Smooth Feedback for Car-Like Vehicles in Polygonal Environments

We introduce a method for constructing provably safe smooth feedback laws for car-like robots in obstacle-cluttered polygonal environments. The robot is taken to be a point with motion that must satisfy bounded path curvature constraints. We construct a global feedback plan (or control policy) by partitioning the environment into convex cells, computing a discrete plan on the resulting cell complex, and generating local control laws on the state space that are safe, consistent with the high level plan, and satisfy smoothness conditions. The trajectories of the resulting global feedback plan are smooth and stabilize the position of the robot in the plane, neglecting the orientation.