Game Theoretic Strategies for Spacecraft Rendezvous and Motion Synchronization

The rendezvous problem between two active spacecraft is formulated as a two player nonzero-sum differential game. The local-vertical local-horizontal (LVLH) rotating reference frame is used to describe the dynamics of the game. Linear quadratic cooperative and noncooperative differential games are applied to obtain a feedback control law. A comparison between Pareto and Nash equilibria was then performed. The state-dependent Riccati equation (SDRE) method is applied to extend the Linear Quadratic differential game theory to obtain a feedback controller in the case of nonlinear relative motion dynamics. Finally, a multiplayer sequential game strategy is synthesized to extend the control law to the relative motion synchronization of multiple vehicles.