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A novel curvature-based method for analyzing the second-order immobility of frictionless grasp

Published online by Cambridge University Press:  28 July 2011

Chen Luo ,
LiMin Zhu  and
Han Ding
Chen Luo
Affiliation:
School of Mechanical Engineering, Southeast University, Nanjing 210096, P. R. China
LiMin Zhu*
Affiliation:
School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, P. R. China
Han Ding
Affiliation:
School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, P. R. China
*
*Corresponding author. E-mail: zhulm@sjtu.edu.cn
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Summary

This paper presents a new method to analyze frictionless grasp immobility based on defined surface-to-surface signed distance function. Distance function's differential properties are analyzed and its second-order Taylor expansion with respect to differential motion is deduced. Based on the non-negative condition of the signed distance function, the first- and second-order free motions are defined and the corresponding conditions for immobility of frictionless grasp are derived. As one benefit of the proposed method, the second-order immobility check can be formulated as a nonlinear programming problem. Numerical examples are used to verify the proposed method.

Keywords

Signed distance functionGraspFrictionless contactFree motion
Type
Articles
Information
Robotica , Volume 30 , Issue 4 , July 2012 , pp. 613 - 625
Copyright
Copyright © Cambridge University Press 2011

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References

1.Kirkpatrich, D., Kosaraju, S. R., Mishra, B. and Yap, C-K., “Quantitative Steinitz's Theorem with Applications to Multifingered Grasping,” T R 460, Robotics Report, 210, Courant Institute of Mathematical Science, New York University, NY, USA (Sep. 1989).Google Scholar
2.Lakshminarayana, K., “Mechanics of Form Closure,” Technical Report, 78-DET-32, ASME Minneapolis, USA (1978).Google Scholar
3.Trinkle, J. C., “On the stability and instantaneous velocity of grasped frictionless objects,” IEEE Trans. Robot. Autom. 8, 560–572 (Oct. 1992).Google Scholar
4.Ohwovoriole, M. S. and Roth, B., “An extension of screw theory,” J. Mech Des. 103, 725–735 (1981).Google Scholar
5.Rimon, E. and Burdick, J. W., “Mobility of bodies in contact. Part I: A 2nd-order mobility index for multiple-finger grasps,” IEEE Trans. Robot. Autom. 14 (5), 696–708 (Oct. 1998).CrossRefGoogle Scholar
6.Rimon, E. and Burdick, J. W., “Mobility of bodies in contact. Part II: How forces are generated by curvature effects,” IEEE Trans. Robot. Autom. 14, 709–717 (Oct. 1998).Google Scholar
7.Rimon, E. and Burdick, J. W., “A configuration space analysis of bodies in contact—1st order mobility and 2nd order mobility,” Mech. Mach. Theory 30 (6), 897–928 (1995).CrossRefGoogle Scholar
8.Rimon, E., “A curvature-based bound on the number of frictionless fingers required to immobilize three-dimensional objects,” IEEE Trans. Robot. Autom. 17 (5) (Oct. 2001).Google Scholar
9.Hanafusa, H. and Asada, H., “Stable Prehension by a Robot Hand with Elastic Fingers,” Proceedings of the 7th International Symposium on Industrial Robots, Tokyo (1977) pp. 384–389.Google Scholar
10.Montana, D. J., “The Condition for Contact Grasp Stability,” Proceedings of the IEEE Conference on Robotics and Automation, Sacramento, California (1991) pp. 412–417.Google Scholar
11.Howard, W. S. and Kumar, V., “On the stability of grasped objects,” IEEE Trans. Robot. Autom., 12, 904–917 (Dec. 1996).CrossRefGoogle Scholar
