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Research Papers

A Unified Approach for Second-Order Control of the Manipulator With Joint Physical Constraints

[+] Author and Article Information
Pei Jiang

College of Mechanical Engineering,
Chongqing University,
Chongqing 400030, China
e-mail: peijiang@cqu.edu.cn

Shuihua Huang

Department of System Science and Engineering,
Zhejiang University,
Hangzhou 310027, China
e-mail: huanggao@zju.edu.cn

Ji Xiang

Department of System Science and Engineering,
Zhejiang University,
Hangzhou 310027, China
e-mail: jxiang@zju.edu.cn

Michael Z. Q. Chen

Department of Mechanical Engineering,
The University of Hong Kong,
Hong Kong 999077, China
e-mail: mzqchen@outlook.com

1Corresponding author.

Manuscript received June 11, 2016; final manuscript received March 23, 2017; published online May 15, 2017. Assoc. Editor: Andreas Mueller.

J. Mechanisms Robotics 9(4), 041009 (May 15, 2017) (11 pages) Paper No: JMR-16-1170; doi: 10.1115/1.4036569 History: Received June 11, 2016; Revised March 23, 2017

Kinematic control of manipulators with joint physical constraints, such as joint limits and joint velocity limits, has received extensive studies. Many studies resolved this problem at the second-order kinematic level, which may suffer from the self-motion instability in the presence of persistent self-motion or unboundedness of joint velocity. In this paper, a unified approach is proposed to control a manipulator with both joint limits and joint velocity limits at the second-order kinematic level. By combining the weighted least-norm (WLN) solution in the revised joint space and the clamping weighted least-norm (CWLN) solution in the real joint space, the unified approach ensures the joint limits and joint velocity limits at the same time. A time-variant clamping factor is incorporated into the unified approach to suppress the self-motion when the joint velocity diverges, or the end-effector stops, which improves the stability of self-motion. The simulations in contrast to the traditional dynamic feedback control scheme and the new minimum-acceleration-norm (MAN) scheme have been made to demonstrate the advantages of the unified approach.

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Figures

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Fig. 1

The 4R manipulator. The arrows are the axes of the joints.

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Fig. 2

The trajectory of the end-effectors in a three-dimensional space. The asterisk is the starting point of the end-effector.

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Fig. 3

Simulation of the nonredundant manipulator under the unified approach: (a) normalized joint position, (b) normalized joint velocity, (c) tracking error, (d) weighting factors of the joint 1, the dashed line is w¯11, and the solid line is w¯21, (e) revised joint velocity of the joint 1, (f) revised joint acceleration of the joint 1, (g) minimal singular value of JW−12, and (h) damping factor λ

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Fig. 4

Simulation of the redundant manipulator under the dynamic feedback control law (51): (a) tracking error, (b) normalized joint position, (c) joint velocity trajectory, and (d) homogeneous joint velocity, the dash line is ||(I−J+J)g||, the solid line is ||(I−J+J)q˙||

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Fig. 5

Simulation of the redundant manipulator under the MAN scheme: (a) normalized joint velocity trajectory, (b) joint velocity trajectory, (c) homogeneous joint velocity ||(I−J+J)q˙||, and (d) tracking error

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Fig. 6

Simulation of the redundant manipulator under the unified approach: (a) joint acceleration trajectory, (b) joint velocity trajectory, (c) normalized joint position trajectory, (d) tracking error, (e) homogeneous joint velocity ||(I−J+J)q˙||, (f) clamping factor c, (g) weighting factors, and (h) weighting factors of the joint 4, the red solid line is w¯14, the blue dash line is w¯24

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