Decentralized Swarm Control via SO(3) Embeddings for 3D Trajectories

TL;DR

This paper introduces a decentralized control method for multi-agent systems that uses SO(3) embeddings to generate stable, periodic 3D trajectories with minimal information sharing, enhancing flexibility and robustness.

Contribution

The paper develops a novel SO(3)-based geometric embedding approach for decentralized swarm control, enabling a wider range of trajectories and eliminating the need for velocity inputs.

Findings

Produces stable, periodic 3D trajectories with minimal communication.

Eliminates velocity inputs by leveraging SO(3) properties.

Validated through simulations and experiments demonstrating robustness.

Abstract

This paper presents a novel decentralized approach for achieving emergent behavior in multi-agent systems with minimal information sharing. Based on prior work in simple orbits, our method produces a broad class of stable, periodic trajectories by stabilizing the system around a Lie group-based geometric embedding. Employing the Lie group SO(3), we generate a wider range of periodic curves than existing quaternion-based methods. Furthermore, we exploit SO(3) properties to eliminate the need for velocity inputs, allowing agents to receive only position inputs. We also propose a novel phase controller that ensures uniform agent separation, along with a formal stability proof. Validation through simulations and experiments showcases the method's adaptability to complex low-level dynamics and disturbances.