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In-hand forward and inverse kinematics with rolling contact

Published online by Cambridge University Press:  27 February 2017

Lei Cui ,
Jie Sun  and
Jian S. Dai
Lei Cui*
Affiliation:
Department of Mechanical Engineering, Curtin University, Perth, Australia
Jie Sun
Affiliation:
Centre for Robotics Research, King's College London, London, UK. E-mails: [email protected], [email protected]
Jian S. Dai
Affiliation:
Centre for Robotics Research, King's College London, London, UK. E-mails: [email protected], [email protected]
*
*Corresponding author. E-mail: [email protected]
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Summary

Robotic hands use rolling contact to manipulate a grasped object to a desired location, even when the finger and the palm linkage mechanisms lack degrees of freedom. This paper presents a systematic approach to the forward and inverse kinematics of in-hand manipulation. The moving frame method in differential geometry is integrated into the product of exponential formula to establish a pure geometric framework of the kinematics of a robot hand. The forward and inverse kinematics of a multifingered hand are obtained in terms of the joint rates and contact trajectories. A two-fingered planar robot hand and a three-fingered spatial robot hand are used to demonstrate the proposed approach. The proposed formulation amounts to solving a univariate polynomial, providing an alternative to the existing ones that require numerical integration.

Keywords

ContactRollingKinematicsMultifingered handsManipulationProduct of exponentialMoving frame method
Type
Articles
Information
Robotica , Volume 35 , Issue 12 , December 2017 , pp. 2381 - 2399
Copyright
Copyright © Cambridge University Press 2017 

