FORMI: A Fast Holonomic Path Planning and Obstacle Representation Method Based on Interval Analysis

This paper presents a path planning approach for mobile robots in 2D spaces. The algorithm uses a quadtree decomposition where the discretization precision is improved until a path to the goal is found if one exists. The algorithm uses interval analysis-based methods to categorize the quadtree decomposition to occupied, free and partly occupied cells. The proposed algorithm is compared against other concurrent path planning algorithms, A on an ordinary quadtree, A for shortest path on a binary occupancy grid, and a Dijkstra's algorithm for lowest collision probability in a continuous-valued occupancy grid, in five different scenarios.Compared to the other methods, the main advantage of our method is achieving a compromise between driving distance, safety, and computation time. The proposed algorithm was found to require significantly fewer collision checks in all scenarios while providing sub-optimum results, based on the obstacle distance and path length criteria. The algorithm is suitable for further extension to include non-euclidean measures and for higher dimensions of configuration spaces. The proposed algorithm will be publicly available on GitHub repository.