From spider robots to half disk robots

Jean-Daniel Boissonnat 1 Olivier Devillers 1 Sylvain Lazard 1
1 PRISME - Geometry, Algorithms and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We study the problem of computing the set F of accessible and stable placements of a spider robot. The body of this robot is a single point and the legs are line segments attached to the body. The robot can only put its feet on some regions, called the foothold regions. Moreover, the robot is subject to two constraints: Each leg has a maximal extension R (accessibility constraint) and the body of the robot must lie above the convex hull of its feet (stability constraint). We present an efficient algorithm to compute F. If the foothold regions are polygons with n edges in total, our algorithm computes F in O(n^2 log n) time and O(n^2 alpha(n)) space where alpha is the inverse of the Ackerman's function. Omega(n^2) is a lower bound for the size of F.
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Jean-Daniel Boissonnat, Olivier Devillers, Sylvain Lazard. From spider robots to half disk robots. IEEE International Conference on Robotics and Automation, 1994, San Diego, United States. pp.953-958. ⟨inria-00442776⟩

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