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Fast convex minimization to detect collisions between polyhedra

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2 Author(s)
C. Mirolo ; Dipartimento di Matematica e Inf., Udine Univ., Italy ; E. Pagello

The subject of the paper is a fast algorithm for detecting collisions of two convex polyhedra translating in space. A major feature is the novelty of the approach: collision detection for two convex bodies is reduced to collision detection for pairs of planar sections and minimization of a bivariate convex function; furthermore, most of the subproblems are solved using two-dimensional geometry. As proved by previous theoretical work, on this basis it is possible to design an algorithm, which runs in O(log2n) time in the average and O(log3n) in the worst case, where n is the total number of vertices. Here the focus is on a more practical version of the algorithm, which is particularly suited to plan collision-free paths on the basis of fine-grain descriptions of the objects in the workspace, as it is the case for the systems supported by sophisticated geometric modelers. After explaining the main ideas underlying the approach, a set of experimental results are presented and discussed in some depth

Published in:

Intelligent Robots and Systems, 2000. (IROS 2000). Proceedings. 2000 IEEE/RSJ International Conference on  (Volume:3 )

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