By Bob Stat
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Extra info for Altogether Fun and Absolutely Understanding Rubik's Pocket Cube
Mason Fig. 4 At top: several example paths combining different values of v and w. Each path pair obeys (3). The value of v affects the “curviness” allowed in paths, while w affects their length. At bottom: this plot, generated numerically, approximates the set of appropriate choices for v and w. The gray region at top right must be avoided, as we show in Lemma 2. Such choices would permit an obstacle to occur between two safe paths that obey (3).
On Robotics and Automation, pp. : Motion planning for robotic manipulation of deformable linear objects. In: Experimental Robotics, pp. 23–32. : Real-time re-planning in high-dimensional configuration spacesusing sets of homotopic paths. In: Proceedings of IEEE Int. Conf. on Robotics and Automation, ICRA 2000, vol. : Capture of homotopy classes with probabilistic road map. In: IEEE/RSJ Int. Conf. on Intelligent Robots and System, vol. : Path deformation roadmaps. In: Algorithmic Foundation of Robotics VII, pp.
When fixing the replan rate at 10 Hz, implicit path evaluation maintains an advantage, despite the overhead, across all navigable obstacle densities. 5 Discussion and Future Work In this paper, we propose an equivalence relation on local paths based on the following constraints: fixed start position and heading, fixed length, and bounded curvature. We describe an algorithm for easily classifying paths using the Hausdorff distance between them. Path classification is a tool that permits collective reasoning about paths, leading to more efficient collision-testing.