A flocking control algorithm of multi-agent systems based on cohesion of the potential function

Flocking cohesion is critical for maintaining a group’s aggregation and integrity. Designing a potential function to maintain flocking cohesion unaffected by social distance is challenging due to the uncertainty of real-world conditions and environments that cause changes in agents’ social distance. Previous flocking research based on potential functions has primarily focused on agents’ same social distance and the attraction–repulsion of the potential function, ignoring another property affecting flocking cohesion: well depth, as well as the effect of changes in agents’ social distance on well depth. This paper investigates the effect of potential function well depths and agent’s social distances on the multi-agent flocking cohesion. Through the analysis, proofs, and classification of these potential functions, we have found that the potential function well depth is proportional to the flocking cohesion. Moreover, we observe that the potential function well depth varies with the agents’ social distance changes. Therefore, we design a segmentation potential function and combine it with the flocking control algorithm in this paper. It enhances flocking cohesion significantly and has good robustness to ensure the flocking cohesion is unaffected by variations in the agents’ social distance. Meanwhile, it reduces the time required for flocking formation. Subsequently, the Lyapunov theorem and the LaSalle invariance principle prove the stability and convergence of the proposed control algorithm. Finally, this paper adopts two subgroups with different potential function well depths and social distances to encounter for simulation verification. The corresponding simulation results demonstrate and verify the effectiveness of the flocking control algorithm.