A hybrid receding horizon control method for path planning in uncertain environments

For an autonomous vehicle navigating in a static environment for which an a priori map is inaccurate, we propose a hybrid receding horizon control method to determine optimal routes when new obstacles are detected. The hybrid method uses the level sets of the solution to either a global or local Eikonal equation in the formulation of the receding horizon control problem. Whenever an obstacle is detected along the path of the autonomous vehicle, a solution to a local Eikonal equation is used to determine whether a new, global Eikonal equation must be solved for use in the receding horizon optimization problem. The decision to select a new level set solution is made based on certain matching conditions that guarantee the optimality of the path. The selection of a global or local solution to the Eikonal equation induces a hybrid system structure in the control formulation. We rigorously prove sufficient conditions that guarantees that the vehicle will converge to the goal as long as the goal is accessible. In the end, simulation results are discussed.