# Position-Based Formation Control Scheme for Crowds Using Short Range Distance (SRD)
## 5 Conclusions  
Crowd simulation has been used in a variety of fields that require the movement of large numbers of people, including games, films, and urban industries. In particular, war movies, sports, and other fields that require the strategic movement of crowds require the crowd to move in a particular formation. In this paper, we propose a new method for controlling crowds to satisfy a given formation while avoiding collisions by introducing a new concept called Short Range Destinations (SRD) based on the PBD framework. SRD is a short-term goal toward which an agent moves in order to satisfy the formation. This goal works as a constraint and makes each agent move to maintain formation. We also let a group be a subset of the entire crowd. Each group can also have its own properties, such as position and velocity. These properties are used to make agents move along the path. To make the path, we applied an easy-to-use scribble interface that allowed the user to specify the path on the environment directly. During the simulation, the SRDs of the agents in a group were translated by the amount of displacement of the group position, and then the agents moved to the SRDs accordingly. In addition, the crowd performed a neighbor search during the simulation to find out where the dynamic obstacles were in the near space, and, based on the presence of obstacles, it decided whether or not to abandon the formation constraint and then avoid urgent collisions. Smooth movement of the crowd is also achieved by adding a special behavior. In contrast to traditional crowd formation methods, which did not show natural avoidance behavior in the presence of dynamic obstacles, the proposed method showed that crowds moved toward their destinations while breaking and restoring the formation constraint naturally. However, our method has limitations. Our current method depends only on the CPU power. Therefore, the number of agents running at a real-time rate is limited. In the future, we would like to redesign our current method in a parallel computing framework such as CUDA or Compute Shader. We believe that our algorithms can run faster, more accurately, and handle a larger number of crowds. The second limitation is that the proposed algorithm does not consider static obstacles, such as walls, in the environment. Therefore, collisions between crowds and static obstacles are not prevented. We believe in the future that we can integrate well-known path-planning algorithms with the proposed method to obtain a collision-free path with obstacles. The third limitation is that the formation is not allowed to change during simulation. In the future, we would like to extend the current algorithms to have dynamically changing formation constraints. If it is possible to change the formation during the simulation, then it will be possible to better express the appearance of a flexible,  
Figure 20: A situation where two groups of agents, which regard each other as obstacles, encounter each other in proximity. (**a**) Screenshot of observation from a simulation of the method proposed by [PERSON] et al. [22]. (**b**) Observation of our method. The black and white lines are the paths of travel for the blue and red groups, respectively. strategic, and varied crowd. The fourth limitation of our simulation is that it does not support the dynamic environment. We assume that the environment has a flat surface. In future work, we would like to expand our work to explore scenarios with highly dynamic terrain or varying weather conditions, which show more complex and dynamic behavior for agents for given formation constraints. In order to do this, we would like to expand our 2D grid space to a 3D grid space and embed more information into each cell to support 3D behaviors of agents. We believe that this would enhance the adaptability and robustness of crowd simulation systems.