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

2024-04-17

AI Summary

This work addresses the problem of achieving collision-free, uniform deployment of point-mass agents on the minimum enclosing circle of their initial configuration in multi-agent systems. We propose a one-shot, deterministic target assignment method: leveraging nested convex layers and normal-region constraints defined by supporting edges, we formulate a static search space and perform target allocation via computational geometry techniques—including hierarchical convex hull computation and supporting line modeling—without online re-planning. The approach guarantees globally collision-free trajectories and achieves 100% task completion, while substantially reducing communication and computational overhead. Our key contribution is the first integration of nested convex layering with normal-region constraints to enable global, conflict-free circular formation generation—thereby departing from conventional distributed re-planning paradigms.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Multiagent Systems: Multiagent Planning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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 demonstrate the effectiveness of the proposed policy.

Problem

• Conflict-free distribution of agents
• Construction of convex layers
• One-shot collision-free solution

Innovation

• Convex layers strategy
• Collision-free paths
• One-shot solution