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    A Dynamical System for Prioritizing and Coordinating Motivations

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    Author
    Reverdy, Paul
    Koditschek, Daniel E.
    Affiliation
    Univ Arizona, Dept Aerosp & Mech Engn
    Issue Date
    2018
    Keywords
    limit cycles
    geometric singular perturbation theory
    relaxation oscillations
    Hopf bifurcation
    decision making
    
    Metadata
    Show full item record
    Publisher
    SIAM PUBLICATIONS
    Citation
    Reverdy, P., & Koditschek, D. E. (2018). A dynamical system for prioritizing and coordinating motivations. SIAM Journal on Applied Dynamical Systems, 17(2), 1683-1715. https://doi.org/10.1137/17M111972X
    Journal
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
    Rights
    © 2018, Society for Industrial and Applied Mathematics.
    Collection Information
    This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.
    Abstract
    We develop a dynamical systems approach to prioritizing and selecting multiple recurring tasks with the aim of conferring a degree of deliberative goal selection to a mobile robot confronted with competing objectives. We take navigation as our prototypical task and use reactive (i.e., vector field) planners derived from navigation functions to encode control policies that achieve each individual task. We associate a scalar "value" with each task representing its current urgency and let that quantity evolve in time as the robot evaluates the importance of its assigned task relative to competing tasks. The robot's motion control input is generated as a convex combination of the individual task vector fields. Their weights, in turn, evolve dynamically according to a decision model adapted from the literature on bioinspired swarm decision making, driven by the values. In this paper we study a simple case with two recurring, competing navigation tasks and derive conditions under which it can be guaranteed that the robot will repeatedly serve each in turn. Specifically, we provide conditions sufficient for the emergence of a stable limit cycle along which the robot repeatedly and alternately navigates to the two goal locations. Numerical study suggests that the basin of attraction is quite large so that significant perturbations are recovered with a reliable return to the desired task coordination pattern.
    ISSN
    1536-0040
    DOI
    10.1137/17M111972X
    Version
    Final published version
    Sponsors
    Air Force Research Laboratory [FA865015D1845, 669737-1]
    Additional Links
    https://epubs.siam.org/doi/10.1137/17M111972X
    ae974a485f413a2113503eed53cd6c53
    10.1137/17M111972X
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    UA Faculty Publications

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