PDE-based robust robotic navigation

In this paper, we propose a general, robust, and fast path planning framework for robotic navigation using level set methods. A medial point of the map is selected automatically to be a point source that transmits two wave fronts of different speeds. The first front propagates with a moderate speed to capture the map topology, while the second one propagates much faster at medial points such that the safest paths intersect the propagating fronts at those points of maximum positive curvature, which are identified by solving an ordinary differential equation (ODE). The motion of the front is governed by a nonlinear partial differential equation (PDE), which is efficiently solved using robust level set methods. The framework is general in the sense that it can be used for both 2D and 3D environments. It generates a collision-free optimum paths for partial or complete configuration space. Optimum planned paths can be controlled according to the surrounding environment and running conditions in order to follow the safest, shortest, or hybrid paths. We demonstrate the robustness of the proposed method by correctly extracting planned paths of complex maps with several obstacles.