The Boltzmann–Hamel equations for the optimal control of mechanical systems with nonholonomic constraints
dc.contributor.author | Maruskin, Jared Michael | en_US |
dc.contributor.author | Bloch, Anthony M. | en_US |
dc.date.accessioned | 2011-02-02T17:59:54Z | |
dc.date.available | 2012-04-03T21:46:58Z | en_US |
dc.date.issued | 2011-03-10 | en_US |
dc.identifier.citation | Maruskin, Jared M.; Bloch, Anthony M. (2011). "The Boltzmann–Hamel equations for the optimal control of mechanical systems with nonholonomic constraints." International Journal of Robust and Nonlinear Control 21(4): 373-386. <http://hdl.handle.net/2027.42/79427> | en_US |
dc.identifier.issn | 1049-8923 | en_US |
dc.identifier.issn | 1099-1239 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/79427 | |
dc.description.abstract | In this paper, we generalize the Boltzmann–Hamel equations for nonholonomic mechanics to a form suited for the kinematic or dynamic optimal control of mechanical systems subject to nonholonomic constraints. In solving these equations one is able to eliminate the controls and compute the optimal trajectory from a set of coupled first-order differential equations with boundary values. By using an appropriate choice of quasi-velocities, one is able to reduce the required number of differential equations by m and 3 m for the kinematic and dynamic optimal control problems, respectively, where m is the number of nonholonomic constraints. In particular we derive a set of differential equations that yields the optimal reorientation path of a free rigid body. In the special case of a sphere, we show that the optimal trajectory coincides with the cubic splines on SO (3). Copyright © 2010 John Wiley & Sons, Ltd. | en_US |
dc.format.extent | 166148 bytes | |
dc.format.extent | 3118 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.publisher | John Wiley & Sons, Ltd. | en_US |
dc.subject.other | Engineering | en_US |
dc.subject.other | Electronic, Electrical & Telecommunications Engineering | en_US |
dc.title | The Boltzmann–Hamel equations for the optimal control of mechanical systems with nonholonomic constraints | en_US |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | en_US |
dc.subject.hlbsecondlevel | Industrial and Operations Engineering | en_US |
dc.subject.hlbsecondlevel | Mechanical Engineering | en_US |
dc.subject.hlbtoplevel | Engineering | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Mathematics, University of Michigan, Ann Arbor, MI, U.S.A. | en_US |
dc.contributor.affiliationother | Department of Mathematics, The San José State University, San José, CA 95192-0103, U.S.A. ; Department of Mathematics, The San José State University, San José, CA 95192-0103, U.S.A. | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/79427/1/1598_ftp.pdf | |
dc.identifier.doi | 10.1002/rnc.1598 | en_US |
dc.identifier.source | International Journal of Robust and Nonlinear Control | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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