On the implementation of velocity control for kinematically redundant manipulators

Abstract

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.