A Preview of Open-Loop and Feedback Nash Trajectories in Racing Scenarios

Trajectory planning for autonomous race cars poses special challenges due to the highly interactive and competitive environment. Prior work has applied game theory as it provides equilibria for such non-cooperative dynamic problems. This contribution introduces a framework to assess the suitability of the Nash equilibrium for racing scenarios. To achieve this, we employ a variant of iLQR, called iLQGame, to find trajectories that satisfy the equilibrium conditions for a linear-quadratic approximation of the original game. In particular, we are interested in the difference between the behavioral outcomes of the open-loop and the feedback Nash equilibria and show how iLQGame can generate both types of equilibria. We provide an overview of open problems and upcoming research, including convergence properties of iLQGame in racing games, cost function parameterization, and moving horizon implementations.