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Strict Nonlinear Normal Modes of Systems Characterized by Scalar Functions on Riemannian Manifolds

Albu-Schäffer, Alin Olimpiu and Lakatos, Dominic and Stramigioli, Stefano (2021) Strict Nonlinear Normal Modes of Systems Characterized by Scalar Functions on Riemannian Manifolds. IEEE Robotics and Automation Letters. IEEE - Institute of Electrical and Electronics Engineers. doi: 10.1109/LRA.2021.3061303. ISSN 2377-3766.

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For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of lowdimensional invariant manifolds in the form of nonlinear normal modes is rather a niche topic, treated mainly in the context of structural mechanics for systems with Euclidean metrics, i.e., for point masses connected by nonlinear springs. In our previous research we recognized, however, that a very rich structure of periodic and low-dimensional solutions exist also within nonlinear systems such as elastic multi-body systems encountered in the biomechanics of humans and animals or of humanoid and quadruped robots, which are characterized by a non-constant metric tensor. This paper briefly discusses different generalizations of linear oscillation modes to nonlinear systems and proposes a definition of strict nonlinear normal modes, which matches most of the relevant properties of the linear modes. The main contributions are a theorem providing necessary and sufficient conditions for the existence of strict oscillation modes on systems endowed with a Riemannian metric and a potential field as well as a constructive example of designing such modes in the case of an elastic double pendulum.

Item URL in elib:https://elib.dlr.de/141122/
Document Type:Article
Title:Strict Nonlinear Normal Modes of Systems Characterized by Scalar Functions on Riemannian Manifolds
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Albu-Schäffer, Alin OlimpiuUNSPECIFIEDhttps://orcid.org/0000-0001-5343-9074142115859
Stramigioli, StefanoUniversity of Twente, NetherlandsUNSPECIFIEDUNSPECIFIED
Date:23 February 2021
Journal or Publication Title:IEEE Robotics and Automation Letters
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In ISI Web of Science:Yes
Publisher:IEEE - Institute of Electrical and Electronics Engineers
Keywords:Dynamics, Flexible Robotics, Modeling, Control, and Learning for Soft Robots
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Robotics
DLR - Research area:Raumfahrt
DLR - Program:R RO - Robotics
DLR - Research theme (Project):R - On-Orbit Servicing [RO]
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Robotics and Mechatronics (since 2013)
Deposited By: Beinhofer, Gabriele
Deposited On:28 Apr 2021 14:31
Last Modified:11 Sep 2023 13:24

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