# Finite-Time Robust Flight Control of Logistic Unmanned Aerial Vehicles Using a Time-Delay Estimation Technique

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

- Construction of a cascaded dual-loop SMC controller. The inner loop adopts the fast nonsingular terminal sliding mode to achieve the finite-time convergence of the system state and improve the response speed. The outer loop employs a PID-type sliding mode surface to enhance the control accuracy.
- TDE technology is introduced for the robust control of rotor logistic UAVs to achieve the online estimation and real-time compensation of unknown disturbances, thereby improving the nominal dynamic model of the controlled object.
- Flight capability tests of the rotor logistic UAV are conducted in three complex scenarios to verify the ability of the proposed algorithm to hover, maneuver flight, and perform self-recovery during fault tolerance.

## 2. Dynamic Modeling of Quadcopter UAVs

_{5}, and ${k}_{6}$, and represent the torque coefficients of rotational aerodynamic resistance in three directions.

## 3. Controller Design and Stability Analysis

#### 3.1. Position Loop Controller Design

**Lemma**

**1.**

#### 3.2. Design of the Attitude Control System

#### 3.3. Stability Analysis of the FNTSM-TDE Controller

**Lemma**

**2.**

## 4. Simulation and Experimentation

#### 4.1. MBD-HIL UAV Development Strategy

#### 4.1.1. HIL for the Hovering Experiment

#### 4.1.2. HIL Experiment for the Crash Recovery

#### 4.1.3. HIL for High Maneuverability Flight

#### 4.2. In-Flight Experiments

#### 4.2.1. The In-Flight Hover Experiment

#### 4.2.2. The Actual Flight Crash Experiment

#### 4.2.3. High Maneuverability Flight Field Experiment

^{2}and 14.95 m/s

^{2}, respectively. Using the PID controller, the maximum speeds of the UAV in the Xe and Ye directions are 13.04 m/s and 13.2 m/s, respectively, with maximum accelerations of 9.7 m/s

^{2}and 9.29 m/s

^{2}, respectively. It is evident that the proposed controller enables the UAV to achieve faster flight speeds and greater maneuverability.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Experimental strategies for SIL, HIL, and flight testing for UAVs. (

**a**) represents the signal transmission process in the Real Machine System, (

**b**) is the functional composition of software-in-the-loop, and (

**c**) is the information transmission process in hardware-in-the-loop.

**Figure 7.**The simulation environment for UAVs was developed by leveraging the powerful UE4 virtual game engine.

**Figure 9.**The displacement curve of the HIL for the hovering experiment. (

**a**) In the Xe direction. (

**b**) In the Ye direction. (

**c**) In the Ze direction.

**Figure 10.**The tracking performance of the four motors in the hovering state when all of them simultaneously stop rotating and stay idle for 0.5 s. (

**a**) In the Xe direction. (

**b**) In the Ye direction. (

**c**) In the Ze direction. (

**d**) The UAV’s roll angle. (

**e**) The UAV’s pitch angle. (

**f**) The UAV’s yaw angle.

**Figure 11.**The trajectory curve of HIL for high maneuverability flight. (

**a**) In the Xe direction. (

**b**) In the Ye direction. (

**c**) In the Ze direction. (

**d**) The UAV’s roll angle using the PID controller. (

**e**) The UAV’s roll angle using the proposed strategy. (

**f**) The UAV’s pitch angle using the PID controller. (

**g**) The UAV’s pitch angle using the proposed strategy. (

**h**) The UAV’s yaw angle.

**Figure 12.**The displacement curve of the UAV during the actual flight hover experiment. (

**a**) In the Xe direction. (

**b**) In the Ye direction. (

**c**) In the Ze direction.

**Figure 13.**The tracking performance of the UAV under hover mode with all four motors simultaneously shut down for 0.5 s. (

**a**) In the Xe direction. (

**b**) In the Ye direction. (

**c**) In the Ze direction. (

**d**) The UAV’s roll angle. (

**e**) The UAV’s pitch angle. (

**f**) The UAV’s yaw angle.

**Figure 15.**The trajectory curves of displacement and attitude angles in high-maneuvering flight. (

**a**) In the Xe direction. (

**b**) In the Ye direction. (

**c**) In the Ze direction. (

**d**) Roll angle trajectory curve using PID controller. (

**e**) Roll angle trajectory curve using the proposed strategy. (

**f**) Yaw angle trajectory curve using the proposed strategy.

Parameter | Value | Parameter | Value |
---|---|---|---|

Acceleration due to gravity g$/(\mathrm{m}\xb7{\mathrm{s}}^{-2}$) | 9.8 | $\mathrm{Moment}\mathrm{of}\mathrm{inertia}\mathrm{about}\mathrm{the}\mathrm{Z-axis}{J}_{\mathrm{z}\mathrm{z}}$$/(\mathrm{kg}\xb7{\mathrm{m}}^{2}$) | 0.0104 |

UAV mass m/kg | 0.752 | $\mathrm{Drag}\mathrm{coefficient}{k}_{d}$$/(\mathrm{N}\xb7\mathrm{m}\xb7{\mathrm{s}}^{2}$) | 0.0251 |

UAV arm length l/m | 0.125 | $\mathrm{Lift}\mathrm{coefficient}{C}_{T}$ | 0.0165 |

$\mathrm{Moment}\mathrm{of}\mathrm{inertia}\mathrm{about}\mathrm{the}\mathrm{X-axis}{J}_{xx}$$/(\mathrm{kg}\xb7{\mathrm{m}}^{2}$) | 0.0056 | $\mathrm{Resistance}\mathrm{coefficient}{C}_{\mathrm{d}}$ | 0.0624 |

$\mathrm{Moment}\mathrm{of}\mathrm{inertia}\mathrm{about}\mathrm{the}\mathrm{Y-axis}{J}_{\mathrm{y}\mathrm{y}}$$/(\mathrm{kg}\xb7{\mathrm{m}}^{2}$) | 0.0056 | $\mathrm{Atmospheric}\mathrm{density}\rho $ | 1.184 |

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**MDPI and ACS Style**

Ma, J.; Yu, S.; Hu, W.; Wu, H.; Li, X.; Zheng, Y.; Zhang, J.; Chen, P.
Finite-Time Robust Flight Control of Logistic Unmanned Aerial Vehicles Using a Time-Delay Estimation Technique. *Drones* **2024**, *8*, 58.
https://doi.org/10.3390/drones8020058

**AMA Style**

Ma J, Yu S, Hu W, Wu H, Li X, Zheng Y, Zhang J, Chen P.
Finite-Time Robust Flight Control of Logistic Unmanned Aerial Vehicles Using a Time-Delay Estimation Technique. *Drones*. 2024; 8(2):58.
https://doi.org/10.3390/drones8020058

**Chicago/Turabian Style**

Ma, Jinyu, Shengdong Yu, Wenke Hu, Hongyuan Wu, Xiaopeng Li, Yilong Zheng, Junhui Zhang, and Puhui Chen.
2024. "Finite-Time Robust Flight Control of Logistic Unmanned Aerial Vehicles Using a Time-Delay Estimation Technique" *Drones* 8, no. 2: 58.
https://doi.org/10.3390/drones8020058