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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.

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References

Figures

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Fig. 1

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

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Fig. 2

Rotation of a vector X

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Fig. 3

Transformation of a vector X

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Fig. 4

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

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Fig. 5

Schematic diagram of a general serial 6R robot manipulator

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Fig. 6

The spray painting robot

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