Abstract
Rather than presenting a specific technique to plan free motions, the main purpose of this paper is discussing the potential of possible approaches from different viewpoints. The focus is on planning simple motions on the basis of a fine grain description of the workspace. We consider the problem of planning translations of a convex polygon in a cluttered polygonal environment, i.e., in the presence of several convex bodies with several sides, as a toy example to address a number of questions: limits of some popular approaches, development of more refined—but practical—techniques, comparison between algorithmic and intuitive motion planning, use of dynamic techniques, potential of parallelization. Most of the ongoing considerations will take the results of a few numerical experiments as their starting point.
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References
M. J. Atallah, R. Cole, and M. T. Goodrich. Cascading divide-and-conquer: A technique for designing parallel algorithms. SIAM J. Comput., 18:499–532, 1989.
J. L. Bentley and T. A. Ottmann. Algorithms for reporting and counting geometric intersections. IEEE Trans. Comput., C-28:643–647, 1979.
S. Cameron. Collision detection by four dimensional intersection testing. IEEE Trans. on Robotics and Automation, RA-6(3):291–302, 1990.
J. Canny. The Complexity of Robot Motion Planning. MIT Press, Cambridge, 1988.
J. Canny and M.C. Lin. An opportunistic global path planner. IEEE Trans. Pattern Analysis and Machine Intelligence, 10:102–120, 1993.
J. D. Cohen, M. C. Lin, D. Manocha, and M. K. Ponamgi. I-collide: An interactive and exact collision detection system for large-scale environments. In Proc. ACM Interactive 3D Graphics Conf., pages 189–196, 1995.
A. P. del Pobil, M. Pérez, and B. Martinez. A practical approach to collision detection between general objects. In Proc. of the IEEE Int. Conf. on Robotics and Automat., pages 779–784, 1996.
D. P. Dobkin and D. G. Kirkpatrick. Fast detection of polyhedral intersection. Theoret. Comput. Sci., 27(3):241–253, 1983.
D. P. Dobkin and D. G. Kirkpatrick. Determining the separation of preprocessed polyhedra — A unified approach. In Proc. 17th ICALP Internat. Colloq. Au-tomata Lang. Program., volume 443 of Lecture Notes Comput. Sci., pages 400–413. Springer-Verlag, 1990.
E. G. Gilbert and C. J. Ong. New distances for the separation and penetration of objects. In Proc. of the IEEE Int. Conf. on Robotics and Automat., pages 579–585, 1994.
O. Günther and E. Wong. A dual approach to detect polyhedral intersections in arbitrary dimensions. Bit, 31(1):2–14, 1991.
P. Jiménez and C. Torras. Speeding up interference detection between polyhedra. In Proc. of the IEEE Int. Conf. on Robotics and Automat., pages 1485–1492, 1996.
J.-C. Latombe. Robot Motion Planning. Kluwer Academic Publishers, Boston, 1991.
M. C. Lin, D. Manocha, and M. Ponamgi. Fast algorithms for penetration and contact determination between non-convex polyhedral models. In Proc. of the IEEE Int. Conf. on Robotics and Automat., pages 2707–2712, 1995.
V. J. Lumelsky. Effect of kinematics on motion planning for planar robot arms moving amidst unknown obstacles. IEEE J. of Robotics and Automation, RA-3(3):207–223, 1987.
C. Mirolo. Convex minimization on a grid and applications. In Proc. 6th Canad. Conf. Comput. Geom., pages 314–319, 1994.
C. Mirolo. Collision detection: Experimental results. Techn. Rep. UDMI/03/97/RR, Dip. di Matematica e Informatica dell'Univ. di Udine, Udine, Italy, February 1997.
C. Mirolo and E. Pagello. A solid modeling system for robot action planning. IEEE Computer Graphics and Applications, 9(1):55–69, 1989.
C. Mirolo and E. Pagello. A cell decomposition approach to motion planning based on collision detection. In Proc. of ICAR'95, pages 481–488, 1995.
C. Mirolo and E. Pagello. A practical motion planning strategy based on a plane-sweep approach. In Proc. of the IEEE Int. Conf. on Robotics and Automat., pages 2705–2712, 1997.
C. Mirolo, E. Pagello, and W. H. Qian. Simplified motion planning strategies in flexible manufacturing. In Proc. of IEEE ISATP'95, pages 394–399, 1995.
K. Mulmuley. Computational Geometry: An Introduction Through Randomized Algorithms. Prentice Hall, Englewood Cliffs, NJ, 1993.
N. J. Nilsson. Principles of Artificial Intelligence. Tioga Publ. Company, Palo Alto, CA, 1980.
J. H. Reif. Complexity of the mover's problem and generalizations. In Proc. 20th Annu. IEEE Sympos. Found. Comput. Sci., pages 421–427, 1979.
R. Seidel. A simple and fast incremental randomized algorithm for computing trapezoidal decompositions and for triangulating polygons. Comput. Geom. Theory Appl., 1:51–64, 1991.
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Mirolo, C., Pagello, E. (1998). Exact geometry and robot motion planning: Speculations on a few numerical experiments. In: Pasqual del Pobil, A., Mira, J., Ali, M. (eds) Tasks and Methods in Applied Artificial Intelligence. IEA/AIE 1998. Lecture Notes in Computer Science, vol 1416. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-64574-8_395
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DOI: https://doi.org/10.1007/3-540-64574-8_395
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