) landed on Titan, taking useful measurements; however obviously it was limited to a small area immediately surrounding the lander. Luckily, the environment on Titan provides almost ideal conditions for flight, having both a dense atmosphere, which increases lift, and low gravity, which decreases weight. An Unmanned Aerial Vehicle (UAV) seems to be the ideal solution for taking detailed readings and pictures over a large area, marrying the quality of imaging achieved by observing below the thick orange haze with the coverage that can be obtained by flying above the surface. This will not be easy to implement, and well-researched design decisions must be taken on materials, power sources, and by what method lift will be generated.
UAVs have been previously used to explore foreign worlds; in 1984, two identical Soviet probes, named
Vega 1 and 2, were sent to Venus. Each probe carried a lander and a balloon which measured wind speed, pressure, and temperature, amongst other things. The atmosphere on Venus is very hostile, with clouds of concentrated sulphuric acid, pressures of up to 90 bar, and temperatures of up to
740K [92] at the surface to contend with. The balloons were forced to operate at high altitude due to the pressures and temperatures; on Titan we will not have this problem. However new challenges will arise as a result of the low temperatures (around 94K). This report aims to determine the optimum form of UAV to be employed on Titan, the best way to power it, and at what altitude it should fly.
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7.2 Operational Conditions on Titan
7.2.1 Location
Titan is the largest moon of Saturn, and so orbits at a distance of ∼9.5AU from the Sun [157], or between 8.5 and 10.5 AU from Earth. It is important to know how long it would take a radio wave to travel from Earth to Titan to determine whether direct control can be used or if the UAV must be at least semi-autonomous.
1AU = 149, 597, 871km (7.1)
Speed of Light = 299, 792, 458ms−1 (7.2)
149597871 × 103 ∴ t = = 499s.AU−1 = 8.3min.AU−1 (7.3) 299792458
So Titan is between 70 and 87 light minutes from Earth, far too far away to directly control a UAV.
It must therefore have sufficient autonomy to operate without constant instructions.
7.2.2 Atmosphere and Terrain
Titan’s atmosphere consists largely of Nitrogen gas, with small amounts of methane (up to 4.9% at the surface [165]), and trace amounts of other gases. The pressure at the surface is ∼1.5 bar, and at 94K has a density of 5.3kgm−3. The low temperatures mean that at the surface, methane is liquid, and in fact above 14 km, the equilibrium state of the CH4-N2 mixture is solid [125]. The surface gravity on Titan is 1.352ms−2, or 0.138 g. This combination of high density and low gravity is ideal for flight — so ideal, in fact, that humans could fly through it by attaching ‘wings’ to their arms [235]. However, the incredibly low temperatures present mean that it is vital to consider carefully the materials used on any UAV so that a long lifetime is ensured.
The methane in the Titan atmosphere forms a solution with the more plentiful nitrogen, which reduces its freezing point such that the methane will freeze out when the temperature of the solution drops. As altitude increases in the troposphere, temperatures decrease, so this is predicted to occur at altitudes above 14km [110] — the ‘snowline’. This means that if the UAV goes higher than 14 km in altitude, methane crystals may start to form on the outside, weighing it down significantly, and potentially sending it crashing down toward the surface. This is known as methane icing. The snowline altitude is higher at the poles due to a smaller fraction of the atmosphere being methane, and so icing occurs
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Figure 7.1: Titan zonal wind height profile at 19km [127].
The UAV also faces hazards at the other end of the altitude scale. Up until the Cassini/Huygens mission, it was not known what the terrain on Titan resembled. However, thanks to Cassini, mountains were recently discovered on the surface of Titan, with heights of up to 2km [179] so the UAV will have to be designed to either avoid these or operate above them.
7.2.3 Meteorological activity
Titan is the only other world in the Solar System than Earth that rain reaches the surface, and it has a methane cycle somewhat similar to the water cycle we know. As such, caution must be taken to prepare for meteorological activity similar to that on earth; it is predicted that storms occur on Titan, which grow from updrafts of up to 20ms−1 and reach altitudes of up to 30 km before dissipating in
5-8 hours [97]. These storms would be comparable to flash flood storms on Earth. However, raindrops on titan would fall at 1.6ms−1, no faster than large snowflakes do on Earth [126] so they would be unlikely to pose any threat to the UAV. Moreover, these storms are predicted to occur very rarely, so the UAV may well not get caught in them.
Also present on Titan are winds, which are mostly zonal (along a latitude) from what we can tell. The
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Cassini orbiter was designed to determine the wind speeds on Titan, however due to a programming error it was unable to listen to the signal coming back from Huygens. Thankfully, an array of radio telescopes on Earth was able to retrieve the data and determine the wind speeds to a reasonable degree of accuracy [76]. Figure 7.1 shows the variation of wind speed as the Huygens probe descended toward the surface [23]. The large dip in wind speed between 65 and 75 km is due to vertical wind shear, also known as turbulence. This could prove dangerous to the UAV, so it should probably avoid this altitude.
7.3 Design Decisions
7.3.1 Heavier or Lighter than Air flight?
Both HTA (Heavier than air) and LTA (Lighter than air) vehicles benefit from the atmospheric conditions present on Titan, and have their own advantages and disadvantages. HTA aircraft by their definition must have some form of powered propulsion to maintain or gain altitude, since they must constantly be moving. This could be disadvantageous, for example if we are particularly interested in one area. On the other hand, they tend to be faster than LTA aircraft, so if it needed to get to a particular area quickly, an HTA aircraft would be better. Also it will clearly increase power requirements over an alternate UAV which doesn’t require constant or any propulsion. Deployment may be an issue with an HTA vehicle; they have not been used on space missions previously, so this would be breaking new ground and would have to be tested extensively. They tend to need to take off with horizontal velocity, and it would be difficult to ensure that if dropped vertically it would successfully stabilise. Because of the need for rigid wings and body, it would require significant storage space on the journey — and the heavier the payload (with power supply, communication devices, sensors, and cameras) is, the larger the wings of the aircraft must be, and so the more space and mass they occupy for the launch and journey.
An LTA aircraft operates on the principle of buoyancy; it has an enclosed volume of gas which is less dense than the surrounding air, and so produces lift. An LTA has significant advantages over an HTA: it does not need constant power to remain buoyant, and so its power requirements can be significantly lower. However, unless it has some form of propulsion it cannot control where it is heading, relying on winds to move it. Even if a form of propulsion is present, owing to the large envelope of light gas which forms an integral part of the airship it cannot move particularly quickly. This is unlikely to be a problem in our situation as we will not need it to be able to travel rapidly. It should also be
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Figure 7.2: Deployment of Vega Lander and Balloon relatively easy to deploy; we have a similar set-up to the Vega missions with a lander and a UAV so it can be released in the same fashion as in Figure 7.2, whereby one of the parachute stages unfurls the balloon when it is being discarded [142]. A large payload does mean the balloon must be bigger
(for a given temperature of gas), however it will not weigh much compared to the payload and can be folded up so that it does not occupy a large volume on the journey.
In summary, it seems that a lighter than air vehicle is a better solution for our requirements due to its ease of deployment, and low power requirements, which will decrease the chance of failure; and its ability to be stationary or travelling at low speeds, which will help with e.g. taking detailed pictures or readings of one specific area.
7.3.2 Balloon Type
A lighter than air vehicle requires an envelope of light gas in order to be buoyant; this can be either a light gas (e.g H or He) or heated air (as is used by a hot air balloon). The latter type is known as a Montgolfi`ere. Clearly, in order to implement the light gas aircraft (similar to those used in the
Vega missions), a canister of that gas must be brought from Earth — this could be quite heavy. In order to determine the mass of gas required, we must make sample calculations; this details the mass of Hydrogen gas required to keep 100 kg afloat at ground level.
− mg = V g(ρair ρH2 ) (7.4)
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∴ m V = − (7.5) ρair ρH2
By the Ideal Gas Law (pv = RT ): Mp ρ = (7.6) H2 RT
−3 −1 −1 − −1 p ≈ 1.5 bar, ρair ≈ 5.3kgm , m = 100kg, T ≈ 93 K, R = 8.314 JK mol , M ≈ 2 × 10 3 kgmol
∴ −3 ρH2 = 0.388kgm (7.7)
−3 So by equation 7.5, V = 20.36m , and using the value of ρH2 , the mass of H2 that would need to be8 kg brought to Titan would be in the region of 8 kg. On balance this is not a particularly significant amount compared to the other items in the payload, although this does not include the mass of the tanks that would be required to store the gas on the journey to Titan. This calculation has been performed for Hydrogen gas, but Helium could also be used although that would require a larger amount of gas; Helium is favoured on Earth because it is inert, however Hydrogen would be suitable on Titan since there is no oxygen present in the atmosphere to react with it. One of the largest benefits of bringing compressed Hydrogen is that the balloon would be very easy to inflate by just letting the gas expand into it. Also since the gas provides all necessary lift, no power is required for altitude control, leaving more for measurements and communication. This is a double edged sword however, since it is not possible to control the altitude at all; if it is necessary to gain or lose height this will not be possible apart from a system of venting gas and dropping ballast to lower or raise the balloon. It is clearly impractical to do this on a long timescale, since only a finite amount of gas and ballast can be brought.
A Montgolfi`ere balloon does not require any gas to be brought from Earth; rather, it would be filled with air from the atmosphere of Titan and heated to provide adequate lift. Filling the balloon would be somewhat harder than with a compressed gas canister; fans might have to be used to blow air in, although tests have been successfully carried out in which the envelope is filled merely by loss of altitude, like a parachute [107]. Some form of power would be required to heat the gas sufficiently to provide heat; however either the heat in or heat out of the balloon could be controlled to provide altitude control, which is the largest benefit over the Hydrogen gas balloon. If a constant heat source is used, a controllable vent can be installed at the top of the balloon to let hot air out and descend.
The balloon will have to be larger than the equivalent Hydrogen gas balloon, since the difference in gas densities will likely be much less. Small leaks or tears in the balloon would not be fatal to the mission, since the balloon operates under the condition of losing hot air anyway; if a Hydrogen filled
133 Chapter 7. UAV Design and Power Michael May balloon developed a leak, the Hydrogen would escape and so the balloon would crash very soon with no way of stabilising at another altitude. In this way, a Montgolfi`ere is more robust than a light gas balloon, and is more likely to have a long lifetime.
Despite the simplicity benefits created by using a Hydrogen balloon, a Montgolfi`ere would be better once set up on Titan since it can control what height it operates at. If a Hydrogen balloon were sent and deployed successfully but at too low or high a height to get good readings, it would be useless and not possible to fix; we cannot have this problem if we use a Montgolfi`ere style UAV. This altitude control, married with the inherent leak durability, means that we shall be using a Montgolfi`ere.
7.3.3 Propulsion
Since a Lighter than air UAV is being used, propulsion is not a necessity; the balloon could simply be left to float around Titan with only the winds to move it. It is true that the prevalent winds on
Titan are zonal, and until recently it was thought that a balloon on Titan would drift due East [128] and be confined to a narrow latitude band, however recent developments suggest that latitudinal movement can be significant, particularly at low altitudes, thanks to meridional winds caused by
Saturn’s gravitational tide, and even a completely passive balloon with no altitude control can access a fairly large fraction of Titan’s surface [214]. However, with no propulsion and the unpredictability of
Titan’s atmosphere it would be incredibly difficult if not impossible to control where a non-propelled balloon could travel. The other major benefit of having a propulsion system would be that the balloon could, if winds were at a low enough speed, be kept stationary to examine a particular area in greater detail. This function may not be particularly useful, however, since the balloon is planned to have a long enough lifespan that it may well pass near enough the same area to perform any further required observations. Added to that, it is not certain that one particular area will be of sufficient interest to require the UAV to slow down or stop to examine it closely, given the UAV will only be moving at wind speed. As shown in Figure 7.1, wind speed tends to decrease with height so if the UAV does need to slow down for some reason, the vent can be opened more and the UAV can drop in height.
The biggest advantage of a propelled UAV is the increased control it has with respect to its movement.
However, it will clearly have a larger power demand than an unpropelled one. The maximum power required for powered flight (in order to overcome aerodynamic drag) is shown in Equation 7.8.
1 P = ρu3 AC (7.8) max 2 max d
134 Chapter 7. UAV Design and Power Michael May
In order to minimise Cd, convention dictates that the major axis length of the hull should be more than three times its maximum diameter. However, even a powered UAV does not need to travel particularly fast at all, merely to have some control over direction and potentially to have enough power to remain stationary in a wind (umax in the equation is the maximum velocity of the UAV relative to wind velocity). Also, for a given volume (the crucial dimension with respect to lift), the less spherical the UAV is, the greater the surface area, and so the greater the rate of heat loss — meaning that despite the propulsion requiring less power, more power might be required overall since the power required for heating the air in the envelope would increase. However, if the balloon is dual-walled, heat loss reduces and increasing the surface area by elongating the balloon may have little effect. Either way, a propelled UAV would use more power than an unpropelled one, leaving less power for other components.
The difficulties introduced by having powered flight are complex, and as a navigation system has been created and outlined in Chapter 8 to reach specific locations by changing altitude and using the wind, propulsion seems unnecessary, so the UAV shall be unpropelled.
7.3.4 Operating Height
Hazards are present on Titan at different altitudes; obviously the UAV must not fly at so low an altitude that it is in danger of crashing into any mountains that are present. It is currently believed [179] that the highest mountains present on Titan are at most 2 km high, so if the UAV stays above this height it is in no danger of crashing. Alternately, if the UAV were fitted with sensors to determine its distance from the terrain, it could operate below this height until getting near high ground, then close the vent and lift off. However, the benefits of operating this low are small unless we are planning to lower tools to the surface, which will not be necessary since we have a lander already on the moon.
Nitrogen is quite soluble in methane, and so any droplets of methane that form will dissolve some nitrogen. Above 14 km, the equilibrium state for this mixture is solid [182], so droplets should freeze.
However, droplets require condensation nuclei to freeze, so clouds of supercooled droplets form if there are few of these nuclei. If the UAV strays into this area, it may act as a nucleus for these droplets to freeze on, and so become a victim of “methane icing”. This refers to large amounts of methane freezing to the balloon and any surrounding instruments and weighing it down. Also, methane contracts upon shrinking, so may put the fabric of the balloon under extra stress. Ultimately, there is no benefit for travelling above 14 km unless the UAV needs to travel faster in the rapid winds at high altitudes. So there are two options: either below or well above 14 km altitude to avoid methane weather (but above
135 Chapter 7. UAV Design and Power Michael May
Figure 7.3: Graph of Yield Stress of Nylon-6 against Temperature
2 km). However, higher quality imaging can be achieved from a lower altitude, so the UAV should operate between 2 and 14 km in altitude (although not necessarily in the whole range).
7.3.5 Materials
The material used in commercial Montgolfi`ere balloons is 60gsm (gm−2) nylon with a coating to reduce porosity [38], however balloons on Earth operate in a very different atmosphere to that on
Titan; in fact around 200 K warmer. The Vega balloons that were sent to Venus were made of 300gsm material [128], but these had to operate in a very hostile environment which is not similar to Titan’s.
The average air temperature at the surface of Titan is 93 K, and this throws up different problems; as shown in Figure 7.3, below ∼ -130◦C or 150 K, Nylon-6 becomes brittle, so is useless to us unless kept above that temperature. This would result in large and undesirable heat loss due to the significant temperature difference, and so require a larger heat source than otherwise. Lamart Inc. and JPL have developed a cryogenic material for use in a Titan balloon [89], which has a density of 94 gsm and a tensile strength of 16400 Nm−1 at 77 K, a laminate of Mylar film glued onto a polyester fabric. This material has been tested at 93 K for several hours under conditions found on Titan successfully and without cracking or leaking, and seems very suited to the task, being light and strong at cryogenic temperatures, so this shall be used
7.4 Power Decisions
A crucial decision to be made is where the power required to heat the balloon and operate instrumen- tation and communication systems is to come from; options are considered below.
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7.4.1 Batteries
Batteries could be used to power the UAV, of which there are two types; primary, which cannot be recharged, and secondary, which can. By definition, if primary batteries are to be used, the UAV will have a finite lifespan, which is likely to be quite short; the longer we want the UAV to be operational, the more batteries we need, and hence the heavier the UAV payload would be. For example, the Vega balloons were powered by 1 kg Lithium batteries with 250 Wh capacity, and only lasted 46 hours [142].
Our balloon would need to operate for much longer than this, and if batteries were used to power the heating system, they would deplete very quickly indeed, so a very large amount would be required for any extended lifetime, weighing down the balloon. So primary batteries are not a viable option for powering the balloon. Secondary batteries are rechargeable, so cannot operate as the principal power source. However, they could be kept as backup if the principal power source failed, or they could be used at high-drain times and recharged during low-drain periods. If the principal power source did fail, the batteries would only provide a buffer time before running out of power, so in essence just lengthening the time for the principal source to start working again; merely delaying the demise of the balloon. If backup is necessary, it would be more fail-safe if a backup principal power source is installed, since the balloon can just switch to that and continue as normal. Secondly, a situation which is so power intensive that the principal power source cannot cope is unlikely to arise, unless the heating of the UAV is variable and run by electricity. In summary, batteries will not be useful on the
UAV.
7.4.2 Solar Power
Solar power is used by many satellites orbiting Earth, and even the Mars rovers currently in operation.
However, Saturn is significantly farther from the Sun than either Earth or Mars, so the intensity (I) of the sunlight, and so its power, will decrease even greater, due to its proportionality with the inverse square of distance. 1 I α (7.9) d2 ( ) 2 dEarth ∴ ISaturn = IEarth × (7.10) dSaturn ( ) 1AU 2 ∴ I = I × (7.11) Saturn Earth 9.539AU
∴ ISaturn = 0.0110 IEarth (7.12)
137 Chapter 7. UAV Design and Power Michael May
−2 −2 ∴ ISaturn = 0.0110 × 1370Wm ≈ 15Wm (7.13)
So we can see that only 15Wm−2 reaches the orbit of Saturn. However, photovoltaic cells (which are used to convert sunlight into electricity) are not very efficient, generally around 10% efficient.
The most efficient solar cells ever produced are 40% efficient [220], but even at this efficiency, only
∼ 6Wm−2 would be produced. The thick atmosphere of Titan would reduce this even more, so that huge amounts of solar cells would be required to power the balloon, which would weigh it down greatly.
Clearly solar power is not a viable method of powering the UAV.
7.4.3 RTGs
Radioisotope Thermoelectric Generators (RTGs) are electrical generators used frequently on remote lighthouses and spacecraft going to the outer Solar System and beyond. They operate by turning the heat produced by radioactive decay of an isotope (commonly 238Pu) into electricity, normally by use of a thermocouple. Due to their nature they cannot be stopped or started at will, so by the time they reach Titan their activity could have decayed to the point that they cannot provide sufficient power.
However 238Pu has a half-life of 87.7 years, so even if the flight takes 7 years it will still be producing almost 95% of its original power (see Equation 7.14). For example, the RTGs on Pioneer 10 operated without problems for three decades, at which point the radio signal was too weak to detect [39].
− t − Current Activity t 7 = 2 1/2 = 2 87.7 = 0.946 (7.14) Initial Activity
The power density of 238Pu is also very impressive, producing about 0.5 W per gram. The thermocou- ple technology is not very efficient, returning rates of under 10%, however it is reliable because there are no moving parts in it at all. Any ”waste” heat can be in fact used to heat the envelope of air, increasing efficiency to near 100%. An RTG using a Stirling engine can have much greater efficiency, over 20%; however these are still under development and so reliability cannot be guaranteed thanks to its moving parts. These SRGs could potentially be used in the future. The two main types of
RTG used in recent years are the GPHS-RTG (General Purpose Heat Source RTG) and the MMRTG
(Multi-Mission RTG); the GPHS-RTG uses parts which are no longer in production, so the MMRTG would have to be used instead. It produces 2 kW of thermal power and 120 W of electrical power initially, and weighs 43kg [39]. The MMRTG is designed to be able to operate both in the vacuum of space and atmospheres, so would be perfect for our needs. If the power requirements of the UAV exceed the amount that can be provided by a single MMRTG, extras can be used in series to boost the
138 Chapter 7. UAV Design and Power Michael May power output to ensure a reliable supply of power to all components since the MMRTG is modular.
Due to the amount of radioactive material contained in these devices, it is important to ensure that if anything goes wrong during takeoff they do not scatter throughout the atmosphere, since the
Plutonium is very dangerous, and could kill animals or contaminate water supplies. The MMRTG, like previous generations of RTGs, is designed to withstand re-entry into the Earth’s atmosphere and impact while containing the Plutonium. This happened successfully in 1968 when a weather satellite failed to launch, and in 1970 when the Apollo 13 lander was jettisoned in the South Pacific. In both of these cases, no plutonium escaped to the environment [39]. In summary, MMRTGs seem to be a very good choice for the UAV.
7.4.4 Other options
As stated above, there is wind on Titan, however generation of electricity from this on a vehicle which is moving with the wind is clearly not feasible.
Research and Development at Los Alamos has started to develop a potentially useful structure made from carbon nanotubes which can generate electricity directly from radiation, without use of heat, with efficiencies of up to 99% possible [173]. However this is in the very early stages of development and so will not be available for use for several years at least.
Power redundancy should be considered, and is employed on the orbiter. However, extra and unneeded power sources would provide no benefit unless the primary source failed; in fact they would weigh the
UAV down, and indeed increase its heat power requirement so that it would be relying on both the primary and the backup source to be working in order to fly! This clearly defeats the point of redundancy. Besides, RTGs are established technology and known to be very reliable. So for these reasons, redundancy shall not be used on the UAV.
7.4.5 RHUs
Radioisotope Heater Units (RHUs) are similar to small RTGs, but do not use the thermal energy for electricity generation, merely heating. If the heat output from the RTGs is not sufficient to heat the air envelope, RHUs could be included to supplement it and increase heat output. RHUs come in various sizes, but the one usually used by NASA is 40 g in mass including shielding and produces 1
W of heat. Again, safety is clearly very important since radioactive materials are being used. The US
139 Chapter 7. UAV Design and Power Michael May
Department of Energy has performed a set of rigorous safety tests more severe than expected to be encountered in the real world, and no radioactive material was released [50]. So if extra heat power is required, RHUs are a good and safe option.
7.5 Balloon Thermodynamics
In order to determine the required buoyancy of the balloon, the total mass of what is to be lifted must be determined. The MMRTG which is to be used to power the UAV weighs 43 kg [39], and the camera weighs approximately 15 kg. Coupled with the communications and processing software that will also need to be carried on board, as well as the weight of the material, we should budget for a payload of around 100 kg. It is better to overestimate the payload, since then the valve can merely be opened further to reduce lift, than to underestimate it, in which case the UAV would not be able to fly properly. It may well be possible to provide enough heat power for lift just from the waste heat of the
MMRTG, since it constantly produces 2 kW of heat energy, a significant amount. CFD has suggested that in order to capture a high enough proportion of this waste heat for buoyancy generation, the
RTG must be located inside the envelope, not just close beneath it [89]. The calculations needed are non-trivial, however as shown in chapter 8 2 kW is sufficient to heat a 10 m diameter balloon enough to keep 200 kg aloft at 10 km. Buoyancy is proportional to the cube of the diameter of the balloon, and radiative heat loss (which is dominant) is proportional to the square, so the size of the balloon can be increased if higher altitudes are unreachable with a 10 m diameter balloon. One negative point about just using the RTG for heat is that the rate of climb is not as high as it would be with extra heat power; however there is no need for a high climb rate, so this is not an issue. In summary, the
MMRTG will be the only heat source used on the RTG.
7.6 Conclusion
In this chapter, I have outlined the benefits of using a UAV on Titan, considered how it should be designed and implemented, and determined how best to power it. I have explained why I think an unpropelled Montgolfi`ere style envelope should be used, and that the MMRTG is the best solution for heating it and fulfilling the power requirements of the instrumentation and communication sys- tems which are defined elsewhere. This is a fairly simple yet long-lasting solution, which has some redundancy against leaks, and could operate for years in the lower atmosphere of Titan, collecting important readings and mapping the surface in intricate detail.
140 CHAPTER 8 - Liam Donovan
UAV Control
8.1 Introduction
Earlier in this report it has been demonstrated that a lighter than air UAV in the form of a montgolfiere or hot air balloon would be a desirable component of a mission to Titan because of its capability to gather valuable and unique data by floating in the thin strip of atmosphere below the hydrocarbon haze and also because of the favourable buoyancy and heat transfer conditions presented by this alien world. Because of the low gravity on Titan, its dense nitrogen-rich atmosphere and its low atmospheric temperature, it has been estimated that such a hot air balloon would require approximately 100 times less power to keep it afloat than an equivalent size and weight of balloon on the Earth[106].
Furthermore the existance of winds of variable direction in the lower reaches of Titan’s atmosphere raise the possibility of controlled, semi-autonomous wind based navigation.[80] This section of the report is concerned with exploring the mechanics and thermodynamics of such a balloon in detail, developing a mathematical model and simulation of the system and designing a controller to make use of the winds to navigate around Titan on demand.
8.1.1 Nomenclature
x Altitude P Pressure ρ Density V Volume T Temperature m mass R Universal gas constant g Gravity cp Specific heat A Cross-sectional Area CD Drag Coefficient Q Heat flow
Table 8.1: Variables
141 Chapter 8. UAV Control Liam Donovan
ss Steady-state 0 Atmospheric I Internal gas
Table 8.2: Subscripts
8.2 Hot Air Balloon Dynamics
8.2.1 Atmospheric properties
Is the atmosphere an ideal gas?
The Titanic atmosphere is around 95% Nitrogen at the surface, with the rest being dominated by
Methane[80]. To simplify things it will be approximated to 100% Nitrogen leaving the question: Do the ideal gas laws accurately describe the behaviour of Nitrogen at the temperature and pressure of
P v relevance here? A modified form of the ideal gas law states: RT = Z where Z = f(Pr) where Pr is P the reduced pressure or [186]. At x = 10km, Pr = 0.0265. From figure(8.1) it can be seen that Pcritical at reduced pressures as low as this Z can easily be approximated to 1, meaning the ideal gas law is valid.
T , P , ρ Profiles
The atmospheric properties of Titan were measured by the Huygens probe during its descent and from the data it collected charts of the atmospheric density and pressure can be drawn up. An approximate temperature profile can be deduced from the ideal gas law. Clearly these paramaters are only approximations to the actual atmospheric conditions which may vary significantly with the local weather and other factors like the amount of sunlight incident on the atmosphere, either direct or reflected off Saturn. Figure(8.2)[80] shows the data for the lowest 25km of the atmosphere. As these three properties are important in understanding and modelling a hot air balloon on Titan a mathematical expression relating them to altitude is necesary. Although the profiles are roughly exponential in nature, if the balloon is confined to a reasonably small height range, for example x = 10km ± 5km, this would allow the expressions to be approximated as linearly dependant upon
142 Chapter 8. UAV Control Liam Donovan altitude like so:
ρ0 = 5.05 − 0.00018x (8.1)
P0 = 142000 − 5.2x (8.2)
P0 T0 = (8.3) Rρ0
8.2.2 Balloon Equations of Motion
The purpose of this section of the report is to derive the equations governing the vertical motion of a hot air balloon using the classical laws of mechanics. The central principles used will be Newton’s laws of motion and Archimedes’ principle of bouyancy.
