Control of Nonlinear Bilateral Teleoperation Systems Subject to Disturbances Alireza Mohammadi, Mahdi Tavakoli and Horacio J. Marquez Abstract— Teleoperation systems, consisting of a pair of master and slave robots are subject to different types of disturbances such as joint frictions, varying contact points, un- modeled dynamics and unknown payloads. Such disturbances, when unaccounted for, cause poor teleoperation transparency and even instability. This paper presents a novel nonlinear bilateral control scheme, based on the concept of disturbance observer based control, to counter these disturbances and their negative effects on the teleoperation systems. The proposed disturbance observer based bilateral control law is able to acheive global asymptotic force tracking, and global exponential position and disturbance tracking in the presence of various disturbances. The minimum exponential convergence rate of the position and the disturbance tracking errors can be tuned by the controller parameters. Simulations are presented to show the effectiveness of the proposed control scheme. I. INTRODUCTION Every teleoperation system consists of a master robot and a slave robot. The master interacts with a human operator and the slave interacts with a remote environment. If force feedback from the slave side to the master side is provided, the system is called a bilateral teleoperation system to dis- tinguish it from a unilateral teleoperation system. A bilateral teleoperation system is said to be transparent if the slave robot precisely follows the position of the master robot and the master robot faithfully displays the slave-environment contact force to the human operator. The most successful control scheme in achieving a fully transparent teleoperation system is the 4-channel architecture [1], [2], which is mostly suitable for teleoperation systems with fixed linear models. Physical robots, however, are nonlinear systems subject to various disturbances, such as unknown dynamics, joint frictions, unknown payloads, etc. [3]. Such disturbances, when unaccounted for, cause poor teleoperation transparency and even instability. One way to suppress these disturbances, is to employ disturbance observers [4]. Disturbance observer based control has been used in applications such as independent robot joint control [5], and robot joint friction estimation and compensation [6], [7]. A considerable part of the existing literature on disturbance observer design for robotic applications uses linearized mod- els or linear system techniques [8], [9]. In order to overcome This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). A. Mohammadi was with the Department of Electrical & Computer Engineering, University of Alberta, Edmonton, AB T6G 2V4 Canada. He is now with the Edward S. Rogers Sr. Department of Electrical & Computer Engineering, University of Toronto, Toronto, ON M5S 3G4 Canada. Email: alireza.mohammadi@mail.utoronto.ca M. Tavakoli is with the Department of Electrical & Computer Engi- neering, University of Alberta, Edmonton, AB T6G 2V4 Canada. Email: tavakoli@ece.ualberta.ca H. J. Marquez is with the Department of Electrical & Computer Engi- neering, University of Alberta, Edmonton, AB T6G 2V4 Canada. Email: marquez@ece.ualberta.ca the linear disturbance observer limitations for the highly nonlinear and coupled dynamics of robotic manipulators, Chen et al. proposed a nonlinear disturbance observer for nonlinear robotic manipulators and designed it such that no acceleration measurement was needed [10]. However, the closed-loop stability of the overall system including the disturbance observer and the controller was not investigated. The investigation of the stability and performance of a master-slave teleoperation system under disturbance observer based control is even more challenging and not studied either. While a distrubance observer based controller was designed for bilateral teleoperation systems in [11], the master and the slave robots were considered to be linear with only one DOF. This serves as the motivation to look for a disturbance observer based control law for nonlinear and n-DOF teleoperation systems. This paper 1 addresses the problem of disturbance observer based control of nonlinear teleoperation systems. A dis- turbance observer based control law will be proposed and incorporated into the framework of the 4-channel teleopera- tion architecture. Under the proposed control law, full trans- parency and exponential disturbance and position tracking are achieved. The organization of this paper is as follows. Section II introduces the nonlinear model of the teleoperation systems and 4-channel bilateral control architecture. Section III pro- poses a novel disturbance observer based controller for non- linear teleoperation systems subject to various disturbances. The teleoperation system transparency is also addressed in this section. Finally, simulations in section IV show the efficiency of the proposed control scheme as compared with the case where no disturbance observer is employed. II. NONLINEAR MODEL OF A TELEOPERATION SYSTEM The dynamical models investigated in this paper and our proposed control law in section III will be in the Cartesian space. This enables us to make a teleoperation system transparent without requiring the master and the slave robots to have similar kinematics and dynamics. A. Model of a teleoperation system in the Cartesian space The dynamic equations describing the motions of the end- effectors of n-DOF master and slave robots, which interact with the human operator and the remote environment, in the presence of disturbances can be written as M xm (q m ) ¨ x m + N xm (q m , ˙ q m ) = f m + f h + d m (1) M xs (q s ) ¨ x s + N xs (q s , ˙ q s ) = f s - f e + d s (2) 1 A more complete version of this paper can be found in [12]. 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC) Orlando, FL, USA, December 12-15, 2011 978-1-61284-799-3/11/$26.00 ©2011 IEEE 1765