A Novel Convex Layers Strategy for Circular Formation in Multi-Agent Systems

This article considers the problem of conflict-free distribution of point-sized agents on a circular periphery encompassing all agents. The two key elements of the proposed policy include the construction of a set of convex layers (nested convex polygons) using the initial positions of the agents, and a novel search space region for each of the agents. The search space for an agent on a convex layer is defined as the region enclosed between the lines passing through the agent's position and normal to its supporting edges. Guaranteeing collision-free paths, a goal assignment policy designates a unique goal position within the search space of an agent at the initial time itself, requiring no further computation thereafter. In contrast to the existing literature, this work presents a one-shot, collision-free solution to the circular distribution problem by utilizing only the initial positions of the agents. Illustrative examples and extensive Monte-Carlo studies considering various practical attributes demonstrate the effectiveness of the proposed method.