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A fast algorithm for distance calculation between convex objects using the optimization approach

Published online by Cambridge University Press:  09 March 2009

SaÏd Zeghloul  and
Patrick Rambeaud
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Summary

This paper describes an efficient and fast algorithm for finding the minimum distance between two convex polyhedrons in a three dimensional space. To obtain the minimal distance, the proposed computational scheme is based on a direct approach to minimizing the distance function which produces a succession of optimal search directions along object boundaries. This algorithm combines the gradient projection method'; and an additional optimal search direction when the gradient projection method leads to a zigzagging phenomenon. In this case, the additional optimal search direction accelerates significantly the convergence of the process. Extensive numerical experiments with convex polyhedra show the performance of this algorithm when compared with that of previous approaches. The proposed algorithm may be very helpful in solving the computation of minimal distance between a pair of convex sets, the collision detection problem or to track the closest points of moving convex objects.

Keywords

Minimal distanceConvex polyhedraOptimizationCollision detection
Type
Article
Information
Robotica , Volume 14 , Issue 4 , July 1996 , pp. 355 - 363
Copyright
Copyright © Cambridge University Press 1996

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References

Rosen, J.B., “The Gradient Projection Method For Nonlinear programming” Part I, S1AM J on Applied Mathematics, 8, 181–217 (1960).Google Scholar
Red, W.E., “Minimum distances for robot task simulation” Robotica 1,231–238(1985).CrossRefGoogle Scholar
Dobkin, D.P. and Kirkpatrick, D.G., “A linear algorithm fordetermining the separation of convex polyhedra” J. Algorithms 6, 381–392 (1985).CrossRefGoogle Scholar
Dobkin, D.P. and Kirkpatrick, D.G., “Determining the separation of preprocessed polyhedra-A unified approach” Proc. of the 17th ICALP, Springer-Verlag Lecture Notes on Computer Science (1990) 443, pp. 400–413.CrossRefGoogle Scholar
Meyer, W, “Distances between boxes: applications to collision detection and clipping” Proc of the IEEE Int. Conf. on Robotics and Automation (1986) pp. 597–602.Google Scholar
Cameron, S.A. and Culley, R.K., “Determine the minimum translational distance between two convex polyhedra” Proc. of the IEEE Int. Conf. on Robotics and Automation (1986) pp. 591–596.Google Scholar
Gilbert, E.G., Johnson, D.W. and Keerthi, S.S., “A fast procedure for computing the distance between complex objects in three-dimensional space” IEEE Trans on Robotics and Automation 4 (2), 193–203 (1988).CrossRefGoogle Scholar
Gilbert, E.G. and Foo, C.P., “Computing the distance between general convex objects in three dimensional space” IEEE Trans on Robotics and Automation 6 (1). 53–61 (1990).CrossRefGoogle Scholar
Hurteau, G. and Stewart, N.F., “Distance calculation for imminent collision indication in a robot system simulation” Robotica 6, Part 1, 47–51 (1988).CrossRefGoogle Scholar
Bobrow, J.E., “A direct minimization approach for obtaining the distance convex polyhedra” Int. J. of Robotics Research, 8 (3), 65–76 (1989).CrossRefGoogle Scholar
Lin, M.C. and Canny, J.F., “A fast algorithm for incremental distance calculation” Proc. of the IEEE Int. Conf. on Robotics and Automation (1991) pp. 1008–1014.Google Scholar
Chang, C., Chung, M.J. and Bein, Z., “Collision-free motion planning for two articulated robot arms using minimum distance functions” Robotica 8, part 2, 137–144 (1990).CrossRefGoogle Scholar
Lumelsky, V.J., “On fast computation of distance between line segments” Inform. Process. Lett. 21, 55–61 (1985).CrossRefGoogle Scholar
Tornero, J., Hamlin, J. and Kelley, R.B., “Spherical object representation and fast distance computation for robotic applications” Proc. of the IEEE Int. Conf. on Robotics and Automation (1991) pp. 1602–1608.Google Scholar
Hamlin, J.G., Kelley, R.B. and Tornero, J., “Efficient distance calculation using the spherically-extended polytope (S-tope) model” Proc. of the IEEE Int. Conf. on Robotics and Automation (1992) pp. 2502–2507.Google Scholar
Fox, R.L., Optimization Methods for Engineering Design: (Addison-Wesley, Reading, Mass., 1971).Google Scholar
Rao, S.S., Optimization Theory and Applications, 2nd edition Wiley Eastern Limited, New York, 1984).Google Scholar
Zeghloul, S. and Rambeaud, P., “Comment on ”A Direct Minimization Approach for Obtaining the Distance between Convex Polyhedra'; by James E. Bobrow” Int. J. of Robotics. Research 11 (5), 499–501 (1992).CrossRefGoogle Scholar
Zeghloul, S., Rambeaud, P. and Lallemand, J.P., “A fast distance calculation between convex objects by optimization approach” Proc. of the IEEE Int. Conf. on Robotics and Automation (1992) pp. 2520–2525.Google Scholar
Zeghloul, S., “Développement d';un systeme de C.A.O. robotique integrant la plantification de taches et la synthese de sites robotisés” Ph.D. Thesis (Poitiers University 1991).Google Scholar
Luenberger, D.G., Introduction to Linear and Nonlinear Programming (Addison-Wesley, Reading, Mass, 1973).Google Scholar