# Adaptive 3D Visual Servoing of a Scara Robot Manipulator with Unknown Dynamic and Vision System Parameters

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Robot Model

#### 2.1. Kinematic Model

#### 2.2. Dynamic Model

## 3. Simulated Experimental Platform and Vision System

## 4. Adaptive Kinematic Servovisual Controller

#### 4.1. Control Law with Measurement of ${\dot{\mathbf{x}}}^{I}$

#### Controller Analysis

#### 4.2. Control Law without Measurement of ${\dot{\mathbf{x}}}^{I}$

#### 4.2.1. Controller Analysis

#### 4.2.2. Remarks

- For positioning $\left|{\dot{\mathbf{x}}}_{{d}_{max}}^{I}\right|=0$; therefore, ${\tilde{\mathbf{x}}}^{I}\left(t\right)\to \mathbf{0}$ with $t\to \infty $
- For trajectories that are persistently exciting, it can be shown that $\parallel \tilde{\mathbf{p}}\left(t\right)\parallel \to 0$ with $t\to \infty $, and therefore ${\tilde{\mathbf{x}}}^{I}\left(t\right)\to \mathbf{0}$ with $t\to \infty $.

## 5. Dynamic Compensation Design

## 6. Simulations

## 7. Discussion

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

- Weiss, L.; Sanderson, A.; Neuman, C. Dynamic sensor-based control of robots with visual feedback. IEEE J. Robot. Autom.
**1987**, 3, 404–417. [Google Scholar] [CrossRef] - Lefeber, E.; Kelly, R.; Ortega, R.; Nijmeijer, H. Adaptive and Filtered Visual Servoing of Planar Robots. IFAC Proc. Vol.
**1998**, 31, 541–546. [Google Scholar] [CrossRef] - Chaumette, F.; Rives, P.; Espiau, B. Positioning of a robot with respect to an object, tracking it and estimating its velocity by visual servoing. In Proceedings of the 1991 IEEE International Conference on Robotics and Automation, Sacramento, CA, USA, 9–11 April 1991; Volume 3, pp. 2248–2253. [Google Scholar]
- Ruf, A.; Tonko, M.; Horaud, R.; Nagel, H. Visual tracking of an end-effector by adaptive kinematic prediction. In Proceedings of the 1997 IEEE/RSJ International Conference on Intelligent Robot and Systems, Innovative Robotics for Real-World Applications, IROS ’97, Grenoble, France, 11–11 September 1997; Volume 2, pp. 893–899. [Google Scholar]
- Nasisi, O.; Carelli, R. Adaptive servo visual robot control. Robot. Auton. Syst.
**2003**, 43, 51–78. [Google Scholar] [CrossRef] - Astolfi, A.; Hsu, L.; Netto, M.; Ortega, R. A solution to the adaptive visual servoing problem. In Proceedings of the 2001 ICRA, IEEE International Conference on Robotics and Automation (Cat. No.01CH37164), Seoul, Korea, 21–26 May 2001; Volume 1, pp. 743–748. [Google Scholar]
- Astolfi, A.; Hsu, L.; Netto, M.S.; Ortega, R. Two solutions to the adaptive visual servoing problem. IEEE Trans. Robot. Autom.
**2002**, 18, 387–392. [Google Scholar] [CrossRef] - Nuño, E.; Ortega, R. New solutions to the 2D adaptive visual servoing problem with relaxed excitation requirements. Int. J. Adapt. Control Signal Process.
**2019**, 33, 1843–1856. [Google Scholar] - Hsu, L.; Aquino, P.L.S. Adaptive visual tracking with uncertain manipulator dynamics and uncalibrated camera. In Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), Phoenix, AZ, USA, 7–10 December 1999; Volume 2, pp. 1248–1253. [Google Scholar]
- Lizarralde, F.; Hsu, L.; Costa, R.R. Adaptive Visual Servoing of Robot Manipulators without Measuring the Image Velocity. IFAC Proc. Vol.
**2008**, 41, 4108–4113. [Google Scholar] [CrossRef] [Green Version] - Sahin, T.; Zergeroglu, E. Adaptive visual servo control of robot manipulators via composite camera inputs. In Proceedings of the Fifth International Workshop on Robot Motion and Control, RoMoCo’05, Poznań, Poland, 23–25 June 2005; pp. 219–224. [Google Scholar]
- Zachi, A.R.L.; Liu, H.; Lizarralde, F.; Leite, A.C. Adaptive control of nonlinear visual servoing systems for 3D cartesian tracking. Sba Controle Automação Soc. Bras. Autom.
**2006**, 17, 381–390. [Google Scholar] [CrossRef] - Behzadikhormouji, H.; Derhami, V.; Rezaeian, M. Adaptive Visual Servoing Control of robot Manipulator for Trajectory Tracking tasks in 3D Space. In Proceedings of the 2017 5th RSI International Conference on Robotics and Mechatronics (ICRoM), Tehran, Iran, 25–27 October 2017; pp. 376–382. [Google Scholar] [CrossRef]
- Wang, S.; Zhang, K.; Herrmann, G. An Adaptive Controller for Robotic Manipulators with Unknown Kinematics and Dynamics. IFAC-PapersOnLine
**2020**, 53, 8796–8801. [Google Scholar] [CrossRef] - Liang, X.; Wang, H.; Liu, Y.; Chen, W. Adaptive visual tracking control of uncertain rigid-link electrically driven robotic manipulators with an uncalibrated fixed camera. In Proceedings of the 2014 IEEE International Conference on Robotics and Biomimetics (ROBIO 2014), Bali, Indonesia, 5–10 December 2014; pp. 1627–1632. [Google Scholar] [CrossRef]
- Wang, H. Adaptive visual tracking for robotic systems without image-space velocity measurement. Automatica
**2015**, 55, 294–301. [Google Scholar] [CrossRef] [Green Version] - Sarapura, J.A.; Roberti, F.; Gimenez, J.; Patiño, D.; Carelli, R. Adaptive Visual Servoing Control of a Manipulator with Uncertainties in Vision and Dynamics. In Proceedings of the 2018 Argentine Conference on Automatic Control (AADECA), Buenos Aires, Argentina, 7–9 November 2018; pp. 1–6. [Google Scholar] [CrossRef]
- Sarapura, J.A. Control Servo Visual Estéreo de un Robot Manipulador. Master’s Thesis, Universidad Nacional de San Juan, Facultad de Ingeniería, Instituto de Automática, San Juan, Argentina, 2013. [Google Scholar]
- Slawiñski, E.; Postigo, J.F.; Mut, V.; Carestía, D.; Castro, F. Estructura abierta de software para un robot industrial. Rev. Iberoam. Autom. Inform. Ind. RIAI
**2007**, 4, 86–95. [Google Scholar] [CrossRef] [Green Version]

