Flocking for leader ability effect and formation obstacle avoidance of multi-agents based on different potential functions

The potential function plays a significant role in influencing interactions among multi-agents during flocking. Most studies that adopt the potential function have primarily focused on attraction and repulsion, neglecting other critical properties, such as well depth. This paper investigates the flocking phenomenon effect when individuals have different social distances and different potential functions with different well depths. Then, two key conclusions are derived. Firstly, a positive correlation between the well depth of the potential function and the attraction observed among intra-group agents. Secondly, agents with smaller social distances will repel agents with larger social distances under the same potential function. Based on this analysis, we propose an integrated flocking algorithm in this paper, which combines different potential functions with flocking and anti-flocking algorithms. Sub-algorithm 1 is the leader ability algorithm. It enables agents to act as actual leader agents that affect other agents, with the ability of their affecting depending on the well depth and social distance. Sub-algorithm 2 is the self-organized formation of multi-level leader agents and obstacle avoidance algorithms. It enables multi-agents to form the desired formation shape through self-organization and maintain the formation's integrity while avoiding obstacles under the effect of the potential function well depth. Furthermore, the potential function model designed in this paper enhances the formation cohesion and reduces the time required to establish formation. Finally, we demonstrate the proposed algorithm's stability and convergence by applying the Lyapunov stability theorem. The corresponding simulation results are presented and effectively verify the effectiveness of the integrated flocking algorithm.