Multi-objective low-thrust spacecraft trajectory design using reachability analysis

TL;DR

This paper introduces a novel reachability analysis-based method for multi-objective low-thrust spacecraft trajectory design, optimizing propellant use and transfer time while handling complex state constraints.

Contribution

It formulates a new approach to multi-objective optimal control problems using reachability analysis and viscosity solutions, applicable to realistic spacecraft transfer scenarios.

Findings

Successfully applied to asteroid orbital transfer problems.

Demonstrates effective handling of state constraints in trajectory optimization.

Provides a new framework for multi-objective control in space missions.

Abstract

One of the fundamental problems in spacecraft trajectory design is finding the optimal transfer trajectory that minimizes the propellant consumption and transfer time simultaneously. We formulate this as a multi-objective optimal control (MOC) problem that involves optimizing over the initial or final state, subject to state constraints. Drawing on recent developments in reachability analysis subject to state constraints, we show that the proposed MOC problem can be stated as an optimization problem subject to a constraint that involves the sub-level set of the viscosity solution of a quasi-variational inequality. We then generalize this approach to account for more general optimal control problems in Bolza form. We relate these problems to the Pareto front of the developed multi-objective programs. The proposed approach is demonstrated on two low-thrust orbital transfer problems around a rotating asteroid.