LTA*: Local tangent based A* for optimal path planning

Abstract

Optimal path planning on non-convex maps is challenging: sampling-based algorithms (such as RRT) do not provide optimal solution in finite time; approaches based on visibility graphs are computationally expensive, while reduced visibility graphs (e.g., tangent graph) fail on such maps. We leverage a well-established, and surprisingly less utilized in path planning, geometrical property of convex decompositions i.e. a concave shape can be decomposed into multiple convex shapes. We propose a novel local tangent based approach, inspired by such convex decompositions, to path planning in non-convex maps. Although our local tangent approach is inspired by geometric convex decompositions, it does not require complex decomposition process. Our second contribution is an efficient corner detection method which reasons on binary pixel occupancy maps. Combined with our novel local tangent approach, which intelligently selects nodes from these corners, we modify the standard A* algorithm by feeding these nodes to its open list. With our local tangent approach, only small number of selected corners are fed to A* open list which keeps its size small even for larger maps, resulting in lower convergence time. We formally prove the optimality of our solution. Simulation on our own maps and public dataset (MAPF http://mapf.info/) as well as real-world experiments show that our proposed LTA* algorithm gives better convergence time and shorter path length in environments with both convex and concave obstacles.