# Time Optimization of Unmanned Aerial Vehicles Using an Augmented Path
## 4 Augmented Path Mapping Algorithm
The Blackbox then provides the values of the respective functions in the algorithm, which gives the next set of coordinates for the drone to move on and this process goes on, thus giving the final path that the drone has to follow for the final destination. The data is sent through the program at every single instance of time as the coordinates are generated throughout the journey for the progress and smooth running of the drone. All the data is processed for the next coordinates and each coordinate is checked to keep track of the ascent and descent. Figure 3 is a small representation of the working of the algorithm from input to output. ## 5 Experimental Setup

In Tables 1-3, below, we calculated the time of the original path and after on the modified path. Our research shows that if we can follow the path, the time optimization and thus the output of these UAVs can be increased for better usage of resources and better output. The efficiency is calculated by Equation (4):

\[\text{Efficiency}=\text{(final time}-\text{initial time)}/\text{initial time}\times 1 00, \tag{4}\]

Figure 3: The flow of data. Table 1 and Figure 4 show the difference in the initial ascent time and the improved time (theoretically). The efficiency is constant in all the cases due to the. fact that the conditions and assumptions are kept constant throughout. Although, in reality, the efficiency may somewhat differ due to some exterior constraints like wind speed, turbulence motor speed, etc, and the graph will always show an increasing curve. These results show that there will be an increase in efficiency if the drone moves on an inclined path with constant speed, thus decreasing time and finally the power usage. Table 2 and Figure 5 prove that the descent time can be decreased drastically. Moreover, regarding the initial and augmented path, both are taken to be free fall, i.e., no power usage. To keep the drone on the specified path, some forces are needed from the motors, but that is cancelled, as in the initial case too. To prevent the drone from losing control during free fall and guaranteeing safety, some thrust is maintained throughout. Thus, the energy is cancelled in both and the time frames can be decreased by the augmented Brachistochrone curve, thus giving more output for the same energy input with increasing efficiency. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \begin{tabular}{c} **X-Axis (in** \\ **Meters)** \\ \end{tabular} & \begin{tabular}{c} **Y-Axis (in** \\ **Meters)** \\ \end{tabular} & \begin{tabular}{c} **Original Time** \\ **of Ascent (in s)** \\ \end{tabular} & \
\begin{tabular}{c} **New Time of** \\ **Ascent (in s)** \\ \end{tabular} &
\begin{tabular}{c} **Efficiency of** \\ **Ascent** \\ \end{tabular} \\ \hline
1 & 1 & 0.1 & 0.05 & 0.5 \\
10 & 10 & 1 & 0.5 & 0.5 \\
20 & 20 & 2 & 1 & 0.5 \\
50 & 50 & 5 & 2.5 & 0.5 \\
100 & 100 & 10 & 5 & 0.5 \\
200 & 200 & 20 & 10 & 0.5 \\
500 & 500 & 50 & 25 & 0.5 \\
1000 & 1000 & 100 & 50 & 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Time of ascent. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \begin{tabular}{c} **X-Axis (in** \\ **Meters)** \end{tabular}  & \begin{tabular}{c} **Y-Axis (in** \\ **Meters)** \\ \end{tabular}  & \begin{tabular}{c} **Original Time** \\ **of Descent (in s)** \\ \end{tabular}  & \ \begin{tabular}{c} **New Time of** \\ **Descent (in s)** \\ \end{tabular}  & \begin{tabular}{c} **Efficiency of** \\ **Descent** \\ \end{tabular}  \\ \hline
1 & 1 & 0.67 & 0.59 & 0.12 \\
10 & 10 & 6.77 & 5.899 & 0.13 \\
20 & 20 & 13.54 & 11.799 & 0.13 \\
50 & 50 & 33.87 & 29.499 & 0.13 \\
100 & 100 & 67.73 & 58.99 & 0.13 \\
200 & 200 & 135.46 & 117.998 & 0.12 \\
500 &All the above graphs are made concerning time. As you can see from Figures 5-7, there is a rate of increase in efficiency in both the ascent and descent. Additionally, from the value of Tables 1-3, it is proved that if we apply the above system and include the changes in the present system, the time can be decreased by a significant factor.