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Abstract: 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. 1

To accomplish a task an autonomous robot must break this task into “primitive ” subtasks and order them to satisfy precedence constraints. Each subtask requires performing a motion. The existence of a feasible trajectory is an additional precondition for the subtask, but a very expensive one to test. Probabilistic RoadMaps (PRM) are an effective approach to plan feasible trajectories when these exist. However, PRM planners are unable to detect that no solution exists. On the other hand, a task/motion planner must often consider many subtasks, a fraction of which, only, admit feasible trajectories. This paper proposes a general algorithm (I‐TMP) that specifically addresses this issue. This algorithm interweaves task and motion planning, and allows distributing computational effort where it is most useful. It is probabilistically complete in the following sense: if I‐TMP can generate a sequence of subtasks that admits a feasible trajectory, such a trajectory will eventually be found with high probability. An application of I‐TMP to multi-limbed robots navigating on rough terrain is presented. I.