Decentralized Swarm Control Via SO(3) Embeddings for 3D Trajectories
Dimitria Silveria, Kleber Cabral, Peter Travis Jardine, Sidney Givigi
AI summary
Problem
Existing decentralized swarm control methods for 3D trajectories are limited to circular paths, require both position and velocity inputs, suffer from quaternion-based collision ambiguities, and lack real-world validation.
Approach
The method embeds swarm coordination into the SO(3) Lie group to deform a base circular path into complex 3D trajectories, using a novel electrostatic-inspired phase controller for uniform spacing and a position-only reference generator.
Key results
- SO(3) embeddings generalize trajectory generation beyond quaternion limitations, enabling diverse 3D formations
- Novel phase controller ensures uniform angular separation with formal Lyapunov stability guarantees
- Position-only reference generation eliminates the need for velocity inputs, broadening UAV applicability
- Experimental validation on physical Crazyflie quadcopters demonstrates robustness to disturbances and unmodeled dynamics
Why it matters
Provides a scalable, theoretically grounded, and practically validated framework for real-world 3D swarm robotics applications like surveillance and dynamic capture.
Abstract
This letter presents a novel decentralized approach for achieving emergent behavior in multi-agent systems with min- imal 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.