On the Utility of Koopman Operator Theory in Learning Dexterous Manipulation Skills

Recent advances in learning-based approaches have led to impressive dexterous manipulation capabilities. Yet, we haven't witnessed widespread adoption of these capabilities beyond the laboratory. This is likely due to practical limitations, such as significant computational burden, inscrutable policy architectures, sensitivity to parameter initializations, and the considerable technical expertise required for implementation. In this work, we investigate the utility of Koopman operator theory in alleviating these limitations. Koopman operators are simple yet powerful control-theoretic structures that help represent complex nonlinear dynamics as linear systems in higher-dimensional spaces. Motivated by the fact that complex nonlinear dynamics underlie dexterous manipulation, we develop an imitation learning framework that leverages Koopman operators to simultaneously learn the desired behavior of both robot and object states. We demonstrate that a Koopman operator-based framework is surprisingly effective for dexterous manipulation and offers a number of unique benefits. First, the learning process is analytical, eliminating the sensitivity to parameter initializations and painstaking hyperparameter optimization. Second, the learned reference dynamics can be combined with a task-agnostic tracking controller such that task changes and variations can be handled with ease. Third, a Koopman operator-based approach can perform comparably to state-of-the-art imitation learning algorithms in terms of task success rate and imitation error, while being an order of magnitude more computationally efficient. In addition, we discuss a number of avenues for future research made available by this work.