# Robot Navigation Based on Human Trajectory Prediction and Multiple Travel Modes
## 3 Results and Analysis
### Trajectory Planning
#### 3.2.1 Validation Experiment with Simulated a Low-Density Crowd  
To comprehensively evaluate our proposed method, a comparative experiment of three scenarios has been designed. The first scenario is to validate the improvement of predicting the pedestrian position with the improved socially conscious model when dealing with two pedestrians walking towards each other. The second scenario is to validate the necessity of trajectory planning with pedestrian position prediction when dealing with a low-density crowd. The third scenario is to validate the necessity of the trajectory planning approach with chasing cost judgment. The simulations are performed in Stage [23] based on ROS. We use a dynamics model for Pioneer 3-DX and a constant velocity model for pedestrian motions. These simulated pedestrians do not react to robot movements. The simulated robot Pioneer 3-DX are equipped with a simulated laser sensor, hokuyo UTM-30 LX, which is supported by ROS. In the simulated environment in this paper, the coordinates of the pedestrians are input to the robot system as a known volume. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multicolumn{2}{c}{**Socially Conscious Model**} & \multicolumn{2}{c}{**Improved Socially Conscious Model**} \\ \cline{2-5}  & **ADE Reduction** & **FDE Reduction** & **ADE Reduction** & **FDE Reduction** \\  & **Percentage** & **Percentage** & **Percentage** & **Percentage** \\ \hline ETH-Univ & \(-\)5.6\% & \(-\)4.7\% & 0.1\% & 1.3\% \\ ETH-Hotel & 11.3\% & 8.4\% & 18.5\% & 14.3\% \\ UCY-Zara 1 & 8.6\% & 9.6\% & 14.6\% & 13.9\% \\ UCY-Zara 2 & 7.2\% & 9.2\% & 10.0\% & 12.7\% \\ UCY-Univ & 10.4\% & 12.1\% & 15.7\% & 17.0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Prediction error reduction percentage. In the first scenario, the initial positions of pedestrians, \(p^{1}\) and \(p^{2}\), are \(p^{1}_{t}\) and \(p^{2}_{t}\), respectively, and the ground-truth positions after 0.5 s are \(p^{1}_{t+0.5}\) and \(p^{2}_{t+0.5}\). The pedestrian's movements are simulated by playing back the recorded data. The robot's task is to predict the position of pedestrians based on different prediction methods, and then generate obstacle avoidance trajectories. The positions of \(p^{1}\) and \(p^{2}\) after 0.5 s predicted by the constant-speed model are \(p^{p1}_{t+0.5}\) and \(p^{p2}_{t+0.5}\), respectively, and two pedestrians will collide; the optimal obstacle avoidance trajectory generated by the constant-speed model leads to a small distance of 0.2 m away from the pedestrian's actual position, \(p^{1}_{t+0.5}\), which penetrates in the pedestrian's safety zone, as shown in Figure 6a. The positions of \(p^{1}\) and \(p^{2}\) predicted by the improved socially conscious model after 0.2 s and 0.5 s are \(p^{p1}_{t+0.2}\), \(p^{p2}_{t+0.2}\), \(p^{p1}_{t+0.5}\), and \(p^{p2}_{t+0.5}\), respectively, as shown in Figure 6b. The optimal obstacle avoidance trajectory generated by our proposed method leads to a minimum distance of 0.7 m away from the pedestrian's actual position, \(p^{1}_{t+0.5}\), which shows the improvement of safety. In the second scenario, there are four pedestrians numbered \(p_{1}\) to \(p_{4}\). The original TEB approach and our proposed TEB approach with pedestrian trajectory prediction (TEBP) are compared in the local trajectory planner. Figure 7 shows the robot's trajectory planning process of avoiding four pedestrians, which is as follows: (1) The TEB and TEBP planner begin to select the trajectory of \(G_{f}(p_{1})\); however, the robot with the TEB planner hit \(p_{1}\), while the TEBP planner smoothly switched to the trajectory of \(G_{b}(p_{1})\), as shown in Figure 7b. (2) The TEB planner selects the trajectory of \(G_{f}(p_{2})\), while the TEBP planner smoothly switches from the trajectory of \(G_{f}(p_{2})\) to \(G_{b}(p_{2})\), as shown in Figure 7c.