# Design and Implementation of a Dual-Axis Tilting Quadcopter

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## Abstract

**:**

## 1. Introduction

## 2. Design Approach

## 3. Modeling and Simulation of Over-Actuated Quadcopter

#### 3.1. Modeling

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#### 3.2. Simulation

^{©}incorporating the motor dynamics, attitude controller for Roll, Pitch and Yaw, and the controller for tilting angles of the rotors (Figure 7). The quadcopter can be simulated to observe the flight behaviour under the influence of different control inputs i.e. attitude commands and tilting rotor angle inputs.

## 4. Experimental Setup

## 5. Results and Discussion

#### 5.1. Flight Test with Conventional Actuation of Quadcopter

#### 5.2. Flight Test with Tilting Rotors

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

$\theta $ | Pitch angle |

$\phi $ | Roll angle |

$\psi $ | Yaw angle |

${\omega}_{i}$ | Angular velocity |

$\mathit{L}$ | Arm length |

$dI{B}_{x}$ | Time derivative of inertia along X axis |

$dI{B}_{y}$ | Time derivative of inertia along Y axis |

$dI{B}_{z}$ | Time derivative of inertia along Z axis |

$I{B}_{xx}$ | Body’s inertia along X axis |

$I{B}_{yy}$ | Body’s inertia along Y axis |

$I{B}_{zz}$ | Body’s inertia along Z axis |

$I{P}_{x}$ | Propeller’s inertia along X axis |

$I{P}_{y}$ | Propeller’s inertia along Y axis |

$I{P}_{z}$ | Propeller’s inertia along Z axis |

i | number of rotor (1, 2, 3, 4) |

${P}_{N,E,D}$ | Position in North, East and Down axis |

P | Angular velocity in X axis |

Q | Angular velocity in Y axis |

R | Angular velocity in Z axis |

${n}_{i}$ or ${\eta}_{i}$ | Rotor tilting angle along the arm |

${b}_{i}$ or ${\beta}_{i}$ | Rotor tilting angle across the arm |

${x}_{W},{y}_{W},{z}_{W}$ | Fixed frame (1) |

${x}_{B},{y}_{B},{z}_{B}$ | Body frame (2) |

${x}_{P},{y}_{P},{z}_{P}$ | Rotor frame (3) |

${R}_{x},{R}_{y},{R}_{z}$ | Rotation matrices in x, y and z axis |

$\alpha $ | Angular acceleration |

u, v, w | Linear velocity in x, y and z axis |

${T}_{i}$ | Thrust generated by the rotor i |

## Appendix A. Coefficients of the Forces and the Torques

## Appendix B. Inertia Values

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**Figure 5.**Rotor numbering and reference frames [29].

**Figure 9.**(

**a**) Rotor tilting angles along the arm ${\mathit{n}}_{1}$ and ${\mathit{n}}_{3}$; (

**b**) Rotor tilting angles along the arm ${\mathit{n}}_{2}$ and ${\mathit{n}}_{4}$.

Parameter | Specifications |
---|---|

UAV Dimensions | 1048 × 1048 mm |

Weight | 4 kg |

Endurance | 20 min |

Payload Capacity | 2 kg |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bin Junaid, A.; Diaz De Cerio Sanchez, A.; Betancor Bosch, J.; Vitzilaios, N.; Zweiri, Y.
Design and Implementation of a Dual-Axis Tilting Quadcopter. *Robotics* **2018**, *7*, 65.
https://doi.org/10.3390/robotics7040065

**AMA Style**

Bin Junaid A, Diaz De Cerio Sanchez A, Betancor Bosch J, Vitzilaios N, Zweiri Y.
Design and Implementation of a Dual-Axis Tilting Quadcopter. *Robotics*. 2018; 7(4):65.
https://doi.org/10.3390/robotics7040065

**Chicago/Turabian Style**

Bin Junaid, Ali, Alejandro Diaz De Cerio Sanchez, Javier Betancor Bosch, Nikolaos Vitzilaios, and Yahya Zweiri.
2018. "Design and Implementation of a Dual-Axis Tilting Quadcopter" *Robotics* 7, no. 4: 65.
https://doi.org/10.3390/robotics7040065