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ROBUST ADAPTIVE CONTROL OF BILATERAL
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TELEOPERATION SYSTEM
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Suangsamorn Nurung and Itthisek Nilkhamhang
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School of Information, Computer and Communication Technology (ICT)
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Sirindhorn International Institute of Tehnology, Thammasat University
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131 Moo 5, Tiwanont Road, Bangkadi, Muang Pathum Thani 12000, Thailand
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E-mail: [email protected]
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Abstract
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Teleoperated manipulators consist of four main parts: a human operator, a
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master device, a slave device, and the environment. The human operator
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inputs the desired movement through the master device that acts as an
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interface to command the robot manipulator or slave device. Simultaneously,
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the slave device sends contact force information between the end-effector and
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its environment back to the human operator. This configuration is considered
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a bilateral system. The control algorithm of bilateral telemanipulators is
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designed for tracking the movement between master and slave device while
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maintaining the closed-loop stability of the system. The contact force
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information which is typically measured by force sensors can provide
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transparency to the system. However, force sensors have many limitations.
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Therefore, this research aims to design a controller that maintains the closed-
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loop stability of the system and includes a force estimation algorithm to
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approximate the contact force. In this operation, the human operator inputs
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the movement information at the master device, which is sent to the slave
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device through a communication channel. Adaptive inverse dynamic control
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is applied to the slave device so that its movement can track the input
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position of the master device, estimate unknown system parameters, and
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maintain stability. The contact force between the slave and its environment is
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approximated by an observer-based force estimation algorithm to avoid the
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limitations of force sensor. The proposed method also includes a scaling
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factor between master and slave device. Simulation results are presented in
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this paper.
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Keywords: telemanipulator, teleoperation, bilateral control, robust
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adaptive control, smooth sliding mode control
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Introduction
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A teleoperation system enables a human operator to control a machine or system
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from a remote location. Teleoperation requires both advanced control theory and
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improved communication system. One of the main challenges of teleoperation is
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transmitting information between the human operator and the slave robot. The
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human operator and master device are included in the local site. The master
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device can be a joystick, mouse, keyboard and other input/output devices. The
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machine or slave device is placed in the remote site, and typically consists of a
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robot with sensor, actuator, control system (Spong et. al., 2006).
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Control algorithms are applied for tracking movement between master and
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slave devices and also maintaining the stability of closed-loop system. Advanced
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control theory is used to provide robustness when the system consists of
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parametric uncertainties and unknown disturbance. The relevant information
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feedback from the robot manipulator is the contact force between the robot and its
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environment. This force can be measured by force sensor and transparency is
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achieved when the human operator received the contact force accurately, but there
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are several limitations of force sensor that can lead the system to lack mechanical
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robustness and stability. Thus, this research is aim to design a controller and force
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estimation algorithm for the bilateral control for telemanipulators (Oboe et. al.,
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1996).
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The bilateral control system has two design goals to establish a
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relationship between the human operator and the remote environment. The first
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goal is that the slave device must track the position of the master manipulator and
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the second goal is that the acting force on the slave must be accurately transmitted
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to the master. The slave to the master device with local force control, the velocity
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signal is transmitted to the slave with local velocity control. The basic control
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architecture is illustrated in Figure 1. The human operator manipulates the master
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device and perceives the force information from the remote environment via the
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haptic interface. The human operator moves their arm holding the master device
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with the velocity vm and applies the force fh. The master device velocity is
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transmitted via the communication channel and acts as desired velocity v d for the
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local velocity control loop of the slave device. The slave controller ensures the
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tracking between desired velocity vd and slave velocity vs by the slave control
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input uS. The reaction force between slave and environment fe is measured by a
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force/torque sensor (F. M. Buss, M. Aracil, R. Melchiorri, and C. Balaguer,2007).
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The reaction force information is transmitted via the communication channel to
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the master device as reference input force fd to the local force, and master
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controller generates the control input (S. Lichiardopol et al., 2007).
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A force control technique is required to control the forces between the
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robot and its environment. For example, a gripper is the tool tip of a robot arm for
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picking and placing the object. If the gripper holds a fragile object, it requires a
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safe contact force so that it does not destroy the object. Typically, a force sensor is
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used, which is attached at the tip of gripper for measuring the contact force. The
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force control system then uses the information from the force sensor to compute
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the contact force and provide the suitable safe force. However, the force sensor
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has several drawbacks such as noise, narrow bandwidth, lack of robustness,
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sensitivity to temperature and high price. An observer-based force estimation error
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is implemented to estimate the external force from the position error, but it
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requires an accurate model.
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Therefore, this research presents a controller design to achieve fast
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response, while improving accuracy, reliability and stability between master and
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slave. Robust adaptive control is designed to provide stability in the case of
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uncertainties in modeling, unknown force disturbance. Another objective is based
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on the concept of force estimation observer-based force estimation. However,
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conventional observer design requires an accurate model of the system. The
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nominal model typically is used, but the actual plant includes parametric
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uncertainties and noise. The smooth sliding mode control is used to deal with the
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parametric uncertainties from the estimated parameter of the mathematical model.
