# A Tactical Conflict Resolution Proposal for U-Space Zu Airspace Volumes

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## Abstract

**:**

## 1. Introduction

## 2. Background

#### 2.1. Tactical Conflict Management in U-Space

#### 2.2. Conflict Resolution Techniques for UAV

## 3. Conflict-Free Navigation

#### 3.1. UAV Dynamic Model

#### 3.2. Conflict Prediction Mechanism

- No real root is obtained. This means that the protected zones of both UAVs do not contact at any time. No conflict situation arises and, therefore, there are not potential collisions.
- A real root is obtained. This means that the protected zones of both UAVs contact each other without overlapping, which does not generate a conflict situation either.
- Two real roots, ${t}_{1}$ and ${t}_{2}$ are obtained. These values indicate the instants of the beginning and end of the conflict. During this time interval, the protected zones of both UAVs are partially overlapped. If both roots are positive, the conflict is predicted in the future. If only one root is negative, ${a}_{1}$ and ${a}_{2}$ are currently in a conflict situation. Finally, if both roots are negative, the conflict was resolved in the past, or it never occurred (the navigation algorithm prevented it).

#### 3.3. Valid Velocity Computation

#### 3.4. Navigation Computation. The PCAN Algorithm

#### 3.5. Airspace Bounding

## 4. Performance Evaluation

#### 4.1. Two-UAV Study

#### 4.2. Multi-UAV Study

#### 4.3. Computation Time

## 5. Conclusions and Future Works

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**UAV dynamic model. (

**a**) Example of a UAV turning 45° clockwise: the red line shows the ideal trajectory followed if the commanded velocity is applied instantaneously ($\left|{\dot{p}}_{0}\right|=\left|v\right|=10\mathrm{m}/\mathrm{s}$); the blue line shows its dynamic trajectory assuming $\tau =0.5\mathrm{s}$. (

**b**) Ideal and real position (every second) of the UAV when turning 45°, 90°, and 135°, respectively.

**Figure 3.**Example of conflict prediction ($r=5\mathrm{m}$; $v=10\mathrm{m}/\mathrm{s}$). The two UAVs maintain a conflict from $t=4.83\mathrm{s}$ (solid lines) to $t=5.63\mathrm{s}$ (dotted lines).

**Figure 4.**Searching for a valid velocity from the direct one. Above, a UAV with direct velocity (${v}_{d}$) flying from the initial position ($p$) to the destination ($w$). In the center, three candidate velocity vectors have been generated in the first iteration. Below, new candidate velocity vectors have been generated, based on those of the previous iteration (if they did not lead to a conflict-free scenario).

**Figure 8.**Two-UAV study. Distance traveled: (

**a**) absolute values; (

**b**) relative increase with respect to the direct algorithm.

**Figure 9.**Two-UAV study. Flight time: (

**a**) absolute values; (

**b**) relative increase with respect to the direct algorithm.

**Figure 10.**Random scenario with 80 UAVs and PCAN. Each number represents the initial position of a UAV; each circle represents the current position of the UAV and its safety radius; each line represents the trajectory followed by the UAV. Units on the X and Y axes are meters.

**Figure 11.**Multi-UAV study. The number of conflicts: (

**a**) not solved conflicts (mean and standard deviation); (

**b**) solved conflicts (%).

**Figure 12.**Multi-UAV study. Distance traveled: (

**a**) absolute values (mean and standard deviation); (

**b**) relative increase with respect to the direct algorithm.

**Figure 13.**Multi-UAV study. Flight time: (

**a**) absolute values (mean and standard deviation); (

**b**) relative increase with respect to the direct algorithm.

$v=DirectNav\left(a\right)$ | |

01 | $\left[pv\left\{w,R\right\}\right]=a$ |

02 | if $\left|\overline{pw}\right|<{v}_{\mathrm{max}}{t}_{\mathrm{nav}}R\ne \varnothing $ |

