Efficient asymptotically-optimal path planning on manifolds

This paper presents an efficient approach for asymptotically-optimal path planning on implicitly-defined configuration spaces. Recently, several asymptotically-optimal path planners have been introduced, but they typically exhibit slow convergence rates. Moreover, these planners can not operate on the configuration spaces that appear in the presence of kinematic or contact constraints, such as when manipulating an object with two arms or with a multifingered hand. In these cases, the configuration space usually becomes an implicit manifold embedded in a higher-dimensional joint ambient space. Existing sampling-based path planners on manifolds focus on finding a feasible solution, but they do not optimize the quality of the path in any sense and, thus, the returned solution is usually not adequate for direct execution. In this paper, we adapt several techniques to accelerate the convergence of the asymptotically-optimal planners and we use higher-dimensional continuation tools to deal with the case of implicitly-defined configuration spaces. The performance of the proposed approach is evaluated through various experiments.