PDE-based robust robotic navigation

In robotic navigation, path planning is aimed at getting the optimum collision-free path between a starting and target locations. The optimality criterion depends on the surrounding environment and the running conditions. In this paper, we propose a general, robust, and fast path planning framework for robotic navigation using level set methods. A level set speed function is proposed such that the minimum cost path between the starting and target locations in the environment, is the optimum planned path. The speed function is controlled by one parameter, which takes one of three possible values to generate either the safest, the shortest, or the hybrid planned path. The hybrid path is much safer than the shortest path, but less shorter than the safest one. The main idea of the proposed technique is to propagate a monotonic wave front with a particular speed function from a starting location until the target is reached and then extracts the optimum planned path between them by solving an ordinary differential equation (ODE) using an efficient numerical scheme. The framework supports both local and global planning for both 2D and 3D environments. The robustness of the proposed framework is demonstrated by correctly extracting planned paths of complex maps.