Stochastic Trajectory and Robust Controller Optimization via Contractive Optimal Control

Optimal stochastic trajectory optimization and robust control is of utmost importance for space missions to achieve success, particularly when faced with the challenges of highly uncertain and dynamic environments. These missions’ intricacy and variable nature necessitates sophisticated techniques that can generate and execute optimal trajectories, whilst simultaneously accounting for the disturbances and time-varying uncertainties that may arise. In this work, we propose a systematic way to optimize robust trajectories under uncertainty, endowed with realtime robust feedback controllers to distribute robustness and develop a less conservative mission design architecture. The novelty of our approach lies in the combination of two techniques: ensemble transcription with pseudospectral optimal control for stochastic trajectory optimization and Continuous Contraction Metrics (CCM) for robust controls against stochastic disturbances and uncertainties. By integrating these techniques, we provide a powerful and unprecedented tool for designing and controlling space trajectories which is highly efficacious in enhancing the safety, efficiency, and success of space missions. Through simulations on a benchmark cross-range maximization re-entry optimal control problem, the effectiveness of our approach is substantiated with non-gaussian uncertainties. The results proffer compelling evidence that our proposed approach can implement and distribute robustness between reference trajectory and the controller with realistic uncertainty propagation.