Complex-Valued GNNs for Distributed Basis-Invariant Control of Planar Systems

TL;DR

This paper introduces a complex-valued GNN architecture for distributed control of planar systems that is invariant to local basis choices, improving data efficiency and performance in GPS- and compass-denied environments.

Contribution

The paper proposes a novel complex-valued GNN parametrization that achieves global basis invariance for distributed control of planar systems.

Findings

Increased data efficiency compared to real-valued baselines

Improved tracking performance in flocking tasks

Enhanced generalization of learned control policies

Abstract

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.