Entry Trajectory Optimization for Mars Science Laboratory Class Missions Using Indirect Unified Trigonometrization Method

TL;DR

This paper applies the advanced Unified Trigonometrization Method (UTM) to optimize Mars entry trajectories, effectively handling control and state constraints, and demonstrating its advantages over traditional methods through comparison with direct optimization results.

Contribution

The study introduces the application of UTM to complex Mars entry problems, enabling simultaneous regularization of control and state constraints, which was challenging with traditional indirect methods.

Findings

UTM successfully handles control and state constraints in Mars entry optimization.

Results align well with direct optimization methods, validating UTM's effectiveness.

Unique control profile features have practical implications for entry trajectory design.

Abstract

Application of traditional indirect optimization methods to optimal control problems (OCPs) with control and state path constraints is not a straightforward task. However, recent advances in regularization techniques and numerical continuation methods have enabled application of indirect methods to very complex OCPs. This study demonstrates the utility and application of an advanced indirect method, the Unified Trigonometrization Method (UTM), to a Mars Science Laboratory type entry problem. The objective is to maximize the parachute deployment altitude for a free-time, fixed-final-velocity entry trajectory. For entry vehicles, in addition to the bank angle that is characterized by bang-bang control profiles, there are typically three state path constraints that have to be considered, namely, the dynamic pressure, heat rate and g-load. This study shows that the UTM enables simultaneous regularization of the bang-bang control and satisfaction of the state path constraints. Two scenarios with and without state path constraints are considered. The results obtained using the UTM for both of these cases are found to be in excellent agreement with a direct optimization method. Furthermore, an interesting feature emerges in the optimal control profile of the UTM during the initial high-altitude part of the resulting optimal trajectory for the scenario with state path constraints, which has an appealing practical implication.