Multi-modal Motion Planning in Non-expansive Spaces

The motion planning problems encountered in manipulation and legged locomotion have a distinctive multi-modal structure, where the space of feasible configurations consists of overlapping submanifolds of non-uniform dimensionality. These spaces do not possess expansiveness, a property that characterizes whether planning queries can be solved with traditional sample-based planners. We present a new sample-based multi-modal planning algorithm and analyze its completeness properties. In particular, it converges quickly when each mode is expansive relative to the submanifold in which it is embedded. We also present a variant that has the same convergence properties, but works better for problems with a large number of modes. These algorithms are demonstrated in a legged locomotion planner.