# Bounded Attitude Control with Active Disturbance Rejection Capabilities for Multirotor UAVs

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Motivations and Background

#### 1.2. Contributions

## 2. Preliminaries

**Definition**

**1**

**Theorem**

**1**

- 1.
- It is ISS.
- 2.
- It admits an ISS-Lyapunov function.
- 3.
- It is robustly stable.

## 3. System Modeling and Problem Statement

#### 3.1. Attitude Representation

**Remark**

**1.**

#### 3.2. Motion Equations of the Multirotor UAVs

#### 3.3. Problem Statement

## 4. ADRC Design for Attitude Tracking

- $\mathbf{\omega}$ and $\mathbf{q}$ are measured, such that ${\mathbf{\omega}}_{e}$ is always available;
- The inertia matrix is diagonal, i.e., $\mathbf{J}=\phantom{\rule{0.166667em}{0ex}}\mathrm{diag}({J}_{1},{J}_{2},{J}_{3})$ with ${J}_{1}={J}_{2}<{J}_{3}$, and its nominal value is known;
- The perturbation function $\xi (\xb7)$ is a uniformly absolutely bounded disturbance, i.e., ${sup}_{t}\parallel \xi (\xb7)\parallel ={\parallel \xi (\xb7)\parallel}_{\infty}\le {K}_{0}$.

#### 4.1. ESO Design for the Attitude Dynamics

**Proposition**

**1.**

#### 4.2. Active Disturbance Rejection Bounded Attitude Control

**Definition**

**2.**

**Proposition**

**2.**

**Proposition**

**3.**

**Proof.**

## 5. Simulation Results

#### 5.1. Scenario Description

^{2}, which is representative of the very small VTOL-UAV Crazyflie 2.0 [53]. According to physical parameters, the maximum torque that can be generated by the propulsion system is $\overline{\Gamma}={\left(9.6\phantom{\rule{4pt}{0ex}}9.6\phantom{\rule{4pt}{0ex}}4.9\right)}^{T}\times {10}^{-3}$ Nm. Then, the saturation functions for the proposed control are chosen as ${M}_{12}={M}_{22}=9.6\times {10}^{-3}$ and ${M}_{32}=4.9\times {10}^{-3}$.

#### 5.2. Quaternion and Angular Velocity Evolution

#### 5.3. Disturbance Estimation and Rejection

#### 5.4. Performance Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Proof of Proposition 1

**Proof.**

## Appendix B. Proof of Proposition 2

**Proof.**

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Guerrero-Castellanos, J.F.; Durand, S.; Munoz-Hernandez, G.A.; Marchand, N.; Romeo, L.L.G.; Linares-Flores, J.; Mino-Aguilar, G.; Guerrero-Sánchez, W.F. Bounded Attitude Control with Active Disturbance Rejection Capabilities for Multirotor UAVs. *Appl. Sci.* **2021**, *11*, 5960.
https://doi.org/10.3390/app11135960

**AMA Style**

Guerrero-Castellanos JF, Durand S, Munoz-Hernandez GA, Marchand N, Romeo LLG, Linares-Flores J, Mino-Aguilar G, Guerrero-Sánchez WF. Bounded Attitude Control with Active Disturbance Rejection Capabilities for Multirotor UAVs. *Applied Sciences*. 2021; 11(13):5960.
https://doi.org/10.3390/app11135960

**Chicago/Turabian Style**

Guerrero-Castellanos, José Fermi, Sylvain Durand, German Ardul Munoz-Hernandez, Nicolas Marchand, Lorenzo L. González Romeo, Jesús Linares-Flores, Gerardo Mino-Aguilar, and Wuiyevaldo F. Guerrero-Sánchez. 2021. "Bounded Attitude Control with Active Disturbance Rejection Capabilities for Multirotor UAVs" *Applied Sciences* 11, no. 13: 5960.
https://doi.org/10.3390/app11135960