Trajectory Optimization and Guidance Methods for Mars Entry

This book systematically investigates the Mars entry problem from the perspectives of deterministic optimization, uncertainty optimization, and guidance. Began with a detailed review of the robotic missions and human-scaled exploration plans to Mars, theories or concepts of optimal control, uncertainty quantification, robust optimization, model predictive control, sequential convex programming, and computational guidance are subsequently introduced. Correspondingly, this book presents a series of trajectory planning and guidance algorithms to improve the robustness, reliability, and safety of the Mars missions. Because the Mars entry problem is studied using advanced mathematics, including probability theory, optimization theory, and cybernetics, thus the book is primarily designed as a textbook for graduate students in aerospace engineering, aeronautics, and astronautics departments. Engineers and researchers may also use this book as a reference or tutorial to help with the modeling and simulation of the Mars entry problem due to its thorough simulations and analyses. Contents Part I Fundamental Knowledge 1 Introduction 1.1 Mission Heritage 1.1.1 Robotic Exploration Missions 1.1.2 Human Mars Landing Plans 1.2 Advances in Mars Entry Trajectory Planning 1.2.1 Indirect Method 1.2.2 Direct Method 1.2.3 Heuristic Method 1.2.4 Uncertainty Optimization 1.3 Progress in Mars Entry Guidance 1.3.1 Reference Trajectory Tracking Guidance 1.3.2 Predictor–Corrector Guidance 1.3.3 Computational Guidance 1.3.4 Artificial Intelligence-Based Guidance 1.4 Discussions 2 Preliminaries 2.1 Entry Vehicle and Environment Models 2.1.1 Mars Gravity Field 2.1.2 Mars Atmospheric Density 2.1.3 Mars Entry Vehicle 2.1.4 Reference Frames 2.1.5 Translational Equations of Motion 2.1.6 Path Constraints 2.2 Convex Optimization 2.2.1 Second-Order Cone Programming, SOCP 2.2.2 Quadratically Constrained Quadratic Programming, QCQP 2.3 Uncertainty Quantification 2.3.1 Definitions and Categories of Uncertainties 2.3.2 Mathematical Foundations of Uncertainty Modeling 2.3.3 Uncertainty Optimization Methods 2.4 Robust Optimization 2.4.1 Deterministic Optimization, DO 2.4.2 Robust Optimization, RO 2.4.3 Reliability-Based Optimization, RBO 2.4.4 Reliability-Based Robust Optimization, RBRO 2.4.5 Typical Methods 2.5 Conclusions Part II Deterministic Optimization 3 Improved Gauss Pseudospectral Method for Mars Entry Trajectory Planning 3.1 Formulation of Mars Entry Problem 3.1.1 Equations of Motion 3.1.2 Constraints 3.1.3 Objective Function 3.1.4 Optimal Mars Entry Problem 3.2 Particle Swarm Optimization 3.3 Gauss Pseudospectral Method 3.4 Hybrid Optimization Strategy 3.5 Numerical Demonstration 3.6 Discussions 4 Improved Sequential Convex Optimization for Mars Entry Trajectory Planning 4.1 Reformulation of Entry Dynamics by Using Downrange Angle 4.2 Sequential Convex Programming Algorithm 4.2.1 Formulation of Problem 4.2.2 Convexification and Discretization of Problem 4.2.3 Summary of Algorithm 4.2.4 Numerical Demonstration 4.3 LGL Pseudospectral Sequential Convex Programming 4.3.1 Formulation of Problem 4.3.2 Convexification of Problem 4.3.3 Discretization of Problem 4.3.4 Summary of Algorithm 4.3.5 Numerical Demonstration 4.4 Discussions 5 Pseudospectral Model Predictive Convex Programming for Mars Entry Trajectory Planning 5.1 Generic Theory of PMPCP 5.1.1 Review of the MPCP Method 5.1.2 Pseudospectral Model Predictive Convex Programming, PMPCP 5.1.3 Implementation of PMPCP 5.1.4 Numerical Simulations 5.2 Mapped Chebyshev Pseudospectral Model Predictive Convex Programming 5.2.1 Synthesized Algorithm 5.2.2 Numerical Simulations 5.3 