0
Research Papers

Solution of Inverse Kinematics for 6R Robot Manipulators With Offset Wrist Based on Geometric Algebra

[+] Author and Article Information
Zhongtao Fu

e-mail: hustfzt@gmail.com

Wenyu Yang

e-mail: mewyang@mail.hust.edu.cn

Zhen Yang

e-mail: yangzhen0607@126.com
State Key Laboratory of Digital Manufacturing Equipment and Technology,
Mechanical School of Science and Engineering,
Huazhong University of Science and Technology,
Wuhan 430074, China

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received October 25, 2012; final manuscript received March 19, 2013; published online June 24, 2013. Assoc. Editor: J. M. Selig.

J. Mechanisms Robotics 5(3), 031010 (Jun 24, 2013) (7 pages) Paper No: JMR-12-1173; doi: 10.1115/1.4024239 History: Received October 25, 2012; Revised March 19, 2013

In this paper, we present an efficient method based on geometric algebra for computing the solutions to the inverse kinematics problem (IKP) of the 6R robot manipulators with offset wrist. Due to the fact that there exist some difficulties to solve the inverse kinematics problem when the kinematics equations are complex, highly nonlinear, coupled and multiple solutions in terms of these robot manipulators stated mathematically, we apply the theory of Geometric Algebra to the kinematic modeling of 6R robot manipulators simply and generate closed-form kinematics equations, reformulate the problem as a generalized eigenvalue problem with symbolic elimination technique, and then yield 16 solutions. Finally, a spray painting robot, which conforms to the type of robot manipulators, is used as an example of implementation for the effectiveness and real-time of this method. The experimental results show that this method has a large advantage over the classical methods on geometric intuition, computation and real-time, and can be directly extended to all serial robot manipulators and completely automatized, which provides a new tool on the analysis and application of general robot manipulators.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Siciliano, B., and Khatib, O., 2008, Springer Handbook of Robotics, Springer-Verlag, New York Inc.
Bingul, Z., Ertunc, H. M., and Oysu, C., 2005, “Comparison of Inverse Kinematics Solutions Using Neural Network for 6R Robot Manipulator With Offset,” Proceedings of the ICSC Congress on Computational Intelligence Methods and Applications, pp. 1–5.
Raghavan, M., and Roth, B., 1993, “Inverse Kinematics of the General 6R Manipulator and Related Linkages,” ASME J. Mech. Des., 115(3), pp. 502–508. [CrossRef]
Manocha, D., and Canny, J. F., 1994, “Efficient Inverse Kinematics for General 6R Manipulators,” IEEE Trans. Rob. Autom., 10(5), pp. 648–657. [CrossRef]
Aspragathos, N. A., and Dimitros, J. K., 1998, “A Comparative Study of Three Methods for Robot Kinematics,” IEEE Trans. Syst., Man, Cybern., Part B: Cybern., 28(2), pp. 135–145. [CrossRef]
Husty, M. L., Pfurner, M., and Shrocker, H. P., 2007, “A New and Efficient Algorithm for the Inverse Kinematics of a General Serial 6R Manipulator,” Mech. Mach. Theory, 42(1), pp. 66–81. [CrossRef]
Qiao, S., Liao, Q., Wei, S., and Su, H. J., 2010, “Inverse Kinematic Analysis of the General 6R Serial Manipulators Based on Double Quaternions,” Mech. Mach. Theory, 45(2), pp. 193–199. [CrossRef]
Cheng, H., and Gupta, K. C., 1991, “A Study of Robot Inverse Kinematics BasedUupon the Solution of Differential Equations,” J. Rob. Syst., 8(2), pp. 159–175. [CrossRef]
Olsen, A. L., and Petersen, H. G., 2011, “Inverse Kinematics by Numerical and Analytical Cyclic Coordinate Descent,” Robotica, 29(3), pp. 619–626. [CrossRef]
