Game Theoretic Planning for Self-Driving Cars in Competitive Scenarios

Abstract

We propose a nonlinear receding horizon game-theoretic planner for autonomous cars in competitive scenarios with other cars. The online planner is specifically formulated for a two car autonomous racing game in which each car tries to advance along a given track as far as possible with respect to the other car. The algorithm extends previous work on game-theoretic planning for single integrator agents to be suitable for autonomous cars in the following ways: (i) by representing the trajectory as a piecewise-polynomial, (ii) incorporating bicycle kinematics into the trajectory, (iii) enforcing constraints on path curvature and acceleration. The game theoretic planner iteratively plans a trajectory for the ego vehicle, then the other vehicle until convergence. Crucially, the trajectory optimization includes a sensitivity term that allows the ego vehicle to reason about how much the other vehicle will yield to the ego vehicle to avoid collisions. The resulting trajectories for the ego vehicle exhibit rich game strategies such as blocking, faking, and opportunistic overtaking. The game-theoretic planner is shown to significantly out-perform a baseline planner using Model Predictive Control which does not take interaction into account. The performance is validated in high-fidelity numerical simulations, in experiments with two scale autonomous cars, and in experiments with a full-scale autonomous car racing against a simulated vehicle.