Medical Robot

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REMOTE CONTROL OF

SURGICAL ROBOT IN

CONSTRAINED ENVIRONMENTQUEK YUEN XIAN (U095846R)

Department of Mechanical Engineering

National University of Singapore

NOVEMBER 4, 2013


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Summary

In the past decades, medical robots have seen a significant growth in assisting surgical

processes. The development of Robotic Master-Slave system enables surgeons to overcome

several conventional limits, and have been widely adopted especially in minimal-invasive

system. However, the growing functionality in medical robots have been imbalanced with a

relatively limited input options at the master console. To reduce interaction time and

distraction for the operator at the master console, different human machine interfaces have

been investigated to provide a more intuitive interaction in the Master-Slave system.

In this project the Microsoft Kinect, a 3D depth camera is used to design and implement a

touch less Master-Slave control system. The system offers operator a more intuitive input

interface by controlling the slave robot movement with his natural arm movement. Specific

control issue of constrained manoeuvring is addressed by proposing a shared-control system

where the movement of the slave robot in obstacle region is controlled through a planned

trajectory using the Pseudoinverse Jacobian to offer a realistic control environment.

The system is designed and implemented in a simulated environment in Matlab. The results

from the simulation show that the proposed constrained manoeuvring method achieved is

able to good accuracy in avoidance obstacles while keeping to the desired trajectory, which

makes this system applicable in surgical environment where obstacle avoidance criterion is

desired.


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Acknowledgement

I would like to express my sincere gratitude to Professor Ren Hong Liang and Professor NitishThakor for providing guidance, supervision, consultations and support during the course of the

project.

I would also like to appreciate the lab staffs in Professor Rens Lab, especially Mr Wang Jiaole

for his time and effort in answering my queries. Without their help, I would not be able to

complete the project in time.


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Table of Contents

1.0 INTRODUCTION1.1PURPOSE STATEMENT

1.2 THE PROBLEM1.3 SCOPE

56

66

2.0

3.0

LITERATURE REVIEW

THEORY

3.1 KINEMATICS

3.2 DENAVIT-HARTENBERG METHOD

3.3 FORWARD KINEMATICS

3.4 INVERSE KINEMATIC SOLVERS

3.5 MATRIX PSEUDOINVERSE

3.6 SINGULARITY ANALYSIS

3.7 OBSTACLE AVOIDANCE

3.8 TASK FUNCTION APPROACH

8

10

1010

11121313

131416

4.0 MASTER-SLAVE SYSTEM DESIGN

4.1 MASTER-SLAVE SYSTEM SET-UP

4.2 KINEMATIC MAPPING

4.3 OBSTACLE AVOIDANCE SET-UP

4.4 SHARED CONTROL MASTER-SLAVE SYSTEM

191920

2122

5.0 RESULT & DISCUSSION5.1 OBSTACLE AVOIDANCE RESULT

242426

6.0 CONCLUSION & RECOMMENDATION6.1CONCULSION6.2 RECOMMENDATION

272727

REFERENCE 28


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List of Figures and Tables

Fig 3.1. Co-ordinate Frame assigned for a general manipulator

Fig 3.2 Comparison on the effect of damping factor on joint velocity near

singularity position.

Fig. 3.3 A path for the manipulator through its workspace, where the trajectory of

the end-effector are darkened.

Fig. 3.4 Robot and obstacles parameters in the task function approach

Fig 4.1. Schematic representation of the Master-Slave interface.

Fig.4.2 Simplified Human Arm Model

Fig. 4.3 Operator Controlling the Slave Robot through Direct Kinematic Mapping

Fig.4.4 Obstacle Avoidance Set up

Fig.4.5 Defining Control Region in the Slave Robot Work Space

Fig.5.1 Distance from obstacle and critical point under different operating condition

Fig.5.2 End-effector trajectory under different operating condition

Fig.5.3 Measuring Consistency in Kinematic Mapping.

.


