# An Improved Super-Twisting Sliding Mode Composite Control for Quadcopter UAV Formation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Dynamic Modeling and Algorithm Design

#### 2.1. Modeling Design

#### 2.2. Composite Formation Controller Design

#### 2.2.1. Observer Design

#### 2.2.2. Controller Design

## 3. Stability Analysis

**Assumption**

**1.**

**Definition**

**1.**

**Lemma**

**1.**

**Lemma**

**2 [25].**

**Lemma**

**3 [24].**

**Lemma**

**4 [26].**

**Lemma**

**5.**

## 4. Experimental Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Results of the wind disturbance resistance experiment.

**a(1)**Position coordinate x;

**a(2)**Position coordinate y;

**a(3)**X channel control output;

**a(4)**Y channel control output;

**a(5)**X channel observation disturbance;

**a(6)**Y channel observation disturbance.

**Figure 6.**Results of the formation flight along a straight trajectory.

**a(1)**Position coordinate x of followers;

**a(2)**Position coordinate y of followers;

**b(1)**Position coordinate x of followers;

**b(2)**Position coordinate y of followers;

**c(1)**Position coordinate x of leader;

**c(2)**Position coordinate y of leader.

**Figure 7.**Results of the formation flight along a circular trajectory.

**a(1)**Position coordinate x of followers;

**a(2)**Position coordinate y of followers;

**b(1)**Position coordinate x of followers;

**b(2)**Position coordinate y of followers;

**c(1)**Position coordinate x of leader;

**c(2)**Position coordinate y of leader.

Parameters Meaning | Parameters |
---|---|

Quadrotor mass | $0.04\mathrm{k}\mathrm{g}$ |

Gravitational acceleration | $9.8\mathrm{m}/{\mathrm{s}}^{2}$ |

x-axis moment of inertia | $1.532\times {10}^{-4}\mathrm{k}\mathrm{g}\cdot {\mathrm{m}}^{2}$ |

y-axis moment of inertia | $1.532\times {10}^{-4}\mathrm{k}\mathrm{g}\cdot {\mathrm{m}}^{2}$ |

z-axis moment of inertia | $3.472\times {10}^{-4}\mathrm{k}\mathrm{g}\cdot {\mathrm{m}}^{2}$ |

Quadcopter wheelbase | $0.12\mathrm{m}$ |

Controller/Observer | Parameters |
---|---|

SMC | $c=1,k=5$ |

ISTSMC | $c=1,{p}_{1}=8,{p}_{2}=0.1,\mathit{\epsilon}=-0.49$ |

FTESO | $\begin{array}{l}{\mathit{\beta}}_{1}=3\mathit{\omega},{\mathit{\beta}}_{2}=3{\mathit{\omega}}^{2},{\mathit{\beta}}_{3}={\mathit{\omega}}^{3}\\ \mathit{\omega}=70,\mathit{\alpha}=-2/9\end{array}$ |

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## Share and Cite

**MDPI and ACS Style**

Ye, Y.; Hu, S.; Zhu, X.; Sun, Z.
An Improved Super-Twisting Sliding Mode Composite Control for Quadcopter UAV Formation. *Machines* **2024**, *12*, 32.
https://doi.org/10.3390/machines12010032

**AMA Style**

Ye Y, Hu S, Zhu X, Sun Z.
An Improved Super-Twisting Sliding Mode Composite Control for Quadcopter UAV Formation. *Machines*. 2024; 12(1):32.
https://doi.org/10.3390/machines12010032

**Chicago/Turabian Style**

Ye, Yulong, Song Hu, Xingyu Zhu, and Zhenxing Sun.
2024. "An Improved Super-Twisting Sliding Mode Composite Control for Quadcopter UAV Formation" *Machines* 12, no. 1: 32.
https://doi.org/10.3390/machines12010032