  Koopman-based learning methods can potentially be practical and powerful
tools for dynamical robotic systems. However, common methods to construct
Koopman representations seek to learn lifted linear models that cannot capture
nonlinear actuation effects inherent in many robotic systems. This paper
presents a learning and control methodology that is a first step towards
overcoming this limitation. Using the Koopman canonical transform,
control-affine dynamics can be expressed by a lifted bilinear model. The
learned model is used for nonlinear model predictive control (NMPC) design
where the bilinear structure can be exploited to improve computational
efficiency. The benefits for control-affine dynamics compared to existing
Koopman-based methods are highlighted through an example of a simulated planar
quadrotor. Prediction error is greatly reduced and closed loop performance
similar to NMPC with full model knowledge is achieved.
