Global Optimality in Multi-Flyby Asteroid Trajectory Optimization: Theory and Application Techniques

TL;DR

This paper introduces a novel method for globally optimal multi-flyby asteroid trajectory design that transforms the problem into a multi-stage decision process, enabling efficient solutions with quantifiable optimality bounds.

Contribution

It develops a new approach transforming complex trajectory optimization into a multi-stage decision problem, allowing dynamic programming application and providing bounds on solution optimality.

Findings

Achieved improved fuel efficiency in benchmark asteroid trajectory problems.

Validated the method's effectiveness across impulsive and low-thrust scenarios.

Demonstrated generality and robustness in complex trajectory optimization cases.

Abstract

Designing optimal trajectories for multi-flyby asteroid missions is scientifically critical but technically challenging due to nonlinear dynamics, intermediate constraints, and numerous local optima. This paper establishes a method that approaches global optimality for multi-flyby trajectory optimization under a given sequence. The original optimal control problem with interior-point equality constraints is transformed into a multi-stage decision formulation. This reformulation enables direct application of dynamic programming in lower dimensions, and follows Bellman's principle of optimality. Moreover, the method provides a quantifiable bound on global optima errors introduced by discretization and approximation assumptions, thus ensuring a measure of confidence in the obtained solution. The method accommodates both impulsive and low-thrust maneuver schemes in rendezvous and flyby scenarios. Several computational techniques are introduced to enhance efficiency, including a specialized solution for bi-impulse cases and an adaptive step refinement strategy. The proposed method is validated through three problems: 1) an impulsive variant of the fourth Global Trajectory Optimization competition problem (GTOC4), 2) the GTOC11 problem, and 3) the original low-thrust GTOC4 problem. Each case demonstrates improvements in fuel consumption over the best-known trajectories. These results give evidence of the generality and effectiveness of the proposed method in global trajectory optimization.