S Sifrony
ABSTRACT
We present here a new and efficient algorithm for planning collision-free motion of a rod in the plane amidst polygonal obstacles. The algorithm calculates the boundary of the space of free positions of the rod, and then uses this boundary for determining the existence of required motions. The algorithm runs in time Ο(K log n) where n is the number of obstacle corners and where K is the total number of pairs of obstacle walls or corners lying from one another at distance less than or equal to the length of the rod. Since K = Ο(n2), the algorithm has the same worst-case complexity as the best previously developed algorithm of Leven and Sharir [LS1], but if the obstacles are not too cluttered together it will run much more efficiently.
- BO.J.L. Bently and A. Ottman, Algorithms for reporting and counting geometric intersections, IEEE Trans. on Computers, Vol C-28 (1979), pp. 643-647.Google Scholar
Digital Library
- CD.P. Chew and R.L. Drysdale, Voronoi diagrams based on convex distance functions, Proc. A CM Syrup. on Computational Geometry (1985) pp. 235-244. Google ScholarDigital Library
- Fo.S. Fortune, A fast algorithm for polygon containment by translation, Proc. 12th Int. Colloq. on Automata, Languages and Programming Lecture Notes in Computer Science 194, Springer Verlag, New York, 1985, pp. 189-198. Google ScholarDigital Library
- KS.K. KeAem and M. Sharir, An efficient motion planning algorithm for a convex rigid polygonal object in 2-dimensional polygonal space, in preparation.Google Scholar
- LS1.D. Leven and M. Sharir, An efficient and simple motion-planning algorithm for a ladder moving in two-dimensional space amidst polygonal barriers, Proc. ACId Syrup. on Computational Geometry (1985) pp. 221- 227. Google ScholarDigital Library
- LS2.D. Leven and M. Shark, Planning a purely translational motion of a convex object in two-dimensional space using generalized Voronoi diagrams, Tech. Rept. 34, The Eskenasy Institute of Computer Science, Tel Aviv University, June 1985 (to appear in Discrete and Computational Geometry.)Google Scholar
- LS3.D. Leven and M. Sharir, On the number of critical free contacts of a convex polygonal object moving in two-dimensional polygonal space, Tech. Rept. 187, Comp. Sci. Dept., Courant Institute, October 1985.Google Scholar
- Mo.E. Moise, Geometric Topology in Dimensions 2 and 3, Springer Verlag, New York 1977.Google Scholar
- OR.J. O'Rourke, Lower bounds on moving a ladder, manuscript, 1985.Google Scholar
- OSY1.C. O'Dunlaing, M. Sharir and C. Yap, Generalized Voronoi diagrams for a ladder: I. Topological considerations, Tech. Rept. 139, Computer Science Dept., Courant Institute, November 1984 (to appear in Comm. Pure Appl. Math.)Google Scholar
- OSY2.C. O'Dunlaing, M. Sharir and C. Yap, Generalized Voronoi diagrams for a ladder: H. Efficient construction of the diagram, Tech. Rept. 140, Computer Science Dept., Courant Institute, November 1984 (to appear in Algorithmica. )Google Scholar
- OY.C. O'Dunlaing and C. Yap, A 'retraction' method for planning the motion of a disc, J. Algorithms 6 (1985) pp. 104-111.Google ScholarCross Ref
- Re.J. Reif, Complexity of the movers problem and generalizations, Proc. 20th IEEE $ymp. on Foundations of Computer Science (1979), pp. 420-427.Google Scholar
- SS1.J.T. Schwartz and M. Sharir, On the piano movers' problem: I. The case of a rigid polygonal body moving amidst polygonal barriers, Comm. Pure Appl. Math. 36 (1983) pp. 345-398.Google Scholar
- SS2.3{. T. Schwartz and M. Shark, On the piano movers' problem: H. The general techniques for computing topological properties of real algebraic manifolds, Adv. in Appl. Math. 4 (1983) pp. 298-351.Google ScholarDigital Library
- SS3.J.T. Schwartz and M. Sharir, On the piano movers' problem: III. Coordinating the motion of several independent bodies: The special case of circular bodies moving amidst polygonal barriers, Robotics Research, 2 (1983) (3) pp. 46-75.Google ScholarCross Ref
- SS4.J.T. Schwartz and M. Sharir, Efficient motion planning algorithms in environments of bounded local complexity, Tech. Rept. 164, Computer Science Dept., Courant Institute, June 1985.Google Scholar
- SS5.J.T. Schwartz and M. Sharir, On the piano movers' problem: V. The case of a rod moving in three-dimensional space amidst polyhedral obstacles, Comm. Pure Appl. Math. 37 (1984) pp. 815-848.Google Scholar
- SA.M. Sharir and E. Ariel-Sheffi, On the piano movers' problem: IV. Various dexx)mposable two-Dimensional motion planning problems, Comm. Pure Appl. Math. 37 (1984) pp. 479- 493.Google ScholarCross Ref
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- A new efficient motion-planning algorithm for a rod in polygonal space
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