Optimal Path Planning Using Generalized Voronoi Graph and Multiple Potential Functions

In this article, we present a novel nonuniform sampling technique, based on the pipeline of rapidly exploring random tree (RRT), for efficiently computing high-quality collision-free paths while maintaining fast asymptotic convergence to the optimal solution. Our nonuniform sampling method focuses on the area where the optimal path may exist so that the path planning process can be further accelerated. First, the environment map is initialized with the generalized Voronoi graph and a heuristic path is calculated. Second, the heuristic path is discretized to construct the multiple potential functions (MPF), where the MPF provides a nonuniform sampling distribution for the path planner. As a meta-algorithm, our method is applicable to other RRT methods and helps to improve the performance of the underlying algorithm dramatically. We also prove the probabilistic completeness and the asymptotic optimality of our algorithm. The time cost and path length are selected to demonstrate the effectiveness of our algorithm. Through a series of simulation and real-world experiments, it is confirmed that the proposed algorithm achieves convincing performance compared with the state-of-the-art path planning algorithms.