Scheduled System Maintenance:
On Monday, April 27th, IEEE Xplore will undergo scheduled maintenance from 1:00 PM - 3:00 PM ET (17:00 - 19:00 UTC). No interruption in service is anticipated.
By Topic

Nonlinear control of mechanical systems with an unactuated cyclic variable

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Grizzle, J.W. ; Electr. Eng. & Comput. Sci. Dept., Univ. of Michigan, Ann Arbor, MI, USA ; Moog, C.H. ; Chevallereau, C.

Numerous robotic tasks associated with underactuation have been studied in the literature. For a large number of these in the plane, the mechanical models have a cyclic variable, the cyclic variable is unactuated, and all shape variables are independently actuated. This paper formulates and solves two control problems for this class of models. If the generalized momentum conjugate to the cyclic variable is not conserved, conditions are found for the existence of a set of outputs that yields a system with a one-dimensional exponentially stable zero dynamics-i.e., an exponentially minimum-phase system-along with a dynamic extension that renders the system locally input-output decouplable. If the generalized momentum conjugate to the cyclic variable is conserved, a reduced system is constructed and conditions are found for the existence of a set of outputs that yields an empty zero dynamics, along with a dynamic extension that renders the system feedback linearizable. A common element in these two feedback problems is the construction of a scalar function of the configuration variables that has relative degree three with respect to one of the input components. The function arises by partially integrating the conjugate momentum. The results are illustrated on two balancing tasks and on a ballistic flip motion.

Published in:

Automatic Control, IEEE Transactions on  (Volume:50 ,  Issue: 5 )