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References

1. Yousef, H., Boukallel, M. and Althoefer, K., “Tactile sensing for dexterous in-hand manipulation in robotics—a review,” Sensors Actuators A: Phys. 167 (2), 171–187 (2011).Google Scholar
2. Sudsang, A. and Phoka, T., “Regrasp Planning for a 4-Fingered Hand Manipulating a Polygon,” Proceedings of the IEEE International Conference on Robotics and Automation, 2003, ICRA'03, Taibei, Taiwan (Sep. 14–19, 2003) pp. 2671–2676.Google Scholar
3. Dafle, N. C., Rodriguez, A., Paolini, R., Tang, B., Srinivasa, S. S., Erdmann, M., Mason, M. T., Lundberg, I., Staab, H. and Fuhlbrigge, T., “Extrinsic Dexterity: In-Hand Manipulation with External Forces,” 2014 IEEE International Conference on Robotics and Automation (ICRA), Hong Kong, China (May 31–Jun. 7, 2014) pp. 1578–1585.Google Scholar
4. Furukawa, N., Namiki, A., Taku, S. and Ishikawa, M., “Dynamic Regrasping using a High-Speed Multifingered Hand and a High-Speed Vision System,” Proceedings of the 2006 IEEE International Conference on Robotics and Automation, 2006, ICRA 2006, Orlando, FL, USA (May 15–19, 2006) pp. 181–187.Google Scholar
5. Cherif, M. and Gupta, K. K., “3D in-Hand Manipulation Planning,” Proceedings of the 1998 IEEE/RSJ International Conference on Intelligent Robots and Systems, 1998, vol. 141, Victoria, British Columbia, Canada (Oct. 13–17, 1998) pp. 146–151.Google Scholar
6. Kondo, M., Ueda, J. and Ogasawara, T., “Recognition of in-hand manipulation using contact state transition for multifingered robot hand control,” Robot. Auton. Syst. 56 (1), 66–81 (2008).Google Scholar
7. Rus, D., “In-hand dexterous manipulation of piecewise-smooth 3-D objects,” Int. J. Robot. Res. 18 (4), 355–381 (1999).Google Scholar
8. Sudsang, A. and Srinivasa, N., “Grasping and in-hand manipulation: Geometry and algorithms,” Algorithmica 26 (3–4), 466–493 (2000).Google Scholar
9. Ueda, J., Kondo, M. and Ogasawara, T., “The multifingered NAIST hand system for robot in-hand manipulation,” Mech. Mach. Theory 45 (2), 224–238 (2010).CrossRefGoogle Scholar
10. Exner, C., “Development of hand functions,” In: Occupational therapy for children (Pratt, P. N. and Allen, A. S., eds.), (Mosby, St. Louis, 1989) pp. 235–259.Google Scholar
11. Pehoski, C., Henderson, A. and Tickle-Degnen, L., “In-hand manipulation in young children: Rotation of an object in the fingers,” Am. J. Occup. Therapy 51 (7), 544–552 (1997).Google Scholar
12. Jeong, H. and Cheong, J., “In-Hand Rolling Motion Planning using Independent Contact Region (ICR) with Guaranteed Grasp Quality Margin,” 2013 IEEE International Conference on Robotics and Automation (ICRA), Karlsruhe, Germany (May 6–10, 2013) pp. 3239–3244.Google Scholar
13. Kim, Y. B., Kang, G., Yee, G. K., Kim, A., You, W. S., Lee, Y. H., Liu, F., Moon, H., Koo, J. C. and Choi, H. R., “Exploration and reconstruction of unknown object by active touch of robot hand,” Intell. Service Robot. 8 (3), 141–149 (2015).Google Scholar
14. Reis, M. F., Leite, A. C., Lizarralde, F. and Hsu, L., “Kinematic Modeling and Control Design of a Multifingered Robot Hand,” 2015 IEEE 24th International Symposium on Industrial Electronics (ISIE), Buzios, Rio de Janeiro, Brazil (Jun. 3–5, 2015) pp. 638–643.Google Scholar
15. van Hoof, H., Hermans, T., Neumann, G. and Peters, J., “Learning Robot in-Hand Manipulation with Tactile Features,” 2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids), Seoul, Korea (South) (Nov. 3–5, 2015) pp. 121–127.Google Scholar
16. Doulgeri, Z. and Droukas, L., “On Rolling Contact Motion by Robotic Fingers Via Prescribed Performance Control,” 2013 IEEE International Conference on Robotics and Automation (ICRA), Karlsruhe, Germany (May 6–10, 2013) pp. 3976–3981.Google Scholar
17. Droukas, L. and Doulgeri, Z., “Rolling contact motion generation and control of robotic fingers,” J. Intell. Robot. Syst. 1, 1–18 (2015).Google Scholar
18. Cui, L. and Dai, J. S., “A Coordinate-Free Approach to Instantaneous Kinematics of Two Rigid Objects with Rolling Contact and Its Implications for Trajectory Planning,” IEEE International Conference on Robotics and Automation, Kobe, Japan (May 12–17, 2009) pp. 612–617.Google Scholar
19. Cui, L. and Dai, J. S., “A darboux-frame-based formulation of spin-rolling motion of rigid objects with point contact,” IEEE Trans. Robot. 26 (2), 383–388 (2010).Google Scholar
20. Cui, L. and Dai, J. S., In: Geometric Kinematics of Point Contact (Lenarčič, J. and Stanisic, M. M., eds.) (Springer, New York, US, 2010) pp. 429–436.Google Scholar
21. Cui, L. and Dai, J. S., “A polynomial formulation of inverse kinematics of rolling contact,” J. Mech. Robot. 7 (4), 041003_041001–041009 (2015).CrossRefGoogle Scholar
22. Cui, L. and Dai, J. S., “From sliding–rolling loci to instantaneous kinematics: An adjoint approach,” Mech. Mach. Theory 85 (0), 161–171 (2015).Google Scholar
23. Cai, C. and Roth, B., “On the planar motion of rigid bodies with point contact,” Mech. Mach. Theory 21 (6), 453–466 (1986).Google Scholar
