  Koopman operator theory has been gaining momentum for model extraction,
planning, and control of data-driven robotic systems. The Koopman operator's
ability to extract dynamics from data depends heavily on the selection of an
appropriate dictionary of lifting functions. In this paper we propose ACD-EDMD,
a new method for Analytical Construction of Dictionaries of appropriate lifting
functions for a range of data-driven Koopman operator based nonlinear robotic
systems. The key insight of this work is that information about fundamental
topological spaces of the nonlinear system (such as its configuration space and
workspace) can be exploited to steer the construction of Hermite
polynomial-based lifting functions. We show that the proposed method leads to
dictionaries that are simple to implement while enjoying provable completeness
and convergence guarantees when observables are weighted bounded. We evaluate
ACD-EDMD using a range of diverse nonlinear robotic systems in both simulated
and physical hardware experimentation (a wheeled mobile robot, a
two-revolute-joint robotic arm, and a soft robotic leg). Results reveal that
our method leads to dictionaries that enable high-accuracy prediction and that
can generalize to diverse validation sets. The associated GitHub repository of
our algorithm can be accessed at
\url{https://github.com/UCR-Robotics/ACD-EDMD}.
