Identifying an effective model of a dynamical system from sensory data and using it for future state prediction and control is challenging. Recent data-driven algorithms based on Koopman theory are a promising approach to this problem, but they typically never update the model once it has been identified from a relatively small set of observation, thus making long-term prediction and control difficult for realistic systems, in robotics or fluid mechanics for example. This paper introduces a novel method for learning an embedding of the state space with linear dynamics from sensory data. Unlike previous approaches, the dynamics model can be updated online and thus easily applied to systems with non-linear dynamics in the original configuration space. The proposed approach is evaluated empirically on several classical dynamical systems and sensory modalities, with good performance on long-term prediction and control.

The ability to adapt to changing conditions is a key feature of a successful autonomous system. In this work, we use the Recursive Gaussian Processes (RGP) for identification of the quadrotor air drag model online, without the need of training data. The identified drag model then augments a physics-based model of the quadrotor dynamics, which allows more accurate quadrotor state prediction with increased ability to adapt to changing conditions. This data-augmented physics-based model is utilized for precise quadrotor trajectory tracking using the suitably modified Model Predictive Control (MPC) algorithm. The proposed modelling and control approach is evaluated using the Gazebo simulator and it is shown that the proposed approach tracks a desired trajectory with a higher accuracy compared to the MPC with the non-augmented (purely physics-based) model.