The traditional design for a hot air balloon involves an envelope filled with heated gas that is open to the atmosphere at the base, the gas inside held at atmospheric pressure and the volume of the envelope held constant. The pressure of the gas inside the balloon is assumed to be uniform throughout. The net vertical force on the stationary balloon is the combined weight of the balloon and the gas inside of it, subtracted from the lift generated due to Archimedes’ principle, which states that the upward force on an object immersed in a fluid is equal to the weight of the fluid which it displaces. If the balloon is moving there is another force due to drag caused by the viscosity of the atmosphere. Expressing this mathematically: 1 F orce = (ρ V − M )g − ρ AC x˙ 2 0 total 2 0 D
Using Newton’s law this can be converted to:
1 M x¨ = (ρ V − M )g − ρ AC x˙ 2 total 0 total 2 0 D
By expressing Mtotal as the sum of the mass of the gas inside the balloon and the mass of the payload,
Mp + ρI V the equation can be simplified to:
1 (M + ρ V )¨x = (ρ − ρ )gV − ρ AC x˙ 2 − M g (8.4) p I 0 I 2 0 D p
By combining the ideal gas law with the earlier assumptions regarding the internal pressure of the
143 Chapter 8. UAV Control Liam Donovan
Figure 8.1: Ideal Gas Law
Figure 8.2: Atmospheric Density and Pressure Profiles
144 Chapter 8. UAV Control Liam Donovan
gas, the internal gas density ρI can be expressed as below:
P0 ρI = (8.5) RTI
As the balloon accelerates it drags with it a quantity of the surrounding atmospheric gas such that the apparent accelerating mass of the balloon can be approximated to double[65]. To account for this the Mtotal term on the left hand side of the equation above is multiplied by a factor of 2.
8.2.3 Linearisation
The first step towards dealing with the problem of controlling the UAV is to model how a simplified balloon with its envelope gas held at a constant temperature reacts to the atmospheric conditions assumed in section(8.2.1). The easiest way to do this is to obtain the transfer function in the laplace domain relating the altitude x to the internal temperature of the gas TI . Laplace transforms can only be taken of linear systems and it can be seen, if equation(8.5) is substituted into equation(8.4), that the relationship between altitude and temperature is non-linear in this case. The system must therefore be linearised before the transfer function can be obtained.
To start with if all the variables in the system, altitude, internal temperature, atmospheric pressure etc are expressed in relation to their steady state values then the constant term Mpg can be eliminated.
P0V Stepping through the equation, the first term on the left hand side, (Mp + )¨x, is clearly non-linear. RTI However if it is assumed that the changes in the mass of the gas are significantly smaller than the constant mass of the payload, the mass term can be approximated to a constant m.
It was shown in section(8.2.1) that the next term, ρ0gV can be approximated to a term linearly
∂ρ0 dependant upon x; i.e kxgv where k is ∂x at ρ0 = ρss.
The next term, P0 gV is somewhat trickier. Firstly a Taylor expansion has to be done on 1 : RTI TI
− 1 ≈ 1 1 + TI ( 2 ) TI Tss Tss
As was shown in section(8.2.1) the atmospheric pressure P0 can be approximated as linearly dependant upon x, however the only way to linearise this term is to approximate it to a constant, Pss.
1 2 2 Finally the damping term 2 ρ0ACDx˙ . Taking the Taylor expansion ofx ˙ gives 2x ˙. In this case ρI can only be approximated to a constant value of ρss.
145 Chapter 8. UAV Control Liam Donovan
Putting all this together yields the linearised equation:
′ mx¨ = (k TI − kx)gV − cx˙
′ Pss Where k = 2 ; k is as above and c = ρssACD. Assuming zero initial conditions and taking laplace RTss transforms gives the transfer function of the system:
X(s) gV k′ = 2 (8.6) TI (s) ms + cs + gvk
8.2.4 Numerical Parameters
−1 ◦ ρss 3.25kgm Pss 0.9bar Tss 105.65 K −2 Mp 200kg g 1.37ms CD 0.075 r 5m A 78.5m2 V 524m3
Table 8.3: Physical Parameters
k 0.00018 k′ 0.02715 m 1703 c 19.1
Table 8.4: Linear Model Paramaters
The tables above show the values of the parameters that shall be used to model the balloon. The steady state altitude was chosen for reasons given in section(8.2.1) as 10km and the atmospheric temperature, pressure and density were calculated using the linearised equations onbtained from the
Huygens data also given in section(8.2.1). The value of g is obviously a property of Titan itself and the altitude is not great enough to affect it for the purpose of modelling the balloon. The values of r and Mp were chosen arbitrarily as potentially realistic values.
The value of the drag coefficient for a smooth sphere varies between 0.05 and 0.1 depending on the
Reynolds number of the fluid. At this stage it will be approximated as a constant at the average value of 0.075. Given the scale of some of the other approximations made the error introduced by this should not be too significant, however variations of the drag coefficient with fluid velocity and
Reynolds number may potentially have a significant effect and should be researched further.
The maximum change in the mass of the balloon due to atmospheric pressure and internal temperature
146 Chapter 8. UAV Control Liam Donovan changes is:
∆Mmax = Mss − Mmin (8.7)
= 688kg (8.8)
Where Mmin is the minimum mass of the balloon at the extreme highest temperature and lowest pressure. This results in a maximum change in the total mass of the balloon of ±40% which could potentially be a significant source of error in the linear model.
8.3 Modelling
In the following section of the report the equations derived in the previous section will be used to create models of the balloon which will be tested and compared to determine their accuracy.
8.3.1 Linear Model
To create the linear model the system has been represented in block diagram form in Simulink
(figure(8.3)). In order to further develop the model and use it as the basis for designing a con-
19 .49 1 1 Ti -K- gvk' s s Integrator Integrator 1 x 1/m
-K-
c
-K- gvk
Figure 8.3: Linear Model Block Diagram troller, it is first neccesary to be confident that it accurately represents the real system in question and that all the approximations and simplifications made when linearising the equation of motion
147 Chapter 8. UAV Control Liam Donovan have not introduced serious errors which compromise the model. To this end a non-linear model of the system was also constructed in block diagram form in Simulink.
8.3.2 Non-Linear Model
200 274 524 [V] Mr V Mrg [M] [C] Velocity [P0] Mass Mass_total Drag 2 1 1 Pressure [U] [X] s s 297 Upthrust2 Acceleration Velocity 2 Altitude 2 Altitude [W] R [W] Force 2 [Ti ] Air Weight 2 Air Weight Air Weight 1 [M] mapp 1.37 Temperature RhoI Mass total Main Loop g
[V] |u| Velocity 1 Abs [C] (142000 -5.2*u) [P0] 3.927 Drag 1 Atmospheric Pressure P0 CdA/2 [X] 297 [T 0] Drag Altitude 1 R1 T 0 [Rho 0] (5.05 -0.00018 *u) [Rho 0] Atmospheric Density 1 Atmospheric Density Rho 0 Atmospheric model Force Calculations Atmospheric Temperature 717 .88
gV [U] [Ti ] [Rho 0] Upthrust 1 Upthrust Step Ti Atmospheric Density 2
Figure 8.4: Non-Linear Model Block Diagram
This model (figure(8.4)) calculates all variables in absolute form as opposed to them being referenced to a steady state level as in the linear model and it is a representation of equation(8.4). The only significant simplifications are the linear approximations for the atmospheric temperature, pressure and density from section(8.2.1) and the approximation of the drag coefficient to a constant value independant of Reynolds number.
8.3.3 Comparison of Models
Both models are to be compared in open-loop configuration in both the time domain (using their step responses, see figure(8.5)) and the frequency domain (using Nyquist diagrams, see figure(8.6)). For
figure(8.5) the non-linear data has been normalised so that it is expressed referenced to the steady state value of x. Clearly the models do not agree. The magnitude of the non-linear system’s step response is an order of magnitude larger than that of the linear system and the frequency response shows that at low frequencies the phase lag and magnitude of the non-linear response are both considerably bigger.
This gives rise to the much larger step response with the non-linear system.
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Figure 8.5: Open Loop Step Responses
Figure 8.6: Frequency Response of Non-Linear and Linear Systems
149 Chapter 8. UAV Control Liam Donovan
The obvious question is what could be causing these serious discrepancies? If the internal gas density of the balloon (figure(8.7) is measured it can be seen that both systems undergo an initial step change due to the temperature input. Then, as this change in density causes a change in the weight and therefore the net force on the balloon, in both systems the balloon begins to climb. The difference between the two systems is that the atmospheric pressure in the non-linear model is linearly dependant upon x and as the balloon gains altitude the pressure reduces quite considerably, causing a change in the internal density of the balloon and a significant reduction in the force, giving rise to the larger change in altitude. In the linear model the pressure is assumed to be constant and the downwards force does not change.
Figure 8.7: The Modelled Internal Gas Density of Both Systems
Another notable difference in the models can be seen if a negative temperature step is input to the systems. The linear system is symetrical about the steady state operating point and produces exactly the same change in altitude just in the opposite direction. The non-linear system shows the behaviour displayed in figure(8.8) (once again the data has been normalised and the magnitudes are displayed).
It can be seen that the negative step response is significantly larger than the positive. This can be explained by the fact that the mass of the balloon increases as it descends because of the increased atmospheric pressure and lower internal temperature. This leads to a decrease in the decceleration of the balloon as it is slowing down, causing it to take longer to come to a steady state position and allowing it to descend further in that time. The linear model does not show this effect because the
150 Chapter 8. UAV Control Liam Donovan mass is assumed to be constant.
Figure 8.8: The Magnitude of Positive and Negative Step Responses of Non-Linear Model
8.4 Thermodynamics
The internal energy if the balloon is governed by the thermodynamic relation:
E = mcpTI
Differentiating this gives an expression for the heat flow into the balloon:
∂T Q = mc I +mc ˙ T (8.9) p ∂t p m
The final term in equation(8.9) is actually the heat flowing into the balloon due to the mass flow rate m˙ through the mouth where Tm is the temperature of that mass, either the atmospheric temperature
T0 if the mass flow is positive into the balloon or the internal temperature TI if the mass flow is negative and out of the balloon. It will be represented as Qm. To be clear the mass flow here is caused by changes in the internal density of the balloon expelling or drawing air into the mouth to maintain a constant volume, it is not being forced by any external means.
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The net heat flow into the balloon can be seperated into three distinct components:
Q = Qb − Qc − Qm
Where Qb is the heat input from a heat source, for example a propane burner, Qc is the heat rejected to the atmosphere through any cooling mechanisms that apply, and Qm is the heat lost due to mass flowing out of the envelope as described above.
Cooling
A significant amount of heat is lost to the atmosphere through infra-red radiation and convection.
When the balloon is stationary it is reasonable to say that the dominant mechanism for heat loss is radiation and convection has only a negligable effect[65]. Given that the maximum velocity the balloon can be expected to experience is fairly low, the approximation will be made that all direct heat losses to the atmosphere can be modelled as radiative emmission, however further work to justify this may be required.
Heat transfer due to the emmission of infra-red radiation can be described by the Stefan-Boltzmann law:
Q = ϵσ(T 4)
Where σ is the Stefan-Boltzmann constant multiplied by the surface area of the balloon, and T is the temperaure of the surface, which, assuming the temperature of the balloon skin is equal to the temperature of the internal gas, is TI . ϵ is the emmisivity of the surface, it is a property of the material and is a number from 0 to 1 representing how perfect a radiator the material is. When considering the total radiated heat from the balloon it is neccesary to include the heat radiated back onto the balloon surface by the atmosphere, meaning the total cooling can be approximated by:
4 − 4 Qc = α(TI T0 ) (8.10)
Where α ≈ 0.000035
8.4.1 Thermodynamic Model
Figure(8.9) below shows how the thermodynamic equations can be modelled in Simulink, ready to be added to the model of the rest of the system in figure(8.4). The blocks in the top left are a
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straightforward representation of equation(8.10) with output Qc, the heat lost to radiative cooling. The blocks in the top right calculate the mass of gas in the envelope using the ideal gas law and information from figure(8.4) regarding the atmospheric pressure. The derivative of the mass is taken and passed to the set of blocks in the bottom left corner which calculate the heat loss due to mass
flow, Qm. The switch calculates the temperature of the flowing mass Tm by passing through the value of TI if the mass flow is positive out of the balloon or T0 if it is negative. The blocks in the bottom right sum all the heats to calculate the net heat, Q. This is then divided by mcp and integrated to give the internal temperature of the balloon envelope TI .
Radiative Cooling [Ti ] 524 du /dt [Mdot ] TI uv V Derivative Mass_flow [P0] 4 Math
Function Pressure [Ma] -K- [Qc] constant1 297 Mass_air
[T 0] a Qc1 R v Cooling [Ti ] [W] To u 1.37 Temperature Weight Air Weight 4 Math Mass g Function 1 Mass Calculations constant
Heat Balance [Qb] [Mdot ] [T 0] Qb To 1 Mass flow [Qc] [Mdot ] [Qm ] Qc massflow Tm Qm 1 1039 1 [Ti ] [Qm] xos Cp [Ti ] 1039 [Ma] Temp Ti heat flow Qm [T 0] Ti 1 Heat in Cp1 mass To 2 Heat Flow Through Mouth Tdot
Figure 8.9: Thermodynamic Model in Simulink
8.5 Titanic ballooning
On Earth the altitude of hot air balloons is simply controlled by varying the amount of heat input given by a propane burner which in this model would be represented by Qb. On Titan however, the atmosphere is Nitrogen and neither propane nor any other practical substance can burn. Even if it could, transporting compressed flammable gas accross the solar system to provide lift for a balloon is not a particularly desirable idea, and the lifetime of the balloon would be limited by the supply of gas.
For this mission the most practical heat source is the waste heat from an RTG, capable of producing around 2kW. The problem with this approach is that, on the time scales relevant here at least, the
153 Chapter 8. UAV Control Liam Donovan heat output from an RTG is constant through time and cannot be varied in the same way that a propane burner on earth can be turned on and off. It is therefore neccesary to develop alternative methods of controlling the heat flowing into the balloon.
8.5.1 A More Refined Atmospheric Model
The linear approximations to the atmospheric density and pressure profiles put forward in section(8.2.1) were useful when attempting to produce a linear model of the system, however an exponential ap- proximation would give a higher degree of accuracy and would also be valid over a larger altitude range, allowing suitably accurate modelling of the balloon descending to the surface or ascending to higher altitudes. The following functions more accurately approximate the measured data between the surface of Titan and around 50km altitude:
(−5x×10−5) ρ0 = 5.540e (8.11)
(−6x×10−5) P0 = 153730e (8.12)
The atmospheric temperature is calculated using the ideal gas law as before. As an aside, figure(8.10) shows what happens when the old atmospheric model in figure(8.4) is replaced with this one. When the simulation is run with the temperature held constant at a temperature slightly higher than what is assumed to be the steady-state temperature, the balloon climbs quickly to an altitude higher than
23km. With the temperature held slightly below steady-state the balloon crashes to the surface. A stable equilibrium between the two altitudes is impossible. This is because as the balloon ascends both the atmospheric pressure and density around it decrease, causing both the upthrust and down- force on the balloon to decrease. With the profiles as they are and the internal temperature constant, until the balloon reaches the stable altitude at around 24km, the upthrust increases faster than the down force as it ascends, giving a positive feedback effect which doesn’t allow the altitude to stabilise.
Similarly during descent the down-force increases faster than the upthrust and the positive feedback effect forces the balloon to crash. When the thermodynamics of the system are taken into account as in figure(8.9), the internal temperature is affected by many factors including for example the radiative cooling effect which is related to the fourth power of the external temperature, meaning the model of the balloon being held at constant temperature is not a realistic predictor of the behaviour of the whole system. This unstable relationship between the internal temperature and the altitude should not affect the stability of the whole system.
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Figure 8.10: A Demonstration of the Unstable Relationship between TI and Altitude
8.5.2 Valving
One of the most obvious ways of controlling heat flow into the balloon is to open a valve at the top of the balloon to allow hot air to escape. This approach is used in terrestrial ballooning to rapidly lower the lift force if a fast descent is needed or if the balloon gas has been heated too strongly and the upward ascent needs to be slowed. On Titan the idea would be that the heat from the RTG would be enough to raise the temperature of the gas when the valve is closed, causing the balloon to rise to a theoretical cieling altitude if left alone. When the balloon is required to descend the valve is opened allowing a flow of hot gas to escape from the top of the balloon. Because the volume of the balloon must remain constant an equal volume of gas will then be drawn in through the mouth of the balloon. This gas will be atmospheric gas, both cooler and heavier than the gas vented from the top of the balloon, causing the density of the internal gas to rise and its temperature to fall, making the balloon heavier and thus descend. The valve could be partially opened to allow for altitude-keeping manouevers.
Modelling the Valve
Figure(8.11) below (designed to be added to figures(8.9) and (8.4)) shows how the vent can be modelled in Simulink. The input signal vent, determined by some control algorithm which may or may not
155 Chapter 8. UAV Control Liam Donovan involve feedback, is multiplied by gain k to produce the desired mass flow rate through the valve. The saturation block following the gain is there to prevent the mass flow from going negative (as a mass
flow in through the upper vent is impossible) and to impose an upper limit on the flow. This upper limit may well be a complex function of the thermodynamic properties of the gas and the atmosphere, however in this analysis it will be assumed to depend solely upon the maximum size of the aperture when the vent is fully open, which is a constant set during the manufacture of the balloon. This mass flow rate is then converted to a heat flow, Qvent representing the heat being lost by the hot gas being vented. It is also scaled by a factor of ρI to represent the mass flow in through the mouth of ρ0 the balloon to compensate for the loss through the vent keeping the volume of the balloon constant.
This is then added to the mass that would be flowing through the mouth anyway due to changing altitude or temperature,m ˙ , calculated in the same way as in figure(8.9). This mass flow rate is then sent to a switching block similar to the one in figure(8.9) which sets the temperature of the mass (Tm) dependant upon the direction of flow. Finally the heat content of this mass is calculated as Qmouth, the heat flow through the mouth.
[Ti ]
Ti 1039 [Qvent ]
Cp Qvent
[Vent] -K- Qv
Vent k Saturation [Mdotmouth ]
[RhoI ] Mass flow through mouth Internal Density mouthmflow [Rho 0] Mass flow [Mdot ] Atmospheric Density mass flow [Tin ] [Qmouth ]
Temperature Qmouth
1039 Qmouth 1 Cp1
Figure 8.11: Modelling the Valve in Simulink
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8.5.3 Building a Controller
By taking the valve signal as the input to the system and the altitude as the output the loop can be closed and a controller designed to force the balloon to track an input signal. Consisting primarily of a traditional P+D controller, the saturation block discussed in section(8.5.2) is also included as a design parameter (figure(8.12)). Because both the system and the control method are non-linear the controller cannot be optimized analytically and so the parameters must be determined through trial and error. Figure(8.13) shows how the system responds to step changes in altitude with the gain k set
−1 at 0.001, the derivative step time Td set to 0 and the saturation block limiting the flow to 1kgs .
-K- du /dt [R] Td Derivative 0.001 In 1 Out1 [X] Control Input sum Error Signal k Saturation Altitude
Balloon System Model
Figure 8.12: Modelling the Control System in Simulink
The first thing of note is how slow the response is, particularly during ascension, taking around 50,000 seconds or almost 6 Earth days to ascend the 5km in this test. The only way to speed up the balloon’s ascent is to increase the heat input by the RTG, as it can be seen that the valve has saturated at 0
(fully closed). In descent the balloon is much faster, taking about a tenth of the time to descend the
5km than to ascend it. This could potentially be made faster by increasing the maximum mass flow rate imposed by the saturation block, as it can be seen that the vent is fully open during the main part of the descent. In both tests the balloon oscillates quite significantly about its resting altitude.
This is because the controller is attempting to stabilise the balloon by sending a negative signal to the vent, which is not allowed by the saturation block. If some derivative action is added to the controller by setting Td to 5000, see figure(8.14), the oscillations seem to dissapear from the altitude graph. Looking at the vent however there is still present a large and unstable oscillation during the positive step response which is undesirable as it could lead to instabilities, and if it happened on the real balloon it would degrade the life of the actuator. Looking at the oscillations before the derivative action was introduced, they have an angular frequency of around 6×10−3rads−1. By low-pass filtering the error signal using a filter with a cutoff frequency at 2 × 10−4rads−1 such that attenuation at the oscillation frequency is large without significantly affecting the response, the behaviour in figure(8.15)
157 Chapter 8. UAV Control Liam Donovan is shown. The filter has transfer function:
1 5000jω + 1
Although this does appear to eliminate the oscillation in the vent signal, it also introduces a quite significant overshoot, particularly in the descent test. By reintroducing derivative action with Td = 5000 into the controller, the overshoot can be much reduced, and an acceptable oscillation-free response obtained (figure(8.16)). Although more derivative action would result in a lower overshoot, it would also result in a significantly slower settling time. The value of 5000 was decided upon as an arbitrarily judged optimum.
8.6 Testing the Controller
8.6.1 Sinusoidal Demand
Figures (8.17 and 8.18) show the results of applying a sinusoidal demand signal to the system. It can be seen that as long as the valve is kept from saturating as in the first test, the balloon follows the demand closely with only a small time lag and a slight error at the peaks and troughs of the signal.
If the amplitude of the demand is increased as in the second test, the valve saturates at 0 and the balloon is unable to heat up and ascend fast enough to keep up with the demand. In fact the highest upward velocity the balloon can achieve with a heat input of 2kW is 0.1ms−1, effectively the slew rate of the system. By increasing the heat input by 1kW, the upward slew rate doubles to 0.2ms−1.
These figures need to be taken into account when considering the balloon’s ability to avoid obstacles; for example if it is cruising at an altitude of around 1km, being blown by horizontal winds of 0.5ms−1 towards a mountain of height 2km, the maximum angle of ascension is 11.3◦ with 2kW of heat input or 21.8◦ with 3kW. That means that the balloon needs to start ascending either 5km or 2.5km away from the mountain in order to avoid a collision, demonstrating that great care must be taken when cruising at low altitudes.
8.6.2 Entry Scenario
The test in figure(8.17) shows that the controller can handle the relatively small and slow changes in altitude which will be routine once the balloon has been stabilised in the desired altitude range, but how does the system react to extraordinary demands such as those experienced during entry to the
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Figure 8.13: Closed Loop Step Responses
Figure 8.14: Closed Loop Step Response with Derivative Action
Figure 8.15: Closed Loop Step Responses with Low-Pass Filter
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Figure 8.16: Closed Loop Step Responses with Filter and Derivative Action
Figure 8.17: Closed Loop System Response
Figure 8.18: Comparison of Response to Sinusoidal Demand with Heat Inputs of 2kW and 3kW
160 Chapter 8. UAV Control Liam Donovan atmosphere? In the following test (figure(8.19))it has been assumed that the balloon capsule has been released into the atmosphere, being slowed by parachutes until finally the balloon envelope is released and inflated at 40km altitude. The initial conditions are therefore assumed to be an altitude of 40km, a substantial negative velocity and an internal gas temperature equal to the atmospheric temperature.
The controller demand is set to a constant level of 10km. The results of the test (figure(8.19)) show that the controller is perfectly capable of stabilising the balloon at the correct altitude.
8.6.3 Landing
One particular manouver which it may be desirable for the balloon to perform is a landing on the surface. To complete a succesful landing the balloon must come to rest at a reasonably low velocity in order not to damage any on-board equipment, it must remain stationary on the surface for as long as is required, and it must also remain inflated and ready to take off as soon as required. Tests were carried out in Simulink on the model using two seperate demand signals; the first a step from 10000m to 0m, the second a ramp over the same range but with a gradient of −0.5ms−1. The results (figure(8.20)) show that neither signal produces a satisfactory response from the system. When given a step demand the balloon falls fast towards the surface, and because the system is somewhat underdamped and suffers an overshoot during its step response, the controller does not slow the balloon sufficiently before it impacts the surface. Because of the steady state error suffered by the system the balloon is then lifted off from the surface to come to rest at an altitude of 150m. The ramp demand brings the balloon towards the surface more slowly, and the balloon begins to slow even more as it approaches the surface which is good, however the steady-state error is still a problem and in fact the balloon never actually touches the surface during the test. The classical way of eliminating steady-state error is to add integral action to the controller, however because the response of this particular system is so slow and many of the error signals are large, integral wind up is a significant problem which severely accentuates the overshoot in the response. It is impossible to add it to the controller using an integral time long enough to have a satisfactory effect on the landing manouver without introducing unpredictable and undesirable behaviour during higher-altitude step responses. The solution to this is to switch on the integral action only when the balloon enters the lowest 100m of the atmosphere approaching the surface, switching it off again and resetting the integrator when it leaves this region.
That leaves the system unnaffected when going about routine changes high in the atmosphere, and also allows the balloon to land on the surface satisfactorily. Figure(8.21) shows a test landing and take-off manouver. It is important to notice that ramp demand signals must be used in order to lower
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Figure 8.19: Potential Entry Scenario
Figure 8.20: The Response of the System to Step and Ramp Demands at 0m Altitude
162 Chapter 8. UAV Control Liam Donovan the approach velocity.
8.6.4 Disturbance Rejection
During its voyage through the Titanic atmosphere the balloon will be subject to a variety of un- predictable disturbances and it is essential that these do not degrade the ability of the controller to maintain an altitude or cause any instabilities in the system which may endanger the UAV. One of the most obvious and predictable disturbances is the degradation of the heat input from the RTG over time as radioactive decay reduces its power output. The effect of this kind of disturbance on the upward slew rate of the system was discussed in section(8.6.1). Another form of disturbance was brought up in chapter and involves the accruition of frozen mass on the balloon when it is above an altitude of 14km. The potential effect of this can be seen in figure(8.22). The increase of mass has been modelled by assuming the build up of frozen material is a linear function of time which continues whenever the balloon is above the threshold altitude. Although this is a very crude model and is almost certainly an exaggeration of the effect, its purpose is to show that unpredictable increases in the mass of the balloon can have a significant effect on the system, as it can be seen in figure(8.22) that the ascent of the balloon is slowed as the mass increases and it is unable maintain the demand altitude of 20km.
8.7 Horizontal Control
The aim of this section of the report is to build a dynamic model of the horizontal motion of the balloon due to the wind fields, and ultimately a controller to navigate the balloon to a specified target location. The model will rely on accurate wind velocity profiles which in this analysis will simply be assumed, however in the real balloon on Titan they will need to be obtained either through predictive calculation or direct measurement using sensors on the balloon or orbiter. One key assumption made is that the balloon’s horizontal velocity is always equal to the velocity of the winds at the given altitiude, the effect of any transient acceleration or drag is ignored.
8.7.1 Wind Data
The Titanic atmosphere is a very complex system with complicated wind profiles; at certain altitudes winds are generally predictable and more or less constant in direction and magnitude, at others they
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Figure 8.21: A Test Landing and Take-Off Manouver Using Integral Action Under 100m Altitude
Figure 8.22: The Effect of an Increase in Mass due to the Formation of Ice Crystals
164 Chapter 8. UAV Control Liam Donovan are unpredictable and variable. For the following analysis a very simplified model is assumed where the magnitude of the wind velocity inreases linearly with altitude from 2km and the direction is a continuous function of altitude and rotates in the horizontal plane at a constant frequency with respect to altitude. The profile is assumed to be constant in time. The result is a tapered helix and a three dimensional graphical representation of the wind velocity relative to a stationary observer at horizontal position (0,0) is shown in figure(8.23) with altitude on the vertical axis and horizontal velocity on the horizontal axes.
8.7.2 Horizontal Dynamics
The governing equations for the horizontal dynamics of the balloon are very simple given the assump- tion that the balloon is always travelling at the horizontal wind velocity and does not undergo any transient acceleration: ∫
Z = WZ ∫
Y = WY
Where WZ and WY are the components of the wind velocity in the Z and Y directions respectively. These equations are implemented in Simulink in figure(8.24). The wind velocity data is held in magnitude-argument form in two lookup tables. It is first converted into its Z and Y component form and then integrated to give the Z and Y position of the balloon.
