Stochastic Differential Dynamic Programming for Trajectory Optimization under Partial Observability

TL;DR

This paper introduces a stochastic differential dynamic programming algorithm for coupled trajectory optimization, orbit determination, and correction planning under uncertainty, improving robustness and efficiency in spacecraft navigation.

Contribution

It develops a novel method that explicitly accounts for covariance dynamics without the separation principle, enabling navigation-aware and uncertainty-robust trajectory solutions.

Findings

Produces navigation-aware, uncertainty-robust trajectories in various dynamical systems.

Achieves lower fuel consumption compared to deterministic methods in the three-body problem.

Demonstrates effectiveness across different observation models and uncertainty levels.

Abstract

Designing spacecraft trajectories remains challenging in the presence of stochastic effects such as maneuver execution errors and observation uncertainties. Although covariance control and belief-space planning provide useful tools for designing robust control policies and information-aware trajectories under uncertainty, practical methods remain limited for partially observable trajectory optimization problems in which trajectory design, orbit determination, and correction maneuver planning are tightly coupled. This paper presents a stochastic differential dynamic programming algorithm for such coupled problems. The proposed method optimizes the nominal control sequence and feedback gains subject to belief dynamics and general mission constraints, explicitly accounting for the dependence of covariance propagation on the nominal trajectory without relying on the separation principle. Numerical examples demonstrate that the proposed algorithm produces navigation-aware and uncertainty-robust solutions across a range of dynamical systems, observation models, and uncertainty levels. In particular, the circular restricted three-body problem shows that the proposed method can exploit the coupling between trajectory design and orbit determination to obtain navigation-aware solutions with substantially lower fuel consumption than those from deterministic local optimization starting from the same initial guess.