https://ntrs.nasa.gov/search.jsp?R=20150010981 2017-12-10T00:41:51+00:00Z Adapting Guidance Methodologies for Trajectory Generation in Entry Shape Optimization
Motivation Flight Feasible Trajectories will Model Realistic In-Flight Thermal States: • Allow for increased accuracy in Thermal Protection System sizing (potential mass savings) • Reduce the number of design cycles required to close an entry spacecraft design (potential cost savings) 2
Novel Research Objective Develop a planetary guidance Develop a planetary guidance Develop a planetary guidance algorithm that is adaptable to: algorithm that is adaptable to: algorithm that is adaptable to: -Mission Profiles -Mission Profiles -Mission Profiles Mission Profiles -Vehicle Shapes -Vehicle Shapes -Vehicle Shapes Vehicle Shapes for integration into vehicle Skip optimization. Altitude Loft Direct Time 3
De-Orbit Sample Concept of Spaceflight Operations * Adapted graphic from NASA Johnson Space Center De-Orbit Separation Exploration : Vehicle completes mission Atmospheric over several day or weeks Entry Launch to: • Earth Orbit • Planetary Body Descent EDL Landing 4
Planetary Entry Spacecraft Design (cont ’ d) Mid - Low L/D Spacecraft L * Ellipsled Garcia et al., AIAA Conf. Paper * MSL Capsule – variable bank angle Prakash et al., * Orion Capsule fixed angle of attack NASA JPL www.nasa.gov High L/D Spacecraft L * NASP * Space Shuttle AIAA 2006-8013 – variable bank angle AIAA 2006-659 variable angle of attack * HL-20 AIAA 2006-239 5
Multi-Disciplinary Design, Analysis, and Optimization (MDAO) Minimize: Computer Generated Spacecraft Models Heat Rate (Trajectory/Shape) Available Ballistic Coefficient (Shape) Descent Technologies Entry Vehicle Un/manned Trajectory Optimization Planetary Modeling Aerodynamic (C D , C L ) & Models Coupled q Aerothermodynamic ( ) Mission Thermal Databases Profile Protection Structures System Decoupled (TPS) Sizing Iterations Decoupled Iterations Flight Feasible Guidance, Trajectory Database Navigation, & Control (replace Traj. Opt.) 6
Trajectory Optimization vs. Guidance Trajectory Optimization Guidance Multiple included Minimal included Constraints Any variable of interest Target specific Objective Combination of numerical and Purely numerical Solution analytical Minutes to hours Seconds Time to Solution Must enforce that a solution is No Guaranteed Solution found Handles large parameter Handles parameter changes Parameter Changes changes that are relatively small Nominal Trajectory – not Flight Feasible Trajectory Result always realistic control with realistic controls 7
Guidance Development Trade-Offs Adaptability Numerical formulation for adaptability to different vehicles and missions without significant changes Rapid Trajectory Generation Analytical driving function keep time to a solution low Minimize Range Error & Heatload Optimal Control theory to introduce heat load as an additional objective 8
Guidance Development Criteria Guidance Specific (In-Flight) • Determine flight feasible control vectors (control rate/acceleration constraints) • Be highly robust to dispersions and perturbations • Include a minimal number of mission dependent guidance parameters Vehicle Design Specific • Be applicable to multiple mission scenarios and vehicle dispersions • Manage the entry heat load in addition to achieving a precision landing 9
Types of Guidance Techniques Reference Tracking Only – follow a pre-defined track In-flight Reference Generation & Tracking – Generate a real-time reference trajectory and follow that track In-flight Controls Search – One dimensional search, usually solving equations of motion numerically In-flight Optimal Control – Requires numerical methods to meet some cost function 10
Types of Guidance Formulations Analytical Guidance Numerical Guidance • Accurate trajectory solutions • Simple to Implement • No simplifying assumptions Advantages • Computation time minimal (possibility of multiple entry cases to be simulated with few • Solution Guaranteed modifications) • Simplifications reduce accuracy of the trajectory solution • Convergence is not assured Disadvantages • Formulation tied to a specific • Convergence is not timely entry case 11
Novel Approach to Guidance for MDAO Real-Time Trajectory Generation and Tracking Adaptability Numerically solve entry equations of motion Use generalized analytical functions to represent the reference Adaptation of Shuttle Entry Guidance Techniques Rapid Trajectory Generation Use analytical driving function keep time to a solution low Use Single Optimal Control Point with Blending Adaptation of Energy State Approximation Techniques Minimize Range Error & Heatload Optimal Control theory used to introduce heat load objective 12
Skip Entry Critical Points Test Case: Orion Capsule, L/D 0.4 Begin with 1 st Entry portion of the trajectory and gradually includes Control: Bank Angle only remaining phases. 13
Trajectory Simulation Validation Simulation of Rocket Trajectories (SORT) Developed by NASA Johnson Space Center for Truth Model Space Shuttle Launch/Entry Simulations Open Loop Simulation (MATLAB) Open Loop Reference (SORT) Closed Loop Simulation (MATLAB) Closed Loop Reference (SORT) 14
Flight Dynamics Z ECF V proj V z b Horizontal Plane Diagrams D L Horizon x b Landing Site V b – body fixed coordinate V r Y ECF L - longitude - latitude – bank angle - flight path angle - azimuth X ECF ECF – Earth Centered Fixed 15
Trajectory Modeling sin r V 2 sin cos sin cos cos sin cos V D g r cos sin V 2 1 V 2 cos cos 2 cos sin cos cos cos sin cos sin L g V r cos r V r 2 2 1 sin cos cos L V r V cos sin tan 2 tan cos cos sin sin sin cos V cos cos V r r State Variables r - radial distance Vehicle and Planet Variables V - relative velocity Control Variables L, D - Lift, Drag Acceleration - bank angle - longitude g - gravity - latitude - angle of attack - Earth ‘ s Rotation - flight path angle – atmospheric density - azimuth 16
General Entry Guidance Block Diagram Send cmd Trajectory Solver to flight simulation Reference Trajectory: Analytical functions adapted from Shuttle Entry Yes Guidance R err ~= 0 Bank Schedule Solution: cmd Range Prediction : numerically solve No equations of motion, range calculation new Targeting Algorithm Solver : Single Point Optimal Control y Dispersed State : disp Solution from Energy State Approximation Purpose : Targeting for precision landing and minimizing heatload 17
Control Solution: Shuttle Entry Guidance Adaptation Shuttle Entry Guidance (SEG) Concept: Temperature Phase • Reference Tracking Algorithm, Closed Form Solution 2 d V C A r D D 2 dt m Bank Schedule Solution ( ) Reference Trajectory Range Prediction 2 D V C ref D h h ref s D V C ref D 2 V D C V C V C 2 f V dV 2 2 ref 2 1 0 D D D D V r r s ref ref ref ref ref = constant h h ref s 2 D g D D V V ref V ref ref 1 ref 2 2 1 h h L V g ref ref g D D V r D D v ref ref ref 18
Control Solution: Shuttle Entry Guidance Adaptation Improvements on Shuttle Entry Guidance “ Drag Based Approach ” • Increase # of segments • Increase order of polynomial • Change Atmospheric Model representation • Modify flight path angle representation Challenges with Drag Based Approach • Discontinuities between segments • Increasing # of coefficients for storage with increasing segments and/or order • Effect of small flight path angle assumption unknown • Formulations are derived from 2DOF Longitudinal EOMs 19
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