The Characteristic Point and the Characteristic Length of Robotic Manipulators

Abstract The characteristic point of a serial manipulator is defined here as a point on the end-effector, at which the condition number of the Jacobian matrix is minimized. However, when evaluating the condition number of the Jacobian matrix, dimensional inhomogeneities arise, that render the condition number physically meaningless. As a means to cope with this problem, the entries of the Jacobian that have units of length are divided by a characteristic length L that is chosen so as to minimize the condition number of the dimensionless Jacobian matrix thus resulting. Finally, the values of the joint variables minimizing the condition number of the dimensionless Jacobian lead to a naturally defined home configuration of the manipulator. The concepts introduced here are illustrated with a few examples involving industrial manipulators.