Nonlinear Modes as a Tool for Comparing the Mathematical Structure of Dynamic Models of Soft Robots

Conference paper (2024)

Authors

P. Pustina Learning & Autonomous Control - Mechanical, Maritime and Materials Engineering , Sapienza University of Rome
Davide Calzolari Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR), Technische Universität München
Alin Albu-Schaffer Technische Universität München, Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR)
Alessandro De Luca Sapienza University of Rome
C. Della Santina Learning & Autonomous Control - Mechanical, Maritime and Materials Engineering , Technische Universität München
Research Group
Learning & Autonomous Control (Mechanical, Maritime and Materials Engineering) (TU Delft)
More Info
expand_more

Published Date

2024

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Mechanical, Maritime and Materials Engineering

Department

Cognitive Robotics

Research Group

Learning & Autonomous Control

Abstract

Continuum soft robots are nonlinear mechanical systems with theoretically infinite degrees of freedom (DoFs) that exhibit complex behaviors. Achieving motor intelligence under dynamic conditions necessitates the development of control-oriented reduced-order models (ROMs), which employ as few DoFs as possible while still accurately capturing the core characteristics of the theoretically infinite-dimensional dynamics. However, there is no quantitative way to measure if the ROM of a soft robot has succeeded in this task. In other fields, like structural dynamics or flexible link robotics, linear normal modes are routinely used to this end. Yet, this theory is not applicable to soft robots due to their nonlinearities. In this work, we propose to use the recent nonlinear extension in modal theory -called eigenmanifolds- as a means to evaluate control-oriented models for soft robots and compare them. To achieve this, we propose three similarity metrics relying on the projection of the nonlinear modes of the system into a task space of interest. We use this approach to compare quantitatively, for the first time, ROMs of increasing order generated under the piecewise constant curvature (PCC) hypothesis with a high-dimensional finite element (FE)-like model of a soft arm. Results show that by increasing the order of the discretization, the eigenmanifolds of the PCC model converge to those of the FE model.