A Circular Formation Method for Biomimetic Robotic Fish Inspired by Fish Milling

Circular motion phenomena, akin to fish milling, are prevalent within the animal kingdom. This paper delineates two fundamental mechanisms underlying such occurrences: forward following and circular topological communication. Leveraging these pivotal concepts, we present a multi-agent formation circular model based on a second-order integrator. This model engenders the attainment of homogeneous intelligence convergence along the circumferential trajectory. The convergence characteristics are intricately linked to the number of agents and the model parameters. Consequently, we propose positive and negative solutions for ascertaining the convergent circle property and model parameters. Furthermore, by integrating our proposed formation control methodology with a robotic fish dynamics model, we have successfully implemented simulations and experiments, demonstrating the circular formation of multiple biomimetic robotic fish. This study provides a mathematical explication for the circular motion observed in animal groups and introduces a novel approach to achieving circular formation in multiple robots inspired by biological phenomena.