Figure 1.
UAS airspace geofencing examples. The left figure shows a keep-out geofence (red) around One World Trade Center in New York City. A transiting UAS keeps clear of this geofence with a path wrapped by a trajectory or keep-in geofence (yellow). The right figure shows a wind turbine being inspected by a small UAS. During inspection, the usual wind turbine keep-out geofence (red) is expanded as depicted in green to also enclose the inspection UAS. Any other nearby UAS will keep clear of this expanded keep-out geofence (green) during inspection activities. This geofence design assures separation between the two illustrated UAS.
Figure 1.
UAS airspace geofencing examples. The left figure shows a keep-out geofence (red) around One World Trade Center in New York City. A transiting UAS keeps clear of this geofence with a path wrapped by a trajectory or keep-in geofence (yellow). The right figure shows a wind turbine being inspected by a small UAS. During inspection, the usual wind turbine keep-out geofence (red) is expanded as depicted in green to also enclose the inspection UAS. Any other nearby UAS will keep clear of this expanded keep-out geofence (green) during inspection activities. This geofence design assures separation between the two illustrated UAS.
Figure 2.
Airspace and environment geofencing functionality and data flow.
Figure 2.
Airspace and environment geofencing functionality and data flow.
Figure 3.
Example application of Algorithm 1. A sample 3-D flight path is shown on the left. A corresponding flight trajectory keep-in geofence is shown on the right.
Figure 3.
Example application of Algorithm 1. A sample 3-D flight path is shown on the left. A corresponding flight trajectory keep-in geofence is shown on the right.
Figure 4.
Example of reducing number of vertices to simplify the associated visibility graph. The left illustration shows three original polygons. The right illustration shows the polygons after applying the vertex downsampling algorithm. and are 15 and 60%, respectively. The time complexity of visibility graph generation is , where n is the total number of vertices in all polygons. The number of vertices in the lower polygon illustrated here is reduced from 15 to 9.
Figure 4.
Example of reducing number of vertices to simplify the associated visibility graph. The left illustration shows three original polygons. The right illustration shows the polygons after applying the vertex downsampling algorithm. and are 15 and 60%, respectively. The time complexity of visibility graph generation is , where n is the total number of vertices in all polygons. The number of vertices in the lower polygon illustrated here is reduced from 15 to 9.
Figure 5.
Illustration of rectangular ROI generation. Start point, destination point, and ROI initial buffer size are used to initialize the rectangular ROI per Algorithm 3.
Figure 5.
Illustration of rectangular ROI generation. Start point, destination point, and ROI initial buffer size are used to initialize the rectangular ROI per Algorithm 3.
Figure 6.
Three candidate flight planning solutions respecting keep-out airspace geofence and obstacle “no-fly” volumes. A turn solution uses a visibility graph to define a constant-altitude path around no-fly zones (left). A cruise altitude solution climbs to an altitude greater than the highest building enroute to the destination (center). The terrain follower defines an altitude profile maintaining minimum safe clearance or greater from no-fly zones (right).
Figure 6.
Three candidate flight planning solutions respecting keep-out airspace geofence and obstacle “no-fly” volumes. A turn solution uses a visibility graph to define a constant-altitude path around no-fly zones (left). A cruise altitude solution climbs to an altitude greater than the highest building enroute to the destination (center). The terrain follower defines an altitude profile maintaining minimum safe clearance or greater from no-fly zones (right).
Figure 7.
Flowchart of post-processing map data. OSM data were converted to a MATLAB format, then processed using polygon set convex hull operators to reduce the number of keep-out geofences in the region of interest (ROI), the area between departure and destination points. If the number of vertices in a geofence is greater than threshold , it is downsampled to . and are user-defined parameters set to 15 and 60%, respectively, in this work. Algorithms 2 and 3 are used in finding ROI and reducing number of map vertices. Three-dimensional keep-out geofences around buildings are generated with safety buffer .
Figure 7.
Flowchart of post-processing map data. OSM data were converted to a MATLAB format, then processed using polygon set convex hull operators to reduce the number of keep-out geofences in the region of interest (ROI), the area between departure and destination points. If the number of vertices in a geofence is greater than threshold , it is downsampled to . and are user-defined parameters set to 15 and 60%, respectively, in this work. Algorithms 2 and 3 are used in finding ROI and reducing number of map vertices. Three-dimensional keep-out geofences around buildings are generated with safety buffer .
Figure 8.
Post-processing map data for southern Manhattan. Buildings with heights greater than 20 m are shown. The rightmost plot shows keep-out geofences enclosing building clusters (black solid lines), individual building keep-out geofences (black dashed lines), and building outlines (colored lines). Geofence maps for 60 m, 122 m, and 400 m altitude cross-sections are constructed in the same manner.
Figure 8.
Post-processing map data for southern Manhattan. Buildings with heights greater than 20 m are shown. The rightmost plot shows keep-out geofences enclosing building clusters (black solid lines), individual building keep-out geofences (black dashed lines), and building outlines (colored lines). Geofence maps for 60 m, 122 m, and 400 m altitude cross-sections are constructed in the same manner.
