# Grey Estimator-Based Tracking Controller Applied to Swarm Robot Formation

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Motion Model of Two-Wheeled Mobile Robot

## 3. Grey Estimator-Based Tracking Control

**Theorem**

**1.**

**Remark**

**1.**

**Remark**

**2.**

## 4. Robot Multi-Agent System and Formation

_{j}, ν

_{i})$\in \epsilon $; ${a}_{ij}$ = 0, for (ν

_{j}, ν

_{i})$\notin \epsilon $; ${a}_{ii}$ = 0; ν

_{j}and ν

_{i}represent the j-th and i-th agents, respectively; $\epsilon $ is ν

_{j}to ν

_{i}connection set; m is the total number of agents. The degree matrix can be written as D = diag{d

_{1}, d

_{2},…, d

_{m}} $\in $ ${R}^{m\times m}$, where i = 1, 2,…, m. Then the Laplacian matrix of the graph is written as

## 5. Simulation Results

#### 5.1. Simulation Case 1

#### 5.2. Simulation Case 2

**Remark**

**3.**

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 7.**(

**a**) Formation control of the swarm robots; (

**b**) position response in the XY axis of the three robots.

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**MDPI and ACS Style**

Chen, Y.-T.; Chiu, C.-S.; Lee, Y.-T.
Grey Estimator-Based Tracking Controller Applied to Swarm Robot Formation. *Axioms* **2021**, *10*, 298.
https://doi.org/10.3390/axioms10040298

**AMA Style**

Chen Y-T, Chiu C-S, Lee Y-T.
Grey Estimator-Based Tracking Controller Applied to Swarm Robot Formation. *Axioms*. 2021; 10(4):298.
https://doi.org/10.3390/axioms10040298

**Chicago/Turabian Style**

Chen, Yu-Ting, Chian-Song Chiu, and Ya-Ting Lee.
2021. "Grey Estimator-Based Tracking Controller Applied to Swarm Robot Formation" *Axioms* 10, no. 4: 298.
https://doi.org/10.3390/axioms10040298