Volume 23, Number 3, July-September 2017
|Page(s)||913 - 935|
|Published online||28 April 2017|
1 Department of Electrical and Computer Engineering, University of Toronto, 10 King’s College Road, Toronto, ON, M5S 3G4, Canada.
2 Dipartimento di Ingegneria dell’Informazione, via Usberti 181/a, 43124 Parma, Italy.
Received: 17 November 2015
Revised: 10 March 2016
Accepted: 20 April 2016
This paper investigates a class of Lagrangian control systems with n degrees-of-freedom (DOF) and n − 1 actuators, assuming that n − 1 virtual holonomic constraints have been enforced via feedback, and a basic regularity condition holds. The reduced dynamics of such systems are described by a second-order unforced differential equation. We present necessary and sufficient conditions under which the reduced dynamics are those of a mechanical system with one DOF and, more generally, under which they have a Lagrangian structure. In both cases, we show that typical solutions satisfying the virtual constraints lie in a restricted class which we completely characterize.
Mathematics Subject Classification: 70Q05 / 93C10 / 93C15 / 49Q99
Key words: Underactuated mechanical systems / virtual holonomic constraints / inverse lagrangian problem
A preliminary version of this paper has been presented at the 9 IFAC Symposium on Nonlinear Control Systems (NOLCOS) .
A. Mohammadi was supported in part by the Ontario Graduate Scholarship (OGS) and by the Natural Sciences and Engineering Research Council of Canada (NSERC).
© EDP Sciences, SMAI 2017
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