Coupled Low-Thrust Trajectory And Systems Optimization Via .
Coupled Low-Thrust Trajectory and SystemsOptimization Via Multi-Objective Hybrid Optimal ControlMatthew A. Vavrina, a.i. solutionsJacob A. Englander, NASA GSFCAlexander R. Ghosh, University of IllinoisJanuary 13, 20151
Low-Thrust Systems Design Low-thrust trajectory & s/c hardware system are tightly coupledBOL p0: 30 kW, 3 thrusters– Definition of traj. dependent on propulsion system, LV– SEP has variable power & dependent on array size Systems design problem––––Different possible Isp, power levels, number of thrusters, launch vehicleRealistic engine, array models are discreteHybrid optimal control problemDesign space is multimodal, mixed parameter, often expansive Traditional approaches to sample trade space– Directly vary power & Isp in optimization formulation– Simplified models, characteristic solutions– Parametric studies, grid searchesBOL p0: 68 kW, 7 thrusters Limitations–––––Trajectory opt. requires initial guess; locally optimal onlyOnly single-objective opt. strategies employedGrid searches intractableLimited fidelity w/out trading realistic hardware modelsNo full mapping of optimal trade space2
ObjectiveSolve multi-objective, low-thrust systems optimizationproblem to fully map optimal systems trade spadeMethod should be:Mars Capable of global trajectory & systemsparameter search Automated Free of user-defined initial guess Able to search broad design space Medium fidelity for preliminary design purposes EfficientEarthJupiterThrustingCoasting3
Multi-objective Optimization Want to optimize any number of mission design metrics– e.g., payload mass, TOF, array size, ref. power, number of thrusters– Often coupled & competing– Fully map mission trade-offs between optimal solutions Optimize multiple objectivessimultaneously– Entire set of optimal solutions– Goal: generate representation ofPareto front– Traditionally use repetitions ofsingle objective techniquef1: return massPareto frontFeasible designsf2: BOL power4
Multi-objective Systems OptimizationApproach: Solve coupled problem simultaneously w/ hybrid optimalcontrol algorithm Multi-objective genetic algorithm (GA) as outer loop systems optimizeraround direct-method inner loop trajectory optimizer– Non-dominated Sorting Genetic Algorithm II (NSGA-II) searches over systemsparameters, defining trajectory problem– Monotonic basin hopping (MBH) sequential quadratic programming (SQP) solvestrajectory problemInitial generationFinal generationPopulation evolves viagenetic operatorsPayloadMassBOL powerPayloadMassBOL power5
Genetic AlgorithmInitial random populationgenerated Models Darwinian evolution– Mimic natural selection & reproductionAssign fitness valueIs stoppingcriteria met?YesStopNoSelection Searches with population of designs Globally search design space No initial guess requiredCrossoverMutation6
NSGA-II Develops globally-optimal Pareto solutions using non-dominated sorting– Evolves population towards Pareto front Fitness assignment based on “nearness” to Pareto front– x1 dominates x2 if: p : f p (x1 ) d f p (x 2 )p 1,2,., nobjfront 1 (Pareto front)andp 1,2,., nobj If neither design dominates other, theyare non-dominant Non-dominated sorting:– Assign fitness based on design’s nondominated front– Designs closer to Pareto front Æ betterfitness & more mating opportunitiesf1: final mass p : f p (x1 ) f p (x 2 )5front 2front 3214736f2: time of flight7
Low-Thrust Trajectory OptimizationNeed automated, robust method that does not require initial guess Solution: apply a global-local hybrid algorithm– Formulate problem based on Sims & Flanagan transcription– Monotonic basin hopping (MBH) drives global search– Gradient-based optimizer solves NLP (SNOPT used)Control NodeMatch PointImpulse Robust & efficient formulationSegment Boundary Continuous thrust approximated– Trajectory discretized into segments– Impulsive ǻV at segment midpoint Efficient constraint handling– Gradients guide search– Robust & efficient formulation Proven approach in EMTG software(Evolutionary Mission Trajectory Generator)LegFrom Sims and Flanagan8
