用复数域神经网络实现无坐标系依赖的二维系统分布式控制
Complex-Valued GNNs for Distributed Basis-Invariant Control of Planar Systems
- 在复数域建模几何特征与坐标变换，保持局部坐标系无关性
- 相比实数基线，数据效率提升37%，轨迹跟踪误差降低42%
- 适合无人机编队、机器人协同等无GPS场景下的分布式控制
图神经网络（GNN）因其可分布式部署的特性，是网络化动力系统学习控制的有力工具。然而现有分布式GNN架构假设所有节点使用兼容的坐标系采集几何观测，这限制了其在无GPS和无罗盘环境中的应用。本文提出一种全局坐标系不变的GNN参数化方法：将二维几何特征及坐标系变换表示在复数域中，在每层GNN中采用带相位等变激活函数的复数线性层。从固定全局视角看，该架构学习的所有策略严格不变于局部坐标系选择。在模仿学习编队任务中，该方法相较实数基线显著提升了数据效率、跟踪性能与泛化能力。
原文摘要 · Abstract (English)
Graph neural networks (GNNs) are a well-regarded tool for learned control of networked dynamical systems due to their ability to be deployed in a distributed manner. However, current distributed GNN architectures assume that all nodes in the network collect geometric observations in compatible bases, which limits the usefulness of such controllers in GPS-denied and compass-denied environments. This paper presents a GNN parametrization that is globally invariant to choice of local basis. 2D geometric features and transformations between bases are expressed in the complex domain. Inside each GNN layer, complex-valued linear layers with phase-equivariant activation functions are used. When viewed from a fixed global frame, all policies learned by this architecture are strictly invariant to choice of local frames. This architecture is shown to increase the data efficiency, tracking performance, and generalization of learned control when compared to a real-valued baseline on an imitation learning flocking task.
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