For biological groups, the behaviors of individuals will have an impact on the alignment efficiency of the collective movement. Motivated by Vicsek's pioneering research on self-organized particles and other related works about flocking behaviors, we propose two mathematical models based on the local information of individuals to include more realistic details in the interaction mechanism between individuals and the rest of the group during the flocking process. The local information of the individual refers to the local consistency, representing the degree of alignment with its neighbors. These two models are the self-introspection model, where the process of orientation adjustment of one individual is ruled by the degree of local consistency with the neighborhood, and the credit evaluation model, where the average orientation of the neighborhoods is weighed using the local consistency of the interacting individuals. Different metrics are calculated to analyze the effects of the model parameters and flocking parameters on groups. Simulation calculations indicate that the two improved models have certain advantages in terms of alignment efficiency for the group. Finally, the optimal model parameters are determined, and the effects of random noise on groups with a single behavior and mixed behaviors are analyzed. The results confirm that individuals with mixed behaviors still possess robustness against noise. This research would contribute to the further interdisciplinary cooperation that involves biology, ethology, and multi-agent complex systems.

In this paper, the circle formation control problem is addressed for a group of cooperative underactuated fish-like robots involving unknown nonlinear dynamics and disturbances. Based on the reinforcement learning and cognitive consistency theory, we propose a decentralized controller without the knowledge of the dynamics of the fish-like robots. The proposed controller can be transferred from simulation to reality. It is only trained in our established simulation environment, and the trained controller can be deployed to real robots without any manual tuning. Simulation results confirm that the proposed model-free robust formation control method is scalable with respect to the group size of the robots and outperforms other representative RL algorithms. Several experiments in the real world verify the effectiveness of our RL-based approach for circle formation control.