Real-time collision avoidance maneuvers for spacecraft proximity operations via discrete-time Hamilton–Jacobi theory

This study presents a sub-optimal feedback control that implements real-time collision avoidance for spacecraft in proximity operations. The penalty function for avoiding collision with obstacles is first incorporated into the performance index of a typical optimal tracking problem. Then, the infinite-horizon feedback control law is derived by employing generating functions in the framework of discrete-time Hamilton–Jacobi theory. The derived control law, which is an explicit function of the reference states and instantaneous positions of obstacles, allows active spacecraft to avoid collision in real-time. The proposed approach has advantages over conventional optimal collision avoidance approaches in that it does not require iterations with initial guesses, repetitive shooting-based process for multiple boundary conditions, and/or trajectories of obstacles to be known a priori. Numerical simulations demonstrate that the proposed algorithm with a properly designed penalty function is suitable for implementing optimal collision-free transfers in real-time.