A Nash-Stackelberg Game Theoretic Planner for Many-to-few Multi-vehicle Racing

Path planning is essential for intelligent vehicles, particularly in environments densely populated with large static and dynamic obstacles. Traditional path planners frequently struggle to balance speed, accuracy, and optimality in their solutions. This study proposes an adaptive defense planner for a multi-vehicle team racing scenario, employing a winner-takes-all rule optimized for speed and near-optimal performance in combative autonomous driving environments. We develop a Nash-Stackelberg nested game framework to simulate racing game scenarios. An interaction-enhanced iterated best response algorithm is introduced for determining each vehicle's optimal trajectory and inferring the adversary's planned path, aiming to find the Nash equilibrium solution in this multi-vehicle racing context. Specifically, in the sniping game phase, it is imperative to consider the track's curvature to adaptively select sniping weights, thereby achieving a balance between the blocking effect and the race progress. The trajectory is ultimately tracked in real-time using a Model Predictive Control (MPC) controller.