Static modeling of linear object deformation based on differential geometry

International Journal of Robotics Research

Volumn 23, Issue 3, 2004, Pages 293-311

  Wakamatsu, Hidefumi ^a   Hirai, Shinichi ^b  

^a OSAKA UNIVERSITY   (Japan)

^b RITSUMEIKAN UNIVERSITY   (Japan)

Author keywords

Deformation; Differential geometry; Linear objects; Modeling; Statics

Indexed keywords

ALGORITHMS; GEOMETRY; MATHEMATICAL MODELS; MATRIX ALGEBRA; MOTION PLANNING; SYSTEM STABILITY;

DEFORMATION MODELING; DIFFERENTIAL GEOMETRY; LINEAR OBJECTS; STATICS;

ROBOTICS;

EID: 1642283450     PISSN: 02783649     EISSN: None     Source Type: Journal    
DOI: 10.1177/0278364904041882     Document Type: Article

References (41)

1. Adams, C. C. 1994. The Know Book: An Elementary Introduction to the Mathematical Theory of Knots, Henry Holt & Co., New York.
2. Avriel, M. 1976. Nonlinear Programming: Analysis and Methods, Prentice-Hall, Englewood Cliffs, NJ.
3. Baraff, D. and Witkin, A. 1998. Large steps in cloth simulation. In Computer Graphics Proceedings (SIGGRAPH 1998), Orlando, FL, pp. 43-54.
4. Belytschko, T., Liu, W. K., and Moran, B. 2000. Beams and shells. In Nonlinear Finite Elements for Continua and Structures, Chap. 9, Wiley, New York, pp. 509-568.
5. Chen, M. Z. and Zheng, Y. F. 1995. Vibration-free handling of deformable beams by robot end-effectors. Journal of Robotic Systems 12(5):331-347.
6. Daldegan, A., Thalmann, N. M., Kurihara, T., and Thalmann, D. 1993. An Integrated System for Modeling, Animating and Rendering Hair. Computer Graphics Forum (Eurographics '93), 12(3):211-221.
7. Debunne, G., Desbrun, M., Cani, M.-P., and Barr, A. H. 2001. Dynamic real-time deformations using space and time adaptive sampling. In Computer Graphics Proceedings (SIGGRAPH 2001), Los Angeles, CA, pp. 31-36.
8. Eberhardt, B., Weber, A., and Strasswer, W. 1996. A fast, flexible, particle-system model for cloth draping. IEEE Computer Graphics and Applications, 16(5):52-59.
9. Eischen, J. W., Deng, S., and Clapp, T. G. 1996. Finite-element modeling and control of flexible fabric parts. IEEE Computer Graphics and Applications, 16(5):71-80.
10. Elsgolc, L. E. 1961. Calculus of Variations, Pergamon, Oxford.
11. Fung, Y. C. 1965. Foundations of Solid Mechanics, Prentice-Hall, Englewood Cliffs, NJ.
12. Goldstein, H. 1980. Classical Mechanics, Addison-Wesley, Reading, MA.
13. Gray, A. 1993. Modern Differential Geometry of Curves and Surfaces, CRC Press, Boca Raton, FL.
14. Henrich, D. and Wörn, H. editors. 2000. Robot Manipulation of Deformable Objects, Advanced Manufacturing Series, Springer-Verlag, Berlin.
15. Hirai, S. 2000. Energy-based modeling of deformable linear objects. In Robot Manipulation of Deformable Objects, D. Henrich and H. Wörn, editors, Advanced Manufacturing Series, Springer-Verlag, Berlin, pp. 11-28.
16. Hirai, S. and Wada, T. 2000. Indirect simultaneous positioning of deformable objects with multi pinching fingers based on uncertain model. Robotica, Millennium Issue on Grasping and Manipulation, 18:3-11.
17. Hopcroft, J. E., Kearney, J. K., and Krafft, D. B. 1991. A case study of flexible object manipulation. International Journal of Robotics Research 10(1):41-50.
18. Irvine, H. M. 1981. Cable Structures, MIT Press, Cambridge, MA.
19. James, D. L. and Pai, D. K. 1999. ArtDefo - accurate real time deformable objects. In Computer Graphics Proceedings (SIGGRAPH 1999), Los Angeles, CA, pp. 65-72.
20. James, D. L. and Pai, D. K. 2002. Real-time simulation of multizone elastokinematic models. In Proceedings of the IEEE International Conference on Robotics and Automation, Washington, DC, pp. 927-932.
