Learning Rigidity-based Flocking Control using Gaussian Processes with Probabilistic Stability Guarantees

Flocking control of multi-agents system is challenging for agents with partially unknown dynamics. These dynamics typically occur due to unfavorable nonlinearities such as friction or production inaccuracies. This paper proposes an online learning-based controller to stabilize flocking motion of double-integrator agents with additional state-dependent, unknown dynamics by using a Gaussian process (GP). Agents interaction is described by a time-invariant infinitesimally minimally rigid undirected graph. We provide a decentralized control law that exponentially stabilizes the motion of the agents and captures Reynold boids motion for swarms by using GPs as an online learning-based oracle for the prediction of the unknown dynamics. In particular the presented approach guarantees a probabilistic bounded tracking error with high probability.