Resolved motion rate control of kinematically redundant manipulators using the simplest of the generalized inverses, the {1}-inverse, is investigated. For the case of a planar articulated coordinate redundant robot with an arbitrary number of axes, closed-form equations for the joint rates are developed. The structure of these equations is such that the redundant joint velocities can be arbitrarily specified. Simple constraints are presented which ensure that closed trajectories in gripper configuration space generate closed trajectories in joint space. A strategy for controlling the redundant joint rates that is applicable to obstacle avoidance is examined and illustrated with examples.

A direct (noniterative) method for solving some singular systems of equations arising from finite difference approximations to partial differential equations is developed. The Moore-Penrose generalized inverse of some large tensor product matrices is expressed in terms of smaller matrices. Some techniques are given to improve computational efficiency.