Learning Koopman Reduced-Order Model for Feedback Control in Dexterous Manipulation

We propose a data-driven feedback control method for dexterous manipulation that uses a Koopman-based reduced-order model (ROM) and a simple static state-feedback law in a lifted state space. From demonstrations, we learn Koopman reference dynamics, and from rollouts with control, we identify a controlled Koopman model using extended Dynamic Mode Decomposition with control (eDMDc); both are projected onto a common reduced subspace where the feedback gain is chosen to match the reduced closed-loop dynamics to the reduced reference. To ensure stability of the learned reference, we apply spectral clipping (SC) to enforce a desired discrete-time stability margin. We also derive a tracking-error bound that separates the effects of model mismatch, projection and invariance errors, and residual disturbances. The method is evaluated on tool-use and door-opening tasks in the MuJoCo Adroit hand environment, using third-order polynomial observables to study success rate, RMS tracking error, final distance to the goal, and controllable modes as functions of the reduced order, with and without SC, and achieves high success with microsecond-level online computation time.