On the implementation of velocity control for kinematically redundant manipulators

The velocity control of kinematically redundant manipulators has been addressed through a variety of approaches. Though they differ widely in their purpose and method of implementation, most are optimizations that can be characterized by Liegeois´s (1977) method. This characterization is used in this article to develop a single framework for implementing different methods by simply selecting a scalar, a function of configuration, and a joint-rate weighting matrix. These quantities are used to form a fully constrained linear system by row augmenting the manipulator Jacobian with a weighted basis of its nullspace and augmenting the desired hand motion with a vector function of the nullspace basis. The framework is shown to be flexible, computationally efficient, and accurate