Repeatable generalized inverse control strategies for kinematically redundant manipulators

The issue of generating a repeatable control strategy which possesses the desirable physical properties of a particular generalized inverse is addressed. The technique described is fully general and only requires a knowledge of the associated mill space of the desired inverse. While an analytical representation of the null vector is desirable, ultimately the calculations are done numerically so that a numerical knowledge of the associated full vector is sufficient. This method first characterizes repeatable strategies using a set of orthonormal basis functions to describe the null space of these transformations. The optimal repeatable inverse is then obtained by projecting the null space of the desired generalized inverse onto each of these basis functions. The resulting inverse is guaranteed to be the closest repeatable inverse to the desired inverse, in an integral norm sense, from the set of all inverses spanned by the selected basis functions. This technique is illustrated for a planar, three-degree-of-freedom manipulator and a seven-degree-of-freedom spatial manipulator