  This paper presents a learning-based approach for impromptu trajectory
tracking for non-minimum phase systems, i.e., systems with unstable inverse
dynamics. Inversion-based feedforward approaches are commonly used for
improving tracking performance; however, these approaches are not directly
applicable to non-minimum phase systems due to their inherent instability. In
order to resolve the instability issue, existing methods have assumed that the
system model is known and used pre-actuation or inverse approximation
techniques. In this work, we propose an approach for learning a stable,
approximate inverse of a non-minimum phase baseline system directly from its
input-output data. Through theoretical discussions, simulations, and
experiments on two different platforms, we show the stability of our proposed
approach and its effectiveness for high-accuracy, impromptu tracking. Our
approach also shows that including more information in the training, as is
commonly assumed to be useful, does not lead to better performance but may
trigger instability and impact the effectiveness of the overall approach.
