Discovering efficient periodic behaviors in mechanical systems via neural approximators

Author:

Wotte Yannik P.1ORCID,Dummer Sven2ORCID,Botteghi Nicolò2,Brune Christoph2,Stramigioli Stefano1,Califano Federico1

Affiliation:

1. Robotics & Mechatronics (RaM) Group University of Twente Enschede The Netherlands

2. Mathematics of Imaging and AI (MIA) Group University of Twente Enschede The Netherlands

Abstract

AbstractIt is well known that conservative mechanical systems exhibit local oscillatory behaviors due to their elastic and gravitational potentials, which completely characterize these periodic motions together with the inertial properties of the system. The classification of these periodic behaviors and their geometric characterization are in an ongoing secular debate, which recently led to the so‐called eigenmanifold theory. The eigenmanifold characterizes nonlinear oscillations as a generalization 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.

Publisher

Wiley

Subject

Applied Mathematics,Control and Optimization,Software,Control and Systems Engineering

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Optimal potential shaping on SE(3) via neural ordinary differential equations on Lie groups;The International Journal of Robotics Research;2024-06-14

2. Nonlinear Modes as a Tool for Comparing the Mathematical Structure of Dynamic Models of Soft Robots;2024 IEEE 7th International Conference on Soft Robotics (RoboSoft);2024-04-14

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