Multi-Objective Optimization of Covariance and Energy for Asteroid Transfers

Abstract

This paper presents a multi-objective optimization approach to minimize both error covariance and energy using indirect methods. Linear covariance dynamics and a continuous thrust model with control-dependent noise are implemented. Two formulations are considered: 1) a weighted-sum cost function with covariance and energy terms, and 2) a covariance cost function with an energy constraint (the epsilon-constraint method). In general, the former is simpler to implement, whereas the latter is more rigorous. However, a theorem is presented to prove that the necessary conditions for optimal control are equivalent in both formulations, and the first can be used to locate Pareto-optimal trajectories without sacrificing optimality. To provide an explicit example, this approach is applied to orbital maneuvers about an asteroid. Terminator orbit transfers, phasing maneuvers, and “proactive station-keeping” maneuvers are optimized, and the results indicate that significant uncertainty reduction is possible with small penalties in energy cost. Finally, Monte Carlo results verify that a linear covariance propagation was sufficient for these applications.