JAQAR Astrodynamics Package
Tools for planetary, interplanetary and Lunar trajectory optimisation
JAQAR Space Engineering Definition
The JAQAR Astrodynamics Package is a set of tools, designed to:
– Enable users to quickly and easily optimise trajectories • Preliminary assessment of both ascent and descent trajectories from and to a generic planet • Planetary transfers (one orbit to another) • Interplanetary transfers (one planet to another) • Lunar transfers (from Earth to the Moon and back)
– Facilitate user in designing complex trajectories
– Trade different orbit transfers in short time
– Visualise results immediately
– Export data to other tools (Excel/STK/etc.) Features
• Dedicated tools for dedicated orbits • Easy to use graphical user interface • Use of both global and local optimisers • Launcher performance evaluation and databases • All tools run on PC using Windows operating system • Free demos on the internet Software overview
JAQAR Astrodynamics consists of 6 packages:
• Swing-by Calculator (SBC) • Lunar Transfer Orbit Calculator (LTOC) • Orbit Transfer Optimiser (OTO) • Orbit Parameters Calculator (OPC) • STK Ephemeris Generator (STKephem) • Descent & Ascent Trajectory Optimiser (DATO) New DATO Descent & Ascent Trajectory Optimiser
Mr. Davide Starnone JAQAR Space Engineering, Italy, [email protected] Mr. Robin Biesbroek JAQAR Space Engineering, The Netherlands, [email protected] DATO Capability
• Preliminary assessment of both ascent and descent trajectories from and to a generic planet, offering the opportunity to optimise the vehicle configuration and performance, and to test some mission critical aspects.
• Relevant results on the trajectory to put a wanted payload in orbit or to land on a planet with the wanted MECO (Main Engine Cut-Off) velocity, can be generated, analysed and graphically visualised. DATO Software Structure (1/2)
DATO is principally built on a structure of the following 5 Units: 1. Main: to generate and manage the User interface; 2. Thread: DE optimisation loops; 3. DE Interface: Fitness function and some procedures to formulate the Physics of the problem; 4. RKN Propagation: numerical integration to propagate the trajectory; 5. Derivative: Equations of Motion and evaluation of the principal flight parameters.
Several additional secondary Units are used to support the primary units and to implement procedures, such as trajectory plots, data visualisation, genetic algorithms evaluation (crossover, mutation, selection). DATO Software Structure (2/2)
Through the GUI interface, the user can define the type of problem, ascent or descent. The User Interface is composed of four sections. DATO Optimisation Method
Genetic Algorithm - Try to mimic a simple picture of natural selection in order to find a good algorithm. Differential Evolution is a fast and reasonably robust stochastic parallel direct search evolution strategy optimisation method.
The crucial idea behind DE is a scheme for generating trial parameter vectors. Basically, DE adds the weighted difference between 2 population vectors to a third vector. This way no separate probability distribution has to be used which makes the scheme completely self-organizing. DATO Problem Modelling Ascent Trajectory (1/4)
Basic Assumptions 1. Rigid body; 2. Two-dimensional motion.
Motion
The motion is considered lying in the XLYL plane and the position of the vehicle is characterised by (R, !). The vehicle’s rotation is represented by "="(t). DATO Problem Modelling Ascent Trajectory (2/4)
Trajectory Phase Subdivision
First Stage: 1. Vertical ascent; 2. Linear pitch law; 3. Constant pitch law; 4. Gravity turn. Upper-Stages: 5. Gravity turn or Optimised pitch law. DATO Problem Modelling Ascent Trajectory (3/4)
Optimised Flight Parameters
DATO is able to optimise both space vehicle design and its trajectory.
For Vehicle Design: (each stage) GLOW • Thrust over Weight ratio at ignition (Gross Lift-Off Weight) • Initial propellant mass DATO Problem Modelling Ascent Trajectory (4/4)
Optimised Flight Parameters
For Trajectory Design: 1. Lift-off sequence 2. Gravity turn or Maximising the DE Fitness Optimised pitch control law ascent function That includes payload mass and Glow ratio, wanted altitude and wanted velocity on the orbit as well as constraints on maximum heat flux and ejection of the fairing
• In case selected by the user, best functioning of the upper stage is obtained via optimisation of Coast-arc duration. DATO Problem Modelling Descent Trajectory (1/3)
Basic Assumptions 1. Rigid body; 2. Two-dimensional motion.
