Feedback motion planning via non-holonomic RRT* for mobile robots

Here we present a non-holonomic distance function for unicycle-type vehicles, and use this distance function to extend the optimal path planner RRT* to handle nonholonomic constraints. The critical feature of our proposed distance function is that it is also a control-Lyapunov function. We show that this allows us to construct feedback policies that stabilizes the system to a target pose, and to generate the optimal path that respects the non-holonomic constraints of the system via the non-holonomic RRT*. The composition of the Lyapunov function that is obtained as a result of this planning process provides stabilizing feedback and the cost-to-go to the final destination in the neighborhood of the planned path, adding much flexibility and robustness to the plan.