Attitude Control of the Sunjammer Mission

Ofer Eldad, E. Glenn Lightsey The University of Texas at Austin August 6th, 2014

“… out in space, even a pressure as small as that can be important—for it’s acting all the time, hour after hour, day after day. Unlike rocket fuel, it’s free and unlimited. If we want to, we can use it; we can build sails to catch the radiation blowing from the .” -Arthur C. Clarke, Sunjammer L’Garde IKAROS LightSail (JAXA) (The Planetary Society) Arthur C. Clarke

1960 1970 1980 1990 2000 2010 2020

NanoSail-D2 Comet Halley Rendezvous (NASA) Trade Study (JPL) Sunjammer (L’Garde) Eldad and Lightsey – Sunjammer Attitude Control Slide 2 AIAA/USU Small Satellite Conference August 2014 Sunjammer Program Context

Space Technology Mission Directorate

Image: L’Garde Prime Contractor Sail Development

Software Development

ACS

Eldad and Lightsey – Sunjammer Attitude Control Slide 3 AIAA/USU Small Satellite Conference August 2014 Mission Objectives

1. Demonstrate segmented deployment of a solar sail 2. Demonstrate attitude control plus passive stability and trim using beam-tip vanes.(± 2º) 3. Execute a navigation sequence with mission-capable accuracy. (~30 days) 4. Fly to and Possibly Maintain Position at L1 and/or Pole Sitter Positions (6 months)

3 DOF active control Completely propellantless Utilize 2-axis passive stability Navigation in interplanetary space

Eldad and Lightsey – Sunjammer Attitude Control Slide 4 AIAA/USU Small Satellite Conference August 2014 The Sail

Sailcraft mass: ~45kg (including bus) Sail area: 1200m2 Each of the four corners of the sail has a control vane • Area: 15 m2 • Controlled using two motors – Cant about y-axis – Twirl about x-axis • Eight control degrees-of-freedom for three-axis attitude control

L’Garde

Eldad and Lightsey – Sunjammer Attitude Control Slide 5 AIAA/USU Small Satellite Conference August 2014 Solar Radiation Moment and Force Model

• SRP simulated using experimentally derived moment model – Provided by L’Garde • Refined model deviates from flat plate behavior – Accounts for sail billowing – Introduces significant restoring moment

-3 x 10 2

1 0 q -2 0 5 10 15 • Without control 0.02

2 0 – Oscillation about equilibrium in x- q -0.02 y- axes 0 5 10 15 0.01

3 0

– Neutral stability in z-axis q

-0.01 0 5 10 15 1

4 0.9998 q

0.9996 0 5 10 15 Time [hour] Open-loop Euler’s equation propagation Eldad and Lightsey – Sunjammer Attitude Control Slide 6 AIAA/USU Small Satellite Conference August 2014 Control Scheme

Operate about a trimmed equilibrium orientation – Determine equilibrium vane orientations for each desired sail orientation a priori Calculate desired moment with PD control law

Orient vanes to achieve desired moment – Cant vanes 2&4 for x-axis control – Cant vanes 1&3 for y-axis control – Twirl all four vanes for z-axis control

Adjust equilibrium orientation based on controller behavior

Passively stabilize 2 axes

Eldad and Lightsey – Sunjammer Attitude Control Slide 7 AIAA/USU Small Satellite Conference August 2014 Moment Allocation Scheme Example

Calculate desired moment and current moment

푀푑푒푠 < Deadband Use trim vane angles End

Calculate 푀푑푒푠 − 푀푐푢푟푟푒푛푡

푀푑푒푠 − 푀푐푢푟푟푒푛푡 < ε 푀푑푒푠 − 푀푐푢푟푟푒푛푡> ε 푀푑푒푠 − 푀푐푢푟푟푒푛푡< ε

No change to vane angles Cant vane 1 towards sun Cant vane 3 towards sun incrementally incrementally

End End End

Cant vane 3 away from Cant vane 1 away from sun incrementally sun incrementally

End End

Eldad and Lightsey – Sunjammer Attitude Control Slide 8 AIAA/USU Small Satellite Conference August 2014 Introduction of Passive Stability

Derbes (2004)

Eldad and Lightsey – Sunjammer Attitude Control Slide 9 AIAA/USU Small Satellite Conference August 2014 Effect of Passive Stability

No Passive Stability

Orientation Control Effort

0

-20 [deg]

Vane 1 Vane Cant -40 0 5 10 15 20 25 30 35 40 45 50

0 [deg]

