Gaussian Process-Based Covariance Control for Autonomous On-Orbit Servicing

This paper presents a novel computational framework for the design of closed-loop guidance and control laws in highly uncertain environments, possibly characterized by unmodeled dynamics, navigation errors, and external disturbances. The proposed methodology integrates the use of Gaussian Process Regression (GPR) to model dynamics uncertainties within a stochastic optimal control framework. GPR provides a probabilistic approach to disturbance estimation, either using real-time or offline data, ensuring these uncertainties are well represented in the optimization problem. Advanced convexification techniques are used to transform the original non-convex stochastic control problem into a sequence of convex problems that can be efficiently solved by state-of-the-art interior-point algorithms. As a study case, the docking maneuver between an active chaser spacecraft and a passive target spacecraft in the presence of differential drag, with uncertainty in the ballistic coefficient is considered. The obtained numerical results suggest the effectiveness of the proposed approach in reducing the trajectory deviations from the nominal case even in the presence of uncertainties.