# Airspace Geofencing and Flight Planning for Low-Altitude, Urban, Small Unmanned Aircraft Systems
## 6 Simulation Results
Dynamic airspace volumization and flight corridor solutions at 150 m are normalized by the two-dimensional straight-line path parameters, indicating the percent increase in average travel distance and power consumption. A normalized benchmark comparison is shown in Table 8. On average, our 3-D airspace geofencing solution increased travel distance by 15% and power consumption by 3% compared to 2-D straight-line paths from start states to destination states. On the other hand, the travel distance increased by 66 % and power increases by 63% when comparing minimum-cost 3-D geofencing solutions with 150 m flight corridor solutions. This analysis indicates our airspace geofencing algorithm generates routes that offer nontrivial distance (time) and power (energy) reductions relative to flight corridor paths, at least for Manhattan. All simulations were executed on a standard laptop PC using uncompiled MATLAB code. The mean runtime and standard deviation over all 1010 Monte Carlo simulations were computed. The average runtime was 10.98 s with \(\sigma=12.68\). The minimum runtime was 0.13 s, and the maximum runtime was 90.66 s. As the number of obstacles inside the fly-zone increase, runtime also increased, as might be expected. A more computationally efficient visibility graph algorithm could be implemented in future work [45], particularly with a large obstacle set. Migration from uncompiled MATLAB to a compiled code (e.g., in C++) will also improve performance. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(H_{d_{150m}}\) & \(\sigma_{d_{150m}}\) & \(H_{P_{150m}}\) & \(\sigma_{P_{150m}}\) & \(min\{d_{150m}\}\) & \(max\{d_{150m}\}\) \\ \hline
2303 (m) & 820 (m) & 149,084 (J) & 53,449 (J) & 479 (m) & 4464 (m) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Mean \(\mu\) and standard deviation \(\sigma\) of 150 m flight corridor solutions. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(H_{d_{fused}}\)/\(H_{d_{2D}~{}path}\) & \(H_{P_{treated}}\)/\(H_{P_{2D~{}path}}\) & \(H_{d_{150m}}\)/\(H_{d_{2D~{}path}}\) & \(H_{P_{150m}}\)/\(H_{P_{2D~{}path}}\) \\ \hline
115 (\%) & 103 (\%) & 166 (\%) & 163 (\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Normalized travel distance comparison between airspace geofencing and 150 m flight corridor solutions. A Monte Carlo simulation generated a suite of random launch (start) and landing (end) points for a single sUAS flying in Lower Manhattan. Start and end points were either located on the ground or a flat building roof to simulate the diverse sUAS flight cases that might be encountered in a densely populated urban environment. Keep-out geofences were generated at each building or around blocks of clustered buildings, representing no-fly zones for the sUAS. Our airspace geofencing pipeline successfully generated flight plans and enclosing geofence volumes for four flight trajectory solution options for all 1010 Monte Carlo simulations. The minimum distance and energy cost was chosen as the best solution. Our geofence-based path planning solutions outperformed a more traditional fixed flight corridor routing option. Our Monte Carlo simulations did not limit the maximum altitude for UAS flight, so the trajectories for some solutions had cruising altitudes greater than 400 ft AGL, beyond the UTM and sUAS ceiling. Our Monte Carlo results showed the \"combined\" solution option (i.e., constant cruise and turn) was preferred most often. A maximum altitude constraint would eliminate all solutions that climbed above UTM-managed airspace, likely resulting in the more frequent use of visibility graph \"turning\" solutions. The results in Table 8 showed that our algorithm generates solutions that are 51% and 60% more efficient than flight corridor solutions at 150 m altitude in terms of normalized average flight distance and power consumption, respectively. It is likely that for AAM airspace corridors accessible to sUAS, above 400 ft AGL will be designated.