Inverse dynamics control in terms of unnormalized quasi-velocities

In this paper a proposition of inverse dynamics control for a manipulator using the unnormalized quasi-velocities (UQV) is presented. These quasi-velocities introduced by Jain and Rodriguez (IEEE Trans. Robotics Automat,16, 2000, 517; 11, 1995, 571) are used here to show some performance obtained from the controller. It is shown that for a two d.o.f. planar manipulator one can assume UQV which are integrable with respect to time. The introduced controller in terms of UQV is exponentially convergent. As a consequence of using UQV inverse dynamics control, one can notice some interesting properties in comparison with the classical controller. Additionally, some geometrical interpretation based on Riemannian geometry is given.