Graph-Based Autonomous Vehicle Motion Planning Using Game Theory

Abstract

Autonomous driving technologies promise safer, more efficient, environmentally friendly, and accessible mobility systems. To realize these benefits, advanced planning and control algorithms are crucial. Given the interactions between Autonomous Vehicles (AVs) and human-driven vehicles in mixed traffic, as well as with pedestrians and cyclists, the deci- sions and trajectories of AVs significantly impact other road users. Therefore, considering these interactions is vital for achieving safe and efficient AV driving behavior. In automated driving, the basic idea is to traverse from point A to point B au- tonomously. This state space is often represented as an occupancy grid or lattice that depicts where objects are in the environment. From the planning point of view, a path can be set by implementing graph-based algorithms that visit different states in the grid, solving the path-planning problem. The graph-based algorithms treat the static and dy- namic objects/actors detected by the perception system as static impassable areas inside their costmap and fail to capture future actions. Considering the intention of road users results in a more reliable path and control for the AV to follow. Game theory is a framework for addressing problems involving multiple decision-making agents, where each agent’s decision is influenced by the choices of others. The appropriate solution depends on the game’s structure and the relationships between players. In this work, we explore Nash, Stackelberg, and Bayesian equilibria as solutions to the interactions between AV and road users. Nash equilibrium ensures that all participants in the game are treated equally, such that no player can reduce their cost by changing their strategy unilaterally. Stackelberg equilibrium considers a hierarchical structure, where leaders and followers exist among the players. Leaders commit to a strategy first, and followers react optimally to this decision. Bayesian equilibrium incorporates uncertainty and incomplete information, where players have beliefs about the types and strategies of other players. By investigating these equilibrium concepts, we aim to develop optimal strategies for both AV and road users, ensuring effective and efficient motion planning for AV. In this research, a graph-based algorithm will be integrated with game theory to plan the motion of AV, considering the future actions and decisions of other road users. Numerical and experimental simulation results demonstrate that the proposed framework effectively manages interactions between AV and other road users, such as human-driven vehicles or pedestrians, across various scenarios.