Microscopic visual piezoelectric-driven positioning with improved extended kalman filtering

YANG Liu; HE He; CHENG Jiajia; LI Dongjie

doi:10.37188/OPE.20243212.1868

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Microscopic visual piezoelectric-driven positioning with improved extended kalman filtering

Micro/Nano Technology and Fine Mechanics | 更新时间：2024-07-26

- Microscopic visual piezoelectric-driven positioning with improved extended kalman filtering
- Optics and Precision Engineering Vol. 32, Issue 12, Pages: 1868-1878(2024)
- 作者机构：
  
  1.哈尔滨理工大学自动化学院，黑龙江哈尔滨 150080
  2.哈尔滨理工大学复杂智能系统与集成黑龙江省重点实验室，黑龙江哈尔滨 150040
- 作者简介：
- 基金信息：
- DOI：10.37188/OPE.20243212.1868
  CLC： TP273
- Published：25 June 2024，
  
  Received：05 March 2024，
  
  Revised：11 April 2024，
- 稿件说明：
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杨柳,何贺,程佳佳等.改进扩展Kalman滤波的显微视觉压电驱动定位[J].光学精密工程,2024,32(12):1868-1878.

YANG Liu,HE He,CHENG Jiajia,et al.Microscopic visual piezoelectric-driven positioning with improved extended kalman filtering[J].Optics and Precision Engineering,2024,32(12):1868-1878.
杨柳,何贺,程佳佳等.改进扩展Kalman滤波的显微视觉压电驱动定位[J].光学精密工程,2024,32(12):1868-1878. DOI： 10.37188/OPE.20243212.1868.

YANG Liu,HE He,CHENG Jiajia,et al.Microscopic visual piezoelectric-driven positioning with improved extended kalman filtering[J].Optics and Precision Engineering,2024,32(12):1868-1878. DOI： 10.37188/OPE.20243212.1868.

摘要

在显微视觉领域，压电驱动定位技术因其在微观尺度的高精度特性和灵活性备受关注。然而，由于定位过程中涉及图像处理、传输和控制等方面的时延，导致图像雅可比矩阵的估计会出现较大误差。因此，本文提出了一种改进扩展Kalman滤波算法用来预测图像雅可比矩阵，大幅度降低时间延迟因素。首先，将辨识得到的Bouc-Wen模型与扩展Kalman滤波算法的状态观测方程相结合，使得状态观测方程更全面地考虑压电平台的迟滞非线性特性，有效地提高了对压电平台速度和位置的预测；其次，结合Bouc-Wen模型的扩展Kalman滤波算法在面对非线性问题时，采用的是泰勒级数，这将导致扩展Kalman滤波算法对高度非线性的函数无法提供良好的近似，从而导致在估计雅可比矩阵的时候引入较大的近似误差，故本文将采用神经网络对高度非线性函数进行近似，进而对图像雅可比矩阵进行估计。最后，通过搭建一个显微视觉的压电驱动实验平台，进行位置跟踪实验，仿真实验表明，输入信号分别为正弦信号和三角波信号时，改进扩展Kalman滤波算法跟踪误差均值分别为0.199 μm和0.132 μm，而扩展Kalman滤波算法的跟踪误差均值分别为0.692 μm和0.513 μm，结果验证了改进算法的优越性和可行性。

Abstract

In the field of microscopic vision， piezoelectric-driven positioning technology has attracted significant attention due to its high precision and flexibility at the microscale. However， the presence of delays in processes such as image processing， transmission， and control during positioning introduces significant estimation errors in the image Jacobian matrix. Therefore， this paper proposed an improved extended Kalman filter algorithm to predict the image Jacobian matrix and substantially reduce the impact of time delays.Firstly， the identified Bouc-Wen model was combined with the state observation equation of the extended Kalman filter algorithm. This comprehensive consideration of the hysteresis nonlinearity of the piezoelectric platform effectively enhanced the prediction of the platform's velocity and position. Secondly， in dealing with nonlinear problems， the extended Kalman filter algorithm traditionally employed Taylor series， which may result in poor approximations for highly nonlinear functions， introducing significant errors when estimating the Jacobian matrix. To address this， the paper employed a neural network to approximate highly nonlinear functions and subsequently estimate the image Jacobian matrix. Finally， by constructing a piezoelectric-driven experimental platform for microscopic vision， position tracking experiments were conducted. Simulation experiments demonstrate that when the input signals are sinusoidal and triangular wave signals， the mean tracking errors of the improved Extended Kalman Filter algorithm are 0.199 μm and 0.132 μm， respectively， while the mean tracking errors of the Extended Kalman Filter algorithm are 0.692 μm and 0.513 μm， respectively. The results validate the superiority and feasibility of the improved algorithm.

关键词

扩展Kalman滤波高度非线性方程图像雅可比矩阵显微视觉压电驱动

Keywords

extended Kalman filteringhighly nonlinear functionsimage Jacobian matricesmicroscopic visionpiezoelectric-drive

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