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Transportation Research Part C

journal homepage: www.elsevier.com/locate/trc

How to assess the capacity of urban airspace: A topologicalapproach using keep-in and keep-out geofence

Jungwoo Cho, Yoonjin Yoon⁎

Department of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea

A R T I C L E I N F O

Keywords:Urban airspace designAirspace capacityGeofenceAlpha shape methodUTM

A B S T R A C T

The anticipated proliferation of small Unmanned Aerial Vehicles (sUAVs) in urban areas hasgarnered greater interest in capacity estimation of the low-altitude airspace. As a first step toassess such capacity, we propose a topological analysis framework to identify free versus usableairspace in a 3D environment filled with abundant geometric elements. To incorporate the un-derlying geospatial complexity as well as vehicle operational requirements, two types of geofence– keep-out and keep-in – are utilized. The keep-out geofence defines a boundary around staticobjects to keep sUAV out. The keep-in geofence is a 3-D sphere to keep a vehicle in. While thekeep-out mainly focuses on public assurance as a mitigation measure against collision andprivacy risk, the keep-in mainly concerns the operational feasibility of a vehicle. Three scenariosof keep-out, keep-in, and dual geofencing were applied and compared in a hypothetical casestudy as well as in the real 3-D environment of Seoul, South Korea. The results show that thekeep-in usability is an upperbound of the keep-out, due to its unique capability to identify cor-ridor segments using the alpha shape method. The dual scenario demonstrated tradeoffs betweentwo types of geofence in a built-up environment, in which the keep-in exhibited more robustbehavior than the keep-out. It is evident that both geofencing methods need to be considered inparallel in urban areas. In addition, decisions on the geofence parameters should be made inaccordance with the geospatial complexity and flight purposes, rather than relying on fixedvalues. The proposed framework is not only capable of evaluating airspace availability in anadaptive and intelligent manner, but also has the potentials to identify departure/arrival loca-tions and design ascent/descent routes.

1. Introduction

The anticipated proliferation of small Unmanned Aerial Vehicles (sUAVs) in urban areas has garnered greater interest in capacityestimation of the low-altitude airspace. Unlike the high-altitude controlled airspace with few obstacles, the low-altitude airspaceneeds to take into account the geospatial complexity derived from geometric variability of existing static obstacles such as buildingsand terrain. Currently, several states have imposed sUAV operational restrictions based on proximity to population and man-madestructures. In Table 1, the UAV flight restrictions of eight countries are summarized: Australia, Canada, Hong Kong, Japan, Singapore,South Korea, the United Kingdom, and the United States. Restrictions generally include (a) flight purpose and the UAV weightcategory, (b) minimum distance from people, (c) minimum distance from a building or structure, and (d) altitude limit. Where

https://doi.org/10.1016/j.trc.2018.05.001Received 20 November 2017; Received in revised form 18 April 2018; Accepted 1 May 2018

⁎ Corresponding author at: Applied Engineering B/D (W1-2), KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea.E-mail address: yoonjin@kaist.ac.kr (Y. Yoon).

Transportation Research Part C 92 (2018) 137–149

Available online 08 May 20180968-090X/ © 2018 Elsevier Ltd. All rights reserved.

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J. Cho, Y. Yoon Transportation Research Part C 92 (2018) 137–149

138

specified, the minimum keep-out distance from existing infrastructure and people ranges between 30 and 150m.Such conservative and uniform flight restrictions can severely limit sUAV operations, especially in a densely built-up area.1 A

more adaptive and intelligent approach is necessary to identify airspace that is not only free of obstacles but also usable or operablewithin an acceptable level of risk (JARUS, 2017; Barr et al., 2017). When it comes to urban UAV operations in the low-altitudeairspace, there are two notable recent studies to consider: the Metropolis project (Schneider et al., 2014; Sunil et al., 2015, 2016a,2016b; Hoekstra et al., 2016; Vidosavljevic et al., 2015) and Singapore’s Traffic Management of UAS (TM-UAS) program (Low et al.,2016; Salleh and Low, 2017; Salleh et al., 2018). In the Metropolis project, four airspace designs were proposed and simulated in theurban airspace of Paris, France. The simplest design assumed no structure, whereas the most complex scenario was based on a pre-defined 4D tube structure. The operational requirement with a minimum cruising altitude of 300 ft AGL and 100 ft above the tallestbuilding created airspace free of static obstacles. Such an assumption of obstacle-free airspace fails to examine the usability of lowerairspace populated with abundant ground structures of various heights. The TM-UAS program proposed a structured airspace designto incorporate not only ground structures such as buildings and trees but also the state’s stringent altitude restriction of 60m AMSL.TM-UAS adopted a static waypoint concept, where waypoints are selected based on various geospatial elements, including groundroad network, building rooftops, Mass Rapid Transit (MRT) tracks, traffic and light poles, and canals and drainage system. Althoughboth studies provided crucial insights in concretizing the operational concepts of urban UAV operations, systematic assessments ofthe airspace capacity based on various geospatial complexities must be researched in parallel.

