Elliptical K-Nearest Neighbors - Path Optimization Via Coulomb's Law and Invalid Vertices in C-Space Obstacles

Path planning has long been an important and active research area in robotics. To address challenges in high- dimensional motion planning, this study introduces the Force Direction Informed Trees (FDIT*), a sampling-based planner designed to enhance speed and cost-effectiveness in pathfinding. FDIT* builds upon the state-of-the-art informed sampling planner, the Effort Informed Trees (EIT*), by capitalizing on often-overlooked information in invalid vertices. It incorporates principles of physical force, particularly Coulomb’s law. This approach proposes the elliptical k-nearest neighbors search method, enabling fast convergence navigation and avoiding high solution cost or infeasible paths by exploring more problem- specific search-worthy areas. It demonstrates benefits in search efficiency and cost reduction, particularly in confined, high- dimensional environments. It can be viewed as an extension of nearest neighbors search techniques. Fusing invalid vertex data with physical dynamics facilitates force-direction-based search regions, resulting in an improved convergence rate to the optimum. FDIT* outperforms existing single-query, sampling- based planners on the tested problems in R4 to R16 and has been demonstrated on a real-world mobile manipulation task.