Motion planning of legged robots

Jean-Daniel Boissonnat 1 Olivier Devillers 1 Sylvain Lazard 2
1 PRISME - Geometry, Algorithms and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
2 ISA - Models, algorithms and geometry for computer graphics and vision
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We study the problem of computing the free space F of a simple legged robot called the spider robot. The body of this robot is a single point and the legs are attached to the body. 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). Moreover, the robot can only put its feet on some regions, called the foothold regions. The free space F is the set of positions of the body of the robot such that there exists a set of accessible footholds for which the robot is stable. We present an efficient algorithm that computes F in O(n2 log n) time using O(n2 alpha(n)) space for n discrete point footholds where alpha(n) is an extremely slowly growing function (alpha(n)\leq 3 for any practical value of n). We also present an algorithm for computing F when the foothold regions are pairwise disjoint polygons with $n$ edges in total. This algorithm computes F in O(n2alpha8(n) log n) time using O(n2 alpha8(n)) space (alpha8(n) is also an extremely slowly growing function). These results are close to optimal since Omega(n2) is a lower bound for the size of F.
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Jean-Daniel Boissonnat, Olivier Devillers, Sylvain Lazard. Motion planning of legged robots. SIAM Journal on Computing, Society for Industrial and Applied Mathematics, 2000, 30 (1), pp.218-246. ⟨10.1137/S0097539797326289⟩. ⟨inria-00099289⟩

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