# Position-Based Formation Control Scheme for Crowds Using Short Range Distance (SRD)
###### Abstract
More specifically, we utilize distance constraints to control the distance between the current positions of agents and the so-called _Short Range Destination_ (SRD). These are new constraints that make agents satisfy a given formation. If we set the short-range destination constraint to zero, then all agents start moving to their final goals to meet the constraint. If we are able to set all destinations to satisfy a formation and let agents move together, then we can make them move to the targets while keeping the formation. In multi-agent simulations such as crowds, because all agents consider other agents as moving obstacles, it is not easy to make them maintain the formation while moving to their targets. This makes things worse when they encounter other agents with different formation constraints. That is, because there would be many conflicts among agents to make a decision regarding their respect formation, the algorithm must know when to maintain or break the constraints automatically. In our algorithms, we set the _hard_ constraints on the interpenetration and collision avoidance between agents and making agents arrive at the targets, and we set the _soft_ constraints on formation. The soft constraints can be broken depending on the situation, but must be recovered as soon as the situations are resolved. These algorithms break the formation when they are in an inevitable situation, but restore the formation when they resolve the inevitable situations. The proposed method has the following contributions:  
* We propose a new algorithm that introduces a scheme called Short Range Destination (SRD) to help crowds move to a destination while satisfying a given shape;* We propose a method of leveling constraints that allows the agent to determine for itself which constraints it should respond to in various situations;
* Our method grids the field in two dimensions and embeds local information, which is combined with the respective leveled constraints to influence the decisions of each agent. A sample result of the proposed algorithm is presented in Figure 1. The red and blue spheres in the figure represent the crowd in different groups while maintaining a particular formation constraint. Note that the blue line is the path along which the blue crowd is moving, whereas the red line is the path along which the red crowds are moving. Both paths are given by scribble. The reason why the crowd moves along the path drawn by the user is to cause intentional collisions between different groups. Because the two paths are sufficiently close, many collisions happen between two groups, which breaks the formation constraint in the middle. However, as soon as they exit the jamming situation, they automatically recover the formation constraint and then eventually arrive at the target positions. The yellow arrow in Figure 1 is the direction of movement of the blue crowd, which forms a bird shape. The remainder of this work is structured as follows. Section 2 introduces related work, where we summarize all prior works and compare them with the proposed method. Section 3 describes the crowd simulations with formation constraints using this PBD technique in detail. Section 4 presents a set of experiments and the results. Finally, Section 5 concludes with a discussion and future research directions.