# Collision Avoidance of Hexacopter UAV Based on LiDAR Data in Dynamic Environment

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## Abstract

**:**

## 1. Introduction

## 2. UAV System

#### 2.1. Dynamics

#### 2.2. Control Design

#### 2.3. LiDAR Data Sensing

## 3. Review of Basic Collision Cone Approach

## 4. Obstacle State Estimator

## 5. Collision Avoidance Strategy Against Moving Obstacle

## 6. Numerical Simulation

#### 6.1. Simulation I: Hovering Situation

#### 6.2. Simulation II: Waypoint Guidance

^{2}, respectively. Also, their unit vector is ${[-0.56\phantom{\rule{4pt}{0ex}}0.83\phantom{\rule{4pt}{0ex}}0.03]}^{T}$.

#### 6.3. Simulation III: Monte Carlo Simulation

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Collision avoidance strategy using predicted trajectory of obstacle: (

**a**) velocity vector outside the collision cone at $t={t}_{0}$, (

**b**) collision at $t={t}_{a}$, (

**c**) pruning process, and (

**d**) final aiming point candidates.

**Figure 6.**Trajectories of the hexacopter and the obstacle (azimuth: −33°, elevation: 37°, Simulation I).

**Figure 7.**Time histories of UAV-related variables (Simulation I): (

**a**) attitude, (

**b**) body rate, (

**c**) minimum distance between UAV and obstacle, (

**d**) absolute velocity, and (e) velocity (body-fixed coordinate system).

**Figure 8.**Time histories of the state estimate (Simulation I): (

**a**) ${x}_{e,k}^{n}$, (

**b**) ${\dot{x}}_{e,k}^{n}$, (

**c**) ${\ddot{x}}_{e,k}^{n}$, (

**d**) ${y}_{e,k}^{n}$, (

**e**) ${\dot{y}}_{e,k}^{n}$, (

**f**) ${\ddot{y}}_{e,k}^{n}$, (

**g**) ${z}_{e,k}^{n}$, (

**h**) ${\dot{z}}_{e,k}^{n}$, and (

**i**) ${\ddot{z}}_{e,k}^{n}$.

**Figure 9.**Trajectories of the hexacopter and the obstacle (azimuth: −60°, elevation: 30°, Simulation II).

**Figure 10.**Time histories of UAV-related variables (Simulation II): (

**a**) attitude, (

**b**) body rate, (

**c**) minimum distance between UAV and obstacle, (

**d**) absolute velocity, and (

**e**) velocity (body-fixed coordinate system).

**Figure 11.**Time histories of the state estimate (Simulation II): (

**a**) ${x}_{e,k}^{n}$, (

**b**) ${\dot{x}}_{e,k}^{n}$, (

**c**) ${\ddot{x}}_{e,k}^{n}$, (

**d**) ${y}_{e,k}^{n}$, (

**e**) ${\dot{y}}_{e,k}^{n}$, (

**f**) ${\ddot{y}}_{e,k}^{n}$, (

**g**) ${z}_{e,k}^{n}$, (

**h**) ${\dot{z}}_{e,k}^{n}$, and (

**i**) ${\ddot{z}}_{e,k}^{n}$.

**Table 1.**Parameters of the hexacopter, Kalman filter, and collision avoidance used in numerical simulation.

Hexacopter dynamics | |||||||

m | 2.356 kg | ${J}_{x}$ | $1.676\times {10}^{-1}$ kg m^{2} | ${J}_{y}$ | $1.676\times {10}^{-1}$ kg m^{2} | ${J}_{z}$ | $2.974\times {10}^{-1}$ kg m^{2} |

l | 0.5 m | ${k}_{f}$ | $1.1\times {10}^{-1}$ Ns^{2} | ${k}_{\tau}$ | $5.2\times {10}^{-2}$ Ns^{2} m | g | 9.8 m/s^{2} |

Hexacopter controller | |||||||

${\omega}_{v}$ | 3 rad/s^{2} | ${\zeta}_{v}$ | 0.8 | ${\omega}_{h}$ | 3 rad/s^{2} | ${\zeta}_{h}$ | 0.8 |

${\omega}_{\varphi}$ | 15 rad/s^{2} | ${\zeta}_{\varphi}$ | 0.7 | ${\omega}_{\theta}$ | 15 rad/s^{2} | ${\zeta}_{\theta}$ | 0.7 |

${\omega}_{\psi}$ | 5 rad/s^{2} | ${\zeta}_{\psi}$ | 0.9 | ||||

LiDAR sensor | |||||||

$\Delta {t}_{l}$ | 0.1 s | ${d}_{a}$ | 10 m | ${H}_{fv}$ | 170° | ${V}_{fv}$ | 30° |

Kalman filter | |||||||

${\widehat{\overrightarrow{x}}}_{0}^{n}$ | ${\left[0\phantom{\rule{4pt}{0ex}}0\phantom{\rule{4pt}{0ex}}0\phantom{\rule{4pt}{0ex}}0\phantom{\rule{4pt}{0ex}}0\phantom{\rule{4pt}{0ex}}0\phantom{\rule{4pt}{0ex}}0\phantom{\rule{4pt}{0ex}}0\phantom{\rule{4pt}{0ex}}0\right]}^{T}$ | ${P}_{0}^{+}$ | diag$[0,\phantom{\rule{4pt}{0ex}}0,\phantom{\rule{4pt}{0ex}}0,\phantom{\rule{4pt}{0ex}}0,\phantom{\rule{4pt}{0ex}}0,\phantom{\rule{4pt}{0ex}}0,\phantom{\rule{4pt}{0ex}}0,\phantom{\rule{4pt}{0ex}}0,\phantom{\rule{4pt}{0ex}}0]$ | ||||

${Q}_{e}$ | diag$[1\times {10}^{-8},\phantom{\rule{4pt}{0ex}}1\times {10}^{-4},\phantom{\rule{4pt}{0ex}}1,\phantom{\rule{4pt}{0ex}}1\times {10}^{-8},\phantom{\rule{4pt}{0ex}}1\times {10}^{-4},\phantom{\rule{4pt}{0ex}}1,\phantom{\rule{4pt}{0ex}}1\times {10}^{-8},\phantom{\rule{4pt}{0ex}}1\times {10}^{-4},\phantom{\rule{4pt}{0ex}}1]$ | ||||||

${R}_{e}$ | diag$[1\times {10}^{-8},\phantom{\rule{4pt}{0ex}}1\times {10}^{-8},\phantom{\rule{4pt}{0ex}}1\times {10}^{-8}]$ | ||||||

Collision avoidance | |||||||

${d}_{sm}$ | 2 m | Max. $\Delta {t}_{d}$ | 30 s | $\Delta {t}_{p}$ | 0.1 s |

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**MDPI and ACS Style**

Park, J.; Cho, N.
Collision Avoidance of Hexacopter UAV Based on LiDAR Data in Dynamic Environment. *Remote Sens.* **2020**, *12*, 975.
https://doi.org/10.3390/rs12060975

**AMA Style**

Park J, Cho N.
Collision Avoidance of Hexacopter UAV Based on LiDAR Data in Dynamic Environment. *Remote Sensing*. 2020; 12(6):975.
https://doi.org/10.3390/rs12060975

**Chicago/Turabian Style**

Park, Jongho, and Namhoon Cho.
2020. "Collision Avoidance of Hexacopter UAV Based on LiDAR Data in Dynamic Environment" *Remote Sensing* 12, no. 6: 975.
https://doi.org/10.3390/rs12060975