Computation on parametric curves with an application in grasping

International Journal of Robotics Research

Volumn 23, Issue 7-8, 2004, Pages 825-855

  Jia, Yan Bin ^a  

^a Iowa State University   (United States)

Author keywords

Antipodal angle; Antipodal point; Common tangent; Convergence rate; Inflection; Monotonicity; Robot grasping

Indexed keywords

ALGORITHMS; GEOMETRY; IMAGE SEGMENTATION; MANIPULATORS; MOTION PLANNING; NONLINEAR PROGRAMMING; SENSORY PERCEPTION;

ANTIPODAL ANGLE; ANTIPODAL POINT; COMMON TANGENT; CONVERGENCE RATE; INFLECTION; MONOTONICITY; ROBOT GRASPING;

ROBOTICS;

EID: 3142705706     PISSN: 02783649     EISSN: None     Source Type: Journal    
DOI: 10.1177/0278364904045478     Document Type: Conference Paper

References (44)

1. Bespamyatnikh, S. 1998. An efficient algorithm for the three-dimensional diameter problem. Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms, San Francisco, CA, January 25-27, pp. 137-146.
2. Bicchi, A. 2000. Hands for dexterous manipulation and robust grasping: a difficult road toward simplicity. IEEE Transactions on Robotics and Automation 16(6):652-662.
3. Bicchi, A., and Kumar, V. 2000. Robotic grasping and contact: a review. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), San Francisco, CA, April 24-28, pp. 348-353.
4. Blake, A., and Taylor, M. 1993. Planning planar grasps of smooth contours. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Atlanta, GA, pp. 834-839.
5. Brost, R. C., and Goldberg, K. Y. 1994. A complete algorithm for synthesizing modular fixtures for polygonal parts. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), San Diego, CA, pp. 535-542.
6. Chazelle, B., Edelsbrunner, H., Guibas, L. J., and Sharir, M. 1993. Diameter, width, closest line pair and parametric searching. Discrete and Computational Geometry 10:183-196.
7. Chen, I.-M., and Burdick, J. W. 1992. Finding antipodal point grasps on irregularly shaped objects. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Nice, France, pp. 2278-2283.
8. Clarkson, K. L., and Shor, P. W. 1989. Applications of random sampling in computational geometry, II. Discrete and Computational Geometry 4:387-421.
9. Erdös, P. 1960. On sets of distances of n points in Euclidean space. Magyar Tud. Akad. Mat. Kut. Int. Kozi 5:165-169.
10. Goodman, T. N. T. 1991. Inflections on curves in two and three dimensions. Computer Aided Geometric Design 8(1):37-50.
11. Grunbaum, B. 1956. A proof of Vazsonyi's conjecture. Bulletin of Research Council Israel 6(A):77-78.
12. Hong, J., Lafferriere, G., Mishra, B., and Tan, X. 1990. Fine manipulation with multifmger hands. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Cincinnati, OH, pp. 1568-1573.
13. Jia, Y.-B. 2000. Grasping curved objects through rolling. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), San Francisco, CA, April 24-28, pp. 377-382.
14. Jia, Y.-B. 2001. Localization on curved objects using tactile information. Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Maui, Hawaii, pp. 701-706.
15. Jia, Y.-B. 2002a. Curvature-based computation of antipodal grasps. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Washington, DC, May 11-15, pp. 1571-1577.
16. Jia, Y.-B. 2002b. Computation on parametric curves with applications in localization and grasping. Proceedings of the 5th International Workshop on Algorithmic Foundations of Robotics (WAFR), Nice, France, December 15-17.
17. Jia, Y.-B. 2003. On the convex hulls of parametric plane curves. Computational Geometry: Theory and Applications submitted (http://www.cs. iastate.edu/~jia/papers/ convex-hull.pdf).
18. Li, Z., and Sastry, S. S. 1988. Task-oriented optimal grasping by multifingered robot hands. IEEE Journal of Robotics and Automation 4(1):32-44.
