Episodic Koopman Learning of Nonlinear Robot Dynamics with Application to Fast Multirotor Landing

This paper presents a novel episodic method to learn a robot's nonlinear dynamics model and an increasingly optimal control sequence for a set of tasks. The method is based on the {\em Koopman operator} approach to nonlinear dynamical systems analysis, which models the flow of {\em observables} in a function space, rather than a flow in a state space. Practically, this method estimates a nonlinear diffeomorphism that lifts the dynamics to a higher dimensional space where they are linear. Efficient Model Predictive Control methods can then be applied to the lifted model. This approach allows for real time implementation in on-board hardware, with rigorous incorporation of both input and state constraints during learning. We demonstrate the method in a real-time implementation of fast multirotor landing, where the nonlinear ground effect is learned and used to improve landing speed and quality.