  Formation control algorithms for multi-agent systems have gained much
attention in the recent years due to the increasing amount of mobile and aerial
robotic swarms. The design of safe controllers for these vehicles is a
substantial aspect for an increasing range of application domains. However,
parts of the vehicle's dynamics and external disturbances are often unknown or
very time-consuming to model. To overcome this issue, we present a safe
formation control law for multiagent systems based on double integrator
dynamics by using Gaussian Processes for an online learning of the unknown
dynamics. The presented approach guarantees a bounded error to desired
formations with high probability, where the bound is explicitly given. A
numerical example highlights the effectiveness of the learning-based formation
control law.