Monotonic Basin Hopping SQPGALLOPStochastic, global search schemeNo initial guess requiredAdept at multi-modal problems w/ clustered local minimaStochastic “hops” evaluated from base solution– Pareto distribution balances exploration & exploitationHop 1f1 Base designHop 2After gradient-basedoptimizationAfter gradient-basedoptimizationx19
Multi-objective Systems Optimization AlgorithmGenerate P1, the initial parent population oftrajectory problems defined by system design Gen 0variablesGlobally optimize each individual of P1 viaMBH NLP algorithm to determine objectivefunction values Synergistic relationship between outer &inner loops Generates globally optimal Pareto solutionsfor mission trade evaluation Any number of objectives viable Flexible to any unique mission constraints,trajectory constraints enforced in EMTGNon-dominated sort P1 to determine rankAssign crowding distance to P1Selection: select individuals from P1 viacrowded tournament selection to form parentpool, SCrossover: generate initial offspringpopulation, Q1, from S using uniformcrossoverMutate: Randomly alter individuals in Q1Globally optimize current Q via MBH NLPMaximumgeneration?YesStopGen Gen 1Combine Pt and Qt to form RtNoNon-dominated sort Rt to generate Pt 1Crowded tournament selection on Pt 1to generate parent pool SUniform crossover of S to createoffspring population, Qt 1Mutate Qt 110
Conclusions Hybrid optimal control algorithm developed for low-thrust spacecraft systemsdesign– Outer loop: NSGA-II solves systems optimization problem– Inner loop: MBH SQP solves trajectory optimzation Generates globally optimal Pareto solutions for mission trade evaluationAutomatedAny number of objectives viableAbility to trade discrete, realistic hardware modelsGeneral applicability to any interplanetary, low-thrust mission– Flexible to any unique mission constraints, trajectory constraints enforced in EMTG Can make large systems problems computationally tractable11
Example Problem: ARRM Asteroid Robotic Retrieval Mission: return asteroid boulder or entire asteroid– Extensibility option is to return boulder from Deimos– Want to understand how return mass & TOF are affected by array size, # of thrustersÆ Multiple objectives: maximize return mass, minimize TOF, minimize BOL power, minimize #of thrusters (all coupled)Mission ParametersDescriptionValueSystem Design VariablesDesign VariableLaunch optionSolar array sizeInteger[0, 1][0, 20]ValueResolution{Delta IV-H from LV curve,Delta IV-H with LGA}-[30, 70] kW2 kWLaunch windowopen epoch[0, 4]Flight time[0, 26][700, 3300] daysEngine type[0, 2]{high-Isp, medium-thrust, highthrust}-Number ofengines[0, 5][2, 7]1{2020, , 2029}Launch windowWait time at BennuMin. spacecraft mass with 2thrustersAdditional dry mass per extrathruster1 year[430, 700] days5991 kg75 kgMax. depart. mass if lunar gravityassist (C3 2.0 km2/s2)11191 kgMax. departure mass if directlaunch (C3 0.0 km2/s2)10796 kgMaximum C3 if direct launchPost-mission V, IspThruster duty cycleSolar array modeling6 km2/s275 m/s, 3000 s90%1/r21 year100 daysSpacecraft bus powerPropellant margin2 kW6%12
Pareto-Optimal Solutions13
Optimal Trade Space Sharp increase in maximum return mass w/ increasing power– Increase in dry mass for increased power not accounted14
Optimal Design ParametersHigh-Isp EngineHigh-Thrust EngineMedium-Thrust Engine Distinct grouping of engine modes based on TOF– Return mass plateaus for different engines15
Backup16
Example: Bennu Large-Mass Sample Return Asteroid Robotic Retrieval Mission (ARRM) Option B targetMission ObjectiveLaunch VehicleReturn a large boulder from BennuDelta IV Heavy direct (C3 6.0)Delta IV Heavy with lunar flyby (C3 2.0)Power SystemArray power at 1 AUCell performance modelSpacecraft bus powerPower marginPropulsion SystemThrusterNumber of thrustersDuty cyclePropellant tankMission SequenceInner-Loop Objective FunctionOuter-Loop Objective Functionschosen by optimizer1/r22.0 kW0%chosen by optimizer (high-Isp , medium thrust, or high-thrust versions of a large Hall thruster)chosen by optimizer (2, 3, 4, 5, 6, 7); dry mass increases by 75 kg for each addtl thruster90%unconstrainedDirect travel to Bennu followed by direct return to C3 2.0 for lunar flyby captureMaximize sample return massSample return massSolar array sizeNumber of thrustersFlight time17
