# Jam Mitigation for Autonomous Convoys via Behavior-Based Robotics
## 4 Results  
To measure the performance of the convoy controllers, we calculated the mean absolute error (MAE) between the follower vehicles' path and the convoy leader's path. The MAE was chosen as the measurement for evaluation as it has a direct interpretation to the real-world quantities being compared, namely the Euclidian distances between follower points and convoy leader points, in addition to not inflating the penalty for larger errors via squaring, which occurs in other commonly used performance measurements such as root mean squared error [47]. The paths of both the followers and the convoy leader were sampled at a rate of 1000 Hz, respectively creating arrays of position points for each vehicle. The Euclidean distance between the follower position points and corresponding convoy leader positions points were then used to calculate the MAE with the following formula:  
\[\text{MAE}=\frac{\sum_{i=1}^{n}\lvert e_{i}\rvert}{n}, \tag{7}\]  
where \(e\) is the Euclidean distance between the follower and convoy leader position points, and \(i=1,\,\dots,\,n\), where \(n\) is the size of the array e. Table 3 shows the average MAE over five runs for each convoy controller for both the square path and roundabout path when under a constant jamming attack. Figure 17 shows the paths of the five runs taken by the followers, overlaid on the convoy leader's goal points for a visual comparison of performance. Figure 16: Jamming zones overlaid onto the preset plans for the lead vehicle: (**a**) square loop and (**b**) roundabout. Figure 15: The preset path plans for the lead vehicle: (**a**) square loop and (**b**) roundabout. Likewise, Table 4 shows the average MAE while under a random jamming attack with tj, and tts set to 10 s and 2 s, while Figure 18 shows the paths taken for the five runs by the followers, overlaid on the convoy leader's goal points for a visual comparison of performance. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Convoy Configuration** & **Square (m)** & **Roundabout (m)** \\ \hline Follower 1 Using Basic Convoy Controller & 0.6844 & 1.2637 \\ Follower 2 Using Basic Convoy Controller & 1.0028 & 1.0697 \\ Follower 1 Using FLJM assemblage & 0.4680 & 0.4821 \\ Follower 2 Using FLJM assemblage & 0.7654 & 0.9271 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average MAE under a random jamming attack. Figure 17: Plot of the paths taken by the followers under constant jamming on the square path for (**a**) follower 1 and (**b**) follower 2; and on the roundabout path for (**c**) follower 1 and (**d**) follower 2. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Convoy Configuration** & **Square (m)** & **Roundabout (m)** \\ \hline Follower 1 Using Basic Convoy Controller & 1.2665 & 3.1334 \\ Follower 2 Using Basic Convoy Controller & 1.9226 & 3.5205 \\ Follower 1 Using FLJM assemblage & 0.4942 & 0.4197 \\ Follower 2 Using FLJM assemblage & 0.7321 & 0.8452 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average MAE under a constant jamming attack. As seen in Table 3, the utilization of the FLJM assemblage significantly improved convoy performance across both path plans when compared to the basic convoy controller under constant jamming. When following the squared loop path, using the FLJM assemblage decreased the average MAE by 60.98% for follower 1 and 61.92% for follower 2. The improvement was even more drastic with the roundabout path, where the average MAE was decreased by 86.61% and 75.99% for follower 1 and follower 2, respectively. These significant improvements were due to the basic convoy controller missing turns that the convoy leader performed in the jamming zones laid out in yellow in Figure 16. As seen in Figure 17, the FLJM assemblage allowed the followers to successfully continue leader-following inside the constant jamming zones, whereas the stoppage of communications prevented the followers from getting proper waypoints when relying solely on basic delayed following.