Recently, several studies explored and researched geofence with focus on its applications in UAS Traffic Management (UTM)(Atkins, 2014; Hayhurst et al., 2015; Dill et al., 2016; D’Souza et al., 2016; Kopardekar et al., 2016; Johnson et al., 2017b, 2017a).Geofence is a widely used concept to ensure safe separation of UAVs. Geofence is categorized into two types based on its purpose –keep-out and keep-in. The more common keep-out geofence is mainly used to define a protection boundary that a vehicle should notintrude (Hayhurst et al., 2015; Dill et al., 2016). As presented in Table 1, the majority of states and regulatory bodies have adoptedthe keep-out geofence to define and create a safety buffer around existing structures. Although a simple concept, the extent of keep-out geofence is a subject of further research (D’Souza et al., 2016; Transport Canada, 2017b). The keep-in geofence is a similarconcept with the Containment Limit (CL) of jet aircraft, which is defined based on the Total System Error (TSE). TSE may includevarious types of errors related to path steering, position estimation, or path definition (ICAO, 2010). With respect to sUAV, there areno established rules to define such CL, even though the necessity is evident.

One of the main subjects of recent studies with specific focus on geofence is the application of keep-in geofence to individualflight, incorporating vehicle dynamics and detect-and-avoid performance characteristics. In NASA UTM TCL2 flight test, geofencewas modeled as three boundary layers separated by a predefined distance (Johnson et al., 2017a). Given the first layer comprising theintended operation area, the second and the third layer were constructed at a distance 40 ft horizontally and 15 ft vertically, and100 ft horizontally and 35 ft vertically from the first layer, respectively. The distance values were set conservatively to initiate alertswhen a vehicle breaches the boundaries. The flight test result showed that 46% of the flights left the intended operation area and thatlateral deviation reached farther than 100 ft in 33% of geofence violation cases. NASA’s Safeguard system also adopted three layers ofgeofence boundaries for both keep-in and keep-out geofencing – warning boundary, soft boundary, and hard boundary (Hayhurstet al., 2015; Dill et al., 2016). The hard boundary is the geospatial region that UAVs should be kept in. Once the hard boundary isobtained, the system constructs a soft and a warning boundary at distance ε and ρε (ρ > 1) from the hard boundary. The computationof ε is based on velocity, vehicle dynamics parameters such as the mass, size of wings, and lift-to-drag ratio, and wind condition.D’Souza et al. (2016) adopted an aerodynamic approach to calculate the lateral and vertical boundary of geofence based on a vehicledynamics model and self-stabilizing PID controller. A simulation study was conducted to calculate flight deviations incorporatingwind disturbances near buildings. Assuming a 1-s control time for self-stabilization, the geofence size was reduced to 5m horizontallyand vertically, which is much smaller than the 30-m used in the earlier NASA UTM flight tests. More recently, Johnson et al. (2017b)conducted a simulation study to investigate the detect-and-avoid behavior of UAVs in narrow air corridors between buildings.Assuming various sizes of buffer space, 10 ft, 15 ft, and 20 ft, around buildings and a well-clear volume assigned to each vehicle, thestudy measured the intrusion frequency to the buffer. It was found that large building buffers reduce the likelihood of collisions withbuildings, but if the corridor is too narrow, the detect-and-avoid algorithm caused UAVs to fly into buildings to avoid traffic.

Note that there is a clear distinction between free or open airspace and its capacity. In the Air Traffic Management, airspacecapacity estimation has been well researched and continuously improved (EUROCONTROL, 1999; Majumdar et al., 2002; Wankeet al., 2005; Song et al., 2008; Krozel et al., 2007). However, one of the fundamental differences in the lower urban airspace lies inthat the airspace is not completely free of static obstacles as in the conventional, controlled higher-altitude airspace.