Figure 9.
Post-processed georeferenced data for the One World Trade Center building in Manhattan. The top left and right show raw OSM data side and top views, respectively. The bottom left and right show post-processed keep-out geofence data (shaded in green) side and top views, respectively.
Figure 9.
Post-processed georeferenced data for the One World Trade Center building in Manhattan. The top left and right show raw OSM data side and top views, respectively. The bottom left and right show post-processed keep-out geofence data (shaded in green) side and top views, respectively.
Figure 10.
Keep-out geofence polygon extraction for UAS flight planning. The initial ROI (green dashed line) is a rectangular box per
Figure 5. Keep-out geofences (solid black lines) inside or intersecting the rectangular ROI box are found using polygon intersection and point-in-polygon operations. The final ROI (red dashed line) is the convex hull around these keep-out geofences. For our simulation,
m.
Figure 10.
Keep-out geofence polygon extraction for UAS flight planning. The initial ROI (green dashed line) is a rectangular box per
Figure 5. Keep-out geofences (solid black lines) inside or intersecting the rectangular ROI box are found using polygon intersection and point-in-polygon operations. The final ROI (red dashed line) is the convex hull around these keep-out geofences. For our simulation,
m.
Figure 11.
Flow chart of pathfinding logic for different start and end locations. In the chart, V.G. abbreviates visibility graph, and is the height of a geofence around a cluster of buildings. If the departure/destination is not inside the keep-out geofence ROI box, at start/end point is set to street/terrain altitude.
Figure 11.
Flow chart of pathfinding logic for different start and end locations. In the chart, V.G. abbreviates visibility graph, and is the height of a geofence around a cluster of buildings. If the departure/destination is not inside the keep-out geofence ROI box, at start/end point is set to street/terrain altitude.
Figure 12.
Example horizontal and vertical airway corridors in Manhattan.
Figure 12.
Example horizontal and vertical airway corridors in Manhattan.
Figure 13.
Top-down view of example flight paths for airspace volumization and fixed flight corridor solutions. Distances traveled are 770 m (turn), 1051 m (constant cruise), 1139 m (terrain follower), 1528 (150 m flight corridor), and 1977m (500 m flight corridor).
Figure 13.
Top-down view of example flight paths for airspace volumization and fixed flight corridor solutions. Distances traveled are 770 m (turn), 1051 m (constant cruise), 1139 m (terrain follower), 1528 (150 m flight corridor), and 1977m (500 m flight corridor).
Figure 14.
Flight altitude time histories for airspace volumization and flight corridor solutions for
Figure 13 example.
Figure 14.
Flight altitude time histories for airspace volumization and flight corridor solutions for
Figure 13 example.
Figure 15.
Example of a 3-D geofence wrapping a “turn” flight plan solution. Polyhedra in green denote keep-out geofences around buildings near the trajectory’s keep-in geofence. The remaining 2-D polygons denote keep-out geofences around buildings that are more distant from the sUAS flight path.
Figure 15.
Example of a 3-D geofence wrapping a “turn” flight plan solution. Polyhedra in green denote keep-out geofences around buildings near the trajectory’s keep-in geofence. The remaining 2-D polygons denote keep-out geofences around buildings that are more distant from the sUAS flight path.
Figure 16.
Example 3-D geofencing solution for a “constant cruise altitude” flight plan solution. Polyhedra in green denote keep-out geofences around buildings near the trajectory’s keep-in geofence. The remaining 2-D polygons denote keep-out geofences around buildings that are more distant from the sUAS flight path.
Figure 16.
Example 3-D geofencing solution for a “constant cruise altitude” flight plan solution. Polyhedra in green denote keep-out geofences around buildings near the trajectory’s keep-in geofence. The remaining 2-D polygons denote keep-out geofences around buildings that are more distant from the sUAS flight path.
Figure 17.
Example 3-D geofencing solution for a “terrain follower” flight plan solution. Polyhedra in green denote keep-out geofences around buildings near the trajectory’s keep-in geofence. The remaining 2-D polygons denote keep-out geofences around buildings that are more distant from the sUAS flight path.
Figure 17.
Example 3-D geofencing solution for a “terrain follower” flight plan solution. Polyhedra in green denote keep-out geofences around buildings near the trajectory’s keep-in geofence. The remaining 2-D polygons denote keep-out geofences around buildings that are more distant from the sUAS flight path.
Figure 18.
Percent frequency distribution of minimum-cost solutions over Monte Carlo simulations.
Figure 18.
Percent frequency distribution of minimum-cost solutions over Monte Carlo simulations.
Figure 19.
Top-down view of sample solutions. Five flight trajectory solutions are generated for . Each solution provides route deconfliction from Manhattan terrain and building geofences and from the flight trajectory geofence. Distances traveled are 2008 m (turn), 1585 m (constant cruise), 1634 (terrain follower), 1983 (150 m flight corridor), and 2395 (500 m flight corridor). The minimum-cost solution for is the constant cruise altitude option.
Figure 19.
