HAL CCSD Motion Planning of Legged Robots Boissonnat, Jean-Daniel Devillers, Olivier Lazard, Sylvain Geometry, Algorithms and Robotics (PRISME) ; Inria Sophia Antipolis - Méditerranée (CRISAM) ; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria) Report N°: RR-3214 INRIA inria-00073475 https://inria.hal.science/inria-00073475 https://inria.hal.science/inria-00073475/document https://inria.hal.science/inria-00073475/file/RR-3214.pdf https://inria.hal.science/inria-00073475 RR-3214, INRIA. 1997 en MOTION PLANNING LEGGED ROBOTS MOBILE ROBOT COMPUTATIONAL GEOMETRY [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH] info:eu-repo/semantics/report Reports We study the problem of computing the free space \Fsimple 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 $\calf$ 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(n^2\log n)$time and$O(n^2\alpha(n))$space for point footholds where$\alpha(n)$is an extremely slowly growing function ($\alpha(n)\leq 3$for any practical value of$n$). We also present an algorithm to compute \Fthe foothold regions are pairwise disjoint polygons with$n$edges in total. This algorithm computes \F(n^2\alpha_8(n)\log n)$ time using $O(n^2\alpha_8(n))$ space ($\alpha_8(n)$ is also an extremely slowly growing function). These results are close to optimal since $Ømega(n^2)$ is a lower bound for the size of~\F 1997-07 info:eu-repo/semantics/OpenAccess