Sufficient Conditions for the Existence of Resolution Complete Planning Algorithms. Yershov, LaValle. Proceedings Workshop on Algorithmic Foundations of Robotics (WAFR), 2010


  1. Kobilarov cited this paper saying the following: “Conditions for resolution completeness of planning with such primitives [parameterizations of open-loop control with actions and corresponding time durations] have been established.”
  2. Establishes metric spaces over the control and trajectory spaces
  3. Based on these metrics, if the domain is Lipshitz, then the mapping between open loop control and trajectories is continuous
  4. Because of this, it is possible to search the space of actions, as opposed to building a reachability graph.
  5. This algorithm has guarantees like most motion planning algs, which is that if a solution exists, it will be found eventually
  6. Not reading this carefully, because I think I already got what I need out of this paper.  Most of it is proofs, which I dont really care about – just what is proved.
  7. Requires continuity, which goes with Lipshitz smoothness
  8. Algorithm is very simple
  9. The algorithm effectively deals with noise, as there is a term that deals with error that arises from integration errors.
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