Game-Theoretic Motion Planning for Multiple Vehicles at Unsignalized Intersection.

The paper addresses the challenges posed by unsignalized intersections, particularly in situations involving multiple autonomous vehicles. Specifically, it focuses on motion planning for multi-vehicle scenarios at such intersections. To this end, we formulate the problem as a M -player general-sum dynamic game with a finite horizon. Given the criticality of efficiency and safety, we adopt a maximum-over-time cost structure and approximate the original game to a linear-quadratic game in the reach-avoid setting, enabling the use of dynamic programming. Game theory allows for a shared information view and consideration of all vehicles’ states. However, traditional methods are not suitable for large numbers of vehicles that meet at intersections. Therefore, we propose a matching policy that decomposes the game into two-player sub-games, allowing for scalability and efficient computation. By conducting simulation verification on our algorithm, we demonstrate its effectiveness in motion planning for multiple autonomous vehicles. Overall, the proposed approach provides a promising solution for motion planning at unsignalized intersections with multiple autonomous vehicles. Our method is released on https://github.com/lakiGuo/Reach-Avoid-Games .