  A motion planning algorithm computes the motion of a robot by computing a
path through its configuration space. To improve the runtime of motion planning
algorithms, we propose to nest robots in each other, creating a nested
quotient-space decomposition of the configuration space. Based on this
decomposition we define a new roadmap-based motion planning algorithm called
the Quotient-space roadMap Planner (QMP). The algorithm starts growing a graph
on the lowest dimensional quotient space, switches to the next quotient space
once a valid path has been found, and keeps updating the graphs on each
quotient space simultaneously until a valid path in the configuration space has
been found. We show that this algorithm is probabilistically complete and
outperforms a set of state-of-the-art algorithms implemented in the open motion
planning library (OMPL).
