# Air Corridors: Concept, Design, Simulation, and Rules of Engagement

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## Abstract

**:**

## 1. Introduction

#### 1.1. Major Contributions

#### 1.2. Organization

## 2. Literature Review

## 3. Definitions and Notations

**Definition**

**1**

**.**In the context of UAS, the term geofencing is used to describe virtual three dimensional “boundaries” each UAS flies within or avoids as a no-fly zone (NFZ).

**Definition**

**2**

**.**An air cube (c) is a building block for a skylane in 3D airspace. An air cube is a static geofence in its most simplified form. All air cubes are similar in size. An air cube is exclusively reserved space for a UAV in transit at any given time. According to Near Mid-Air-Collision (NMAC) avoidance rules, the standard safe distance between two manned aircraft is 500 ft. or 152.4 m [13]. In our model, the side length (s) of each air cube is set to 200 m.

**Definition**

**3**

**.**A skylane (S) is a designated region of airspace for UAV (Unmanned Air Vehicle) in transit. An aircraft must fly within the skylane during its transit. A skylane can be defined as a volume consisting of a number of cubes with the same direction. An entrance gate is used to enter the skylane and one exit gate is used to exit the skylane. Gates are defined in Definition 6.

**Definition**

**4**

**.**An intersection is the junction where one skylane crosses another in the horizontal plane. In the skylane, it is the place where vehicles turn or change their direction. In order to avoid collisions, an intersection is designed to include three layers. The middle layer is used for a temporary hovering before a UAV actually makes the intended turn.

**Definition**

**5**

**.**A vertical airport or vertiport (V) is a place for take-off and landing for UAVs.

**Definition**

**6**

**.**A gate is a connection between a skylane and a vertiport. It regulates the takeoff and landing operations of the UAVs. Vehicles need to go through the gates to enter or exit the skylanes.

**Definition**

**7**

**.**An air corridor is a 3D volume of airspace reserved for UASs. It is a complete airspace structure that includes all skylanes, intersections, and gates. Cube, skylanes, and air corridor definitions assume end-to-end cube placement for a continuous segment but real GPS signals with uncertainty will require clear rules for unambiguous cube occupancy.

## 4. Air Corridor Design and Rules of Engagement

#### 4.1. Multi-Layered Air Corridor Design

#### 4.2. Basic Rules of Engagement

#### 4.3. Flight Path from One Vertiport to Another

## 5. Intersection Handling

- Time step 1: At time ${t}_{1}$, only two vehicles are inside the intersection: UAV 1 in cube 3A and UAV 4 in cube 3D (Figure 5a).
- Time step 2: In step 2 (${t}_{2}$), all vehicles move one cube further. Thus, UAVs 2 and 1 go to cubes 3A and 3C, respectively. Similarly, UAVs 3 and 4 go to cubes 3D and 3B respectively (Figure 5b).
- Time step 3: In this step, all vehicles will change their heading direction to make a turn. AT time step 3 (${t}_{3}$), all four UAVs will change their altitude and move to level 2 from level 3 (Figure 5c).
- Time step 4: Two possible scenarios arise in step 4. In the first scenario, the UAVs observe that all cubes in level 1 are empty. As a result, the UAVs will move to level 1 at time step 4, while the UAV position remains constant but the altitude changes (Figure 5d). In the second scenario, assume that cubes 1B and 1D in level 1 are occupied by UAV 5 and UAV 6 respectively, at time step 4. So the negotiation between the UAVs can be carried out in two possible ways. In the first approach (Figure 6a), both UAV 3 and 4 will stay in level 2 (in cubes 2D and 2B), and UAV 1 and UAV 2 will move to level 1 (to cubes 1A and 1C) at step 4 . At time step 5; UAV 2, UAV 5, and UAV 1 will move one cube further. Thus UAV 5 and UAV 1 will be at cubes 1A and 1D, respectively, which gives UAV 4 the opportunity to move to cube 1B. UAV 3 will still be hovering in the second level at time step 5. UAV 3 will move towards level 1 at time step 6. In this negotiation process, the UAV that finds an empty cube first, will get the right of way. In the second approach (Figure 6b), UAVs 1, 3, and 4 will stay at level 2 (in cubes 2A, 2D, and 2B) and UAV 2 will move to level 1 (1A) at time step 4. UAV 4, UAV 1, and UAV 3 will go to level 1 at time step 5 and keep moving towards their destination. In this negotiation procedure, UAVs in the front get priority over the ones that are behind. This intersection design allows implementation and utilization of multiple negotiation procedures.

## 6. Capacity of an Air Corridor

**Definition**

**8**

**.**Capacity of an air corridor is defined by the maximum number of vehicles that can fly in the corridor maintaining minimum safe distance among them.

#### Travel Time

## 7. Mobility Model and Stationary Node Distribution

#### 7.1. Manhattan Mobility Model with Safety Distance Rules

#### 7.2. Probability Density Function of UAV Locations

**Lemma**

**1.**

## 8. Collision Probability

**Definition**

**9**

**.**Collisions occur when two or more UAVs occupy a cube at the same time.

**Lemma**

**2.**

**Proof.**

## 9. Simulations and Results

#### 9.1. Simulation Comparing Different Velocities

#### 9.1.1. Convergence

#### 9.1.2. Vehicle Distribution along the Skylane

#### 9.1.3. Trajectories

#### 9.2. Simulation Comparing Different Traffic Volumes

#### 9.2.1. Probability Density

#### 9.2.2. Convergence

#### 9.2.3. Location Distribution along the Skylane

#### 9.2.4. Trajectory

## 10. Summary and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

UAV | Unmanned Air Vehicle |

UAS | Unmanned Aircraft System |

AAM | Advanced Air Mobility |

UAM | Urban Air Mobility |

UTM | UAS Traffic Management |

FAA | Federal Aviation Administration |

BS | Base Station |

NFZ | No-Fly Zone |

MSL | Mean Sea Level |

MAC | Mid-Air-Collision |

## References

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- Federal Aviation Authority. Urban Air Mobility: Concept of Operations; Department of Transportation: Washington, DC, USA, 2020.
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**Figure 1.**Skylane structure. Blue boxes represent variables that define the data elements of skylane. Green boxes represent variables that define movement directions of vehicles inside the skylane.