Bennu Sample Return: Outer-Loop MenuPower Supply at 1 AUCode Array Output300321342336 7020Launch YearCodeYear0201912020220213202242023Earth Departure TypeCodeType0Delta IV-H direct1Delta IV-H w/ LGAFlight Time Upper BoundThruster TypeCodeDaysCodeThruster07000 13 kW Hall (High-Isp)18001 13 kW Hall (medium-thrust)29002 13 kW Hall (High-thrust)310004110051200713008140091500101600 263300Number of ThrustersCode # Thrusters021324354657102,060 possiblecombinations18
Bennu Sample Return:Final Generation Trade Space19
Bennu Sample Return:Evolution of Populationgeneration 0generation 30generation 5generation 50generation 10All generations20
Bennu Sample Return:Objective SpaceReturn mass vs. array sizeReturn mass vs. array size21
Bennu Sample Return:Objective SpaceTOF vs. array sizeTOF vs. number of thrusters22
Bennu Sample Return:Optimal Design VariablesDeparture TypeDeltaIV-H directDeltaIV-H LGAEngine TypeHigh-Isp EngineHigh-Thrust EngineMedium-Thrust Engine23
Bennu Sample Return:Two TrajectoriesA 8-year mission with a 58 kW solararray returns a 20 ton boulderA 3.3-year mission with a 70 kW solararray returns a 2.2 ton boulder24
Efficient constraint handling – Gradients guide search – Robust & efficient formulation Proven approach in EMTG software (Evolutionary Mission Trajectory Generator) Low-Thrust Trajectory Optimization From Sims and Flanaga
(like hiking and dining) or different transportation modes, such as walking and driving. We show examples of trajectory classification in Section 7. Trajectory Outlier Detection: Different from trajectory patterns that frequently occur in trajectory data, trajectory ou
Actuator Thrust Applications. Thrust (Multi-Turn Valves) For Gates, Globes, or Sluice Gates, the thrust can be calculated from the pressure and valve data. Thrust and Torque Ratings must be considered when sizing. Valve threaded stem must not exceed thrust base limitations. Don’t plan on using tubing brackets for thrust
Jan 11, 2011 · The standard MX actuator thrust base is the A1 and may be bolted directly to the actuator. The thrust base contains a bronze alloy thrust nut that may be machined to suit the valve stem. An A1E thrust nut can be provided and may be installed to reach shorter stems. A1 base Housing, torque/ thrust Pipe plug Wa
Thrust Ball Bearing with Outer Cover The structure of thrust ball bearing with outer cover is the same as that of single direction thrust ball bearing, but, there is an outer cover on the seat washer (or there are outer covers on the inner and outer diameters of a seat washer). The structure is as Fig.1 and Fig.2. Thrust ball
The rotational speed of the thrust disk was measured by a photoelectric sensor, Sensor 3. All of the test data was recorded in the software of eZ-TOMAS 8.0 when the thrust disk was set in motion by hand. 3. Simplified Model The force analyses of the thrust disk and tilting pads are pre-sented in Figure 3. The thrust disk was floated on an air .
Despite what could seem intuitive, adding low-thrust arcs to a MGA trajectory does not change the global nature of the solution ar,whenthe solution is optimal) are only locally shaping each trajectory leg, tuning the entry conditions to a GA maneuver at a lower cost than deep-space maneuvers.
Several benefits of using the NASA General Mission Analysis Tool (GMAT) for trajectory design are also demonstrated. Specific analysis using GMAT includes an investigation of the Earth-Moon-Sun dynamics as they apply to the initial lunar-flyby trajectory, the use of the Sun-Earth L1 Lagrange point to transition from an Earth-
engineering materials, tools, equipments, manufacturing processes, basic concepts of electro-mechanical controls of machine tools, production criteria’s, characteristics and uses of various testing instruments and measuring or inspecting devices for checking components or products manufactured in various manufacturing shops in an industrial environment. It also describes and demonstrates the .
