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

ACD-EDMD: Analytical Construction for Dictionaries of Lifting Functions in Koopman Operator-based Nonlinear Robotic Systems