Visual servoing tracking control of uncalibrated manipulators with a moving feature point

ABSTRACT

The paper is concerned with the problem of uncalibrated visual servoing robots tracking a dynamic feature point along with the desired trajectory. A nonlinear observer and a nonlinear controller are proposed, which allow the considered uncalibrated visual servoing robotic system to fulfil the desired tracking task. Based on this novel control method, a dynamic feature point with unknown motion parameters can be tracked effectively along with the desired trajectory, even with multiple uncertainties existing in the camera, the kinematics and the manipulator dynamics. By the Lyapunov theory, asymptotic convergence of the image errors to zero with the proposed control scheme is rigorously proven. Simulations have been conducted to verify the performance of the proposed control scheme. The results demonstrated good convergence of the image errors.

KEYWORDS:

• Visual servoing
• adaptive control
• tracking control
• Lyapunov stability
• manipulator control
• moving feature point

Acknowledgements

The authors would like to thank the editor and the anonymous reviewers for their valuable suggestions to improve the quality of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Tao Li   http://orcid.org/0000-0002-7522-5090

Notes

1 For the detail of matrix A, please refer to Equation (3) in Malis, Chaumette, and Boudet (1999) and Equation (4) in Liu et al. (2006).

2 Due to much use of the coordinates w.r.t. ${\mathcal{F}}_b$ in this paper, we omit the subscript b on purpose hereafter for simplicity.

3 From (33(32) $\begin{array}{rl}z\mathrm{\Delta }\dot{\phantom{a}}{y}_{ob}& +\frac{1}{2}\dot{z}(\mathrm{\Delta }{y}_{ob}-\mathrm{\Delta }y)=-W_z(q,\dot{q},\dot{q},y_{ob},y_d)\mathrm{\Delta }{\theta }_z\\ & +Y_r(y,q,\dot{q},y_{ob},y_d)\mathrm{\Delta }{\theta }_r\\ & +Y_k(q,\dot{q},\dot{q},y_{ob},y_d)\mathrm{\Delta }{\theta }_k-\alpha z\mathrm{\Delta }{y}_{ob}.\end{array}$(32) ), (45(44) $\begin{array}{rl}\hat{Q}{s}_q& =z\mathrm{\Delta }\dot{\phantom{a}}y+\lambda z(\mathrm{\Delta }{y}_{ob}+\mathrm{\Delta }y)-{\tilde{W}}_z(q,\dot{q},y_{ob},y_d,{\dot{y}}_d)\mathrm{\Delta }{\theta }_z\\ & +\frac{1}{2}\dot{z}(\mathrm{\Delta }{y}_{ob}+\mathrm{\Delta }y)+{\tilde{Y}}_k(q,\dot{q},y_{ob},y_d)\mathrm{\Delta }{\theta }_k\\ & +{\tilde{Y}}_r(q,\dot{q},y_{ob},y_d)\mathrm{\Delta }{\theta }_r,\end{array}$(44) ), it can be clearly seen that these regression matrices consist of the trigonometric functions $Y(y,q,\dot{q}),\tilde{Y}(q,\dot{q}),Y_{r,y}(y,q,\dot{q}),Y_{r,z}(q,\dot{q}),Y_z\left(q\right)$ and $y_{ob},y,y_d,{\dot{y}}_r$. Their boundedness can be obtained from the boundedness of the components.

Additional information

Funding

This work was financed by Science and Technology Program of Tianjin, China [grant number 15ZXZNGX00290].

Notes on contributors

Tao Li

Tao Li received the B.S. degree in telecommunication engineering from Hunan University of Science and Technology, Hunan, China, in 2010, the M.Eng. degree in the Department of Automation degrees in control engineering from the Tianjin University of Technology, Tianjin, China, in 2013. He is currently pursuing the Ph.D. degree in control engineering from Tianjin University, Tianjin, China. His current research interests include robot control, visual servoing, adaptive control, and control of networked systems.

Hui Zhao

Hui Zhao received the B.S. in control engineering from the China University of Petroleum, Beijing, China and the M.Eng and Ph.D. degrees in control engineering from the Tianjin University, Tianjin, China, in 1993 and 2005, respectively. He was an Associate Professor in the School of Automation, Tianjin University of Technology from 1998 to 2010. He is currently a Full Professor with the School of Engineering and Technology and the Vice President of Tianjin Agricultural University, Tianjin, China. His current research interests include robot control, precision agricultural intelligent technology, visual servoing robotic control, adaptive control and computer vision.

Yu Chang

Yu Chang received the B.S. degree in industry design from the Beijing University of Chemical Technology, Beijing, China, in 2009 and the M.A. in product design from the Hebei University of Technology, Tianjin, China, in 2014. He is currently a lecturer with the school of design, Tianjin University of Commerce. His current research interests include applications of control, interaction design, control of complicated system, modeling design of robot and product design evaluation.