8.7.3 The Horizontal Controller
The purpose of the horizontal controller is to move the balloon to a specified position in the horizontal plane and then to keep it there. It does this by calculating the desired direction for the balloon to travel in and then passing the altitude at which the winds are blowing in that direction to the altitude controller in figure(8.12) in the form of an altitude demand. The Simulink implementation of the controller is in figure(8.25). The desired direction is calculated by creating an error vector from the two components of the position error and then calculating the argument of the vector. The complex- to-angle function in Simulink outputs an angle in the form −180◦ < θ < 180◦ where θ is defined in the usual way as the angle between the vector and the Z axis in this case. A problem arises when the angle goes over 180◦ because the value flips from 180◦ to −180◦ instantaneously, causing a large discontinuity. Because the altitiude demand is calculated from the desired direction using a lookup table, this discontinuity does get passed on to the demand and can lead to unstable behaviour and
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Figure 8.23: A Three Dimensional Representation of the Assumed Horizontal Wind Velocity Profile
1 [Zpos] s x to magnitude |u| Re [X] Integrator Z Position u Im Altitiude Magnitude -Angle Complex to 1 [Ypos] to Complex Real -Imag s Integrator 1 Y Position x to argument
Figure 8.24: Wind Velocity Model Block Diagram
166 Chapter 8. UAV Control Liam Donovan large sub-optimal changes in direction of the balloon. The derivate, hit crossing and integrator boxes in figure(8.25) compensate for these discontinuities by detecting when the large spikes in the derivate of the angle which they cause occur and then adding an offset of ±360◦ to the angle depending on whether the vector is rotating clockwise or anticlockwise, thereby expressing the angle as a completely continuous variable. Figure(8.26) shows the results of a test with target position (500,-500). The
-C- [Magnitude ] Z Demand [Zpos ] Total Error Re |u| 1 Z Position u -K- du /dt [Demand ] Im s Demand Vector Complex to Derivative Hit Integrator Altitude Demand [Ypos] Magnitude -Angle -K- Crossing theta to x Y Position 1 -C- du /dt s Y Demand Derivative 1 Hit Integrator 1 Crossing1
Figure 8.25: Horizontal Controller Block Diagram controller increases the altitude of the balloon in order to bring it into an area of wind blowing towards the target. When the balloon gets close to the target however, it overshoots and the controller tries to increase the altitude further to bring the balloon back around towards the target. Because the upward slew rate of the system is limited the balloon is unable to rise quickly enough and this simply results in the balloon spiralling upwards and circling the target, which is neither sustainable nor desirable.
The problem of maintaining a horizontal position is simplified if there are altitudes at which the magitude of the winds are effectively 0, and in the simplified wind profile used in this analysis this occurs at an altitiude of 2km. If when the balloon is within roughly 100m of its target horizontally, i.e. the magnitude of the error vector calculated by the controller is less than 100, the current altitude demand is overridden by a demand to move to the nearest altitude of roughly stationary wind, then the balloon should be able to come to rest close to the target. The steady state error of the vertical response of the balloon presents a problem here because the balloon will drift away from the stationary altitude into the wind. To eliminate this a signal is sent to the altitude controller to switch on the integral action when the balloon is approaching the correct altitude, similar to the landing scenario.
Figure(8.27) shows a test with this system implemented and a target this time of (-5000,5000). It can be seen that the balloon immediately rises until it is being blown directly towards its target. Then, as it approaches to within 100m the altitude drops to 2km and the balloon spirals down towards the target coming to a stop approximately 50m away.
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Figure 8.26: Horizontal Response with Target (500, −500)
Figure 8.27: Horizontal Response with Target (−5000, 5000) (including a close-up of the approach to the target)
168 Chapter 8. UAV Control Liam Donovan
8.8 Conclusion
This chapter of the report began by analysing the vertical dynamics and the thermodynamics of the hot air balloon. A method of controlling the altitude of the balloon was then proposed and the system was modelled in Simulink. Two potential areas were identified as requiring more research to ensure accuracy: the relationship between the drag coefficient of the balloon and other factors and the exact methods for and relationships between the different mechanisms of cooling for the balloon. Because the model was non-linear in order to avoid large inaccuracies due to excessive approximations the parameters of the proposed controller were determined through trial and error until the desired closed-loop response was obtained. The effect of increasing the input power to the system was examined and several demand scenarios were tested with the controller being modified slightly to allow safe landings. The altitude controller’s reaction to disturbances was also examined and found to be acceptable. Finally a control algorithm was developed to demonstrate how the altitude controller could be used to navigate the balloon through simplified wind fields. More research needs to be done on whether the algorithm would function correctly in the real wind profiles found on Titan.
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[Mr] -K-
Mass9 g [V] tdot [Q] Ti 1 [C] Velocity x F Heat in Drag 2 1 [U] 1 1 1039 [X] [Ti ] s s xos Upthrust 2 Cp 1 Accelaration Velocity 2 Altitude 2 Altitude [Ma] Temp Ti [W] 2 Force Step Ti 4 96 mass Air Weight 1 a2 Tdot 1 [M] X Tinit [Ti ] 3000 v Mass2 To File 1 u V Temperature 1 RTG M3 [T0] Math 1 4 [Qcool ] [X] f(u) [P0] Function -K- [Qcool ] To 1 Tin 2 V1 Q1 Heat in 1 Altitude 1 Atmospheric Pressure 1 P0 a cooling 1 [Q] [T 0] v u [Qmouth ] [Mdotmouth ] [Tin ] Cooling Heat in 5 f(u) [Rho 0] M2 To Math Heat in 2 massflow 1 Switch 1 Switch 2 Tin 4 Atmospheric Density 4 Rho 0 Function 1 [Qvent ] -1 Q2 cooling [Ti ] 200 Heat in 3 V3 0 Cooling 1 [V] |u| Temperature 3 Mr2 drag V6 Velocity 1 Abs 1 [Mr] [X] [P0] [T0] s Mass7 Mass_air1 [C] Altitude 4 Pressure1 T0 0 Switch 4 Velocity 4 3.927 M8 Drag 1 Demand ] V7 CdA /2 297 Altitude 6 5000 du /dt Drag R1 [Rho 0] [U] Ti 2 Td Derivative 1 0.001 [Valve ] [Rho 0] Atmospheric Density 1 1 Upthrust Mass4 k Saturation Heat in 9 Atmospheric Density 5 [X] 5000 s+1 717 .88 Flow rate 3 0 Transfer Fcn Mass5 Altitude 3 gv 1 V4 up [Rho 0] Upthrust1 -K- 1 s M9 Atmospheric Density 2 [RhoI ] Switch 3 Td 1 Velocity 3 Upthrust4 Rho 1 0
V10 524 M1 [Integral ] -K- 1 V2 du /dt [Mdot ] s Altitude 7 Switch 6 Td 2 Velocity 5 Derivative Mass_flow
[P0] [Ma] [Ti ] Pressure2 Mass_air M [Mr] Temperature 5 297 1039 [Qvent ] Mass8 [M] R2 Cp2 Heat in 4 [Ti ] Mass_total 1 Mass3 Temperature 2 Flow rate 1 [Valve ] Qv [W] down 1 Internal Density 1 [Tin ] [Qmouth ] Upthrust 3 1.37 Air Weight 3 Temperature 6 [RhoI ] Heat in 6 gv 3 1039 Internal Density 1 -5000 [RealD ] Cp 3 [Real ] mouthmflow Qv1 s Mass1 Goto Constant 1 Goto 2 [Rho 0] Integrator [Mdot ] [Mdotmouth ] |u| Re x to mag Atmospheric Density 6 u Atmospheric Density 7 [X] -K- Im Heat in 7 Magnitude -Angle Complex to 1 Altitude 5 Gain to Complex Real -Imag x to theta s [Imaginary ] Integrator 1 Goto 1 5000 [ImaginaryD ]
Constant 2 Goto 3
Scope Scope 3 Scope 4
Scope 13 1 du /dt double [RealD ] s Scope 5 Derivative 2 Hit Data Type Conversion 1 Integrator 2 Scope 10 From 1 Re |u| Crossing Im u -K- [ImaginaryD ] Real -Imag to Complex to [Demand ] Complex 1 Magnitude -Angle 1 Gain 2 1 From 4 du /dt double s Add 4 Heat in 8 theta to x 1 Derivative 3 Hit Data Type Conversion 2 Integrator 3 360 Add 2 Crossing1 Qv2 Scope 14 Gain 1 Add 1 Scope 6 Scope 7 Scope 11 1
V12 [Integral ] Goto 4 u-1 -1900
Switch 7 Bias Gain 3
0 V13 Scope 9
Figure 8.28: Full Working Model
170 CHAPTER 9 - James Coates
Remote Sensing
9.1 Introduction
The only reason for sending technology to Titan is to glean information, to find out information that wasn’t already known, therefore sensing is of utmost importance. Having decided to design a stationary lander rather than a rover, this would limit the scope of sensing to a stationary postion on the ground; to combat this, it was decided to explore remote sensing options. There will be sensors on the lander, the UAV and potentially from a remote sensor network; this section will explore the feasibility of different types of sensor, along with the feasibility of deploying such a network. Various aspects of remote sensing are researched, analysed and evaluated, there are important discussions on what can feasibly be sensed, what is desirable or useful to sense, and how these measurements are transmitted back through the system (ultimately to Earth).
I will look at using remote sensor platforms (a device with sensors, a battery, a processor, and an antenna), these are commonly called motes, short for ‘Remote Nodes’. Together, a collection of motes can be ‘Smart Dust’ or a ‘Wireless Sensor Network’ (WSN).
9.2 Information to Sense
This section explores the kinds of information that is desirable to sense, whether it could be small enough to be implemented remotely, the advantages and disadvantages of doing so, and how it could be achieved.
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9.2.1 Temperature
Standard temperature sensing equipment doesn’t work with the temperature range on Titan, it is far too cold, at around 90 K, so special thin wire thermo-couples are generally used for space missions.
Previous missions to Mars use thin wire thermo-couples (using Chromel and Constantan) to determine temperature. The Huygens lander also measured temperature based on the speed of sound in the atmosphere on decent. This is certainly feasible, and desirable. The speed of sound (cideal) in an ideal gas obeys a simple relationship to the temperature (T ), adiabatic index (γ), and the specific universal gas constant (R∗ = R/Mgas). While this does change, I’m assuming that changes to the composition of the atmosphere are largely negligible, and that it remains constant.
√ cideal = γ · R∗ · T (9.1)
This would be easily implemented using a pair of ultrasound devices, a known distance apart, one transmitting, and one receiving, and using the ‘time of flight’. The underlying electronics could be assumed instantaneous by comparison. Another advantage to implementing this is that if the temperature is worked out elsewhere, this result then tells us more about the gas compound that is surrounding the lander, through the decent, and once landed.
The NASA team then used platinum thermocouples on the surface. The problem with thermocouples is that they require a reference temperature somewhere; they are however, advantageous for other reasons.The circuitry to process the input signals can be displaced from the sensors, so placed in a warm electronics box (WEB) for example, kept warm by the radioactive battery (see chapter 5) and also by passing a current through varying resistances to vary the heat output. This means the circuitry can be less complex, they are also extremely robust.
Thermocouples work because of the Seebeck effect: the basis that a temperature gradient across two materials produces a small, but measurable voltage. This is approximately linear, the non-linear change is of the order nV per K [197], so assumed negligible. Different materials have different thermoelectric sensitivities (or Seebeck coefficients Sx). If these are known, then the temperature can be calculated as follows [79]. ∫ TT ip Vout = [SA(T ) − SB(T )]dT (9.2) TRef
Assuming that the Seebeck coefficients are constant across the required temperature range, this sim-
172 Chapter 9. Remote Sensing James Coates plifies to:
Vout = (SA − Sb)(TT ip − Tref ) (9.3)
Vout => TT ip = TRef + (9.4) SA − SB
This gives us a basic formula that can be used in the software to calculate a temperature. The
−1 coefficient values depend on the metals chosen, (for Chromel and Constantan ∆Sc = 70 VK [221]). Another good pair of metals would be the industrial ‘type T’ pair, copper and copper-nickel, which work well down to 23 K [169].
It must be remembered that thermocouples are only relative and not absolute; therefore another absolute sensor is needed somewhere. On Earth, commonly this would be an ice bath, held at freezing point, this isn’t really possible on Titan. A thermistor within the WEB (perhaps the same that would be used to provide information to keep the temperature constant by selecting resistors) would provide a good reference point. The voltages would be monitored using an analogue to digital convertor
(ADC), and a software function call would update the two voltages in the program, and convert them into an outside temperature. A low pass filter could also be used to reject noise, some of which could come from radiation.
Whilst sensing the temperature is advantageous, having one sensor on the lander, and one on the UAV should be sufficient. Temperature doesn’t change vastly across small areas, and it could be sensed remotely via an infra-red emission detector (or thermal imaging camera). This negates the need for true remote sensing.
9.2.2 Chemical
Detecting the substances that make up the atmosphere, and the ground is of utmost scientific impor- tance, it reveals a lot about the long term history of a planet, it’s suitability to sustain life; either it’s own or for future manned missions. The presence of water for example is essential for all known forms of life. Reports suggest that current technology is too large to be implemented on a small device [20], however the following research suggests otherwise.
Traditionally, chemicals have been detected with the use of a mass spectrometer, however these tend to be large and heavy. They work by first heating the compound to vaporise it, and then it is ionised. These ions are passed through to the analyser, which contains electro-magnetic fields that apply forces to the particles, which change their motion. Using Newton’s second law, the change in
173 Chapter 9. Remote Sensing James Coates velocity is proportionate to the force applied and to the body’s mass. A detector senses the amount of ions at each charge applied, and therefore knows what mass they should be, hence the element [85].
Equating the Lorentz force law, to Newtons second law gives us an expression for the mass-to-charge ratio (m/Q), used to identify the particles.
F = Q(E + v × B) (9.5)
F = ma (9.6)
∴ (m/Q)a = E + v × B (9.7)
Where F is the force on the ion, m is the mass, a is the acceleration, E is the applied electric field,
Q is the ion charge, v × B is the cross product of the ion velocity and the magnetic field. Using this equation, and the particle’s initial conditions the particle’s motion in space is completely determined by m/Q.
The spectrometer is often preceded with chromatographic separation to enhance results. A gas chro- matography mass spectrometer was sent on the Huygens lander [70]. This separates out components of the gas first differences in absorbency, to make the end results more selective. The sample inlet system and the spectrometer were sealed under vacuum until exposed to the ambient atmosphere after jettison of the lander’s heat shield. The measurement sequence was pre-programmed, direct atmospheric samples were taken during the entire descent, into different sampling tubes, which could then be properly analysed later on, and the results sent back to Earth.
Since the Huygens lander technology has moved on, and there have been some notable advances in spectrometry. Rather than using gas chromatography to separate particles, ion mobility has proven to work well, by selecting particles based on the drift time of the ions under an applied potential gradient, only ions of a certain mobility are allowed to pass through to the detector. Miniaturisation has allowed such a technology to be fabricated into a single small chip, produced commercially by
Owlstone Nanotech, Inc. [229].
NASA have also been developing a prototype chemical sensor [140]. After separating the incoming gasses into their constituant parts, their device then uses Single Walled Nano Tubes (SWNTs). These have a very large surface area (1600 m2g−1), which translates into large adsorption rates for gases; they make a long channel, and solution-cast across the two electrodes with purified SWNT’s to form a conducting channel. It has been shown that the conductivity changes reproducibly upon adsorption
174 Chapter 9. Remote Sensing James Coates of gases, this forms the basis of the chemical detection, the sensitivity is approximately 40ppb. Shining a UV source across the nanotubes after the experiment accelerates desorption of the vapour, to start a new trial. A prototype has been launched into space on a satellite, and this confirmed it can survive the launch conditions and in space itself.
(a) The electrodes (b) Close-up view of the SWNTs
Figure 9.1: The system in NASA’s prototype
Using one of these devices would reduce the weight and complexity of the lander, as well as the power consumption. Where-as traditional spectrometers are far too big, it is feasible to attach one of these to remote sensors, to get readings of the atmosphere and surface composition from across a large area.
9.2.3 Life
The Viking lander went to Mars in 1976, and its main mission was to look for life [159]. One experiment it performed was to put soil in a container with radioactive CO2. It was left in for 5 days, and then the soil was tested to see if it contained any of the carbon from the surrounding atmosphere, if there was this would suggest that a form of life has performed respiration (as plants do on Earth). Another experiment was to mix the soil with nutrients in water solutions, and watch for any changes. This returned promising results, but as other tests had failed, they concluded that there may have been
H2O2 present, which reacts with water to produce oxygen, so this is an inconclusive test.
One easier, more reliable approach is to look for chemical or thermodynamic disequilibrium [21], this implies something is changing the steady state of the atmosphere. Oxygen is very reactive, and if there wasn’t a continuous process releasing it from CO2 to form carbon, it would soon react with substances, to form oxides. Another method [217] is decomposing organic materials in an aqueous sample by simultaneous exposure to ultraviolet radiation and acoustic energy to get products such as ammonium ions, halogen ions, alkyl ammonium ions, or sulphate ions which would then be detected
175 Chapter 9. Remote Sensing James Coates by a spectrometer.
Yet another idea, developed by NASA is the Mars Oxidant Instrument (MOI) [14, 158], which detects amino acids. These can be produced non-biologically, but they come in two variations, left-handed and right-handed, all life on Earth utilises chains of just left-handed to make proteins. It would be assumed that any form of life would use just one of these types, as a mixture would complicate the biochemistry. If an even mix is found, that would indicate a lack of life, if there is a swing either way, that would indicate the presence of life.
To test for this, water is added to a sample, and different organic compounds dissolve into the liquid as the temperature changes. The water is then stripped away with heat, created high concentrations of the dissolved compounds. A fluorescent chemical is added, and any glowing, picked up by a detector, would indicate amino acids. An applied electric charge then separated the different types of acid
(electrophoresis). This has been developed onto a single chip, see figure 9.1b.
(a) A single MOI chemical sensor array (b) Six MOI sensor arrays configured into a soil cup
Figure 9.2: The Mars Oxidant Instrument
This would also require a robotic arm to drill the rock, and deliver the samples to the inputs, which adds complexity, is heavy, and power intensive (both robotic arms and drills can often easily consume a kW).
9.2.4 Light
Light intensity is particularly low on Titan [209], about one thousandth that of Earth’s daytime, being about ten times the distance from the Sun as Earth, so getting only a fraction of the sunlight
Earth does. Studying the light level characteristics over time might be interesting to study, not just day and night but also seasonal differances. This is simple to achieve. A simple photodiode [113]
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(basically an LED used in reverse) accurately converts light intensity into and electric potential, or a
Light Dependant Resistor (LDR) changes it’s resistance according to light intensity, which would be connected into a bridge circuit to transform that into a voltage.
They are both very small and versatile and the output would pass through an ADC, and the results loaded into the software for transmission along with other sensor values. These are small enough to be implemented on the remote sensors.
9.2.5 Sound
The first and only time sound has so far been recorded on another planetary body, was the Huygens lander on Titan [78] although this was very poor quality because of bandwidth issues, the microphone was limited to just 480 bits per second [201], nearly 300 times less than standard quality recording.
It was only originally designed to detect thunder, with the ambient sound reconstituted from the data later on. Sound would be interesting to record, mainly for engaging public interest, but it is very bandwidth intensive. An average quality recording, even after compression is 128kbits−1. Just 3 minutes of audio, would therefore be 23Mbit (even after compression!). Compression is very power intensive, but not as much as RF transmission, so compressing any audio would prove worth it for the power consumption.
There are lots of different compression standards, that achieve similar rates of compression, MP3 is the more pop- ular lossy format, however Ogg Vorbis is open-source, and free from patents and license costs, and is technically su- perior, it creates a smaller file size for a similar quality
[207]. There are open source implementations in hardware
(see figure 9.3) as well as software which is good because hardware implementations are generally more power effi- cient than software implementations. They would be small enough to implement on any of the devices.
Figure 9.3: An open source hardware im- 9.2.6 Acceleration plementation of Ogg Vorbis.
The inclusion of an accelerometer is easy to do, and can tell us a lot. If the sensor were to land in a river, it could
177 Chapter 9. Remote Sensing James Coates tell us how turbulent the river was. It could tell us how turbulent the air is when the device is falling.
Combined with a tri-axis tilt switch, it would tell us the current state of the device.
(a) ADXL330 accelerometer and tilt chip. (b) A Wheatstone half bridge circuit.
Figure 9.4: Accelerometer Electronics
To implement a sturdy reliable option in silicon is straightforward [16], and consists of a cantilever beam-mass structure made from a silicon wafer. Using selective diffusion, two piezoresistors are formed, one on the beam, and one in the frame, their resistances then change under acceleration.
Using 3 of these orthogonal to each other provide 3D motion information. They are connected within a half-bridge circuit, the output is a voltage directly proportional to the acceleration. In figure 9.4b resistors 2 and 4 would be the respective piezoresistors, and resistors 1 and 3 would be two standard equal resistances. R2 R4 ∴ V = VEX − VEX (9.8) R1 + R2 R3 + R4
R1 = R3, if R2 = R4 (i.e. no acceleration) then V = 0. If there is a differential in the two resistors, i.e. an acceleration, the output would be a voltage linearly proportional to the difference in resistances, therefore acceleration.
These are widely available cheaply, so there would be no need to make one from scratch. One example is the ADXL330 chip (see figure 9.4a). This costs less than £5, is 0.1cm2 in area, and draws 0.1A when in use [52]. For a lower power consumption, the DE-ACCM3D chip draws just 0.9mA [66] but is slightly larger.
Accelerometers would be straightforward to implement, they are small, and power efficient. They could be included them on the lander and on the motes.
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9.2.7 Wind Speed
Wind speed is measured using an anemometer. Wind speed and air density are intrinsically linked
(see equation 9.9) and many anemometers take advantage of this relation by using the pressure of the air to move a mechanism. 1 p = ρv2 (9.9) 2
Care must be taken not just to transport an anemometer made for Earth, one would have to be specifically designed, or at least the results would have to be corrected for the difference.
The standard way to measure wind is using hemispherical cups (usually three) mounted onto an axis, the wind then causes the axis to rotate, and the wind speed is then related to the rotational speed, calculated with an odometer. The number of turns can be logged over a time, and divided by that time to provide an average speed. These could be collated in an array, ready for sending along the network on request. These are large, fragile and complicated however, there needs to be a better solution.
NASA often experiment with different types of anemome- ter. On the Phoenix Mars Lander they used a weight on a string, (like a plumb-line) and view the deviation from the central hanging position, corresponding to no wind. This allows for accurate measuring of wind speed and direction, but it is rather big and bulky, and so could only be imple- mented on the lander.
If ϕ was the angle the weight makes with the vertical cen- tre line, the mass of the ball was m, and a gravity field of strength g, then the tension in the (light, inextensible) string is given by
T = mg cos(ϕ) (9.10)
If the ball had an area A presenting to the wind of velocity Figure 9.5: The Phoenix Mars Lander v, air density ρ, the force on the ball is wind instrument. F = ρAv2 (9.11)
Putting together these two equations gives us a relation for the angle made by the string and the
179 Chapter 9. Remote Sensing James Coates centre, with the wind strength.
F = T sin(ϕ) (9.12)
ρAv2 = mg cos(ϕ) sin(ϕ) (9.13) √ mg sin(2ϕ) v = (9.14) 2ρA
From equation 9.14 the angle corresponding to the wind speed can be worked out, by using constants known about Titan. For example, if the ball was 100g, with a surface area of 5cm2 and it made a small angle of 10 ◦, this gives us a predicted wind speed of nearly 3ms−1 (from equation 9.15); this seems a reasonable figure. This calculation could be implemented in the software of the device. √ 0.1 · 1.35 · sin(2 · 10 ◦) v = = 2.92... (9.15) 2 · 4.5 · 1.2 · 0.0005
Another type NASA have experimented with, sending one to Venus, is the hot-wire anemometer [208].
A fine wire made of Platinum or Tungsten is heated and the air flowing past cools it down, the faster the flow, the faster the cooling. Measuring the resistance of the wire determines the temperature, and therefore the change in temperature over time. Alternatively, the temperature is kept constant, and the current or voltage is monitored.
Assuming that the wire is in thermal equilibrium, and has a current in, I, and the wire has resistance
R. The power lost because of convective heat transfer is related to the wire surface area, A, the temperature differential, ∆T, and the heat transfer coefficient, h. This leads to equation 9.16, which would be solvable for the velocity given more detailed analysis (h is roughly proportional to the square root of the fluid flow velocity from King’s law) [61].
I2R = h · A · ∆T (9.16)
Having multiple wires allows a direction of the wind to be calculated, along with providing redundancy and a certain amount of self calibration. Hot-wires though have an extremely high frequency response, typically in the tens of kilohertz, they are used when rapid velocity fluctuations are of interest. They are also small and easy, and having no moving parts they are robust. This seems the best solution.
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9.3 Communications
This section explores the ways in which data from the sensors could be transmitted back to the lander, the UAV, or the satellite, and the aspects affecting this operation.
It explores the possible protocols for networking the remote sensing network, and comes to a conclusion on the overall best way to achieve the aims.
9.3.1 Radiation Hardening Chips
Memory is highly affected by cosmic rays [130]. Without the ozone layer on Earth, it becomes much more susceptible. The Sun produces not just visible light, but also x-rays and gamma rays. Cosmic rays coming from outer space can also carry ionising radiation.
This radiation disrupts the memory chips in different ways. The more serious affect the memory permanently, others make it unpredictable by changing the balance of energy, making some switches harder to turn on. More common are soft errors than can flip bits the wrong way given a dose, but this is often recoverable afterwards.
Performance can be improved [94] by better placement of component junctions, or different silicon technologies (such as Silicon-On-Saphire). Increasing spacing between the components makes striking a particular part of the chip affect less of the chip, and thicker wiring between components can handle bigger currents in the instance of a strike.
These modifications can be expensive as they can require redesigning chips. Another alternative is to use commerical off the shelf (COTS) parts, using these off-the-shelf components is recommended in space [155]. Every chip behaves differently under test, even chips from the same batch. Chips that are made in bulk do offer some predictability in use, and it would be possible to test and select the chips in question. This also allows for easy upgrading of technologies for future missions as technology advances. NASA now use COTS parts in the International Space Station.
Taking this into account, a team [223] has tested commercially available designs, and come up with the best available. The top two commercially available performance wise were the ‘High Powered
Modules’ mote made by Jennic, and the ‘TelosB’ mote, made by Crossbow. The TelosB would be a good choice, the report said this about it: “very good overall, excellent power consumption, robust design, small size, high data rate and considerably easy to program”. If chips are used, they must be
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Standard USB Firewire Cat5 (Ethernet) Max Data Rate (MB/s) 120 400 120 Number of Connected Devices 127 63 5 Power Supply (V) 5 3 48 Rated Cable Length (m) 5 4.5 100
Table 9.1: Quantitive comparison of the wire candidates [109, 180]. extensively tested, and safe-guarded against radiation [231], memory units are particularly vulnerable.
Another option is rather than buy pre-constructed devices, buy a processor, and fabricate peripherals such as housing, batteries and antenna. A good processor for these devices is the Texas Instruments
CC2530 chipset, being small, and very power efficient.
9.3.2 Wired Communication
Having physical wires between the lander and the motes is a rather extreme idea, but worth mentioning.
The sensors could be powered from the lander, controlled by the lander’s processor, eliminating the need for processing chips, antennas and batteries on the devices, making them as small as the individual sensors. There would also be a fantastic bit-rate compared to wireless. Once deployed, they could even be reeled slowly in to the lander to obtain a range of readings from different locations.
The main contenders terrestrially are USB and Firewire, used for connecting peripherals to computers, and Category 5 cable (Cat5), used for Ethernet networking. Quantitative comparisons can be found in table 9.1.
As one can see from the table, Cat5 seems the best all rounder, especially given the length of cable allowed; although technically any cable could be any length, just with corresponding decreases in bit rate due to signal attenuation. Assuming that a standard cable is 1cm in diameter, this gives just
100m of cable a volume of nearly 80cm2. This is clearly an unsustainable volume (even assuming it’s perfectly packed) for having multiple devices. The components for wireless transmission are not that big in size per device, and can achieve a far greater range, so are more useful. There would also be added complexity in the distribution of the devices. They couldn’t just be dropped randomly, the wires could tangle, data couldn’t be collected in free fall either.
The only advantage really is the ability to move the devices after the distribution by pulling on the cable. The mechanism for this would be fairly complex, but it would provide a more in-depth study of a concise area. This added benefit doesn’t outweigh the disadvantages of wired communication in this situation.
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9.3.3 Light Communication
One team [224] has managed to build a mote with a tiny beam-steering mirror for active optical transmission, a retro-reflecting corner cube (that reflects any incoming light path back to the source, adding modulation), an optical receiver, signal processing and control circuitry and a power source onto a device that is less than half a centimetre long.
