Numerical Solution Using Nonlinear Least-Squares Method for Inverse Kinematics Calculation of Redundant Manipulators

Shunsuke Toritani; Ruhizan Liza Ahmad Shauri; Kenzo Nonami; Daigo Fujiwara

doi:10.20965/jrm.2012.p0363

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JRM Vol.24 No.2 pp. 363-371

doi: 10.20965/jrm.2012.p0363

(2012)

Paper:

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Numerical Solution Using Nonlinear Least-Squares Method for Inverse Kinematics Calculation of Redundant Manipulators

Shunsuke Toritani, Ruhizan Liza Ahmad Shauri,
Kenzo Nonami, and Daigo Fujiwara

Department of Mechanical Engineering, Division of Artificial Systems Science, Graduate School of Engineering, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba-shi, Chiba 263-8522, Japan

Received:

October 22, 2011

Accepted:

January 31, 2012

Published:

April 20, 2012

Keywords:

inverse kinematics, numerical robustness, nonlinear least-squares method, Levenberg-Marquardt method, redundant manipulator

Abstract

In this paper, we present an Inverse Kinematics (IK) algorithm based on the nonlinear least-squares method for redundant manipulators. The Newton-Raphson (NR) method is a commonmethod for IK calculation of redundant manipulators. The NR method, however, causes many problems in terms of joint angle limits, singularity, and solvability. Severalmethods have therefore been proposed to solve these problems. Most, however, focus only on IK calculation performance when a desired trajectory moves outside of the workspace. A manipulator is required to move continuously, even after a desired trajectory moves outside of the workspace. It is thus also necessary to implement the IK calculation method for bringing a desired trajectory back into the workspace. In this study, we propose a user-friendly method for robotic manipulation that is capable of implementing accurate IK calculation when a desired trajectorymust be returned to the workspace.

Cite this article as:

S. Toritani, R. Shauri, K. Nonami, and D. Fujiwara, “Numerical Solution Using Nonlinear Least-Squares Method for Inverse Kinematics Calculation of Redundant Manipulators,” J. Robot. Mechatron., Vol.24 No.2, pp. 363-371, 2012.

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References

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[3] T. F. Chan and R. V. Dubey, “A Weighted Least-Norm Solution Based Scheme for Avoiding Joint Limits for Redundant Manipulators,” Proc. of the 1993 IEEE Int. Conf. on Robotics and Automation, pp. 395-402, 1993.
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[7] W. Shen and J. Gu, “Multi-Criteria Kinematics Control of the PA10-7C Robot Arm with Robust Singularities,” Int. Conf. on Robotics and Biomimetics, pp. 1242-1248, Dec. 2007.
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[11] T. Sugihara, “Solvability-Unconcerned Inverse Kinematics by the Levenberg-Marquardt Methods,” IEEE Trans. on Robotics, Vol.27, No.5, pp. 984-991, 2011.
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[13] K. Wedeward and A. Engelmann, “Singularity Robustness method for joint-space and task-space control,” Proc. of 1997 IEEE Int. Conf. on Control Applications, pp. 22-27, 1997.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] A. Liegeois, “Automatic Supervisory Control of the Configuration and Behavior of Multibody Mechanisms,” IEEE Trans. on Systems, Man and Cybernetics, Vol.7, No.12, pp. 868-871, Dec. 1977.

[2] [2] T. Yoshikawa, “Analysis and control of robot manipulators with redundancy,” Robotics Research: The First Int. Symposium, M. Brady and R. Paul (Eds.), Cambridge, MA: MIT Press, pp. 735-747, 1984.

[3] [3] T. F. Chan and R. V. Dubey, “A Weighted Least-Norm Solution Based Scheme for Avoiding Joint Limits for Redundant Manipulators,” Proc. of the 1993 IEEE Int. Conf. on Robotics and Automation, pp. 395-402, 1993.

[4] [4] A. S. Deo and I. D. Walker, “Robot Subtask Performance with Singularity Robustness using Optimal Damped Least-Squares,” Proc. of the 1992 IEEE Int. Conf. on Robotics and Automation, pp. 434-441, 1992.

[5] [5] Y. Nakamura and H. Hanafusa, “Inverse Kinematics Solutions with Singularity Robustness for Robot Manipulator Control,” J. of Dynamic Systems Measurement and Control Vol.108, pp. 163-171, 1986.

[6] [6] C. W. Wampler, “Manipulator Inverse Kinematic Solutions Based on Vector Formulations and Damped Least-Squares Methods,” IEEE Trans. on Systems, Man, and Cybernetics, Vol.SMC-16, No.1, pp. 93-101, 1986.

[7] [7] W. Shen and J. Gu, “Multi-Criteria Kinematics Control of the PA10-7C Robot Arm with Robust Singularities,” Int. Conf. on Robotics and Biomimetics, pp. 1242-1248, Dec. 2007.

[8] [8] A. S. Deo and I. D. Walker, “Adaptive Non-linear Least Squares for Inverse Kinematics,” Proc. of 1993 IEEE Int. Conf. on Robotics and Automation, pp. 186-193, 1993.

[9] [9] S. K. Chan and P. D. Lawrence, “General Inverse Kinematics with the Error Damped Pseudoinverse,” Proc. of IEEE Int. Conf. on Robotics and Automation, pp. 834-839, 1988.

[10] [10] R. Konietschke and G. Hirzinger, “Inverse Kinematics with Closed Form Solutions for Highly Redundant Robotic Systems,” IEEE Int. Conf. on Robotics and Automation, pp. 2945-2950, 2009.

[11] [11] T. Sugihara, “Solvability-Unconcerned Inverse Kinematics by the Levenberg-Marquardt Methods,” IEEE Trans. on Robotics, Vol.27, No.5, pp. 984-991, 2011.

[12] [12] A. A. Maciejewski and C. A. Klein, “Numerical Filtering for the Operation of Robotic Manipulators through Kinematically Singular Configurations,” J. of Robotic Systems, Vol.5, No.6, pp. 527-552, 1988.

[13] [13] K. Wedeward and A. Engelmann, “Singularity Robustness method for joint-space and task-space control,” Proc. of 1997 IEEE Int. Conf. on Control Applications, pp. 22-27, 1997.

Numerical Solution Using Nonlinear Least-Squares Method for Inverse Kinematics Calculation of Redundant Manipulators

Shunsuke Toritani, Ruhizan Liza Ahmad Shauri, Kenzo Nonami, and Daigo Fujiwara

Shunsuke Toritani, Ruhizan Liza Ahmad Shauri,
Kenzo Nonami, and Daigo Fujiwara