Safe Distributed Control of Multi-Robot Systems with Communication Delays

TL;DR

This work addresses safety in networked multi-robot systems where inter-robot communication incurs delays. It formalizes a distributed control barrier function (CBF) framework that achieves safety with local communication, and augments it with graph neural networks to learn a safe distributed controller. To tackle realistic delays, it introduces a predictor-based architecture that estimates current neighbor states from delayed information and Age-of-Information, enabling safe operation even under imperfect information exchange. Empirical results on collision avoidance demonstrate that the predictor-enhanced framework significantly improves safety compared to delay-agnostic learning, while maintaining scalability through local communication. The approach provides a principled path to certifiable, scalable safety in distributed robotic networks operating in challenging environments with degraded communication.

Abstract

Safe operation of multi-robot systems is critical, especially in communication-degraded environments such as underwater for seabed mapping, underground caves for navigation, and in extraterrestrial missions for assembly and construction. We address safety of networked autonomous systems where the information exchanged between robots incurs communication delays. We formalize a notion of distributed control barrier function for multi-robot systems, a safety certificate amenable to a distributed implementation, which provides formal ground to using graph neural networks to learn safe distributed controllers. Further, we observe that learning a distributed controller ignoring delays can severely degrade safety. We finally propose a predictor-based framework to train a safe distributed controller under communication delays, where the current state of nearby robots is predicted from received data and age-of-information. Numerical experiments on multi-robot collision avoidance show that our predictor-based approach can significantly improve the safety of a learned distributed controller under communication delays. A video abstract is available at https://youtu.be/Hcu1Ri32Spk.

Figures (10)

• Figure 1: We propose a control strategy that keeps an autonomous multi-robot system safe via inter-robot communication. In this example, the controllers $\pi_\text{safe}^i$ and $\pi_\text{safe}^j$ of drones $i$ and $j$ use data sent by the other drone to avoid collisions while reaching the goals.
• Figure 2: Safe control via wireless communication is crucially affected by transmission delays. We propose a predictor that uses delayed measurement ${\bm x}_{j} (t-\delta)$ to compute the estimate $\hat{{\bm x}}_{j} {(t)}$ that is used by the controller $\pi_\text{safe}^i$ of robot $i$ for safe real-time operation.
• Figure 3: Proposed distributed controller implemented on robot $i$. Robot $i$ receives information from nearby robots $\ell$, $j$, and $k$ and computes minimally invasive control actions ${\bm u}_{i} (t)$. Communication delays $\delta(t)$ are compensated by the predictor $\lambda_\zeta$ (red block). The GNN-based controller $\pi_\xi$ (green block) computes corrective actions $\tilde{{\bm u}}_{i} {(t)}$ to ensure safety.
• Figure 4: Snapshot of simulation. Robots (blue) have to reach goals (green) without colliding. The inner circles around robots marks the closest distance before collision. The outer circles determine the safe set, namely robots outside them are tagged safe in training.
• Figure 5: Safety rates with controller \ref{['eq:controller-gnn']} in the perfect information-exchange case.

Theorems & Definitions (13)

• Definition 1: Control Barrier Function Ames17tac-cbf
• Theorem 2: Safe control Ames17tac-cbf
• Remark 3: Time derivative of CBF
• Remark 4: CBF with distributed communication
• Remark 5: Convexity
• Example 8: Collision avoidance
• Remark 9
• Definition 10: Distributed CBF
• Theorem 11: Distributed safety certification
• proof