Nearest Neighborhood search in Motion Planning

Nearest Neighbor Search plays a vital role in building road-maps in Motion Planning. These are implemented in any Road-map building method such as PRM, OBPRM, Gauss PRM, etc. Motion Planning is the science of designing a successfully implementable plan in any Configuration Space (often called C-space) in order to move the Robot from a given Start Configuration to a Goal Configuration by avoiding collisions with obstacles lying in the C-space. Obstacles can be either static or dynamic. In this process of building Road-maps, Node-generator randomly generate the nodes throughout the C-space wherein each node represents the possible position of the Robot that might be attained while in motion. From all the above nodes generated by Node-generator, Road-map stores the portion of the nodes that are free from possible collisions which is determined by Collision-detection-test. One such Collisiondetection-test that is currently used is RAPID. The nodes stored in the Road-map are connected using Local-planner such as Straight-line, Rotate AT S, etc. Nearest Neighborhood Search problem comes here where this paper focused towards after serious investigation of various environments and each environment was investigated by varying number of Nearestneighbors(K), number of Nodes(N ) and Epsilon ǫ. Investigation into various environments by variation of K, N and ǫ over a wide range can help in finding suitable K, N and ǫ values that could optimize the total time to build the Road-map with out loosing realiability and quality of Road-map.