Koopman Eigenfunctions
Discovering linear evolution of dynamical systems
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 quadrotor landing, where the nonlinear ground effect is learned and used to improve landing speed and quality.
References
Folkestad, C., Pastor, D., Mezic, I., Mohr, R., Fonoberova, M., & Burdick, J. W. (2020). Extended Dynamic Mode Decomposition with Learned Koopman Eigenfunctions for Prediction and Control. In Proc. American Control Conf.
Folkestad, C., Pastor, D., & Burdick, J. W. (2020). Episodic Koopman Learning of Nonlinear Robot Dynamics with Application to Fast Quadrotor Landing. In Proc. International Conference of Robotics and Autonomy.
