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Control of a Class of Underactuated Systems by Successive Submanifold Stabilization

Beck, Fabian and Sakamoto, Noboru and Ott, Christian (2021) Control of a Class of Underactuated Systems by Successive Submanifold Stabilization. In: IFAC-PapersOnLine. IFAC Secretariat. 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, 11-13 Oct 2021, Berlin, Germany. ISSN 2405-8963.

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Abstract

Many control design methods for underactuated systems require solving a partial differential equation, which can be complex for systems with many degrees of freedom. In order to reduce the complexity, it is proposed to decompose the dynamics into several subsystems. The problem then reduces to the successive stabilization of the individual subsystems, i.e., each step is a submanifold stabilization problem of reduced dimension. In this way, control methods which are only practicable for lower dimensional systems can be applied to the overall complex dynamical system. To ensure that the subsystems can be stabilized independently, the dynamics are transformed by a change of coordinates to a form with block-diagonal inertia metric. For the unactuated part kinetic symmetries can be utilized, whereas for the actuated part null space projectors are employed to decouple the dynamics with respect to the inertia metric. The subsystems are then stabilized by optimal control or PD-like feedback. In the stability analysis semidefinite Lyapunov functions are employed. The procedure is demonstrated for a manipulator on an elastic base and validated in simulation.

Item URL in elib:https://elib.dlr.de/145893/
Document Type:Conference or Workshop Item (Speech)
Title:Control of a Class of Underactuated Systems by Successive Submanifold Stabilization
Authors:
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Beck, FabianFabian.Beck (at) dlr.dehttps://orcid.org/0000-0003-3239-5505
Sakamoto, NoboruUNSPECIFIEDhttps://orcid.org/0000-0002-4684-0297
Ott, ChristianChristian.Ott (at) dlr.dehttps://orcid.org/0000-0003-0987-7493
Date:October 2021
Journal or Publication Title:IFAC-PapersOnLine
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Publisher:IFAC Secretariat
ISSN:2405-8963
Status:Published
Keywords:Hamiltonian dynamics, Robotics, Nonlinear control
Event Title:7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control
Event Location:Berlin, Germany
Event Type:international Conference
Event Dates:11-13 Oct 2021
Organizer:IFAC
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 - Walking robot/locomotion [RO]
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Robotics and Mechatronics (since 2013) > Analysis and Control of Advanced Robotic Systems
Deposited By: Beck, Fabian
Deposited On:19 Nov 2021 10:38
Last Modified:19 Nov 2021 10:38

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