Zhang, X., and Nelson, C. A., 2011, “Multiple-Criteria Kinematic Optimization for the Design of Spherical Serial Mechanisms Using Genetic Algorithms,” ASME J. Mech. Des., 133, pp. 1–11.
Olaru, A., Olaru, S., and Paune, D., 2011, “Assisted Research and Optimization of the Proper Neural Network Solving the Inverse Kinematics Problem,” Proceedings of 2011 International Conference on Optimization of the Robots and Manipulators, Romania, pp. 26–28.
Feng, Y., Yao-nan, W., and Yi-min, Y., 2012, “Inverse Kinematics Solution for Robot Manipulator Based on Neural Network Under Joint Subspace,” Int. of Comput. Commun., 7(3), pp. 459–472.
Hestens, D., and Sobczyk, G., 1987, Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics, Springer-Verlag, Berlin, Heidelberg, New York.
Hestens, D., 2001, “Old Wine in New Bottles: A New Algebraic Framework for Computational Geometry,” Advances in Geometric Algebra With Applications in Science and Engineering, E.Bayro-Corrochano, and G.Sobczyk, eds., Birkauser, Boston, pp. 1–14.
Zamora, J., and Bayro-Corrochano, E., 2004, “Inverse Kinematics, Fixation and Grasping Using Conformal Geometric Algebra,” IROS 2004, Sendai, Japan.
Hildenbrand, D., 2006, “Geometric Computing in Computer Graphics and Robotics using Conformal Geometric Algebra,” Ph.D. thesis, Darmstadt University of Technology, Darmstadt.
Hildenbrand, D., Lange, H., and Stock, F., 2008, “Efficient Inverse Kinematics Algorithm Based on Conformal Geometric Algebra,” Proceedings of the 3rd International Conference on Computer Graphics Theory and Applications, Medeira, Portugal.
Aristidou, A., and Lasenby, J., 2011, “Inverse Kinematics Solutions Using Conformal Geometric Algebra,” Guide to Geometric Algebra in Practice, Vol. 1, Springer Verlag, pp. 47–62.
Aristidou, A., and Lasenby, J., 2011, “FABRIK: A Fast, Iterative Solver for the Inverse Kinematics Problem,” Graphical Models, 73(5), pp. 243–260. [CrossRef]
Dorst, L., Fontijne, D., and Mann, S., 2007, Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry, Morgan Kaufmann Publishers/Elsevier, San Francisco, CA.
Cheng, H. H., 1994, Programming With Dual Numbers and its Applications in Mechanism Design. Engineering With Computers, 10(4), pp. 212–229.
Bayro-Corrochano, E., and Scheuermann, G., 2009, Geometric Algebra Computing for Engineering and Computer Science, Springer–Verlag, New York.
Hestenes, D., 2010, “New Tools for Computational Geometry and Rejuvenation of Screw Theory,” Geometric Algebra Computing in Engineering and Computer Science, E.Bayro-Corrochano, and G.Scheuermann, eds., Springer-Verlag, pp. 3–35.
Bayro-Corrochano, E., 2010, Geometric Computing for Wavelet Transforms, Robot Vision, Learning, Control and Action, Spring-Verlag, London, pp. 169–203.
Selig, J. M., 2005, Geometric Fundamentals of Robotics, Monographs in Computer Science, Springer, New York, pp. 206–278.
Li, H., Hestenes, D., and Rockwood, A., 2001, “Generalized Homogeneous Coordinates for Computational Geometry,” Geometric Computing With Clifford Algebra, G.Sommer, ed., Springer-Verlag, pp. 25–58.
Gohberg, I., Lancaster, P., and Rodman, L., 1982, Matrix Polynomials, Academic Press, New York.

Figures

Grahic Jump Location
Fig. 1

Dual angle θ∧ = θ + ɛd between lines S1 and S2

Grahic Jump Location
Fig. 2

Rotation of a vector X

Grahic Jump Location
Fig. 3

Transformation of a vector X

Grahic Jump Location
Fig. 4

D_H parameters and frames between relative links and the transformation i-1Mi from Γi-1 to Γi

Grahic Jump Location
Fig. 5

Schematic diagram of a general serial 6R robot manipulator

Grahic Jump Location
Fig. 6

The spray painting robot

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In