# A Simulation Study of Risk-Aware Path Planning in Mitigating the Third-Party Risk of a Commercial UAS Operation in an Urban Area

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## Abstract

**:**

## 1. Introduction

## 2. Third-Party Risk Indicators and Path Planning

#### 2.1. Third-Party Risk Indicators

#### 2.2. TPR Indicators in Path-Planning

## 3. Assessment of Annual Third-Party Risks for a Commercial UAS Service

Algorithm 1: Monte Carlo simulation-based evaluation of annual Third-Party Risk indicators for a commercial UAS operation [30]. |

#### 3.1. Generation of N OD Pairs (Step 0)

#### 3.2. Nominal Flight Path Generation (Step 1)

#### 3.3. Risk Assessment via Monte Carlo Simulation

## 4. Simulation Results

#### 4.1. Experiment I: Risk Weight Ratio

#### 4.2. Experiment II: # of Packages per Person per Annum

#### 4.3. Experiment III: Sensitivity Analysis on Parameters in Risk Assessment

#### 4.3.1. Sensitivity Analysis for Failure Model

#### 4.3.2. Sensitivity Analysis for Descent Model

#### 4.3.3. Sensitivity Analysis for Fatality Model

## 5. Discussion for Simulation Results

- 1.
- For annual flights, current UAS path planning can reduce CGRfh and annual CGR but it may lead to more areas with a high annual IR. The trade-off on weight risk ratio in current UAS path planning should be carefully considered.
- 2.
- Annual IR and annual CGR increase linearly as the number of flights increases. Current UAS path planning fails to generate paths that satisfy safety risk criteria if the flight volume is larger than a certain threshold.
- 3.
- Both the annual IR and annual CGR reduce linearly as the system’s failure rate reduces.
- 4.
- Increasing the drag coefficient reduces the impact energy, but drones can fly away to highly populated areas.

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Model in Risk Assessment | Parameter | Value |
---|---|---|

Failure model | failure rate (per hour) $\lambda $ | 3.42 × 10${}^{-4}$ [46] |

Descent model | drag coefficient ${C}_{D}$ | $N\text{}(0.7,\text{}0.2)$ [43] |

surface area ${A}_{S}$ (m${}^{2}$) | $[0.1,\text{}0.4]$ | |

wind speed w | from KNMI [48] | |

Fatality model | mid-point value a(Joule) | 101.6 [45] |

standard deviation b | 0.538 [45] | |

Others | mass with parcel m [kg] | 3.7 [40] |

cruise speed ${v}_{c}$ (m/s) | 12 [41] | |

ascent speed ${v}_{a}$ (m/s) | 7.5 [41] | |

descent speed ${v}_{d}$ (m/s) | 6 [41] | |

horizontal position errors ${\sigma}_{H}^{p}$ (m) | 3.68 [42] | |

vertical position errors ${\sigma}_{V}^{p}$ (m) | 7.65 [42] | |

horizontal velocity errors ${\sigma}_{H}^{v}$ (m/s) | 2.0 [43] | |

vertical velocity errors ${\sigma}_{V}^{v}$ (m/s) | 2.0 [43] |

a | 53 | 103 | 153 | 203 | 253 |

Annual CGR (# of fatalities per annum) | 1.96 × 10${}^{-3}$ | 1.96 × 10${}^{-3}$ | 1.95 × 10${}^{-3}$ | 1.94 × 10${}^{-3}$ | 1.93 × 10${}^{-3}$ |

b | $0.138$ | $0.338$ | $0.538$ | $0.738$ | $0.938$ |

Annual CGR (# of fatalities per annum) | 1.96 × 10${}^{-3}$ | 1.96 × 10${}^{-3}$ | 1.96 × 10${}^{-3}$ | 1.95 × 10${}^{-3}$ | 1.94 × 10${}^{-3}$ |

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**Figure 2.**An example of generated paths by setting (

**a**) ${\omega}_{ratio}=$ 1:0: a path over low-populated areas; (

**b**) ${\omega}_{ratio}=$ 0:1: a short path.

CGRfh | Annual IR | Annual CGR | |
---|---|---|---|

Formula | ${R}_{Cground}^{i}/{T}_{i}$ | ${R}_{I}^{UAS}\left(y\right)=1-{\prod}_{i=1}^{N}[1-{R}_{I}^{i}\left(y\right)]$ | ${R}_{Cground}^{UAS}={\sum}_{i=1}^{N}{R}_{Cground}^{i}$ |

# of flights | single | multiple | multiple |

Unit | # of fatalities per flight hour | probability of fatality per annum | # of fatalities per annum |

Safety threshold | ${10}^{-6}$ | ${10}^{-6}$ | $1.65\phantom{\rule{3.33333pt}{0ex}}\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-3}$ |

${\mathit{\omega}}_{\mathbf{ratio}}$ | 0:1 | 1:4 | 1:1 | 4:1 | 1:0 |
---|---|---|---|---|---|

Area size with annual $IR>{10}^{-6}$ (km${}^{2}$) | 0.75 | 1.06 | 1.22 | 1.86 | 2.47 |

