# Model Predictive Controller Design Based on Residual Model Trained by Gaussian Process for Robots

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## Abstract

**:**

## 1. Introduction

#### 1.1. Related Work

#### 1.2. Contributions

## 2. Mobile Robot Kinematics Model

- O denotes the geometric center of the mobile robot.
- $\overrightarrow{v}$ denotes the translational velocity of the mobile robot in its own coordinate system.
- ${\overrightarrow{v}}_{x}$ denotes the component of the mobile robot in the x-axis direction in its own coordinate system.
- ${\overrightarrow{v}}_{y}$ denotes the component of the mobile robot in the direction of y-axis in its own coordinate system.
- $\overrightarrow{\omega}$ denotes the rotation speed of the mobile robot around its geometric center in its own coordinate system.
- a denotes the distance from the center of the mobile robot axis in the x-axis direction to the geometric center of the mobile robot mechanism.
- b denotes the distance from the axis center of the mobile robot in the y-axis direction to the geometric center of the mobile robot mechanism.
- r denotes the radius of the mobile robot.

## 3. Mobile Robot Dynamics Model

**Assumption**

**A1.**

**Assumption**

**A2.**

**Assumption**

**A3.**

## 4. Gaussian Process Based Model Predictive Control

#### 4.1. Model Predictive Control

**Assumption**

**A4.**

**Assumption**

**A5.**

#### 4.2. GPR Model Mismatch Online Modelling

**Remark**

**1.**

## 5. Controller Design

## 6. Simulation

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Parameters | Numerical Value |
---|---|

r | 50 mm |

a | 150 mm |

b | 125 mm |

Prediction horizon | 5 |

Control horizon | 3 |

Sample time | 0.1 s |

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**MDPI and ACS Style**

Wu, C.; Tang, X.; Xu, X.
Model Predictive Controller Design Based on Residual Model Trained by Gaussian Process for Robots. *J. Mar. Sci. Eng.* **2023**, *11*, 893.
https://doi.org/10.3390/jmse11050893

**AMA Style**

Wu C, Tang X, Xu X.
Model Predictive Controller Design Based on Residual Model Trained by Gaussian Process for Robots. *Journal of Marine Science and Engineering*. 2023; 11(5):893.
https://doi.org/10.3390/jmse11050893

**Chicago/Turabian Style**

Wu, Changjie, Xiaolong Tang, and Xiaoyan Xu.
2023. "Model Predictive Controller Design Based on Residual Model Trained by Gaussian Process for Robots" *Journal of Marine Science and Engineering* 11, no. 5: 893.
https://doi.org/10.3390/jmse11050893