Predictive Flocking of an Omnidirectional Multi-Agent System for Lattice Formation: Sigma-Norm Design and Comparative Performance Assessment

This paper presents a decentralized Model Predictive Control (MPC) flocking algorithm based on the sigma norm, designed to achieve coordinated motion among agents while ensuring collision avoidance and lattice formation. The proposed method is rigorously compared against a seminal classic flocking model and two advanced MPC-based strategies that incorporate lattice-structured cost functions. Through a series of statistical hypothesis tests, we demonstrate that the proposed approach reliably achieves the target lattice configuration, ensures convergence to a common velocity, and prevents collisions with both obstacles and neighboring agents. The results show that our method consistently outperforms existing approaches, offering superior performance and reliability for multi-agent systems modeled as omnidirectional four-wheeled robots.