A symbolic approach to determining exciting trajectories for identification of manipulator dynamic models

In experiments aimed at the identification of parameters in the dynamic model of a robotic manipulator, the use of a trajectory that excites the parameters so that the numerical estimation procedure is well-conditioned is important for an accurate estimation. This paper presents a new approach, based upon symbolic computations, to determine such “exciting trajectories”. Herein, the concept of mutually productwise odd (MPO) functions is introduced, and the problem of determining an exciting trajectory is reformulated as one of rendering time histories of the regressor functions of the associated dynamic equation MPO. Parametrized joint-angle time histories whose parameters take on a discrete set of values form the search space of an algorithm that renders the regressor time histories MPO. The overall approach exploits the use of test motions to reduce the complexity of the search procedure. The approach is successfully applied to a three-link spatial manipulator, thereby showing how all required inertial parameters can be identified using exciting trajectories