# Effect of Formation Size on Flocking Formation Performance for the Goal Reach Problem
## 5 Conclusions  
In this paper, we studied the impact of changing the flock size on the performance of the flock task. We developed a flock controller using a behavior-based swarm approach and conducted experiments on the problem of reaching a goal zone. Our flock controller depends on the behavior of a flock's agents, with respect to their neighbors and to the environment. Moreover, the flock controller also introduces the concept of sensing power that replicates the phenomenon observed in nature where migrating birds have a sense of where they need to head, even if they do not precisely know the target. The sensing power provides better take-off results. In this work, we studied the impact of flock size on flock formation and flock performance through nine different parameters, including the goal zone localization time, the distance to the center of mass, the collisions per member, and the rate of application of the flocking rules. These parameters were measured for ten flocks with increasing size. The flocking behavior was simulated in two different environments, with and without obstacles. The results demonstrated that the developed flock controller is able to deliver the flock to the goal zone, regardless of its size. The experiments concluded that the time required to complete the task in minutes, and the goal localization window increased along with an increase in flock size. The same behavior was observed for the average collisions per member, the average number of applied separations, and the average number of cohesion steps. On the contrary, the results also concluded that the average distance to center of mass, as well as the speed matching time, tend to decrease along with the increase in the flock size. We also observed that the remaining analyzed parameters, namely the goal localization time and the number of applied alignment steps, had no clear association with the variations in the flock size. Overall, similar results were observed in both situations with and without obstacles. As mentioned above, spatial organization is an area where behavior-based swarm approaches can be applied. This paper studied the impact of the number of agents on the different parameters involved in moving individual robots to spatially organize themselves in a specific region of the environment. As the number of collisions and separations tends to increase with the number of involved agents and certainly impacts the time required to complete the task, in future studies, we intend to work on minimizing the collisions among agents in order to improve the task completion time. We will also study the impact of using the sensing power continuously for motion coordination among the flock and to improve the navigation process. Moreover, the flock controller may integrate other features to memorize discovered areas, which could help reduce the time required to reach the goal. Conceptualization, A.T. and R.A.; methodology, S.A. and N.A. ; software, R.A.; validation, A.T., R.A., and S.Q. ; formal analysis, S.A. and N.A. ;writing--original draft preparation, S.A. and R.A.; writing--review and editing, S.A., A.T., S.Q. and N.A. ; visualization, R.A.; supervision, A.T.; project administration, S.Q. ; funding acquisition, S.Q. All authors have read and agreed to the published version of the manuscript. This work was funded by the National Plan for Science, Technology and Innovation (MAARIFAH), King Abdulaziz City for Science and Technology, Kingdom of Saudi Arabia, Award Number (13-SPA1130-02). Not applicable. The authors would like to thank the anonymous reviewers for their constructive comments. Special thanks to [PERSON] from the Department of Statistics and Operations Research, College of Science, King Saud University for her useful comments. The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.