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Dissipation-Induced Self-Recovery in Systems on Principal Bundles

[+] Author Affiliations
Tony Dear, Matthew Travers, Howie Choset

Carnegie Mellon University, Pittsburgh, PA

Scott David Kelly

University of North Carolina at Charlotte, Charlotte, NC

Paper No. DSCC2014-6212, pp. V001T11A004; 5 pages
doi:10.1115/DSCC2014-6212
From:
  • ASME 2014 Dynamic Systems and Control Conference
  • Volume 1: Active Control of Aerospace Structure; Motion Control; Aerospace Control; Assistive Robotic Systems; Bio-Inspired Systems; Biomedical/Bioengineering Applications; Building Energy Systems; Condition Based Monitoring; Control Design for Drilling Automation; Control of Ground Vehicles, Manipulators, Mechatronic Systems; Controls for Manufacturing; Distributed Control; Dynamic Modeling for Vehicle Systems; Dynamics and Control of Mobile and Locomotion Robots; Electrochemical Energy Systems
  • San Antonio, Texas, USA, October 22–24, 2014
  • Conference Sponsors: Dynamic Systems and Control Division
  • ISBN: 978-0-7918-4618-6
  • Copyright © 2014 by ASME

abstract

The “self-recovery” phenomenon is a seemingly curious property of certain underactuated dissipative systems in which dissipative forces always push the system to a pre-determined equilibrium state dependent on the initial conditions. The systems for which this has been studied are Abelian, with all system velocity interactions due entirely to inertial effects. In this paper we also consider Abelian systems, but in the context of principal bundles, and introduce drag in addition to inertial interactions, allowing us to show that the same conservation that induces self-recovery now depends on the trajectories of the system inputs in addition to initial conditions. We conclude by demonstrating an example illustrating the conditions derived from our proof, along with an observation that the present analysis is insufficient for self-recovery in non-Abelian systems.

Copyright © 2014 by ASME

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