Practical Problem Solving on Fast Trajectory Optimization

Transcription

1 Practical Problem Solving on Fast Trajectory Optimization Senior Lecture on Trajectory Optimization 3 rd Astrodynamics Workshop, Oct , ESTEC GmbH Andreas.Wiegand@astos.de

2 Intension What can be done with optimization? What means PRACTICAL? What dominates the optimization work? CPU time Operator time What means FAST? Using state of the art technology and hardware CPU-time is defined by computational accuracy and model complexity (c) GmbH 2

3 Optimization in Retrospect 1996: Straight forward optimization 500 optimizable parameter CPU critical 2006: up to 150,000 parameter and more Trajectory optimization and vehicle design optimization in parallel Low Thrust problems Not CPU critical Optimization with more than several dozen of parameters makes no sense. Don t waste time on the initial guess. (c) GmbH 3

4 Content Overview: applications of trajectory optimisation Requirements for fast and practical optimisation software Existing Software Possible Improvements Outlook (c) GmbH 4

5 Interplanetary Aero-Assisted Maneuvers Ascent Reentry Entry Destruction Formations Rendezvous Constellations Station Keeping Typical Aerospace Optimisation Applications Orbit Transfer Libration Point Missions (c) GmbH 5

6 Reentry Applications Reentry Entry Manoeuvre Entry trajectory Minimum possible loads Reference trajectory for entry guidance Determination of entry and landing window Cross-/Downrange computations (c) GmbH 7

7 Flight-Path - Planning Special trajectory for ATD flight experiments (c) GmbH 8

8 Ascent & Branched Trajectories Performance Indices maximize payload minimize fuel consumption minimize structural mass Boundary Conditions: initial conditions (launch pad) target orbit return of rocket stages staging conditions visibility from ground stations splash down of stages... Path Constraints: max. dynamic pressure max. heat-flux bending moment (qα) max. acceleration constraints on flight path... (c) GmbH 9

9 Safety Analysis Entry destruction analysis of upper stages (ASTOS-EDA) Trajectory modifications to ensure safe impact points in case of an failure Ballistic coefficients analysis Abort trajectory scenarios Collision avoidance during low-thrust flight main trajectory stage break-up EDA Impact Impact with Drag Impact without Drag demise (c) GmbH 10

10 Vehicle Design trajectory and vehicle parameter optimization structural masses of stages tanks engine parameters at chemical equilibrium Considering constraints (loads, safety) Shape optimization performance assessment of upper stage modifications Examples of design studies Mars ascent vehicle (MAV) Heavy Lift Launch Vehicle (HLLV) VEGA: upper stage with low thrust (c) GmbH 11

11 System Concept Validation Design reviews Nominal vs. non-nominal performance Sensitivity analysis Adjustment of mission parameters Investigation of alternate stages of a launcher different engine performance vs payload Different tank design LOX vs. Kerosene (c) GmbH 12

12 Low-Thrust Orbit Transfer Mission GTO-GEO transfer Optimization of Minimum transfer time Minimum fuel consumption Minimum degradation Pareto optimal solutions Consideration of Disturbances Eclipses Battery power Phasing with target longitude Slew rates (c) GmbH 13

13 Low-Thrust Orbit Transfer Mission (c) GmbH 14

14 Key points of an optimization model Point mass No moments Attitude control can be considered as commanded control Only two controls (side slip angle = 0) Optimised attitude controls allows to integrate the flight-path, but does not ensure, that this trajectory is flyable or useful for 6-dof simulation 6-dof attitude control with inverse dynamics provides 3 attitude controls Required control torque Additional constraints No geometry unless used for computation of Forces Volume of tanks Diameter of nozzles and stage (c) GmbH 15

15 Software Requirements How to handle all these different applications? A specialized tool for each application Difficult maintenance Duplication of code Learning time One tool which is Flexible/Modular Model definition Optimisation methods Complex like the problems User Guidance System manageable by nonexpert users Continuously maintained (c) GmbH 16

16 A Single Tool Solution Common properties EoM of one body Central body Cost functions related to Time Mass Other typical astrodynamic values Constraints Position Velocity Acceleration Forces One tool for atmospheric flight Launcher Reentry Possible extensions Orbit transfer Additional perturbations Various solvers Gradient methods Global optimization (c) GmbH 17