Kinematic Model | Dynamic Model |
---|---|

${\scriptstyle \mathbf{\lambda}=\left[\begin{array}{ccc}10& 0& 0\\ 0& 10& 0\\ 0& 0& 10\end{array}\right]}$ | ${\scriptstyle \mathbf{\lambda}=\left[\begin{array}{ccc}15& 0& 0\\ 0& 15& 0\\ 0& 0& 0.0004\end{array}\right]}$ |

${\scriptstyle \mathbf{\gamma}={10}^{5}\left[\begin{array}{ccc}800& 0& 0\\ 0& 0.02& 0\\ 0& 0& 0.08\end{array}\right]}$ | ${\scriptstyle \mathbf{\gamma}=2\left[\begin{array}{ccc}{10}^{10}& 0& 0\\ 0& {10}^{3}& 0\\ 0& 0& 1\end{array}\right]}$ |

Kinematic Model | Dynamic Model | Compensation Dynamic Model |
---|---|---|

${\scriptstyle \mathbf{\lambda}=\left[\begin{array}{ccc}200& 0& 0\\ 0& 400& 0\\ 0& 0& 20\end{array}\right]}$ | ${\scriptstyle \mathbf{\lambda}=\left[\begin{array}{ccc}100& 0& 0\\ 0& 300& 0\\ 0& 0& 10\end{array}\right]}$ | ${\scriptstyle \mathbf{\lambda}=\left[\begin{array}{ccc}60& 0& 0\\ 0& 610& 0\\ 0& 0& 20\end{array}\right]}$ |

${\scriptstyle \mathbf{\gamma}={10}^{5}\left[\begin{array}{ccc}200& 0& 0\\ 0& 200& 0\\ 0& 0& 0.008\end{array}\right]}$ | ${\scriptstyle \mathbf{\gamma}={10}^{9}\left[\begin{array}{ccc}100& 0& 0\\ 0& 10& 0\\ 0& 0& 0.002\end{array}\right]}$ | ${\scriptstyle \mathbf{\gamma}={10}^{5}\left[\begin{array}{ccc}400& 0& 0\\ 0& 400& 0\\ 0& 0& 2\end{array}\right]}$ |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sarapura, J.A.; Roberti, F.; Carelli, R.
Adaptive 3D Visual Servoing of a Scara Robot Manipulator with Unknown Dynamic and Vision System Parameters. *Automation* **2021**, *2*, 127-140.
https://doi.org/10.3390/automation2030008

**AMA Style**

Sarapura JA, Roberti F, Carelli R.
Adaptive 3D Visual Servoing of a Scara Robot Manipulator with Unknown Dynamic and Vision System Parameters. *Automation*. 2021; 2(3):127-140.
https://doi.org/10.3390/automation2030008

**Chicago/Turabian Style**

Sarapura, Jorge Antonio, Flavio Roberti, and Ricardo Carelli.
2021. "Adaptive 3D Visual Servoing of a Scara Robot Manipulator with Unknown Dynamic and Vision System Parameters" *Automation* 2, no. 3: 127-140.
https://doi.org/10.3390/automation2030008