12.Trinkle, J. C., Farahat, A. O. and Stiller, P. F., “Second-Order Stability Cells of a Frictionless Rigid Body Grasped by Rigid Fingers,” Proceedings of the IEEE International Conference on Robotics and Automation, San Diego, CA, USA (1994) pp. 2815–2821.Google Scholar
13.Myeong, E. J. and Lee, J. H., “Grasp stability analysis based on acceleration convex polytopes for multi-fingered robot hands,” Int. J. Control Autom. Syst. 7 (2), 253–266 (2009).Google Scholar
14.Yamada, T., Yamanaka, S., Yamada, M., Funahashi, Y. and Yamamoto, H., “Grasp Stability Analysis of Multiple Planar Objects,” Proceedings of the 2009 IEEE International Conference on Robotics and Biomimetics (ROBIO '09), Guilin, China (Dec. 2009) pp. 1032–1038.Google Scholar
15.Yamada, T., Yamanaka, S., Yamada, M., Funahashi, Y. and Yamamoto, H., “Static stability analysis of grasping multiple objects in 2D,” Int. J. Inf. Acquis. 7 (2), 119–134 (2010).CrossRefGoogle Scholar
16.Yamada, T., Taki, T., Yamada, M., Funahashi, Y. and Yamamoto, H., “Static stability analysis of spatial grasps including contact surface geometry,” Adv. Robot. 25 (3), 447–472 (2011).CrossRefGoogle Scholar
17.Stappen, A. F. van der, Wentink, C. and Overmars, M. H., “Computing immobilizing grasps of polygonal parts,” Int. J. Robot. Res. 19 (5), 467–479 (May 2000).CrossRefGoogle Scholar
18.Czyzowicz, J., Stojmenovic, I. and Urrutia, J., “Immobilizing a shape,” Int. J. Comput. Geom. Appl. 9 (2), 181–206 (Apr. 1999).CrossRefGoogle Scholar
19.Kragten, G. A., Herder, J. L. and Schwab, A. L., “On the Influence of Contact Geometry on Grasp Stability,” Proceedings of the IDETC/ CIE 2008 ASME International Conference, DETC2008–49400, New York City, NY (2008).Google Scholar
20.Zhu, L. M. and Ding, H., “A unified approach for least-squares surface fitting,” Sci. China E, 45 (12), 1–5 (2004).Google Scholar
21.Zhu, L. M., “Distance function based models and algorithms for fitting of geometric elements to measured coordinate points,” Postdoctoral Technical Report. School of Mechanical Science & Engineering, Huazhong University of Science & Technology, China (2002).Google Scholar
22.Zhu, L. M., Xiong, Z. H., Ding, H. and Xiong, Y. L., “A distance function based approach for localization and profile error evaluation of complex surface,” Trans. ASME, J. Manuf. Sci. Eng. 126 (3), 484–501 (2004).CrossRefGoogle Scholar
23.Murray, R. M., Li, Z. and Sastry, S. S., A Mathematical Introduction to Robotic Manipulation (CRC Press, Boca Rato, 1994).Google Scholar
24.Lou, C., Zhu, L. and Ding, H., “Identification and reconstruction of surfaces based on distance function,” Proc. IMechE, Part B: J. Eng. Manuf. 223 (B8), 981–994 (2009).CrossRefGoogle Scholar
25.Anitescu, M., Cremer, J. F. and Potra, F. A., “Formulating 3D Contact Dynamics Problems,” Reports on Computational Mathematics, No. 80. Department of Mathematics, University of IOWA Iowa City, USA (1995).Google Scholar
26.Montana, D. J., “The kinematics of contact and grasp,” Int. J. Robot.Res. 7 (3), 17–25 (1988).CrossRefGoogle Scholar
27.Avriel, M., Nonlinear Programming: Analysis and Methods (Prentice-Hall, Inc., Englewood Cliffs, NJ, USA, 1976).Google Scholar
28.Carlson, J. S., “Quadratic sensitivity analysis of fixtures and locating schemes for rigid parts,” J. Manuf. Sci. Eng. 123, 462–470 (2001).Google Scholar
29.Wang, M. Y., Liu, T. and Pelinescu, D. M., “Fixture kinematic analysis based on the full contact model of rigid bodies,” J. Manuf. Sci. Eng. 316, 316–324 (2003).CrossRefGoogle Scholar