Multi-objective minimum time optimal control for low-thrust trajectory design

TL;DR

This paper introduces a reachability-based method for multi-objective optimal control in low-thrust spacecraft trajectory design, enabling efficient Pareto front construction and trajectory optimization.

Contribution

It presents a novel reachability approach using Hamilton-Jacobi-Bellman equations to compute Pareto fronts and optimal trajectories for low-thrust spacecraft missions.

Findings

Efficient construction of Pareto fronts from the HJB equation's zero level set.

Analytic derivation of Hamiltonian and optimal control policy.

Guaranteed weak Pareto optimality of reconstructed trajectories.

Abstract

We propose a reachability approach for infinite and finite horizon multi-objective optimization problems for low-thrust spacecraft trajectory design. The main advantage of the proposed method is that the Pareto front can be efficiently constructed from the zero level set of the solution to a Hamilton-Jacobi-Bellman equation. We demonstrate the proposed method by applying it to a low-thrust spacecraft trajectory design problem. By deriving the analytic expression for the Hamiltonian and the optimal control policy, we are able to efficiently compute the backward reachable set and reconstruct the optimal trajectories. Furthermore, we show that any reconstructed trajectory will be guaranteed to be weakly Pareto optimal. The proposed method can be used as a benchmark for future research of applying reachability analysis to low-thrust spacecraft trajectory design.