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Recently, Koopman operator theory has been shown capable of constructing control-oriented soft robot models from data. However, building these models requires extensive data collection and they do not necessarily generalize well outside of the training observations. This paper presents a more data-efficient and generalizable approach to soft robot modeling that first identifies a physics-based Koopman model then supplements it with a data-driven residual Koopman model. The resulting combined model is linear and thus compatible with real-time model-based control techniques such as Model Predictive Control (MPC). The efficacy of the approach is demonstrated on several simulated systems and on a real soft robot arm, where it is shown to generate models that are more accurate than purely physics-based models and require less data to construct than purely data-driven models. Using a model-based controller, the soft arm is able to successfully track end effector trajectories, perform a pick-and-place task, and write on a dry-erase board, showcasing the applicability of this framework to increase the capabilities of soft robotic systems.<\/jats:p>","DOI":"10.1177\/02783649241272114","type":"journal-article","created":{"date-parts":[[2024,10,8]],"date-time":"2024-10-08T13:06:52Z","timestamp":1728392812000},"page":"388-406","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":14,"title":["A Koopman-based residual modeling approach for the control of a soft robot arm"],"prefix":"10.1177","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7683-2725","authenticated-orcid":false,"given":"Daniel","family":"Bruder","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Bombara","sequence":"additional","affiliation":[{"name":"John A. 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