A gauge-invariant formulation for constrained robotic systems using square-root factorization and unitary transformation

A gauge-invariant formulation for deriving the equations of motion of constrained or unconstrained multi-body systems (MBS) in terms of (reduced) quasi-velocities is presented. We show that the square-root factorization of mass matrix and hence the quasi-velocities are not unique, rather they are related by unitary transformations. Subsequently, we show that a particular transformation leads to significant simplification of the dynamic modeling. In this formulation the equations of motion are decoupled from those of constrained force and each system has its own independent input (that is not attainable by other formulations). This allows the possibility to develop a simpler force control action that is totally independent from the motion control action. Moreover, the square-root of the mass matrix is used to transform disparate units into homogeneous units for all the reduced quasi-velocities making the formulation suitable for hybrid force/motion control of robots.