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Optimal configuration selection method for stiffness identification of serial manipulators based on the κf(A)−1 criterion

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Abstract

In real industrial environment, the stiffness identification accuracy of manipulators is affected by various measurement errors. However, research that deals with the inevitable error perturbation is scarce. The κF(A)−1 criterion is adopted for measurement configuration selection to solve this problem according to the perturbation analysis and derivation of solutions to systems of stiffness identification equations. The optimal measurement configurations are finally obtained using the DETMAX optimization algorithm based on the deduced criterion, which is the main contribution of this work. Results illustrate that the optimal configurations optimized by the DETMAX algorithm based on the κF(A)−1 criterion can better overcome the influence of measurement errors, improve the identification accuracy, and reduce the compensated position error and fluctuation compared with the other optimization algorithms. Furthermore, the proposed criterion can be applied to the stiffness identification of serial manipulators in a real industrial environment.

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Abbreviations

ΩJ :

N alternative configuration sets selected by means of κF(J)−1

ΩF :

N alternative external force sets

ζi :

ith measurement configuration

γ M = [ζ 1,ζ 2,⋯, ζ i,⋯ζ M]:

M selected measurement configurations

Ω = [ζ 1,ζ 2,⋯, ζ i,⋯ζ N]:

N alternative configuration sets in the whole workspace

ΩR = Ω−γ M :

U residual unselected configurations (U = N−M)

κ F(γ M)−1 :

Enhanced evaluation index of selected configurations

ζ + :

Configuration chosen inside ΩR (ζ+ ∈ ζR) to be added to γM+1=γM+ζ+, to maximize the current κF(γM+1)−1

ζ− :

Configuration chosen inside γM+1 to be eliminated to maximize the current κF(γM)−1, γM=γM+1−ζ

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Acknowledgments

This work is supported by Research Program supported by the National Natural Science Foundation of China (No. 51575092) and the Central Leading Local Science and Technology Development Foundation of Liaoning Province (No. 2021JH6/10500132).

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110819, China

    Xuejie Jiang

  2. Faculty of Robot Science and Engineering, Northeastern University, Shenyang, 110819, China

    Lijin Fang

Authors
  1. Xuejie Jiang
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Correspondence to Lijin Fang.

Additional information

Xuejie Jiang is currently a Ph.D. student of the School of Mechanical Engineering and Automation, Northeastern University, Shenyang, China. Her current research interests include robot kinematic calibration, stiffness identification, and trajectory planning.

Lijin Fang (corresponding author) is currently a Professor and a Ph.D. candidate supervisor of the Faculty of Robot Science and Engineering, Northeastern University, Shenyang, China. His current research interests include robot accuracy control and humanoid control of variable stiffness robot.

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Jiang, X., Fang, L. Optimal configuration selection method for stiffness identification of serial manipulators based on the κf(A)−1 criterion. J Mech Sci Technol 36, 2559–2570 (2022). https://doi.org/10.1007/s12206-022-0437-7

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  • DOI: https://doi.org/10.1007/s12206-022-0437-7

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