#
Path Planning Using Concatenated Analytically-Defined Trajectories for Quadrotor UAVs^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Quadrotor Dynamics and Kinematics

## 3. Trajectory Planning

#### 3.1. Sub-Riemannian Curves for Quadrotor Trajectory Planning

#### 3.2. Trajectory Repositioning and Reorientation

## 4. Obstacle Detection

## 5. Simulations

#### 5.1. Tracking Controller

#### 5.2. Waypoints

Waypoint | ${\mathit{x}}_{\mathbf{1}}$ | ${\mathit{x}}_{\mathbf{2}}$ | ${\mathit{x}}_{\mathbf{3}}$ |
---|---|---|---|

1 | 3 | 4 | 5 |

2 | −2 | 7 | 3 |

3 | −2 | 0 | 6 |

4 | 3 | −4 | 6 |

5 | 2 | 0 | 0 |

Segment | ${\mathit{\lambda}}_{\mathbf{1}}$ | ${\mathit{\lambda}}_{\mathbf{2}}$ | ${\mathit{\lambda}}_{\mathbf{4}}$ | T | Solution Time (ms) |
---|---|---|---|---|---|

1 | −14.136 | 14.281 | 2.773 | 7.858 | 526 |

2 | −28.675 | −15.967 | −9.2926 | 9.656 | 183 |

3 | −11.621 | −10.550 | 3.025 | 8.161 | 108 |

4 | −15.955 | 10.789 | 2.482 | 6.898 | 194 |

5 | −23.425 | 13.467 | 4.527 | 10.224 | 130 |

**Figure 4.**Tracking controller performance. (

**a**) Position error ${e}_{x}$; (

**b**) control thrust (N); (

**c**) control moment (N m).

#### 5.3. Obstacle Collision Detection

## 6. Conclusions

## Author Contributions

## Conflicts of Interest

## Appendix: Analytical Curves Proof

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**MDPI and ACS Style**

Jamieson, J.; Biggs, J.
Path Planning Using Concatenated Analytically-Defined Trajectories for Quadrotor UAVs. *Aerospace* **2015**, *2*, 155-170.
https://doi.org/10.3390/aerospace2020155

**AMA Style**

Jamieson J, Biggs J.
Path Planning Using Concatenated Analytically-Defined Trajectories for Quadrotor UAVs. *Aerospace*. 2015; 2(2):155-170.
https://doi.org/10.3390/aerospace2020155

**Chicago/Turabian Style**

Jamieson, Jonathan, and James Biggs.
2015. "Path Planning Using Concatenated Analytically-Defined Trajectories for Quadrotor UAVs" *Aerospace* 2, no. 2: 155-170.
https://doi.org/10.3390/aerospace2020155