Observability Issues in Kinematic Error Parameter Identification of Manipulators

This paper addresses some observability issues in the kinematic error parameter identification of manipulators through derivation and analysis of a generic error model that is independent of any particular choice of robot kinematic modeling convention. It is pointed out that a consistent differential transformation formalism needs to be taken to construct error models in order to assure that the Identification Jacobian is a matrix function of all joint variables and that the joint variables are about the actual joint axes of the manipulator. It is shown that if robot calibration measurements do not provide the information about the end-effector's orientation, orientational parameters in either the Oth link transformation (i.e., from the robot base frame to the world frame) or the nth link transformation (i.e., from the tool frame to the last link frame) become unobservable. It is also shown that under additional conditions of the tool or world frames, a further reduction in the number of observable kinematic parameters may occur, depending upon the choice of error models. The paper also investigates the relationship between common observability measures and the irreducibility of the error model.