Computation of Approximate Solutions for Guided Sampling-Based Motion Planning of 3D Objects

Motion planning of 3D solid objects leads to a search in a 6D configuration space. Sampling-based planners randomly sample the configuration space and store the collision-free samples into a graph (roadmap) that can be searched by standard graph-search methods. The well-known issue of the sampling-based planners is the narrow passage problem. Narrow passages are small collision-free regions in the configuration space that are, due to their low volume, difficult to cover by the random samples, which prevents the sampling-based planners to find a path leading through the passages. By decreasing the size of the object, the relative volume of the narrow passages is increased, which helps to cover them more densely. This allows the planner to find an approximate solution, i.e., a solution feasible for the smaller object. The approximate solution can be then used to iteratively guide the sampling in the configuration space, while increasing the size of the object, until a solution for the original object is found. In this paper, we propose a modification of the iterative guiding process. To avoid a situation where the part of the guiding path is too close to obstacles of the configuration space, we shift it away from the obstacles. This requires to estimate the surface of the obstacle region, which is achieved by detecting its boundary configurations during the sampling process. Experiments have shown that the proposed modification outperforms the simple guiding using approximate solutions, as well as other related state-of-the-art planners.