  This paper presents a formulation of Lagrangian dynamics of constrained
mechanical systems in terms of reduced quasi-velocities and quasi-forces that
can be used for simulation, analysis, and control purposes. In this
formulation, Cholesky decomposition of the mass matrix in conjunction with
adequate orthogonal matrices are used to define reduced-quasi velocities, input
quasi-forces, and constraint quasi-forces which possess natural metric. The new
state and input variables always have homogeneous units despite the generalized
coordinates may involve in both translational and rotational components and the
constraint wrench may involve in both force and moment components. Therefore,
this formulation is inherently invariant with respect to changes in dimensional
units without requiring weighting matrices. Moreover, in this formulation the
equations of motion are completely decoupled from those of constrained force.
This allows the possibility of a simple force control action that is totally
independent of the motion control action facilitating a hybrid force/motion
control. The properties of the new dynamics formulation are investigated and
subsequently, force/motion tracking control and regulation of constrained
multibody systems based on quasi-velocities and quasi-forces are presented.
