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New computational method for three-fingered force-closure test

Published online by Cambridge University Press:  05 December 2013

Nattee Niparnan ,
Thanathorn Phoka ,
Yuttana Suttasupa  and
Attawith Sudsang
Nattee Niparnan
Affiliation:
Department of Computer Engineering, Faculty of Engineering, Chulalongkorn University, 10330, Thailand
Thanathorn Phoka
Affiliation:
Department of Computer Engineering, Faculty of Engineering, Chulalongkorn University, 10330, Thailand
Yuttana Suttasupa
Affiliation:
Department of Computer Engineering, Faculty of Engineering, Chulalongkorn University, 10330, Thailand
Attawith Sudsang*
Affiliation:
Department of Computer Engineering, Faculty of Engineering, Chulalongkorn University, 10330, Thailand
*
*Corresponding author. E-mail: attawith@gmail.com
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Summary

This paper proposes an efficient implementation of a force-closure test for frictional three-finger grasps. The implementation is based on a condition that transforms force-closure testing into the problem of convex hull intersection in projective space. The proposed implementation further reduces the problem into the problem of computing whether a line segment intersects a convex hull of at most four points. Implementation results are presented along with a thorough performance analysis and comparison with several existing methods. The results are also verified with arbitrary precision floating point computation. This provides comparison of qualitative error resulting from floating point roundoff. The result shows that the proposed implementation outperforms other methods in terms of speed and precision.

Keywords

GraspingForce closureProjective geometry
Type
Articles
Information
Robotica , Volume 32 , Issue 6 , September 2014 , pp. 867 - 887
Copyright
Copyright © Cambridge University Press 2013 

