Motion Planning at Intersections with Safe Differential Games based on Control Barrier Function

Motion planning at intersections is a challenging problem in autonomous driving due to the complicated interactions. The existing pipeline of "planning after predicting" is too conservative, can reduce traffic efficiency. Using game theory to model the non-cooperative coupling relationships between multiple vehicles can resolve the above problems, but such methods cannot guarantee safety without collision. This paper presents motion planning for autonomous driving with safe differential games based on Control Barrier Function (CBF), and also provides a safety-critical generalized Nash equilibrium seeking algorithm. We handle the hard CBF constraints through augmented Lagrangian multiplier method. Motivated by iterative Linear-Quadratic Game (iLQG) algorithm, we use the Taylor expansion method to approximate the model into an Linear-Quadratic (LQ) structure, and then incrementally solve this problem with an iterative feedback LQ game algorithm. Through Carla simulation and hardware testing, our results indicate that the algorithm can find a balance between safety and efficiency while maintaining real-time implementation performance.