This paper presents procedural guidelines for the construction of discontinuous state feedback controllers for driftless, kinematic nonholonomic systems, with extensions to a class of dynamic nonholonomic systems with drift. Given an n-dimensional kinematic nonholonomic system subject to κ Pfaffian constraints, system states are partitioned into “leafwise” and “transverse,” based on the structure of the Pfaffian constraint matrix. A reference vector field F is defined as a function of the leafwise states only in a way that it is nonsingular everywhere except for a submanifold containing the origin. The induced decomposition of the configuration space, together with requiring the system vector field to be aligned with F, suggests choices for Lyapunov-like functions. The proposed approach recasts the original nonholonomic control problem as an output regulation problem, which although nontrivial, may admit solutions based on standard tools.
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August 2015
Research-Article
Control Design for a Class of Nonholonomic Systems Via Reference Vector Fields and Output Regulation
Dimitra Panagou,
Dimitra Panagou
1
Assistant Professor
Department of Aerospace Engineering,
e-mail: dpanagou@umich.edu
Department of Aerospace Engineering,
University of Michigan
,Ann Arbor, MI 48109
e-mail: dpanagou@umich.edu
1Corresponding author.
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Herbert G. Tanner,
Herbert G. Tanner
Associate Professor
Mechanical Engineering Department,
e-mail: btanner@udel.edu
Mechanical Engineering Department,
University of Delaware
,Newark, DE 19716
e-mail: btanner@udel.edu
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Kostas J. Kyriakopoulos
Kostas J. Kyriakopoulos
Professor
School of Mechanical Engineering,
e-mail: kkyria@mail.ntua.gr
School of Mechanical Engineering,
National Technical University of Athens
,Zografou
,Athens 15780
, Greece
e-mail: kkyria@mail.ntua.gr
Search for other works by this author on:
Dimitra Panagou
Assistant Professor
Department of Aerospace Engineering,
e-mail: dpanagou@umich.edu
Department of Aerospace Engineering,
University of Michigan
,Ann Arbor, MI 48109
e-mail: dpanagou@umich.edu
Herbert G. Tanner
Associate Professor
Mechanical Engineering Department,
e-mail: btanner@udel.edu
Mechanical Engineering Department,
University of Delaware
,Newark, DE 19716
e-mail: btanner@udel.edu
Kostas J. Kyriakopoulos
Professor
School of Mechanical Engineering,
e-mail: kkyria@mail.ntua.gr
School of Mechanical Engineering,
National Technical University of Athens
,Zografou
,Athens 15780
, Greece
e-mail: kkyria@mail.ntua.gr
1Corresponding author.
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 4, 2013; final manuscript received March 31, 2015; published online May 26, 2015. Assoc. Editor: Evangelos Papadopoulos.
J. Dyn. Sys., Meas., Control. Aug 2015, 137(8): 081011 (9 pages)
Published Online: August 1, 2015
Article history
Received:
January 4, 2013
Revision Received:
March 31, 2015
Online:
May 26, 2015
Citation
Panagou, D., Tanner, H. G., and Kyriakopoulos, K. J. (August 1, 2015). "Control Design for a Class of Nonholonomic Systems Via Reference Vector Fields and Output Regulation." ASME. J. Dyn. Sys., Meas., Control. August 2015; 137(8): 081011. https://doi.org/10.1115/1.4030335
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