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References

1. Salisbury, J., “Kinematic and Force Analysis of Articulated Hands.” PhD thesis (Stanford University, Stanford, CA, 1982).CrossRefGoogle Scholar
2. Salisbury, J. and Roth, B., “Kinematic and force analysis of articulated hands,” ASME J. Mech. Transm. Autom. Des. 105, 33–41 (1982).Google Scholar
3. Bicchi, A. and Kumar, V., “Robotic Grasping and Contact: A Review,” In: IEEE International Conference on Robotics and Automation, San Francisco, CA (2000) pp. 348–353.Google Scholar
4. Bicchi, A., “Hands for dexterous manipulation and robust grasping: A difficult road toward simplicity,” IEEE Trans. Robot. Autom. 16 (16), 652–662 (2000).CrossRefGoogle Scholar
5. Ferrari, C. and Canny, J., “Planning Optimal Grasps.” In: IEEE International Conference on Robotics and Automation (1992) pp. 2290–2295.Google Scholar
6. Liu, Y.-H., “Qualitative test and force optimization of 3-D frictional form-closure grasps using linear programming,” IEEE Trans. Robot. Autom. 15 (1), 163–173 (1999).Google Scholar
7. Zhu, X. and Wang, J., “Synthesis of force-closure grasps on 3-D objects based on the q distance,” IEEE Trans. Robot. Autom. 19 (4), 669–679 (2003).Google Scholar
8. Zhu, X. and Ding, H., “Computation of force-closure grasps: An iterative algorithm,” IEEE Trans. Robot. 22 (1), 172–179 (2006).Google Scholar
9. Gilbert, E. G., Johnson, D. W. and Keerthi, S. S., “A fast procedure for computing the distance between complex objects in three-dimentional space,” IEEE Trans. Robot. Autom. 4, 193–203 (1988).CrossRefGoogle Scholar
10. Zhu, X., Ding, H. and Tso, S. K., “A pseudodistance function and its applications,” IEEE Trans. Robot. Autom. 20 (2), 344–352 (2004).CrossRefGoogle Scholar
11. Zheng, Y. and Chew, C.-M., “A Numerical Solution to the Ray-Shooting Problem and Its Applications in Robotic Grasping”, IEEE International Conference on Robotics and Automation (2009).Google Scholar
12. Zheng, Y. and Chew, C.-M., “Distance between a point and a convex cone in n-dimensional space: Computation and applications,” IEEE Trans. Robot. 25 (6), 1397–1412 (2009).CrossRefGoogle Scholar
13. Nguyen, V.-D., “Constructing force-closure grasps,” Int. J. Robot. Res. 7 (3), 3–16 (1988).CrossRefGoogle Scholar
14. Ponce, J. and Faverjon, B., “On computing three-finger force-closure grasps of polygonal objects,” IEEE Trans. Robot. Autom. 11 (6), 868–881 (1995).CrossRefGoogle Scholar
15. Li, J.-W., Liu, H. and Cai, H.-G., “On computing three-finger force-closure grasps of 2-D and 3-D objects,” IEEE Trans. Robot. Autom. 19 (1), 155–161 (2003).Google Scholar
16. Brost, R. C. and Mason, M. T., “Graphical analysis of planar rigid-body dynamics with multiple frictional contacts,” In: International Symposium on Robotics Research, Tokyo, Japan (MIT Press, Cambridge, MA, 1989) pp. 293–300.Google Scholar
17. Mason, M. T., Mechanics of Robotic Manipulation, Intelligent Robotics and Autonomous Agents series (MIT Press, Cambridge, MA, 2001).CrossRefGoogle Scholar
18. Mishra, B., Schwartz, J. and Sharir, M., “On the existence and synthesis of multifinger positive grips,” Algorithmica Spec. Issue Robot. 2 (4), 541–558 (1987).Google Scholar
19. Bix, R., Topics in Geometry (Academic Press, Waltham, MA, 1994).Google Scholar
20. Goodman, J. E. and O'Rourke, J. (eds.), Handbook of Discrete and Computational Geometry (CRC Press, Boca Raton, FL, 1997). ISBN 0-8493-8524-5.Google Scholar
21. Han, L., Trinkle, J. C. and Li, Z. X., “Grasp analysis as linear matrix inequality problems,” IEEE Trans. Robot. Autom. 16 (6), 663–674 (2000).CrossRefGoogle Scholar
22. Cornella, J. and Suarez, R., “Fast and Flexible Determination of Force-Closure Independent Regions to Grasp Polygonal Objects,” In: IEEE International Conference on Robotics and Automation, Barcelona, Spain (2005) pp. 778–783.Google Scholar
23. Cornella, J. and Suarez, R., “A New Framework for Planning Three-Finger Grasps of 2D Irregular Objects,” In: IEEE/RSJ International Conference on Intelligent Robots and Systems, Beijing, China (2006) pp. 5688–5694.Google Scholar
24. Tung, C.-P. and Kak, A. C., “Fast construction of force-closure grasps,” IEEE Trans. Robot. Autom. 12 (4), 615–626 (1996).CrossRefGoogle Scholar
25. Faverjon, B. and Ponce, J., “On Computing Two-Finger Force-Closure Grasps of Curved 2D Objects,” In: IEEE International Conference on Robotics and Automation, Sacramento, CA (1991) pp. 424–429.Google Scholar
26. Ponce, J., Sullivan, S., Boissonnat, J.-D. and Merlet, J.-P., “On Characterizing and Computing Three- and Four-Finger Force-Closure Grasps of Polyhedral Objects,” In: IEEE International Conference on Robotics and Automation, Atlanta, GA (1993) pp. 821–827.Google Scholar
27. Pollard, N. S. and Wolf, A., “5 Grasp Synthesis from Example: Tuning the Example to a Task or Object,” In: Springer Tracts in Advanced Robotics, Vol. 18 Multi-Point Interaction with Real and Virtual Objects (Barbagli, F., Prattichizzo, D. and Salisbury, K., eds.) (Springer, Berlin, Germany, 2005) pp. 77–90. ISBN 978-3-540-26036-3.Google Scholar
28. Cheong, J.-S. and van der Stappen, A. F., “Output-Sensitive Computation of All Form-Closure Grasps of a Semi-Algebraic Set,” In: IEEE International Conference on Robotics and Automation, Barcelona, Spain (2005) pp. 772–778.Google Scholar
29. Cheong, J.-S., Haverkort, H. J. and van der Stappen, A. F., “On computing all immobilizing grasps of a simple polygon with few contacts,” Algorithmica 44, 117–136 (2006).CrossRefGoogle Scholar
30. van den Bergen, G., “A fast and robust GJK implementation for collision detection of convex objects,” J. Graph Tools 4 (2), 7–25 (1999).Google Scholar
31. Barber, C. B., Dobkin, D. P. and Huhdanpaa, H., “The quickhull algorithm for convex hulls,” ACM Trans. Math. Soft. 22 (4), 469–483 (1996).CrossRefGoogle Scholar
32. Ong, C. J. and Gilbert, E., “The Gilbert-Johnson-Keerthi Distance Algorithm: A Fast Version for Incremental Motions,” In: Proceedings of 1997 IEEE International Conference on Robotics and Automation, Vol. 2 (1997) pp. 1183–1189. doi:10.1109/ROBOT.1997.614298.Google Scholar
33. Ding, D., Liu, Y.-H., Wang, M. Y. and Wang, S., “Automatic selection of fixturing surfaces and fixturing points for polyhedral workpieces,” IEEE Trans. Robot. Autom. 17 (6), 833–841 (2001).CrossRefGoogle Scholar
34. Liu, Y.-H., Lam, M.-L. and Ding, D., “A complete and efficient algorithm for searching 3-D form-closure grasps in the discrete domain,” IEEE Trans. Robot. 20 (5), 805–816 (2004).CrossRefGoogle Scholar
35. The CGAL Project, CGAL User and Reference Manual (2013) (CGAL Editorial Board), available at http://doc.cgal.org/4.3/Manual/packages.html.Google Scholar
36. Granlund, T., The GNU Multiple Precision Arithmetic Library, 4.2.1 edition (Free Software Foundation, Boston, MA, 2006).Google Scholar
37. Zheng, Y. and Qian, W.-H., “An enhanced ray-shooting approach to force-closure problems,” J. Manuf. Sci. Eng. 128 (4), 960–968 (2006).CrossRefGoogle Scholar