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Chapter1: Introduction

Robotic devices in surgical applications have seen significant development in the past

decades, especially in minimal-invasive system. While the growing functionalities of medical

robots have allow surgeons to overcome many conventional limits, it is imbalanced by the

relatively limited input options available at the master console. This has led to the

investigation friendly human machine interface to achieve less interaction time between the

operator and the console.

Kinect Sensor, without any physical obstruction, could provide a more intuitive human-

machine interface interaction. In this paper, a touch less master-slave system controlled by

direct kinematic mapping is designed and implemented in a simulated environment. In order

for the operator to teach the slave robot to perform complex task intuitively, it is important

for the slave robot to be able to imitate the movement of the operator. Therefore, a kinematic

mapping method which uses a simplified kinematic model to define the arm configuration

and convert it into joint angles relative to the slave robot is implemented.

In application for surgical environment, it is necessary to restrict the motions of the end-

effector and other parts of the robotic system to avoid contact with surrounding patient

anatomy. To resolve this problem, a shared control system is proposed, where obstacle

avoidance region is defined. As the robot arm enters the defined region, its movement is

guided by a planned trajectory to avoid the obstacle.

To control the trajectory of the robotic end-effector, the system make use of the

Pseudoinverse Jacobian techniques, introduced by [1]. This method can be illustrated by the

equation

= + ( +) (1.1)


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where x is a 6-vector Cartesian coordinates of the robots end effector, J is the Jacobian

Matrix and I is an identity matrix. Vector Z is an arbitrary vector in the null space of the

Jacobian used to calculate the joint angles change needed for the rest of the joints to avoid an

obstacle.

The rest of the chapters in this report describes in details the theory behind the proposed

method and the design of the Master-Slave system in Matlab as well as the performance of

the system based on simulation result.

1.1 Purpose (or objective) Statement

The purpose of this project is to propose, implement and test the feasibility of a touch-less

master-slave control method which make use of the natural interface provided by Kinect to

connect the human arm motion to the robotic arm, and operate it in confined environment.

1.2 The Problem

With the imbalance between the growing functionality of medical robots and the limited

input options available at the master console, there has been a need for other friendly human-

machine interface which could reduce interaction needed at the console, so that surgeon can

focus on the surgical process.

1.3 Scope

The remaining of the report is divided into 5 Chapters. Chapter 2 provides a literature review

of the current development of medical robot in surgical applications so as to provide a

comparison with the control system proposed in this paper. To control the slave robot in

obstacle avoidance region, the Pseudoinverse Jacobian method is implement in the system.

The theory behind the implementations is described in in Chapter 3. This includes the


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calculations of the different kinematic equation, the Jacobian matrix as well as the derivation

of the constraint set on the robot control.

In Chapter 4 & 5, the design and set-up of the Master-Slave system in Matlab is explained,

followed by analysis of the simulation results to discuss the performance of the Master-Slave

system. Finally conclusion and further recommendations based on the results are proposed

Chapter 6.


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Chapter 2: Literature Review

Medical robots are playing an increasing significant role in surgical processes the past decades.

An area of development that has generate strong interest is the possibility of remote operation

between surgeon and patient through robotic assisted surgery.

The earliest tele-operated robots were invented in the 1950s [2], and since then, teleoperation

technology has undergo continuous development [3]. One of the most advanced system

currently is The Machine [4] developed by Intuitive Surgical Inc. (ISI),which is a

robot-assisted minimally invasive systems (RMIS) that enables surgeon to operate with

enhanced vision, precision, dexterity and control. Smaller surgical tele-operated systems like

the RAVEN [5]which is more deployable is also being developed. These systems have tools

that are smaller than the human hand for operation in small body cavities and have allowed

surgeon to be connected to patient across large distance for remote surgery [6].

Various assistance functions are being developed for surgical robots to improve safety and

operation time during teleoperation. These include virtual constraints [7] and supervision of

manipulation forces [8] aim to prevent tissue damages, as well as autonomous execution of

error-prone or recurrent tasks.

