Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-08T08:23:35.988Z Has data issue: false hasContentIssue false
  • English
  • Français

Inverse kinematics by numerical and analytical cyclic coordinate descent

Published online by Cambridge University Press:  20 August 2010

Anders Lau Olsen  and
Henrik Gordon Petersen
Anders Lau Olsen*
Affiliation:
The Maersk Mc-Kinney Moller Institute, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark E-mail: [email protected]
Henrik Gordon Petersen
Affiliation:
The Maersk Mc-Kinney Moller Institute, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark E-mail: [email protected]
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

Cyclic coordinate descent (CCD) inverse kinematics methods are traditionally derived only for manipulators with revolute and prismatic joints. We propose a new numerical CCD method for any differentiable type of joint and demonstrate its use for serial-chain manipulators with coupled joints. At the same time more general and simpler to derive, the method performs as well in experiments as the existing analytical CCD methods and is more robust with respect to parameter settings. Moreover, the numerical method can be applied to a wider range of cost functions.

Keywords

Inverse kinematicsCyclic coordinate descentCoupled joints
Type
Articles
Information
Robotica , Volume 29 , Issue 4 , July 2011 , pp. 619 - 626
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Craig, J. J., Introduction to Robotics: Mechanics and Control, 2. ed. (Addison-Wesley Publishing Company, Reading, MA, 1989).Google Scholar
2.Manocha, D. and Zhu, Y., “A fast algorithm and system for the inverse kinematics of general serial manipulators,” IEEE Int. Conf. Robot. Autom. 4, 3348–3353 (1994).Google Scholar
3.Tolani, D., Goswami, A. and Badler, N. I., “Real-time inverse kinematics techniques for anthropomorphic limbs,” Graph. Models Image Process. 62, 353–388 (2000).CrossRefGoogle ScholarPubMed
4.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,” ASME J. Mech. Des. 129, 793–798 (2007).CrossRefGoogle Scholar
5.Han, L. and Amato, N. M., “A Kinematics-based Probabilistic Roadmap Method for Closed Chain Systems,” Workshop on Algorithmic Foundations of Robotics, Hanover, NH (2000) pp. 233–246.Google Scholar
6.Whitney, D. E., “Resolved motion rate control of manipulators and human protheses,” IEEE Trans. Man-Mach. Syst. 10 (2), 49–53 (1969).CrossRefGoogle Scholar
7.Angeles, J., “On the numerical solution of the inverse kinematic problem,” Int. J. Robot. Res. 4 (2), 21–37 (1985).CrossRefGoogle Scholar
8.Wampler, C. W., “Manipulator inverse kinematic solutions based on vector formulations and damped least-squares methods,” IEEE Trans. Syst. Man Cybern. 16 (1), 93–101 (1986).CrossRefGoogle Scholar
9.Wolovich, W. A. and Elliott, H., “A computational technique for inverse kinematics,” IEEE Conf. Decis. Control 23, 1359–1363 (1984).Google Scholar
10.Chin, K. W., von Konsky, B. R. and Marriott, A., “Closed-form and generalized inverse kinematics solutions for the analysis of human motion,” Int. Conf. IEEE Eng. Med. Bio. Soc. 5, 1911–1914 (1997).Google Scholar
11.Llinares, J. and Page, A., “Position analysis of spatial mechanisms,” ASME J. Mech. Trans. Autom. Des. 106, 252–255 (1984).CrossRefGoogle Scholar
12.Kazerounian, K., “On the numerical inverse kinematics of robotic manipulators,” ASME J. Mech. Trans. Autom. Des. 109, 8–13 (1987).CrossRefGoogle Scholar
13.Wang, L.-C. T. and Chen, C. C., “A combined optimization method for solving the inverse kinematics problems of mechanical manipulators,” IEEE Trans. Robot. Autom. 7, 489–499 (1991).CrossRefGoogle Scholar
14.Ahuactzin, J. M. and Gupta, K., “A motion planning based approach for inverse kinematics of redundant robots: The kinematic roadmap,” IEEE Int. Conf. Robot. Autom. 4, 3609–3614 (1997).Google Scholar
15.Regnier, S., Ouezdou, F. B. and Bidaud, P., “Distributed method for inverse kinematics of all serial manipulators,” Mech. Mach. Theory 32, 855–867 (1997).CrossRefGoogle Scholar
16.From, P. J. and Gravdahl, J. T., “General Solutions to Functional and Kinematic Redundancy,” IEEE Conference on Decision and Control, New Orleans, LA (2007) pp. 5779–5786.Google Scholar
17.Buss, S. R., “Introduction to Inverse Kinematics with Jacobian Transpose, Pseudoinverse and Damped Least Squares Methods,” April 2004. Available at online: http://math.ucsd.edu/~sbuss/ResearchWeb.Google Scholar
18.Nocedal, J. and Wright, S. J., Numerical Optimization, 2nd ed. (Springer Series in Operations Research and Financial Engineering, Springer, New York, 2006).Google Scholar
19.Latombe, J.-C., Robot Motion Planning (Kluwer Academic, Boston, MA, 1991).CrossRefGoogle Scholar
20.Barraquand, J. and Latombe, J.-C., “Robot motion planning: A distributed representation approach,” Int. J. Robot. Res. 10, 628–649 (1991).CrossRefGoogle Scholar
21.Zhao, X. and Peng, S., “A successive approximation algorithm for the inverse position analysis of the serial manipulators,” Robotica 17 (6), 487–489 (1999).CrossRefGoogle Scholar
22.Leven, P. and Hutchinson, S., “A framework for real-time path planning in changing environments,” Int. J. Robot. Res. 21 (12), 999–1030 (2002).CrossRefGoogle Scholar