MODELING AND SIMULATION OF A NEW PARALLEL ROBOT

USED IN MINIMALLY INVASIVE SURGERY

Doina Pisla, Calin Vaida, Nicolae Plitea

Technical University of Cluj-Napoca, Department of Mechanics and Computer Programming

Constantin Daicoviciu 15, RO-400020 Cluj-Napoca, Romania

Jürgen Hesselbach, Annika Raatz, Marc Simnofske, Arne Burisch

Technical University of Braunschweig, Institute of Machine Tools and Production Technology

19B Langer Kamp, D-38106 Braunschweig, Germany

Liviu Vlad

University of Medicine and Pharmacy “Iuliu Hatieganu”, Surgery Clinic III

Emil Isac 13, 400023 Cluj-Napoca, Romania

Keywords: Parallel robots, Minimally invasive surgery, Modeling, Simulation, Kinematics, Workspace.

Abstract: Surgery is one of the fields where robots have been introduced due to their positioning accuracy which

exceed the human capabilities. Parallel robots offer higher stiffness and smaller mobile mass than serial

ones, thus allowing faster and more precise manipulations that fit medical applications. In the paper is

presented the modeling and simulation of a new parallel robot, based on an innovative structure, used in

minimally invasive surgery. The parallel architecture has been chosen for its superiority in precision,

repeatability, stiffness, higher speeds and occupied volume. The robot kinematics, singular position

identification and workspace generation are illustrated. Using the developed virtual model of the parallel

robot, some simulation tests are presented.

1 INTRODUCTION

Simulation is one of the essential aspects in the

robots research field. The industrial trend is to

develop simulation systems, which could be helpful

for the robot off-line control and for the robot

operational workspace generation. Due to the high

graphical possibilities and memory capacities, the

personal computers offer already the necessary

instruments to achieve efficient simulation systems.

Within the simulation system, an important role

plays the achievement of a virtual robot functional

model, which allows its interactive visualization and

functional simulation.

The first important application of the simulation

systems is during the design process of a new robot

structure or a new flexible cell. In both cases it is

possible to test the functionality and the restrictions

influence without the actual building of the

prototype. In this way the costs, the implementation

and testing time are considerable reduced.

The second kind of important application of the

simulation systems refers to the existent robots that

could be better programmed, analyzed and

optimized if the research activity is considered.

Within the simulation systems, the visualization

of the robot trajectory with collision detection is

achieved, offering a safer system especially for the

case in which several robots are coupled, situation

that requires a more rigorous planning.

The robotized system performance can be tested

without any danger for the man or for the robot. The

programs generated within the simulation system

could be optimized before their practical

implementation leading to any damage avoidance

due to programming facilities, cost reduction and

quality improvement.

194

Pisla D., Vaida C., Plitea N., Hesselbach J., Raatz A., Simnofske M., Burisch A. and Vlad L. (2008).

MODELING AND SIMULATION OF A NEW PARALLEL ROBOT USED IN MINIMALLY INVASIVE SURGERY.

In Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics - RA, pages 194-201

DOI: 10.5220/0001500201940201

Copyright

c

SciTePress

Another advantage of the simulation systems

consist in their use in the research field. New control

algorithms can be created and tested before

investments in the necessary hardware devices for

the robot control to be made.

To the parallel robots simulation systems are

attributed different meanings: numerical simulation

for a specific robot function or element in transition;

parallel computing for the robot state and transitions

definition; the graphical simulation of the robot

structure and motion. In some cases the animation is

considered as simulation.

Geometric modeling is one of the keystones of

CAD systems. It uses mathematical descriptions of

geometric elements to facilitate the representation

and manipulation of graphical images on a computer

display screen. In three-dimensional representations,

there are four types of modeling approaches, (Foley

et al., 1990) and (Pisla, 2001): Wire frame

modelling; Surface modeling; Solid modeling;

Hybrid solid modeling.

Simplifying the virtual model enables

researchers to apply for the use of different methods

(usually starting with the most recommended one) in

correspondence with the available time and existing

endowment in order to compare the obtained results

and refine only the most adequate solution. In

practice, the application of simulation techniques is

used in two situations: for already made structures to

improve their characteristics; for new designed

structures to forecast their behaviour before

construction.

Lately is considered more the second case, due to

the intense development in creating new structures

with better dynamics and larger cinematic facilities,

or considering the parallel kinematic, a multibody

system can be designed to be used like a machine

tool or like a robot, therefore the same kinematical

structure must respond to different tasks that can be

demonstrated with the simulation techniques.

One of the first achieved models in order to

achieve the robot simulation is the geometric model.

There are many possibilities to create this model

also in this case. In respect with the chosen model,

different aspects regarding the mechanism properties

or actuating methods are emphasized.

The modeling process is oriented to the

correlation between the method and the structure in

order to point out the influence of the modeling

instruments on the structure design.

Considering that the robot performances depend

on the adequate combination between the designed

structure, the actuating and the control system, the

applying of suitable modeling and simulation

techniques could improve the robot design and

control through: identification of standardized

element behaviour with modular dimensions;

identification and visualization of the operational

workspace, which is harder to be achieved in the

parallel robot case; identification of different parallel

robot singularities and their avoiding; trajectory

visualization which must be programmed for certain

parallel robot tasks; speeds and acceleration

visualization in different trajectory points.

