A comparison of certain quasi-velocities approaches in PD joint space control

This paper presents a comparison of PD controls in joints space for serial manipulators whose dynamics is expressed in terms of two different kinds of quasi-velocities. Robot dynamic algorithms in terms of so called normalized and unnormalized quasi-velocities are recursive in nature and consists of two recursions: one starts from a base of the manipulator towards its tip, and the other in an opposite direction. Both recursions are described by using a vector-matrix notation. An instantaneous eigenstructure quasi-velocity formulation, as a result of numerical mass matrix factorization, is introduced. The two PD controls were tested on the model of a manipulator with two degrees of freedom. The standard control algorithms known in robotic literature are considered for a case when the robot dynamics is formulated in terms of quasi-velocities.