a b s t r a c t   Robotic manipulators are highly nonlinear and coupled systems that are subject to different types of disturbances such as joint frictions, unknown payloads, varying contact points, and unmodeled dynamics。 These disturbances, when unaccounted for, adversely affect the performance of the manipulator。 Employing a disturbance observer is a common method to reject such disturbances。 In addition to disturbance rejection, disturbance observers can be used in force control applications。 Recently, research has been done regarding the design of nonlinear disturbance observers (NLDOs) for robotic manipulators。 In spite of good results in terms of disturbance tracking, the previously designed nonlinear disturbance observers can merely be used for planar serial manipulators with revolute joints [Chen, W。 H。, Ballance, D。 J。, Gawthorp, P。 J。, O’Reilly, J。 (2000)。 A nonlinear disturbance observer for robotic manipulators。 IEEE Transactions on Industrial Electronics, 47 (August (4)), 932–938; Nikoobin, A。, Haghighi, R。 (2009)。 Lyapunov-based nonlinear disturbance observer for serial n-link manipulators。 Journal of Intelligent & Robotic Systems, 55 (July (2–3)), 135–153]。 In this paper, a general systematic approach is proposed to solve the disturbance observer design problem for robotic manipulators without

 restrictions   on  the  number   of  degrees-of-freedom   (DOFs),   the  types   of  joints,   or  the    manipulator 

 configuration。 Moreover, this design method does not need the exact dynamic model of the serial robotic

 manipulator。 This method also unifies the previously proposed linear and nonlinear disturbance observers in a general framework。 Simulations are presented for a 4-DOF SCARA manipulator to show the effectiveness of the proposed disturbance observer design method。 Experimental results using a PHANToM Omni haptic device further illustrate the effectiveness of the design method。

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1。Introduction

Robotic manipulators are subject to different types of distur- bances that adversely affect their performance such as  positioning

 accuracy and repeatability; it is, therefore, imperative to employ some form of  disturbance  suppression  or  attenuation  in  order to achieve the desired performance。 Adaptive control (Danesh, Sheikholeslam, & Keshmiri, 2005; Kim, Seok, Noh, & Won, 2008), active Kalman filtering (Cortesao, 2007; Ji & Sul, 1995), H1 control (Khelfi & Abdessameud, 2007; Sato & Tsuruta, 2006), predictive control (Bauchspiess, Alfaro, & Dobrzanski, 2001; Cassemiro, Rosario, &  Dumur,  2005)  and  sliding  mode  control  (Corradini et al。, 2012; Parlakci, Jafarov, & Istefanopulos, 2004; Pi & Wang, 2011), are among the disturbance rejection techniques proposed in the literature for robotic   applications。

n Corresponding author。 Tel。: þ1 647 978 0140。

nn Principal corresponding author。 Tel。: þ 1 780 492 8935;

fax: þ 1 780 492 1811。

E-mail addresses: alireza。mohammadi@mail。utoronto。ca (A。 Mohammadi), mahdi。tavakoli@ualberta。ca (M。 Tavakoli), hmarquez@ualberta。ca (H。J。 Marquez), farzad。hashemzadeh@ualberta。ca  (F。  Hashemzadeh)。

An alternative to these techniques that has emerged in recent years is the use of the so-called ‘‘disturbance observers’’ (Ohnishi, Shibata, & Murakami, 1996)。 Fig。 1 shows the block diagram of a typical disturbance observer that is used in a robotic application。

 dynamic   uncertainties   are   collectively   treated   as   the lumped