A receding horizon controller for motion planning in the presence of moving obstacles

We address the minimal risk motion planning problem in a two dimensional environment in the presence of both moving and static obstacles. Our approach is inspired by recent results due to Vladimirsky in which path planning on time-varying maps is addressed using a new level-set approach, and for which computational costs are remarkably low. Toward practical implementation of these results for path planning in unstructured environments, we develop a receding-horizon formulation in which path planning for moving and static obstacles is addressed locally, while path planning for static obstacles is addressed globally. This formulation reduces the overall computational burden of path planning and makes it suitable for very large domains. The result is a suboptimal receding horizon planner and a matching condition that connects local planning with global planning. We present a rigorous analysis from which convergence to a desired endpoint is guaranteed.