Sub-optimal cooperative collision avoidance maneuvers of multiple active spacecraft via discrete-time generating functions

This study presents real-time sub-optimal control for cooperative collision-free transfers of multiple active (actuated) spacecraft in proximity operations. The constrained optimal control problem for collision-free transfers of multiple active spacecraft is decentralized and approximated as an unconstrained optimal control problem for single active spacecraft to mitigate the complexity and difficulty. The new penalty function is proposed by considering relative velocities for cooperative maneuvers between multiple active spacecraft, and is integrated with the quadratic cost function for optimal tracking by continuous-thrust control instead of the inequality constraints for avoiding collision. Then, the infinite-horizon control law applicable to each of multiple active spacecraft is obtained as an algebraic function of the states of both reference solutions and obstacles by employing discrete-time generating functions. Unlike conventional methods based on shooting, the proposed approach does not require repetitive process and initial guesses regardless of the number of active spacecraft. Illustrative examples demonstrate the effectiveness of the proposed approach with the new penalty function especially in simultaneous collision avoidance maneuvers of multiple active spacecraft.