They found that a mote utilising an external source of light, can direct this onto the receiver and achieve a data rate of 1 kbits−1 over distances of 150 m. Distances of over 20 km have been tested, although with drastic drops in bit rate. This is achieved by modulating the light using a diffraction grating, which creates a spot pattern that can be related to the Fourier transform. By changing the grating, these transforms can alter the wavelength and amplitude of the spectral peaks, which is the method of encoding. Tuning these two parameters offers over a million different codes [193].
This sounds good, however, using an external light source would not really be possible on Titan, the ambient light is low; the UAV could provide a light source but aiming onto a centimetre sized device from 10km high would be too great a challenge. This option is not really feasible. Using the lander is a possible option, as they will all be scattered around that area, but that would require a direct line of sight to communicate, a precise direction mechanism, and the motes wouldn’t be able to communicate with each other to pass messages on, unless they were equipped with wireless too, but then that would render this communication form obsolete.
9.3.4 Wireless Protocols
There are three main contenders for the protocol to use on the motes: Wi-Fi, Bluetooth, and Zigbee.
Wi-Fi and Bluetooth are commonly used domestically to create wireless local area networks, Wi-Fi is commonly between computer systems, and Bluetooth is commonly for between mobile phones. Zigbee is an open standard designed for low power and low data rate applications like home automation, security, industrial device control. The advantages and disadvantages of each will be discussed now, and the quantitative analysis is available in table 9.2. The last row, overall metric, I’ve defined as the values where the bigger number is better in the numerator, and the smaller the better is on the denominator (see equation 9.17); the resulting metric means a bigger number is better overall.
DataRate · Range · NumberofNodes (9.17) P ower · P rotocols · JoinT ime
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Standard Bluetooth Zigbee Wi-Fi IEEE Spec 802.15.1 802.15.4 802.11 Frequency Band (Ghz) 2.4 2.4 2.4 Max Data Rate (Mb/s) 1 0.25 54 Nominal Range (m) 10 10-100 100 Max number of nodes 8 >65000 20 TX (mA) 57 24.7 219 VDD (volts) 1.8 3 3.3 Power (mW) 102.6 74.1 722.7 Packet Transfer Protocols 188 48 75 Network Join Time (s) 4 <0.03 10 Overall Metric 0.001 9137 0.199
Table 9.2: Quantitive comparison of the wireless protocol candidates [119, 87].
For Wi-Fi, the big advantage is the fast data rate available, it is over fifty times faster than the competition, it does use ten times the power however; if the power was normalised to the bit rate, this appears to make Wi-Fi five times more power efficient. The next version of Bluetooth (4.0) is an ultra low power version, which could compete with Zigbee, but isn’t ready yet. Both WiFi and Zigbee use the QPSK modulation scheme, Bluetooth uses GFSK. QPSK is often thought to be superior to
GFSK, having a smaller bit error rate.
There are other issues to consider however. The complexity of Bluetooth and Wi-Fi means that there are more hand-shaking protocols, so more data must be sent per packet, reducing transmission efficiency, the amount of transfer protocols can be a measure of the complexity and inefficiency of a protocol. Using this metric, Zigbee appears the least complex.
Wi-Fi takes a long time for the node to connect to a network, about 10 seconds. This is three hundred times as long as Zigbee, and during that time it will be consuming power, therefore reducing node life, given the limited power source.
The specified ranges of the protocols are somewhat negligible as these are conforming to the broad- casting laws on Earth. In space, you could theoretically amplify your signal as much you want, and coupled with a high-gain antenna (see section 9.4.1) these ranges could achieve kilometres.
It appears that the Zigbee protocol beats Bluetooth and Wi-Fi in most areas specific to this application, the quantifiable metric figure is thousands of times bigger for Zigbee.
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9.3.5 Localisation
Knowing where the individual devices are, in relation to the lander at least, would be useful. Whilst results of remote tests would still be interesting without having any localisation, the spatial awareness adds extra information to make it more interesting, it could then be visualised on a map for example.
Not being on Earth, they obviously don’t have the advantage of the GPS system. This is quite power intensive anyway. What it could make use of, is the fact that received signal power is (ideally) inversely and squarely related to the distance, as shown by Friis’ free space transmission equation [86].
λ P = P · G · G ( )2 (9.18) RX TX TX RX 4πd
Where PRX is the remaining power of the wave at the receiver, PTX is the transmission power of the sender, GTX and GRX are the transmitter and receiver gains, λ is the wavelength, and d is the distance. Knowing all these variables allows a simple relation for the received signal strength to the distance between the devices.
Section 9.4.1 talks more in detail about the antenna design, however the conclusion is to have a rotating high gain antenna on the lander. Having the servo coupled with an optical or magnetic absolute rotary encoder, this could generate the angle of the highest strength transmission to a particular device, and the received signal strength, averaged over many transmissions this would produce a map of all the devices in a polar co-ordinate system.
If all the individual devices listened out for each others transmissions (only occasionally to save on battery life), and worked out their own perceived distances, these could all be collated by the lander, averaged and an optimised location would be found. Just finding them centrally can have discreprancies due to obstacles and interference affecting strengths. Interference would only be from other devices, the Lander-to-UAV link is operating in X-Band.
Another method, time-of-flight analysis requires good time synchronisation between the devices. If two devices were 1km away for example, the time difference between sending and receiving the signal would be 3.3µs from equation 9.19. This obviously requires extremely synchronised clocks on the motes. d 103 t = = = 3.3µs (9.19) c 3 × 108
The devices could also include additional transmitters and receivers of a different waveform such as
185 Chapter 9. Remote Sensing James Coates ultrasound. Sound travels at about 340m s−1. If this was transmitted over 1km, it would take nearly
3 seconds. Thus, the device could issue a warning that it is going to send a sound wave over RF, taking microseconds, whilst simultaneously sending the sound wave. This microsecond difference would not × 3.3×10−6 affect the overall time very much (it is 100 3 = 0.0001% of the total time), and then the device could measure the difference in time of the two signals.
This wouldn’t necessarily require the devices to be in sync with each other, simplifying the process in one way, but the extra components on each mote would complicate things slightly. It seems a tad superfluous if this is already possible using the strength of received RF signals, eliminating needing extra electronics.
It is proven to be beneficial to have some more powerful detectors interspersed with the average power detectors [83]. Having a spectrum spread out means that the less powerful can take advantage of the more accurate results of the more powerful, making them more accurate than they otherwise would be, perhaps 1 in 20 devices could be fitted with an ultrasound pair to provide extra reference locations.
9.4 Module Design
This section brings together other aspects of the design that need to be considered: the antennas on the lander and devices, the protection for the device from being dropped at a large height, the ability to stay afloat if dropped in a methane lake, and the space saving design.
9.4.1 Antenna Design
Devices like this are normally only designed to work in the range of about 100m. This would be inadequate, as the motes are likely to be spread across a larger distance; a larger sample area would give us more useful and interesting data. To achieve these larger distances, the lander could be fitted with a small rotating high gain antenna, rather than a standard isotropic antenna. Additionally, the devices themselves could be fitted with small external antenna to boost their signal.
Titan seems better for electromagnetic attenuation than Earth at the required frequency [24]. This is because there isn’t as much ammonia or water in the atmosphere, these absorb radio frequencies of wavelength around 14cm (=2GHz); the attenuation on Titan is 80% from collision-induced absorption by molecular nitrogen. In this section the use of high-gain antennas will be looked at, and theory used to calculate a theoretical distance of communication between the lander and the devices.
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A parabolic high gain antenna has the approximate relation:
πD G ≈ ( )2 (9.20) λ
fπD ∴ G ≈ ( )2 (9.21) c
For a frequency of 2.4Ghz, and modestly assuming it is 50% efficient, this (as shown in figure 9.6)
250
200
150 Gain
100
50
0 0 10 20 30 40 50 60 70 80 Dish diameter (cm)
Figure 9.6: A graph relating the dish size to the antenna gain. gives
G ≈ 631.7 × 0.5 × D2 (9.22)
Realistically, a diameter of 30cm would be appropriate. This gives a Receiver gain of
631.7 × 0.5 × 0.32 = 28.4 = 14.5dBi (9.23)
We can use the link budget formula to account for all of the gains and losses in the system from transmitter to receiver, and work out the distance at limiting path loss. If PR = the received power
(dBm); PT = transmitter output power (dBm);
GT = transmitter antenna gain (dBi); LF = free space loss or path loss (dB); GR = receiver an- tenna gain (dBi); and other losses incorporated as efficiencies in the figures for power and gain, then the link budget formula is: Figure 9.7: 3D CAD design for the 3cm quarter- wave dipole antenna. PR = PT + GT + LF + GR (9.24)
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If the Texas instruments CC2530 chipset was used, this has a received power sensitivity of -97dBm, and a transmitter power of 4.5dBm. Knowing that c = λ · f, for the system at 2.4 GHz, λ would be = 12.5cm. A quarter-wave dipole antenna would be suitable on the devices, as this would be
3.125cm long, having a gain of 2.2dBi [10]. Quarter wavelength antennas are very efficient in terms of transmission and space taken up, this is similar to the antennas you would find domestically on a
Wi-Fi router (this operates at the same wavelength). There is a model in figure 9.4.1.
Path loss [227], caused by the dispersion of the signal, and how well a particular frequency can be received is given by: λ L = 20 log ( ) (9.25) F 10 4πd
∴ − − LF = 40 20 log10(d) (9.26)
Plugging all the above results into equation 9.24 to find the distance gives:
− 20 log10(d) = 97 + 4.5 + 14.5 40 + 2.2 (9.27)
∴ d = 8128m (9.28)
This shows that the motes, using a 30cm parabolic high gain dish antenna on the lander, and the TX
CC2530 processor on the devices, with a 3cm antenna can communicate with the lander up to about
8km away.
9.4.2 Landing Protection
The motes would have to be spread out around the lander. There are a few options of doing this, mostly involving being released from the lander before landing (or the UAV could also drop them).
To make sure they landed safely, they would need to be fitted with safety features. As the atmosphere is very conducive to flying, it is also better for falling, the atmosphere is nearly five times as thick as
Earth’s, and the gravity is around one seventh of the strength of Earth.
We could take inspiration from nature. Falling seeds have been a busy area of study recently, with researchers trying to mimic and harness to ability of the seeds. This would be much easier on Titan.
To implement this the size of the wing span that would be needed to carry the device safely to the ground needs to be calculated. It will be assumed that a safe speed for the motes to land would be
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Species Mass (mg) Disk Loading (mg cm−2) Terminal Velocity (cm s−1) White Ash 70.4 2.8 160 Green Ash 26 2.6 162 Tuliptree 31.2 1.9 121 Sugar Maple 53.4 3.3 102 Boxelder 42.3 2.9 92 Red Maple 14.2 2.1 66 Silver Maple 158.9 3.3 87
Table 9.3: Falling seed data by species [84].
5ms−1 and that their mass is approximately 60g.
We can use a standard formula [37] for the dynamics of the falling body, where D is the drag force, L is the lift force, m is the mass, g is the gravity, and γ is the angle to the horizontal.
dv m = mg − D sin γ − L cos γ (9.29) dt
For now, only the speed it will land at will be taken into consideration, it must land safely. This will be the terminal
dv ◦ velocity, when dt = 0 and for vertical motion, γ = 90 . The lift force, L, is given by
1 L = ρV 2AC (9.30) 2 L
Where CL is a coefficient of lift, A is the effective area of the wing, ρ is the density of the fluid, and V is the veloc- ity. This can now be substitued, along with the previous assumptions, into equation 9.29.
2mg A = 2 (9.31) ρV CL Figure 9.8: A falling maple seed.
To calculate the coefficient of lift, one could use previous data from falling seeds, to work out an average. The data from table 9.3 was obtained, converted into appropriate units, (the area was found by diving the mass by the ‘disk loading’) and substituted into equation 9.31 to obtain values for CL. This was then averaged, and found to be 0.45.
189 Chapter 9. Remote Sensing James Coates
Now, using this value, and other previous values (g = 1.35ms−2 and ρ = 5.4kg m3) the area of the wing(s) can now be calculated, to see if it is practical.
2 × 0.06 × 1.35 A = = 26.6cm2 (9.32) 5.4 × 52 × 0.45
Figure 9.9: A 3D model of the wing design.
This means, if there were two wings, each just approximately 2cm wide and 7cm long, the mote could safely, without any mechanisms or deployment systems to go wrong (as with a parachute). This is using conservative numbers, in reality, they could be even smaller.
The seeds normally have an angle of attack; a sampled average of seed types is −11.2 ◦ in the plane of rotation. If they were pitched at this angle, then the depth of storage would be 2 sin 11.2 = 0.388... ≈
4mm. That means both wings could easily be stored within 1cm depth of the device. More about this in section 9.4.4.
9.4.3 Flotation
Some of Titan is covered in lakes of liquid ethane and methane [205]. If the landing site was in one of these lakes, the device would need to be protected, even though both ethane and methane are non-conductive and so couldn’t do too much damage, the device sinking would be bad, it would be unable to communicate.
There could be a device that inflates upon contact, or during flight, to maintain buoyancy without taking up space. To work out the volume needed to stay buoyant, some calculations can be done.
The density of the device must be less than the density of the fluid in which it is sitting. It is known
190 Chapter 9. Remote Sensing James Coates
m that ρ = V . The device is roughly estimated at around 60g, but it’s dimensions haven’t yet been established . Let’s assume it is very large for a device of its kind, and choose the footprint at 8cm by 4cm, this means that the wings could fold inside the device during transit to save space. How tall would it have to be to float with the aid of an inflatable?
Bearing in mind the differences in temperature, and atmospheric pressure, the liquid ethane and
−3 −3 methane would be fairly dense. At 93K and 1.46kPa, ρethane = 648.5kg m and ρmethane = 448kg m [172]. Taking the smaller of these two values makes sense, planning for the worst case scenario, and at limiting buoyancy: m 0.06 ρ = 448 = = (9.33) methane v 0.08 × 0.04 × h
∴ h = 0.0418 (9.34)
So the height of the device must be taller than just 4cm to float, given the 8 × 4 footprint, this is without any inflatable flotation aid.
9.4.4 Storage and Deployment
Section 9.4.3 came to the conclusion that the device must be approximately 8cm x 4cm x 4.5cm to
float. This is very large, considering the components inside the device are all small, the TI CC2530 processor is less than 1cm2. To save space for during transit, to pack in more sensors, there could be a folding design where the antenna and both wings fold into the case, to be unfolded on release from the lander. The case itself could also be compacted in size, with all the circuitry in the bottom 1cm of the case. Assuming the wings and antenna took up another 1cm. then perhaps the case could have a cascading design, where the bulk of the volume is pulled open on decent, the top half would slot into the bottom half for storage, and once extended, lock into place, to provide the volume needed for
flotation in the methane.
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(a) The upper half. (b) The lower half.
Figure 9.10: The upper and lower halves of the folding mechanism.
The folding out mechanism of both the wings, the antenna, and the extruding of the casing could all be connected together by gears, and spring loaded, so as soon as the device is released from it’s confines in storage, it would spring apart, opening out the wings, protruding the antenna, and expanding the device to full volume.
(a) The device fully opened for deployment. (b) The device folded for transit.
Figure 9.11: The device modelled with wings and antenna attatched.
This action could also activate the battery. The battery can’t be stored connected to the device as it would leak all the charge away, it could have a tab in between the battery on the connections, which is pulled out as the device extends outwards, solving the battery leakage issue.
How many could be taken then? The overall volume, given by equation 9.36 tells us that a cubic meter of space could fit over twelve thousand devices. That many wouldn’t be taken, but this seems
192 Chapter 9. Remote Sensing James Coates a simple, very effective solution for sensing values all over the surface of Titan.
V olume storage = Capacity (9.35) V olumemote
1 = 12500 (9.36) 0.08 × 0.04 × 0.025
9.5 Conclusion
In this report it has been shown that values such as wind speed, temperature, the chemical composition of the atmosphere, light intensity along with device orientation and accelerating could be sensed accurately over large areas of Titan, and report that data back to Earth effectively for a long period of time, without the need for an autonomous rover. This is a better solution, with hundreds or thousands of devices there is redundancy, and extra richness of results being spread over large areas simultaneously it becomes possible to monitor things like weather patterns. There is little to go wrong with the uncomplicated automatic mechanisms that guide it safely to the ground, and one mistake that might be fatal on a rover (such as getting stuck), is insignificant with this elegant, futuristic, but easily achievable solution.
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Deep space communications
10.1 Introduction
The orbiter is set to travel over a billion kilometres to Titan. Once there, it will collect a wealth of data, ranging from measurements of physical properties to images of the surface. This information, along with telemetry data, needs to be sent back to Earth. This can achieved through a radio or microwave link.
This chapter specifies the design for a communications system that can reliably transmit 1Mbit/second from the Titan orbiter to Earth, while meeting the power and space constraints of the orbiter itself.
It uses a 16QAM signal modulated onto a 32GHz (Ka-band) microwave carrier.
The design process was split into four stages. First, the power budget and likely signal to noise ratio were estimated for the orbiter transmitting from Titan to Earth. Next, a modulation scheme was chosen to maximise the data rate given the noise levels in the channel. Given this modulation scheme, a modulator and demodulator were implemented in MATLAB and tested with appropriate noise levels to ensure that they worked. Finally, commercially available digital electronics and microwave hardware were found that would allow the system to be implemented in reality.
10.1.1 Challenges and Requirements
Part of the mission is to take photos of the entire surface of Titan. Along with other measurements and telemetry, this will add up to hundreds of gigabytes of data. In order to send them all back to
Earth, a high data rate is required. As with all communication systems, the maximum data rate is governed by the amount of noise in the channel and the amount of power available in transmission.
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When developing the communications system, the following were considered and determined:
• Modulation scheme
• Carrier frequency and bandwidth available
• Noise levels
• Transmission distance and latency
• Error detection and recovery
• Power consumption
The system provides the maximum bit rate possible given constraints of power supply, noise and available channel bandwidth. Other challenges include a very long latency, because of the signal propagation time. Latency is the time taken for a message to propagate through the system. Assuming that microwaves propagate in space at the speed of light:
d 1bn km 1012 t = = = = 3300 s = 55 minutes (10.1) v c 3 × 108
55 minutes (effectively 110 minutes for a round trip) is such a long latency that the system must just send data in bulk, as any flow control or acknowledge signals would be impractical. Instead, the system uses extensive error checking and correction to ensure data is delivered safely to Earth.
The final challenge was that once the orbiter reaches Titan, it will begin an orbit where Titan obscures the line of sight to Earth for the majority of the time. The system therefore defines an internal protocol that allows data to be queued until a communications link can be established.
10.2 Link Budget and Signal to Noise Ratio
The power reaching Earth can be calculated using the link budget formula:
Preceived = Ptransmitted + Gantenna − Ltransmission − Lpath + Gantenna − Lreceiver (10.2)
P represents power in dBW, G represents antenna gain in dBi and L represents losses in dB.1 A
Preceived value of around -100dBW is generally acceptable, but this is because of noise. If the received
1 dB = deciBels; dBW = 10log10(power in W); dBi = antenna gain relative to an isotropic antenna = 10log10(gain)
195 Chapter 10. Deep space communications Alex Chadwick power level were lower, it would be possible to amplify it but the thermal noise in the receiver would also be amplified without improving the signal to noise ratio.
Table 10.1 shows the link budget calculation for the communications downlink: the orbiter transmitting data to Earth. The values in the table and the justification for them are explained in this section of the report. Because of the power and space limitations on the orbiter, it must transmit at a lower power and have a lower gain antenna than is possible on Earth. The received power is -103dBW, representing 50pW. This is enough power to be processed using consumer grade CMOS electronics; for example, GSM mobile phones work with signals at -110dBW.
Item Value Comment
Ptransmitter 12dBW 100W TWTA at 16% efficiency
Gantenna 58dBi Orbiter antenna gain. See Section 10.2.3.
Lpath -302.5dB Path loss, see Section 10.2.2
Gantenna 86dBi Gain of antenna on Earth. See Section 10.2.4.
GLNA 43dB Low Noise Amplifier on Earth antenna.
Preceived -103dBW Sum of the powers, gains and losses above.
Table 10.1: Link power budget
While the link budget provides useful information on the power received at the Earth station, it is also important to consider the signal to noise ratio at the receiver. As already explained, amplifying a very low power signal is pointless as the noise in the signal is similarly amplified. The noise in each stage of the transmission and reception system is therefore important. The noise margin for the system is
7.09dB. The calculation for this is detailed in Table 10.2.
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Stage TN /K Gain G / dB Cumulative noise Cumulative SNR / dB N / W/Hz power P / W
Modulator output 0 0 0 1 ∞
Transmit power 70 12.5 9.66E-22 17.78 160.15
amplifier
Transmit antenna 0 60 9.66E-16 1.778E7 160.15
Path loss 0 -302.5 5.43E-46 1.00E-23 160.15
Receiver antenna 3 86 4.14E-23 3.98E-15 7.09
Receiver LNA 9.3 43.2 8.65E-19 8.32E-11 7.09
Total 7.09
Table 10.2: Link noise budget
When calculating the noise budget, the output of the modulator is assumed to be perfect. All subse- quent stages add noise dependent on their noise temperature. The cumulative noise for the ith row is calculated as follows:
Ni = Ni−1 × Gi + (TN i × k) (10.3)
This is effectively the noise from the previous stage amplified by the current gain, added to the noise from the current stage. The noise in the current stage is the noise temperature (or equivalent noise temperature) TN multiplied by the Boltzmann constant k, giving the equivalent thermal noise. The cumulative power is the product of the previous power and the gain of the current stage:
Pi = Pi−1 × Gi (10.4)
The SNR is then the ratio of the signal power to the noise spectral density for the 50MHz bandwidth of the system:
( ) Pi SNR = 10 log 6 (10.5) N0 × 50 × 10
As shown in Table 10.2, the overall SNR is 7dB. However, this does not account for atmospheric losses of up to 2dB in bad weather, or antenna mis-alignment errors which may also cause losses of up to
2dB. To be safe, these two losses should be subtracted from the calculated SNR, leaving SNR = 7-2-2
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= 3dB.
10.2.1 Frequency selection
In order to determine most of the values in the link budget Table 10.1 the carrier frequency was required. 32GHz was chosen and this section explains the justification behind that choice.
Previous NASA and ESA missions have used X-band communications, modulated about an 8.4GHz carrier. Since the mid 1990s NASA have been trialling Ka-band communications, defined as anything between 26GHz and 40GHz. Using higher frequencies (for example, V-band at 60GHz) has also been trialled, but requires significantly more precise microwave engineering and is not feasible yet. Higher frequencies are preferable because they allow for smaller high gain antennas and there is less cosmic noise at higher frequencies. Cosmic noise originating from the Sun results in an effective antenna noise
2 temperature related to the signal wavelength: TA ∝ λ . [41] As thermal noise power PN = kBTA, (with k the Boltzmann constant and B the channel bandwidth) there is significant advantage in using higher microwave frequencies. For example, comparing NASA 8.4GHz X-band with 32GHz Ka-band yields:
− λ2 f 2 (8.4 × 109)−2 Noise power advantage = X = X = = 14.51 = 11.6dB (10.6) λ2 f −2 (32 × 109)−2 Ka Ka
60GHz V-band would provide a further advantage:
(32 × 109)−2 = 3.51 = 5.46dB (10.7) (60 × 109)−2
However, the microwave electronics required for amplification and mixing are much harder to imple- ment. The wavelength of 60GHz signals is half that of 32GHz signals, and microwave electronics and connectors therefore have to be designed and manufactured to much tighter tolerances. The expense associated with this, and the difficulty in manufacturing mixers makes V-band currently unfeasible.
In addition to the solar noise advantage, using a higher carrier frequency allows dish antennas of the same area to have higher gain: [58]
4πA G = effective (10.8) λ2
Again, the gain is proportional to the inverse of wavelength squared: G ∝ λ−2. This therefore gives
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Ka-band a power advantage for an antenna of the same effective area:
− λ 2 f 2 (32 × 109)2 Antenna gain advantage = Ka = Ka = = 14.51 = 11.6dB (10.9) −2 2 × 9 2 λX fX (8.4 10 )
The third consideration is path loss. Signals with shorter wavelengths spread more in free space. This is represented by re-arranging the Friis transmission equation: [58]
( ) 2 Pr λ = GtGr (10.10) Pt 4πR
Assuming antenna gains G of 1 (unity), this can be rearranged to find the path loss. For microwave signals path loss is how much of the signal is ‘wasted’ because the signal spreads out as the surface of a sphere through space away from the transmitter:
( ) 4πd 2 Path loss = (10.11) λ
Where d is the distance between transmitter and receiver, and λ is the wavelength of the transmitted signal. As λ = c/f for microwaves in free space, the Lpath disadvantage for Ka-band compared to
X-band may be calculated. The loss is proportional to wavelength squared, so Ka-band has a -11.6dB disadvantage compared to X-band for the same transmission distance.
Despite the path loss disadvantage, the gain on the transmit and receive antennas and the solar noise advantages make Ka-band the best compromise between feasibility and noise level.
The frequency and bandwidth choice is somewhat dictated by regulations regarding international frequency allocations. Ofcom, the United Kingdom Office of Communications, publishes a spectrum allocation diagram for terrestrial and space bandwidth use. [167] 31.8GHz to 32.0GHz is available for
“Radio Navigation” and “Space Research”, the latter of which is appropriate. This gives 200MHz, but the bandwidth is also in use by the NASA Kepler mission, and other missions are planned to use it as well. It therefore makes sense to restrict the bandwidth to 50MHz up and 50MHz down, leaving half of the channel bandwidth for other missions. The orbiter cannot receive or transmit for about half of the time, while its view of Earth is obscured by Titan. The 100MHz may be used by other missions during these periods.
The centre frequencies are therefore 31.925GHz and 31.975GHz for uplink and downlink respectively, with both allocated a bandwidth of 50MHz.
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10.2.2 Path loss
Using the path loss calculation (Equation 10.11) for a distance of 1bn km and a carrier frequency of
32GHz gives: ( ) 4π1012 L = 20 log = 302.5dB (10.12) path 10 (3 × 108)/(32 × 109)
10.2.3 Orbiter antenna
The NASA Mars Reconnaissance Orbiter used a 3m parabolic dish High Gain Antenna (HGA) with a gain of 57.9dBi. [204] This figure matches the expected value for a dish:
4πA 4π(πr2) 4π(π(3/2)2) G = effective = = = 1010647 = 60.0dBi (10.13) λ2 (c/f)2 ((3 × 108)/(32 × 109))2
The difference between the predicted 60dBi and the measured 57.9dBi is because Aeffective was treated as a the area of a circle 3m in diameter. In reality, the effective area is slightly smaller because of the curvature of the dish, and losses around the edge of the dish. A TWTA consuming 100W of power is capable of transmitting RF with a power of 16W (see Section 10.5.3). Combined with a 3m diameter dish, this gives an effective Effective Isotropic Radiated Power (EIRP) of
PEIRP = Ptransmitter + Gantenna = 12.0 + 57.9 = 69.9dBW (10.14)
An alternative to a large dish antenna is a phased array of horn antennas. In a phased array there are many small, comparatively low gain antennas, each attached to an independent microwave phase shifter and amplifier. The output of all the amplifiers is then mixed into a single output signal. By manipulating the phase shift value for each of the small antenna, it is possible to make the system appear as a single very high gain antenna, with a steerable focus. This is a huge advantage over a dish
- moving a large dish requires either moving the dish, or rotating the entire orbiter towards Earth.
Ka-band phased array antennas have been demonstrated with an Effective Isotropic Radiated Power of 54dBW. However, they use more than 750W, which is far to inefficient to be justifiable in this mission. The more traditional 3m parabolic dish high gain antenna is therefore the best choice for the orbiter.
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10.2.4 Earth antenna
NASA’s Deep Space Network antennas on Earth are generally dishes with a diameter of 34m. Using the same gain formula as in Equation 10.8, the Earth antenna could have a gain of up to
4πA 4π(π(34/2)2) G = effective = = 129800000 = 81.1dBi (10.15) λ2 ((3 × 108)/(32 × 109))2
The antenna is then 2dBi less effective than predicted (as seen in Section 10.2.3), giving 79dBi.
