Differential-algebraic equations of programmed motions of Lagrangian dynamical systems

We suggest a method for constructing the dynamic equations of manipulator systems in canonical variables. The system of differential dynamic equations has an integral manifold corresponding to the holonomic and nonholonomic constraint equations. The controls are determined so as to ensure the stability of this manifold. We state conditions for the exponential stability of the manifold and for constraint stabilization when solving the dynamic equations numerically by a simplest difference method. We also present the solution of the problem of control of a plane two-link manipulator. © 2011 Allerton Press, Inc