Motion
The motion is considered lying in the XLYL plane and the position of the vehicle is characterised by spherical coordinates (R, !), with !=90 [deg]. The vehicle’s rotation is represented by the pitch angle "="(t). DATO Problem Modelling Descent Trajectory (2/3)
Trajectory Phase Subdivision
Flight phase 1 – Descent Orbit Insertion (DOI): Impulsive manoeuvre from parking orbit (circular, elliptic or hyperbolic) to a lower altitude (optimised);
Flight phase 2, 3, 4 – Powered Descent Initiation (PDI): divided into three operational phases (Braking, Approach, and Landing). During the three powered descent phases, the vehicle’s mass decreases its value during the motion, because of the consumption of the propellant and for the eventual ejection of stages. DATO Problem Modelling Descent Trajectory (3/3)
Optimised Flight Parameters
• Depending from the user selection, altitude or velocity to reach at the end of each phase is considered to optimise the duration of the descent trajectory. • True anomaly at start of PDI phase is the initial condition to optimise the initiation of the powered descent. • Initial angle of attack and its rate of variation are instead optimal parameters for the control law, guiding the vehicle to land. • An optimal descent trajectory is achieved, minimising the DE Fitness descent function, which principally acts on the difference between the flight and the maximum MECO velocity. 2 2 R0 # x $ y DATO Problem Modelling Equations of Motion
& V ' d &R' R # (V ) ( ) ( ! ) dt ,! - * + % ,( R -) Integration via
& F ' X L Runge-Kutta method ( ) V & 2 ' m(t) d & R ' 1 V! ( ) ( ) # ( ) $ dt V R *V .V ( F ) , ! - Local , ! R - YL Local ( ) ,( m(t) -) Local
Ascent Initial Condition Descent Initial Condition
Initial R # x2 $ y2 R # R% $ hLaunchPad 0 Initial y ! # ! !0 # arctg( ) LaunchPad x Initial V # */V .sin ! $V .cos! 0 VR # 0 R0 y 0 x 0 V Initial # R .+ V # * V .cos ! *V .sin ! ! % % !0 / y 0 x 0 0 2 2 R0 # x $ y DATO Test Cases
• Two optimisation of trajectory (ascent and descent test cases) are presented.
• Examples are given for a lift launch vehicle and Lunar descent vehicles.
• The obtained results are compared to referenced data. 2 2 R0 # x $ y DATO Test Cases
Ascent Trajectory – VEGA launcher
Deliver a payload of 2250 [kg] at 400 [km] of altitude without coast-arc during the upper stage burn.
VEGA Flight Data DATO Optimisation
Total ascent time 690 [s] 698.9 [s] Gross lift off mass 138 [tonnes] 141 [tonnes] T/W ratio 2.2 2.1 Stage 1 T/W ratio 3 2.9 Stage 2 T/W ratio 2 1.9 Stage 3 T/W ratio 0.082 0.080 Stage 4 2 2 R0 # x $ y DATO Test Cases
Ascent Trajectory – VEGA launcher
450 400 350 ]
m 300 k [ 250 e
d 200 u t i t
l 150 A 100 50 0 00.00 02.53 05.46 08.38 11.31 14.24
Time [min:sec] 2 2 R0 # x $ y DATO Test Cases
Descent Trajectory – LES-3 vehicle
• The spacecraft was designed to transport a payload to the Lunar Surface.
• A Soyuz-ST launch, followed by a direct transfer to the Moon and Lunar Orbit Insertion, leaves a mass of 1800 [kg] in Low Lunar Orbit (LLO). This is the starting mass for the DOI.
• That mission has the aim to land with the Lunar Exploration Module on the Moon surface with a maximum allowed vertical velocity at MECO equal to 2 [m/s]. Descent is assumed to take place starting out from a 100 [km] LLO. 2 2 R0 # x $ y DATO Test Cases
Descent Trajectory – LES-3 vehicle
LES-3 Data DATO Optimisation
Total descent 651 [s] 642 [s] time Landing Mass 971 [kg] 947 [kg]
Ground track 540 [km] 532 [km] 2 2 R0 # x $ y DATO Conclusions (1/2)
• Fundamental aspect: Opportunity to optimise, via differential evolution algorithms, the vehicle performance and to test some mission critical aspects of both ascent and descent trajectories from and to a generic planet. 2 2 R0 # x $ y DATO Conclusions (2/2)
DATO main features: 1. Extremely flexibility; 2. Fast capability of evaluation; 3. User friendly Interface.
Next upgrades: 1. Extension of motion at three-dimensional trajectories; 2. Implementation of issues such as wind, thrust misalignment, launcher deflection, etc., causing the real trajectory to deviate from the nominal one. JAQAR and STK
• JAQAR and engineers of the Satellite Tool Kit (STK) have worked together to establish an effective interface between STK and the JAQAR Astrodynamics Package.
• As a result: – SBC and LTOC create complete STK scenarios with trajectory files already imported – SBC, OTO and LTOC create complete STK scenarios based on numerical propagation using STK/Astrogator.
• An extra package exists to convert user-defined trajectory files to STK format (STKephem). Conclusions
• The JAQAR Astrodynamics Package is a Commercially Off-The-Shelf set of tools, applicable to a wide variety of orbit transfers – Easy to use – Fast results – Exportability
• JAQAR Astrodynamics is available to customers at an affordable price. – Customers include ESA, NASA (Goddard), SSTL (UK), MD Robotics (Canada), Orbital Sciences (USA).
• Student license available – Hundreds of students all over the world are using it. Questions?
For more information:
• Contact JAQAR at [email protected]
• Or: visit the web-site and download our demos: www.jaqar.com