# A Depth-Based Hybrid Approach for Safe Flight Corridor Generation in Memoryless Planning
## 6 Implementations and Results
### Results  
Polyhedral SFCs, like the pyramids we produce, will enforce multiple Euclidean planes as boundaries for our straight-line paths. Therefore, regarding computing workload, a small number of SFCs covering large areas of free space would be computationally cheaper for path planning than a collection of overlapping ones. We compare the overall intersection over union (IoU) of generated SFCs from our method with that of SFCs from the exhaustive inflating algorithm. We run two methods on a library of 600 actual depth images captured from Intel RealSense D435i. The lower the overall IoU is, the better the collection of SFCs is. Also, the higher the average max depth and volume of SFCs, the better. We can notice that the average of the deepest SFC's depth and the average of the largest SFC's volume from the proposed method are slightly lower than the inflating method due to the conservative verification. Although SFCs in inflating collection overlap by an IoU of 42.27%, our detected SFCs' IoU is only 1.35% on average. The straight-line path planner runs faster on given less-overlapping SFCs generated by the proposed method than exhaustive inflating ones and produces the same average path direction reward. Comparisons are summarized in Table 1.  
Given safe corridors generated by our proposed method, the path planner always finds a feasible path for the quadrotor with success rates for three scenarios are 99.7%, 99.9%, and 99.6%, respectively. All the trials were successful except for a few failed corner cases due to failures of tracking controllers. Simulation flight results are summarized in Table 2.  
Figure 14 illustrates several traveled paths in the simulation Medium scenario. It can be noticed that the FSD planner can effectively generate a collision-free and smooth path for the drone to move toward the goal.  
Executed trajectory in real flight experiment has been captured in the flight log and illustrated in Figure 15. A demonstration video of how the quadrotor navigates through obstacle-dense environments in both simulation and real flight can be found at [[https://youtu.be/0](https://youtu.be/0) awjK_5 kGfw]([https://youtu.be/0](https://youtu.be/0) awjK_5 kGfw) (accessed on 1 June 2023).  
Results of calculated path's direction rewards show that the path-planning algorithm works effectively on generated SFCs. When the robot is in front of a large free space, reward values are always 1 (maximum). They only decrease to a lower value when the vehicle is steering away from an obstacle on the route. Reward values saved from a trial are illustrated in Figure 16.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Platform**} & \multirow{2}{*}{**SFC Generator**} & \multirow{2}{*}{**Overall**} & **Number of SFCs** & **Average** & **Average** \\  & & **IoU** & **Generated per** & **Planning** & **Direction** \\  & & **Frame** & **Time** & **Reward** \\ \hline Xavier NX & Exhaustive inflating & 42.27\% & 16.53 & 78.16 ms & 0.97 \\  & Proposed **FSD** & **1.35**\% & **5.88** & **26.73 ms** & **0.97** \\ \hline i7 laptop & Exhaustive inflating & 51.78\% & 56 & 4.05 ms & 0.97 \\  & Proposed **FSD** & **1.35**\% & **5.88** & **0.44 ms** & **0.97** \\ \hline \hline \end{tabular}
\end{table}
Table 1: SFC generation methods comparison with actual data.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Success Rate** & **Average Flight Time** \\ \hline Easy & 99.9\% & 23.8 s \\ Medium & 99.8\% & 22.8 s \\ Hard & 99.6\% & 23.9 s \\ \hline \hline \end{tabular}
\end{table}
Table 2: Success rate and average flight time of the planning system for three simulated scenarios.