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Analytical inverse kinematics for 5-DOF humanoid manipulator under arbitrarily specified unconstrained orientation of end-effector

Published online by Cambridge University Press:  13 March 2014

Masayuki Shimizu*
Affiliation:
Department of Mechanical Engineering, Shizuoka University, Hamamatsu, Japan
*
*Corresponding author. E-mail: tmsimiz@ipc.shizuoka.ac.jp
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This paper proposes an analytical method of solving the inverse kinematic problem for a humanoid manipulator with five degrees-of-freedom (DOF) under the condition that the target orientation of the manipulator's end-effector is not constrained around an axis fixed with respect to the environment. Since the number of the joints is less than six, the inverse kinematic problem cannot be solved for arbitrarily specified position and orientation of the end-effector. To cope with the problem, a generalized unconstrained orientation is introduced in this paper. In addition, this paper conducts the singularity analysis to identify all singular conditions.

Type
Articles
Creative Commons
Creative Common License - CCCreative Common License - BY
The online version of this article is published within an Open Access environment subject to the conditions of the Creative Commons Attribution licence http://creativecommons.org/licenses/by/3.0/
Copyright
Copyright © Cambridge University Press 2014

References

1. Wampler, C. and Morgan, A., “Solving the 6R inverse position problem using a generic-case solution methodology,” Mech. Mach. Theory 26 (1), 91106 (1991).Google Scholar
2. Raghavan, M. and Roth, B., “Inverse kinematics for the general 6R manipulator and related linkages,” Trans. ASME J. Mech. Des. 115 (3), 502508 (1993).Google Scholar
3. Kohli, D. and Osvatic, M., “Inverse kinematics of general 6R and 5R, P serial manipulators,” Trans. ASME J. Mech. Des. 115 (4), 922931 (1993).Google Scholar
4. Manocha, D. and Canny, J. F., “Efficient inverse kinematics for general 6R manipulators,” IEEE Trans. Robot. Autom. 10 (5), 648657 (1994).CrossRefGoogle Scholar
5. Lee, H. Y. and Reinholtz, C. F., “Inverse kinematics of serial-chain manipulators,” Trans. ASME J. Mech. Des. 118 (3), 396404 (1996).Google Scholar
6. Xin, S. Z., Feng, L. Y., Bing, H. L. and Li, Y. T., “A simple method for inverse kinematic analysis of the general 6R serial robot,” Trans. ASME J. Mech. Des. 129 (8), pp. 793798 (2007).CrossRefGoogle Scholar
7. Sugimoto, K. and Duffy, J., “Analysis of five-degree-of-freedom robot arms,” Trans. ASME J. Mech. Transmiss. Automn Des. 105 (1), 2327 (1983).CrossRefGoogle Scholar
8. Tsai, L. W. and Morgan, A. P., “Solving the kinematics of the most general six- and five-degree-of-freedom manipulators by continuation methods,” Trans. ASME J. Mech. Transmiss. Automn Des. 107 (2), 189200 (1985).CrossRefGoogle Scholar
9. Angeles, J., “Iterative kinematic inversion of general five-axis robot manipulators,” Int. J. Robot. Res. 4 (4), 5970 (1986).Google Scholar
10. Manseur, R. and Doty, K. L., “A complete kinematic analysis of four-revolute-axis robot manipulators,” Mech. Mach. Theory 27 (5), 575586 (1992).Google Scholar
11. Manseur, R. and Doty, K. L., “Fast inverse kinematics of five-revolute-axis robot manipulators,” Mech. Mach. Theory 27 (5), 587597 (1992).Google Scholar
12. Zhou, Y. B., Buchal, R. O. and Fenton, R. G., “Analysis of the general 4R and 5R robots using a vector algebraic approach,” Mech. Mach. Theory 30 (3), 421432 (1995).Google Scholar
13. Zhou, Y. B. and Xi, F. F., “Exact kinematic analysis of the general 5R robot,” Mech. Mach. Theory 33 (1/2), 175184 (1998).Google Scholar
14. Chen, I. M. and Gao, Y., “Closed-Form Inverse Kinematics Solver for Reconfigurable Robots,” Proceedings of the 2001 IEEE International Conference Robotics and Automation, vol. 3 (2001) pp. 2395–2400.Google Scholar
15. Goel, P. K., “The Inverse Kinematics Solution, Closed-Form Dynamics and Simulation of Adeptone Industrial Robot,” Proceedings of the 1988 IEEE International Conference Robotics and Automation, vol. 3 (1988) pp. 1688–1693.Google Scholar
16. Gan, J. Q., Oyama, E., Rosales, E. M. and Hu, H., “A complete analytical solution to the inverse kinematics of the pioneer 2 robotic arm,” Robotica 23 (1), 123129 (2005).Google Scholar
17. Xu, D., Acosta Calderon, C. A., Gan, J. Q. and Hu, H., “An analysis of the inverse kinematics for a 5-DOF manipulator,” Int. J. Autom. Comput. 2 (2), 114124 (2005).Google Scholar
18. Ramírez-Torres, J. G., Toscano-Pulido, G., Ramírez-Saldívar, A. and Hernández-Ramírez, A., “A Complete Closed-Form Solution to the Inverse Kinematics Problem for the P2Arm Manipulator Robot,” Proceedings of the 2010 Electronics, Robotics and Automotive Mechanics Conf. (2010) pp. 372–377.Google Scholar
19. Wang, H. B. and Ishimatsu, T., “Kinematics of a five degree-of-freedom prosthetic arm,” Mech. Mach. Theory 33 (7), 895908 (1998).Google Scholar
20. Wang, H., “Kinematics and Control for a Personal Robot with Five Degrees-of-Freedom Arms,” Proceedings of the 2007 IEEE International Conference Networking, Sensing and Control (2007) pp. 507–512.Google Scholar
21. Sato, F., Nishii, T., Takahashi, J., Yoshida, Y., Mitsuhashi, M. and Nenchev, D., “Experimental Evaluation of a Trajectory/Force Tracking Controller for a Humanoid Robot Cleaning a Vertical Surface,” Proceedings of the 2007 IEEE International Conference Networking, Sensing and Control (2011) pp. 3179–3184.Google Scholar
22. Jazar, R. N., Theory of Applied Robotics: Kinematics, Dynamics, and Control, 2nd ed. (Springer, New York, Dordrecht, Heidelberg, London, 2010).Google Scholar
23. McCarthy, J. M., An Introduction to Theoretical Kinematics (The MIT Press, Cambridge, MA, London, 1990).Google Scholar
24. The Mathematical Society of Japan, Encyclopedic Dictionary of Mathematics, 2nd ed. (The MIT Press, Cambridge, MA, London, 1993).Google Scholar
25. Bedrossian, N. S., “Classification of Singular Configurations for Redundant Manipulators,” Proceedings of the 1990 IEEE International Conference Robotics and Automation (1990) pp. 818–823.Google Scholar
26. Shimizu, M., Kakuya, H., Yoon, W. K., Kitagaki, K. and Kosuge, K., “Analytical inverse kinematic computation for 7-DOF redundant manipulators with joint limits and its application to redundancy resolution,” IEEE Trans. Robot. 24 (5), 11311142 (2008).CrossRefGoogle Scholar