Planification de trajectoires de robots mobiles non-holonomes et de robots à pattes

Sylvain Lazard 1
1 PRISME - Geometry, Algorithms and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : The work presented in this thesis deals with optimal motion planning, in the presence of obstacles, of car-like robots and legged robots. The model of car-like robot studied is the one of Dubins. That is, roughly speaking, a car moving forward with a minimum turning radius. We consider the problem of computing a convex hull of bounded curvature of a set S of points in the plane, that is a set containing S and whose boundary is a curve of bounded curvature of minimal length. We prove that, if the radius of the smallest disk that contains S is greater than 1, such a hull is unique. We show that the computation of a convex hull of bounded curvature reduces to convex programming or to solving a set of algebraic systems. We also present an exact polynomial-time algorithm for computing a shortest path for the Dubins robot moving amidst moderate obstacles, that is obstacles whose boundaries are curves of bounded curvature made of line segments and arcs of circle. Such obstacles can be found by computing convex hulls of bounded curvature of polygonal obstacles. The algorithm computes a graph and finds a shortest path in this graph. The graph is computed using computational geometry methods and resolution of algebraic systems. We also worked on the motion planning problem of a legged robot whose body is a single point and whose legs are attached to the body. The legs have a bounded length and the robot can only put its feet in some polygonal regions of the plane. We present an almost optimal time algorithm for computing the set of stable placements of the body of the robot. By a clever transformation, we turn the problem into the computation of the free space of a half-disk robot moving amidst obstacles.
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Sylvain Lazard. Planification de trajectoires de robots mobiles non-holonomes et de robots à pattes. Informatique [cs]. Université Pierre et Marie Curie - Paris VI, 1996. Français. ⟨tel-00442770⟩

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