# Real-Time Hybrid Navigation System-Based Path Planning and Obstacle Avoidance for Mobile Robots
## 8 Experiments and Discussions
### Path Planning Performance  
In the first experiment, we will investigate the processing speed, memory usage and length of paths produced by original A-heuristic and multi-agent A-heuristic path planning with the presence or absence of the significant points extraction algorithm (SPEA). The memory usage of each algorithm is measured by the number of checked spots. In Tables 3 and 4, respectively, the indices obtained by the algorithms through the two scenarios mentioned above are presented. The trajectories produced by fed the path point set of different algorithms to the C2 PCBC generator are also illustrated in Figure 18. In both scenarios, we see the superiority of the ability to optimize length of the path produced by the original algorithm even with or without the presence of SPEA compared to a multi-agent algorithm. However, A-heuristic in the presence of SPEA not only reduces the size of the path set, but also reduces the length of the path. Therefore, the variance of path length produced by two algorithms is no longer a problem. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Scenario \#** & **Initial Position** & **Initial Heading** & **Destination Position** & **Destination Heading** \\ \hline
1 & (560, 120) & 90 degree & (900, 450) & 0 degree \\
2 & (900, 250) & \(-\)90 degree & (500, 625) & 0 degree \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Robot’s task for each scenario. Figure 16: Mobile platform for experiments. Figure 17: The map of lab pre-built by the robot. Furthermore, the presence of SPEA reduce the oscillation and curvature-magnitude of the path that presented in Figure 18. In the first scenario, when the robot uses a multi-agent algorithm, its processing time is reduced by 58.3%, but the number of spots checked is 3.2 times that of original A-heuristic. In the second scenario, with average numbers of agents is 9.7, 119% more spot-checked and processing time only decreased by 11.1%, this is the case where the multi-agent algorithm performs not really well compared to the amount of memory it consumes. the initial trajectory. The reason is keeping continuous curvature at \(\mathbf{P}_{back}(t)\). If the curvature is greatly changed on the whole main trajectory, the robot will not be able to respond to the position error because of the difference between changed main trajectory and initial trajectory. However, the re-path algorithm only affects a small segment around \(\mathbf{P}_{back}(t)\), which can be demonstrated by the series of curvature of main and reshaped trajectory respect to arc length in Figures 19 and 20, according to the first and second scenario, respectively. In both scenarios, the robot re-paths three times at the points where the accumulated position error (Figures 21 and 22) exceeds the allowed deviation on its entire trajectory from start position to destination position. Figure 19: Trajectories’ curvature of the first scenario. Figure 20: Trajectory curvature of the second scenario. In this experiment, the geometric parameters and kinematic limits of the robots are shown in the following Table 5.  
Figure 21: Left and right wheel angular speed, position error and heading error of the robot’s pose, with respect to desired pose on trajectory of the first scenario. Figure 22: Left and right wheel angular speed, position error and heading error of the robot’s pose, with respect to desired pose on trajectory of the second scenario. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(R_{R}\) & 0.4 m \\ \(l_{w}\) & 0.36 m \\ \(r_{w}\) & 0.06 m \\ \(\theta_{\max}\) & 220 rpm \\ \(\tilde{\theta}_{\max}\) & 2.2 rad/s\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Robot geometric parameters and kinematic limits. Let \(\varepsilon_{\text{max}}=10\) cm.