During the last decade, incremental sampling-based motion planning algorithms, such as the Rapidly-exploring Random Trees (RRTs), have been shown to work well in practice and to possess theoretical guarantees such as probabilistic completeness. However, no theoretical bounds on the quality of the solution obtained by these algorithms, e.g., in terms of a given cost function, have been establish...

Motion planning problems can be simplified by admissible projections of the configuration space to sequences lower-dimensional quotient-spaces, called sequential simplifications. To exploit simplifications, we present Quotient-space Rapidly-exploring Random Trees (QRRT) algorithm. QRRT takes as input a start and goal configuration, sequence quotient-spaces. The algorithm grows trees on quotient...