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Separable Nonlinear Least Squares Algorithm for Robust Kinematic Calibration of Serial Robots

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Abstract

Kinematic calibration of robots is an effective way to guarantee and promote their performance characteristics. There are many mature researches on kinematic calibration, and methods based on MDH model are the most common ones. However, when employing these calibration methods, it occasionally happens that the objective function cannot converge during iterations. Through analyzing robotic forward kinematics, we found out that the Cartesian coordinates of the end-point are affine to length-related MDH parameters, where linear and nonlinear parameters can be separated. Thanks to the distinctive characteristic of the MDH model, the kinematic calibration problem can be converted into a separable nonlinear least squares problem, which can further be partitioned into two subproblems: a linear least squares problem and a reduced problem involving only nonlinear parameters. Eventually, the optimal structural parameters can be identified by solving this problem iteratively. The results of numerical and experimental validations show that: 1) the robustness during identification procedure is enhanced by eliminating the partial linear structural parameters, the convergence rate is promoted from 68.98% to 100% with different deviation vector pairs; 2) the initial values to be pre-set for kinematic calibration problem are fewer and 3) fewer parameters are to be identified by nonlinear least squares regression, resulting in fewer iterations and faster convergence, where average runtime is reduced from 33.931s to 1.874s.

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Acknowledgements

This work was supported by the 2017 National Key R&D Program of China (No.2017YFB1301400).

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Authors and Affiliations

  1. State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, China

    Chentao Mao & Zhangwei Chen

  2. College of Engineering, Swansea University, Swansea, UK

    Shuai Li

  3. School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou, China

    Xiang Zhang

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  1. Chentao Mao
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  2. Zhangwei Chen
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  3. Shuai Li
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  4. Xiang Zhang
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Correspondence to Chentao Mao.

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Mao, C., Chen, Z., Li, S. et al. Separable Nonlinear Least Squares Algorithm for Robust Kinematic Calibration of Serial Robots. J Intell Robot Syst 101, 2 (2021). https://doi.org/10.1007/s10846-020-01268-z

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  • DOI: https://doi.org/10.1007/s10846-020-01268-z

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