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Research Papers

Singularity-Robust Inverse Kinematics Using Lagrange Multiplier for Redundant Manipulators

[+] Author and Article Information
Youngjin Choi

Division of Electrical Engineering and Computer Science, Hanyang University, Ansan 426-791, Republic of Koreacyj@hanyang.ac.kr

J. Dyn. Sys., Meas., Control 130(5), 051009 (Aug 04, 2008) (7 pages) doi:10.1115/1.2957632 History: Received September 28, 2007; Revised May 12, 2008; Published August 04, 2008

In this paper, a singularity-robust inverse kinematics is newly suggested by using a Lagrange multiplier for redundant manipulator systems. Two tasks are considered with priority orders under the assumption that a primary task has no singularity. First, an inverse kinematics problem is formulated to be an optimization one subject to an equality constraint, in other words, to be a minimization problem of secondary task error subject to an equality constraint for primary task execution. Second, in the procedure of minimization for a given objective function, a new inverse kinematics algorithm is derived. Third, since nonzero Lagrange multiplier values appear in the neighborhood of a singular configuration of a robotic manipulator, we choose them as a natural choice of the dampening factor to alleviate the ill-conditioning of matrix inversion, ultimately for singularity-robust inverse kinematics. Finally, the effectiveness of the suggested singularity-robust inverse kinematics is shown through a numerical simulation about deburring and conveyance tasks of a dual arm manipulator system.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Conceptual diagram of Eqs. 15,16

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Figure 2

Desired tasks for dual arm manipulation, where (a) primary task (de-burring) and (b) secondary task (conveyance)

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Figure 3

Configurations of dual arms according to time progress, where (a) when α=0.0001, (b) when α=0.1, and (c) when α=100

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Figure 4

Execution performances of primary task, where o error means the tool orientation error, (a) when α=0.0001, (b) when α=0.1, and (c) when α=100

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Figure 5

Execution performances of secondary task, where (a) when α=0.0001, (b) when α=0.1, and (c) when α=100

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Figure 6

Lagrange multipliers, where (a) when α=0.0001, (b) when α=0.1, and (c) when α=100

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Figure 7

Performance of Maciejewski's or Nakamura's algorithm using the SVD tolerance of 0.0001 for matrix inversion (same condition with the suggested algorithm), where (a) arm configuration, (b) primary task error, and (c) secondary task error

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Figure 8

Performance of the Maciejewski's or Nakamura's algorithm using the SVD tolerance of 0.01 for matrix inversion (different condition from the suggested algorithm), where (a) arm configuration, (b) primary task error, and (c) secondary task error

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