In this paper, we propose to apply two types of the geofencing method in combination, to identify usable airspace as a first step toassess the airspace capacity. The main objective is to analyze the urban airspace by incorporating vehicle operational requirements(keep-in) as well as providing an adequate level of protection in the surrounding environments (keep-out) at the same time. Theconcepts, methods, and numerical analyses are presented and discussed in a hypothetical case as well as using a real 3-D geospatialdataset of the Gangnam area of Seoul, South Korea. The rest of the paper is organized as follows. Section 2 contains terminologydefinitions and methodological details of the proposed framework. A hypothetical case study is presented and discussed in Section 3,and the case study results for the actual urban environment are presented in Section 4. Section 5 provides conclusions and futurestudy ideas.

1 Built-up area is defined as any group of structures such as houses, factories, service stations, grain elevators, apartment buildings, or other man-made structuresthat could interfere with UAV operations (Transport Canada, 2017b).

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2. Methodology

2.1. Terminology and geofence specifications

We first define several terms to represent the airspace availability. Free airspace is an airspace that is free of static obstacles, whichrepresents the raw availability. Free airspace is further classified into usable and unusable airspace. Airspace is unusable if it is affectedby geofence and closed for operational use. The rest of free airspace is a usable airspace, which represents the airspace that is not onlyfree of static obstacles but also unaffected by geofence.

A keep-out geofence defines and creates a buffer space of fixed magnitude around ground structures. In this study, the keep-outgeofence is modeled as a uniform space around the surface of static obstacles. A keep-in geofence is defined as a spherical ball tocontain a vehicle, which is modeled as α-ball in the alpha shape method. The idea of an alpha shape was first proposed byEdelsbrunner as an attempt to reconstruct the shape of a finite point set using spherical disks, or α-ball (Edelsbrunner et al., 1983).Edelsbrunner’s eraser analogy intuitively explains the construction of an alpha shape, as illustrated in Fig. 1. Assume a 2-D spacecontaining a set of points S. Suppose there is an eraser that can remove any circular area of radius α > 0. If the eraser removes allthe points not in S without touching any point in S, the resulting shape will consist of the set of arc-shaped boundaries thatencloses S. The alpha shape of S is then obtained by replacing the arcs with straight lines. Note that the shapes derived from apoint set vary upon the radius of the eraser or α-ball. The mathematical definition is based on the concept of α-ball and p-simplex(Edelsbrunner and Mücke, 1994; Edelsbrunner et al., 2000; Edelsbrunner, 2010). Given a set of points S, suppose that u is an openball, or α-ball, of radius α, where u is called empty if ∩ =u S ϕ. For any subset T of S with cardinality p+1 (p=0, 1, 2, 3), p-simplex is geometrically interpreted as the convex hull of T denoted as σT . σT is called α-exposed if there exists an empty open ballu satisfying ∂ ∩ =u S T , where ∂u is the surface of u. The set of α-exposed p-simplices is referred as the alpha shape given filtrationradius r .

In our framework, the α-ball represents the keep-in geofence of size r , or the containment limit of a vehicle. Once we determinewhether each cell is occupied by static objects or not, the alpha shape method is applied to the set of center points of occupied/closedcells to generate edges between pairs of the cells given α-ball of size r . The result is closing any free airspace that a vehicle of keep-inrequirement larger than r should not penetrate. To further illustrate the effect of keep-out buffer and alpha shape method on airspaceusability, consider a 2-D Cartesian grid with unit size of l0 in Fig. 2. Now, consider a keep-out and keep-in geofence of identical size ofl20 . Application of the keep-out geofence will close the entire free airspace, resulting in availability of near zero. On the other hand,

applying the keep-in geofence will close none of the free airspace, since α-ball of radius l20 can fit in the open corridor spaces.

