Cyclic pursuit formation control for arbitrary desired shapes

TL;DR

The paper investigates cyclic-pursuit formation control in a 2D multi-agent system to realize arbitrary closed shapes described by $gamma:[0,1]→R^2$. It proposes two methods: Method 1 operates under shared coordinates with a decomposition into shape-driving and coordination components, while Method 2 handles unknown orientations by aligning coordinate frames and estimating predecessor angles using observed motions and a probabilistic rotation parameter $beta$. Through Fourier-series shaped targets and a Fréchet-distance metric, the authors demonstrate that the approach can achieve and stabilize diverse shapes, with the Achievement-decrease strategy in Method 2 yielding the most robust performance and minimal coordinate-rotation activity after formation. The results highlight the potential for scalable, low-information formation control in MAS, and point to future work on collision avoidance, noise robustness, and reducing information requirements for arbitrary shape formation.

Abstract

A multi-agent system comprises numerous agents that autonomously make decisions to collectively accomplish tasks, drawing significant attention for their wide-ranging applications. Within this context, formation control emerges as a prominent task, wherein agents collaboratively shape and maneuver while preserving formation integrity. Our focus centers on cyclic pursuit, a method facilitating the formation of circles, ellipses, and figure-eights under the assumption that agents can only perceive the relative positions of those preceding them. However, this method's scope has been restricted to these specific shapes, leaving the feasibility of forming other shapes uncertain. In response, our study proposes a novel method based on cyclic pursuit capable of forming a broader array of shapes, enabling agents to individually shape while pursuing preceding agents, thereby extending the repertoire of achievable formations. We present two scenarios concerning the information available to agents and devise formation control methods tailored to each scenario. Through extensive simulations, we demonstrate the efficacy of our proposed method in forming multiple shapes, including those represented as Fourier series, thereby underscoring the versatility and effectiveness of our approach.

Figures (13)

• Figure 1: Schematic of Eq. \ref{['eq:x_ideal']}. The black arrow indicates the movement vector $v_{n(i)1}(k-\ell)$. The agent $i$ calculates the ideal position $\tilde{x}_i(k)$ by repeating the computation of this vector $v_{n(i)1}(k-\ell)$.
• Figure 2: Five desired shapes generated from Fourier series \ref{['eq:fourier']}.
• Figure 3: The agents' trajectories for the desired shape 1 when using Method 1.
• Figure 4: The agents' trajectory for each desired shape when using Method 2, Constant.
• Figure 5: The agents' trajectory for each desired shape when using Method 2, Time--decrease.