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

SW ARM is a decentralized form of multi-agent system (MAS) that displays emergent behavior --that is, complex behaviors arising from local interactions governed by simple rules without centralized coordination [1]. Swarm agents are often robotic platforms such as uncrewed aerial vehicles (UA V s) used in various domains, including entertainment, surveillance, and defense. This paper addresses the challenge of generating stable, closed 3D formations around a fixed point for UA V s using only local position information. Such formations are relevant in dynamic capture, surveillance, and mobbing scenarios [2], and relate to applications such as lattice formation [3], encirclement [4], epitrochoidal motion [5], target enclosing [6], and other dynamic patterns [7]. Existing approaches often rely on consensus-based algorithms. For example, [8] uses consensus control and heading error compensation for 2D circular trajectories, with particle swarm optimization (PSO) applied to tune controller gains. However, this method scales poorly, lacks real-world validation, and is vulnerable to agent loss. Similarly, [9] applies consensus-based optimization for simulated circular patrolling.