2.2. 3-D airspace availability assessment framework

A block diagram of the proposed framework is shown in Fig. 3. In the first step, 3-D map data is discretized into a Cartesian grid.Discretization provides modeling and computational efficiency in processing the 3-D information without losing the shape in-formation in the raw dataset. Let = ⩽ ⩽ ⩽ ⩽ ⩽ ⩽Γ g l N m N n N{ : 1 ,1 ,1 }lmn x y z be the Cartesian grid with a size of × ×N N Nx y z,which is the discretized 3-D lattice of the region of interest with a unit cube of size ∊. When a grid is blocked by static obstacles, wecall it occupied. Likewise, when a grid becomes unavailable due to geofence, we call it closed. Now, let us define three subsets of Γ asfollows: =Γo { ∈g Γ g:lmn lmn is occupied by static obstacles}, = ∈Γ g Γ{ :out

δlmn glmn is closed by keep-out geofence of size δ} and

=Γinr { ∈g Γ g:lmn lmn is closed by alpha shapes of radius r}. Given the availability of cell glmn defined as an indicator function

Fig. 1. (a) Alpha shape of point set with α-ball (Sun et al., 2016); (b) Construction of alpha shapes with increasing filtration radius in 2-D.

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= ⎧⎨⎩

∈ ∪ ∪cell g δ r g Γ Γ Γotherwise

( ; , ) 0,1,lmn

lmn o outδ

inr, the usability of airspace at altitude h is defined as =

∑

×⩽ ⩽ ⩽ ⩽( )

U h δ r( ; , ): .cell g δ r

N N

( ; , )l Nx m Ny lmn

x y

1 ,1

Lastly, we define loss ratio = −ρ h δ r( ; , ): 1 ,U h δ rU h

( ; , )( ;0,0) which is the amount of unusable airspace given geofence size of δ and r at altitude h,

divided by the amount of free airspace.One of the main advantages of the proposed framework is its capability to model both keep-out and keep-in geofence at the same

time. In Fig. 4, an illustrative example of 9×5 2-D Cartesian grid is presented, in which the cells are color-coded according to theirusability. Black cells are occupied by static obstacles, grey cells are closed by the keep-out geofence of size δ, and orange cells are closedby alpha shapes of size r . The amount of free airspace is =U (·;0,0) ,33

45 which reduces to =U δ(·; ,0) 545 when the keep-out is applied.

When the keep-in is further considered, the usability reduces to =U δ r(·; , ) 045 .

Fig. 2. Illustration of the effect of keep-out versus keep-in geofence on airspace usability.

Fig. 3. Block diagram of the proposed framework.

Fig. 4. Illustration of the effect of dual geofencing on airspace usability.

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Fig. 5. Airspace usability curves of two contrasting geospatial distributions.

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3. Hypothetical case study of contrasting geospatial distribution

Given a 2-D Cartesian grid with a size of 10 by 10, suppose that 16 out of 100 cells are occupied and 84 cells are free of obstacles.In the hypothetical case study, we consider two grid configurations with contrasting geometry as presented in Fig. 5. Grid A has asingle blockage concentrated at the center, while grid B has blockage equally distributed at four corners. The raw availability is 84%in both cases before geofencing. Three geofencing scenarios–keep-out only; keep-in only; and dual geofencing–were applied. Thecorresponding plots of U δ r(·; , ) are shown in Fig. 5.

The ‘keep-out only’ scenario shows the identical usability in both grid A and grid B, which is intuitive since the method is designedto create a buffer space around the static obstacles. The ‘keep-in only’ scenario shows a more interesting outcome. While grid A isimmune to changes in r , U r(·;0, ) curves of grid B exhibits a gradual reduction with increasing r . Considering the contrastinggeospatial distribution of two grids, our results demonstrate the unique capability of alpha shape method to capture the corridoreffect. In other words, the alpha shape method identifies open corridors that can accommodate flights with the spherical containmentlimit of size r , among the occupied and closed cells. Such a difference between two geofencing methods also results in the keep-inusability being an upperbound to the keep-out. In the dual geofence scenario, an overall reduction inU δ r(·; , ) is more severe in B thanin A due to the combined effect. Contours of grid B also indicate that usability is more sensitive to changes in δ than r , whichcorresponds to our earlier finding of the keep-in usability being an upperbound of the keep-out.

In a real environment, grid A can be considered as a simplification of an airspace intruded by a single structure such as a mountainor a hill, but free of obstacles otherwise. Grid B can be considered as a simplification of an urban airspace with abundant corridorsamong closely located geometric elements. Findings from the single application scenarios provide several critical insights of uniqueproperties of two geofencing methods. The keep-out geofence is mainly concerned with protecting ground structures from sUAVintrusion, and treats each structure individually without considering the geospatial complexity of surrounding environment. On theother hand, the alpha shape method is capable of identifying corridors among ground structures that can safely accommodate flightswith a certain keep-in requirement. In the dual application scenario, we found that tradeoffs between the keep-out and the keep-inare much more evident in the urban-like configuration of grid B than A.

