# Position-Based Formation Control Scheme for Crowds Using Short Range Distance (SRD)
## 4 Experiments
### Comparison with Other Methods  
Second, we compared the proposed method with two prior methods. The first prior method was the crowd control technique based on PBD proposed by [PERSON] et al. [4], and the second was the method that transforms crowd formation focusing on a least-effort pair assignment proposed by [PERSON] et al. [1].  
Figure 16: The simulations are shown in order from (**a–f**), two groups with a different formation constraints are crossing each other. There is a breakdown of the formation on the both groups in the middle, but they regain the formation automatically and then reach their respective final destinations.  
Figure 17: Experiments in which various shapes of the crowd formations are crossed. (**a**) Two groups with the same shape formations. (**b**) Two groups with different shapes of formations from each other.  
Figure 15: Two groups with formation constraints are moving along the path set by user. Yellow arrows indicate the direction of travel for each group.  
Figure 18 shows an observation of crowd behavior after obstacle avoidance. Figure 18a shows the result of using the method proposed in [4] where the crowd avoided obstacles and then simply moved to destinations without hesitation. Since there was no formation constraint in this method, the crowds did not consider any other target except their final destinations. On the other hand, Figure 18b shows the result of applying the proposed method, and we could see that the crowd, after avoiding the obstacle, restored the original formation, a bird formation, while still moving toward the destination.  
To check the overall performance, we calculated the FPS (Frames Per Second) as we increased the number of agents. Since the proposed method was an extension of an existing method, it required additional computations compared to existing methods, and it was expected that this would result in performance degradation. Figure 19 shows a graph comparing the FPS between the proposed method and the original crowd method based on PBD as we increased the number of agents to 1500. The chart shows that there is no significant performance drop.  
We also compared our method with other formation control methods. [PERSON] et al. proposed an algorithm that transforms crowd formation with least-effort pair assignment [1]. Figure 20a shows the behavior of two groups of crowds crossing each other to reach their destination based on [1]. One of the limitations of this algorithm is that it could not handle an environment with dynamic obstacles, as shown in Figure 20a [1]. Figure 20a shows what happens when the crowd encounters a dynamic obstacle such as another group during the transformation of the formation. Instead of avoiding it, the crowd collides with it and slides past it.  
On the other hand, Figure 20b shows the result of the proposed method for the same scenario. The proposed method shows that the agents detected obstacles and then escaped from the given formation for the obstacle avoidance behavior. This demonstrates that the proposed method can handle the dynamic environment more naturally.  
Figure 19: Performance comparison between the original PBD-based crowds and the proposed method.  
Figure 18: Comparison of crowd behaviour after obstacle avoidance behaviour. (**a**) The algorithm from [4] applied, with no recovery after formation breakdown. (**b**) Proposed algorithm applied, with recovery after formation breakdown.