21. Joukhader, A., Dequet, A., and Laugie, C. 1998. A collision model for rigid and deformable bodies. In Proceedings of the IEEE International Conference on Robotics and Automation, Leuven, Belgium, pp. 982-988.
22. Kühnapfel, U., Çakmak, H. K., and Maass, H. 2000. Endoscopic surgery training using virtual reality and deformable tissue simulation. Computers and Graphics 24(5):671-682.
23. Leaf, B. G. A. V. 1960. Models of the plain-knitted loop. Journal of the Textile Institute Transactions, pp. 49-58.
24. Mason, M. T. 2001. Mechanics of Robotics Manipulation, MIT Press, Cambridge, MA.
25. Nakagaki, H., Kitagaki, K., Ogasawara, T., and Tsukune, H. 1997. Study of Deformation and Insertion Tasks of a Flexible Wire. In Proceedings of the IEEE International Conference on Robotics and Automation, Albuquerque, NM, pp. 2397-2402.
26. Pai, D. K. 2002. STRANDS: Interactive Simulation of Thin Solids using Cosserat Models. Computer Graphics Forum 21(3):347-352.
27. Phillips, J., Ladd, A., and Kavraki, L. E. 2002. Simulated knot tying. In Proceedings of the IEEE International Conference on Robotics and Automation, Washington, DC, pp. 841-846.
28. Picinbono, G., Delingette, H., and Ayache, N. 2001. Nonlinear and anisotropic elastic soft tissue models for medical simulation. In Proceedings of the IEEE International Conference on Robotics and Automation, Seoul, Korea, pp. 1371-1376.
29. Remde, A. and Henrich, D. 2000. Direct and inverse simulation of deformable linear objects. In Robot Manipulation of Deformable Objects, D. Henrich and H. Wörn, editors, Advanced Manufacturing Series, Springer-Verlag, Berlin, pp. 43-70.
30. Rosenblum, R. E., Carlson, W. E., and Tripp, E. 1991. Simulating the structure and dynamics of human hair: modelling, rendering and animation. Journal of Visualization and Computer Animation 2(4): 141-148.
31. Taylor, P.M. 1990. Sensory Robotics for the Handling of Limp Materials, Springer-Verlag, Berlin.
32. Terzopoulos, D. and Witkin, A. 1988. Deformable models-physically based models with rigid and deformable components. IEEE Computer Graphics and Applications 41-51.
33. Terzopoulos, D., Platt, J., Barr, A., and Fleischer, K. 1987. Elastically deformable models. Computer Graphics 21(4):205-214.
34. Timoshenko, S. 1955. Strength of Materials, Part I: Elementary Theory and Problems, D. Van Nostrand, Princeton, NJ.
35. Villarreal, A. and Asada, H. 1991. A geometric representation of distributed compliance for the assembly of flexible parts. In Proceedings of the IEEE International Conference on Robotics and Automation, Sacramento, CA, pp. 2708-2715.
36. Wakamatsu, H, Hirai, S., and Iwata, K. 1995. Modeling of linear objects considering bend, twist, and extensional deformations. In Proceedings of the IEEE International Conference on Robotics and Automation, Nagoya, Japan, pp. 433-438.
37. Weil, J. 1986. The synthesis of cloth objects. Computer Graphics 20(4):49-54.
38. Witkin, A. and Welch, W. 1990. Fast animation and control of non-rigid structures. Computer Graphics Proceedings (SIGGRAPH 1990), Dallas, TX, pp.243-252.
39. Yue, S. and Henrich, D. 2002. Manipulating deformable linear objects: sensor-based fast manipulation during vibration. In Proceedings of the IEEE International Conference on Robotics and Automation, Washington, DC, pp. 2467-2472.
40. Zheng, Y. F., Pei, R., and Chen, C. 1991. Strategies for automatic assembly of deformable objects. In Proceedings of the IEEE International Conference on Robotics and Automation, Sacramento, CA, pp. 2598-2603.
41. Zhuang, Y. and Canny, J. 2000. Haptic interaction of global deformations. In Proceedings of the IEEE International Conference on Robotics and Automation, San Francisco, CA, pp. 2428-2433.