In summary, it is imperative to measure and assess tradeoffs between safety protection and operational capacity in an urbanenvironment, and the proposed framework provides such capabilities by considering both geofencing methods simultaneously. Notethat our method can also be applied to the vertical airspace assessment, which will be useful to determine the operational feasibility ofvarious phases of flight. For example, the keep-in method can be used to identify the minimum altitude of usable vertical corridorsections, to specify origin/departure locations as well as to design ascending/descending routes.

4. Case study of the Gangnam district in Seoul, South Korea

A case study of a real 3-D urban area was conducted in the 3 km by 3 km area of the Gangnam district in Seoul, South Korea. The9 km2 area is in the heart of the Gangnam district, which is the busiest and most built-up area in metropolitan Seoul. Airspace below150m AMSL was discretized into a three-dimensional regular grid of 5m, resulting in a 600×600×30 Cartesian grid. Fig. 6 shows (a)the aerial map and (b) the height distribution of ground structures.

The area is a typical example of mixed-use development, being populated with various commercial and residential buildings aswell as several open park areas. The majority of the highest buildings are located along the major road sections with 6–8 lanes, whichcreated several long and wide corridors in (b). In the case study, U h δ r( ; , ) was analyzed for ⩽ ⩽δ r0 , 50 in 5-m increments, or a totalof 121 parameter combinations. The three scenarios used in the hypothetical case study were applied to the case study: keep-outgeofence only, keep-in geofence only, and dual geofence. The results are presented and discussed in the following two sections.

Fig. 6. (a) Aerial image of the study area; (b) Height distribution of ground structures.

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4.1. Individual effect of keep-out and keep-in geofence

In this section, we present and discuss the individual effect of keep-out and keep-in geofence on U h δ r( ; , ). Fig. 7 shows the resultsof the ‘keep-out only’ scenario with δ =20 and ‘keep-in only’ scenario with r =20, at altitudes h =40 and 70. At h =40, themajority of the area is occupied with static obstacles, colored in black on the map, and each geofencing scenario produced

=U (40;20,0) 6.8% and =U (40;0,20) 20.7%, respectively. Such a large difference originated from the long and wide corridor segments,as one can observe by inspecting U (40;20,0) and U (40;0,20) figures in juxtaposition. The alpha shape method identified a set ofcorridor segments that can accommodate vehicles with minimum separation of 20m or less in this lower altitude area. When h =70,the overall usability improves significantly in either scenario, yielding =U (70;20,0) 45.2% and =U (70;0,20) 68.3%. However, thekeep-out scenario generated open spaces that are spread out in silos, while the keep-in scenario preserved several corridors con-necting the open segments. Note that such observations are consistent with our findings in the hypothetical case, and the results fromthe Seoul case study prove the benefit of using alpha shape method in a highly built-up environment.

In Fig. 8, the curves of U h δ r( ; , ) are shown with respect to altitude when ⩽ ⩽δ r0 , 50. The topmost solid curves are the rawavailability with no geofencing, orU h( ;0,0). Overall, the effect of geofencing was most restrictive in the lower altitude, roughly when

⩽h 40, and the airspace gain followed the rate of increase of U h( ;0,0) afterwards. The keep-in curve is the upperbound of the keep-out curve, which coincides with our finding in the hypothetical case. In the keep-out scenario, even the smallest δ of 10 or 20m closedthe majority of free space when ⩽h 40, despite a robust gain in U h( ;0,0). Such an observation not only indicates that the area ispopulated with abundant buildings and other static obstacles, but also implies that those are located in close proximity. In otherwords, buildings located right next to each other had the effect of closing twice the buffer space required for the keep-out. In the keep-in scenario, the lower airspace was less prone to the effect of geofencing as severe as the keep-out scenario, particularly when r wassufficiently small. Moreover, the rate of increase of those small keep-in radii was mostly proportional toU h( ;0,0) curve. Inferring fromour earlier findings in the hypothetical case, we concluded that such a difference is the result of the corridor effect. In other words,there is a reasonable amount of usable airspace even in the lowest airspace, if we exclusively consider the sUAV separation minimum.

Fig. 7. 2D snapshots of the individual effect of keep-out and keep-in geofence of size 20 at altitude 40 and 70m.

