# A High-Fidelity Energy Efficient Path Planner for Unmanned Airships
## 6 Numerical Simulations
### Results and Discussion
\begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \multicolumn{4}{c}{(**a**)} \\ \multirow{2}{*}{**Planner**} & **Convergence** & **Avg. comp. time** & **Avg. flight time** & **Avg. energy** \\  & **(\%)** & **(s)** & **(s)** & **(Wh)** \\ \hline
**Low terrain resolution** & \(57\) & \(15.2\) & \(388.9\) & \(181.7\) \\
**Complete planner** & \(94\) & \(41.7\) & \(206.9\) & \(43.9\) \\
**Change** & \(+64.9\%\) & \(+173.9\%\) & \(-46.8\%\) & \(-75.8\%\) \\ \hline  & \multicolumn{4}{c}{(**b**)} \\ \multirow{2}{*}{**Planner**} & **Convergence** & **Avg. comp. time** & **Avg. flight time** & **Avg. energy** \\  & **(\%)** & **(s)** & **(s)** & **(Wh)** \\ \hline
**Constant velocity** & \(74\) & \(43.6\) & \(325.2\) & \(94.0\) \\
**Complete planner** & \(94\) & \(41.7\) & \(206.9\) & \(43.9\) \\
**Change** & \(+27.0\%\) & \(-4.2\%\) & \(-36.4\%\) & \(-53.3\%\) \\ \hline  & \multicolumn{4}{c}{(**c**)} \\ \multirow{2}{*}{**Planner**} & **Convergence** & **Avg. comp. time** & **Avg. flight time** & **Avg. energy** \\  & **(\%)** & **(s)** & **(s)** & **(Wh)** \\ \hline
**Uniform WVF** & \(83\) & \(44.4\) & \(185.2\) & \(114.8\) \\
**Complete planner** & \(94\) & \(41.7\) & \(206.9\) & \(43.9\) \\
**Change** & \(+13.3\%\) & \(-6.0\%\) & \(+11.7\%\) & \(-61.8\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance comparison between trajectories generated by the four planners. (**a**) impact of nodal resolution; (**b**) impact of path planning versus trajectory planning; (**c**) impact of fixed versus variable WVF. The third comparison, shown in Table 2c, illustrates the impact of using a fixed WVF path planner. The trajectories generated with this planner tended to be similar to those generated by the low terrain resolution planning, discussed earlier. Since the WVF was considered to be uniform, the UAV would climb into higher magnitude winds resulting in considerable energy consumption increases. The uniform WVF planner converged less often due to the lack of awareness and planning for stronger head winds. In the cases where the planner converged, the resulting viable trajectories were faster on average, but exhibited greater variability. The standard deviation in flight times for the uniform WVF and the complete planners was 135 s and 74 s, respectively. The full planner was slightly faster on average then the constant velocity and the uniform WVF planners. This can be explained by the fact that fewer connections between the nodes were feasible in the full planner case as a consequence of more connections exhibiting negative ground velocities. The reduction in the number of feasible connections reduces the computational load and the processing time of the optimization. In individual tests with low wind velocity seeds, the fixed WVF path planner converged faster than the complete planner; however energy savings could still be achieved using the complete planner, as airships are highly sensitive to wind disturbances. It is worth noting that the mean wind velocity seed used in the simulation was 3.61 m/s or 13 km/h and that this is considered low wind for heavier-than-air UAVs. In addition to these comparisons, it is worth commenting on the design of the trajectory planner. The complete trajectory planner has a consistently higher convergence rate than any other planner considering only two of the three key factors. The limited flight speed for small-scale UAVs imposes severe path restrictions and even impassible regions at high altitudes where wind magnitudes can be higher. The inability to adapt the path or vehicle velocity to avoid these conditions has been shown to reduce the feasibility of the trajectories that were produced. More importantly, the energy consumed by trajectories generated by the complete trajectory planner using a variable trajectory and variable WVF data was found to be at least 50% lower on average over all scenarios simulated. Figure 10 shows the average energy consumed for each planner with a 95% confidence interval.