03 | $a=\left[pvR\right]$ |

04 | $\left\{w,~\right\}=R$ |

05 | end if |

06 | $v=\frac{\overline{pw}}{\left|\overline{pw}\right|}{v}_{\mathrm{max}}$ |

${\mathit{t}}_{c}=ConflictPrediction\left(v,{a}_{1},{a}_{2}\right)$ | |

01 | $\mathrm{assume}r$ |

02 | $\left[{p}_{1}{v}_{1}~\right]={a}_{1}$ |

03 | $\left[{p}_{2}{v}_{2}~\right]={a}_{2}$ |

04 | if v ~= null |

05 | ${v}_{2}=v$ |

06 | end if |

07 | ${t}_{2}={\left({v}_{1}-{v}_{2}\right)}^{2}$ |

08 | ${t}_{1}=2\left({p}_{1}-{p}_{2}\right)\left({v}_{1}-{v}_{2}\right)$ |

09 | ${t}_{0}={\left({p}_{1}-{p}_{2}\right)}^{2}-4{r}^{2}$ |

10 | ${t}_{c}=\mathrm{roots}\left(\left[{t}_{2}{t}_{1}{t}_{0}\right]\right)$ |

11 | if $\mathrm{isreal}\left({t}_{c}\right){t}_{c}0$ |

12 | ${t}_{c}=\mathrm{min}\left({t}_{c}\right)$ |

13 | else |

14 | ${t}_{c}=\infty $ |

15 | end if |

$boolean=\mathrm{AirspaceConflicts}\left(v,{a}_{1},\mathbb{A}\right)$ | |

01 | for all ${a}_{2}\in \mathbb{A}$ do |

02 | if ${a}_{1}={a}_{2}$ |

03 | continue |

04 | end if |

05 | if $\mathrm{ConflictPrediction}\left(v,{a}_{1},{a}_{2}\right)=\infty $ |

06 | return true |

07 | end if |

08 | end do |

09 | return false |

$v=\mathrm{ValidVelocity}\left({a}_{1},\mathbb{A}\right)$ | |

01 | $\mathrm{assume}m,coef,\alpha $ |

02 | ${v}_{1}={v}_{2}={v}_{3}=\mathrm{DirectNav}\left({a}_{1}\right)$ |

03 | while m > 0 |

04 | ${v}_{1}={v}_{1}\ast coef$ |

05 | ${v}_{2}=\mathrm{Veer}\left({v}_{2},\alpha ,counterclockwise\right)$ |

06 | ${v}_{3}=\mathrm{Veer}\left({v}_{3},\alpha ,clockwise\right)$ |

07 | if $\mathrm{not}\mathrm{AirspaceConflicts}\left({v}_{1},{a}_{1},\mathbb{A}\right)$ |

08 | return $v={v}_{1}$ |

09 | end if |

10 | if $\mathrm{not}\mathrm{AirspaceConflicts}\left({v}_{2},{a}_{1},\mathbb{A}\right)$ |

11 | return $v={v}_{2}$ |

12 | end if |

13 | if $\mathrm{not}\mathrm{AirspaceConflicts}\left({v}_{3},{a}_{1},\mathbb{A}\right)$ |

14 | return $v={v}_{3}$ |

15 | end if |

16 | m = m − 1 |

17 | end while |

18 | return v = 0 |

${v}^{\prime}=\mathrm{Veer}\left(v,\alpha ,\mathrm{direction}\right)$ | |

01 | if $\mathrm{direction}=clockwise$ |

02 | $\alpha =-\alpha $ |

03 | end if |

04 | ${v}^{\prime}=v\times \left[\begin{array}{cc}\mathrm{cos}\left(\alpha \right)& \mathrm{sen}\left(\alpha \right)\\ -\mathrm{sen}\left(\alpha \right)& \mathrm{cos}\left(\alpha \right)\end{array}\right]$ |

$\mathbb{A}=\mathrm{PCAN}\left(\mathbb{A}\right)$ | |

01 | assume $r$ |

02 | for all $a\in \mathbb{A}$ do |

03 | $\left[p~R\right]=a$ |

04 | $v=\mathrm{DirectNav}\left(a\right)$ |

05 | $a=\left[pvR\right]$ |

06 | end do |

07 | for all ${a}_{i}\in \mathbb{A}$ do |

08 | if $\mathrm{AirspaceConflicts}\left(v,{a}_{i},\mathbb{A}\right)$ |

09 | $v=\mathrm{ValidVelocity}\left({a}_{i},\mathbb{A}\right)$ |

10 | if $v=0$ |

11 | $\mathbb{A}=\mathrm{PCAN}\left(\left\{{a}_{1}\dots {a}_{i-1}\right\}\right){{\displaystyle \cup}}^{}\left\{{a}_{i}\dots {a}_{n}\right\}$ |

12 | end if |

13 | end if |

14 | $\left[p~R\right]={a}_{i}$ |

15 | ${a}_{i}=\left[pvR\right]$ |

16 | end do |

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Jover, J.; Bermúdez, A.; Casado, R.
A Tactical Conflict Resolution Proposal for U-Space Zu Airspace Volumes. *Sensors* **2021**, *21*, 5649.
https://doi.org/10.3390/s21165649

**AMA Style**

Jover J, Bermúdez A, Casado R.
A Tactical Conflict Resolution Proposal for U-Space Zu Airspace Volumes. *Sensors*. 2021; 21(16):5649.
https://doi.org/10.3390/s21165649

**Chicago/Turabian Style**

Jover, Jesús, Aurelio Bermúdez, and Rafael Casado.
2021. "A Tactical Conflict Resolution Proposal for U-Space Zu Airspace Volumes" *Sensors* 21, no. 16: 5649.
https://doi.org/10.3390/s21165649