Paper:

# Online Estimation of Image Jacobian Matrix with Time-Delay Compensation

## Xinmei Wang^{*}, Wu Wei^{**}, Feng Liu^{*}, Longsheng Wei^{*}, and Zhihui Liu^{***}

^{*}School of Automation, China University of Geosciences

Wuhan, Hubei 430074, China

^{**}College of Automation Science and Engineering, South China University of Technology

Guangzhou, Guangdong 510640, China

^{***}School of Mathematics and Physics, China University of Geosciences

Wuhan, Hubei 430074, China

Time delay exists in image-based visual servoing system. To compensate for the impact of time delay, the feature point image and image Jacobian matrix with time-delay compensation is discussed in this paper. Firstly, the current position and velocity estimation of the feature point in the image space is based on Kalman filtering, but Markov chain model is applied in the description of the measurement noise, then the cross-correlation between the process noise and measurement noise is produced, the traditional Kalman filtering algorithm is restricted, by introducing a filtering revision matrix, the process equation and measurement equation are redefined, under the mathematical properties of the noise in Kalman filtering algorithm, the filtering revision matrix can be obtained for the elimination of the cross-correlation, a robust Kalman filtering model can be constructed. Secondly, for the measurement vectors which cannot be obtained during time delay in the robust Kalman filtering model, a polynomial fitting method is proposed in which the selection of the polynomial includes the position, the velocity and the acceleration of the feature point which impact the feature point trajectory. Finally, from the current predicted position and velocity of the feature point in the image space, the current accurate image Jacobian matrix with time-delay compensation can be obtained. Simulation and experimental results verify the feasibility and superiority of this method.

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