Classical and Data-Driven Reduced Order Modeling and Control for Slender Soft Robots

Abstract

Soft robots present significant challenges in design, modeling, and control, primarily due to their virtually infinite degrees of freedom (DOFs). Accurate modeling of these systems is essential for advancing design optimization, model-based control, and estimation algorithms. Thus, their inherent complexity has driven researchers to adopt Reduced Order Modeling (ROM) approaches. This thesis builds upon the Geometric Variable Strain (GVS) model, which is a ROM framework that parameterizes and discretizes strain fields to capture the complex dynamics of soft robots with a finite number of DOFs. The primary contributions of this thesis extend strain-based models through the data-driven discovery of optimal parameterizations for strain fields, enabling significant reduction of DOFs while preserving model accuracy. By employing Proper Orthogonal Decomposition (POD), we identify optimal parameterizations for linear strain bases, achieving significant reductions in DOFs and computational cost. POD also offers valuable physical insights, facilitating the formulation of well-posed shape estimation algorithms and providing deeper understanding of system behavior. Additionally, Autoencoders (AE), the nonlinear counterpart of POD, are leveraged to discover optimal parameterizations for nonlinear bases. This unsupervised learning approach allows for even greater DOFs reduction in complex cases and reveals the intrinsic dimensionality of the system through the latent space manifold. Together, these contributions advance the state-of-the-art in soft robot modeling, providing tools for efficient and accurate modeling applicable to a wide range of scenarios, and extending existing approaches to hybrid soft-rigid systems for the first time. Beyond these primary contributions, this thesis explores various classical parameterization techniques, including local, global (linear), and state-dependent (nonlinear) bases, to enhance modeling efficiency and accuracy in the strain-based models. Furthermore, these models are utilized for two classes of soft/continuum robots —Concentric Tube Robots (CTRs) and cable-driven soft manipulators— enabling accurate shape and external force estimation. These additional contributions highlight the versatility and practical utility of the strain-based models, furthering their impact on soft robotics research.

Date of Award	5 May 2025
Original language	American English
Supervisor	Federico Renda (Supervisor)