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 PredictorâCorrector 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