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Reduced Euler-Lagrange Equations of Floating-base Robots: Computation, Properties & Applications

Mishra, Hrishik and Garofalo, Gianluca and Giordano, Alessandro Massimo and De Stefano, Marco and Ott, Christian and Kugi, Andreas (2022) Reduced Euler-Lagrange Equations of Floating-base Robots: Computation, Properties & Applications. IEEE Transactions on Robotics. IEEE - Institute of Electrical and Electronics Engineers. doi: 10.1109/TRO.2022.3206716. ISSN 1552-3098.

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Official URL: https://ieeexplore.ieee.org/document/9929266


At first glance, a floating-base robotic system is a kinematic chain, and its equations of motion are described by the inertia-coupled dynamics of its shape and movable base. However, the dynamics embody an additional structure due to the momentum evolution, which acts as a velocity constraint. In prior works of robot dynamics, matrix transformations of the dynamics revealed a block-diagonal inertia. However, the structure of the transformed matrix of Coriolis/Centrifugal (CC) terms was not examined, and is the primary contribution of this article. To this end, we simplify the CC terms from robot dynamics and derive the analogous terms from geometric mechanics. Using this interdisciplinary link, we derive a two-part structure of the CC matrix, in which each partition is iteratively computed using a self-evident velocity dependency. Through this CC matrix, we reveal a commutative property, the velocity dependencies of the skew-symmetry property, the invariance of the shape dynamics to the basis of momentum, and the curvature as a matrix operator. Finally, we show the application of the proposed CC matrix structure through controller design and locomotion analysis.

Item URL in elib:https://elib.dlr.de/189344/
Document Type:Article
Title:Reduced Euler-Lagrange Equations of Floating-base Robots: Computation, Properties & Applications
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Mishra, HrishikUNSPECIFIEDhttps://orcid.org/0000-0002-5025-2447UNSPECIFIED
Garofalo, GianlucaUNSPECIFIEDhttps://orcid.org/0000-0002-7481-3464UNSPECIFIED
Giordano, Alessandro MassimoUNSPECIFIEDhttps://orcid.org/0000-0003-2291-7525UNSPECIFIED
De Stefano, MarcoUNSPECIFIEDhttps://orcid.org/0000-0003-3777-9487UNSPECIFIED
Ott, ChristianUNSPECIFIEDhttps://orcid.org/0000-0003-0987-7493UNSPECIFIED
Kugi, AndreasUNSPECIFIEDhttps://orcid.org/0000-0001-7995-1690UNSPECIFIED
Date:25 October 2022
Journal or Publication Title:IEEE Transactions on Robotics
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In ISI Web of Science:Yes
EditorsEmailEditor's ORCID iDORCID Put Code
Publisher:IEEE - Institute of Electrical and Electronics Engineers
Series Name:IEEE Transactions on Robotics
Keywords:Lagrangian dynamics, dynamics, motion control, nonholonomic mechanisms and systems
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) > Analysis and Control of Advanced Robotic Systems
Deposited By: Mishra, Hrishik
Deposited On:26 Oct 2022 20:54
Last Modified:26 Oct 2022 20:54

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