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Mathematical Model
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The system is assumed to have one degree of freedom representing a generalized
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mass spring-damper model, which is a simple and useful model. The dynamic
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model of the master-slave configuration is shown as follows:
(1)
(2)
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where um and us are the control input to the master and slave, fh is human operator
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disturbance force, mm, dm, and km are the mass, damping coefficient and stiffness
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of the master device. fenv is environment disturbance force bounded with a
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constant, ms, ds, and ks are the mass, damping coefficient and stiffness of the slave
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device. The environment disturbance force is defined as:
(3)
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where ξ is the unknown stiffness of the environment or object, and xe is the
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displacement of the unknown environment. The idea of bilateral control is defined
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as follows:
(4)
(5)
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where fm is the contact force at the master device and fenv is the estimated contact
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force between slave device and its environment. Equation (2) indicates that the
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position of the slave device should track the position of master device. Equation
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(1) gives the force that must be generated on the master device to allow the human
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operator to sense the contact force between slave and its environment. The scaling
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factor between master and slave device is a positive constant.
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Robust Adaptive Control for Bilateral Control
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In this operation, the human operator inputs the desired position by directly
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manipulating the master device. Inverse dynamics control is used to achieve
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trajectory tracking of the desired position by the slave device. However, the real
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system typically suffers from issues of parametric uncertainties and disturbances.
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This research addresses these problems by combining adaptive control, sliding
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mode control, and σ-modification technique to ensure robustness and stability of
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the system. Additionally, the human operator needs to sense the interaction
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between the slave interactions with its environment. Force estimation algorithm is
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implemented to replace force sensor. The scaling factor between master and slave
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device is implemented to eliminate the need for dedicated force sensors. The
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method can be generalized to include a scaling factor between master and slave
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device.
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The mathematical model of the slave is assumed to be given by (2), where
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the parameters are unknown or time-varying. A smooth sliding-mode controller
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will be designed to ensure stability, robustness, and performance of the system
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only in the slave device. The position error signals are defined as follows:
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(6)
(7)
(8)
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where e1 is position error, e2 is the velocity error with guarantee error and k1 is a
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positive constant. The robust adaptive controller with smooth sliding mode control
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is given as:
(9)
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where κ is a positive constant. Define the parameter estimation errors as:
(10)
(11)
(12)
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are estimated system parameters. The adaptation laws with σ-
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where
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modification can now be given as:
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and
(13)
(14)
(15)
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Stability Analysis
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The stability of the proposed controller will be analyzed by considering the
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following candidate Lyapunov function, which consists of the energy of all
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relevant error signals:
(16)
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Taking the derivative to (16)
(17)
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Substitute the adaptive law into (17):
(18)
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From (9)
(19)
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Combining (2) and (19)
(20)
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By inserting control law to (20)
(21)
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Using the adaptive control law into (21)
(22)
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Performing simple mathematical manipulation yields the following result:
(23)
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Rearrange (23)
(24)
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The final result is shown below:
(25)
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From the stability analysis, the system can be shown to be asymptotically
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stable. This is because the candidate of Lyapunov energy function and the first
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derivative of candidate of Lyapunov energy function satisfies of the condition of
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Lyapunov functions.
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Force Estimation
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This research uses the concept of force observer to estimate the external
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environment force. The estimated plant can be defined as:
(26)
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where
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device obtain from robust adaptive control,
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estimated plant and
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parametric uncertainties between the actual and the estimated plant. In addition, if
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,
can track
,
are the estimated mass, damping and stiffness of the slave
, then
is the estimated position from
is the estimated contact force. The system consists of the
. Conventional sliding mode control can be used
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to ensure that the estimated plant position converge to the actual plant position
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regardless of small parameter estimation error and external disturbance. However,
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it suffers from Chattering phenomenon. The sliding mode control has limitation
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from the chattering phenomenon. Therefore, the smooth sliding mode control is
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applied to avoid this problem, the estimation environment force is now defined as:
(27)
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where
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-
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is the position error between the slave and the estimated position
=
, k is the gain of smooth sliding mode control, and is the thickness of
boundary error.
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Stability Analysis
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Rearranging the stability analysis is also derived by the Lyapunov candidate
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function (12) as a state-space model presented below:
(28)
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where
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In the same way, the estimated plant (26) is rewritten into a state-space equation:
(29)
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where
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The position error between
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Then,
=
-
(30)
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The sliding surface is defined as follows:
(31)
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where a1 > 0 is some constant. Assume also that the following inequality holds,
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The derivative of the sliding surface
(32)
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The Lyapunov candidate function is expressed as:
(33)
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Taking the derivative (33)
(34)
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Substitute the bounded inequality to (34)
(35)
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By inserting the sliding surface into (35)
(36)
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Rearrange (36)
(37)
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The final result is below:
(47)
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, when t→. The estimated plant is asymptotic stable by
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Thus,
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using estimated environmental force.
approach to
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Result and Discussion
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The master position serves as the command trajectory for the slave device
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governed by the robust adaptive control. The contact force between slave and
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external environment is estimated by the proposed force estimation algorithm and
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sent to the master device to create force feedback. The master model is assumed to
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be known, but the slave device contains unknown parameters. The robust adaptive
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control algorithm can ensure the stability of the system. The contact force between
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the slave device and its environment is considered as an unknown disturbance that
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is estimated by a smooth sliding mode controller designed using the force
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observer concept.
