Journal of Mechanical Science and Technology

  • 제15권8호
  • /
  • Pages.1119-1131
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  • 2001
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  • 1738-494X(pISSN)
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  • 1976-3824(eISSN)
대한기계학회 (The Korean Society of Mechanical Engineers)
권호 표지

Finding the Maximally Inscribed Rectangle in a Robots Workspace

  • Park, Frank-Chongwoo (School of Mechanical and Aerospace Engineering, Seoul National University) ;
  • Jonghyun Baek (School of Mechanical and Aerospace Engineering, Seoul National University) ;
  • Inrascu, Cornel-Constantin (School of Mechanical and Aerospace Engineering, Seoul National University)
  • 발행 : 2001.08.01
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초록

In this paper we formulate an optimization based approach to determining the maximally inscribed rectangle in a robots workspace. The size and location of the maximally inscribed rectangle is an effective index for evaluating the size and quality of a robots workspace. Such information is useful for, e. g., optimal worktable placement, and the placement of cooperating robots. For general robot workspaces we show how the problem can be formulated as a constrained nonlinear optimization problem possessing a special structure, to which standard numerical algorithms can be applied. Key to the rapid convergence of these algorithms is the choice of a starting point; in this paper we develop an efficient computational geometric algorithm for rapidly obtaining an approximate solution suitable as an initial starting point. We also develop an improved version of the algorithm of Haug et al. for calculating a robots workspace boundary.

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참고문헌

  1. Agarwal, P. K., Amernta, N., Aronov, B., and Sharir, M., 1996, 'Largest Placements and Motion Planning of a Convex Polygon,' 2nd International Workshop on Algorithmic Foundation of Robotics
  2. Allgower, E. L., Georg, K., 1990, Numerical Continuation Methods, Springer Verlag, Berlin Heidelberg
  3. Bajpai, A., Roth, B., 1986, 'Workspace and Mobility of a Closed-Loop Manipulator,' The Int.J.of Robotics Research https://doi.org/10.1177/027836498600500214
  4. Ceccarelli, M., 1996, 'A Formulation for the Workspace Boundary of General N-Revolute Manipulators,' Mach.Mach,Theory, Vol. 31, No. 5, pp. 637-646 https://doi.org/10.1016/0094-114X(95)00096-H
  5. Daniels, K. M., Milenkovic, V. J., Roth, D., 1997, 'Finding the Maximum Area Axis-Parallel Rectangle in a Simple Polygon,' In Computational Geometry: Theory and Applications, Vol. 7, pp. 125-148
  6. Gupta, K. C., 1986, 'On the Nature of Robot Workspace,' The Int.J.of Robotics Research, Vol. 5, No. 2 https://doi.org/10.1177/027836498600500212
  7. Haug, E. J., Luh, C. M., Adkins, F. A., Wang, J. Y., 1996, 'Numerical Alogorithms for Mapping Boundaries of Manipulator Workspaces,' J.of Mechanical Design, Vol. 118, No. 2. pp. 228-234
  8. Hong, K. S., Kim, Y. M., Choi, C., 1997, 'Inverse Kinematics of a Reclaimer : Closed Form Solution by Exploiting Geometric Constraints,' KSME Int.J., Vol. 11, No. 6, pp. 629-638
  9. Hyundai Industrial Robot Brochure, 1999, Hyundai Heavy Insustries Co
  10. Liu, B., Ku L. P., Hsu, W., 1997, 'Discovering Interesting Holes in Data,' Proceedings of Fifteenth International Joint Conference on Artificial Intelligence(IJCAI-97), Nagoya,Japan, pp. 930-935
  11. Luenberger, D. G., 1989, Linear and Nonlinear Programming, Addison Wesley
  12. Murray, R. M., Li, Z., Sastry, S. S., 1994, A Mathematical Interoduction to Robotic Manipulation, Boca Raton, CRC Press
  13. O'Rouke, J., 1998, Computational Geometry in C, Cambridge University Press
  14. Strang, G., 1986, Linear Algebra and its Applications,Harcourt Brace & Company
  15. Vandenberghe, L., Boyd, S. P., Wu, S.P., 1998, 'Determinant maximization with linear matrix inequality constraints,' SIAM Journal on Matrix Analysis and Applications,April https://doi.org/10.1137/S0895479896303430
  16. Yoshikawa, T., 1985. 'Manipulability of Robotic Mechanisms,' The Int. J. of Robotics Research, Vol. 4, No. 2, pp. 3-9 https://doi.org/10.1177/027836498500400201
  17. You, S. S., Jeong, S. K., 1998, 'Kinematics and Dynamics Modeling for Holonomic Constrained Multiple Robot Systems through Principle of Workspace Orthogonalization,' KSME Int. J., Vol. 12, No. 2, pp. 170-180
  18. de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O., 1997, Computational Geometry Algorithms and Applications,Springer-Verlag, Berlin Heidelberg