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Discovering Efficient Periodic Behaviours in Mechanical Systems via Neural Approximators
  • +3
  • Yannik P. Wotte,
  • Sven Dummer,
  • Nicolò Botteghi,
  • Christoph Brune,
  • stefano Stramigioli,
  • Federico Califano
Yannik P. Wotte
Universiteit Twente Faculteit Elektrotechniek Wiskunde en Informatica

Corresponding Author:y.p.wotte@utwente.nl

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Sven Dummer
Universiteit Twente Faculteit Elektrotechniek Wiskunde en Informatica
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Nicolò Botteghi
Universiteit Twente Faculteit Elektrotechniek Wiskunde en Informatica
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Christoph Brune
Universiteit Twente Faculteit Elektrotechniek Wiskunde en Informatica
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stefano Stramigioli
Universiteit Twente Faculteit Elektrotechniek Wiskunde en Informatica
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Federico Califano
Universiteit Twente Faculteit Elektrotechniek Wiskunde en Informatica
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Abstract

It is well known that conservative mechanical systems exhibit local oscillatory behaviours due to their elastic and gravitational potentials, which completely characterise these periodic motions together with the inertial properties of the system. The classification of these periodic behaviours and their geometric characterisation are in an on-going secular debate, which recently led to the so-called eigenmanifold theory. The eigenmanifold characterises nonlinear oscillations as a generalisation of linear eigenspaces. With the motivation of performing periodic tasks efficiently, we use tools coming from this theory to construct an optimization problem aimed at inducing desired closed-loop oscillations through a state feedback law. We solve the constructed optimization problem via gradient-descent methods involving neural networks. Extensive simulations show the validity of the approach.
21 Dec 2022Submitted to Optimal Control, Applications and Methods
22 Dec 2022Submission Checks Completed
22 Dec 2022Assigned to Editor
22 Dec 2022Review(s) Completed, Editorial Evaluation Pending
25 Dec 2022Reviewer(s) Assigned
02 Mar 2023Editorial Decision: Revise Minor
14 Apr 20231st Revision Received
20 Apr 2023Submission Checks Completed
20 Apr 2023Assigned to Editor
20 Apr 2023Review(s) Completed, Editorial Evaluation Pending
21 Apr 2023Reviewer(s) Assigned
04 Jun 2023Editorial Decision: Accept