A highly powerful calibration method for robotic smoothing system calibration via using adaptive residual extended Kalman filter

Achieving high absolute positioning accuracy is crucial for obtaining aspheric optical components with remarkable surface quality using a robotic smoothing system. Robot kinematic calibration is an effective means of improving absolute positioning accuracy. The calibration algorithms that use gradient direction have been shown to significantly improve computational efficiency compared to other calibration methods. However, these algorithms usually suffer from gradient degradation or vanishing after several iterations. In particular, the extended Kalman filter depends on the initial covariance matrix, which must be continually adjusted to reasonable values using artificial means. To address this challenge, an adaptive residual extended Kalman filter is proposed for robot kinematic calibration. This method involves using the residual generated from the current iteration to avoid gradient degradation or vanishing in the next iteration. An improved butterfly optimization algorithm is also used to adapt the system covariance matrix, the covariance matrix of system noises, and the covariance matrix of measurement noises of the extended Kalman filter to improve the identification accuracy. Finally, the proposed method's feasibility is demonstrated through sufficient calibration experiments. The method improved the RMSE positioning accuracy from 0.9328 to 0.4786 mm, a 48.69 % increase from before calibration. The smoothing compensation experimental results show that the proposed method achieves optical components with excellent surface quality. The PV and RMS are, respectively 10.46 % and 20.96 % lower than before compensation, and the PSD curve is superior to before compensation.