THE MINIMUM-TIME CRASHING PROBLEM FOR THE DUBINS' CAR

This paper determines the time-optimal trajectories bringing a car-like robot, whose driving velocity is constrained to be strictly positive (Dubins' car), in collision with the obstacles in its workspace. Both the robot and the obstacles are assumed to have polygonal shape. Based on these trajectories, a distance function is defined and computed that takes into account the nonholonomic constraints and captures the non-symmetric nature of the system.