# Environment for Planning Unmanned Aerial Vehicles Operations

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

_{P}, if N

_{P}is the number of primitives used. For a given trajectory, the corridor swept on the ground by either the lethal area (for the deterministic approach) or the statistical impact footprint (for the statistical approach) is identified and a measure of risk is obtained, which depends on vehicle reliability and population density inside the corridor, which may vary along the trajectory. Given the limited number of variables necessary for describing the whole trajectory, this approach lends itself to be used within an optimization procedure, for the design of mission trajectories with an acceptable risk level [17].

## 2. UAV Flight Planning Scenario

- Data of the vehicle(s) involved;
- Data of the operation(s) to be performed;
- Data of the environment where the operation(s) will be performed.

## 3. Routes Calculation and Optimization: The Risk Assessment Methodology

#### 3.1. Motion Primitives and Trajectory Discretization

_{P}motion primitive elements (arcs or segments), each element is univocally defined by the three kinematic variables plus a fourth parameter, either a time interval Δt or arc-length Δs counted along the trajectory, which determines its size. A total of four N

_{P}+ four parameters is thus sufficient for identifying the whole trajectory, where the four additional parameters are represented by three coordinates of the starting point and an initial value for the course angle.

#### 3.2. Trajectory Feasibility

- (1)
- geometrically feasible if it does not interfere with obstacles and terrain;
- (2)
- dynamically feasible if every motion primitive can be flown by the vehicle without violating aerodynamic, structural or propulsion performance limits.

- (a)
- minimum altitude above the ground is greater than a prescribed clearance, which accounts for most of the obstacles (such as buildings, trees);
- (b)
- distance from high obstacles (communication towers, power lines, isolated trees) is greater than a prescribed safety threshold;
- (c)
- minimum distance from waypoints that need to be flown over during the mission is below a prescribed accuracy threshold.

- (a)
- power required for flying the trajectory arc, P
_{r}, is smaller than the maximum available power, P_{r}≤ η_{P}× P_{max}, where η_{P}is propeller efficiency and P_{max}is the maximum power delivered by the engine; - (b)
- the wing lift coefficient C
_{L}is sufficiently far from stall, C_{L}≤ C_{L}_{max}; - (c)
- the normal load factor n
_{z}required in turning motion primitives is smaller than the maximum structural design maximum load factor, n_{z}≤ n_{z}_{,max}.

- n
_{z}= cosγ ≈ 1 in straight flight; - n
_{z}= 1 + (Ω × V/g)^{2}in turning flight.

_{z}is known, lift coefficient and required power are equal to [34]

- C
_{L}= n_{z}× W/(½ρ × V^{3}× S) - P
_{r}= ½ρ × V^{3}× S × C_{D}+ W × V × sinγ

_{D}= C

_{D}

_{0}+ KC

_{L}

^{2}, far from stall. All the inequality constraints at points (a), (b) and (c) can thus be easily evaluated from the three parameters of each trajectory arc (namely V, γ, and Ω) and vehicle characteristics (engine, aerodynamic and structural load limits, P

_{max}, C

_{L}

_{max}, and n

_{z,}

_{max}, vehicle weight W, and wing area S, aerodynamic drag coefficients C

_{D}

_{0}and K, propeller efficiency, η

_{P}). A trajectory is dynamically feasible if all the inequality constraints are satisfied for all primitive arcs along the considered trajectory. The transition from one primitive to the following one is not considered in the analysis.

#### 3.3. Risk Evaluation

_{L}of the lethal area depends on vehicle size (e.g., wing span b), kinetic energy (T = ½ × (W/g) × V

_{i}

^{2}) and glide angle (γ

_{i}) at impact. Its position with respect to that of the vehicle at the time of catastrophic failure t

_{cf}depends on vehicle velocity V, course angle χ and altitude h at time t

_{cf}. The impact point is assumed to lie at the end of a parabolic fall trajectory. When population density ρ

_{P}is uniform in the area of operations, the risk R is given by

_{F}× p

_{I}× A

_{L}× ρ

_{P}

_{F}is the probability of a failure during vehicle operations and p

_{I}is the probability that vehicle impact inside the lethal area results into casualties and/or serious injuries.

