Robust Game-theoretic Motion Planning over Extended Time Horizons

Abstract

This work presents a solution to nonconvex, game-theoretic motion planning problems subject to disturbances over long time horizons. The problem is posed as a partially-decoupled generalized Nash equilibrium problem, in which each agent's dynamics depend only on its own state and control, admitting fast solution methods for competitive multi-agent motion planning. An algorithm, WOLF, is developed that applies receding-horizon model predictive control to an open-loop differential games solver based on sequential convexification. In contrast to robust formulations that fix the uncertainty description offline, the robustness tube here is itself a dynamic state, co-optimized with the trajectory, and its thickness directly sets the tightening of the shared coupling constraints. A sufficient condition is derived under which a nominal trajectory satisfying constraints tightened against all agents'error bounds remains feasible for every admissible disturbance realization. The method is demonstrated on two adversarial on-orbit games with coupled translational-attitude dynamics: a stealthy co-orbital jamming game under an active detection-probability bound, and a sun-blocking game in which an adversary disables an evader by decreasing solar power