Most RMIS master consoles, which includes the & come with

several foot pedals and touchpad for operator to alter the setting of system or switching surgical

tool. However, this form of interaction is time-consuming and distracting to the surgical

process. This has led to investigation of more human friendly machine interface which can

reduce interaction time.

Various humanmachine interfaces for teleoperation of the robotic devices have been

investigated for different industries, which includes exoskeleton devices [9] and instrumented


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gloves [10].These methods usually involve physical contacting devices which could obstruct

the operators motion.

A touch less control interface without any physical obstruction, could provide a more intuitive

human-machine interaction. Teleoperation of robot by natural sign language is proposed in

[11], where the operators signs are interpreted from finger encoder readings. In [12], a gesture-

based user interface is also proposed, whereas intuitive gestures are learned by the system and

linked to a certain command which is recalled during operation as the gesture is presented by

the surgeon.

In this project, instead of using gesture input to control specific built in functions in the

robotic system, the slave robot is directly controlled through kinematic mapping which

convert the input data from the motion sensor to motion command for the slave robots.

Additional constraints is then added to the system by defining obstacle regions. Through this

proposed method of Master-Slave control which offers intuitive interaction between the

operator and machine, more functionality can be develop for application in surgical

environment.


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Chapter 3: Theory

3.1 Kinematics

Motion of surgical robots are relatively slow for safety reasons, hence the dynamic behaviour

of the manipulator is not required to be considered in the formulation of motion control [13].

Similarly, only the kinematics of the manipulator is taken into consideration in this project.

Six coordinates, three for position and three for orientation are required to define a point in

space. A manipulator and its end-effectorsposition & orientation is represented as a function

of its joints. If a manipulator has more number of degrees of freedom than required to define

a point in space, it is considered to be a redundant manipulator. Forward kinematics defines

the end-effectorsposition and orientation from the joint while Inverse Kinematic calculates

the corresponding joints angles from the end-effectorsposition and orientation.

Both Forward and Inverse Kinematic is used in the Master-Slave system in controlling the

slave robot to avoid obstacle along its path. Therefore, the theory behind each of the method

used is elaborated in details in the following section.

3.2 Denavit-Hartenberg method

To apply forward kinematics for a robot mechanism in a systematic manner, a suitable

kinematics model is needed. The Denavit-Hartenberg (DH) Method is used to develop the

kinematic model for the robotic arm [14] The DH method which uses 4 parameters is the most

common method to describe arm kinematic. A co-ordinate frame is attached to each joint to

determine the DH parameters.


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In this method, each joint is modelled as a 1DoF revolute joint. The axis of rotation is located

and identify as the z axis. axis is located as pointing along the common normal line

between the axis. axis is establish to complete a right-hand coordinate system.

With these joint axes, four parameters specify the joint-to-joint transformation: r, , d and :

Link Length (): the distance from measured alongaxis

Link Offset (): the distance from measured along

Joint Angle (): angle measured about the axes, from

Link Twist (): angle measured aboutaxes, from _ .

Fig 3.1. Co-ordinate Frame assigned for a general manipulator. Taken from [15]

3.3 Forward Kinematics

In Forward Kinematics, the position and orientation of each segment of the manipulator is

uniquely defined by specifying its joint angles.

By assigning Cartesian Coordinate frames to each link and identifying the DH parameters,

the position and orientation of the i-th coordinate frame can be expressed in the (i-1)-th

coordinate frame by the following homogenous transformation


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=

0

0 0 0 1 (3.1)

The position and orientation of the end-effector coordinate frame in then expressed in the

base coordinate frame by the following transformation matrix:

=

= =

0 0 0 1 (3.2)

Where the 4thcolumn represent the position of the end-effector in the X, Y and Z axis. Based

on this transformation matrix, the position of the end-effector can be determine from the

value of the joint angles. The position of the end-effector is needed in the system to calculate

the required changes in joint angles at each time frame to move the slave robot along its

trajectory.