**Figure 2.**Design of a Multi-layered Air Corridor. (

**a**) Side view of an intersection. (

**b**) Top view of an intersection: skylanes in level 1 (East-to-West) are in black color, skylanes in level 3 (North-to-South) are in blue color, and red boxes represent vertiports.

**Figure 6.**Traffic management at intersections: second illustration. (

**a**) Time step 4: scenario 2, approach 1. (

**b**) Time step 4: scenario 2, approach 2.

**Figure 7.**North-to-south skylanes are represented in blue color, east-to-west skylanes are represented in green color, intersections are shown in yellow color, and vertiports are colored in red. Indices $i-1$, i, and $i+1$ represent three vehicles in level three and the distance between any pair of vehicles is $\Delta {x}_{i}$. Similarly, j, $j+1$, and $j-1$ represent three vehicles in level one and the distance between any pair of vehicles in this level is $\Delta {x}_{j}$.

**Figure 11.**Location distribution of fast vs. slow moving vehicles. (

**a**) Time steps = 100,000. (

**b**) Time steps = 10,000,000.

**Figure 12.**Trajectories of fast vs. slow moving vehicles. Only the first 200 time steps are shown. (

**a**) Fast moving vehicles. (

**b**) Slow moving vehicles.

**Figure 13.**Probability density for different traffic volumes. (

**a**) Ratio of vehicles to air cubes in skylane ($\frac{N}{nc}$) = 0.1. (

**b**) Ratio of vehicles to air cubes in skylane ($\frac{N}{nc}$) = 0.5.

**Figure 14.**Convergence for different traffic volumes. (

**a**) Ratio of vehicles to air cubes in skylane ($\frac{N}{nc}$) = 0.1. (

**b**) Ratio of vehicles to air cubes in skylane ($\frac{N}{nc}$) = 0.5.

**Figure 15.**Location distribution along the skylane for different traffic volumes. (

**a**) Ratio of vehicles to air cubes in skylane ($\frac{N}{nc}$) = 0.1. (

**b**) Ratio of vehicles to air cubes in skylane ($\frac{N}{nc}$) = 0.5.

**Figure 16.**Vehicle trajectory analysis for different traffic volumes. Only the first 200 time steps are shown. (

**a**) Ratio of vehicles to air cubes in skylane ($\frac{N}{nc}$) = 0.1. (

**b**) Ratio of vehicles to air cubes in skylane ($\frac{N}{nc}$) = 0.5.

Symbol | Description | Symbol | Description |
---|---|---|---|

$S\left[\phantom{\rule{3.33333pt}{0ex}}\right]$ | List of skylanes | sid | Skylane identifier |

ids[ ] | List of identification numbers of the permitted UAVs | $gc$ | Gap between UAVs in terms of number of air cubes |

V[ ] | Vertiport | $vpid$ | Vertiport identifier |

c[ ] | List of air cubes | cid | Air cube identifier |

nc | Number of air cube | s | Side length of air cube |

g | Geofence | ${h}_{i}$ | Home location |

n | Number of vertices in geofence | v | List of vertices in geofence |

${z}_{f}$ | Minimum floor altitude | ${z}_{c}$ | Maximum ceiling altitude |

$\varphi $ | Latitude | $\lambda $ | Longitude |

${z}_{i}$ | Altitude | ${t}_{i}$ | Activation time |

C | Capacity | N | Number of UAVs |

l | Number of skylanes | L | Length of a skylane |

T | Travel time | ${T}_{delay}$ | Delay time |

SD | Safety distance | $\alpha $ | Acceleration |

${u}_{max}$ | Maximum speed | ${u}_{min}$ | Minimum speed |

${u}_{i}$ | Speed of vehicle i | ${x}_{i}$ | Position of vehicle i |

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**MDPI and ACS Style**

Muna, S.I.; Mukherjee, S.; Namuduri, K.; Compere, M.; Akbas, M.I.; Molnár, P.; Subramanian, R. Air Corridors: Concept, Design, Simulation, and Rules of Engagement. *Sensors* **2021**, *21*, 7536.
https://doi.org/10.3390/s21227536

**AMA Style**

Muna SI, Mukherjee S, Namuduri K, Compere M, Akbas MI, Molnár P, Subramanian R. Air Corridors: Concept, Design, Simulation, and Rules of Engagement. *Sensors*. 2021; 21(22):7536.
https://doi.org/10.3390/s21227536

**Chicago/Turabian Style**

Muna, Sabrina Islam, Srijita Mukherjee, Kamesh Namuduri, Marc Compere, Mustafa Ilhan Akbas, Péter Molnár, and Ravichandran Subramanian. 2021. "Air Corridors: Concept, Design, Simulation, and Rules of Engagement" *Sensors* 21, no. 22: 7536.
https://doi.org/10.3390/s21227536