Closed kinematic chain mechanical systems promise advantages over open chains in terms of less moving inertia, faster and stiffer motion, and much better force-to-weight ratio. However, derivation of dynamic equations of motion for closed chain mechanisms suitable for controller design is still a challenge because of the complexity of the kinematics, dynamics, and control analyses. This research identifies the central difficulties in the modeling and control of these systems and provides an analytical framework to derive dynamics models appropriate for advanced model-based control laws. Two modeling-for-control approaches are investigated. In the first approach, a formulation of the dynamics equations of closed chain mechanisms in terms of independent generalized coordinates (reduced model) is developed. Methods to extend the wealth of control laws of open chains to closed chains while taking into consideration the local and implicit nature of the reduced model are considered. The second approach is to transform the Differential Algebraic Equations (DAE) describing closed kinematic chains into a singularly perturbed differential equation system with asymptotically stable fast dynamics. It follows that when a proper control design is made for the singularly perturbed system, then for a small value of an artificially introduced small parameter, the response of the controlled singularly perturbed system would be quite close to that of the controlled DAE system (closed chain mechanism). The techniques developed in this research potentially have applications to many other systems described by DAE. The educational objective of this research is to help introduce dynamic modeling and control of complex closed chain dynamical systems in the traditional dynamics and control courses and laboratories. In particular, a robotic device will be made accessible for control experimentation over the World Wide Web for a more effective dissemination of the results of this research and integration in control education.

Project Start
Project End
Budget Start
1999-09-01
Budget End
2003-08-31
Support Year
Fiscal Year
1999
Total Cost
$210,000
Indirect Cost
Name
Rice University
Department
Type
DUNS #
City
Houston
State
TX
Country
United States
Zip Code
77005