# Realistic Multi-Agent Formation Using Discretionary Group Behavior (DGB)
## 2 Related Work
### Velocity-Based Avoidance Methods  
Some methods [4; 5] use the Social Force Model (SFM) [6] for their collision avoidance strategy. These methods provide an ability for the group to change its formation in critical situations. For example, [PERSON] et al. [5] proposed the techniques for simulating group behavior in a dense crowd. According to this model, agents can switch between two formations based on the density of other agents around the group, which are the wide and narrow formation for the small and large density, respectively. The SFM is not providing a collision-free motion for agents; besides, this strategy is limited to a fixed number of agents and formations. Also, there is no path planning algorithm used for the leader to find the best way to the target position. Furthermore, with this method, agents do not have realistic and human-like behavior in front of obstacles due to their limited behavior confronting the other components in the environment (all of our claims are explicit in their provided video). As with the previously proposed model [5], [PERSON] and [PERSON] [7] also demonstrate specific formations for agents to make the group transform into them in crowded areas. In their approach, they introduce three basic formations for the movement of small social groups in a virtual world which are line-abreast, V-like and river shapes that are inspired by a study from [PERSON] et al. [8], stating that real people tend to walk in small groups in common situations. Also, they used a velocity-selection approach for both collision avoidance and grouping behaviors, which is inspired by their previous work [9]. [PERSON] and [PERSON] used two predefined matrixes for setting the member-to-member and group-to-group influences during the simulation [10]. The RVO2 [2] is one of the most accepted models for the collision avoidance idea in crowd simulation and is an extension of their previous work called Reciprocal Velocity Obstacle (RVO) [11]. The new method is innovative in that it aims to create ORCA half-planes in the velocity space and reduce the problem to be solved with three linear programs. Then, by picking a velocity from the intersection of all half-planes which is the nearest one to the preferred velocity, the agent can find the best and collision-free way among other agents and obstacles to go to its target position (we encourage the reader to see the referenced paper for having a better understanding of our method). Our method is built on the half-planes concept and we introduce a modified model of this work for grouping issues. Some existing works [1; 12] take advantage of the velocity obstacle and some others [13; 14] consider the RVO2 library [15] to provide collision-free motion for groups of agents. [PERSON] et al. [12] use the velocity obstacle to perform agent-agent and group-group collision avoidance by adding a velocity obstacle to the whole group. This method provides collision avoidance constraints for group maintenance and navigation. [PERSON] et al. allege that members in a group can keep their cohesion by communicating and adapting their behaviors in a virtual environment [13]. Additionally, it aims to have several subgoals assigned on the path of each agent to help it reach the main goal. Also, agents can respond to events and scenarios during their motion. On the other hand, [PERSON] et al. [14] use ORCA half-planes to perform the collision-free motion of small groups with equal or less than 3 members. This paper provides a method based on attraction rules and communication of agents in a group. Another velocity-based approach for modeling groups of agents is introduced by [PERSON] et al. [1]. This model is a unified solution for diverse types of groups by modifying the Velocity Obstacle approach and having Velocity Connection for each agent which is the set of velocities that keep agents moving together while avoiding the collision. This process, by using a relation matrix, forces agents to be connected to the fixed nearby members.