Quasi-coordinates based dynamics control design for constrained systems

Abstract

The paper presents model-based dynamics control design for constrained systems which exploits dynamics modeling in quasi-coordinates. These non-inertial coordinates are useful in motion description of constrained systems as well as in a controller design, since they offer many advantages in both areas. Specifically, dynamics model formulation results in a reduced-state form of the motion equations. The selection of quasi-coordinates is arbitrary so they may satisfy the constraint equations and be control inputs directly. The paper presents an approach to control oriented modeling and a controller design based on the generalized Boltzmann-Hamel equations where the generalization refers to constraint kinds which may be put upon systems, i.e. constraints may be material or artificial like control constraints. The control design framework applies to fully actuated and underactuated systems and it is computationally efficient. Examples of controller designs and their comparisons to a traditional, Lagrange model- based framework are presented.