Percentage of improvement | $0.0\%$ | $-41.3\%$ | $-62.7\%$ | $-148.0\%$ | $-229.3\%$ |

${\mathit{\omega}}_{\mathbf{ratio}}$ | 0:1 | 1:4 | 1:1 | 4:1 | 1:0 |
---|---|---|---|---|---|

Annual CGR (# of fatalities per annum) | 3.00 × 10 ${}^{-3}$ | 2.11 × 10 ${}^{-3}$ | 1.96 × 10 ${}^{-3}$ | 1.87 × 10 ${}^{-3}$ | 1.57 × 10 ${}^{-3}$ |

Percentage of improvement | $0\%$ | $29.7\%$ | $34.7\%$ | $37.7\%$ | $47.7\%$ |

Model in Risk Assessment | Parameter | Value |
---|---|---|

Failure model | $\lambda $ | [1.50 × 10${}^{-3}$, 1.28 × 10${}^{-6}$] |

Descent model | $\overline{{C}_{D}}$ | $[0.1,\text{}1.3]$ |

${A}_{S}$ [m${}^{2}]$ | $[0.1,\text{}0.4]$ | |

w | $[0.50\ast {w}_{raw},\text{}1.50\ast {w}_{raw}]$ | |

Fatality model | a | [53, 253] |

b | [0.138, 0.938] |

Drag coefficient $\overline{{\mathit{C}}_{\mathit{D}}}$ | $0.1$ | $0.4$ | $0.7$ | $1.0$ | $1.3$ |

Annual CGR (# of fatalities per annum) | 1.74 × 10${}^{-3}$ | 1.85 × 10${}^{-3}$ | 1.96 × 10${}^{-3}$ | 2.02 × 10${}^{-3}$ | 2.07 × 10${}^{-3}$ |

Surface area size ${A}_{S}$ (m${}^{2})$ | $0.1$ | $0.175$ | $0.25$ | $0.325$ | $0.4$ |

Annual CGR (# of fatalities per annum) | 1.96 × 10${}^{-3}$ | 2.06 × 10${}^{-3}$ | 2.11 × 10${}^{-3}$ | 2.13 × 10${}^{-3}$ | 2.12 × 10${}^{-3}$ |

Wind speed w | $0.5\ast {w}_{raw}$ | $0.75\ast {w}_{raw}$ | $1.0\ast {w}_{raw}$ | $1.25\ast {w}_{raw}$ | $1.5\ast {w}_{raw}$ |

Annual CGR (# of fatalities per annum) | 1.79 × 10${}^{-3}$ | 1.88 × 10${}^{-3}$ | 1.96 × 10${}^{-3}$ | 2.02 × 10${}^{-3}$ | 2.08 × 10${}^{-3}$ |

**Table 6.**A case of velocity and energy when crashing to the ground for different $\overline{{C}_{D}}$.

drag coefficient $\overline{{\mathit{C}}_{\mathit{D}}}$ | $0.1$ | $0.4$ | $0.7$ | $1.0$ | $1.3$ |

X-axis horizontal speed ${V}_{x}$ (m/s) | $1.9$ | $4.9$ | $5.7$ | $5.7$ | $5.5$ |

Y-axis horizontal speed ${V}_{y}$ (m/s) | $-9.5$ | $-3.5$ | $-1.3$ | $-0.5$ | $-0.2$ |

Vertical speed ${V}_{z}$ (m/s) | $-50.6$ | $-35.5$ | $-28.7$ | $-24.6$ | $-21.7$ |

Impact energy ${E}_{imp}$ (Joule) | 4719 | 2402 | 1584 | 1182 | 926 |

Initial state when crash down: $height$ = 187.3 m, ${V}_{x}$ = $-1.6$ m/s, ${V}_{y}$ = −15.3 m/s, | |||||

${V}_{z}$ = $-0.8$ m/s, mass m = 3.7 kg, wind speed ${w}_{x}$ = 7.9 m/s, ${w}_{y}$ = 0 m/s |

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**MDPI and ACS Style**

He, X.; Jiang, C.; Li, L.; Blom, H. A Simulation Study of Risk-Aware Path Planning in Mitigating the Third-Party Risk of a Commercial UAS Operation in an Urban Area. *Aerospace* **2022**, *9*, 682.
https://doi.org/10.3390/aerospace9110682

**AMA Style**

He X, Jiang C, Li L, Blom H. A Simulation Study of Risk-Aware Path Planning in Mitigating the Third-Party Risk of a Commercial UAS Operation in an Urban Area. *Aerospace*. 2022; 9(11):682.
https://doi.org/10.3390/aerospace9110682

**Chicago/Turabian Style**

He, Xinyu, Chengpeng Jiang, Lishuai Li, and Henk Blom. 2022. "A Simulation Study of Risk-Aware Path Planning in Mitigating the Third-Party Risk of a Commercial UAS Operation in an Urban Area" *Aerospace* 9, no. 11: 682.
https://doi.org/10.3390/aerospace9110682