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Simulation Results without Scaling Factor
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Assume a teleoperated manipulator system with 1 DOF and parameters as
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shown on Table 1. This section considers the cases of no time delay, constant time
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delay and varying time delay when there is no scaling factor between master and
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slave devices The slave position is able to track the master position almost
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perfectly, as shown on Figure 3. The performance of the controller depends on the
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gain k1 and also initial parameters estimates. Figure 4 shows the convergence of
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all estimates to the true value within 2 seconds of free motion.
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Simulation Results with Scaling factor
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In the following simulation, the communication channel is assumed to have no
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transmission delay and the master position is scaled by 4. The tracking results are
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shown on Figure 6, which shows the successful tracking of the master and slave
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position with the indicated scaling factor. The fast and accurate convergence of
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the estimated system parameters are shown on Figure 7. These parameters are
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used by force estimation algorithm to determine the contact force between the
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slave and its environment. Figure 8 shows the estimated contact force, which is
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scaled down by 4 from the actual force.
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Conclusions
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This research has been proposed to achieve the bilateral control for teleoperated
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manipulator system. The human operator directly manipulates the master device.
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The position of master device is sent to the slave device via the communication
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system. Robust adaptive control is applied only in the slave device. This controller
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can deal with parametric uncertainties, unknown parameter and unknown
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disturbance. The estimation of unknown parameters yield almost perfect results.
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The robust adaptive control can maintain the closed-loop stability of the system,
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even when the communication channel contains constant and varying time delay.
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The contact force between the slave device and ts environment can be estimated
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by smooth sliding mode control and smoothing the estimated contact force by a
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low pass filter with acceptable result. The estimated contact force is the feedback
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information to the master device to generate the interaction torque between he
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human operator and the master device. The interaction torque is created by the
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current of the master device to provide the transparency of the system. The scaling
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factor is also applied for scaling the information between the master and the slave
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devices.
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MATLAB/Simulink. However, this algorithm needs o be implemented on the
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simple experiment first which is already designed. In the future, his research can
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be extended to other applications.
This
research
presents
the
simulation
results
by
using
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References
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(ตรวจสอบวิธีการขียนเอกสารอ้างอิงตามรูปแบบของวารสารได้ที่
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http://ird.sut.ac.th/e-journal/guideforauthor.php
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และขอให้มีการอ้างอิงตรงกันทัง้ ในเนื้อหาบทความและในรายการเอกสารอ้าง
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อิง)
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Bruno, S. and Oussama, K. (2008). Springer Handbook of Robotics. Insert book
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Lewis, F.L., Dawson, D.M., and Abdallah, C.T. (2004). Robot Manipulator
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Control Theory and Practice. 2nd ed. Revised and Expanded, Marcle
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Dekker, Inc., insert total number of pages.
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Spong, M.W., Hutchinso, S., and Vidyasagar, M. (2006). Robot Modeling and
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Control. Insert book edition. JohnWiley and Son Inc., insert total number
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of pages.
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F. M. Buss, M. Aracil, R. Melchiorri, and C. Balaguer , 2007, Advances in
Telerobotics, Springer,
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S. Lichiardopol, 2007, ”A Survey on Teleoperation”,December
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P. F. Hokayem, M. W. Spong, 2006,”Bilateral teleoperation:An historical survey”,
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Automatica, Vol.42.
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J. Cui , S. Tosunoglu , R. Roberts , C. Moore , D. W. Repperger , 2003, ”A
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the Florida Conference on Recent Advances in Robotics-FCRAR, Boca
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H. C. Cho, J. H. Park and J. Park, 2001, ”Sliding-Mode-Based Impedance
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Controller for Bilateral Teleoperation under Varying Time-Delay”,
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Figure 1. Architecture of two channel controller
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Figure 2. The block diagram of proposed method
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Figure 3. Trajectory tracking between the master and the slave device
position
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Figure 4. Convergence of parameter estimates
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Figure 5. The estimated contact force by smooth sliding mode control
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Figure 6. Trajectory tracking between the scaled master and slave device by
the robust adaptive control and scaling factor
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Figure 7. Convergence of parameter estimates with no time delay and scaling
factor
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Figure 8. The estimated contact force between the slave device and its
environment and the scaled estimated force
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Table 1. Table of parameters
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(please make the Table in MS.word format, not a picture.)
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