_{e}) multiplied by the population density in that point and the total area spanned by the lethal area, that is, the area inside the risk corridor. Exposed time is evaluated for various shapes of the feasible motion primitives, but it mainly depends on vehicle airspeed, being roughly inversely proportional to V. Exposed time is constant along a rectilinear motion primitive. Although some variations of exposed time are present across the corridor width, for curved trajectory elements, it is possible to assume an approximately constant value of t

_{e}also in the transverse direction, with minor errors, which barely affect the results when evaluating the total risk.

_{L}are lethal (that is, p

_{I}= 1), the total risk along the whole trajectory can be estimated as

_{k}and ρ

_{k}are the surface of the risk corridor and population density inside the k-th grid element, respectively, t

_{e,k}is the exposed time for points inside S

_{k}, and t

_{M}is the total mission time.

_{F}, multiplies the whole expression of risk. Vehicle reliability thus plays a decisive role: risk being proportional to the probability of a catastrophic failure that results in a total loss of control of the vehicle. A conservative risk estimate is derived assuming that failure occurs during the mission. If the total risk of providing damage to third parties is below an acceptable threshold, the actual risk is much lower. At the same time, if the risk is above the acceptable limit, whichever the trajectory, the factor required to bring risk below the threshold is inversely proportional to the number of missions that need to be flown without failure. This provides a requirement for vehicle reliability in terms of time-between-failures.

_{x}and σ

_{y}of the distance of impact points with respect to the nominal one in the along- and cross-track directions, respectively. The σ, 2-σ, and 3-σ ellipses respectively encompass 39.4%, 86.5% and 99% of total impact points. Three risk corridors are determined in a way similar to that derived for the lethal area, where an additional factor weights the total risk inside each corridor, which becomes proportional to the fraction of impact points inside the considered ellipse, but outside the inner one(s).

## 4. The FLIP Environment

## 5. Test and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**FLIP dashboards: (

**a**) Map view, (

**b**) orthophoto view, (

**c**) obstacles view, (

**d**) population density view, (

**e**) Isolevel curves view.

Data of the Vehicles | Data of the Operation | Data of the Environment |
---|---|---|

Reliability | Start point | Orthophoto |

Aerodynamic characteristics | End point | Orography |

Structural performance limits | Waypoints | Obstacles |

Propulsion performance limits | Schedule | Population density |

Parameter | Symbol | Value | Units |
---|---|---|---|

Takeoff weight (max.) | W | 21.5 | kg |

Wing span | b | 3.3 | m |

Wing area | S | 0.79 | m^{2} |

Max. propulsion power | P_{s}_{,max} | 2700 | W |

Max. lift coefficient (clean) | C_{L}_{max} | 1.3 | |

Max. lift coefficient (with flap) | C_{L}_{max} | 1.7 | |

Drag polar coefficients (estimated from performance data) | C_{D}_{0} | 0.05 | |

K | 0.03 |

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**MDPI and ACS Style**

Pascarelli, C.; Marra, M.; Avanzini, G.; Corallo, A.
Environment for Planning Unmanned Aerial Vehicles Operations. *Aerospace* **2019**, *6*, 51.
https://doi.org/10.3390/aerospace6050051

**AMA Style**

Pascarelli C, Marra M, Avanzini G, Corallo A.
Environment for Planning Unmanned Aerial Vehicles Operations. *Aerospace*. 2019; 6(5):51.
https://doi.org/10.3390/aerospace6050051

**Chicago/Turabian Style**

Pascarelli, Claudio, Manuela Marra, Giulio Avanzini, and Angelo Corallo.
2019. "Environment for Planning Unmanned Aerial Vehicles Operations" *Aerospace* 6, no. 5: 51.
https://doi.org/10.3390/aerospace6050051