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

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## 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

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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 |
---|---|---|

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

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

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**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