Structured learning of rigid‐body dynamics: A survey and unified view from a robotics perspective. Issue 2 (9th June 2021)

• Record Type: Journal Article
• Authors: Geist, A. René; Trimpe, Sebastian
• Other Names: Benner Peter guestEditor.; Klawonn Axel guestEditor.; Stoll Martin guestEditor.
• Is Part Of: Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik. Volume 44:Issue 2(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-06-09
• Subjects: analytical mechanics -- hybrid modeling -- informed machine learning; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; 510.5
• DOI: 10.1002/gamm.202100009
• Languages: English
• ISSNs: 0936-7195

Abstract

Abstract: Accurate models of mechanical system dynamics are often critical for model‐based control and reinforcement learning. Fully data‐driven dynamics models promise to ease the process of modeling and analysis, but require considerable amounts of data for training and often do not generalize well to unseen parts of the state space. Combining data‐driven modeling with prior analytical knowledge is an attractive alternative as the inclusion of structural knowledge into a regression model improves the model's data efficiency and physical integrity. In this article, we survey supervised regression models that combine rigid‐body mechanics with data‐driven modeling techniques. We analyze the different latent functions (such as kinetic energy or dissipative forces) and operators (such as differential operators and projection matrices) underlying common descriptions of rigid‐body mechanics. Based on this analysis, we provide a unified view on the combination of data‐driven regression models, such as neural networks and Gaussian processes, with analytical model priors. Furthermore, we review and discuss key techniques for designing structured models such as automatic differentiation.