# A Free Simulation Environment Based on ROS for Teaching Autonomous Vehicle Navigation Algorithms
## 3 Results
The distance between the location of the robot and the target point was calculated using the following formula: \(d=\sqrt{\left(X_{2}-X_{1}\right)^{2}+\left(Y_{2}-Y_{1}\right)^{2}}\), where \(X_{2}\) and \(Y_{2}\) are the endpoint coordinates and \(X_{1}\) and \(Y_{1}\) are the coordinates of the initial position of the robot (see Figure 13). Figure 11: Example of paths in the same scenario: simple path (**a**) and complex path (**b**). Students were asked to perform the set of simulations in each scenario during the class session. At the beginning of the activity, they were given the datasheet shown in Table 2 for recording and further comparison of their simulation results. The teacher and students can perform a detailed analysis and data comparison in each scenario of the autonomous driven algorithms. For this analysis, \(t\)-tests, a statistical study comparing two means of two independent groups of data, are recommended. This test determines if there is a statistically significant difference between the two means of both groups when the \(p\)-value is equal to or less than 0.05. Table 3 summarizes the data obtained after the simulations were run in each scenario on both paths. These results depend on the initial and final position from the trajectory; in this case, these positions were the same for all the tests. It illustrates the average speed, calculated using the time and distance traveled, the time it takes the vehicle to finish the route, and the error with respect to the target point. Figure 14 shows the comparison between the results of the written exams of phase 1 (traditional method) and phase 2 (ROS and simulations). These results show that students obtained a higher grade in phase 2 when the professor used the proposed platform and the simulations in class. \begin{table}
\begin{tabular}{c|c|c|c|c|c|c} \hline \multicolumn{2}{c|}{Scenario:} & \multicolumn{4}{c}{Path 1:} & \multicolumn{4}{c}{Path 2:} \\ \hline Parameters: & Distance & Time & Error & Distance & Time & Error \\ \hline Algorithm 1 & & & & & & \\ \hline Algorithm 2 & & & & & & \\ \hline \end{tabular}
\end{table} 
Table 2: Example of sheet report for results obtained. Figure 12: Example of the time for different paths. In this example, in the simple path (**a**), the robot requires less time to arrive to the target point in comparison with the complex path (**b**). Figure 13: Examples of the mean error value for different paths. In this example, in the simple path (**a**), the distance between the robot and the target point is less than in the complex path (**b**). In addition, at the end of both stages of this study, participants had to evaluate a set of affirmations in order to assess the usability of the platform using a 5-point Likert Scale. The affirmations are listed below:  
1. I think there is a difference in my learning when using ROS's simulations in class. 2. The use of simulations helped me to better understand the theoretical concepts. 3. The use of simulations helped me understand the advantages and disadvantages of each algorithm. 4. The use of simulations motivated me to pay attention in class. 5. The use of simulations made the class session more interesting. 6. I think that the platform used to run the simulations is simple and easy to use. 7. I feel more confident now that I have learned by using the simulations in class. 8. I think that the simulations should always be used as a support tool in class. Table 4 summarizes the results of the usability evaluation. In this case, a value of 1 means \"totally agree\", while a value of 5 means \"totally disagree\".