Homogeneous set point control for serial manipulators in terms of normalized quasi-velocities

Set point control using the method given in Jain and Rodriguez (1995) is presented. It is shown that by proper selection of the Lyapunov function candidate a dynamic system with appropriate feedback is asymptotically globally stable in joint space. The presented control is new in the sense that it is derived in terms of normalized quasi-velocities described by Jain and Rodriguez. The new control was tested on a model of a manipulator with two degrees of freedom. The paper presents also a comparison with PD control in joint space for serial manipulators whose dynamics are expressed in classical form and PD normalized quasi-velocity control. Robot dynamic algorithms in terms of so called normalized quasi-velocities are recursive in nature and consist of two recursions: one starts from a base of the manipulator towards its tip and the second in the opposite direction. Both recursions are described using vector-matrix notation. We show differences between classical PD control and the new set point control which uses quasi-velocities.