Verification of the Positive Definiteness of the Inertial Matrix of Manipulators Using Base Inertial Parameters

Abstract

The computation of the inertial matrix of dynamic model for manipulator using some sets of base-parameter values may be not positive definite for some configurations. Such sets of base-parameter values are physically impossible. The result of the study on physical impossibility of the set of base-parameter values could be used to judge if a set of base-parameter values, which are obtained through parameter identification or other methods, is physically impossible or not and to modify the set of base-parameter values that was judged to be physically impossible. Hence, the result would directly contribute to model-based control of manipulators or motion simulation for manipulators. In this paper, a sufficient condition for the inertial matrix to be positive definite for each configuration of the manipulator is given by use of physical inertial parameters of the links composing the manipulator. By use of this condition and a set of “virtual parameters,” a scheme is given to judge if a set of base-parameter values determine the inertial matrix to be always positive definite or not.