compliant   surface   and   a   force   control   scheme   is   needed  to

 guarantee good system performance。 Therefore, a force sensor is needed  to  measure  these  contact  forces。  Disturbance  observers

 can be employed in these applications when there is no sensor available for  measuring  torques  and forces。  For instance,  distur-

 bance  observers  have  been  employed  successfully  in sensorless

 force control (Eom, Suh, Chung, & Oh, 1998; Katsura, Matsumoto, & Ohnishi, 2003; Lee,  Chan,  &  Mital,  1993;  Shimada,  Ohishi,  Kumagai, &   Miyazaki,   2010)。   Another   potential   application   of    disturbance

observers can be in micro/nano manipulation tasks, e。g。, microinjec- tion to introduce foreign materials into biological cells (Tan, Sun, Huang, & Chen, 2008), where there is a lack of small enough force sensors with good precision and signal to noise ratio (Rakotondrabe, Clevy, Rabenorosoa, & Ncir,  2010)。

Recently, a new system has been developed to teach motion to robots in order to improve their dexterity (Katsura, Matsumoto, & Ohnishi, 2010)。 The so-called shadow robot system consists of two identical robots。 The robots are controlled by bilateral acceleration control schemes based on a disturbance observer。 One  robot is guided by a human operator in teaching motion mode and the other robot is unconstrained and imitates the motion of the constrained robot with the same position, velocity and acceleration。 It is desired that the human operator’s pure force is extracted from the con- strained robot。 In order to find the operator’s force, a disturbance observer is employed to estimate the disturbance forces such as friction and gravity in the unconstrained robot。 The  disturbance forces acting on the constrained and the  unconstrained  robots  are the same。 The human operator’s force is then estimated by sub- tracting the disturbance forces acting on the unconstrained robot from the total force in the constrained robot。 As a result, the shadow robot system observes the human force in the presence of gravity and friction without a need for force sensors。 Lastly, industrial  robots

 employ fault detection systems in order to determine if a fault, such as a collision or an abrupt increase in reaction forces, has occurred in the system。 Disturbance observers have been used  for  fault detec- tion in a number of  robotic applications (Chan, 1995;  Ohishi & Ohde, 1994; Sneider & Frank, 1996)。 Table 1 summarizes the most important  applications  of disturbance  observers  in robotics。

A considerable part of the existing literature on disturbance observer design for robotic applications uses linearized models or linear system techniques (Bickel & Tomizuka, 1995; Kim & Chung, 2003; Komada, Machii, & Hori, 2000; Liu & Peng, 2000)。 In order to overcome the linear disturbance observer limitations for the highly nonlinear and coupled dynamics of robotic manipulators, Chen, Ballance, Gawthrop, and O’Reilly (2000) proposed a general nonlinear disturbance observer structure for nonlinear robotic manipulators。   Using   Chen   et   al。   NDOB,   the   observer   design

problem reduces to finding an observer gain matrix such that disturbance tracking is achieved。 However, Chen et al。 could find

 such  a  gain matrix for a  2-link planar manipulator with    revolute

 joints。 Later, Nikoobin et al。 generalized Chen’s solution to n-link