Verification of the positive definiteness of the inertial matrix of manipulators using base inertial parameters

The computation of the inertial matrix of dynamic model for manipulator usi ng some sets of base-parameter values may be not positive definite for some configurations. Such sets of base-parameter values are physically impossib le. The result of the study on physical impossibility of the set of base-pa rameter values could be used to judge if a set of base-parameter values, wh ich are obtained through parameter identification or other methods, is phys ically impossible or not and to modify the set of base-parameter values tha t 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 manipula tor. By use of this condition and a set of "virtual parameters," a scheme i s given to judge if a set of base-parameter values determine the inertial m atrix to be always positive definite or not.