Strict Nonlinear Normal Modes of Systems Characterized by Scalar Functions on Riemannian Manifolds
| Autor: | Dominic Lakatos, Stefano Stramigioli, Alin Albu-Schaffer |
|---|---|
| Přispěvatelé: | Digital Society Institute, Robotics and Mechatronics |
| Rok vydání: | 2021 |
| Předmět: |
0209 industrial biotechnology
Pure mathematics Control and Optimization Double pendulum Biomedical Engineering Linear systems Tensors 02 engineering and technology Robot kinematics Flexible Robotics 03 medical and health sciences 020901 industrial engineering & automation Artificial Intelligence Normal mode Control Nonlinear systems Metric tensor Invariant (mathematics) Manifolds 030304 developmental biology Mathematics Measurement 0303 health sciences Oscillation Mechanical Engineering Linear system Modeling Scalar (physics) and Learning for Soft Robots Dynamics Computer Science Applications Human-Computer Interaction Nonlinear system Control and Systems Engineering Computer Vision and Pattern Recognition Robots |
| Zdroj: | IEEE Robotics and automation letters, 6(2):9361317, 1910-1917. IEEE Robotics and Automation Letters |
| ISSN: | 2377-3774 2377-3766 |
| DOI: | 10.1109/lra.2021.3061303 |
| Popis: | 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 low-dimensional 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 [1] , [16] , [17] 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 letter 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. |
| Databáze: | OpenAIRE |
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