# Position-Based Formation Control Scheme for Crowds Using Short Range Distance (SRD)
## 2 Related Work
### Crowd Formation Control Methods  
One of the challenges in crowd simulation is how to generate crowd behavior in specific situations, for example, simulating people evacuating through a narrow exit, standing in line, etc., in a virtual space. Similarly, making crowds move in groups or formations can be considered another specific situation.  
[PERSON] et al. proposed a group modeling method for crowd formation with different sizes [15]. Group modeling was a unified solution to control the movement of a crowd in which the size of each group, the relationships among its members, and the goals of each  
Figure 2: Comparison of processes in dynamical systems and PBD. The * symbol means multiplication.  
group were considered. This solution introduced the idea of the velocity connection, which allowed the crowd to move together while avoiding collisions and achieving goals. This research is similar to our paper in that it uses the property of a group to represent crowd behavior in a specific situation, but there is a difference where we focus on representing crowd behavior under the constraint of formation.  
[PERSON] et al. proposed an optimized crowd formation transformation technique [1]. This work aimed to transform a crowd in a formation into another user-specified form of the formation. In this research, the focus was on transforming the crowd into an optimized movement. They used the Kuhn-Munkres algorithm [9] to determine the most efficient destination for each agent, where the destination was within another formation that the crowd would form. And they used a social force model [12] and mutual information to avoid collisions between moving agents and minimized confusion. Through this method, the crowd could transform the formation based on optimized directional decisions. However, when an agent encountered an obstacle while transforming, it did not consider collision avoidance, which meant that the crowd control method was somewhat limited in its ability to adapt to unpredictable obstacle crossing locations (such as dynamic obstacles) and to transform in real time.  
There was another study related to multi-agent formation. This method, proposed by [PERSON], combined PBD and the shape-matching constraint [16], and was able to move multiple agents in a formation while maintaining a given shape [17]. Agents in formation could be dynamically reconfigured. Agents could be assigned to closer positions based on a linear sum assignment approach [18]. As a result, this method allowed users to simulate crowds with a variety of group numbers and formation shapes in real time, but this method had the limitation that all agents had only a linear movement path and the same speed.  
To overcome the shortcomings in these studies with respect to crowd formation, we propose a dynamic crowd formation control method based on PBD techniques that allows a formed crowd to move toward a goal while prioritizing collision avoidance when encountering dynamic obstacles, breaking up the crowd formation freely, but recovering its own formation when conditions are suitable.