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

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 multistage decision formulation. This reformulation enables the direct application of dynamic programming in lower dimensions and follows Bellman's principle of optimality. Moreover, the method provides a quantifiable bound on global optimum 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 on three Global Trajectory Optimization Competition problems, showing improved fuel efficiency over the best-known solutions and demonstrating its generality and effectiveness in global trajectory optimization.