NASA’s DSS-13 network of antennas are spread across the globe, with sites in the USA, Spain and
Australia.[143] This means that, regardless of the time of day or night, one of the high gain antennas may be pointed at Titan to pick up the orbiter’s transmissions.
10.2.5 Conclusion
The proposed antennas, amplifiers and transmission distances for the orbiter give a received signal power of -103dBW and an SNR of 3dB, across a bandwidth of 50MHz. With these figures specified it is possible to choose a modulation scheme.
10.3 Modulation scheme
Given the available bandwidth of 50MHz and an SNR of 3dB, it is theoretically possible to develop a system to deliver several million bits per second (Mbit/sec).
The Shannon-Hartley theorem allows the maximum bitrate capacity of a channel to be calculated.
[58]
C = B log2(1 + S/R) (10.16)
C is capacity, B is channel bandwidth and S/R is the signal to noise ratio expressed as a fraction. By convention, SNR refers to the signal to noise ratio in decibels. SNR = 10 log10(S/R)
Substituting the values calculated for B and S/R gives
× 6 × 3/10 C = 50 10 log2(1 + 10 ) = 79.1Mbit/sec (10.17)
However, achieving such a high capacity requires extremely good error correction, multiple carriers and aggressive pulse shaping to reduce inter-symbol interference. For example, to achieve 30Mbit/sec
201 Chapter 10. Deep space communications Alex Chadwick in 8MHz of bandwidth, DVB-T (the digital television transmission standard) uses 8192 separate 64-
QAM signals spaced 100kHz apart.[176] Simulating the link and a proposed design for a 16QAM demodulator showed that the maximum sustainable bit-rate is more realistically 1Mbit/second.
10.3.1 Appropriate schemes
There are tens of methods for modulating digital information onto a high frequency carrier. They all involve modulating (or ‘keying’ if discrete levels are used) the phase, amplitude and/or frequency of the carrier wave.
The most basic schemes rely on switching between two states. For example, Frequency Shift Keying uses many frequencies, each representing a specific number. In 2-FSK, two frequencies are used and the modulator enables the lower one to represent a logical 0 and the higher frequency to represent a logical 1. For each bit period, one of the frequencies is transmitted, conveying the data. Amplitude
Shift Keying is similar, except that the frequency is kept constant and the amplitude of the carrier is altered for each bit to be transmitted.
The most simple schemes generally have a low bandwidth efficiency: they convey comparatively little data considering how much bandwidth they use. Modern communications systems therefore use ‘higher order’ modulation schemes that take advantage of orthogonal carriers and multiple levels of phase and amplitude modulation. Three such schemes were considered, and their relative merits are explained below. 16QAM was deemed to be the best, in terms of data rate, power consumption and ease of modulation.
Differential Phase Shift Keying (DPSK)
Phase Shift Keying is a modulation scheme where the carrier’s phase ϕ is manipulated to convey information, while amplitude and frequency remain constant. In Binary PSK there are only two states: a phase shift of ϕ=0 radians, and ϕ=π radians, with each state representing 0 and 1 respectively, although this arrangement is arbitrary. Figure 10.1 shows a binary data stream modulated onto a carrier using BPSK. The carrier in the figure is much lower frequency relative to the bit rate than it would be in a real system so that the phase changes are visible in the plot.
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Input data 1
0.8
0.6
0.4
0.2
0 0 500 1000 1500 2000 2500 Time / us PSK signal 1
0.5
0
−0.5
−1 0 500 1000 1500 2000 2500 Time / us
Figure 10.1: Example PSK signal
A difficultly in demodulating a PSK signal is that there is no reference phase so it is impossible to tell which parts of the signal have ϕ=π radians and which parts have ϕ=0 radians. In order to make detection easier and avoid this ambiguity in phase, Differential PSK can be used. In DPSK, the phase is sampled once every bit period and a change in phase since the last period represents a 1, while no change represents a 0. The change detector is implemented by creating a π phase shifted copy of the signal, then superposing it with the original. When the phase change occurs, the superposed signals are in phase and can be read as a logical one; when there is no change, the superposed signals cancel, reading as a logical zero.
Quadrature Phase Shift Keying (QPSK)
Quadrature PSK is similar to Binary PSK, except that four phase states are used: ϕ = π/4, 3π/4, 5π/4 or 7π/4. Again, phase ambiguity means that differential QPSK is easier to demodulate than straight
QPSK. Because there are four states in QPSK, each transmitted state is referred to as a two bit
“symbol”. In order to achieve the same bit rate as PSK, QPSK only needs half the symbol rate, therefore saving bandwidth. This is demonstrated in Section 10.3.2.
16 level Quadrature Amplitude Modulation (16QAM)
Quadrature Amplitude Modulation uses two orthogonal carriers; by being 90 degrees out of phase with each other, they are in quadrature. This is most easily achieved with a sine wave, I (in phase), and a cosine wave, Q (quadrature phase). The amplitudes of I and Q are modulated at the symbol rate to convey the data. In 16QAM, there are 16 distinct states in the constellation diagram, which
2 gives log2(16) = 4 bits per symbol, and therefore 4/2 = 2 bits each for I and Q. This requires 2 = 4 levels each for I and Q, which can be chosen reasonably arbitrarily, so -3, -1, 1 and 3 are used to
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Figure 10.2: 16QAM square constellation [203] provide a constant distance between each symbol, producing a square constellation diagram, shown in Figure 10.2.
It is possible to choose different coefficients for I and Q that give a circular constellation, with the symbols spaced further apart, potentially making the modulation scheme more robust against noise.
However, the added complexity in modulator and demodulator design does not justify the small noise rejection advantage.
10.3.2 Spectral efficiency
Assuming an IF carrier of 650MHz, three simulations were run to find the bandwidth use of BPSK,
QPSK and 16QAM. The transmitted message was a string of 128 8-bit characters (therefore 1024 bits). Table 10.3 shows the results. 16QAM is clearly the most bandwidth efficient scheme. The power distribution was calculated by taking the Fourier transform of the example signal then summing the squares of the coefficients:
∑ 675 2 ∑ i=625 ci η50MHz = ∞ 2 (10.18) i=−∞ ci
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BPSK QPSK 16QAM
Bit rate / Mbit/sec 10 10 10
Bits/symbol 1 2 4
Symbol rate / MHz 10 5 2.5
% of power within ± 25MHz 96.0 97.8 99.1
Spectrum Fig 10.3 Fig 10.4 Fig 10.5
Table 10.3: Modulation scheme bandwidth use
Single−Sided Amplitude Spectrum of s(t) 0.25
0.2
0.15 |S(f)|
0.1
0.05
0 6.25 6.3 6.35 6.4 6.45 6.5 6.55 6.6 6.65 6.7 6.75 8 Frequency (Hz) x 10
Figure 10.3: PSK spectrum
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Single−Sided Amplitude Spectrum of s(t) 0.25
0.2
0.15 |S(f)|
0.1
0.05
0 6.25 6.3 6.35 6.4 6.45 6.5 6.55 6.6 6.65 6.7 6.75 8 Frequency (Hz) x 10
Figure 10.4: QPSK spectrum
10Mbit/sec, 650MHz 16QAM signal spectrum 1.4
1.2
1
0.8 |S(f)| 0.6
0.4
0.2
0 6.25 6.3 6.35 6.4 6.45 6.5 6.55 6.6 6.65 6.7 6.75 8 Frequency (Hz) x 10
Figure 10.5: 16QAM spectrum
10.3.3 Pulse shaping
To reduce the bandwidth use of a modulation scheme (effectively to ensure that more of the signal power is inside the first harmonic) pulse shaping can be used. Pulse shaping occurs between the symbol generation stage and the modulation stage.
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10.3.4 Bit error rate and noise rejection
Bit error rate (BER) is the proportion of transmitted bits that are expected to be interpreted incor- rectly at the demodulation stage, and depends only on the modulation scheme used and the commu- nication channel’s signal to noise ratio. A worse signal to noise ratio will cause a higher bit error rate.
If the bit error rate exceeds what can be corrected with the error checking and correction system, too many non-recoverable errors occur and the communications system is useless. It is possible to calculate the bit error rate (as a proportion of transmitted bits) for a modulation scheme, based on the signal to noise ratio at the receiver/demodulator.
For PSK systems, the BER is [28] (√ ) 2Eb BERPSK = Q (10.19) N0
Where Eb is the energy per bit (effectively the received signal power divided by the bit rate) and N0 is the noise power in W/Hz. Q is a scaled normal distribution: [28]
( ) 1 x Q(x) = erfc √ (10.20) 2 2
As QPSK systems are effectively two PSK channels superposed, the BER is defined in terms of the
PSK figure: [28]
2 BERQP SK = 1 − (1 − BERPSK ) (10.21)
For QAM with M possible symbols, the symbol error rate (SER) is calculated as Amplitude Shift
Keying for each carrier, then combined: [28]
( ) (√ ) 1 3 Es SERASK = 2 1 − √ Q (10.22) M M − 1 N0
2 SERQAM = 1 − (1 − SERASK ) (10.23)
The conversion between symbol error rate and bit error rate depends on how low the signal to noise ratio is. However, if the QAM constellation is Gray coded, the bit error rate is very close to the symbol error rate. This is intuitive from looking at Figure 10.2; if the signal to noise ratio is good enough that symbols are only misinterpreted as their nearest neighbour in the I or Q direction, there is only one
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Bit Error Rate for QPSK, PSK, 16QAM signals 0 QPSK 16QAM PSK
-5 ) BER ( 10 log
-10
-15 0 5 10 15 20 Eb N0 /dB
Figure 10.6: Bit Error Rate for different modulation schemes bit difference between the correct symbol value and the interpreted symbol value. For lower signal to noise ratios, this approximation is not valid and the BER must be determined by simulation.
Figure 10.6 shows the three BER functions plotted on one graph. However, these BER figures are only in terms of Additive White Gaussian Noise, which means that they only account for thermal and cosmic noise. There are several other types of noise that can effect the system: Shot noise may occur when ionising radiation hits part of the system. This is considered in the simulation in Section 10.4.3.
However, the BER diagram is helpful as a starting point for calculating possible bit rate. For example,
−9 for a bit error rate of 10 , a Eb/N0 ratio of 13dB, 17dB or 18dB is required for QPSK, PSK and 16QAM respectively. This superficially makes QPSK the best choice. However, the SNR is known to be between 3dB and 7dB, where the three modulation schemes give very similar performance. For the same Eb, 16QAM provides double the bitrate of QPSK and four times the bitrate of PSK. 16QAM therefore remains the best choice, assuming that the error checking and correction system can recover from errors occurring at a rate of 10−2. This BER value is only a guideline though; the simulations in Section 10.4.3 show that the system has a BER of much less than 10−3 for an SNR of 3dB.
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10.3.5 Microwave mixing
Trigonometric identities show that
1 sin ω · sin ω = (cos(ω − ω ) − cos(ω + ω )) (10.24) A B 2 A B A B
Therefore, by substituting ωA = 650MHz and ωA + ωB = 31975MHz, it is possible to produce a signal centred about 31.975GHz from a signal centred about 650MHz, as long as ωB = 31325MHz.
The output then requires a band-pass filter to remove the ωB − ωA = 31325MHz signal that is also produced. The specification of a microwave mixer requires three frequencies: the Intermediate
Frequency (IF), the Local Oscillator frequency (LO) and the Radio Frequency (RF). In this case,
IF=650MHz, LO=29775MHz, RF=31075MHz.
10.4 Simulation of modulator/transmitter and receiver/demodula-
tor
To simulate the performance and resilience of the communications system, all of its components were mathematically modelled in MATLAB. First, input data was modulated onto the 650MHz IF carrier, then mixed to 32GHz to produce a transmitted signal. This is the signal that was used to produce the spectra in Section 10.3.2.
Noise, attenuation and a phase error were then introduced to the signal, simulating how it would arrive at the receiver antenna. Finally, a 16QAM demodulator was implemented to test the system’s tolerance for noise.
10.4.1 Transmitter design
Regardless of which modulation scheme is used, a transmitter has the same basic layout, shown in
Figure 10.7. The baseband digital data (complete with packet headers and addressing) is first read into the system. The symbol generation stage adds Forward Error Correction and converts the data into symbols of the correct bit length. As explained in the PSK and QAM sections above, the symbols take integer values between 0 and 2M in a system with symbols of length M. The pulse shaping stage is used to reduce bandwidth consumption, and is explained in Section 10.3.3. The shaped symbols are then modulated according to the modulation scheme (one of PSK, QAM etc), at an intermediate
209 Chapter 10. Deep space communications Alex Chadwick frequency, IF. The IF is set as 650MHz, because this is high enough to cope with the signal bandwidth of 50MHz, yet low enough to be easy to process with digital electronics. The IF signal is then mixed with a microwave signal to provide the correct carrier frequency of 32GHz. Finally, this signal is band pass filtered, then amplified and transmitted.
Parallel data input Symbol Pulse Modulation formation shaping
Microwave Mixer oscillator
Band‐pass filtering
Microwave output Antenna Amplifier
Figure 10.7: General layout for a transmitter
10.4.2 Receiver design
The receiver antenna is discussed in Section 10.2.4. In each of the DSS-13 dishes themselves, there is a
54dB Low Noise Amplifier which boosts incoming signal power to a level that may be processed by the demodulation electronics.[233] Before the signal can be sent to the demodulator, the 32GHz carrier component must be removed by coherent mixing. This leaves the 650MHz intermediate frequency that may be processed by the demodulator.
10.4.3 Demodulation
Demodulation works by reversing the modulation process. The basic layout of the demodulator is shown in Figure 10.8. This was implemented in MATLAB to ensure that it would work, and find out at what noise margin the system would not be able to recover the original data.
Low ADC pass 90° Input Level detector and decoder ~ sin(ωt) Low ADC pass
Figure 10.8: 16QAM demodulator
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Original signal (red) and noisy signal (blue) for SNR=-1dB 40
30
20
10
0
Amplitude / mV -10
-20
-30
-40 0 50 100 150 200 250 300 Time / ns
Figure 10.9
Product detector
When the signal is received at the demodulator, it contains a lot of noise, as well as being modulated about the 650MHz IF. The first stage is to separate the two I and Q carriers out. This can be achieved by multiplying the incoming signal by a local oscillator of the same phase and frequency. As seen in
Section 10.3.5, this will produce a much higher frequency signal (of around 650MHz×2=1.3GHz) and a lower frequency signal, the original I and Q amplitudes.
As an example, Figure 10.9 shows the incoming signal: it features wide bandwidth noise, with an SNR of -1dB, making the original signal unintelligible visually. The original signal is overlayed in red, while the noisy received signal is shown in blue. In the demodulator, this noisy input signal is mixed with a sine wave and a cosine wave of the carrier frequency, then four-pole low pass filtered with ωc=650MHz. The waveform mixed with the sine wave at this stage is then shown in black in Figure 10.10. The
figure shows the I channel amplitudes, but the signal is still very noisy. This is best filtered with a moving average filter. Setting the moving average length to 1/3 of the symbol length gives excellent results, shown in red.
Finally, the filtered signal is auto-scaled to have a peak to peak amplitude of 6 (= 3 - -3) and then quantised to the original levels of -3, -1, 1 and 3. This is done for both the Q and I data. Figure 10.11 shows a plot of Q against I for 1024 example bits, encoded as 256 4-bit symbols. These symbols have not been quantised yet. The diagram serves no purpose in the decoding process, but helps visualise what is happening: the more tightly clustered the dots are about the quantised levels, the less likely an error is to occur. If the noise level were greater, the points in the diagram would be more spread out and would overlap, causing mis-interpretation at the quantising stage and therefore producing
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Signal after first (black) and second (red) stages of filtering for SNR=-1dB 6
4
2
0 Amplitude / mV -2
-4
-6 0 2 4 6 8 10 5 Time / ns x 10
Figure 10.10
Constellation diagram for SNR=-1dB 4
3
2
1
Q 0
-1
-2
-3
-4 -4 -3 -2 -1 0 1 2 3 4 I
Figure 10.11 errors.
Phase errors
As the local 650MHz oscillator in the demodulator is not synchronised with the original 650MHz oscillator at the transmitter, a phase error exists between them. However, correcting for this is relatively straightforward, and can be achieved one of two ways. The first method uses hardware: A
Phase Locked Loop in the demodulator may be used to ensure that the local 650MHz oscillator is at precisely the same phase and frequency as the incoming signal. For the Phase Locked Loop to work, the 650MHz carrier must be strong in the received signal. Considering the spectrum in Figure 10.12, this is not a problem as the 650MHz peak is clearly visible.
The second method is software based. Figure 10.13 shows the decoded signal if there is a phase error of
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Received 16QAM spectrum for SNR=-1dB 0.5
0.45
0.4
0.35
0.3
0.25
Amplitude 0.2
0.15
0.1
0.05
0 6.25 6.3 6.35 6.4 6.45 6.5 6.55 6.6 6.65 6.7 6.75 8 Frequency / Hz x 10
Figure 10.12
Constellation diagram for SNR=-1dB; phase error = π/3 4
3
2
1
Q 0
-1
-2
-3
-4 -4 -3 -2 -1 0 1 2 3 4 I
Figure 10.13
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π/3 radians between the modulator and demodulator oscillators. The constellation is rotated precisely by the phase error. To rotate the constellation back to how it should be, the system need only measure the inclination of the top row, θ, then multiply the matrix of received values by a rotation matrix.
I0 I1 I2 I3 ··· Recieved data D = (10.25) Q0 Q1 Q2 Q3 ···
cos(−θ) − sin(−θ) cos(θ) sin(θ) R = (10.26) sin(−θ) cos(−θ) − sin(θ) cos(θ)
Corrected data = RD (10.27)
The corrected constellation diagram then looks just like Figure 10.11 and may be quantised and decoded without further issue. This system may fail if the received signal were more than 90 degrees out of phase with the local oscillator: the constellation diagram would be incorrect, but look plausible if it were rotated precisely 180 for example. In order to prevent this from happening, the communications specification requires that all messages begin with a string of 128 symbols at (I,Q) = (-3,3), (-3,-3),
(3,-3). This means that there will be no points at (3,3) and the receiver software may rotate the constellation diagram until this is satisfied.
10.5 Hardware and software implementation
For the modulator, transmitter, receiver and demodulator to work in reality, they must be made from real hardware. This section details one possible and feasible implementation of the complete system.
10.5.1 Implementation of the digital stages
Up to the intermediate frequency stage of the transmitter, the system may be implemented digitally.
This helps reduce noise and allows the system to be re-configured easily should the specification change. The Forward Error Coding, pulse shaping and modulation stages may all be performed on an FPGA, or on a general purpose microprocessor. To produce the IF signal, a Digital to Analogue
Converter (DAC) must be used.
FPGA stands for Field Programmable Gate Array. FPGAs are integrated circuits made up of thou- sands (up to hundreds of thousands) of configurable ‘logic cells’ and configurable links between them.
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Figure 10.14: Xilinx Virtex-5Q Logic Cell structure
A logic cell from a Xilinx Virtex-5Q FPGA is shown in Figure 10.14. By configuring the input/output values of the lookup table (LUT) and how the cells are wired together (for example, B in the diagram may be connected to B2 of another cell) it is possible to implement extremely complicated logic func- tions that operate at several hundred MHz. This gives FPGAs an advantage over microprocessors operating at the same clock frequency; a particularly complicated operation that would take a micro- processor several clock cycles to perform may be streamlined into a single operation on an FPGA. The other main advantage that FPGAs offer is that different tasks may be performed in parallel without slowing each other down; the time taken to perform a task is guaranteed.
Both the modulator and demodulator may be implemented digitally. The components required are:
Gray coder, symbol coder, Butterworth low-pass filters, an FFT unit, a moving average filter, mul- tipliers for ‘mixing’ the data with a 650MHz carrier in the digital domain and a sine/cosine look up table. All of these modules may be written in VHDL or Verilog and compiled into a hardware image that can be run on an FPGA. The Xilinx Virtex-5Q series of FPGAs are radiation-hardened, work in extended temperature ranges of -40C to 85C and are certified for space use. This is ideal for the orbiter and the ground station.
Error coding
Error checking and correction systems work by adding redundant bits to the data stream. The redundant bits may be interleaved or appended to packets of data, and are a function of the valid data to be sent. TurboCodes and Low Density Parity Check (LDPC) codes are widely accepted to be the most efficient and reliable error coding schemes available, with comparable performance. For example, 3G/UTMS mobile phone systems use TurboCodes and DVB-S2 (digital video broadcasting
215 Chapter 10. Deep space communications Alex Chadwick for satellite) uses LDPC.
Xilinx provide software libraries (written in VHDL) for both LDPC [101] and TurboCodes [102]. The
LDPC library is more efficient, both in terms of logic usage and operation speed. Given that the two schemes offer similar performance, it makes sense to use the LDPC library.
10.5.2 Mixers
The microwave mixers are as described in Section 10.3.5. At the transmitter, the Spacek Labs M2-33
High Level Upconverter [100] meets the specification perfectly. For the receiver, the Spacek Labs
M32.5 is the Downconverter equivalent and therefore also matches the specification.
10.5.3 Amplification
As explained in Chapter 12.1, Section 12.3, travelling wave tube amplifiers are best suited to microwave amplification. Unfortunately Ka-band TWTA power amplifiers are only around 16% efficient. The power system on the orbiter is only guaranteed to supply 100W, which means a transmit power of
16W, or 12dBW.
10.5.4 Conclusion
Most of the transmitter and receiver may be implemented in digital hardware on FPGAs. The mi- crowave stages only require mixing between the 650MHz IF and the 32GHz carrier, which can be achieved with commercially available mixers. The Earth antennas are the 34m dishes in the NASA
DSS-13 network. The orbiter antenna is a 3m parabolic dish: a design proven on the Mars Recon- naissance mission. All of this hardware is proven and reliable.
Overall, the microwave communications system matches the required specification. It can transmit at
1Mbit/second: a data rate high enough to convey the mission’s data back to Earth faster than the data is created. It does this reliably, even in the presence of high levels of noise.
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10.6 Internal communications
The orbiter contains several different systems, all of which need to communicate with each other. For example, the Titan Imaging system needs to know the current time and position and therefore has to communicate with the navigation system to obtain these numbers. Additionally, the photos and accompanying data need to be sent back to earth via the microwave communications system. An internal communications system is therefore required to allow all of this to happen. The requirements are:
• Support for dozens of nodes
• Peer to peer
• Fast (tens to hundreds of Mbit/sec)
• Well defined error handling and correction
NASA and the ESA use Spacewire, an implementation of IEEE 1355. It is a serial communications network that has been proven to be reliable and appropriate on several missions. It requires signal routers rather than using a bus, but this means that it can operate peer to peer, which is ideal.
The standard supports speeds of up to 200Mbit/sec, which is more than enough for this application.
The Spacewire standard defines communication layers 1 through 4. This includes the physical layer
(electrical levels and signalling), the data link layer (the packet shape, error detection and correction), the network layer (addressing, routing) and the transport layer. Because the standard is so well defined, only the application level protocol for requesting, sending and receiving information needs to be defined.
10.6.1 Internal Protocol
The internal protocol works with requests and responses. Any device on the bus may make a request of another device.
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Microwave Earth link
Request GET status This may be called to see if the microwave
transmitter is ready to accept data to send
to Earth.
Response 200 OK The transmitter is ready to send data
Ready
Response 503 Busy Communications channel busy. xxx is re-
Ready:xxx placed with the POSIX microtime that the
transmitter expects to be free at.
Table 10.4
Clock
Request GET time
Response 200 OK Returns current time. xxx is replaced with
Time:xxx the current POSIX microtime
Table 10.5
Navigation system
Request GET position
Response 200 OK Returns current position. xxx is replaced
Position:xxx yyy zzz aaa bbb with the current POSIX microtime
ccc
Table 10.6
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Navigation Systems
11.1 Introduction
Each of the three units (orbiter, lander and UAV) requires a means of knowing where it is relative to both Titan and the rest of the solar system. During deployment, the lander must be set down at the correct point on the moon’s surface. The lander deploys the UAV as it is descending, which will begin to gather data. Any one datum collected must be accompanied by the current time and relevant coordinates. Hence it will be possible to form records of the way in which data vary as a function of space and time.
Titan’s lack of magnetic field means that there is no easy way of navigating under the dense opaque layer of gases in the moon’s atmosphere. On Earth, one would be able to use a compass to determine one’s position, but on Titan this is impossible due to the lack of a magnetic field. Instead, both the lander and the UAV must rely on the orbiter to calculate their positions, or derive information from the sky. However, it will not be possible to take photographs of sufficient quality through the smog in order to use for navigational purposes. Therefore, the only knowledge the lander or UAV will have of anything more distant than the atmospheric shroud will come from direct communication with the orbiter. Hence the orbiter is the key to all navigation, and it must have an accurate and infallible navigation system.
Additionally, the orbiter will be in a polar orbit around the moon, and may not always be in naviga- tional communication range of either the lander or the UAV, and so it would be ideal if the lander and
UAV were able to work out their positions relative to each other. As long as the UAV is in navigational range of either the orbiter or the lander, it will be aware of where it is around the moon and hence the data collected will be of use. If the UAV were out of touch with both the other units simultaneously,
219 Chapter 11. Navigation Systems Hugo Grimmett the only way it might calculate its position would be by means of taking pictures of the surface below and trying to piece them together, or for the orbiter to locate the UAV optically and overlay location information on to the data retrospectively. Figure 11.1 shows the interactions between the units and their environments. The maximum ranges are taking into account the curvature of Titan as calculated in Section 12.5. It has also been shown that the range of transmission between the lander and the
UAV is too small to be useful for transmitting navigational information.
It is imperative that all three units should have synchronised internal clocks, so that if the navigational information were spread over two distant units, they could be easily reunited using the time label.
.Orbiter
. Max range = 4000km
. .UAV Max range = 3800km .
. Max range = 230km .Lander . .Titan’s surface
Figure 11.1: The flow of information between the three units, and the communication ranges.
11.2 Coordinate Systems
At the heart of every navigation system is a well-defined coordinate system. The units on this mission will require the use of two systems: one which describes the location of celestial bodies in the solar system and surrounding galaxy, and one which accurately defines position relative to Titan. As it happens these systems are very similar, but they must be considered separately.
The celestial coordinate system will be used primarily by the orbiter, and the one best suited to the task is called the equatorial coordinate system. This is usually defined with respect to Earth, because it is used for positioning telescopes and locating stars in the sky. However, since we will be viewing from a position outside Titan, the same set of rules will be used, only they will be defined from the centre of Titan rather than Earth. A direction is defined by two parameters (Figure 11.2): right ascension (RA), and declination (DEC). The declination is defined as the angle North of the equator
220 Chapter 11. Navigation Systems Hugo Grimmett
.DEC= +90◦
.RA= ±12 : 00 : 00 .
.RA= −6 : 00 : 00 . .RA= +6 : 00 : 00 . .RA=DEC= 0
.DEC= −90◦
Figure 11.2: The equatorial coordinate system used for identifying celestial bodies in degrees. North on Titan is the direction in the axis of rotation which points towards the North of the solar system. The right ascension is defined by the angle in sidereal hours (so 24 hours is equivalent to one full 360◦ rotation) from a direction called the vertical equinox or the first point of Aries. This vertical equinox is defined as a line through intersection of the equatorial plane with the orbital plane of Titan around the sun [57].
The coordinate system local to Titan will be the same as that used on Earth, with parameters lat- itude, longitude and altitude. Similarly to the celestial system, longitude is measured by the angle
North relative to the equatorial plane in the range −90◦ ≤ λ ≤ +90◦ (Figure 11.3). Longitude is similar to RA, but rather than being measured in sidereal hours it is measured in degrees about an arbitrary point, which on Earth is the Greenwich observatory in the UK. On Titan, the meridian is the direction towards the centre of Saturn because it is tidally-locked. This tidal-locking results in the same hemisphere on Titan always pointing towards Saturn, as is the case with Earth’s moon.
11.3 Orbiter Navigation
As previously discussed, a reliable navigation system for the orbiter is absolutely imperative for the navigation of the other units.
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.ϕ = +90◦
.λ = ±180◦ .
