Cyclic pursuit formation control for arbitrary desired shapes

Abstract

A multi-agent system (MAS) comprises numerous agents that autonomously make decisions to collectively accomplish tasks, drawing significant attention due to their wide range of applications. Within this context, formation control has emerged as a prominent task, wherein agents collaboratively shape and maneuver while preserving formation integrity. This study focuses on cyclic pursuit, a method that facilitates the formation of circles, ellipses, and figure eights under the assumption that agents can only perceive the relative positions of those preceding them. However, the scope of this method has been restricted to these specific shapes, rendering the feasibility of forming other shapes uncertain. To overcome this limitation, we propose a novel method based on cyclic pursuit that is capable of forming a broader array of shapes, enabling agents to individually form the desired shape while pursuing preceding agents, thereby extending the repertoire of achievable formations. We develop two scenarios concerning the information available to the agents and devise formation control methods tailored to each scenario. Through extensive simulations, we demonstrate the efficacy of the proposed method in forming multiple shapes, including those represented as a Fourier series, thereby underscoring the versatility and effectiveness of the proposed approach.