Nonconcentric Boundary-Constrained Circular Formation Control for Multi-Agent Systems in the Presence of Spatio-Temporal Flow Fields

Abstract In multi-agent formation control, external flow fields introduce additional forces that affect the agents' speed and heading angles, posing significant challenges to the formation stability. This paper addresses the challenge of achieving multi-agent circular formation control in dynamic environments influenced by time-varying and spatially nonuniform flow fields. We consider the kinematics of the agents' model as a second-order unicycle framework, where we control the linear acceleration and turn rate to facilitate smoother motion control. Moreover, while stabilizing the agents on the desired circle in different phase arrangements with limited communication topology, we impose the nonuniform motion constraint by considering the outer boundary nonconcentric. By leveraging the properties of Mobius transformation, we map the agents' motion to a transformed plane where the motion constraints become uniform. In the transformed plane, we utilize the concept of the barrier Lyapunov function to stabilize the agents on the desired circular orbit without violating the constraints. Additionally, by utilizing the properties of Mobius transformation and its inverse mapping, we establish a connection between the control laws of the two planes and derive the actual plane control laws that depend solely on the parameters of the actual plane, ensuring applicability to real-world scenarios. Finally, we conduct numerical simulations to validate the effectiveness of the proposed approach.