.λ = −90◦ . .λ = +90◦ . .λ = ϕ = 0◦
. Towards Saturn
.ϕ = −90◦
Figure 11.3: The coordinate system local to Titan for assigning locations to data
11.3.1 Potential Methods and Analysis
Most space-dwelling craft have navigation systems based upon either one, or an amalgamation of the methods listed below:
• Using the sun’s position [12],
• Using electro-magnetic (EM) pulses from Earth to determine position and velocity [147], or
• Taking photographs of celestial bodies and triangulating their location using models of the solar-
system and distant suns [148].
On a trip to the moon, all of these options would be viable. However, Titan is much further away, and itself orbits about Saturn. Since the orbiter is in a polar orbit, the sun will be obscured from view in the order of 50% of the time due to the day-night cycle. The first proposed method will therefore not be considered.
Using EM pulses from Earth
This method requires two pieces of information in order to pinpoint a spacecraft: distance and direc- tion, of which direction is problematic. Usefully, the radial craft velocity can also be determined. A pulse is sent from Earth, and by the time it reaches the orbiter it will have been Doppler shifted by
222 Chapter 11. Navigation Systems Hugo Grimmett the relative velocity between the two. This shift can be quantified by measuring the frequency change and turned into the speed of separation of the orbiter relative to Earth. Earth’s velocity relative to the solar system is known, and so the orbiter’s velocity along the vector joining it to Earth is calculated.
This is useful information, but on its own will not be an accurate navigational tool.
Distance is measured using the same principle as RADAR, whereby an Earth DSN (Deep Space
Network) station antenna immediately re-transmits the received pulse, and so the computers on the orbiter can calculate the time taken for the pulse to travel there and back. Given the speed of light in a vacuum, the distance to Earth can be calculated.
Direction is usually determined using VLBI, or Very Long Baseline Interferometry, which is a two-step process. Firstly two DSN antennas positioned at great distances from each other on Earth receive the pulses from the orbiter and determine the direction by triangulation. Then they very quickly reorientate themselves to point at a distant quasar for which precise locational information is already known. This constant calibration process ensures that the precise timing required to triangulate the direction of the orbiter is accurate [147]. The problem is that at the time of measuring, only
Earth knows the location of the orbiter. Earth could just send that information to the orbiter upon calculation, but due to the distances involved it would take just under an hour to arrive. This is clearly unsatisfactory, and so even though the directional element to this method is useful on Earth, it will not suffice for the orbiter. The distance and velocity calculations however, can be performed in either direction and thus can add precision to another navigational method.
Using an optical navigational method
This process involves taking pictures of areas of space where both short-range (local to the planetary system) and long-range (outside our solar system) celestial bodies are visible. Using an internal model of the bodies in question, the distances between the identified entities on the image can be used to build up the locational information of the observer. One picture will put the observer along a particular vector, and a second will pinpoint their position. Any further pictures will remove error from the previous calculations. This is a useful method because it is implementable anywhere in the planetary system, given a sufficiently large internal model of the photographed bodies. This method has been tested by the Mars Reconnaissance Orbiter (MRO) and has been deemed successful [148]. It was then used on the Cassini mission [145], and so this technology has been tested and deemed successful in a very similar setting. Figure 11.4 shows a photograph taken by the MRO of Deimos, one of Mars’ moons, against a background of distant stars.
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Figure 11.4: A photograph taken by the Mars Reconnaissance Orbiter testing an optical navigation method. [156]
Conclusions
The orbiter should therefore use a combination of the Doppler-shift and optical navigational methods.
This would add a layer of redundancy in case a piece of hardware fails or another problem is encoun- tered (such as the communication with Earth being temporarily cut off). The optical method would be the primary system.
A camera should take photographs of at least two nearby objects (e.g. Rhea and Iapetus, Saturn’s second and third largest moons after Titan respectively) and use the visible background stars to triangulate its location based on a locally-stored model of the bodies in question.
The hardware for receiving and transmitting pulses will already be in place, so adding the software required for calculating Doppler shifts and protocols for carrying out the method is a free way of increasing the amount of information known about the orbiter’s movements. Due to the time required for signals to bounce between Titan and Earth, these readings will be sporadic, but can still be useful.
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11.3.2 Software
In order to make use of the photographs taken, it is necessary to have a locally-stored model of the celestial bodies under scrutiny. The data from the simulation come from an application written by
NASA called “Horizons” [146] which allows the user to choose an observer location and a target location, and the resulting output is the ephemeris in the coordinate system of my choosing. An ephemeris is simply information which allows an observer to know where in the sky a target can be found. This is perfectly adequate for the feasibility tests, but the orbiter would need to have a similar model stored. This is because a one-way communication to Earth takes approximately one hour, so constantly requesting data is not a feasible option. Since the preferred bodies may be obscured for extended periods of time, it would be necessary to work out how extensive the local model needs to be, in order to provide the orbiter with enough reference points for its entire lifetime around Titan.
There are two ways this software could work. One way, which was easier to simulate, is that the orbiter measures the movement of a nearby object (the simulation described here uses Rhea) across a series of photographs to measure the error in the current position estimate. Then either another photograph is taken of a different object, or the size of the original body is used to estimate how far away it is. The second method is to take two or more photographs of short-range and long-range bodies and use the relationship between them to triangulate position as described in Section 11.3.1.
The way this simulation works is that firstly the the orbiter makes an estimate of its current location.
It then consults the mathematical model and works out where certain nearby bodies should be visible.
The orbiter moves its camera to point in the predicted direction and takes a picture. If the body is not in the image, it moves the camera in a spiral fashion and repeats the step. If the body is visible, it calculates the error between where it thought it would lie on the picture, and where it actually was.
Using this error and the angles between the short-distance body and the very distant background stars, it calculates a new estimate of its current position. This process (which is represented in Figure 11.5) is continually repeated throughout the life of the orbiter. If the usually selected bodies are obscured or a greater accuracy is required, the orbiter will choose additional visible moons to navigate from.
Part of this process has been simulated, firstly by using the output of the NASA ephemeris web page
[146] to generate an ephemeris with the following parameters:
Target body name: Rhea (605) {source: SAT317}
Center body name: Titan (606) {source: SAT317}
Start time : A.D. 2010-Jan-25 00:00:00.0000 UT
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. Generate . . Take photo- Triangulate new ephemeris . . . . graph in desired . location estimate . . for current direction from image location estimate
. . Update current . location estimate
Figure 11.5: Navigation process flowchart.
Stop time : A.D. 2010-Feb-25 00:00:00.0000 UT
Step-size : 60 minutes
Target pole/equ : IAU_RHEA {East-longitude -}
Target radii : 767.2 x 762.5 x 763.1 km {Equator, meridian, pole}
Center geodetic : 0.00000000,0.00000000,0.0000000 {E-lon(deg),Lat(deg),Alt(km)}
Center cylindric: 0.00000000,2575.00000,0.0000000 {E-lon(deg),Dxy(km),Dz(km)}
Center pole/equ : IAU_TITAN {East-longitude -}
This request results in a lot of information about the two chosen bodies: one observation per hour for a month. The most important details for the navigation system are the right ascension and declination coordinates, and the distance (δ) for the centre of Rhea relative to the centre of Titan. There are other details such as apparent sun brightness and whether the target body is actually visible. Using a
MATLAB script (see Appendix E), Rhea’s movement relative to the centre of Titan has been plotted in Figure 11.6. This is merely to test the viability of the method. The orbiter would be generating the ephemeris using the latest estimate of its current position as the observer location (in Lat/Lon/Alt coordinates), rather than from the centre of the moon as the simulation does.
Figure 11.6 shows that relative to Titan, Rhea will perform approximately two rotations per month.
It also shows that the distance between the two fluctuates a considerable amount, and therefore measuring the size of Rhea on the image could be a viable option for determining the observed distance. If this turns out to be unrealistic, then the orbiter should take a photograph of different objects in order to gain more information to tie into the local model.
226 Chapter 11. Navigation Systems Hugo Grimmett
Figure 11.6: Plotting Rhea relative to the centre of Titan over 30 days.
11.3.3 Hardware
The orbiter will need the following minimum components in order for the navigation system to function:
• A camera,
• An accurate tilt and pan mechanism on which to mount the camera,
• Internal memory on which to store data from which the ephemerides are generated, and
• A CPU capable of performing all the necessary calculations in real-time.
The camera will be taking pictures of objects at various distances. The picture could be used to estimate their distance from the orbiter by using the apparent size on the image and their true size.
For example, Saturn’s moon Rhea ranges from approximately 0.005 to 0.01 AU (see Figure 11.6).
Therefore the apparent change in size of Rhea on the image would also vary enough to lead to a useful calculation. The diameter of Rhea is approximately 1.5 × 103km, so without a zoom would appear minuscule on any image taken. Hence an appropriate lens focal length would have to be calculated for this to be made possible.
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11.4 UAV and Lander Navigation
The UAV will be collecting the majority of the data during the mission. It is the most mobile, and so will take readings of temperature, radiation, wind speed (amongst other things, see Section 9.2), and take pictures along its entire trajectory. The data collected will be useless without knowing their origins, and so it is of great importance that a reliable navigation system is in place. If the UAV is sure that there is no way of its location being known with sufficient accuracy, it should pause data-collection in order to conserve energy.
By definition, once the lander has arrived on Titan, it will be stationary and will not require any further navigational services. It will also not be able to communicate with the UAV over distances of further than 230km (see Section 12.5). Hence I have investigated alternative means of lander to UAV navigation, and more importantly the ways in which the orbiter can aid the UAV navigation.
11.4.1 Potential Methods and Analysis
In order to maximise the proportion of time for which the UAV knows where it is relative to Titan, it is important to explore every possible avenue when it comes to navigation systems. The navigation system must fulfill the following criteria:
• The system must be robust and reliable in Titan’s atmosphere and high winds,
• It must work by using only the lander and/or the orbiter, no more beacons may be used,
• The range must be large enough to allow the UAV to explore a significant portion of Titan’s
surface, and
• The error should be small (e.g. within 100m).
It would also be convenient if the required hardware were able to double up as required communication hardware, but this is not a necessity. These criteria limit the system to using only a few methods of calculating the UAV’s location, and these are listed below:
• EM communication with the lander, where a signal-based beacon from the lander is used,
• EM communication with the orbiter, a long range signal-based beacon,
• Optical navigation from the orbiter, using a photographic method via the orbiter, or
• Optical navigation from the UAV itself.
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EM communication with the lander or orbiter
There are many already well-established systems for EM navigation used on Earth, all of which should theoretically work in the same way on Titan. However, many of these require a minimum number of base stations in order to function. LORAN (or LOng RAnge Navigation) for example, has a maximum range of approximately 650-2000km which would be ideal, but it requires at least one master station and 2 or more slave stations [198]. Another such system is DECCA. Currently this mission to Titan is limited to the only orbiter and lander for emitting navigational signals, which greatly reduces the number of potential methods. If more investigation were done, it could be feasible to let the UAV drop extra beacons and widen the navigation range, but in this report it has been assumed that this is not an option.
There are a few systems which only require one emitter to pinpoint local position, and these work by calculating two things: the direction the wave was sent from, and how far away it was. By using this polar coordinate system, 2D navigation is achieved. The range is determined by calculating the length of time taken for the wave to propagate between the emitter and receiver, and the bearing by using the phase of the wave. By rotating the transmitter, the wave phase (0 − 360 ◦) corresponds to a compass bearing, and so on a circle of radius r each phase gives a precise direction.
One particular system used for aircraft navigation on Earth is called TACAN (or TACtical Air Nav- igation). Both the bearing and distance are calculated using the same wave, which conventionally is a 15Hz AM wave transmitted from an antenna mounted on a shaft rotating at 900rpm. This is, however, a short-range system with an accuracy of ±1 ◦ over 3.5km [17]. This is much too short for what is required, since the orbiter will be a minimum of 2000km away and otherwise the UAV would have to stay in very close proximity to the lander, which of course is unacceptable.
Optical navigation from the orbiter
An additional method by which the UAV position can be calculated is optically from the orbiter.
The orbiter is equipped with a camera pointing towards Titan which uses a particular wavelength of
938nm, allowing it to see through the otherwise opaque atmosphere (see Section 13.5.1). If the UAV can be seen on an image then its location can be narrowed down to a single line joining the orbiter to a point on Titan’s surface. With another piece of information about the UAV’s whereabouts, such as its altitude, it is possible to pinpoint it in space (as seen in Figure 11.7). Many types of LASER can emit light at 938nm, so it would be easy to connect one of these to the UAV with a diffuser in order for it to act as a beacon. This would cause it to show brightly on on a photograph taken by the
229 Chapter 11. Navigation Systems Hugo Grimmett
.Orbiter
.Line of projection derived from image
.
.UAV
.
.Altitude
. . . .Titan’s surface
Figure 11.7: Pinpointing UAV position from an image and an altitude reading. orbiter.
The way in which the UAV altitude is calculated is visualised in Figure 11.8. The way this works is that an ultrasound emitter attached to the bottom of the basket pointing downwards sends a signal containing a few ∼ 1ms-wide pulses towards the surface. Simultaneously, an internal clock starts counting. The pulse train will partially reflect off the ground, and be scattered in all directions. Some of this scattered signal will make its way back up and be detected by the ultrasound receiver. At this moment, the internal clock is stopped and a calculation (see Equation 11.1) is done to calculate the distance. There may be several echoes picked up, but the first detected echo must have taken the shortest path, and therefore will lead to the closest true altitude.
T Altitude = echo × c (11.1) 2 where c is the speed of the wave through the atmosphere, which can be approximated to the speed of sound (300ms−1).
Optical navigation from the UAV
Since the UAV is equipped with a camera to take pictures of the surface, it is possible for the UAV to calculate relative positions by stitching the images together and noting how the landmarks below it are changing. This is not a precise system, because small errors in stitching a linear sequence of photographs together compound, and the overall error will grow with distance travelled. However, it might give enough locational information for it to be worth taking data on the surroundings. In
230 Chapter 11. Navigation Systems Hugo Grimmett
.UAV
.Ultrasound emitter .Receiver .
.Outward path .Echo path
.Titan’s surface
Figure 11.8: UAV altitude sensing system using ultrasound order to do this in real-time, the UAV would require a computer capable of doing the image analysis, which would be a significant power drain. Fortunately this is not necessary; with the images taken, a computer either on the orbiter or most likely on Earth could overlay these small photographs onto a much larger picture taken by the orbiter to calculate the true path taken by the orbiter, as seen in
Figure 11.9. Similar mapping technology is being researched currently at Oxford University by Dr.
Paul Newman and his research group [199].
Hardware
The hardware required on board the UAV for the navigation processes is as follows:
• A processor capable of handling requests for data and organising storage,
• A camera (pointing downwards),
• Memory to store images and data between transmission periods,
• A 938nm laser with a diffuser,
• An ultrasound range-module pointing downwards.
In order to estimate how much memory the UAV will require, some assumptions need to be made.
Suppose it is equipped with a 10M pixel camera, and needs to be able to distinguish objects which are
231 Chapter 11. Navigation Systems Hugo Grimmett
.x .x .x .o . .x .o .o .o .o .o .Image 1 .Image 2 .Image 3
.x .x .o .o .o
.o
.Deduced map and path
Figure 11.9: Stitching together overlapping images by identifying landmarks and calculating observer trajectory. larger than 1m. This maps to 1 pixel per square metre of ground below. A square 10M pixel sensor is 3162 × 3162 pixels, which maps to just over a 3km square. Assuming that a 10% overlap would be required to stitch images together, the UAV would have to take a picture every 0.9 × 3162 ≃ 2850 metres of lateral movement. The UAV moves at approximately 1ms−1, so a picture would have to be taken every 50 minutes. An uncompressed 10M pixel colour image would be about 30MB, but with a
JPEG2000 compression of approximately 30 : 1 it could be reduced to 1MB.
This raises the question of exactly for how long the UAV will be out of navigational range, which depends strongly on where it is on Titan. The orbiter will be mapping the moon in a polar orbit
(see Section 13.5.4 for details) and slowly processing in circles around the equator. The time between orbiter-passes is greatest at the equator, and smallest at the poles. One orbiter orbit takes 5.8 hours, and there are approximately 33 orbits before it covers the whole moon. Therefore if the UAV were to stay stationary, the longest it would have to go without the orbiter passing directly over it would be
8 days.
During this time the UAV would have to take 230 images continuously, amounting to 230MB of data.
On Earth this is a trivial amount of storage, but since any equipment taken to Titan would have to be radiation-hardened, memory becomes much more bulky, expensive, and unreliable. 230MB is not an unreasonable quantity of data, however, so this method is indeed feasible.
232 Chapter 11. Navigation Systems Hugo Grimmett
11.4.2 Conclusions
Seeing as it is currently impossible to use more than two base-stations with EM navigation (although that option should be further investigated), none of the systems mentioned are sufficient on their own. Together however, there will be a greater proportion of time for which the UAV will be in
‘navigational range’ of the other two units, and at best there will be a welcome amount of redundancy in the readings gathered. The TACAN system has much too short a range, and so it is not worth adding the bulky and power-hungry hardware to the lander. Instead, both optical methods will be used together. It has been shown that the UAV would be able to store all the pictures taken during this period of time, and that some degree of navigation will be possible at all times on Titan.
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Titanic Communication Systems
12.1 Overview of UAV, Lander and Orbiter Communication
This part of the report deals with the internal communication systems between the three units, which are vital in order to supply the orbiter with the necessary information to send back to Earth. Since there are three channels and three different sets of hardware, the maximum range of each channel will be calculated separately.
The three communication channels that must be considered are the orbiter to lander, orbiter to UAV, and UAV to lander. Before determining the range, it is necessary to choose a type of amplifier to use, and estimate the likely sizes of the antennas on each unit.
The protocols used for the data collected to be sent between the three units is described in Section
10.6.1.
12.2 Antennas
Seeing as the orbiter and the lander are unimpeded by heavy objects, it would be beneficial for them to make use of parabolic high gain antennas (HGAs) to extend their communication ranges.
The UAV, however, will be moving in too erratic a way to be able to point a HGA at its desired target with sufficient accuracy. This means that the UAV will have to be equipped with an array of omnidirectional (or isotropic) antennas instead. Fortunately, if it is calculated that a communication system will function when transmitted by the orbiter and received by the UAV, the law of reciprocity states that the inverse will also work, and that the UAV will be able to emit signals that the orbiter can detect.
234 Chapter 12. Titanic Communication Systems Hugo Grimmett
Most space craft use X-band communication, which is the range of 8 to 12GHz. This is because it combines the advantages of using a high frequency such as increased data-rate, and means that the antennas required are compact. An average value of 10GHz will be used for all the calculations in this section.
It is also assumed that the UAV will have an isotropic antenna, but in reality this will be an array of three dipole antennas at 60◦ to each other. The size of a dipole antenna is usually half the characteristic wavelength [177], which in this case equates to
c λ = (12.1) f 3 × 108 = 1010 = 0.03m (12.2)
∴ Lantenna = 1.5cm. (12.3)
A 1.5cm antenna is perfect because it is not difficult to manufacture (and so is inexpensive), and simultaneously will not be bulky or heavy. Unfortunately as shown in Section 12.5, path loss is proportional to f 2, and so this high frequency has a disadvantage. However, as the range calculations will show, this is not the dominating factor and so it is reasonable that all internal communications should make use of this frequency.
The gain of an antenna is calculated using the following equation [200][163],
( ) µ · 4π · A Gain = 10 × log effective (12.4) dB λ2 where µ is the efficiency, typically ∼ 0.55. Judging by past missions into the solar system, a reasonable estimate of orbiter dish size is 1m, which gives in an effective area of approximately 0.80m2. The lander
HGA will have to be more compact because it must be able to fold up and survive entry through the atmosphere. It will therefore be assumed that the lander will carry a dish with a diameter in the order of 0.4m, giving it an effective area of 0.13m2. The wavelength at 10GHz has already been calculated to be 0.03m (see Equation 12.2). Therefore,
Orbiter HGA Gain = 43.8dB (12.5)
Lander HGA Gain = 35.9dB. (12.6)
These figures will be very useful when calculating the maximum range of the communication channels
235 Chapter 12. Titanic Communication Systems Hugo Grimmett
Amplifier TWTA: Bosch [26] TWTA: Tesat [202] SSPA: Mars Rover [133] Power in (W) 240 70 17 Dimensions (dm3) 1.0 3.6 1.0 Mass (kg) 4.6 3.5 1.4 Efficiency (%) 60 64 30 Lifetime (years) > 15 > 15 7 − 10
Table 12.1: Comparing types of amplifier. between the three units.
12.3 Amplifiers
There are two different technologies which result in the amplification of a signal, and they are solid state power amplifiers (SSPA) and tube amplifiers. The main type of tube amplifier is called a travelling wave tube amplifier (TWTA). Table 12.1 shows a comparison of three different amplifiers, two TWTAs and a SSPA. The reason for which there are two is that TWTAs come in a much wider variety of amplification power, and so I have chosen both a low power and a high power amplifier to compare to the solid state device. It is difficult to find detailed information even on commercially- available amplifiers because they are often custom-made to a required specification. This results in many companies giving wide ranges of values for amplifier power and very limited data on gains. It has been remarked that TWTAs have lower failure rates [206], and since X-band and Ka-band are both being used for the mission, the wide frequency range for which TWTAs are available is clearly beneficial. Table 12.1 shows that although SSPAs are lighter, their more expensive counterparts are more powerful, more efficient, and last a longer time. Even though they are slightly heavier, the difference is not large enough to detract from the other benefits that TWTAs bring. All three units should be equipped with two TWTAs: a master and a back up device.
12.4 Noise
It is important to calculate the noise temperature of the antennas, and to predict whether it will be an issue for the system. Background cosmic radiation is often a potential issue with satellite communications, but that tends to be mainly when using frequencies of under 1GHz, which is not the case here.
There are four potential sources of noise with the systems, and those are the amplifier and antenna at each end of the communication link. One standard way to estimate noise power is using noise
236 Chapter 12. Titanic Communication Systems Hugo Grimmett temperature.
Nantenna = kTnB (12.7) where k is the Boltzmann constant, Tn is the noise temperature and B is the bandwidth. It is difficult to find information on typical noise temperatures for the TWTAs used in space, so further analysis is required to obtain concrete data. If the observed noise power were too large, the transmitter could boost the signal power until it were no longer a problem.
12.5 Range of Transmission
The goal is now to calculate the maximum ranges of the three communication channels. The power available to the lander in total is 65W, so approximately 50W can be used for communications.
The orbiter’s communications with Earth uses approximately 100W, and so while it is not using this channel, this power could be diverted to the local communication system. The UAV will have approximately 80W of transmitting power. A typical mobile phone is capable of receiving signals in the order of −100dBW, which is equivalent to about 0.1pW. This is the value for which the signal power is sufficiently larger than the noise in order to differentiate and extract it, and what will be used as a minimum received power for all three units. It is assumed that all the supplied power will be transmitted as a wave.
Path loss is proportional to the amount that the signal has been attenuated, and is measured in
Decibels. It is defined in [187] as
Path lossdB = −27.6 + 20 × log(f) + 20 × log(d) (12.8)
= 52.4 + 20 × log(d) (12.9) where f is the frequency in MHz taken to be 104, and d is the distance in m. This loss can be reduced by including the gains of the antennas Gantenna at either end of the channel. The UAV’s isotropic antenna has a gain of 0dB by definition. Adding this in and rearranging, the maximum transmittable distance in terms of the total system loss becomes
dmax = 10A (12.10)
where A = (−52.4 + Path loss + Gantenna)/20. (12.11)
Under the assumption that all receiver powers are the same, we can calculate the maximum allowable
237 Chapter 12. Titanic Communication Systems Hugo Grimmett signal attenuation for each unit separately:
( ) P − × receiver Max lossdB = 10 log , (12.12) Ptransmitter where the powers are in Watts. Using the maximum transmission power for each unit, it follows that the maximum allowable path losses are
Max lossdB from orbiter = 150 (12.13)
Max lossdB from lander = 147 (12.14)
Max lossdB from UAV = 149. (12.15)
In space, electromagnetic waves emitted by an isotropic antenna are attenuated by a factor propor- tional to the reciprocal of the distance away from the antenna squared. In a dense atmosphere such as Earth’s or Titan’s, that attenuation can increase at an even greater rate. Although Titan’s atmo- sphere is 1.5bar, the atmospheric attenuation will be very similar to that of Earth’s and will even lack losses caused by signal absorption in water droplets. Therefore, these differences have been neglected in the following calculations. Equation 12.9 will be used to calculate the maximum two-way transmis- sion distance for each channel separately. The minimum allowable path loss is used for each channel.
Therefore,
dmax for orbiter ↔ UAV = 10, 500km (12.16)
dmax for orbiter ↔ lander = 650, 000km (12.17)
dmax for lander ↔ UAV = 4, 200km. (12.18)
These are the maximum range values, and Figure 12.1 shows the transmitter power required for a range of distances on log axes.
Line of Sight Limitations
Communications at such a high frequency work as long as there is line of sight between the emitter and the receiver. The radius of Titan is 2575km [154] and the altitudes of the orbiter and UAV are
2000km and 10km respectively. Using Pythagoras’ theorem, we can calculate that the maximum line
238 Chapter 12. Titanic Communication Systems Hugo Grimmett
Figure 12.1: The power required for the three two-way communication channels over distance.
of sight smax for each channel is
smax for orbiter ↔ UAV = 4, 000km (12.19)
smax for orbiter ↔ lander = 3, 800km (12.20)
smax for lander ↔ UAV = 230km. (12.21)
This means that the maximum line of sight is the limiting factor for all three channels, and so it would be useful to calculate the theoretical maximum transmission powers required to travel these distances.
By back-calculating with a these maximum distances, the following transmission powers are required:
↔ Ptransmitter for orbiter UAV = 11.5W (12.22) ↔ Ptransmitter for orbiter lander = 2.7mW (12.23) ↔ Ptransmitter for lander UAV = 236mW. (12.24)
These figures, particularly for the lander power, are tiny. This would mean that less power would have to be allocated to local communications, and perhaps could result in a longer life or lighter payload for all three units. It is important to bear in mind that these figures hold under the assumption that transmission only works within direct line of sight, when in fact there can be slight curvature in the
239 Chapter 12. Titanic Communication Systems Hugo Grimmett channels. The theoretical and line-of-sight maxima have been overlaid onto the plot in Figure 12.1.
12.6 Conclusions
It has been shown that with the use of one HGA and one isotropic antenna that the maximum communication ranges for the orbiter ↔ UAV and orbiter ↔ lander channels are in the order of
4000km, and that the noise is likely to be negligible. Unfortunately, the lander ↔ UAV channel has such a limited range that it will be practically useless once the UAV has drifted away from its launch site. The line-of-sight estimations give an approximate lower bound on transmission power required of 11.5W for the orbiter and UAV, and 2.7mW for the lander. If the UAV were to go above the height estimate of 10km, its maximum range and hence necessary power would increase accordingly.
A long range communication system is required for the optical navigation methods laid out in Chapter
11. The viability of this communication system therefore reinforces the strengths and viability of the local navigation systems.
240 CHAPTER 13 - Jack Andrews
Imaging Systems
13.1 Introduction
The surface of Titan remained shrouded by an almost impenetrable atmosphere for many years. It was not until 2005 that the first direct images of the surface were obtained by NASA’s Huygens probe. This chapter proposes the design of new imaging systems to build upon the success of the
Cassini-Huygens mission.
The aim is to acquire a high quality map of the entire surface of Titan along with detailed photographs of surface features such as methane lakes, rock formation and soil. This will allow scientific analysis of these features to be carried out, providing a better understanding of Titan’s climate and geology.
It is beyond the scope of this report to provide a detailed design of the proposed systems. Much of the work presented will address problems the imaging systems will face and ways of addressing them in an optimal fashion. Emphasis has been placed on justifying the specifications suggested. Further work would be required to take these design specifications and produce a working system.
13.2 Systems Overview
13.2.1 The Three Imaging Systems
Three separate imaging systems have been designed. Table 13.1 summarises the location and task of each system. In order to simplify the design process, a base system was created and duplicated across each platform. Additional features were then added to this base so that each system can perform its task.
241 Chapter 13. Imaging Systems Jack Andrews
Platform Task Orbiter Map entire surface of Titan from above the atmosphere. UAV Acquire higher quality photographs of sur- face features. Lander Acquire photographs of features such as rocks and soil next to the landing site.