3.4 Inverse Kinematic Solvers

In Inverse kinematics, equations are non-linear unlike direct kinematics. This led to some key

issues in the inverse kinematic problem as listed below:

1. Multiple solutions exists

2. Infinite solutions in case of kinematically redundant manipulators.

3. No solution in certain manipulator configurations.


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While inverse kinematic solutions can be derived both analytically and numerically,

analytical approach would lead to infinite solution for redundant robots. Therefore in this

project, a numerical approach is taken to derive the inverse kinematic solution.

Numerical solutions to the inverse kinematic problem usually involve obtaining a Jacobian

matrix [16] and solving the linear matrix system.

= (3.3)

The matrix J is an mn matrix, where n is the number of joints and m is the dimension of the

end effector vector, which is 3 for a positioning task, or 6 for a position and orientation task.

3.5 Matrix Pseudoinverse

In this paper, the pseudoinverse method [1] is adopted to solve the linear matrix system. By

applying the pseudoinverse method, the equation 2.3 is transformed to

= + (3.4)

Which gives the unique least-squares solution even when the system is redundant.

3.6 Singularities Analysis

When the robot arm approaches singular configuration, the Jacobian loses its rank and the

robot is unable to generate the required velocity. In this situation, the classical inverse of the

Jacobian results in very high joint velocities [17] which are not achievable and result in

inaccurate motion of the end- effector. Such motions could post threat to the users. Hence, a

constant damping factor is added to the inverse of the Jacobian matrix to move the robot

through singularity. Fig 2.2, shows the effect of the damping factor which will prevent high

joint velocities near singularity.


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Fig.3.2 Comparison on the effect of damping factor on joint velocity near singularity

position.

3.7 Obstacle Avoidance

Redundancy in a system can be used to accomplish various secondary tasks which includes

obstacle avoidance. However, the obstacle avoidance in this paper must be achieve with

certainty instead of a secondary goal. Therefore, the first step is finding a collision-free path

for the end-effector, which is computed off-line because of the high computational load

required. A graphical demonstration of determining the collision-free path is shown in Fig.3.3

By running the collision-free path on a simulation, the critical point of the robot-arm that will

first collide with the obstacles can be identified for use in the computation of the obstacle

avoidance criterion.


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Fig 3.3. A path for the manipulator through its workspace, where the trajectory of the end-

effector are darkened. Taken from [18]

In equation 3.3, the Jacobian matrix relates the end-effector velocity to the change in each joint

angles. It is shown in [19] that the general solution to equation 2.3 is:

= + ( +) (3.5)


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where I is an nn identity matrix and z is an arbitrary vector in -space. The projection operator

(IJ+J) describes the degrees of redundancy of the system. It maps an arbitrary z into the null

space of the transformation.

By using specific function to compute the vector z, reconfiguration of the manipulator can be

obtained to achieve the desirable criterion of obstacle avoidance, without affecting the joint

trajectory.

2.8 Task Function Approach

The Task Function Approach from [20] computes z as the gradient of an objective function

P (q,t) and projects it to the null space of the Jacobian as shown

= + ( +)

(3.6)

Where is a gain function that is used to adjust the influence of the null space Jacobian and

(, ) = (, ) (3.7)

Where > 0, (, ) = ||(,). In equation 2.7, point R and point S are

critical points defined on the robot and obstacles, while d is the smallest distance defined

between the obstacles and the robot as shown in Fig.2.4 below

Fig 3.4 Robot and obstacles parameters in the task function approach. Taken from [20]


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From equation 3.7, the vector Z,

that needs to be calculated becomes

= (, )(+)

(,) (3.8)

Hence to be able to compute vector Z, we need to compute the function

(,).

From Fig 2.4, =

(,)( ) (3.9)

Where are the position vector of S and R respectively.

