# Effect of Formation Size on Flocking Formation Performance for the Goal Reach Problem
## 4 Discussion  
The relationship between the flock size and its effect on the flocking system's performance was analyzed, as measured with respect to several factors, including the flexibility towards reaching the goal (i.e., the time to reach the goal zone, the number of agents within the goal area), the speed matching time, the number of the applied flocking rules (collision avoidance, attraction, and alignment), the localization window, the number of collisions that occurred, the flock's average distance to the center of mass, and the goal localization time. Our experiments indicated that the flock was able to reach the goal zone, regardless of the number of agents in the flock; however, the time needed to reach the goal increased as the flock size increased, both in environments with and without obstacles. This was due to the significant increase in applying the rules of separation and cohesion, rather than the rule of alignment. This means that the flock was unable to reach stable flocking behavior properly. Furthermore, as the flock did not possess stable flocking behavior, the chances of collision between its members increased. Although we did not study the effect of changing the perception zone size as a main factor in this study, it served as a preprocessing step in designing the flock controller. The flocking behavior is highly dependent on the perception zone's size, as the flocking behavior improves when the orientation zone's size is large, and the repulsion and attraction zones are small in size. These findings contradict reference [14] in that the zone of attraction is large rather than small; however, the second paper had a smaller flock size, which might affect the results. Our experiments suggested that flocking behavior becomes more difficult as the flock size increases. This issue is due to the average distance to the center of mass, which becomes smaller with larger flock sizes, as the number of flock members increase in the flocking zone. Moreover, it is related to the size of the perception zone chosen, which may be unsuitable for large-scale flocks. The small average distance to the center of mass indicates that the flock members were close to each other, such that they must keep separating to avoid collisions, in contrast to smaller flock sizes, where the flock members have a high probability of being detected in the orientation zone (alignment with each other), leading to stable flocking behavior. On the other hand, having a larger flock indicates that more agents have a high probability of being detected within the attraction zone (i.e., cohesion with other members), such that the flock members will keep attracting farther members,  
Figure 8: Illustration of flock splitting and rejoining. (**a**) Flock splitting. (**b**) Flock rejoin. according to their perception, while avoiding collisions with closer members within the repulsion zone which, in turn, results in unstable flocking behavior. As the flock size increases, so do the number of collisions, cohesion, and separations. This is expected because of the increase in probability of these events as the number of flock members increases. An increase in the scatter for larger flock sizes can be similarly observed. The increase in flock size creates a more complex environment for the flock to navigate, resulting in a larger variance of flock behavior. Our findings indicated that the speed matching time slightly decreased along with an increase in the number of agents in an environment without obstacles. On the other hand, the speed matching time was slightly increased in the environments with obstacles. This means that obstacles affect the time to reach the goal, as they hinder exploration. However, the reach time was logically affected by the average speed of the flock. Speed matching time has a larger scatter as the flock size decreases. This is because there are fewer flock members overall within the attraction zone of each flock member, compared with larger flock sizes.