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A Constructive Methodology for the IDA-PBC of Underactuated 2-DoF Mechanical Systems with Explicit Solution of PDEs

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Abstract

This paper presents a passivity-based control strategy dealing with underactuated two-degree-of-freedom (2-DoF) mechanical systems. Such a methodology, which is based on the interconnection and damping assignment passivity-based control (IDA-PBC), rooted within the port-controlled Hamiltonian framework, can be applied to a very large class of underactuated 2-DoF mechanical systems. The main contribution, compared to the previous literature, is that the new methodology does not involve the resolution of any partial differential equation, since explicit solutions are given, while no singularities depending on generalised momenta are introduced by the controller. The proposed strategy is applied to two case studies: a) the stabilisation of a translational oscillator with a rotational actuator (TORA) system; b) the gait generation for an underactuated compass-like biped robot. The performances of the presented solution are evaluated through numerical simulations.

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Authors and Affiliations

  1. Department of Electrical Engineering and Information Technology, University of Naples, Via Claudio 21, 80125, Naples, Italy

    Pierluigi Arpenti, Fabio Ruggiero & Vincenzo Lippiello

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  1. Pierluigi Arpenti
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  2. Fabio Ruggiero
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  3. Vincenzo Lippiello
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Correspondence to Pierluigi Arpenti.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The research leading to these results has been supported by both the PRINBOT project (in the frame of the PRIN 2017 research program, grant number 20172HHNK5_002) and the WELDON project (in the frame of Programme STAR, financially supported by UniNA and Compagnia di San Paolo). The authors are solely responsible for its content. The authors would like to thank Alejandro Donaire and José Guadalupe Romero for their support and the useful comments during the derivation of the work.

Pierluigi Arpenti received his M.Sc. degree in automation engineering from the University of Naples Federico II in 2016. He got a Ph.D. degree from the same institution in 2021. His research interests are focused on passivity-based control, underactuated mechanical systems, legged robots, and robotics for logistics and manufacturing.

Fabio Ruggiero received his M.Sc. degree in automation engineering from the University of Naples Federico II in 2007. He got a Ph.D. degree from the same institution in 2010. He spent seven months at Northwestern University as a visiting Ph.D. student from September 2009 to March 2010. After several PostDoctoral positions from 2011 to 2016, he has been holding an Assistant Professor position at the University of Naples Federico II. His research interests are focused on dexterous and dual-hand robotic manipulation, even by using UAVs with small robotic arms, dynamic nonprehensile manipulation, legged robotics. He has co-authored more than 50 among journal papers, book chapters, and conference papers.

Vincenzo Lippiello was born in Naples, Italy, on June 19, 1975. He received his Laurea degree in electronic engineering and the Research Doctorate degree in information engineering from the University of Naples Federico II, in 2000 and 2004, respectively. He is a Professor of Automatic Control in the Department of Electrical Engineering and Information Technology, University of Naples Federico II. His research interests include visual servoing of robot manipulators, hybrid visual/force control, adaptive control, grasping and manipulation, aerial robotics, and visual object tracking and reconstruction. He has published more than 120 journal and conference papers and book chapters.

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Arpenti, P., Ruggiero, F. & Lippiello, V. A Constructive Methodology for the IDA-PBC of Underactuated 2-DoF Mechanical Systems with Explicit Solution of PDEs. Int. J. Control Autom. Syst. 20, 283–297 (2022). https://doi.org/10.1007/s12555-020-0839-1

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  • DOI: https://doi.org/10.1007/s12555-020-0839-1

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