From equation (2.9),(, ) < , >, which when differentiated gives

= < , > < , > (3.10)

Replacing with in the equation = and substituting equation (2.9) to (2.10), we get

= < , > (3.11)

By inspection of Fig 2.4, < , > =

(3.12)

Recall the relationship =

(3.13)

Combining equation (3.10)- (3.13), we get

=

(3.14)

Simplifying equation 3.14, we achieve the function for

(,)

(, ) =

(,)( ) (3.15)


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Finally, substituting equation (3.15) back to (3.8), we can calculate the vector Z as the

following function:

= (, )(+)

(,)

( ) (3.16)

In (3.16), K and are gain factors that can be adjust according to the desired smoothness of

the trajectory and degree of influence of the null space of the Jacobian matrix. By setting the

gain factors and the minimum distance between the obstacle & critical point, vector Z can be

computed and project to the null space of the Jacobian matrix to achieve the criterion of

obstacle avoidance.


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Chapter 4: Touch-less Master-Slave System Design

4.1 Set-up of Touch less Master-Slave System

Fig. 4.1. Schematic representation of the Master-Slave interface

The touch less master-slave interface was developed for teleoperation of a six-degree-of-

freedom robot manipulator in a simulated environment in Matlab. The interface designed

consists of four main components, shown schematically in Fig. 1 and described below:

1. The Microsoft Kinect is used to track the human handarm motion and obtain joint

coordinates of the operator in real time. The 3-D coordinates of the shoulder, elbow

and hand in the Kinect coordinate frame is sent to the Matlab program to be processed

to motion command for the slave robot.

2.

The control software convert the 3-D joint co-ordinates into joint angles relative to the

slave robot in real time for imitation of the operator movement. The change in the

Jacobian and slave robots end-effector position during its movement is also

calculated in real-time for use in fulfilling the obstacle avoidance criterion.

3. A simulated environment is created with a pre-defined obstacle avoidance region

based on the obstacle position and the minimum distance the slave robot need to

maintain from the obstacle. This obstacle avoidance region serve as the boundary for

the shared control system in the simulation.


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4. A visual display feedback system is provided to the operator through a monitor screen

which display continuous images of the slave robot interacting with objects in its

environment. This is to allow the operator to gauge the slave robot movement with

respect to his own and also the position of the obstacles.

4.2 Kinematic Mapping

Fig 4.2 Simplified Human Arm Model (Right)

The main aim of the kinematic mapping is to effectively convert the input data, which is the

3-D joint coordinates into motion command for the slave robot to imitate the operators arm

motion. An accuracy mapping would allow the users to teach more complex movements to

the slave robot. In this method proposed, the converted motion command are the joint

angles relative to the slave robot calculated based on the input joint co-ordinates. The steps

in implementing the kinematic mapping is describe below:

Step 1: Human arm is simplified into 4-degree-of- freedom robot arm which adequately

represent the configuration of the human arm. Based on position of shoulder, position of

shoulder to elbow can be fully defined by &. Similarly, position of wrist to elbow canbe fully defined by &. Thus configuration of arm can be fully defined by to ateach time frame.


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Fig 4.3 Operator Controlling the Slave Robot through Direct Kinematic Mapping

Step 2: The simplified arm model allows the inverse Kinematic Algorithm to be decomposed

into a per-time-frame problem. At each time frame, joint angles base on human posture is

generated.

Step 3: Due to high frame rate of Kinect, the calculated joint angle is processed with a

moving average algorithm to smooth out short term fluctuation. Repeated run were

conducted in the simulation and a moving average of period 5 were determined to ensure a

smooth arm movement of the slave robot.

4.3 Obstacle Avoidance

Fig 4.4 Obstacle Avoidance Set up

The obstacle avoidance method is designed on the assumption that the slave robot operates ina known environment. In the obstacle avoidance region, the slave robot is controlled tofollow a planned trajectory for its end-effector, similar to the example shown in Fig 4.3 toavoid the obstacle along its path and reach the desired position. The path for the trajectory isconfined within the obstacle avoidance region to allow the robot to remain close to theobstacle without violating the minimum distance required.

