# Control for Autonomous Intersection Management Based on Adaptive Control Barrier Function
## 4 Simulations and Experiments
### Simulations  
In this section, we showcase the effectiveness of the proposed CBF-based controller through simulation. We set up a one-way, two-lane intersection scenario in the Gazebo environment. The scenario is depicted in Figure 5. There are a total of eight robots--yellow, blue, green, and red colored--with two robots of each color in both directions. To simulate a busy intersection, all lane robots enter simultaneously to reach maximum capacity. The objective is for yellow robots to swap positions with green ones and blue robots with red ones without collisions. The simulation outcomes are displayed in Figures 5 and 8. Figure 5 exhibits snapshots from the simulation, while the initial robot configuration is shown in Figure 5a. As evident from Figure 5b,c, under the proposed acBF control, each robot maintains safe spacing from others and autonomously plans its path towards the goal position, successfully avoiding collisions as demonstrated by Figure 5d. This collision-free motion is further illustrated in Figure 8c; here, the blue curve represents minimum distances among any two robot pairs which consistently exceed the safety distance \(2r_{\text{safe}}=0.3\) m (red dotted curve), ensuring no collisions occur throughout the simulation process. Figure 8f records all the paths of by the eight robots during simulation controlled by the acBF. To demonstrate the effectiveness of avoiding collisions at intersections, the results under the three-dimensional potential field (TriPField) method were compared with those under the proposed CBF-based controller. In the same simulation environment, we used the TriPField method to control these eight robots. Under the TriPField method, although each robot autonomously plans its path towards the goal position, as illustrated in Figure 6d, collisions are not completely avoided. As evident from Figure 6b,c, when all robots reach the center of the intersection, there are minor collisions between robots. Figure 8a further illustrates the collisions between robots, showing that at t = 10.5 s, the minimum distance  
Figure 4: The autonomous vehicle of AIM in simulations and experiments: the Raspberry Pi Mouse mobile robot. between robots is less than the safety distance. Figure 8d records all paths of the eight robots during the simulation controlled by TriPField. Through comparison, it is concluded that robots controlled by the CBF-based method are safer than those controlled by the TriPField method when passing through the intersection. To further validate that the aCBF method ensures greater safety compared to the traditional CBF algorithm under power transmission loss, we conducted simulations in the same environment, setting the power transmission efficiency \(\theta=0.5\) for each robot. Under the traditional CBF method, although each robot autonomously plans its path to the target position, collisions between robots occur, as shown in Figure 7b. From Figure 7d, it can be observed that a significant collision occurs between the red and yellow vehicles as they move toward their target positions. Figure 8b further illustrates these collisions, revealing that the minimum distance between robots falls below the safety threshold at \(t=12\) s. Additionally, Figure 8e records the paths of all eight robots controlled by the traditional CBF algorithm during the simulation. A comparison demonstrates that robots controlled by the aCBF method are safer than those controlled by the traditional CBF method when passing through intersections under power transmission loss.