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The area between the free and usable airspace availability is the amount of airspace closed by geofencing, and the loss ratiocurves, ρ h δ r( ; , ), are shown in Fig. 9. While the usability curves represent the amount of usable airspace with respect to the entire areaof interest, the loss ratio curves represent the proportion of unusable airspace in the free airspace. Note that the keep-in curve is thelowerbound of the keep-out curve in this case.

The loss curves in both scenarios were nearly flat at lower altitudes around ⩽h 40 and then tilted downward. The flat portion isan indication that the amount of airspace closed by geofencing increases proportionally to the amount of free airspace. In addition,the difference in loss between the two scenarios was significant at the lower altitude, showing more than 100% difference in somecases. For instance, nearly 65% of free airspace was closed when δ =10, while approximately 30% was closed when r =10 and

⩽h 40. Such findings correspond to the underlying geospatial distribution shown in Fig. 6. The shorter span of the flat portion in thekeep-in loss curves also confirms that most of the open space at the lower altitude is in fact corridors among closely located geometricelements.

4.2. Dual effect of keep-out and keep-in geofence

This section presents the results of the dual application of both geofencing methods. Since the increase in U h δ r( ; , ) was insig-nificant in the single application scenarios when h⩽40, we focus on altitude between 40 and 120m in the dual scenario. In Fig. 10,sample aerial images of U (40;10,10) and U (70;10,10) are shown. In Fig. 11(a), the dual effect of δ and r on U h δ r( ; , ) is shown in a 3-Dcontour plot for ⩽ ⩽δ r0 , 50 and ⩽ ⩽h40 120. As anticipated, altitude is the main determinant of overall usability. For instance,

Fig. 8. Airspace usability curves of keep-out only and keep-in only scenarios.

Fig. 9. Airspace loss ratio curves of keep-out only and keep-in only scenarios.

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Fig. 10. 2D snapshots of the dual effect of keep-out and keep-in geofence of size 10 at altitude of 40 and 70m.

Fig. 11. 3-D contour plot of airspace usability by the dual application of keep-out and keep-in geofence.

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h=40 yieldsU h δ r( ; , ) of 40% or less in most parameter combinations, whereas h=70 and 100 result inU h δ r( ; , ) larger than 30% and70%, respectively. Reduction in the usable airspace is much greater in the lower altitude, while the effect of geofence becomesminimal at an altitude of 100m or higher. Another interpretation of such observations is that the area is nearly free of obstacles above100m.

In Fig. 11(b), (c), (d), three contour slices of h =40, 70, 100 are shown. In each 2-D contour plot, parameter combinations on thesame contour are associated with the same airspace usability. For example, =δ r( , ) (15,8) and(5,33) produce the identical usability of50% at altitude 70m. The case of δ =15 and r =8 requires a keep-out geofence of size 15m and a keep-in radius of 8m or less, whileδ =5 and r =33 requires a keep-out distance of 5m and a keep-in radius of 33m or less. In the contour plot, we also observe that theinfluence of two parameters is not symmetric, as the overall usability is more sensitive to changes in δ than r . In other words, thekeep-in parameter r shows a more robust behavior than the keep-out parameter δ . Even though = =U U(70;15,8) (70;5,33) 50%,reducing δ from 15 to 5m increases the amount of usable airspace by 17% given r =8. On the other hand, increasing r from 8 to 33mreduces the amount of usable airspace by 8% given δ =15.

Although larger δ might seem like a simple solution for enhanced safety, our results show that it comes at a cost of greatlyreducing usable airspace that can safely accommodate vehicles of various containment limits. In addition, we also observe thatthe contours are more tilted toward r at higher altitudes of h =100. Such shapes indicate that the area becomes more sensitive tochanges δ than r in the higher airspace with fewer corridors, as we have observed in the hypothetical case. One important caveat ofsuch findings is that they are not universal, and is relevant in the context of the area under consideration. The 3-D contour plotpresented in Fig. 11 may serve as a guidance to find the set of geofence parameter combinations to achieve a desired level of usability,and to evaluate the operational feasibility based on tradeoffs between δ and r .