Table 13.1: The imaging systems and their tasks.
13.2.2 System Specialisations
The specialisations required for each imaging system will be discussed in greater detail in subsequent sections. Table 13.2 gives a brief overview of the additional features required so that each system can perform its task.
Orbiter UAV Lander Lens filter Lens filter Lamp (section 13.5.1) (section 13.6.2) (section 13.4.2) Infinity focus Infinity focus Auto focus (section 13.5.2) (section 13.6.1) (section 13.4.3) Mapping algorithm Controllable camera mounting (section 13.5.4) (section 13.4.1)
Table 13.2: Specific specialisations required for each imaging system.
13.3 Base Imaging System
The base system is common to each platform. It performs the tasks which are required by each imaging system, which are as follows:
• Image capture
• Image compression
• Image storage
• Image transmission
This section will now describe the design and specifications of the base system.
242 Chapter 13. Imaging Systems Jack Andrews
13.3.1 CCD Sensor
A charge-coupled device (CCD) will be used to capture images. CMOS active pixel-sensors are a viable alternative, but CCD is a more mature technology and hence more robust. To obtain the best possible image quality, the highest available CCD resolution will be used. A 49 megapixel (7032×7032 pixels)
CCD was chosen. This represents the best technology available before reaching highly specialised, and thus expensive, devices.
13.3.2 Computer Hardware
All computational tasks for the imaging systems, including specialisations, will be performed in soft- ware using a microprocessor. In some cases improved power efficiency and reduced processing time could be achieved with the use of application-specific integrated circuits (ASICs). However, it has been decided to perform all tasks in software for several reasons. There is no open-source VHDL available for complicated algorithms such as PNG or JPEG2000 compression (described in section
13.3.4). Commercial designs which do exist are expensive and do not encode to the high resolutions required. It is beyond the scope of this project to produce such code from scratch and so if an ASIC system was proposed, it would be purely hypothetical. No quantification of its performance could therefore be made. Using a microprocessor based system also opens up a wealth of freely available open source code which can be used. This has allowed the performance of the system to be estimated.
The Proton400k™[99] computer designed by Space Micro Inc. has been chosen as the base system processor. Table 13.3 shows the relevant specifications. The Proton400k™was chosen due to its combination of high processing power and ‘commercial space grade’ radiation hardening. As will be shown in section 13.3.4, processor intensive algorithms have been chosen which require a powerful processor to execute in a reasonable amount of time. The extensive built–in radiation hardening of the Proton400k™solves the issues of the radiation based errors such that their effect can be ignored during the design of the imaging systems.
Comparison of the Proton400k™with the test machine
A comparison needs to be made between the processing power of the Proton400k™and the test machine used to throughout the project. This will allow estimates of the implemented algorithm’s performance on the Proton400k™to be made without physical access to it. The processing power of the Pro- ton400k™is given as 7200 DMIPS, which equates to 3600 DMIPS per core. DMIPS refers to the
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Processor Clock 1.5GHz Cores 2 Speed 7200 DMIPS Radiation protection TTMR, H-Core, TMR, Hamming Code EDAC and Time redundancy Volatile memory SDRAM 512MB RAM error detection Hamming Code RAM error correction 8 bit data, 8 bit check Non-volatile memory Flash 512MB Access speed 64Mbps Radiation protection SEU (all single bit errors corrected), SEFI (No SEFI or block errors), TID (>100 krad)
Table 13.3: Specifications of the Proton400k™used in the image processing module [99].
Dhrystone Million of Instructions Per Second benchmark[226]. This benchmark is used to make a rough comparison between different processors.
The test machine used has a 2.8GHz Intel®Core™2 Duo processor. The Dhrystone “C” benchmark
[124] measured its performance as 9210 DMIPS per core. This means the test processor is roughly 2.6 times faster than the Proton400k™.
This comparison of performance must be used carefully. The Proton400k™uses the PowerPC (RISC) architecture whereas the Core™2 Duo uses the x86 (CISC) architecture. The two architectures use completely different design philosophies (RISC vs. CISC) which makes comparison difficult. This, combined with the fact that the Dhrystone benchmark does not take modern compiler optimisations into account, makes the comparison highly tenuous. It is however the best approximation that can be made given the limited information. A high factor of safety will therefore be employed in all calculations that use this comparison.
13.3.3 Operating System
VxWorks [3] was chosen as the operating system to use on the base system computer. VxWorks is a real time operating system (RTOS). An RTOS is required as it serves application requests at near real time, allowing tighter control over process priorities than a standard operating system. As will be shown in section 13.5, timing is an important constraint on the operation of some of the algorithms used. VxWorks is the most mature and tested RTOS available. It has been used in several NASA missions including the Phoenix Mars Lander. It is therefore a proven technology and well suited to the base system requirements.
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13.3.4 Image Compression
Data transmission from Titan to Earth is a complex problem due to the distance involved. As such, an important requirement for the imaging system is compression. The aim is to significantly reduce the amount of data being transmitted back to Earth. This will reduce the time, and hence power, required to transmit images back to Earth. However, this comes at the cost of power being used to encode the images.
Two forms of image compression are employed. Lossless image compression allows the original image to be reconstructed on reception. This is useful if a high detail and high accuracy image is required for scientific measurement. Lossy image compression removes data from the signal which the human eye cannot detect. This means that the original image cannot be reconstructed, but the image will look much like the original.
Lossless Image Compression
The performance of three lossless compression algorithms were compared. 500 lossless images taken of Titan during the Cassini-Huygens mission [160] were used as a test data set, as these represented images similar to those that our mission will be capturing. NASA data accompanying the images also recorded the Huffman compression ratio achieved and is used as a benchmark. These test images were processed using two other common algorithms: Deflate and PNG. Deflate and Huffman compression are multipurpose algorithms which can be used on any data, whilst PNG is designed specifically for images. The averaged encoding times and compression ratios achieved of all 500 images are presented in table 13.4. Encoding times were calculated on the test machine and estimated for the
Proton400k™. Relative power consumption was based on 15W power usage of the Proton400k™[99] and 100W consumption for 1Mbit/s transmission (see section 10.5.3).
Algorithm Compression Ratio Encoding Time (s) Total power consumption (relative to Huffman) Huffman 3.71 5.1 1 Deflate 4.2 9.7 0.94 PNG 5.53 14.6 0.81
Table 13.4: Comparison of three lossless image compression schemes.
Whilst PNG takes the longest to encode, the saving in transmission power outweighs the cost of en- coding. It is for this reason PNG compression was chosen as the lossless image compression algorithm.
245 If we just consider PSNR to compare JPEG and JPEG2000, which is shown in Figure 10, we find JPEG2000 to be a better encoder than JPEG for all compression ratios. This confirms again that the MOS prediction by Image Optimacy is a better indicator of image quality than PSNR.
55 JPEG JPEG2000 50
45
Chapter 13. Imaging Systems40 Jack Andrews
Average PSNR [dB] 35 Lossy Image Compression
30 Choosing a lossy algorithm is slightly more involved. The choice becomes more subjective due to the fact that information is25 being lost in the compression process. To simplify the task of choosing between 0 20 40 60 80 100 many potential algorithms, two popular, matureCompression algorithms ratio were picked and the choice made between them. These wereFigure JPEG 10. Average and JPEG2000. PSNR as a function JPEG of is compression ubiquitous, ratio withfor JPEG widespread and JPEG2000. use throughout the internetThe average and consumer blockiness cameras. and the Itaverage was designed blur are inshown 1992 as and a function was used of to the compress compression images ratio in in the Figure Cassini 11. As expected, the JPEG2000 encoder produces a lot of blur but virtually no blockiness, while for JPEG-encoded imagesImaging blockiness Science is Subsystem. the main artifact. JPEG2000 This is was in line released with the in encoder-specific 2000 and provides compression numerous algorithms enhancements (wavelets vs. block-based DCT) and demonstrates the correct responses of the two artifact metrics. over JPEG.
70 35 JPEG JPEG JPEG2000 JPEG2000 60 30
50 25
40 20
30 Blur [%] 15 Blockiness [%] 20 10
10 5
0 0 0 20 40 60 80 100 0 20 40 60 80 100 Compression ratio Compression ratio
(a) Blockiness (b) Blur
Figure 13.1:Figure Average 11. Average blockiness blockiness (a) (a) and and blur blur (b) as (b) a function as a function of compression of compression ratio for JPEG and ratio JPEG2000. for JPEG and JPEG2000 [60].
The underlying encoding mechanism in JPEG is applying the Discrete Cosine Transform (DCT) to
8×8 pixel blocks. Certain frequencies are less apparent to the human eye. The accuracy (and hence bits required) of the binary representation of these frequencies found in each block is then reduced.
At high compression ratios this results in ‘blockiness’ of the image at the boundaries of the 8×8 pixel block [192]. Research done into the perceived blockiness of JPEG and JPEG2000 images can be seen in figure 13.1.
JPEG2000 uses wavelet transforms instead of the DCT, but removes frequencies in an analogous way.
It can also be applied to much larger blocks than 8×8, up to the full size of the image. At low compression ratios JPEG2000 has blurred, instead of blocky, edges. JPEG2000 has a final encoding algorithm which breaks the data stream into progressive chunks. If a chuck is lost when transmitted, the area represented by the chunk has reduced quality, but the overall picture is not lost [42].
Research comparing the performance of the two algorithms was used. The first test was an objective
246 Chapter 13. Imaging Systems Jack Andrews
5 55 JPEG JPEG JPEG2000 JPEG2000 50 4.5
45 4
40
Average MOS 3.5
Average PSNR [dB] 35
3 30
2.5 25 0 20 40 60 80 100 0 20 40 60 80 100 Compression ratio Compression ratio (a) Average Mos (b) Average PSNR.
Figure 13.2: (a) Average MOS predictions as a function of compression ratio for JPEG and JPEG2000 [60]. (b) Average PSNR as a function of compression ratio for JPEG and JPEG2000 [60]. test: measuring the peak-signal-to-noise-ratio (PSNR) of the two algorithms. This is a measure of how well the compressed image reproduces the original image. It is purely a fidelity test and does not measure how well the image is perceived by the viewer. Figure 13.2 shows JPEG2000 outperforms
JPEG in this test at all compression ratios.
The second test was subjective: the Mean Opinion Score (MOS). Humans vote on the perceived quality of the image, rating the quality from 1 to 5. The results in figure 13.2 show that JPEG2000 out performs JPEG at compression ratios of greater than 20:1, but that JPEG has a higher MOS at lower ratios.
Choosing between JPEG and JPEG2000
Table 13.5 was used to choose between JPEG and JPEG2000. It shows that JPEG2000 is better in every way except for the increased encoding time. However, as will be shown in section 13.5.9, there is a 300 second window of opportunity between each photo in which encoding can be performed. This will provide more than enough time to compress a large image using JPEG2000. Therefore JPEG2000 has been chosen as the lossy image compression algorithm.
Libraries Used for Image Compression
VxWorks has POSIX certified conformance and can therefore run any POSIX based library. JasPer
[5] has been chosen for JPEG2000 and OptiPNG [2] has been chosen for PNG compression. These are both POSIX libraries and little modification would be needed to make them run on VxWorks. Section
13.5.9 characterises the performance of these libraries.
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JPEG JPEG2000 Image artifacts Blocky Blurred Perceived image quality Better at compression ratios Better at compression ratios below 20:1 above 20:1 PSNR Poor Good Complexity Low High Average compression time 0.3µs/pxiel [194] 1.7µs/pixel [194] Bit stream Non-progressive Progressive
Table 13.5: Overall comparison of JPEG and JPEG2000.
13.3.5 Image Storage
Once the image has been compressed, it must be saved in memory ready for transmission. This is because the communications link will not always have a line of sight to the destination (e.g. lander to orbiter or orbiter to Earth) and so cannot transmit data all the time. The entire 512MB of flash memory will be used to create a First In, First Out (FIFO) buffer to store the images while the link is down. This behaves like people standing in a queue. The first image into the buffer will be the first image to be processed once the transmission line is active. If the buffer becomes full then no more images will be saved to the queue until space has been made due to an image being transmitted.
The photo will be accompanied by a short 163 bit label including the information listed in table 13.6.
Label name bit length description source 2 00=orbiter, 01=lander, 10=UAV compression 1 0=PNG, 1=JPEG2000 time 32 POSIX timestamp of when image was captured position 128 Polar coordinates of where image was taken
Table 13.6: A 163 bit label which accompanies each photo.
13.3.6 Hierarchy of Transmission
The orbiter is the only system which can communicate with Earth, hence all photos taken from the
UAV and lander will have to be transmitted via the orbiter. This is shown in figure 13.3.
UAV cameraUAV buffer Orbiter camera
Lander bufferLandercamera Orbiter buffer Earth
Figure 13.3: Hierarchy of transmission.
Whenever there is opportunity for transmission, it will be taken. If the orbiter buffer becomes full, it will not accept images from the lander or UAV. In such a case, the lander or UAV will buffer the
248 Chapter 13. Imaging Systems Jack Andrews rejected image for as long as possible. Orbiter photographs take priority over UAV and lander images.
This is because if a photo from the orbiter is lost, it will take another 16 days before the orbiter is in the same position again.
13.4 Lander Imaging System
The goal of the lander imaging system is to take high fidelity photographs of features immediately next to the landing site, such as soil and rocks. Upon landing, the camera mount will rotate through 360 ◦ and acquire a panoramic image of the surroundings. Once a panoramic view has been transmitted back to Earth, commands can be sent to the lander requesting photographs of specific objects and positions.
Thus the lander imaging system requires two specialisations of the base system. Firstly, a controllable camera mount is needed. Secondly, due to the time delay of transmission between Earth and the lander of approximately 55 minutes (see section 10.1.1), an autofocusing system has been developed.
This means that no interaction between Earth and the lander is needed in order to focus the camera.
This section will now discuss these specialisations, with emphasis placed on the harder problem of auto–focusing.
13.4.1 Camera Mounting
The camera will be mounted in such a way as to allow 360 ◦ rotation. The tilt of the camera will be controllable to allow rotation from 0 ◦ (the horizontal) to −60 ◦ (looking down). This will allow the aforementioned panoramic images to be acquired.
The precise design of the mounting is beyond the scope of this report.
13.4.2 Lamp
As will be discussed in section 13.5.1, the thick methane atmosphere of Titan absorbs much of the sun’s light. This makes the surface very dark. To aquire good quality images in the visible light spectrum, a source of artificial light is required.
A capacitor bank will be charged up until enough energy has been stored for the exposure time required. A 2W focused LED lamp will then be used to illuminate the surface [222]. This produces
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1000 lumens, providing 100 lux for 10m 2. This level of light will allow for a short exposure time of approximately 1/60 of a second , resulting in an image with a high signal to noise ratio [4].
13.4.3 Autofocusing Method
Passive and Active Autofocus
There are two types of autofocusing system. Passive autofocusing determines the correct focus purely by passive analysis of the image being captured. Active autofocus uses a device independent of the optical system, such as sonar or infrared, to measure the distance to the subject. The focus is then adjusted based on this measurement. Passive autofocus was chosen as no extra components are needed for implementation. The autofocusing system will be based in software and will run on the
Proton400k™.
Calculating the Focus Value
The Focus Value (FV) is a measure of image focus. The general equation used to calculate the FV of an x × y pixel image is as follows [91]:
∑ ∑ FV = |g(x, y)| (13.1) x y
Where g(x, y) is the illumination gradient of an image. A simple illumination gradient function was used which calculates the difference in pixel intensity of neighbouring pixels. If the intensity of a pixel
(range 0-255) at point (x, y) is given as px,y, then:
g(i, j) = |pi,j − pi,j+1| + |pi,j − pi+1,j| (13.2)
Testing the accuracy of the FV
To test the accuracy of the FV calculation Gaussian blur was applied to an in-focus image to model the image becoming out of focus, as shown in figure 13.4. This can only be done if all points being captured are assumed to be equidistant from the camera.
A MATLAB script was created to simulate the lens and autofocus system. The results can be seen in
figure 13.5. Note the peak in FV when zero Gaussian blur is applied. This peak is therefore the lens position such that the image is in maximum focus.
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(a) In-focus picture of rocks. (b) Picture of rocks with Gaussian blur applied.
Figure 13.4: (a) shows an in-focus image, which should result in maximum FV. (b) is the same image with a Gaussian blur of radius 12 pixels applied. This simulates the image being out of focus.
Figure 13.5: Results of the FV calculation. A range of Gaussian blurs is applied to simulate different lens positions, with only one position representing the in-focus point (lens position 20).
13.4.4 Autofocus Noise Rejection
To test if the simple illumination gradient function used is susceptible to noise, ‘salt and pepper’ impulsive noise was applied after the Gaussian blur and prior to FV calculation. Sources of impulsive noise include mechanisms such as ‘dark noise’ and ‘shot noise’[104]. Impulsive noise is the most likely type of noise to affect the FV calculation. Suppose an image was out of focus. Coordinates (i, j) are unaffected by noise, but (i + 1, j) has an impulsive spike. The value of |pi,j − pi+1,j| will therefore be high, when it should have been low, hence artificially inflating the FV value.
To simulate absolute worst case scenario noise, 100 bursts of impulsive noise were applied to the
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500×500px test image. The results in figure 13.6 show that even under extremely high noise conditions, the algorithm performs well and the in-focus lens position can still be easily identified.
Figure 13.6: Results of the FV calculation when impulsive ‘salt and pepper’ noise has been applied to the blurred image.
13.4.5 Focus Window
The simplistic model used in section 13.4.3 assumes that all points being captured are equidistant from the camera. Clearly this will not be the case. Without defining an area of interest for the autofocus, the peak FV value is likely to occur when the largest object in the current view is in focus. This may not be the desired object to focus on. A small subset of the current view is therefore defined as the
‘focus window’. The FV algorithm is then only applied to this focus window. This means that the autofocusing system will focus on what is in the focus window and disregards everything else. It also significantly reduces the area for which the FV needs to be calculated, greatly speeding up calculation time.
A small 100×100 pixel focus window was chosen, as shown in figure 13.7. This allows a reasonable sample of pixels to be used in the FV calculation. After implementing the focus window code, the time taken to calcuate the FV of an image reduced by a factor of 300. In the example image in figure
13.7, the camera was centered on the rock. The focus window will ensure that it is the rock in the centre of the image which is in focus, and not anything else.
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Focus Window
100px
100px
Figure 13.7: The 100×100 pixel focus window only calculates the FV for a small region of the image.
13.4.6 Climbing Search Algorithm
Figure 13.6 shows the calculated FV for all focus positions. To acquire this graph using a real camera, a photo must be taken at each lens position and the FV calculated. This would take a long time. An algorithm is required to quickly find the peak in figure 13.6 whilst taking the minimum number of photos possible. A popular algorithm is called the climbing search algorithm. It works as follows:
1. Move the lens using a large step size until the rough position of the peak (see figure 13.6) is
found.
2. Starting from the highest found value in step 1, user a small step size to determine the gradient
of the peak at the current position.
3. Use fine steps and knowledge of the gradient to move the lens to the highest peak value.
13.5 Orbiter Imaging System
The task of the orbiter imaging system is to map the entire surface of Titan from above the atmosphere.
Two specialisations are required. Firstly, a lens filter is needed to allow good quality images of the surface to be taken. Secondly, a mapping algorithm is required to efficiently map the surface of Titan.
The majority of this section will investigate the design, simulation and implementation of the mapping algorithm. The simulation will then be used to choose optimal values for many of the orbiter mission variables, such as orbital radius and the camera field of view.
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13.5.1 Lens Filter
The 1981 Voyager mission struggled to capture the surface of Titan due to the thick atmosphere. Only recent work found signs of the surface in Voyager’s images at a SNR ratio of around 2:1 [185]. The atmosphere of Titan primarily consists of nitrogen, with Methane being the second most abundant species at a concentration of around 5% [166]. It is the methane in Titan’s atmosphere which gives it its orange haze and absorbs much of the incident light, making the surface very dark. The Cassini ARTICLE IN PRESS imaging system used filters to capture light from 6 inter-methane-band-windows from 600 to 1000nm M.G. Tomasko et al. / Planetary and Space Science 56 (2008) 624–647 631 [174]. The most successful filter was a narrow, contiuum-band filter centred at 938nm [175]. ULVS I over F from 295 to 348 deg Secondly, we must evaluate the methane absorption
141.9 29.8 coefficients for the conditions at each altitude and at each 128.4 23.4 spectral interval. Longward of a wavelength of 1050 nm, 1.6 99.1 11.1 57.7 5.33 methane absorption for the radiative transfer calculations 47.9 2.39 37.6 was based on Irwin et al. (2006) who used a band model with 1.2 five parameters varying with wavenumber. They published these five variables as function of wavenumber shortward of 9500 cm 1 with a spacing of 5 cm 1. The five variables are: 0.8 the absorption coefficient, two energy levels defining the ULVS I/F temperature dependence (weight 0.5 each), a line-width variable defining mostly the pressure dependence, and a line- 0.4 spacing variable defining mostly the curve of growth. Shortward of 1050 nm, no sophisticated models for the methane absorption exist, mostly because the dependences 0.0 on temperature and pressure are minor. In order to create a 500 600 700 800 900 consistent data base for the whole wavelength range of the Wavelength (nm) DISR spectrometers, we estimated the five variables shortward of 1050 nm by the following method. We took Figure 13.8: MeasurementsFig. 10. taken The valueby the of I/ HuygensF (where the upward-looking flux in the incident solar visible beam isspectrometerpF) the methane (ULVS) absorption during coefficient at 80 K from Karkosch- is shown plotted versus wavelength for the ULVS spectra at the altitudes descent through Titan’s(in atmosphere km) shown in the [216]. inset. The The intensity legend is the shows average lines intensity representing in the field altitude,ka (1998). in We km. assumedI/F both energy levels to be equal to is a measure of the intensityof view, of and the includes light the flux diffuse incident intensity onfield the as well sensor. as the contribution Higher valueseach mean other higher and calculated light them based on the ratio of intensity. As the probe fallsof the through direct solar the beam. atmosphere, The responsivity much to the of direct the solar incident beam varies light beginsmethane to be absorption absorbed coefficients between Karkoschka according to the spatial response pattern shown in Fig. 1. The data shown (1998) at 80 K and Fink et al. (1977) at 296 K. We by methane. At the surface, only a handful of windows exist where little light is absorbed, for example are collected when the azimuth of the instrument was centered at angles calculated the line-width variable based on the measured at 938nm. between 2951 and 3481 from the sun, where the response of the ULVS is a relative maximum for the direct solar beam. Note the growth of the pressure coefficients by Fink et al. (1977). Finally, we methane absorption bands as the instrument falls to lower altitudes. found a moderate correlation between absorption coeffi- cient and line spacing in Irwin’s data, and we adopted the Figure 13.8 clearly shows large amounts of absorption around wavelengths 610nm,line-spacing 730nm, 790nm variable and by assuming that the same correlation 890nm. The windows indirection. the spectrum As a result, can the be sun seen sensor at wavelengths system aboard 750nm, DISR 820nmis valid and below 938nm. 1050 As nm wavelength. Knowledge of this that controlled data collection produced a set of measurements variable is not critical since methane absorption below wavelength increases, theessentially amount randomly of light absorbed distributed by in eachazimuth window instead reduces. of at This1050 nm means has only that a the very small dependence on this variable. the preplanned azimuth angles relative to the sun. When The methane absorption coefficients were used to highest wavelength windowthe ULVS is most intensities desirable. at two wavelengths are plotted versus compute the transmission through each of 30 layers of altitude, a scatter diagram results due to the rotation of the Titan’s atmosphere (each at fixed temperature and pressure There exist further windowsprobe at during wavelengths the descent greater (see Fig. than 8). theAfter 960nm the azimuth limit ofshownamd in figurehaving the13.8. methane The mixing ratio measured by Niemann the probe was determined as a function of mission time, the et al., 2005)andforasetof60abundanceslogarithmically next window, for example,data is could at 1060nm be sorted [216]. by azimuth However, and current scaled to CCD compare technologyspaced can between, only capture and the transmissions were convolved to with a model, as shown in Fig. 9, to permit detailed the resolutions of our visible and IR spectrometers. We then photons within a certaincomparison range, as of illustrated the data with in figure radiative 13.9. transfer At 1060nm, models of the quantumfit the transmission efficiency through of each layer of atmosphere with the haze in Titan’s atmosphere. an exponential sum having up to 16 terms using Gaussian CCDs is no greater than 10%.The reduced It is for average this reason intensities that in windows the field of beyond view of 938nm the quadrature are not considered. for the weights of the exponential terms. A layer ULVS during the descent as functions of azimuth and doubling and adding code was used to evaluate the intensity A good compromise canaltitude be made are by contained using the in the 938nm Planetary window. Science The Archive. best CCD A sensorfield in has the a atmosphere quantum at each of 30 altitudes for 22 zenith sample set of spectra looking upward including the sun in angles and all azimuth angles using 16 computations at each efficiency of approximatelythe 50% field ofat viewthis wavelength are shown in andFig. the 10. window itself absorbsspectral the least pixel, light of each any using one term of the methane exponential sum. The models computed for each term in 3. Comparison of published methane coefficients with the exponential function were then summed at each DISR spectra 254 wavelength to give the radiation field at each altitude, direction, and wavelength in Titan’s atmosphere. Three types of information are necessary to compare the In the third step, we used the housekeeping data of each DISR spectra with models of the methane bands. First, the DISR observation to determine the azimuths at which the vertical distribution, single-scatering albedos, and phase shutter of the IR spectrometer was open and the relative functions of the aerosols must be known at continuum exposure times at each azimuth. The radiation field model wavelengths across the spectral range of interest. We take was used with the relative spatial response of the spectro- these from Tomasko et al. (2008) where the spectral and meter to weight the radiation field as it was weighted in the solar aureole measurements from DISR are used to derive observations. For some of the early measurements where these parameters. there was significant wind shear, we used tips of the probe 208 P. Magnan / Nuclear Instruments and Methods in Physics Research A 504 (2003) 199–212
75 dB for Front Illumination and 90 dB for Back- minimization of Cfd and QE improvements of side Illumination). It offers very large-size arrays frontside illuminated CCDs through the use of in terms of both pixel number (6 Mpix, 16 Mpix, transparent gate material such as Indium Tin y, 63 Mpix with minimum pixel pitch ranging Oxide (ITO) [18] that have been associated from 5 to 9 mm), and area (up to 40 Â 55 mm or recently with micro-lenses that focus the photon even a full 600 wafer size). CCDmanufacturers flux on the transparent gate [19]. Fig. 15 shows the have been continuously very innovative since the QE data for several CCDtechnologies and invention of concepts to circumvent the key demonstrates the strong improvement obtained difficulties and to improve the performances: by this technique. The use of charge multiplication buried channel adoption to improve the charge by impact ionization in an additional section of transfer efficiency, anti-blooming devices (often at output register driven by higher clock value (up the expense of reduced Fill-Factor), inverted to 40 V) [20] allows one to address very low (Multi Phase Pinned) mode to reduce the DC, light conditions requirements without the use reduction of phase number, use of open-gate or of intensifier. thinning plus backside illumination associated Despite this impressive amount of progress, with antireflective (AR) coating to improve QE, CCDstill suffers from several drawbacks, most of development of UV conversion layers to extend them related to CCDarchitecture ( Fig. 1): serial the response in the UV region or high resistivity access to image being slow for large-size arrays, devices (deep depletion CCD) for X-rays detec- high power dissipation (as CV 2f ) due to intrinsic tion. However, it should be noted that only a very capacitive nature of gates and the use of large limited set of manufacturers in the world has the voltage drive levels for vertical and horizontal capability of producing the ultimate performances clocks that allow for efficient charge transfer, backside illuminated thinned CCDs. Recent lack of random access and windowing capability. advances have focused on reduction of noise Some others are related to the technology itself by increasing the sensitivity up to 15 mV/e by that do not allow, due to the lack of powerful Chapter 13. Imaging Systems Jack Andrews QUANTUM EFFICIENCY OF VARIOUS CCD TECHNOLOGIES
1 CCD BI With Broadband AR coa CCD BI With IR AR coating 0.9 CCD with ITO gates CCD with poly gates 0.8 CCD with ITO gates&µlens
0.7
0.6
0.5
0.4
0.3
0.2 QUANTUM EFFICIENCY 0.1
0
0 0 0 0 0 0 0 0 0 35 40 45 50 55 60 65 700 750 80 85 900 950 1000 WAVELENGTH FigureFig. 15. Comparison 13.9: Quantum of QE for efficiency various CCDtechnologies: of various Backside CCD technologies illuminated (EEV [132]. 30-11 BI) Quantum with broadband efficiency AR coating is the and with per- IR AR coating, traditional poly-gates (Kodak KAF 1400), ITO gates (Kodak KAF 1401E), ITO gates with micro-lenses (Kodak from centageRef. [19]). of photons hitting the CCD that will produce an electron–hole pair. available window. Also, past experience shows that this filter performed the best out of all windows during the Cassini mission. It is for these reasons that a narrow contiuum-band filter centred at 938nm will be used.
