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An iterative identification method for the dynamics and hysteresis of robots with elastic joints

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Abstract

Dynamics-based methods have wide applications in the control of elastic joint robots. These methods require accurate robot dynamic parameters and hysteresis models of elastic elements for the controller designs. Existing independent identification procedures for the dynamic parameters and hysteresis models are challenging to efficiently implement without specific calibration equipment. In this paper, an iterative identification method that unifies the dynamic parameter identification and hysteresis model identification based on an energy identification model is proposed. This method can be conveniently implemented through simple trajectory tracking experiments. The energy identification model includes the elastic potential energy caused by the elastic elements with hysteresis. Any derivative of velocity can be avoided in this form. A two-step iterative strategy is proposed, including the initialization and main steps. The initialization step is implemented to obtain the a priori knowledge of the dynamic parameters as the initial values for iteration. The main step aims to identify the hysteresis model and dynamic parameters iteratively. Experiments on a two-degrees-of-freedom elastic joint robot verify the effectiveness of the proposed method.

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Funding

The work was supported by the National Natural Science Foundation of China [Grant No. 91648112].

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  1. State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Jiexin Zhang & Bo Zhang

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  1. Jiexin Zhang
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JZ: Conceptualization, Methodology, Software, Investigation, Data curation, Writing original draft. BZ: Validation, Supervision, Funding acquisition.

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Correspondence to Bo Zhang.

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Appendix

Appendix

The independent identification processes for the dynamic parameters [32] and hysteresis models [38] are applied in Case 2 of the trajectory-tracking experiment. The following is a brief introduction to their implementation in this paper.

  1. 1.

    The independent identification of the dynamic parameters [32].

    We perform steps similar to those in [32] and derive a regression equation with the base parameter set based on filter dynamics. The regression equation is solved with the LS algorithm. We perform the same trajectories as used in the experiments in [32] to collect the signals for the observation matrix. The trajectories are as follows:

    $${\text{q}}_{{\text{d}}} (t) = \frac{\pi }{60}\left[ {\begin{array}{*{20}c} {{\text{sin}}(2\pi t) + {\text{sin}}\left(\pi t + \frac{\pi }{6}\right) + {\text{sin}}\left(0.4\pi t + \frac{\pi }{4}\right)} \\ {{\text{sin}}(0.4\pi t) + {\text{sin}}\left(2\pi t + \frac{\pi }{5}\right) + {\text{sin}}\left(\pi t + \frac{\pi }{2}\right)} \\ \end{array} } \right]{\text{(rad}})$$
  2. 2.

    The independent identification for the hysteresis models [38],

    This method utilizes a series of data samples from the motor side to calculate the joint torques and torsions. Joint one and joint two sequentially track trajectories similar to those in [38] to obtain the relevant data, and the trajectory is displayed as follows:

    $${\text{q}}_{{{\text{d}}_{j} }} (t) = \frac{\pi }{2}( - 0.02t + \, 1) \, (sin(0.2\pi t - 1.5\pi ))({{rad}})$$

    The MPI model (11) is also applied in this method to fit the hysteresis loops. It is notable that the friction data are needed to calculate the joint torque, in which the friction parameters are obtained by the above independent identification process for dynamic parameters.

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Zhang, J., Zhang, B. An iterative identification method for the dynamics and hysteresis of robots with elastic joints. Nonlinear Dyn 111, 13939–13953 (2023). https://doi.org/10.1007/s11071-023-08597-2

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