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Research Papers

Control of an Underactuated Three-Link Passive–Active–Active Manipulator Based on Three Stages and Stability Analysis

[+] Author and Article Information
Xu-Zhi Lai

School of Automation,
China University of Geosciences,
Wuhan, Hubei 430074, China
e-mail: laixz@cug.edu.cn

Chang-Zhong Pan

School of Information and Electrical Engineering,
Hunan University of Science and Technology,
Xiangtan, Hunan 411201, China
e-mail: cpan@hnust.edu.cn

Min Wu

School of Automation,
China University of Geosciences,
Wuhan, Hubei 430074, China
e-mail: wumin@cug.edu.cn

Simon X. Yang

School of Engineering,
University of Guelph,
Guelph, ON N1G 2W1, Canada
e-mail: syang@uoguelph.ca

Wei-Hua Cao

School of Automation,
China University of Geosciences,
Wuhan, Hubei 430074, China
e-mail: weihuacao@cug.edu.cn

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 18, 2014; final manuscript received July 16, 2014; published online September 10, 2014. Assoc. Editor: Heikki Handroos.

J. Dyn. Sys., Meas., Control 137(2), 021007 (Sep 10, 2014) (9 pages) Paper No: DS-14-1124; doi: 10.1115/1.4028051 History: Received March 18, 2014; Revised July 16, 2014

This paper presents a novel three-stage control strategy for the motion control of an underactuated three-link passive–active–active (PAA) manipulator. First, a nonlinear control law is designed to make the angle and angular velocity of the third link convergent to zero. Then, a swing-up control law is designed to increase the system energy and control the posture of the second link. Finally, an integrated method with linear control and nonlinear control is introduced to stabilize the manipulator at the straight-up position. The stability of the control system is guaranteed by Lyapunov theory and LaSalle’s invariance principle. Compared to other approaches, the proposed strategy innovatively introduces a preparatory stage to drive the third link to stretch-out toward the second link in a natural way, which makes the swing-up control easy and quick. Besides, the intergraded method ensures the manipulator moving into the balancing stage smoothly and easily. The effectiveness and efficiency of the control strategy are demonstrated by numerical simulations.

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References

Figures

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Fig. 1

Model of a PAA manipulator

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Fig. 2

Control result of the first stage

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Fig. 3

Control result of the second stage

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Fig. 4

The angles qi (i = 1, 2, 3), the torques τ2 and τ3, and the energy E of the PAA manipulator with initial state x = [π π/8 π 0 0 1.7]

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Fig. 5

The angles qi (i = 1, 2, 3), the torques τ2 and τ3, and the energy E of the PAA manipulator with initial state x = [17π/18 0 0 0 0 0]

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