C. Bajaj
ABSTRACT
We present algebraic algorithms to generate the boundary of configuration space obstacles arising from the translatory motion of objects amongst obstacles. In particular we consider obtaining compliant motion paths where a curved convex object with fixed orientation moves in continuous contact with the boundary of curved convex obstacles in three Dimensions. Both the boundaries of the objects and obstacles are given by patches of algebraic surfaces. We also give a method to obtain approximate geodesic paths on convex C-space obstacles with algebraic boundary surfaces.
- Abhyankar. S., (1976) Historical Ramblings in Algebraic Geometry and Related Algebra,American Ma&anatical Monthly, 83.6,409&448.Google Scholar
- Abhyankar, S., and Bajaj. C., (1987) Automatic Rational Paramekrixatiou of Curves aud Surfaces I: Conies and Conicoids, Cornpurer Aided Design, 19, 1, 11-14. Google ScholarDigital Library
- Abhyankar. S. and Bajaj, C., (1986a) Automatic Ralional Paramelerization of Curves and ,Surfaces II: Cubits and Cubicoids. Computer Science Technical Report CSD-TR-592. Purdue University.Google Scholar
- Abhyankar, S., and Bajaj, C., (1986b) Automatic Rational Parameterization of Curves and Surjkces III: Algebraic PIane Curves, Computer Science Technical Report CSD-TR-619. Purdue University.Google Scholar
- Adamowicx, M., and Albano, A., (1976) Nesting two-dimensional shapes in rectangular modules, Cornpurer Aided Design, 2.1, U-33.Google Scholar
- Bajaj, C., and Kim, M., (1986) Generation of Configuration Space Obstacles II: The Case of Moving Algebraic Swfaces, Computer Science Technical Report CSD-TR-586, Purdue University.Google Scholar
- Bajaj, C., and Kim, M. (1987) Generation of Configuration Space Obstacles III: The Cast of Moving Algebraic Curves, Proc. 1987 IEEE Inrernafional Conference on Robotics and Automation, North CarolinaGoogle ScholarCross Ref
- Beck, J. Famuki. R. and Hinds. J. (1986) Surface Analysis Methods, IEEE Comp. Graphics and Appl. 18- 36.Google Scholar
- Buchberger, B., Collins, G., and Loos, R.,(editors), (1982) Computer Algebra. Symbolic and Aigebraic Compuladon, Computing Suppkmentum 4. Springer Vcrlag, Wien New York. Google ScholarDigital Library
- Canny. J. (1984) Collision Dctecdon for Moving Polykdra, AI. Memo o. 806,MIT. Google ScholarDigital Library
- Chazelle, B. (1984) Convex Partitions of Polyhedra: A lower bound and worst-case optimal algorithm, SIAM J. on Computing, 13,3.488-507. Google ScholarDigital Library
- Collins, G., (1971) The Calculation of Multivariate Polynomial Resultants, Journal of the ACM. 18, 4,515-532. Google ScholarDigital Library
- Dixon, A., (1908) The Elhninant of Three Quantics in Two Independent Variables,Proc. London Mathemadcal Society, 2.6,468-478.Google ScholarCross Ref
- do Carmo. M. (1976) Differential Geometry of Curves and Surfaces, Prentice Hall,Engelwood, NJ.Google Scholar
- Donald, B. (1984) Motion Planning whh Sir Degrees of Freedbm A.I. Technical Report 79 1, MIT. Google ScholarDigital Library
- Franklin, W. and Akman. V., (1984) Shortest Paths Bctwcen Source and Goal Points Located On/Around a Convex Polyhedron, 22nd Allerton Conference on Communication, Control and Computing, 103-l 12.Google Scholar
- Freeman, H., (1975) On the packing of arbitrary shaped templates, Proc. 2nd USA-Japan Computer Conference, 102-107.Google Scholar
- Guibas, L., Ramshaw, L., and Stolti, J., (1983) A Kinetic Framework for Compmadonal Geomeay, Proc. 24th Annual Symp. on Foundations of Computer Science, 100-111.Google Scholar
- Guibas, L. and Seidel, R., (1986) Computing Convolutions by Reciprocal Search, Proc. of 2nd ACM Symposium on ComputarionaI Geometry. 90-99. Google ScholarDigital Library
- Hoffmann, C., and Hopcroft, J., (1986) Geomelric Ambiguides in Boundary Represenuuion. 7X86-725,Computer Science, Cornell University. Google ScholarDigital Library
- Hopcroft, J. and Krafft, D., (1985) The Challenge of Roborics for Computer Science. Manuscript.Google Scholar
- Horn, B.K.P., (1986) Robor Vision, McGraw-Hill Book Co, MIT Press. Google ScholarDigital Library
- Kelly. P. and Weiss. M., (1979) Geomerry and Convexity, John Wiley & Sons, New York.Google Scholar
- Lozarlo-Perez. T. (1983) Spatial Planning: A Configuration Space Approach, IEEE Trans. on Computers, v.C-32.108-120.Google Scholar
- Lozano-Perez, T. and Wesley, M.A., (1979) An algorithm for planning collision free Paths among polyhedral obstacles. Communications of the ACM, 22.560-570. Google ScholarDigital Library
- Lozano-Perez. T. Mason, M., and Taylor. R. (1984) Automatic Synthesis of Fine-Motion Sttategies for Robots, TheInt. J. of Robotics Research, v. 3,1,3-24.Google ScholarCross Ref
- Mitchell, J. Mount, D., and Papmlimitriou. C. (1985) The Discrete Geodesic Problem, Manuscript.Google Scholar
- Mount, D., (1985) On Finding Shortest Paths on Convex Polyhedra, Technical Report 120. Center for Automation Research. University of Maryland.Google ScholarCross Ref
- 0' Rourke, J., Smi, S. and Booth. H., (1985) Shortest Paths on Polyhedral Surfaces, Proc. Symposium on Theoretical Aspects of Compruing. 243 -254. Google ScholarDigital Library
- Pogorelov. A.V., (1978) The Minkowski Mulddimensional Problem, Winston, New York.Google Scholar
- Requicha, A., (1980) Representations of Rigid Solid Objects, Computer Aided Dcri~n, Springer Lecture Notes in Computer Science 89.2-78. Google ScholarDigital Library
- Requicha, A., and Voelcker, H., (1983) Solid Modeling: Current Status and Research Directions, I/X!? Comp. Graphics and Appl. 25-37.Google ScholarDigital Library
- Schwartz, J. and Shark, M. (1983) On the Pi Movers Problem: II. General Techniques for Computing Topological Propcstics of Real Algebraic Manifolds, Adv. Appl. Math 4.298-351.Google ScholarDigital Library
- Sharir. M., and Schorr, A., (1984) On Shortest Paths in Polyhedral Spaces, Proc. 161h ACM Symposium on Theory of Computing, 144-153. Google ScholarDigital Library
- Tiller. W. and Hanson, E. (1984) Offsets of Two-Dimensional Profik. IEEE Computer Graphics & Applications, Sept., 36-46.Google Scholar
- Udupa. S. (1977) CoIlisIen detection and avoidance in computer controlled manipulators, Proc. 5th Inr. Joint Conf. Artificial Intelligence. MIT, 737-748.Google Scholar
- Walker, R. (1978) Algebraic Curves. Springer Verkg. Now York.Google Scholar
- Yap, C., (1985) Algorithmic Motion Planning, Manuscript.Google Scholar
Index Terms
- Compliant motion planning with geometric models
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