A Frequency-Domain Approach for Flexible-Joint Robot Modeling and Identification Maria Makarov ∗,∗∗ Mathieu Grossard ∗ Pedro Rodr´ ıguez-Ayerbe ∗∗ Didier Dumur ∗∗ ∗ CEA, LIST, Interactive Robotics Laboratory, Fontenay aux Roses, F-92265, France (e-mail: maria.makarov@cea.fr) ∗∗ SUPELEC Systems Sciences (E3S), Control Department, Gif sur Yvette Cedex F-91192, France Abstract: This paper proposes a control-oriented modeling and identification framework for flexible-joint robot arms using motor-side measurements only. From the perspective of model- based control strategies including an inner feedback linearization loop, the proposed method allows an explicit treatment of the vibrational behavior induced by the flexibilities. A theoretical model of the partially decoupled system is derived and a frequency-domain identification procedure allowing an estimation of the flexible parameters is detailed. The obtained description of the system is experimentally validated on the CEA lightweight robot arm ASSIST. Keywords: robotic manipulators, flexible arms, feedback linearization, control-oriented models. 1. INTRODUCTION Over the last two decades modeling and control of flexible robots have attracted a special attention of the robotic community (Dwivedy and Eberhard, 2006; De Luca and Book, 2008). These studies are all the more motivated today by emerging applications in service, medical, space or industrial fields. Innovative mechanical designs provide the desired features for these applications, such as safety in case of shared human-robot workspace, leading to an expansive development of lightweight robots (KUKA; DLR; ABB; Barrett Technology; Sugano Laboratory). These mechanisms are often intrinsically flexible due to their slender structure and/or transmissions and can be subject to resonant modes. In this context, advanced control techniques taking into account the flexibilities are required to reach a high control bandwidth for precise high-speed operation. The present study focuses on flexible-joint robots, where the transmissions between the motors and the rigid links are assumed to concentrate the essential part of the elastic- ities (possibly due to harmonic drives, transmission belts or cable driven mechanisms) and are modeled as springs. When compared with the robot dynamics under standard rigid body assumptions, these flexibilities introduce sup- plementary degrees of freedom between the motor and the joint angles. To cope with this issue, a large number of solutions propose additional sensors to measure the elastic deformations between the motors and the joints. These additional measurements allow powerful and theoretically well founded control strategies such as flexible feedback linearization (De Luca and Book, 2008) or full state feed- back (Petit and Albu-Schaffer, 2011; Albu-Schaffer and Hirzinger, 2000). However, these relatively complex so- lutions can not always be implemented on robots in a standard industrial configuration, i.e. equipped only with motor position sensors and controlled in real-time at a high sampling rate. Possible control strategies in this case are motor feedback which may be completed with feedforward terms based on the desired joint reference trajectory and the flexible model (De Luca, 2000). Similarly to the above cited control strategies, the model- ing and identification approaches for flexible-joint robots heavily depend on the available measurements and the intended use of the model. A control-oriented description must provide an adequate level of details while remaining exploitable for control design. The simplest model is the single joint model (the inertial couplings between the joints being neglected), suitable for single-input single-output (SISO) control strategies. Such a physically parametrized linear model has been identified on an industrial robot by ¨ Ostring et al. (2003). When a higher level of preci- sion is required, the coupled vibration effects have to be taken into account and a multivariable model has to be considered. In most approaches the rigid body dynamics are assumed to be known, from CAD estimates or exper- imental identification, reducing the identification problem to the stiffness parameters estimation. Following this ap- proach, Albu-Schaffer and Hirzinger (2001) use additional joint torque sensors to identify the elasticity and damping separately for each joint on testbed before the assembly of the robot. Oaki and Adachi (2009) employ additional link accelerometers in a gray-box modeling approach. Pham et al. (2001) propose an identification procedure based on bandpass filtering which uses only motor-side measure- ments, identifying one joint at a time. Hovland et al. (2000) describe a frequency-based identification method under linearizing assumptions for an industrial robot with two coupled flexible joints. Nonlinear gray-box identification and multivariable nonparametric methods for frequency 16th IFAC Symposium on System Identification The International Federation of Automatic Control Brussels, Belgium. July 11-13, 2012 978-3-902823-06-9/12/$20.00 © 2012 IFAC 583 10.3182/20120711-3-BE-2027.00127