Cyclic pursuit formation control for arbitrary desired shapes

Its inherent ability to tackle challenges surpassing the capacity of individual agents, coupled with its robustness against failures and disturbances, renders it applicable across diverse domains, ranging from robotics to social networks [2, 3]. Among the myriad of tasks within MAS, formation control emerges as a quintessential endeavor, entailing multiple agents orchestrating themselves into various formations while preserving the integrity of the ensemble, a task that has garnered considerable research interest in recent years [4]. Despite the plethora of control algorithms proposed for multi-agent tasks, many of these approaches hinge on the premise of dense interaction dynamics, necessitating rigid interaction topologies among agents to achieve desired outcomes effectively [5, 6]. For instance, the method proposed by De Marina et al. underscores the importance of a rigid interaction topology for successful task execution [5]. In contrast, the cyclic pursuit method stands out for its remarkable ability to achieve formation control with limited information, relying solely on the relative position of the agent ahead, thus offering a more flexible and scalable approach to formation control within MAS [7, 8, 9, 10]. Originating as an attempt to mimic biological entities such as dogs and ants, cyclic pursuit has since evolved into a versatile approach known as the "bugs" problem, which has garnered considerable attention in both academic and industrial circles [7, 8]. Previous studies have extensively explored its dynamics across various agent models, encompassing ants, crickets, frogs, and others, further solidifying its status as a cornerstone of formation control within MAS [10, 11]. Motivated by the question of whether cyclic pursuit enables agents to form shapes beyond those previously demonstrated, this study proposes a novel method for forming desired shapes based on the cyclic pursuit strategy. Addressing two distinct problem settings, we investigate the sufficiency of information for agents to achieve formation for any given shape.