Deep Equivariant Multi-Agent Control Barrier Functions

With multi-agent systems increasingly deployed autonomously at scale in complex environments, ensuring safety of the data-driven policies is critical. Control Barrier Functions have emerged as an effective tool for enforcing safety constraints, yet existing learning-based methods often lack in scalability, generalization and sampling efficiency as they overlook inherent geometric structures of the system. To address this gap, we introduce symmetries-infused distributed CBFs, enforcing the satisfaction of intrinsic symmetries on learnable graph-based safety certificates. We theoretically motivate the need for equivariant parametrization of CBFs and policies, and propose a simple, yet efficient and adaptable methodology for constructing such equivariant group-modular networks via the compatible group actions. This approach encodes safety constraints in a distributed data-efficient manner, enabling zero-shot generalization to larger and denser swarms. Through extensive simulations on multi-robot navigation tasks, we demonstrate that our method outperforms state-of-the-art baselines in terms of safety, scalability, and task success rates, highlighting the importance of embedding symmetries in safe distributed neural policies.

Authors

• Nikolaos Bousias
• Lars Lindemann
• George J. Pappas

Keywords

• Learning systems
• Adaptation models
• Navigation
• Scalability
• Neural networks
• Safety
• Intelligent robots
• Multi-agent systems
• Control Barrier Functions
• Scalable
• Sampling Efficiency
• Safety Constraints
• Loss Function
• Neural Network
• Collision
• Dynamical
• System State
• Graphical Representation
• Optimal Policy
• Computationally Intractable
• Group Elements
• Target State
• Policy Learning
• Local Frame
• Safety Policies
• Safe Set
• Lie Group
• Nominal Control
• Smooth Manifold
• Haar Measure
• Swarm Size
• Geometric Symmetry
• Identification Of Elements
• Submanifold
• Infinite-dimensional Space
• Vector Field
• Smooth Vector Field