Top-down view of sample solutions. Five flight trajectory solutions are generated for . Each solution provides route deconfliction from Manhattan terrain and building geofences and from the flight trajectory geofence. Distances traveled are 2008 m (turn), 1585 m (constant cruise), 1634 (terrain follower), 1983 (150 m flight corridor), and 2395 (500 m flight corridor). The minimum-cost solution for is the constant cruise altitude option.
Figure 20.
Flight altitude time histories for airspace volumization and flight corridor solutions for
in
Figure 19 example.
Figure 20.
Flight altitude time histories for airspace volumization and flight corridor solutions for
in
Figure 19 example.
Figure 21.
Example of a 3-D geofence wrapping a “turn” flight plan for . The trajectory is shown in black, and the trajectory is shown in blue. Polyhedra (green) denote keep-out geofences around buildings. The remaining 2-D polygons denote keep-out geofences around buildings that are outside the combined ROI.
Figure 21.
Example of a 3-D geofence wrapping a “turn” flight plan for . The trajectory is shown in black, and the trajectory is shown in blue. Polyhedra (green) denote keep-out geofences around buildings. The remaining 2-D polygons denote keep-out geofences around buildings that are outside the combined ROI.
Figure 22.
Example of a 3-D geofence wrapping a “constant cruise altitude” flight plan for . The trajectory is shown in black, and the trajectory is shown in blue. Polyhedra (green) denote keep-out geofences around buildings. The remaining 2-D polygons denote keep-out geofences around buildings that are outside the combined ROI.
Figure 22.
Example of a 3-D geofence wrapping a “constant cruise altitude” flight plan for . The trajectory is shown in black, and the trajectory is shown in blue. Polyhedra (green) denote keep-out geofences around buildings. The remaining 2-D polygons denote keep-out geofences around buildings that are outside the combined ROI.
Figure 23.
Example of a 3-D geofence wrapping a “terrain follower” flight plan for . The trajectory is shown in black, and the trajectory is shown in blue. Polyhedra (green) denote keep-out geofences around buildings. The remaining 2-D polygons denote keep-out geofences around buildings that are outside the combined ROI.
Figure 23.
Example of a 3-D geofence wrapping a “terrain follower” flight plan for . The trajectory is shown in black, and the trajectory is shown in blue. Polyhedra (green) denote keep-out geofences around buildings. The remaining 2-D polygons denote keep-out geofences around buildings that are outside the combined ROI.
Table 1.
Control parameters for geofenced flight planning case studies.
Table 1.
Control parameters for geofenced flight planning case studies.
| | | | |
---|
5 (m/s) | 2 (m) | 5 (m) | 5 | 50 (m) |
Table 2.
Flight power consumption data from [
44].
Table 2.
Flight power consumption data from [
44].
Climb | Descent | Forward Flight |
---|
312 (J/s) | 300 (J/s) | 328 (J/s) |
Table 3.
Number of cases where airspace volumization has minimum cost (left) and number of cases where the flight corridor at 150 m has lower cost than the corridor at 500 m.
Table 3.
Number of cases where airspace volumization has minimum cost (left) and number of cases where the flight corridor at 150 m has lower cost than the corridor at 500 m.
} | } |
---|
698 out of 712 cases | 702 out of 712 cases |
Table 4.
Average distance (d), power consumption (P), and minimum and maximum distances of 2D straight-line paths between start and destination states for the Monte Carlo simulations.
Table 4.
Average distance (d), power consumption (P), and minimum and maximum distances of 2D straight-line paths between start and destination states for the Monte Carlo simulations.
| | | |
---|
1391 (m) | 91259 (J) | 189 (m) | 3003 (m) |
Table 5.
Mean and standard deviation of the minimum-cost airspace volumization solution.
Table 5.
Mean and standard deviation of the minimum-cost airspace volumization solution.
| | | | | |
---|
1595 (m) | 606 (m) | 94,338 (J) | 39,609 (J) | 254 (m) | 3349 (m) |
Table 6.
Mean and standard deviation of 150 m flight corridor solutions.
Table 6.
Mean and standard deviation of 150 m flight corridor solutions.
| | | | | |
---|
2303 (m) | 820 (m) | 149,084 (J) | 53,449 (J) | 479 (m) | 4464 (m) |
Table 7.
Mean and standard deviation of 500 m flight corridor solutions.
Table 7.
Mean and standard deviation of 500 m flight corridor solutions.
| | | | | |
---|
2796 (m) | 788 (m) | 179,363 (J) | 51,502 (J) | 1142 (m) | 4836 (m) |
Table 8.
Normalized travel distance comparison between airspace geofencing and 150 m flight corridor solutions.
Table 8.
Normalized travel distance comparison between airspace geofencing and 150 m flight corridor solutions.
| | | |
---|
115 (%) | 103 (%) | 166 (%) | 163 (%) |
Table 9.
Flight plan parameters for and .
Table 9.
Flight plan parameters for and .
| | | | |
---|
| [584,085; 4,508,093; 0] | [584,248; 4,506,598; 0] | 30 | 50 |
| [583,600; 4,507,000; 0] | [584,460; 4,507,660; 0] | 20 | 50 |