# A UAV Formation Control Method Based on Sliding-Mode Control under Communication Constraints

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## Abstract

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## 1. Introduction

- (1)
- The formation control problem of fixed-wing UAVs in an uncommunicated situation was studied. UAVs use only onboard vision sensors to obtain the status of UAVs in the neighborhood and to achieve formation control.
- (2)
- In this paper, we considered sensor measurements and used Extended Kalman Filtering to reduce errors and designed a sliding mode controller to reduce sensitivity to measurement errors.
- (3)
- In this paper, the formation control was divided into a two-layer control structure of position control and attitude control, and a suitable Lyapunov function was constructed to prove the system’s stability.
- (4)
- The UAV state transfer delay was considered, the UAV error state equation was given, and a suitable Lyapunov- Krasovskii generalized function was constructed to derive sufficient conditions for the stability of the delayed system, and finally, the obtained theoretical results were illustrated by three numerical simulations.

## 2. Extended Kalman Filter-Based State Estimation

#### 2.1. Equation of Motion for Single Machine

_{i}, and L

_{i}as the inertial coordinate frame, the follower velocity frame of the UAV $i$, and the line of sight frame. The origin of the follower velocity frame and the line of sight frame is the mass point of the UAV. The relative relationship between the coordinate frames is shown in Figure 1.

#### 2.2. Leader UAV Status Estimation

## 3. Controller Design

#### 3.1. Controller Design

#### 3.2. System Stability Proof

**Theorem 1.**

#### 3.3. Delayed System Stability Proof

**Theorem 2.**

**Proof of Theorem 2.**

## 4. Simulation and Test Results

#### 4.1. Case 1

#### 4.2. Case 2

#### 4.3. Case 3

#### 4.4. Discussion

- The designed controller can be effectively applied to the formation control of fixed-wing UAVs, even in the presence of measurement errors as well as state transfer time delays in multiple UAV formations.
- It can be seen from the computation times of the three examples that, since the controller was distributed, it did not increase the solution time of individual UAVs as the number of UAVs increased. However, there was a long initial moment at the beginning of each phase in the time of each numerical simulation, which would be the next step to improve.
- When there were multiple UAVs in the neighborhood, the selection of the follower UAV for the desired leader UAV became an issue. In the next step of the study, rules need to be developed or the research method updated to ensure the efficiency and accuracy of the follower UAV’s selection of the desired leader UAV.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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Parameter Name | Symbols | Numerical Value |
---|---|---|

Sampling interval | ${T}_{k}$ | 0.01 |

Sampling time | $T$ | 30 |

Number of drones | ${N}_{v}$ | 4 |

Intermachine delay | $h$ | 0.004 |

UAV Number | Initial Location | $\mathit{v}\left(\mathit{m}/\mathit{s}\right)$ | Yaw Angle |
---|---|---|---|

1 | ${\left[2,-2,0\right]}^{T}$ | 0 | $\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$3$}\right.$ |

2 | ${\left[-2,3,0\right]}^{T}$ | 0 | $\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$3$}\right.$ |

3 | ${\left[2,-1,0\right]}^{T}$ | 0 | $\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$3$}\right.$ |

4 | ${\left[-2,-1,0\right]}^{T}$ | 0 | $\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$3$}\right.$ |

UAV Number | Initial Location | $\mathit{v}\left(\mathit{m}/\mathit{s}\right)$ | Yaw Angle |
---|---|---|---|

1 | ${\left[2,-2,0\right]}^{T}$ | 0 | $\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$3$}\right.$ |

2 | ${\left[-2,3,0\right]}^{T}$ | 0 | $\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$3$}\right.$ |

3 | ${\left[2,-1,0\right]}^{T}$ | 0 | $\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$3$}\right.$ |

4 | ${\left[-2,-1,0\right]}^{T}$ | 0 | $\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$3$}\right.$ |

5 | ${\left[-2,2,0\right]}^{T}$ | 0 | $\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$3$}\right.$ |

6 | ${\left[2,-3,0\right]}^{T}$ | 0 | $\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$3$}\right.$ |

7 | ${\left[-2,1,0\right]}^{T}$ | 0 | $\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$3$}\right.$ |

8 | ${\left[-2,-2,0\right]}^{T}$ | 0 | $\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$3$}\right.$ |

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**MDPI and ACS Style**

Chen, Q.; Wang, T.; Jin, Y.; Wang, Y.; Qian, B. A UAV Formation Control Method Based on Sliding-Mode Control under Communication Constraints. *Drones* **2023**, *7*, 231.
https://doi.org/10.3390/drones7040231

**AMA Style**

Chen Q, Wang T, Jin Y, Wang Y, Qian B. A UAV Formation Control Method Based on Sliding-Mode Control under Communication Constraints. *Drones*. 2023; 7(4):231.
https://doi.org/10.3390/drones7040231

**Chicago/Turabian Style**

Chen, Qijie, Taoyu Wang, Yuqiang Jin, Yao Wang, and Bei Qian. 2023. "A UAV Formation Control Method Based on Sliding-Mode Control under Communication Constraints" *Drones* 7, no. 4: 231.
https://doi.org/10.3390/drones7040231