Kinect Sensor

Virtual Feedback


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The movement of the slave robot arm along the planned trajectory is controlled using thepseudoinverse of the Jacobian matrix represented by equation (1.1) first shown in Chapter 1.

= + ( +) (1.1)

Where the changes in angles need for the slave robot to avoid the obstacle is determined by Z,which is represented in equation (2.16) which is described in detail in Chapter 2.

=

= (, )(+)1

(, )

( ) (2.16)

A program is build based on these equation to control the movement of the slave robot whileit enter the obstacle avoidance region to fulfil the obstacle avoidance criterion.

4.4 Shared Control Master-Slave System

Fig 4.5 Defining Control Region in the Slave Robot Work Space

A shared control system between the operator and controller is implemented in the simulation

by defining an obstacle avoidance region in the work space of the slave robot arm as shown

in Fig 4.5. Out of the control region, the slave robot move by imitating the motion of the

operator. When the operator direct the slave robot into the obstacle avoidance region, the

control of the slave robot is transferred to the Matlab program to guide the slave robot around

the obstacle. As the destination and trajectory of the slave robot in the control region is pre-

calculated in the program, simulation results is obtained to determine the accuracy between


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the desired and actual movement of the slave robot for evaluation of the accuracy of the

control method.


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Chapter 5: Results and Discussion

5.1 Obstacle Avoidance Results

Fig. 5.1 Distance from obstacle and critical point under different operating condition.

During the simulation, the distance between the obstacle and critical point are calculated and

recorded. The procedure is repeated under condition when no constraint is added to the robot

arm for comparison. In the graph, the blue line show the critical distance between the robot

and obstacle, the red line is the minimum distance need to be keep from the obstacle. We can

see that the method describe is able to control the robot maintain the required distance

throughout its trajectory. A comparison is made with movement when no constraint is added

as seen in the green line.


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Fig 5.2 End-effector trajectory under different operating condition.

From the graph above, it is shown that the control method proposed is able to achieve very

close result between the desired and actually trajectory of the end effector while avoiding the

obstacle. Therefore, I would concluded that this control system would be possible to be

implemented in environment with narrow operating region where we need the arm to keep to

specific trajectory. By adjusting the appropriate gain value in the null space of the Jacobian

Matrix, we can control the robot to move through the narrow space without hitting any

obstacle along its path.

However, it should be note that in this project, only the position of the end-effector is

considered. In specified surgical environment, the orientation of the end effector is also an

important consideration. In such scenario, a manipulator with more redundancy is needed to

be able to achieve the obstacle avoidance criterion while maintaining the required orientation.


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5.2. Kinematic Mapping

Fig 5.3. Measuring Consistency in Kinematic Mapping

Specific movement were executed by the human subject and repeated over time at the same

magnitude to measure the consistency of the robot in imitating the human arm motion. The

graph above shows relative good consistency but small fluctuation of the still exist, therefore

further filter algorithm should be added to process calculated data.


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Chapter 6: Conclusion & Recommendation

6.1 Conclusion

The proposed touch-less master-slave control system provide a new approach for the user to

directly control the slave robot naturally with relatively good consistency and successfully uses

its redundancy to avoid obstacles along its path. While this has been an approach frequently

used in industrial robot, the good accuracy from the simulation show that its application may

be possible in surgical environment when manipulator needs to move through narrow path and

avoid obstacles. Base on the proposed control interface, more constraints can be added to the

system for application in specific surgical environment.

6.2 Recommendations for Further Work

Further work should focus on adding functionality that improves the precision of the robot

control for use in RMIS application. A more detailed research can be done on the

functionalities being developed in current Master-Slave system to determine which one of

them can be modify and apply to the system in this paper. As the current system is not

designed to work in specific scenario, the obstacle avoidance method should also be

implemented on more specific surgical tasks.


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[17] H. K. Le Minh Phuoc, "Damped least square based genetic algorithm with Ggaussian

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