Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Simple mechanical control systems with constraints and symmetry
J. Cortés, S. Martínez, J.P. Ostrowski, H. Zhang
SIAM Journal on Control and Optimization 41 (3) (2002), 851-874
Abstract
We develop tools for studying the control of underactuated mechanical
systems that evolve on a configuration space with a principal fiber
bundle structure. Taking the viewpoint of affine connection control
systems, we derive reduced formulations of the Levi-Civita and the
nonholonomic affine connections, along with the symmetric product, in
the presence of symmetries and nonholonomic constraints. We note that
there are naturally two kinds of connections to be considered here,
affine and principal connections, leading to what we term a
``connection within a connection''. These results are then used to
describe controllability tests that are specialized to simple,
underactuated mechanical systems on principal fiber bundles, including
the notion of fiber configuration controllability. We present examples
of the use of these tools in studying the planar rigid body with a
variable direction (vectored) thruster and the snakeboard robot.
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Mechanical and Aerospace Engineering,
University of California, San Diego
9500 Gilman Dr,
La Jolla, California, 92093-0411
Ph: 1-858-822-7930
Fax: 1-858-822-3107
cortes at ucsd.edu
Skype id:
jorgilliyo