17 ASTOS AeroSpace Trajectory Optimization Software Completely data configurable (frequent changes in model data) Easy, intuitive Graphical User Interface Various optimization techniques Easy generation of Initial Guess Automatic scaling techniques Handles flat minima Large convergence radius Robust w.r.t. bad models Handles linear data interpolation Data visualization (c) GmbH 18

18 Product Interfaces 3rd party models NASA/CEA NASA/GRAM99 JPL/Ephemeris Pre-/Post processing Mathworks Matlab MS Excel Data Import/Export HTG/EDA ASTOS AeroSpace Trajectory Optimization Software GESOP Graphical Environment for Simulation and OPtimization User interface GUI Command Line Model interface Win32 DLL s, so-libs Ada, C, F77,.. Mathworks Simulink Intec / Simpack AGI / STK Celestia OrbiterSim (c) GmbH 19

19 ASTOS User Interfaces (c) GmbH 20

20 Optimisation Workflow Mission & Model Definition User Action Software Vehicle & Mission Requirements Initial Guess Generation Using Control Laws or existing solutions Control and State Discretization Specification of Constraints and Cost function considering quality of initial guess Optimization User & Software Change of Mission Requirements Yes Converged Result? Refinement of Constraints, Cost and Discretization (c) GmbH 21

21 Initial Guess with Control Laws Obtain Initial Guess from Existing state/control history Global optimisation Control Laws for Attitude Controls Constant or Linear Law Profile as Function of Time or Machnumber Vertical Take Off Gravity Turn Required Velocity Target Orbit Bi-Linear Tangent Law Dynamic Pressure Controllers for ascent and decent Constant Turnrate... Examples Launcher Start Sequence Vertical Take-Off Pitch Over Constant Pitch Gravity Turn Bi-linear tangent law (c) GmbH 22

22 Model Library Heart of application Object oriented design to ensure Flexibility, how to transcribe a subcomponent by a coded model object. Maintainability capsulated code easy to extend Fully data driven approach increases reliability no coding of developer/user to change the problem Becomes expandable due to user programming interface (c) GmbH 23

23 User coded models User programming interface for Propulsions Aerodynamics Vehicle Components provides functions for computation of Forces Masses as function of user defined variables ASTOS state vector: t Burn, t current, h, p, ρ, Ma, α, β, q, m total, a, dynamic viscosity Provides functions for definition and computation of Controls (thrust vector) Design Parameter Constraints Geometry Engine => max Isp Cost functions Auxiliary States Can be linked to ASTOS as DLL so-lib (c) GmbH 24

24 Optimizers of ASTOS Collocation Methods Multiple Shooting Methods TROPIC / SNOPT 3rd party solver SNOPT 5000 parameters SOCS automatic mesh refinement sparse solver 150,000 parameters PROMIS / SLLSQP integrated solver SLLSQP 500 parameters PROMIS / SNOPT CAMTOS / SNOPT 3rd party solver SNOPT hybrid optimizer 5000 parameters (colloc. & shoot.) indirect methods 5000 parameters Genetic Algorithm incl. local search refinement (c) GmbH 25

25 Transcription Methods and NLP Solvers Situation Transcription methods like collocation and multiple shooting have achieved a technical sophisticated level. Sparse NLP solver can solve large problems in acceptable time. The CPU time is comparable with operator time. (c) GmbH 26

26 Analysis Methods NLP- Solver output Constraint violation Merit function DoF Step Size Review Iteration Monitor Graphical History for each iteration of NLP status Optimizable parameters and constraints Additional Optimiser Output Gradient check Additional Optimiser Functions Automatic Mesh Refinement But at the end the operator has to analyse the complex output bring it in relation to the real problem Know how to influence the behaviour of the optimiser (c) GmbH 27

27 TSTO Saenger ascent from Istres with branched lower stage return 128 iterat. (c) GmbH 28

28 What are the real user wishes? Important Requirements of an Engineer Accurate? Fast? Robust is most important! How can robustness be improved Reduction of operator time Start from bad initial guess infeasible point Robust w.r.t. bad models Support in case of problems Reduction of complex know how: Current point cannot be improved (c) GmbH 29

