Rule-based Optimal Control for Autonomous Driving

We develop optimal control strategies for Autonomous Vehicles (AVs) that are required to meet complex specifications imposed by traffic laws and cultural expectations of reasonable driving behavior. We formulate these specifications as rules, and specify their priorities by constructing a priority structure, called Total ORder over eQuivalence classes (TORQ). We propose a recursive framework, in which the satisfaction of the rules in the priority structure are iteratively relaxed based on their priorities. Central to this framework is an optimal control problem, where convergence to desired states is achieved using Control Lyapunov Functions (CLFs), and safety is enforced through Control Barrier Functions (CBFs). We also show how the proposed framework can be used for after-the-fact, pass/fail evaluation of trajectories - a given trajectory is rejected if we can find a controller producing a trajectory that leads to less violation of the rule priority structure. We present case studies with multiple driving scenarios to demonstrate the effectiveness of the proposed framework.