Bounded extremum seeking for angular velocity actuated control of nonholonomic unicycle
Abstract
Here, we study control of the angularvelocity actuated nonholonomic unicycle, via a simple, bounded extremum seeking controller which is robust to external disturbances and measurement noise. The vehicle performs source seeking despite not having any position information about itself or the source, able only to sense a noise corrupted scalar value whose extremum coincides with the unknown source location. In order to control the angular velocity, rather than the angular heading directly, a controller is developed such that the closed loop system exhibits multiple time scales and requires an analysis approach expanding the previous work of Kurzweil, Jarnik, Sussmann, and Liu, utilizing weak limits. We provide analytic proof of stability and demonstrate how this simple scheme can be extended to include positionindependent source seeking, tracking, and collision avoidance of groups on autonomous vehicles in GPSdenied environments, based only on a measure of distance to an obstacle, which is an especially important feature for an autonomous agent.
 Authors:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1329912
 Report Number(s):
 LAUR1627104
Journal ID: ISSN 01432087
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Optimal Control Applications and Methods
 Additional Journal Information:
 Journal Name: Optimal Control Applications and Methods; Journal ID: ISSN 01432087
 Publisher:
 Wiley
 Country of Publication:
 United States
 Language:
 English
 Subject:
 33 ADVANCED PROPULSION SYSTEMS; 97 MATHEMATICS AND COMPUTING; mathematics; nonlinear; robust; extremum seeking; autonomous systems
Citation Formats
Scheinker, Alexander. Bounded extremum seeking for angular velocity actuated control of nonholonomic unicycle. United States: N. p., 2016.
Web. doi:10.1002/oca.2272.
Scheinker, Alexander. Bounded extremum seeking for angular velocity actuated control of nonholonomic unicycle. United States. doi:10.1002/oca.2272.
Scheinker, Alexander. Wed .
"Bounded extremum seeking for angular velocity actuated control of nonholonomic unicycle". United States. doi:10.1002/oca.2272. https://www.osti.gov/servlets/purl/1329912.
@article{osti_1329912,
title = {Bounded extremum seeking for angular velocity actuated control of nonholonomic unicycle},
author = {Scheinker, Alexander},
abstractNote = {Here, we study control of the angularvelocity actuated nonholonomic unicycle, via a simple, bounded extremum seeking controller which is robust to external disturbances and measurement noise. The vehicle performs source seeking despite not having any position information about itself or the source, able only to sense a noise corrupted scalar value whose extremum coincides with the unknown source location. In order to control the angular velocity, rather than the angular heading directly, a controller is developed such that the closed loop system exhibits multiple time scales and requires an analysis approach expanding the previous work of Kurzweil, Jarnik, Sussmann, and Liu, utilizing weak limits. We provide analytic proof of stability and demonstrate how this simple scheme can be extended to include positionindependent source seeking, tracking, and collision avoidance of groups on autonomous vehicles in GPSdenied environments, based only on a measure of distance to an obstacle, which is an especially important feature for an autonomous agent.},
doi = {10.1002/oca.2272},
journal = {Optimal Control Applications and Methods},
number = ,
volume = ,
place = {United States},
year = {2016},
month = {8}
}
Works referenced in this record:
Extremum seeking with bounded update rates
journal, January 2014
 Scheinker, Alexander; Krstić, Miroslav
 Systems & Control Letters, Vol. 63
Inhardware demonstration of modelindependent adaptive tuning of noisy systems with arbitrary phase drift
journal, August 2014
 Scheinker, Alexander; Baily, Scott; Young, Daniel
 Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 756
Design and simulation of extremumseeking openloop optimal control of current profile in the DIIID tokamak
journal, September 2008
 Ou, Y.; Xu, C.; Schuster, E.
 Plasma Physics and Controlled Fusion, Vol. 50, Issue 11
MinimumSeeking for CLFs: Universal Semiglobally Stabilizing Feedback Under Unknown Control Directions
journal, May 2013
 Scheinker, Alexander; Krstic, Miroslav
 IEEE Transactions on Automatic Control, Vol. 58, Issue 5
Bounded extremum seeking with discontinuous dithers
journal, July 2016
 Scheinker, Alexander; Scheinker, David
 Automatica, Vol. 69