This project develops the theoretical framework for the study of feedback stabilization and control problems associated with constrained mechanical systems. A controller which achieves certain performance objectives for an unconstrained mechanical system may be unsuited if external constraints are imposed. The work is strongly motivated by important engineering problems associated with robots and space systems. The constraint arises when contact is made between bodies. In robotics, this occurs when there is contact between end effectors and payload objects. For example, such operations as contour following, deburring, fastening, and pick and place fall within this class. For space systems, constraints arise in satellite docking maneuvers. Constrained robot problems have been the motivation for much recent research in compliance and impedance control, but always without explicit consideration of contact forces required to maintain satisfaction of the constraints. The research makes substantial use of mathematical methods for nonlinear analysis of dynamic systems. Computer simulation experiments will be performed to verify the theory developed and to suggest new theoretical issues for study. The example to be simulated and investigated comprises a particle constrained to move on a smooth elliptic wire. The theory may also be tested experimentally on an instrumented x-y table.
