REPEATABLE GENERALIZED INVERSE CONTROL STRATEGIES FOR KINEMATICALLY REDUNDANT MANIPULATORS

Kinematically redundant manipulators possess an infinite number of joi nt angle trajectories which satisfy a given desired end effector traje ctory. The joint angle trajectories considered in this work are locall y described by generalized inverses which satisfy the Jacobian equatio n relating the instantaneous joint angle velocities to the velocity of the end effector. One typically selects a solution from this set base d on the local optimization of some desired physical property such as the minimization of the norm of the joint angle velocities, kinetic en ergy, etc. Unfortunately, this type of solution frequently does not po ssess the desirable property of repeatability in the sense that closed trajectories in the workspace are not necessarily mapped to closed tr ajectories in the joint space. In this work, the issue of generating a repeatable control strategy which possesses the desirable physical pr operties of a particular generalized inverse is addressed. The techniq ue described is fully general and only requires a knowledge of the ass ociated null space of the desired inverse. While an analytical represe ntation of the null vector is desirable, ultimately the calculations a re done numerically so that a numerical knowledge of the associated nu ll vector is sufficient. This method first characterizes repeatable st rategies using a set of orthonormal basis functions to describe the nu ll space of these transformations. The optimal repeatable inverse is t hen obtained by projecting the null space of the desired generalized i nverse onto each of these basis functions. The resulting inverse is gu aranteed 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 spa tial manipulator.