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Research Papers

Gradient Projection of Weighted Jacobian Matrix Method for Inverse Kinematics of a Space Robot With a Controlled-Floating Base

[+] Author and Article Information
Tianjin Hu

School of Aerospace Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: htj13@mails.tsinghua.edu.cn

Tianshu Wang

School of Aerospace Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: tswang@tsinghua.edu.cn

Junfeng Li

School of Aerospace Engineering,
Tsinghua University,
Beijing 100084, China
e-mail: lijunf@tsinghua.edu.cn

Weiping Qian

Beijing Institute of Tracking
and Telecommunication Technology,
Beijing 100094, China
e-mail: qianweipingbittt@sina.com

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 5, 2016; final manuscript received November 23, 2016; published online March 22, 2017. Assoc. Editor: Yongchun Fang.

J. Dyn. Sys., Meas., Control 139(5), 051013 (Mar 22, 2017) (10 pages) Paper No: DS-16-1009; doi: 10.1115/1.4035398 History: Received January 05, 2016; Revised November 23, 2016

This paper studies the inverse kinematics (IKs) of a space robot with a controlled-floating base. Different from the traditional space robot which has a free-floating base, the momentum conservation is no longer satisfied so that the degrees-of-freedom (DOFs) and redundancy of the robot obviously increase, and motion limits exist for both base and manipulator. To deal with such a problem, a gradient projection of weighted Jacobian matrix (GPWJM) method is proposed. The Jacobian matrix is derived considering the additional DOFs of the base, and the trajectory tracking by the end-effector is chosen as the main task. A clamping weighted least norm scheme is introduced into the derived Jacobian matrix to avoid the motion limits, and the singular-robustness is enhanced by the damping least-squares. The convergence and accuracy analysis indicates the calculation of damping factor; while the verification of motion limits avoidance indicates the inequality constraint of clamping velocity. Finally, the effectiveness of the proposed GPWJM method is investigated by the numerical simulation in which a planar 3DOF manipulator on a 3DOF base is taken as a demo.

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Figures

Grahic Jump Location
Fig. 1

Scenario of the space robot with a redundant manipulator fastened on a 6DOF base

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Fig. 2

Value of weight wi and gradient function hi via the ith generalized coordinate qi

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Fig. 3

Basic process of GPWJM method

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Fig. 4

Numerical demo: a planar 3DOF manipulator on a 3DOF controlled-floating base

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Fig. 5

Base motion of the robot in the local periodic painting task

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Fig. 6

Joint angles of the manipulator in the local periodic painting task

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Fig. 7

Robot configuration in the local periodic painting task

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Fig. 8

Base motion of the robot in the large-scale translation task

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Fig. 9

Joint angles of the manipulator in the large-scale translation task

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Fig. 10

Weights wi during the large-scale translation task

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Fig. 11

Robot configuration during the large-scale translation task

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Fig. 12

Base motion of the robot with a sudden change of the end-effector's trajectory

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Fig. 13

Joint angles of the manipulator with a sudden change of the end-effector's trajectory

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Fig. 14

Weighted coefficients with a sudden change of the desired trajectory

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Fig. 15

Damp factor of the GPWJM method with a sudden change of the desired trajectory

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Fig. 16

Robot configuration with a sudden change of the desired trajectory

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