Deep Equivariant Multi-Agent Control Barrier Functions

2 min read

Bousias, Lindemann and Pappas learn a distributed control barrier function and a policy for quadrotor swarms with a graph network, as in GCBF+, but force both to respect the symmetries of the problem. Each robot canonicalises its local graph using a group element taken from its own pose, runs a standard graph transformer, then maps the output back. The barrier is invariant and the policy equivariant under that group, so the network learns one behaviour per equivalence class of situations. They argue these local symmetries hold whatever the swarm size, which should help zero-shot transfer to bigger, denser swarms.

Findings

  • Trained with 8 quadrotors and 5 obstacles, tested zero-shot on 8 to 512 robots, with density ranging from 0.125 to 8.
  • With 8 robots all methods were safe, but the hand-written centralised and decentralised CBF-QPs and the models trained against the nominal controller were overly conservative.
  • The CBF-QP baselines could not run beyond 16 robots in their (centralised) simulation because of time and memory.
  • Models trained against the nominal controller lost about 70 % of safety and 60 % of success as N grew, while reach stayed high, which the authors read as slow progress with possible deadlocks.
  • With 512 drones the equivariant model with QP-refined training had about 0.5 collisions per drone, against more than 1.5 for its non-equivariant counterpart. Equivariant models also converged faster in training.

Limits

  • A learned barrier certifies safety only where the network satisfies the barrier conditions, and the paper offers no verification of that. Safety rates fall below 100 % at scale.
  • Simulation only, with perfect state and cooperative, identical agents. Nothing is said about a neighbour that does not follow the shared policy.
  • In clutter, reach rates drop because the nominal controller cannot resolve deadlocks.
  • The authors leave open what happens when the dynamics and the safe set have different symmetries.

Relevance

Follows qin-2021-neural-barrier-certificates and the hand-written wang-2016-safety-barrier-certificates. Like most learned barrier work it assumes every robot runs the same policy. See safe control and aerial swarms.