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

arXiv: https://arxiv.org/abs/2303.13446 · HTML: https://mlsanity.com/paper/2303.13446/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Robot manipulation imitation learning, one of 13 directions in Offline RL and imitation learning from data.
- First posted on arXiv 23 Mar 2023.

## Placed in

- Offline RL and imitation learning from data / [Robot manipulation imitation learning](https://mlsanity.com/offlinerl/robot-manipulation-imitation-learning/)

## Built on by (most cited first, 6 of 6)

- [ViViDex: Learning Vision-based Dexterous Manipulation from Human Videos](https://mlsanity.com/paper/2404.15709/) (2024)
- [MimicTouch: Leveraging Multi-modal Human Tactile Demonstrations for Contact-rich Manipulation](https://mlsanity.com/paper/2310.16917/) (2023)
- [Imitation Learning with Limited Actions via Diffusion Planners and Deep Koopman Controllers](https://mlsanity.com/paper/2410.07584/) (2024)
- [KoopMotion: Learning Almost Divergence Free Koopman Flow Fields for Motion Planning](https://mlsanity.com/paper/2509.09074/) (2025)
- [Phase-Amplitude Reduction-Based Imitation Learning](https://mlsanity.com/paper/2406.03735/) (2024)
- [AsymDex: Asymmetry and Relative Coordinates for RL-based Bimanual Dexterity](https://mlsanity.com/paper/2411.13020/) (2024)

## Abstract (arXiv)

Despite impressive dexterous manipulation capabilities enabled by learning-based approaches, we are yet to witness widespread adoption beyond well-resourced laboratories. This is likely due to practical limitations, such as significant computational burden, inscrutable learned behaviors, sensitivity to initialization, 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 to represent complex nonlinear dynamics as linear systems in higher dimensions. Motivated by the fact that complex nonlinear dynamics underlie dexterous manipulation, we develop a Koopman operator-based imitation learning framework to learn the desired motions of both the robotic hand and the object simultaneously. We show that Koopman operators are surprisingly effective for dexterous manipulation and offer a number of unique benefits. Notably, policies can be learned analytically, drastically reducing computation burden and eliminating sensitivity to initialization and the need for painstaking hyperparameter optimization. Our experiments reveal that a Koopman operator-based approach can perform comparably to state-of-the-art imitation learning algorithms in terms of success rate and sample efficiency, while being an order of magnitude faster. Policy videos can be viewed at https://sites.google.com/view/kodex-corl.