29 ASTOS - Daily Work Are these requirements applicable to the daily optimisation work? (c) GmbH 30

30 Example: Pre-Phase A Study Launcher Design Nominal trajectory Sensitivity analysis Engine performance: Isp, thrust Structural index Different payload orbits Different propellants Different strategy for jettisoning the fairing Different strategy for splash down of upper stages Consideration of additional coast arcs Requirements Simple modification of mission and model definition restart of optimization based on old result Capability to modify phase structure and used EOM and controls Because of new mission requirements To avoid singularities in case of changed mission => fast over all process (c) GmbH 31

31 Concurrent Design 1. Subsystem mass correlation No CAD models available, too complex Fast model, accurate enough within margins 2. Design of Propulsion System (full stage design of launcher) Thrust and mass flow shall be optimizable Both values are coupled by chem./physical laws Complete cycle computation too complex (c) GmbH 32

32 Reduced view of trajectory optimization Prop. Sys. Definition Trajectory Thrust dm/dt Propell. Type Tank System 3-DoF view mass Propellant loading constraint cost θ,ψ,α,µ L/D force Shape design TPS Control Trimming Aerodynamics (c) GmbH 33

33 Work methodology Trajectory: not just a result, connecting part Mission Level Trajectory Reduced Level Ma-regime Accelerations Loads Altitudes Overall masses... Propulsion M&S ATD GNC Costs Constraints Objectives... Propulsion M&S ATD GNC Costs Cycle Program CAD Navier Stokes... Subsystem Level Specialist Level (c) GmbH 34

34 Mass Correlation Important criterion: m dry /m propellant Splitting of dry mass into subcomponents which depends on variable quantities: Tank mass (propellant mass) Shell mass (shell area) Truss mass (over all)... Constant masses kg Definition of analytical relationship Definition of correlation factors using linear, quadratic, exponential or logarithmic inter-or extrapolation LOX/LH2 0 kn (c) GmbH 36

35 Thrust & Massflow 2500 c * = f ( p, 0 A Trajectory optimization t, r) T = m& b ce η kg C*(r, p0) 2300 p0=10 p0= p0= p0=150 p0= p0= r m& b t = r p c 0 * A t Isp c = e p a LOX/LH2 A Ce (p0=100bar; r=5) A f ( p0, At, r, A m & = t Ae A t & m b Ae/At e t ) (# engines) CEA software ASTOS Optimizable Parameters p 0 = chamber pressure A A e = t expansion ratio A t = throat r = mixture #engines t r = throttle area ratio factor Engine Mass: Correlation from existing engines kn Aerodynamic Area = f Ae ( At,,# engines) A t Propulsion System Mass (c) GmbHAerodynamic Ref Area 37

36 Exhaust and Characteristic Velocity At Chemical Equilibrium Blue plane = Upper Isp (m/s) limit C* LH mixture ratio chamber pressure Only the surface below the plane provides realistic values with today s technology (c) GmbH 38

37 Practical Aspects of Engine Design System engineer can specify the bounds of parameters and the characteristics of the reduced model Engine throttling can be defined depending on the used model. Mixture Ratio can be considered as constant Optimizable but constant with switching point(s), which are optimizable Time variable and optimizable (control) Model can be easily changed Propellant loading of oxidizer and fuel tank is automatically adjusted considering mixture ratio and throttling Changing tank masses can be considered using mass correlation (c) GmbH 39

38 Summary of Efficient Trajectory Optimisation Interchangeability of data input Data handling Exchangeability between software tools of different domains Optimization Subsystem Calculation GNC design Visualization Version management of data driven model objects Improvements of numerical methods Numerical code more tailored to the requirements of an engineer Not pure CPU time is decisive factor but net process time of operator. (c) GmbH 41

39 Future of Optimisation Black Box Optimiser User is engineer not mathematician He needs to understand physical background of his problem, but not the difficult background of optimisation methods In 10 years every engineer will use optimization software similar to Matlab today Difficulties during the optimization run will be solved automatically or by intelligent support, where an error is transcribed into the physical meaning of the problem. => As important as faster solvers and faster CPUs (c) GmbH 42