# Quadrotor Formation Control via Terminal Sliding Mode Approach: Theory and Experiment Results

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## Abstract

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## 1. Introduction

- We develop formation tracking control with a disturbance observer—the proposed method can provide faster finite-time convergence, less steady-state errors, and robustness;
- The stability of the whole system is validated using Lyapunov theory;
- We compare the proposed method with the existing algorithm in [41];
- We implement it on a real quadcopter platform for verification, which is lacking in [41].

## 2. Preliminaries and Multi-Agent System

#### 2.1. Notation

#### 2.2. Graph Theory

#### 2.3. Multi-Agent System

**Lemma**

**1.**

#### 2.4. Control Objective

**Remark**

**1.**

**Remark**

**2.**

## 3. Disturbance Observer Design

**Theorem**

**1.**

**Proof.**

## 4. Formation Tracking Control Design

**Theorem**

**2.**

**Proof.**

**Remark**

**3.**

**Remark**

**4.**

## 5. Simulation Results

#### 5.1. Case 1: Absence of Disturbance Observer Mechanism

#### 5.2. Case 2: Presence of Disturbance of Observer Mechanism

## 6. Experiment

#### 6.1. Experimental Setup

#### 6.2. Experimental Results

#### 6.2.1. Case 1: Straight Line

#### 6.2.2. Case 2: Circular Trajectory

#### 6.2.3. Case 3: Formation with External Disturbances

## 7. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 8.**(

**a**) Position, velocity, and acceleration in x-direction of straight line; (

**b**) position, velocity, and acceleration in y-direction of straight line.

**Figure 10.**(

**a**) Position, velocity, and acceleration in x-direction of circular trajectory; (

**b**) position, velocity, and acceleration in y-direction of circular trajectory.

**Figure 12.**(

**a**) Position, velocity, and acceleration in x-direction; (

**b**) Position, velocity, and acceleration in y-direction with disturbance observer.

**Figure 13.**(

**a**) Position, velocity, and acceleration in x-direction; Position, velocity, and acceleration in y-direction without disturbance observer.

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**MDPI and ACS Style**

Nguyen, N.P.; Park, D.; Ngoc, D.N.; Xuan-Mung, N.; Huynh, T.T.; Nguyen, T.N.; Hong, S.K.
Quadrotor Formation Control via Terminal Sliding Mode Approach: Theory and Experiment Results. *Drones* **2022**, *6*, 172.
https://doi.org/10.3390/drones6070172

**AMA Style**

Nguyen NP, Park D, Ngoc DN, Xuan-Mung N, Huynh TT, Nguyen TN, Hong SK.
Quadrotor Formation Control via Terminal Sliding Mode Approach: Theory and Experiment Results. *Drones*. 2022; 6(7):172.
https://doi.org/10.3390/drones6070172

**Chicago/Turabian Style**

Nguyen, Ngoc Phi, Daewon Park, Dao N. Ngoc, Nguyen Xuan-Mung, Tuan Tu Huynh, Tan N. Nguyen, and Sung Kyung Hong.
2022. "Quadrotor Formation Control via Terminal Sliding Mode Approach: Theory and Experiment Results" *Drones* 6, no. 7: 172.
https://doi.org/10.3390/drones6070172