13.5.2 Infinity Focus
Infinity focus is used on the orbiter for the same reason as on the UAV. See section 13.6.1 for further details.
13.5.3 Mapping Algorithm
The orbiter camera will be used to photograph the entire surface of Titan. An algorithm has been devised to achieve this in an efficient manner such that no one area of Titan is captured twice. This vastly reduces the amount of data which has to be transmitted back to Earth, saving power and reducing transmission time. An overview of the algorithm can be seen in figure 13.10.
MATLAB scripts were written to simulate the performance of the algorithm in figure 13.10. The full simulation is broken into two parts: the simulator and controller. The simulator models the orbit around Titan (exposing data to the controller for box A of figure 13.10) and plots results and statistics.
The controller performs all of the tasks shown in figure 13.10, with the exception of boxes B and C which are out of the scope of this report. The controller is the part of the simulation that would be implemented on the Proton400k™.
The rest of this section will describe the workings and implementation of this simulation. Finally, the
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A Retrieve current position from the navigation system
B Wait for orbiter to move Yes Is the orbiter on the to a new position dark side of Titan?
C G Yes Is the orbiter eclipsed Compress the image by Saturn? and save to memory.
D
Has any previous photo No captured part of the Take photo current camera view?
E F Has the whole area Yes No Take photo and crop out of the current view been (no need to take photo) previously captured? any previously captured area
Figure 13.10: Mapping algorithm. simulation will be used to choose optimum values of all the variables used, such as orbital radius of the orbiter and the camera field of view.
13.5.4 Modeling the Orbit
The primary task of the simulator is to model the path of the orbiter so that the controller has data on its position. As described in chapter 3, a polar orbit is used. Using Newton’s universal law of gravitation, the period of the orbit can be derived: √ r3 T = 2π (13.3) GM
Where r is the orbital radius, G is the gravitational constant and M is the mass of Titan. Equation
(13.3) allows the latitude of the orbiter to be determined in the simulation. Titan has a synchronous orbit around Saturn of period 16 days [149]. Titan is now taken to be a static frame of reference.
Hence the orbiter will orbit in the longitudinal direction with a period of 16 days. This information was used to program the simulator, which models the orbit of the orbiter.
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13.5.5 Locating previous photos which have captured portions of the current view
The aim of this part of the algorithm is to quickly find all previous photos which overlap with the current view (box D of figure 13.10). Once these photos have been found, slower, more accurate calculations can be made (boxes E and F). This improves speed as the accurate calculations need only be applied to the few photos within a small range of the current view.
The polar coordinates of all previous photos are stored in the controller memory. An algorithm has been devised to run through all previous photo coordinates and pick out any which overlap with the current view. Figure 13.11 demonstrates how this is done. The figure shows the limiting case of a previous photo just touching the current view. If the distance between the two photos, δ, is any smaller then they would overlap. Hence θmin can be defined, which is the minimum angle between a previous photo and the current view such that they do not overlap.
Centre of Titan
θmin rT itan
Titan x y
Space
rorbiter
βfov βfov
rvo s poourn view previous photocurrent
δ Figure 13.11: 2D diagram (not to scale) showing the area captured by the current view, x, and the area captured by a previous photo, y. These are determined by βfov, the camera field of view. In ◦ practice, βfov ≈ 5 , hence the curvature of Titan can be ignored. If θ, the angle between the current position and the previous photo, is less than θmin, then the previous photo is overlapping with the current view.
From symmetry, x = δ. δ can therefore be derived from the camera’s field of view, βfov: ( ) β δ = 2(r − r ) tan fov (13.4) orbiter T itan 2
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δ can also be defined in terms of θmin, ( ) θ δ = 2r tan min (13.5) orbiter 2
Combining (13.4) and (13.5) and applying the small angle approximation obtains:
βfov(rorbiter − rT itan) θmin = (13.6) rorbiter
Thus to check if a previous photo is overlapping, the following equalities can be checked. In the latitudinal direction, defined by θ:
|θcurrent − θprevious| < θmin (13.7)
In the longitudinal direction, defined by ϕ:
|ϕcurrent − ϕprevious| < ϕmin cos(θcurrent) (13.8)
Where ‘cos(θcurrent)’ in equation (13.8) is an approximation to account for the fact that lines of longitude converge when approaching the poles. If both equations (13.7) and (13.8) evaluate to true then the previous photo being checked overlaps with the current view.
Incorporation of these checks into the simulation can be seen in figure 13.12. All photos taken are stored in memory and as the orbiter moves to a new position, all photos are checked to see if any overlap. A photo is only taken if no previous photo overlaps with the current view. Figure 13.12 is included to illustrate the validity of equations (13.7) and (13.8). There are clearly parts of Titan which are not yet being captured. This will now be dealt with.
13.5.6 Determining the useful region of a photo
The previous section describes how to find all captured photos which overlap with the current view.
Accurate calculations are now applied to these photo coordinates to determine which region of the cur- rent view has yet to be captured (box E of 13.10). Given a photo taken at coordinates (rorbiter, θp, ϕp), a 2D projection of the area captured by the photo onto the sphere of Titan is calculated. A square, the size of the area captured, has sides:
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m
Figure 13.12: Simulation of photos being taken such that no two photos overlap. The blue line is the path of the orbiter. The red dots represent the position of the orbiter at the time of a photo being taken. Red squares show the area of Titan captured in each image.
( ) β x = 2(r − r ) tan fov (13.9) orbiter T itan 2
This is shown in figure 13.11. In Cartesian coordinates, a square of this size is created, centered on
(0, 0, rT itan). This is then rotated in the y-axis by −θp and the z-axis by (ϕp −π/2), using the rotation matrices:
cos ϕ 0 sin ϕ cos θ sin θ 0 Ry(ϕ) = 0 1 0 , Rz(θ) = sin θ cos θ 0 (13.10) − sin ϕ 0 cos ϕ 0 0 1
For example, to determine the coordinates of the top left vertex of a captured square (defined in
(x, y, z) coordinates as vtl) the following calculation is made:
x/2 vtl = Ry(ϕp − π/2)Rz(−θp) x/2 (13.11)
rT itan
This is performed on all vertices of a square representing an overlapping previous photo, correctly placing it relative to Titan. The simulator plotter also uses equation 13.11 on all previous photos (not just overlapping ones) to render the squares in figure 13.12.
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The position of previously captured areas is now known relative to Titan. To understand how these photos overlap with the current view, their positions must be determined relative to the current view.
This is done by rotating all overlapping photos by (θorbiter, π/2 − ϕorbiter). These angles represent the polar coordinates of the orbiter, and hence the current camera view, relative to the pole with
rel Cartesian coordinates (0, 0, rT itan). For example vtl , the position of vtl relative to the current view, can be calculated as follows:
rel − vtl = Ry(π/2 ϕorbiter)Rz(θorbiter)vtl (13.12)
This rotation is applied to all vertices representing the squares of overlapping previous photos. This puts these squares in the x, y plane, hence z coordinates can now be discarded. The centre of the current view is now at (0, 0) in x, y plane.
The current view is a square of dimension x centered at (0, 0). The coordinates of the vertices of the current view and all previous photos are now normalised and discretised. This is done so that the current view forms a square of dimension overlap accuracy, a script variable. Each point in this square is checked to see if a previous photo overlaps with it. Hence increasing overlap accuracy improves the accuracy of the algorithm at the cost of increased processing time, which requires
Θ(overlap accuracy2) calculations.
Figure 13.13: Calculation of overlapping region of current view. Previous photos and current view have been projected onto a 2D plane for calculation. Red squares represent previous overlapping photos and the filled square in the centre of the figure is the current view. Magenta regions of the current view have already been captured and will be discarded. The blue region has yet to be captured and will be transmitted to Earth.
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The output of this algorithm is shown in figure 13.13. In this example, overlap accuracy is set to 50, so that the current view has been broken into a 50×50 box. This means 2500 points must be checked.
13.5.7 The complete Simulation
Figure 13.14 shows the completed MATLAB simulation. Table 13.7 shows all the files in the MATLAB simulation and a link to download them.
File Type Description simulate.m – The main simulation script. step simulation.m Simulator function Simulates position of orbiter relative to Titan. control.m Controller function Determines when to take a photo and which region to transmit. photo should be taken.m Auxillary function Determines if a photo should be taken. take photo.m Auxillary function Stores photo location in memory. point in quad.m Auxillary function Determines if a given point is inside a given quad. find overlapping photos.m Auxillary function Finds overlapping photos. difference between angles.m Auxillary function Finds the relative difference between two angles. Total lines of code: 421 Download files: http://users.ox.ac.uk/∼chri2970/3ypmapper.zip
Table 13.7: List of files used in the MATLAB simulation and a brief description.
261 Chapter 13. Imaging Systems Jack Andrews Figure 13.14: Still frameare from statistics the and Titan lower Mapping right System is simulation. a visualisation Left of is the an overlapping animation region of calculator. the orbiter (green dot) moving around Titan. Upper right
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13.5.8 Optimisation and Implementation
The controller part of the mapping algorithm will be run on the Proton400k™. Using MATLAB for the final algorithm would be highly inefficient and take up of much of the available resources. A programming language such as C++ is much better suited to the task.
The controller algorithm was therefore rewritten in C++. Table 13.8 shows all the files in the C++ controller and a link to download them. This allowed the performance of the algorithm running on the
Proton400k™to be estimated, as used in section 13.5.9. There are many opportunities the optimise the code further. For example, ‘quick sort’ and binary search algorithms could be used in the overlapping photo detector described in section 13.5.5. However, this is outside the scope of the report.
File Description simulator.cpp Basic simulator for modeling the orbit. titanmapper.cpp Controller functions. plotting.cpp Uses MATLAB shared libraries to access MATLAB plotting functions for visual output and debugging. (header files) Header files for definitions and function prototypes not listed. Total lines of code: 379 Download files: http://users.ox.ac.uk/∼chri2970/3ypmappercpp.zip
Table 13.8: List of files used in the C++ controller and a brief description.
13.5.9 Choosing parameters based on simulation
The simulation contains variables which need to be set for optimal performance. These are listed in table 13.9. Explanations for how these values were chosen will now be given.
Variable Value Description orbital radius 4.576 ×106m Orbital radius from centre of Titan. camera fov 0.125 radians Horizontal and vertical field of view of camera. wait time 300 seconds Time to wait since previous photo until checking if next photo should be taken. overlap accuracy 703 Accuracy of overlapping region algorithm. camera resolution 7032x7032px Camera pixel resolution. compression ratio 0.3 Compression ratio of lossy encoder.
Table 13.9: Simulation variables to be determined.
263 Chapter 13. Imaging Systems Jack Andrews
Orbital radius, camera Field Of View (FOV) and ‘wait time’
The closer the orbiter is to Titan, the better the quality of the photographs. However, the atmosphere of Titan extends to an altitude of approximately 1400km [114][15]. To ensure that the orbiter would not be affected by atmospheric drag the orbital altitude was set to 2000km. The FOV was chosen such that on the the equator, there was no gap between the current photo and the photo taken exactly one orbital period before. Figure 13.14 shows how there is no gap in the longitudinal direction between photos on the equator. If the FOV is made smaller, there would be a gap. The FOV was then chosen to minimise the overlap between these equatorial photos. Trial and error was used to obtain the value of 0.125 radians.
The ‘wait time’ was chosen to to minimise the gap between each successive photo in the latitudinal direction. Note how in figure 13.14, the photo directly below the current view only slightly overlaps.
This small overlap is set by the ‘wait time’, which was chosen to be 300 seconds.
Overlap accuracy
Referring to figure 13.10, the following tasks must be performed in this 300 second ‘wait time’:
1. (box D) the mapping controller locates previous photos which overlap with the current view
(section 13.5.5).
2. (box E and F) the controller performs the overlapping region detection (section 13.5.6).
3. (box G) the image processing module (section 13.3.4) must compress the image and save to
memory.
The execution time of item 1 cannot be changed. The execution time of item 2 can be reduced by making overlap accuracy smaller. The execution time of item 3 can be reduced by making camera resolution smaller. Clearly, it is desired to make both overlap accuracy and camera resolution as large as possible. As described in section 13.3.1, the resolution has already been set at 49 megapixel.
We are limited by the processing power of the Proton400k™. Section 13.3.2 estimates that the test machine is roughly 2.6 times faster than the Proton400k™. A factor of safety of 3 is used for reasons given in section 13.3.2. It is therefore assumed that if the processing is completed in 39 seconds on the test machine, then the processing will complete within the 300 second limit on the Proton400k™.
By running the full length simulation using the variables defined so far, it was found that the most photos the overlapping region algorithm had to deal with at any one time was 96. This worst case
264 Chapter 13. Imaging Systems Jack Andrews scenario occurs when 96 different photos all overlap at the poles. The C++ implementation of the overlapping region algorithm was adapted to measure the time of execution given 96 overlapping photos. It was found that when overlap accuracy was set to 703 (i.e. 10×10 pixel blocks) execution took just 3 seconds on the test machine. When it was set to 7032, execution time rose to 162 seconds, which is well outside the limit. 703 strikes a good compromise between speed and accuracy and was therefore chosen as the final value.
The following results were obtained when encoding a 49 megapixel image on the test machine:
Encoding Scheme Time taken (s) RAM usage (MB) JPEG2000 28.6 320 PNG 15 60
Table 13.10: Results from encoding a 50 megapixel image on the test machine.
The maximum combined execution time of both the overlapping region algorithm and the image compression is therefore 32.6 seconds. This is within the limit of 39 seconds and allows 6.4 seconds for the algorithm to find overlapping photos (box D of figure 13.10). The worst case scenario of searching through 3600 photos took just 1.2 seconds using the C++ implementation.
Hence the proposed values of overlap accuracy and camera resolution result in the greatest pos- sible accuracy and detail, whilst ensuring that all jobs are executed in the 300 second ‘wait time’.
Compression ratio
The final variable to set is the image compression ratio. Referring to figure 13.2 in section 13.3.4, the
JPEG2000 image compression algorithm chosen outperforms JPEG in subjective tests at compression ratios above 20:1. This will therefore be the lower bound on the compression ratio. At compression ratios above 50:1 the image quality starts to deteriorate fairly rapidly and hence this will be the upper bound.
Figure 13.15 shows a plot of megabytes per hour generated used the above variables and a compression ratio of 20:1. The peak data rate of 28MB/h is well within the capabilities of the orbiter to earth communications link (see section 10.5.4) which has a speed of 1Mbit/s (or 450MB/h). However, this link must also be used for other data. The UAV will be taking more frequent, higher detail photos, so using a 20th of the possible data rate seems reasonable. Power consumption must also be taken into account. The transmitter uses 100W of power (see section 10.5.3) and so the less time spent transmitting the better.
Finally, consider the 512MB FIFO buffer (section 13.3.5) which is used to store photos. The FIFO
265 Chapter 13. Imaging Systems Jack Andrews
Figure 13.15: Megabytes per hour generated at a compression ratio of 20:1. Oscillation is due to a large percentage of data being discarded at the poles. buffer in the orbiter must store photos from both the UAV and orbiter before transmission. If 20:1 compression is used, this means 200 50 megapixel photos can be stored. The orbiter can be out of view of Earth for up to approximately 3 hours at a time (half an orbit period). The orbiter will generate
40 photos in this time. This leaves space for 160 extra photos from the UAV and lander. If for some reason the communication link is down for more time (e.g. occlusion due to Saturn), then the FIFO buffer store up to 15 hours worth of orbiter photos before photos have to be dropped. It is therefore worthwhile using a reasonably high compression ratio so that more photos can be stored whilst the link is down.
For these reasons a compression rate of 30:1 has been chosen as a good compromise. This will allow up to 300 photos to be stored in the FIFO buffer while still providing a very high fidelity image.
13.6 UAV Imaging System
The task of the UAV is to take high quality images of surface features. It will be controlled to move to areas of interest and photographs will then be taken. The UAV is the simplest of the imaging systems and the only specialisations required are infinity focus and a lens filter.
13.6.1 Infinity Focus
The operating height of the UAV is between 2 and 14km. The camera must therefore be able to focus on the surface at all distances within this range. However, even at the lowest altitude of 2km, light can assumed to be parallel and therefore approximated to originating from infinity. Hence in order to focus, the CCD must be placed at the focal length (f) of the lens.
266 Chapter . Imaging Systems Jack Andrews
The lens for the UAV was chosen to have a field of view of 20 ◦ so that at a height of 5km a 49MP
CDD will have a resolution of 0.25m per pixel.
13.6.2 Lens Filter
As discussed in section 13.5.1, the methane atmosphere of Titan absorbs much of the sun’s light.
Due to the operating height of the UAV, an illuminating lamp such as that used on the lander is not practical. Therefore, the 938nm filter used on the orbiter will also be used on the UAV.
13.7 Conclusion
The design of three separate imaging systems have been proposed. At the heart of the proposal is a base system designed to meet the core requirements of all three imaging systems. Specialisations were then added to the base system so that each separate imaging system could perform its designated task.
A detailed evaluation of an autofocusing algorithm for the lander camera was made, which was found to be robust and tolerant to noise. Research determined that capturing images from the orbiter through Titan’s methane atmosphere is possible by using specialised lens filters. Finally, a mapping algorithm was devised for the efficient imaging of the entire surface of Titan. This was used to choose optimal values for mission parameters.
Further work would be required to take this proposal and produce working imaging systems. However, it is hoped that the information presented here would form a solid base from which to start.
267 Appendices
268 APPENDIX A - Joshua McFarlane
Calculating Launch Windows In Matlab
% Function to calculate the appropriate times to initiate Hohmann transfer
% orbits from Earth to Venus and from Venus to Saturn
% Written by Joshua McFarlane
% Current version 26/04/2010
function calculate_launch_window()
% Read the planetary data in from text files and store the coordinates in
% an array
coords=read_planetary_data();
% format of coords is:
% row number is the timestep
% the columns are the row coords
% the third index refers to body in question:
% 1 - Sun
% 2 - Mercury
% ... continuing in order of orbital distance until
% 7 - Saturn
% 8 - Titan
% constants for the planetary orbit radii
r_earth=1.495978875e11;
r_venus=1.08208930e11;
% calculate the semi-major axis, ’a’
269 Chapter A. Calculating Launch Windows In Matlab Joshua McFarlane
a=(r_earth+r_venus)/2;
% phi is the angle through which venus will travel durin the transfer
% of the orbiter
phi= pi*sqrt(a^3/r_venus^3);
delta=phi-pi;
%delta is the angle between earth and venus with earth ahead of venus
% calculate the times at which the angle is as specified
timesteps_earth_venus= launch_window(coords(:,:,3), coords(:,:,4), delta);
% calculate the launch windows from venus to saturn
r_saturn=1.433449370e12;
a=(r_saturn+r_venus)/2;
phi= pi*sqrt(a^3/r_saturn^3);
delta=pi-phi;
% here delta is the angle between saturn and venus with saturn ahead of
% venus
timesteps_venus_saturn= launch_window(coords(:,:,3), coords(:,:,7), delta);
% convert the time in hours to a date
disp(sprintf(’Dates for transfer from Earth to Venus:’));
convert_to_date(timesteps_earth_venus);
disp(sprintf(’Dates for transfer from Venus to Saturn:’))
convert_to_date(timesteps_venus_saturn); end
% this function will calculate the times at which the angle between two given
% bodies is as specified with the 1st body behind the 2nd body
% 2D consideration assuming orbital planes are co-incident with x-y plane function results= launch_window(coords1, coords2, angle)
270 Chapter A. Calculating Launch Windows In Matlab Joshua McFarlane
% create an empty results array
results=[];
old_delta=0;
for i=1:size(coords1, 1)
arg1=atan(coords1(i,2)/coords1(i,1));
if coords1(i,1)<0
arg1=arg1+pi;
end
arg2=atan(coords2(i,2)/coords2(i,1));
if coords2(i,1)<0
arg2=arg2+pi;
end
%arg1 and arg2 range from -pi/2 to 3pi/2
new_delta=arg2-arg1;
%delta will range from -2pi to 2pi so restrict to -pi to pi
if new_delta<-pi
new_delta=new_delta+2*pi;
elseif new_delta>pi
new_delta=new_delta-2*pi;
end
if ((old_delta
|| (old_delta>angle && new_delta && norm(old_delta-new_delta) && i~=1 % record the index (elapsed hours) if the angle has crossed the % desired value unless it has wrapped around Pi to -pi % also exclude first reading as there is no previous value of % angle available results= [results, i-1]; end old_delta=new_delta; end end 271 APPENDIX B - Aamir Aziz The PD Controller in Matlab %PID Controller (continuous-time) de=0.2; %demand/reference num=1; %plant numerator den=[1 0 0]; %plant denominator plant=tf(num,den); %plant transfer function Kp=5.5; %proportional gain Kd=9.5; %derivative gain Ki=0; %integral gain contr=tf([Kd Kp],[1]); %PID controller transfer function sys_cl=feedback(contr*plant,1); %closed loop transfer function t=0:0.01:5; %time interval figure %create figure step(de*sys_cl,t) %plot step response figure rlocus(sys_cl) %plot root locus 272 APPENDIX C - Aamir Aziz Optimal Control: LQR Controller in Matlab %Optimal Control : LQR controller (continuous time) t = 0:0.1:10; %time vector de = .2*ones(size(t)); %demand vector yo = [0 0]; %equiibrium output state A=[0 1;0 0]; %sytem model B=[0;1]; C=[1 0]; D=0; plant=ss(A,B,C,D); %create state-space model of plant co = ctrb(plant); %controllability matrix ob = obsv(plant); %observability matrix Controllability = rank(co); %rank of controllability matrix Observability = rank(ob); %rank of observability matrix p = 50; Q = p*(C’*C); %state weighting matrix R=1; %control weighting K = lqr(A,B,Q,R) %compute optimal feedback controller 273 Chapter C. Optimal Control: LQR Controller in Matlab Aamir Aziz Nbar = rscale(A,B,C,D,K); %scale the reference input using rscale sys_cl = ss(A-B*K,B*Nbar,C,D); %create closed-loop state-space model of system %lsim (sys_cl,de,t,yo); %run simulation of system figure step(sys_cl,10) figure rlocus(sys_cl) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function [Nbar] = rscale(A,B,C,D,K) % Given the single-input linear system: %. % x = Ax + Bu % y = Cx + Du % and the feedback matrix K,the function rscale(A,B,C,D,K) finds the scale % factor N which will eliminate the steady-state error to a step reference % using the schematic below: % ______ % R + u | . | % ---> N --->( ) ---->| X=Ax+Bu |--> y=Cx ---> y % - | \------/ % | | % |<---- K <----| %8/21/96 Yanjie Sun of the University of Michigan % under the supervision of Prof. D. Tilbury s = size(A,1); Z = [zeros([1,s]) 1]; N = inv([A,B;C,D])*Z’; Nx = N(1:s); Nu = N(1+s); Nbar = Nu + K*Nx; 274 APPENDIX D - Aamir Aziz Estimator Design in Matlab %Current Estimator Design Ts=0.06; Phi= [1 Ts;0 1]; %Digital system model Gam= [(Ts^2)/2;Ts]; C=[1 0]; z1=0.6730 + 1i*0.2402; %z-plane poles z2=0.6730 - 1i*0.2402; z=[z1;z2]; Lc=acker(Phi’,Phi’*C’,z)’ %estimator gain matrix x0=[0;1]; %initial state error vector numberiterations=50; %number of iterations X=zeros(2,numberiterations); %empty matrix to store state errors X(:,1)=x0; %enter initial state error for k=1:numberiterations X(:,k+1)=(Phi-(Lc*C*Phi))*X(:,k); %estimator error difference eq end x1=X(1,:); x2=X(2,:); plot(x1) 275 Chapter D. Estimator Design in Matlab Aamir Aziz hold all; plot(x2) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Reduced Order Estimator Design Ts=0.06; Phi= [1 Ts;0 1]; %Digital system model phi_aa=Phi(1,1); %partition Phi matrix phi_ab=Phi(1,2); phi_ba=Phi(2,1); phi_bb=Phi(2,2); Gam= [(Ts^2)/2;Ts]; gam_a=Gam(1,1); %partition Gam matrix gam_b=Gam(2,1); C=[1 0]; z=0.7; %z-plane pole Lr=acker(phi_bb’,phi_ab’,z)’; %estimator gain x0=1; %initial error numberiterations=50; %number of iterations X=zeros(1,numberiterations); %empty matrix to store state errors X(1)=x0; %enter initial state error for k=1:numberiterations X(k+1)=(phi_bb-(Lr*phi_ab))*X(k); %estimator error difference eq end plot(X) 276 APPENDIX E - Hugo Grimmett Orbiter Navigation Simulation in MATLAB % This program plots the position of Rhea relative to the centre of Titan. % Program written by Hugo Grimmett, current version 21.01.10 % extract of data gathered from NASA ephemeris website % (ssd.jpl.nasa.gov/horizons.cgi) data_raw = [ 2010 01 25 00 10 02 24.39 +02 29 50.1 -4.83 6.27 0.01089439240779 ... 2010 01 25 01 10 09 02.58 +02 39 55.7 -4.82 6.28 0.01095856925568 ... ... 2010 02 26 03 11 05 53.89 +03 59 53.8 -4.72 6.33 0.01145224266388 ... 2010 02 26 04 11 12 43.68 +04 08 35.7 -4.72 6.33 0.01145915210917 ... ]; Rconst = 100; % constant by which distance to Rhea is multiplied ra_dec_cart = []; % initialising matrix hold on title(’The Position of Rhea from the centre of Titan’); xlabel(’x-axis’); ylabel(’y-axis’); zlabel(’z-axis’); axis([-2 2 -2 2 -2 2]); plot3(0,0,0,’gx’,’MarkerSize’,10); % plot origin 277 Chapter E. Orbiter Navigation Simulation in MATLAB Hugo Grimmett % extracting useful data data_ext = [data_raw(:,1:3) data_raw(:,5:7) data_raw(:,8:10) data_raw(:,13:14)]; % columns =[ Date Stamp | RA | DEC | distance ] % [ 1 2 3 | 4 5 6 | 7 8 9 | 10 11 ] % processing the data for k = 1:size(data_ext) % set up sign flag for dec. >=0 and it’s +1, otherwise -1 if data_ext(k,7) ~= 0 sign_dec = sign(data_ext(k,7)); else sign_dec = 1; end % add up hours, minutes and seconds for right ascension ra = abs(data_ext(k,4)) + data_ext(k,5)/60 + data_ext(k,6)/3600; % add up degrees, arc-minutes and arc-seconds for declination dec = sign_dec*(abs(data_ext(k,7)) + data_ext(k,8)/60 + data_ext(k,9)/3600); phi = (ra/24*360); % ra goes from 0-24, phi goes from 0-360 degrees theta = -dec + 90; % dec is in degrees, but from +90 to -90 % work out polar co-ordinates r_now = Rconst*data_ext(k,10); x_now = r_now*sind(theta)*cosd(phi); y_now = r_now*sind(theta)*sind(phi); z_now = r_now*cosd(theta); % plot the point and label it with the date plot3(x_now,y_now,z_now,’ro’,’MarkerSize’,4); label = fliplr(data_ext(k,1:3)); text(x_now,y_now,z_now,’’); 278 Chapter E. 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