19. Manocha, D., and Canny, J. F. 1992. Detecting cusps and inflection points in curves. Computer Aided Geometric Design 9(1): 1-24.
20. Markenscoff, X., and Papadimitriou, C. H. 1989. Optimum grip of a polygon. International Journal of Robotics Research 8(2): 17-29.
21. Markenscoff, X., Ni, L., and Papadimitriou, C. H. 1990. The geometry of grasping. International Journal of Robotics Research 9(1):61-74.
22. MatouSek, J., and Schwarzkopf, O. 1996. A deterministic algorithm for the three-dimensional diameter problem. Computational Geometry: Theory and Applications 6:253-362.
23. Mirtich, B., and Canny, J. 1994. Easily computable optimum grasps in 2D and 3D. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), San Diego, CA, pp. 739-741.
24. Mishra, B. 1991. Workholding: analysis and planning. Proceedings of the IEEE/RSJ International Workshop on Intelligent Robots and Systems (IROS), Osaka, Japan, pp. 53-57.
25. Mishra, B. 1994. Grasp metrics: optimality and complexity. Proceedings of the 1st International Workshop on the Algorithmic Foundations of Robotics (WAFR), Stanford, CA, pp. 137-165.
26. Mishra, B., Schwartz, J. T., and Shark, M. 1987. On the existence and synthesis of multifinger positive grips. Algorithmica 2(4):541-558.
27. Nguyen, V.-D. 1988. Constructing force-closure grasps. International Journal of Robotics Research 7(3):3-16.
28. O'Neill, B. 1966. Elementary Differential Geometry. Academic, New York.
29. Ponce, J., Stam, D., and Faverjon, B. 1993. On computing two-finger force-closure grasps of curved 2D objects. International Journal of Robotics Research 12(3):263-273.
30. Ponce, J., Sullivan, S., Boissonnat, J.-D., and Merlet, J.-P. 1993. On characterizing and computing three- and four-finger force-closure grasps of polyhedral objects. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Atlanta, GA, pp. 821-827.
31. Preparata, F. P. 1979. An optimal real time algorithm for planar convex hulls. Communications of the ACM 22:402-405.
32. Preparata, F. P., and Hong, S. J. 1977. Convex hulls of finite sets of points in two and three dimensions. Communications of the ACM 20(2):87-93.
33. Preparata, F. P., and Shamos, M. I. 1985. Computational Geometry: an Introduction. Springer-Verlag, Berlin.
34. Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T. 1988. Numerical Recipes in C. Cambridge University Press, Cambridge.
35. Ramos, E. A. 1997. Construction of ID lower envelopes and applications. Proceedings of the 13th ACM Symposium on Computational Geometry, Nice, France, June 4-6, pp. 57-66.
36. Rao, A., and Goldberg, K. 1995. Manipulating algebraic parts in the plane. IEEE Transactions on Robotics and Automation 11(4):598-602.
37. Rutter, J. W. 2000. Geometry of Curves. CRC Press, Boca Raton, FL.
38. Sakai, M. 1999. Inflection points and singularities on planar rational cubic curve segments. Computer Aided Geometric Design 16:149-156.
39. Shikin, E. V. 1995. Handbook and Atlas of Curves. CRC Press, Boca Raton, FL.
40. Stoer, J., and Bulirsch, R. 1993. Introduction to Numerical Analysis, 2nd edition. Springer-Verlag, Berlin.
41. Teichmann, M. 1995. Grasping and Fixturing: a Geometric Study and an Implementation. PhD thesis, New York University.
42. Teichmann, M., and Mishra, B. 2000. Reactive robotics I: reactive grasping with a modified gripper and multifingered hands. International Journal of Robotics Research 19(7):697-708.
43. Trinkle, J. C. 1992. A quantitative test for form closure grasps. Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Raleigh, NC, pp. 1670-1677.
44. Yao, A.C.-C. 1982. On constructing minimum spanning trees in k-dimensional space and related problems. SIAM Journal of Computing 11(4):721-736.