用SO(3)嵌入实现3D蜂群的无速度分布式控制
Decentralized Swarm Control via SO(3) Embeddings for 3D Trajectories
- 基于SO(3)几何嵌入，实现无速度输入的分布式控制
- 生成比四元数方法更广泛的稳定周期轨迹
- 适合需低通信、高鲁棒性的多智能体系统
本文提出一种新型去中心化方法，用于在多智能体系统中实现涌现行为，仅需最小信息共享。基于前期简单轨道研究，该方法通过稳定在基于李群的几何嵌入上，生成一大类稳定周期轨迹。采用李群SO(3)，生成的周期曲线范围比现有四元数方法更广。同时利用SO(3)特性，消除对速度输入的需求，使智能体仅接收位置输入。还提出一种新型相位控制器，确保智能体均匀分布，并给出正式稳定性证明。通过仿真与实验验证，该方法对复杂底层动态和扰动具有强适应性。
原文摘要 · Abstract (English)
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.
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