Conclusions 6 Indirect Sequential Convex Programming for Mars Entry Trajectory Planning 6.1 Mars Entry Terminal Altitude Maximization Problem 6.2 Improvements to Unified Trigonometrization Method 6.2.1 Review of the UTM 6.2.2 Improved Optimal Solution 6.3 Indirect Sequential Convex Programming 6.3.1 Convexification and Discretization 6.3.2 Further Discussions of UTM, SCP, and ISCP 6.4 Numerical Demonstration 6.4.1 Mars Entry Without Path Constraints 6.4.2 Mars Entry with Path Constraints 6.4.3 Further Comparison and Analyses 6.5 Discussions 7 Mars Entry and Powered Descent Using Collaborative Optimization 7.1 Problem Formulation 7.1.1 Optimal Mars Atmospheric Entry Problem 7.1.2 Optimal Mars Powered Descent Problem 7.2 Integrated Guidance Strategy Design 7.2.1 Optimal Handover 7.2.2 Integrated Guidance Framework 7.3 Methods of Solution 7.3.1 Reinforcement Learning 7.3.2 Hp-Adaptive Pseudospectral Method 7.4 Numerical Simulations 7.4.1 Simulation Setup 7.4.2 Simulation Results 7.4.3 Discussions 7.5 Conclusions Part III Uncertainty Optimization 8 Mars Entry Trajectory Optimization with Desensitized Optimal Control 8.1 Mars Entry Dynamics 8.2 Mars Entry Optimal Control Problem 8.3 Mars Entry Optimal Control with Sensitivity Penalties 8.4 Optimal Nominal Trajectory and Command Generation Using DCNLP 8.5 Simulation and Results 8.6 Discussions 9 Uncertainty Quantification for Mars Entry 9.1 Stochastic Nonlinear Dynamics for Mars Atmospheric Entry 9.2 Adaptive Generalized Polynomial Chaos Approach 9.2.1 Equivalent Deterministic Differential Equations via GPC 9.2.2 Spectral Decomposition 9.2.3 Random Space Decomposition 9.2.4 Obtaining Statistics of State Trajectory for Mars Entry 9.3 Numerical Simulations 9.3.1 Simulations Setup 9.3.2 Case 1: Uniform Uncertainty 9.3.3 Case 2: Gaussian Uncertainty 9.3.4 Analysis and Discussions 9.4 Conclusions 10 Robust Trajectory Optimization for Mars Entry 10.1 Trajectory Optimization Problem Formulation 10.1.1 Dynamics of Mars Entry 10.1.2 Constraints 10.1.3 Objective Functions 10.1.4 Optimization Problem Formulations 10.2 Uncertainty Quantification and Propagation 10.3 Robust Optimization Procedure 10.3.1 Reformulation of Robust Trajectory Optimization Problem 10.4 Quantification of Objective Function and Constraints Under Uncertainties 10.4.1 Quantification of Objective Function with Uncertainties 10.4.2 Quantification of Constraints with Uncertainties 10.5 Hp-Adaptive Pseudospectral Method 10.6 Assessment of Reliability and Robustness 10.7 Numerical Simulations 10.7.1 Simulation Setup 10.7.2 Case I: Final Altitude Maximization 10.7.3 Case II: Final Horizontal Position Deviation Minimization 10.7.4 Analysis and Discussion 10.8 Conclusions Part IV Robust Optimal Guidance Method 11 Direct Model Reference Adaptive Tracking Guidance for Mars Entry 11.1 Mars Atmospheric Entry Dynamics 11.2 Reference Drag Acceleration Profile 11.2.1 Drag Dynamics with Energy as Variable 11.2.2 Reference Drag Acceleration Profile 11.3 CGT-Based Direct Model Reference Adaptive Control 11.4 Longitudinal Entry Guidance Using Adaptive Controller 11.5 Heading Alignment Guidance Law 11.6 Simulation and Results 11.7 Conclusions 12 Computational Guidance Method for Mars Entry 12.1 Entry Guidance Problem 12.1.1 Mars Entry Dynamics 12.1.2 Constraints 12.1.3 Tracking Guidance via LQR 12.2 QCQP-Based Tracking Guidance Law 12.2.1 Quadratically Constrained Quadratic Programming 12.2.2 Pseudospectral Discretization 12.3 Implementation of Algorithm 12.3.1 Guidance Cycle 12.3.2 Improvements of Objective Function 12.3.3 Synthesized Tracking Guidance Algorithm 12.4 Numerical Simulation 12.4.1 Simulation Set-Ups 12.4.2 Monte-Carlo Campaign 12.5 Discussions References