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Error Bounds for PD-Controlled Mechanical Systems Under Bounded Disturbances Using Interval Arithmetic

Calzolari, Davide and Giordano, Alessandro Massimo and Albu-Schäffer, Alin Olimpiu (2020) Error Bounds for PD-Controlled Mechanical Systems Under Bounded Disturbances Using Interval Arithmetic. IEEE Robotics and Automation Letters, 5 (2), pp. 1231-1238. IEEE - Institute of Electrical and Electronics Engineers. doi: 10.1109/LRA.2020.2967315. ISSN 2377-3766.

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We present a numerical algorithm based on invariant set theory to evaluate the worst-case performance of PD-controlled mechanical systems affected by bounded disturbances. By performing a specific coordinate transformation, the search and computation of positive invariant sets is simplified. It is shown that, thanks to the preservation of problem structure, the proposed method allows to obtain tight, component-wise bounds on the states, which are especially useful for performance evaluation and tuning of a PD controller. The bounds are formally guaranteed and can be used for safety certification. The method is compared to ultimate boundedness, and the superior results are shown via numerical simulations.

Item URL in elib:https://elib.dlr.de/134024/
Document Type:Article
Title:Error Bounds for PD-Controlled Mechanical Systems Under Bounded Disturbances Using Interval Arithmetic
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Giordano, Alessandro MassimoUNSPECIFIEDhttps://orcid.org/0000-0003-2291-7525UNSPECIFIED
Albu-Schäffer, Alin OlimpiuUNSPECIFIEDhttps://orcid.org/0000-0001-5343-9074142115812
Date:17 January 2020
Journal or Publication Title:IEEE Robotics and Automation Letters
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In ISI Web of Science:Yes
Page Range:pp. 1231-1238
Publisher:IEEE - Institute of Electrical and Electronics Engineers
Series Name:IEEE Xplore Digital
Keywords:Performance evaluation and benchmarking, industrial robots, PD control, disturbance bounds, invariant sets
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Space System Technology
DLR - Research area:Raumfahrt
DLR - Program:R SY - Space System Technology
DLR - Research theme (Project):R - On-Orbit Servicing [SY]
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Robotics and Mechatronics (since 2013)
Deposited By: Beinhofer, Gabriele
Deposited On:10 Feb 2020 12:46
Last Modified:24 Oct 2023 12:46

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