5. Conclusions and future study

In this study, we proposed an airspace availability assessment framework that effectively identifies usable airspace in a highlybuilt-up urban environment. By incorporating both keep-out and keep-in geofence, our approach not only captures the inherentbenefits of the individual geofencing methods but also measures tradeoffs between them. In the hypothetical case of two contrastinggeometries, we found that the keep-out method was unable to distinguish the geospatial differences between two contrasting geo-metric configurations, while the keep-in method successfully identified the corridor sections. A case study of the Gangnam district inSeoul, South Korea provided further insights into the nature of geofencing outcomes in a real 3-D environment. The keep-out geo-fence mainly focuses on protecting the static ground structures, while the keep-in geofence mainly concerns the vehicle operationalfeasibility. The keep-out geofence is simple to apply and can mitigate risks of undesirable consequences on people and infrastructureswith UAV intrusions. The keep-in geofence is more adaptive and can deliver the maximum amount of usable airspace even in aseverely restricted airspace.

The proposed framework successfully demonstrated the ability to analyze the dual effect of geofence combinations in the hy-pothetical and Seoul case studies. The overall usability was more sensitive to keep-out parameter changes than keep-in, whichsuggests that the current approach relying on the conservative keep-out measure needs further evaluation for effective urban sUAVoperations. Although findings from both case studies strongly suggest that the keep-in geofence can deliver the maximum systemcapacity, it is far from the reality to conclude that it should be the sole determinant of airspace availability and usability (JARUS,2017; Barr et al., 2017; Belcastro et al., 2017). Tradeoffs between two geofencing methods need to be evaluated thoroughly con-sidering various geofencing parameter combinations, and decisions on the minimum operational requirements need to be tailor-madeto the nature of the area of interest and flight purposes.

One of the possible limitations of the proposed framework is that its immediate applicability in practical settings. If someone seeksa single threshold of geofence parameter that can apply to all cases of urban sUAV flight operations, it can either be prone to conflictsor severely restrict the amount of usable airspace and vehicle choice. In addition, the fundamental challenge of urban airspace lies inthe diverse geospatial complexity. Although one can identify usable airspace in a variety of geospatial dataset for a variety ofgeofence parameters using our framework, the decisions on the final set of flight restriction rules require further research efforts.

In addition to evaluating the airspace usability, our approach generates a crucial dataset to model geospatial continuity in 3-D.Identifying the continuity of open segments will be necessary for structured urban airspace design and path planning. In the future,we plan to apply various topological analysis techniques, including topological data analysis (Carlsson, 2009) and medial axisanalysis (Jain, 1989; Maurer et al., 2003) to model such continuity of usable airspace.

Data statement

The 3-D spatial information of buildings, man-made structures, and terrain used in this study is restricted-use data and is availableupon request to SPACEN of Republic of Korea (spacen@space.or.kr).

Acknowledgement

This research was supported in part by Ministry of Land, Infrastructure and Transport of Korean government under Grant18USTR-B127901-02.

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Glossary

Acronym: Full MeaningAC: Advisory CircularAGL: Above Ground LevelAMSL: Above Mean Sea LevelCFR: Code of Federal RegulationCL: Containment LimitICAO: International Civil Aviation OrganizationJARUS: Joint Authorities for Rulemaking on Unmanned SystemssUAVs: small Unmanned Aerial VehiclesTCL2: Technology Capability Level 2TM-UAS: Traffic Management of UASTSE: Total System ErrorUAS: Unmanned Aerial SystemsUTM: UAS Traffic Management

Terminology

Term: Definitionfree airspace: airspace that is free of static obstaclesusable airspace: airspace that is not only free of static obstacles but also not affected by geofencing protectionunusable airspace: airspace is unusable if it is affected by geofence and closed for operational useclosed: a cell is closed if it becomes unavailable due to geofenceoccupied: a cell is occupied if it is blocked by static obstaclescell availability: a cell is available if it is neither occupied nor closedairspace usability: the amount to which airspace is usableloss ratio: the amount of unusable airspace divided by the amount of free airspace

Symbols and nomenclature

Γ: a set of gridsN N N, ,x y z : the size of a grid space in each dimensionglmn: grid∊: a unit size of gridδ: keep-out geofence parameterr : keep-in geofence parameterΓo: a set of glmn occupied by static obstaclesΓout

δ : a set of glmn closed by keep-out geofence of size δΓin

r : a set of glmn closed by alpha shapes of radius rcell g δ r( ; , )lmn : the availability of cell when the keep-out geofence of δ and the keep-in geofence of r are appliedU h δ r( ; , ): the usability of airspace at altitude h when the keep-out geofence of δ and the keep-in geofence of r are appliedρ h δ r( ; , ): the amount of unusable airspace given geofence size of δ and r at altitude h, divided by the amount of free airspace

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