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Recent Results in Analytical Dynamics and Trajectory Control of Nonlinear Systems

This talk deals with the general structure of the explicit equations of motion for general mechanical systems subjected to holonomic and nonholonomic equality constraints. The constraints here need not satisfy D'Alembert's principle, and our derivation is not based on the principle of virtual work. Therefore the equations obtained are of general applicability. The equations show that Nature appears to be working like a control engineer using a feedback control law to ensure the exact satisfaction of the constraints. The explicitly determined force of constraint is shown to be made up of the sum of two components: the first is the constraint force that would have existed were the constraints ideal; the second is caused by the non-ideal nature of the constraints, and though it needs specification by the mechanician, and depends on the particular mechanical system at hand, it nontheless has a specific form. Application of the use of these explicit equations of motion for trajec tory control of nonlinear mechanical sytems will be discussed. The control law used by Nature is shown work exceedingly well for the control of mechanical systems in application areas like robotics, and it is currently being used by NASA for the control of multiple spacecraft so that they fly in tight formations.

Type of Seminar:
Public Seminar
Prof. Firdaus Udwadia
University of Southern California
Jun 02, 2005   17:15

ETH Zentrum, Building ETZ , Room E6
Contact Person:

Prof. M. Morari
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Biographical Sketch:
Firdaus Udwadia is Professor of Aerospace Engineering and Mechanical Engineering, Mathetamics, Civil Engineering and Information and Operations Management at the University of Southern California, Los Angeles. He is the current editor of the Journal of Aerospace Engineering and an associate editor of several journals in Applied Mathematics and Engineering. His interests are in the areas of analytical dynamics, structural control, and applied mathematics.