Identifying Moments of Inertia Parameters for Rigid-Body Manipulators Rodrigo S. Jamisola, Jr. † and Elmer P. Dadios ‡ Abstract—Among rigid-body dynamics parameters, the inertia is more difficult to identify or verify. In fact, some robot manu- facturers provide information on masses and centers of masses, but not on inertias. This work will propose an experimental procedure in identifying inertia parameters through natural oscillation. The experiment proceeds by letting the rigid-body system achieve a linear second-order system response and its oscillation is measured. A well-defined value of the desired natural oscillation transforms the identification experiment into an optimization problem. A theorem is presented to justify the validity of the experimental approach, and experimental results are shown. Index Terms—moment of inertia, identification experiment, dynamics model, natural oscillation I. INTRODUCTION Identifying the values of moments of inertia is significant to mathematical modeling and control. In robotics research, it is a well-known fact that incorporating the full dynamics information into its control significantly improves a robot’s performance. Full dynamics control in a robot manipulator can only be achieved with complete information on its dynamics parameters. In some cases, masses and centers of masses are provided by robot manufacturers but not the moments of inertia. But even if all the dynamics parameters are provided, it is helpful if there is a method to verify the accurateness of the given values. This work will present method to experimentally identify or verify the moments of inertia of a given rigid-body. In a different study, the same authors provide an experimental procedure to identify the masses and centers of masses of rigid bodies. One possible hesitation in providing the inertia values by manufacturers is the fact that at best, they only provide inertia values based on the type of material used and CAD drawing of the physical system. However, values derived through this method can be inadequate because of other factors like gear ratio and motor inertia, which could offset the true values of the inertia parameters. Thus, an experimental procedure to identify the inertia values can be more appropriate. There are several studies in inertia parameter identification designed to accurately model and control a physical system. Among such studies include a moment of inertia identification for mechatronic systems with limited strokes [1] in utilizing † Dept. of Electronics and Communications Engineering and ‡ Dept. of Manufacturing Engineering and Management, De La Salle University - Manila, 2401 Taft Ave, 1004 Manila, Philippines {rodrigo.jamisola,elmer.dadios}@dlsu.edu.ph. This work is supported by the University Research Council of De La Salle University - Manila. periodic position reference input identification of inertia based on the time average of the product of torque reference input and motor position. This study showed the moment of inertia error is within ±25%. On tracking a desired trajectory and noting the error response, inertia parameters are identified using adaptive feedback control [2] where angular velocity tracking are observed and inertia parameters are changed, while a globally convergent adaptive tracking of angular velocity is shown in [3]. In other studies, least squares error in the response is used in inertial and friction parameters identification for excavator arms [4]. It is also used to identify inertias of loaded and unloaded rigid bodies for test facilities [5], and in another experimental set up [6]. Inertias that are dependent on the same joint variables, and is also referred to as the minimal linear combinations of the inertia parameters [7], can be combined to form lumped inertias. This inertia model has been shown even in an earlier work on a complete mathematical model of a manipulator [8]. In most cases lumped inertias, instead of individual inertias, are identified. This is because lumped inertias are easier to identify. A similar work that identified lumped inertias through natural oscillation is shown in [9]. The shown full dynam- ics identification method was the foundation in a successful implementation of a mobile manipulator performing an aircraft canopy polishing at a controlled normal force of 10 N [10]. This work will propose an experimental procedure, based on natural oscillation, to identify the individual inertia parameters of rigid body manipulators. The objective it to make the rigid-body manipulator achieve linear second-order response such that a desired value of its natural oscillation is known. When the desired natural oscillation is reached, the correct inertia parameters are found. This work is aimed at providing an alternative in inertia identification methods that is easily implementable, that identifies individual inertia parameters, and with comparably accurate results. A theorem is presented to support the mathematical principles behind the experimental procedure together with experimental results. II. OVERVIEW A. Linear Second-Order Systems The sum of the kinetic energy K and potential energy P of an upright pendulum consisting of a slender bar with mass m and length l is [11] K + P = 1 2 I  dθ dt  2 - 1 2 mgl cos θ (1)