# Effect of Formation Size on Flocking Formation Performance for the Goal Reach Problem
## 1 Introduction
On the other hand, the behavior-based approach allows for the handling of multiple tasks using a single controller [4]. Notably, in the literature, most researchers have used the behavior approach, due to the fact that the flocking task is usually directly inspired by natural animal behavior. The flock size is the number of individuals within the flock. In nature, animals tend to have higher survival rates when being part of a group. In fact, group size is one of the primary defense mechanisms that animals adopt in order to limit predation risks [27; 28]. The size of a flock in nature can range from one species to hundreds of different species. Accordingly, flocking applications use different flock sizes, based on the application objectives [29]. As the flock size increases, the rate of successful attacks decreases [30]. Nevertheless, there are several disadvantages to grouping [30], including greater competition between group members and greater exposure to predators. On the other hand, some of the advantages of grouping are foraging, defense, alertness, and risk reduction [27; 31]. Indeed, flock size is one of the main behavioral mechanisms used by animals to manage their vulnerability to predation. [PERSON] et al. [32] studied the direct effect of flock size on foraging success with respect to the predation risk. [PERSON] [30] investigated how the flock size risk thresholds differ for attack rate, success rate, or dilution. The optimal flock size reflects a dynamic interplay between a diverse range of costs (competition, visibility, etc.) and benefits (defense, vigilance, etc.) associated with joining a group [27]. Most research has focused on constructing new methods or enhancing existing methods related to flock formation and control. Consequently, fewer efforts have been made in studying the effects of flocking parameters, such as flock size, on the performance of the developed systems. [PERSON] et al. [26] have studied the impact of changing flock size on reaching the goal in a specific time. They conducted two types of experiments; the first one was applied to test their work, with the objective of reaching the goal in a fixed time. For this experiment, they used 30 robots, and found that the flock could converge within a specific time. The second experiment focused on showing the effect of converging time when the flock size changed, with experiments using \(2,4,6,\ldots,40\) robots. They con cluded that the convergence time decreases as the number of agents increases. Moreover, [PERSON] et al. [14] have used three types of experiments to test (i) the cooperative behavior, (ii) the optimized control parameters, and (iii) the objective functions, when using 5, 10, or 20 agents. They found that the number of agents and the existence of obstacles did not affect the flock's performance. Moreover, the performance of the flock was improved when the repulsion zone was small, and the orientation and attraction zones were large. Figure 1 depicts these three different zones. The flock direction in the proposed work was decided in consensus between the different agents. Therefore, they found that the complexity of the determined direction increases as the flock size increases. The importance of the orientation radius also increased as the flock size increased. On the other hand, [PERSON] [23] has proposed different algorithms to simulate and study the flock behavior, according to their number and distribution in free space and with obstacles. However, these works did not study how the flock size affects the formation, whether the flock size affects the time it takes to reach the goal, whether all agents successfully reach the goal, how much time the flock takes to match the velocity, and whether the flock maintains the flocking roles while exploring. In this paper, we study the relationship between flock size and its effect on the flocking system's formation and performance. Inspired by previous works [13; 14; 16], a flocking system is constructed.