On the Complexity of the Contact Space between

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This research has been supported by the ESPRIT II Basic Research Actions ... tem, and identifying points on the manifold with rigid transformations applied to P. ... in which P is rst rotated by the angle about the origin and then translated by ... between features (vertices and edges) of P and features of Q. More precisely, a.
On the Complexity of the Contact Space between Convex Polyhedra David Parsons and Carme Torras  Institut de Cibernetica Universitat Politecnica de Catalunya Barcelona Spain

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Introduction

This report describes some work in progress on determining the complexity of the contact space between two convex polyhedra. This question arises in the context of a particular motion planning problem, in which one wishes to plan motions between contact con gurations of two convex polyhedra with the constraint that the polyhedra must maintain contact throughout their motion. The latter problem is a rst step towards the more general problem of planning contact motions for several non-convex polyhedra, which is a fundamental problem in ne motion planning and assembly planning. The contact space of a pair of polyhedra is de ned as the set of their relative con gurations in which they are in contact. This can be viewed as the boundary of the con guration space obstacle which results when one of the polyhedra is held xed and the other may move arbitrarily. This obstacle is a subset of the con guration space

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