• Login
    View Item 
    •   Home
    • UA Graduate and Undergraduate Research
    • UA Theses and Dissertations
    • Dissertations
    • View Item
    •   Home
    • UA Graduate and Undergraduate Research
    • UA Theses and Dissertations
    • Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of UA Campus RepositoryCommunitiesTitleAuthorsIssue DateSubmit DateSubjectsPublisherJournalThis CollectionTitleAuthorsIssue DateSubmit DateSubjectsPublisherJournal

    My Account

    LoginRegister

    About

    AboutUA Faculty PublicationsUA DissertationsUA Master's ThesesUA Honors ThesesUA PressUA YearbooksUA CatalogsUA Libraries

    Statistics

    Most Popular ItemsStatistics by CountryMost Popular Authors

    Consensus Control of Multi-Agent Rigid Body Systems using Rotation Matrices and Exponential Coordinates

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Thumbnail
    Name:
    azu_etd_19111_sip1_m.pdf
    Size:
    19.18Mb
    Format:
    PDF
    Download
    Author
    Maadani, Mohammad
    Issue Date
    2021
    Keywords
    Consensus control
    Exponential coordinates
    Multi-agent systems
    Rigid body
    Rotation matrix
    Advisor
    Butcher, Eric
    
    Metadata
    Show full item record
    Publisher
    The University of Arizona.
    Rights
    Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction, presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
    Abstract
    This dissertation addresses the 6-DOF consensus control problem of multi-agent rigid body systems. The consensus protocols are designed using two different attitude representations: rotation matrices and principal rotation vectors (exponential coordinates). The control objective is stabilizing the system of rigid bodies to a configuration where all the rigid bodies have a common attitude and prescribed relative positions with velocity synchronization. In this work, for the most part, a fixed and undirected communication topology is considered for the consensus control design and analysis. However, the stability of consensus in multi-agent systems with periodically switched communication topology is also studied using Floquet theory. In addition, the application of Floquet theory in analyzing cases such as switched systems with joint connectivity, unstable subsystems (antagonistic interactions), and nonlinear systems is also studied. As the first methodology for consensus control of multi-agent rigid body systems, the configurations of the rigid bodies are described in terms of the exponential coordinates associated with the Lie groups SO(3) and SE(3). Moreover, the stability of the consensus in multi-agent rigid body systems with periodically switched communication topology is studied using Floquet theory and linearizing the closed-loop systems. The second type of protocols for consensus control of a multi-agent system of $N$ heterogeneous rigid bodies are proposed in the framework of the tangent bundles TSO(3) and TSE(3) associated with Lie groups SO(3) and SE(3), respectively. The feedback control design uses the rotation matrix as opposed to various attitude parameterizations. Almost global asymptotic stability of the consensus subspace is demonstrated using an extension of the Morse-Lyapunov (M-L) approach. Also, the presence of unstable non-consensus equilibria in the closed-loop dynamics is discussed and shown in illustrative examples. A new strategy for full pose and velocity consensus control of multi-agent rigid body systems in the presence of communication delays is presented in this dissertation. Specifically, consensus protocols are proposed on the Banach manifold associated with the tangent bundle TSE(3)^N. The stability argument is strengthened from that used in prior studies by using an extension of Morse-Lyapunov-Krasovskii (M-L-K) approach, and sufficient conditions are derived to achieve almost global asymptotic stability of the consensus subspace. This work also investigates the finite-time pose consensus control of multi-agent rigid body systems using Morse-Lyapunov analysis in the framework of the tangent bundle TSE(3) associated with SE(3). Almost global finite-time stability of the consensus subspace in the nonlinear state space is demonstrated. As another finite-time consensus control problem, the prescribed-time consensus of multi-agent rigid body systems using exponential coordinates is also studied. Specifically, the control objective is to stabilize the relative pose configurations with velocity synchronization of a multi-agent rigid body system in a user-defined convergence time. In this dissertation, the consensus control of multi-agent rigid body spacecraft in orbital relative motion is explored using two approaches. In the first approach, a proportional-derivative (PD) consensus control method, an extension of the Morse-Lyapunov analysis in the framework of the tangent bundle TSE(3) associated with Lie group SE(3) is used. In the second approach, a proportional-integral-derivative (PID) consensus control protocol is introduced where the configurations of the rigid bodies are described in terms of the exponential coordinates associated with the Lie group SE(3). In general, the rigid-body attitude control problems are formulated in terms of full attitude configurations. However, in cases involving control objectives stated in terms of pointing the rigid body, reduced-attitude configurations defined in S^2 are exploited. In this dissertation, distributed control algorithms are proposed for asymptotically stable synchronization and balancing of a multi-agent rigid body reduced-attitude system using Lyapunov analysis. The control objective in the balancing problem is the maximization of the minimum relative angular distance between each pair of rigid body reduced attitudes.
    Type
    text
    Electronic Dissertation
    Degree Name
    Ph.D.
    Degree Level
    doctoral
    Degree Program
    Graduate College
    Mechanical Engineering
    Degree Grantor
    University of Arizona
    Collections
    Dissertations

    entitlement

     
    The University of Arizona Libraries | 1510 E. University Blvd. | Tucson, AZ 85721-0055
    Tel 520-621-6442 | repository@u.library.arizona.edu
    DSpace software copyright © 2002-2017  DuraSpace
    Quick Guide | Contact Us | Send Feedback
    Open Repository is a service operated by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.