Fourier-Based Multi-Agent Formation Control to Track Evolving Closed Boundaries

The automatic monitoring/tracking of environmental boundaries by multi-agent systems is a fundamental problem which has many practical applications. In this paper, we address this problem with formation control techniques based on parametric curves that represent the boundary’s feedback shape. For that, we approximate the curve with truncated Fourier series, whose finite coefficients are utilized to characterize the curve’s shape and to automatically distribute the agents along it. These feedback Fourier coefficients are exploited to design a new type of formation controller that drives the agents to form desired curves. A detailed stability analysis is provided for the proposed control methodology, considering both fixed and switching multi-agent topologies. The reported numerical simulation study demonstrates the performance and feasibility of our new method to track closed boundaries of different shapes.