The Provable Virtue of Laziness in Motion Planning
This provides theoretical guarantees for motion planning algorithms in robotics, though it is incremental as it builds on existing LazySP methods.
The paper tackles the problem of minimizing edge evaluations in motion planning by analyzing LazySP algorithms, showing they are asymptotically optimal with matching upper and lower bounds in a probabilistic model.
The Lazy Shortest Path (LazySP) class consists of motion-planning algorithms that only evaluate edges along shortest paths between the source and target. These algorithms were designed to minimize the number of edge evaluations in settings where edge evaluation dominates the running time of the algorithm; but how close to optimal are LazySP algorithms in terms of this objective? Our main result is an analytical upper bound, in a probabilistic model, on the number of edge evaluations required by LazySP algorithms; a matching lower bound shows that these algorithms are asymptotically optimal in the worst case.