Persistently Exciting Trajectories for Estimation

Abstract

The model-based manipulator control methods achieve complete decoupling and linearization with the assumption that the dynamic model is exactly known. This assumption has been satisfied recently and both symbolic and numerical algorithms to estimate the dynamics parameters have been proposed. In deriving these algorithms the lack of sensing the full torque/force vector at each joint leads to the unidentifiability of some of the dynamics parameters. Moreover, the maximum number of parameters that may be estimated depends on the trajectory used for estimation and the kinematic structure of the manipulator. In this paper, we address the problem of generating persistently exciting trajectories for parameter estimation. To achieve our goal, we propose an algorithm that categorizes the dynamics parameters of a manipulator into three classes: uniquely identifiable, identifiable in linear combinations only and unidentifiable. Since the proposed algorithm categorizes the parameters only on the basis of the kinematic configuration of the manipulator, it allows one to determine if a chosen trajectory (for estimation) is persistently exciting. This knowledge also helps in making the estimation procedure more robust.