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Despite impressive dexterous manipulation capabilities enabled bylearning-based approaches, we are yet to witness widespread adoption beyondwell-resourced laboratories. This is likely due to practical limitations, suchas significant computational burden, inscrutable learned behaviors, sensitivityto initialization, and the considerable technical expertise required forimplementation. In this work, we investigate the utility of Koopman operatortheory in alleviating these limitations. Koopman operators are simple yetpowerful control-theoretic structures to represent complex nonlinear dynamicsas linear systems in higher dimensions. Motivated by the fact that complexnonlinear dynamics underlie dexterous manipulation, we develop a Koopmanoperator-based imitation learning framework to learn the desired motions ofboth the robotic hand and the object simultaneously. We show that Koopmanoperators are surprisingly effective for dexterous manipulation and offer anumber of unique benefits. Notably, policies can be learned analytically,drastically reducing computation burden and eliminating sensitivity toinitialization and the need for painstaking hyperparameter optimization. Ourexperiments reveal that a Koopman operator-based approach can performcomparably to state-of-the-art imitation learning algorithms in terms ofsuccess rate and sample efficiency, while being an order of magnitude faster.Policy videos can be viewed at https://sites.google.com/view/kodex-corl.

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