Vane 2 Vane Cant -50 0 5 10 15 20 25 30 35 40 45 20

0 [deg]

Vane 3 Vane Cant -20 0 5 10 15 20 25 30 35 40 45 20

0 [deg]

Vane 4 Vane Cant -20 0 5 10 15 20 25 30 35 40 45 Time [hour]

Trouble maintaining attitude in the presence of disturbances

Eldad and Lightsey – Sunjammer Attitude Control Slide 10 AIAA/USU Small Satellite Conference August 2014 Effect of Passive Stability

Added Passive Stability

Orientation Control Effort

100 0

50 -20 Vane1

[deg] 0

Cant[deg] -40

0 5 10 15 20 25 30 35 40 45 TopAngle -50 50 0 5 10 15 20 25 30 35 40 45

40 0 Vane2

Cant[deg] -50 20 0 5 10 15 20 25 30 35 40 45 20

Angle[deg] 0 0

Sun-Incidence 0 5 10 15 20 25 30 35 40 45 Vane3

50 Cant[deg] -20 0 5 10 15 20 25 30 35 40 45 40 0 20 -50

0

Flat SpinFlat

Vane4 Angle[deg]

-100 Cant[deg] -20 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 Time [hour] Time [hour]

Passive Stability Improves Performance

Eldad and Lightsey – Sunjammer Attitude Control Slide 11 AIAA/USU Small Satellite Conference August 2014 Handling On-Orbit Uncertainty • Cannot rely on a priori trim computation – Uncertainty in generated moments – Imperfect actuators – Poor knowledge of flexible effects – On-orbit faults • Solution  – Adapt trim angles based on control history – Use new trim angles to estimate bias and feed back into control – Results in operating about an equilibrium vane orientation

Load Pre- Begin Calculated Maneuver Trim Angles

Adjust Trim Estimate End PD Control Angles Moment Bias Maneuver

Eldad and Lightsey – Sunjammer Attitude Control Slide 12 AIAA/USU Small Satellite Conference August 2014 Adjusting Trim Angles Example

10

0 [deg]

Vane Vane 1 Cant -10 A priori trim = 4° 0 5 10 15 20 25 30 35 40 45 20

• Excessive control effort 10 [deg]

Vane Vane 2 Cant 0 • Inaccurate pointing 0 5 10 15 20 25 30 35 40 45 20

0 [deg]

Vane Vane 3 Cant -20 Adjustment begins to t = 15 0 5 10 15 20 25 30 35 40 45 hours 20

10 [deg]

Vane 4 Cant 0 0 5 10 15 20 25 30 35 40 45 Time [hour] Trim converges to truth ~-6° • Cant motion settles 15 10

• Attitude converges 5 [deg]

0 Top +Top Flat Spin Angle -5 Improvement in control effort 0 5 10 15 20 25 30 35 40 45 and pointing performance 40 Target 30

20

[deg]

10 Sun-Incidence Sun-Incidence Angle 0 0 5 10 15 20 25 30 35 40 45 Time [hours] Eldad and Lightsey – Sunjammer Attitude Control Slide 13 AIAA/USU Small Satellite Conference August 2014 Robustness Checks

Error Source Error Level Tolerated

Scaling error in moment and ± 30% force coefficients Moment of inertia error ± 50% Frequency Unknown Disturbance Moment ± 3x10-4 Nm in all 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 Bias axes Pointing Error Distribution [deg] Un-modeled Vane Bend ± 10° [deg] Un-modeled Vane Twist ± 5° Varying CG Locations +1.1m and -0.5m From center of sail

Six baseline maneuvers tested Four levels of increasing errors Fifty simulations runs per scenario 50 Simulation runs for one of the baseline maneuvers, moment bias in x-axis

Eldad and Lightsey – Sunjammer Attitude Control Slide 14 AIAA/USU Small Satellite Conference August 2014 Future Work

• Shift from MATLAB to flight code • Testing with hardware in the loop • Drive for increased accuracy  – Investigation of flexibility effects – Optimization of passive stability angles – Advanced moment allocation schemes

L’Garde

Eldad and Lightsey – Sunjammer Attitude Control Slide 15 AIAA/USU Small Satellite Conference August 2014 Summary

• In this decade, solar sails are emerging from science fiction into reality • Sunjammer will demonstrate largest and highest performance solar sail flown to date • Accurate and robust control a stepping stone for wider adoption • This research is producing a flyable attitude control system for solar sails

Bajoran Lightship Warp-Capable Eldad and Lightsey – Sunjammer Attitude Control Slide 16 AIAA/USU Small Satellite Conference August 2014