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On the problem of translating an elliptic object through a workspace of elliptic obstacles*

Published online by Cambridge University Press:  09 March 2009

B. John Oommen  and
Irwin Reichstein
B. John Oommen
Affiliation:
School of Computer Science, Carleton University, Ottawa: K1S 5B6, (Canada)
Irwin Reichstein
Affiliation:
School of Computer Science, Carleton University, Ottawa: K1S 5B6, (Canada)
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Summary

Two algorithms are presented which deal with translating an elliptic object, A, without collision amidst elliptic obstacles. These are:

(i) An exact algorithm, of complexity O(N log N), where N is the number of obstacles, yielding all directions along which the object is separable from the obstacles by a single translation.

(ii) An algorithm quadratic in N, which yields, with a degree of approximation determined by the user, a path of the object from its initial to its final position.

Type
Article
Information
Robotica , Volume 5 , Issue 3 , July 1987 , pp. 187 - 196
Copyright
Copyright © Cambridge University Press 1987

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References

1.Schwartz, J.T. and Sharir, M., “On the Piano Movers Problem I: The Case of a Two-Dimensional Rigid Polygonal Body Moving amidst Polygonal Barriers” Report 39 (Dept. of Computer Science, Courant Institute of Mathematical Sciences, NYU, 1981).Google Scholar
2.Schwartz, J.T. and Sharir, M., “On the Piano Movers Problem II: General Properties for Computing Topological Properties of Real Algebraic Manifolds” Report 41 (Dept. of Computer Science, Courant Institute of Mathematical Sciences, NYU, 1982).Google Scholar
3.Reif, J.H., “Complexity of the Movers Problem and Generalizations” Twentieth Annual Symposium on Foundations of Computer Science, San Juan, Puerto Rico (10 1979) pp. 421–427.Google Scholar
4.Brooks, R.A., “Solving the Find-Path Problem by Representing Free Space as Generalized Cones” Artificial Intelligence Laboratory, Massachusetts Institute of Technology AI Memo 674 (05 1982).Google Scholar
5.Brooks, R.A., “Planning Collision-Free Motions for Pick-and-Place Operations” Robotics Research 19–44 (1983).CrossRefGoogle Scholar
6.Brooks, R.A. and Lozano-Perez, T., “A Subdivision Algorithm in Configuration Space for Findpath with Rotation” IEEE Trans. on Systems, Man and Cybernetics 224–233 (03/04, 1985).Google Scholar
7.Udapa, S.M., “Collision Detection and Avoidance in Computer Controlled Manipulators” Proceedings of the IJCAI-5, MIT, Cambridge, MA (08 1977) pp. 737–748.Google Scholar
8.Lozano-Perez, T., “Automatic Planning of Manipulator Transfer Movements”, IEEE Transactions on Systems, Man and Cybernetics 681–698 (1981).Google Scholar
9.Lozano-Perez, T., “Task Planning” In: Robot Motion: Planning and Control (Brady, M. et al. , eds.) (MIT Press, Cambridge, Mass., 1983).Google Scholar
10.Lozano-Perez, T., “Spatial Planning: A Configuration Space Approach” IEEE Transactions on Computers 108–120 (1983).CrossRefGoogle Scholar
11.Lozano-Perez, T. and Wesley, M.A., “An algorithm for Planning Collision-Free Paths among Polyhedral Obstacles” Comm. of the ACM 560–570 (1979).CrossRefGoogle Scholar
12.Whitesides, S., “Computational Geometry and Motion Planning” In: Computational Geometry (Ed. by Toussaint, G.) (North Holland, Amsterdam, 1985).Google Scholar
13.Guibas, L.J. and Yao, F.F., “On Translating a Set of Rectangles” Proceedings of the Twelfth Annual Symposium on the Theory of Computing, Los Angeles (04 1980) pp. 154–160.Google Scholar
14.Sack, J.-R., “Translating Polygons in the Plane” Proceedings of the 1985 Second Annual Symposium on the Theoretical Aspects of Computer Science, Saarbrucken, Germany (1985) pp. 310–321.Google Scholar
15.Imai, H., Asano, T. and Asano, T., “Visibility of Disjoint Polygons” Research Memorandum RMI-85–02 (Dept. of Mathematical Engineering and Instrumentation Physics, Tokyo, Japan, 02 1985).Google Scholar
16.Post, M., “A Minimum Spanning Ellipse Algorithm” Proc. of the 1981 IEEE Conference on the Foundations of Computer Science (1981) pp. 115–122.Google Scholar