24. Montana, D. J., “The kinematics of contact and grasp,” Int. J. Robot. Res. 7 (3), 17–32 (1988).Google Scholar
25. Marigo, A. and Bicchi, A., “Rolling bodies with regular surface: Controllability theory and application,” IEEE Trans. Autom. Control 45 (9), 1586–1599 (2000).CrossRefGoogle Scholar
26. Cui, L., “Differential Geometry Based Kinematics of Sliding-Rolling Contact and Its Use for Multifingered Hands,” In: Centre for Robotics Research (King's College London, London, UK, 2010).Google Scholar
27. Hwang, C. S., Takano, M. and Sasaki, K., “Kinematics of grasping and manipulation of a B-spline surface object by a multifingered robot hand,” J. Robot. Syst. 16 (8), 445–460 (1999).3.0.CO;2-1>CrossRefGoogle Scholar
28. Trinkle, J. C. and Paul, R. P., “Planning for dexterous manipulation with sliding contacts,” Int. J. Robot. Res. 9 (3), 24–48 (1990).Google Scholar
29. Kao, I. and Cutkosky, M. R., “Quasistatic manipulation with compliance and sliding,” Int. J. Robot. Res. 11 (1), 20–40 (1992).Google Scholar
30. Vatani, M., Engeberg, E. D. and Choi, J.-W., “Detection of the position, direction and speed of sliding contact with a multi-layer compliant tactile sensor fabricated using direct-print technology,” Smart Mater. Struct. 23 (9), 095008 (2014).Google Scholar
31. Vatani, M., Engeberg, E. D. and Choi, J.-W., “Force and slip detection with direct-write compliant tactile sensors using multi-walled carbon nanotube/polymer composites,” Sensors Actuators A: Phys. 195, 90–97 (2013).CrossRefGoogle Scholar
32. Okamura, A. M., Smaby, N. and Cutkosky, M. R., “An Overview of Dexterous Manipulation,” Proceedings of the IEEE International Conference on Robotics and Automation, 2000, ICRA '00, vol. 251, San Francisco, CA, USA (Apr. 24–28, 2000) pp. 255–262.Google Scholar
33. Murray, R. M., Li, Z. and Sastry, S. S., A Mathematical Introduction to Robotic Manipulation (CRC Press, Boca Raton, USA, 1994).Google Scholar
34. Park, F. C. and Brockett, R. W., “Kinematic dexterity of robotic mechanisms,” Int. J. Robot. Res. 13 (1), 1–15 (1994).Google Scholar
35. Brockett, R. W., Robotic Manipulators and the Product of Exponentials Formula (Springer, Berlin, 1984).Google Scholar
36. Romdhane, L. and Duffy, J., “Kinestatic analysis of multifingered hands,” Int. J. Robot. Res. 9 (6), 3–18 (1990).Google Scholar
37. Cui, L. and Dai, J. S., “Posture, workspace, and manipulability of the metamorphic multifingered hand with an articulated palm ASME,” J. Mech. Robot. 3 (2), 021001_021001–021007 (2011).Google Scholar
38. Cui, L. and Dai, J. S., “Reciprocity-based singular value decomposition for inverse kinematic analysis of the metamorphic multifingered hand ASME,” J. Mech. Robot. 4 (3), 034502_034501_034506 (2012).CrossRefGoogle Scholar
39. Cui, L., Cupcic, U. and Dai, J. S., “An optimization approach to teleoperation of the thumb of a humanoid robot hand: Kinematic mapping and calibration,” J. Mech. Des. 136 (9), 091005_091001_091007 (2014).Google Scholar
40. Cui, L., Tan, T., Do, K. D. and Teunissen, P., “Challenges and solutions for autonomous robotic mobile manipulation for outdoor sample collection,” J. Electr. Electron. Eng. 3 (5), 156–164 (2015).Google Scholar
41. Cartan, E., Riemannian Geometry in an Orthogonal Frame (World Scientific Press, Singapore, 2002).Google Scholar
42. Cartan, H., Differential Forms (Dover Publisher, New York, 1996).Google Scholar
43. Carmo, M. P., Differential Geometry of Curves and Surfaces (Prentice-Hall, Englewood Cliffs, 1976).Google Scholar
44. Gray, A., Modern Differential Geometry of Curves and Surfaces with Mathematica (CRC Press, Inc., Boca Raton, Florida, 1996).Google Scholar
45. Wei, G., Sun, J., Zhang, X., Pensky, D., Piater, J. and Dai, J. S., “Metamorphic Hand based Grasp Constraint and Affordance,” ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, American Society of Mechanical Engineers, Boston, Massachusetts, US (Aug. 2–5, 2015) pp. V05BT08A008–V005BT008A008.Google Scholar
46. Dai, J. S. and Kerr, D. R., “Analysis of force distribution in grasps using augmentation,” J. Mech. Eng. Sci. 210 (1), 15–22 (1996).Google Scholar
47. Dai, J. S. and Rees Jones, J., “Interrelationship between screw systems and corresponding reciprocal systems and applications,” Mech. Mach. Theory 36 (5), 633–651 (2001).Google Scholar
48. Dai, J. S., Wang, D. and Cui, L., “Orientation and workspace analysis of the multifingered metamorphic hand-metahand,” IEEE Trans. Robot. 25 (4), 942–947 (2009).Google Scholar
49. Mason, M. T., Mechanics of Robotic Manipulation (MIT Press, Cambridge, Massachusetts, 2001).Google Scholar
50. Trinkle, J. C., “A Quasi-Static Analysis of Dextrous Manipulation with Sliding and Rolling Contacts,” Proceedings of the 1989 IEEE International Conference on Robotics and Automation, 1989, (1989) pp. 788–793.Google Scholar
51. Cherif, M. and Gupta, K. K., “Planning quasi-static fingertip manipulations for reconfiguring objects,” IEEE Trans. Robot. Autom. 15 (5), 837–848 (1999).Google Scholar