medical robot
TRANSCRIPT
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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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