Conisiderations About the Use of Minimum Norm Criteria for the Solution of Kinematic Problems

Several techniques have been proposed in literature to solve the inverse kinematic problem for redundant manipulators. A large part of these techniques is based on generalized inverses, or on the pseudoinverse, of the Jacobian of the manipulator. One of the reasons of using such inverses is to obtain least squares or minimum norm solutions in the task velocity space and/or in the joint velocity space. However, concepts as the norm of the velocity vectors, both in joint and task space, are not clearly defined. This fact may generate problems in the interpretation of the velocities, leading to noninvariant results. In this paper, the problem of the noninvariance is formulated, and examples and implications on the redundant manipulators case are reported and discussed.