Regarding the application of robots for medical

applications there are some investigators focused on

exploring the capabilities of parallel robots in this

field (Ben-Porat, 2000), (Glozman, 2001), (Grace,

1993). AESOP robotic arm, used to guide a tiny

camera inside the body, was the first robotic system

used in surgery dating from 1993 (Brown

University, 2005). It was produced by Computer

Motion, which developed several such versions of

AESOP until they created Zeus

TM

Robotic Surgical

System with three robotic arms attached on the side

of the operating table. A competitor of Computer

Motion, Intuitive Surgical, designed another

revolutionary equipment, da Vinci

TM

Surgical

System, which became the market competitor of

Zeus until 2003 when the two companies merged

(Brown University, 2005).

Most of the robots, which assist the surgeons, are

serial robots (Brown University, 2005). The serial

module generates a large workspace while the

parallel module is steadier and offers a high

accuracy during the surgical operation. In this case,

there are used force control algorithms in order to

ensure the safety behavior and the accepted

accuracy.

Parallel robots offer a higher stiffness and

smaller mobile mass than serial robots, thus they

allow faster and more precise manipulations. The

problems concerning parallel structures kinematics

are usually more complicated than for the serial

structures. The drawbacks of serial robots,

determined by their structural construction, motivate

the research in the field of robotic assisted surgery

for a continuous search of task oriented robot

architectures that best fit a specific group of medical

applications.

The paper is organized as follows: Section 2 is

dedicated to modeling techniques; Section 3 deals

with kinematic modeling of the new parallel

structure designated to minimally invasive surgery;

Section 4 presents its workspace modeling, Section

5 presents the developed simulation program for

parallel robots with some simulation tests on a

studied parallel robot. The conclusions of this work

are presented in Section 6.

MODELING AND SIMULATION OF A NEW PARALLEL ROBOT USED IN MINIMALLY INVASIVE SURGERY

195

2 MODELING TECHNIQUES

Bottom-up Modeling Assembly Approach is the

modeling technique where component parts are

designed and edited in isolation of their usage within

some higher level assembly (Pisla, 2004). All

assemblies using the component are automatically

updated when opened to reflect the geometric edits

made at the piece part level. Using the bottom-up

approach, characteristic of traditional engineering

design practices, designs are built from known

components (embodiments) in anticipation of

satisfying functional requirements. The bottom-up

approach is known to be highly iterative. In the case

of large or complex designs, the problem quickly

leads to combinatorial explosion, inefficiency in the

design process, and difficulties assessing the

effectiveness and merits of design alternatives.

Bottom-up design is the traditional method. In

bottom-up design, you create parts, insert them into

an assembly, and mate them as required by your

design. Bottom-up design is the preferred technique

when you are using previously constructed, off-the-

shelf parts. An advantage of bottom-up design is that

because components are designed independently,

their relationships and regeneration behavior are

simpler than in top-down design. Working bottom-

up allows you to focus on the individual parts.

Top-Down Modeling Assembly approach is the

modeling technique where component parts can be

created and edited while working at the assembly

level (Pisla, 2004). Geometric changes made at the

assembly level are automatically reflected in the

individual component part immediately. In the top-

down approach, characteristic of a systems

engineering process, design is driven from

functional requirements toward solution alternatives.

While design solutions using this approach are likely

to meet functional requirements, there is no

guarantee that solutions are realizable in terms of

physical manifestations.

Top-down design is different because you start

your work in the assembly. You can use the

geometry of one part to help define other parts, or to

create machined features that are added only after

the parts are assembled. You can start with a layout

sketch, define fixed part locations, planes, and so on,

then design the parts referencing these definitions.

For example, you can insert a part in an assembly,

then build a fixture based on this part. Working top-

down allows you to reference model geometry, so

you can control the dimensions of the fixture by

creating geometric relations to the original part. That

way, if you change a dimension of the part, the

fixture is updated.

Analyzing both techniques characteristics, the

bottom-up assembly approach has been chosen for

parallel robot modeling due to their advantages.

3 KINEMATIC MODELING OF

THE PARAMIS ROBOT

In Figure 1 is presented the kinematic scheme of the

new parallel structure – PARAMIS, which can be

used for surgical instruments positioning (Plitea,

2007). The structure has three degrees of freedom in

space and it consists of three active joints (two of

them are prismatic and one is rotational). The

passive joints are two cylindrical joints, one

prismatic joint and one Cardan joint. The robot must

position the end of the laparoscope, namely the

video camera in any point of the operational field.

prismatic

joint

Cardan

joint

cylindrical

joint

cylindrical

joint

rotational

joint

prismatic joints

EEE

E(X , Y , Z )

BBB

B(X , Y , Z )

AAA

A(X , Y , Z )

d

h

e

f=2

f=4

b

r

A

2

q

q

1

3

q

X

Y

Z

Figure 1: Kinematic scheme of the new parallel robot.

The particularity of this motion is the fact that

the endoscope will move around a fixed point in

space, which is the entrance point of the trocar in the

abdominal wall of the patient (namely the point B).

The presence of the passive Cardan joint before the

laparoscope will allow the motion around the fixed

point of the abdominal wall. The trocar, the

abdominal entrance point and the endoscope can be

seen as a virtual joint with four degrees of freedom,

which allow the camera the rotation around the three

axis and a translation parallel with the axis of the

trocar. Thus, the endoscope can be positioned in any

point of the abdominal area using the three degrees

of freedom of the robot. The geometrical parameters

of the PARAMIS robot are given by

BBB

Z,Y,X;h,d,b (figure 1). In (Plitea, 2007)

the inverse and direct geometric and kinematic

ICINCO 2008 - International Conference on Informatics in Control, Automation and Robotics

196

models for speeds and accelerations of the structure

have been already presented.

Z

1

h

h

laparoscope

X

Y

E

y'

E

x'

z'

E

AAA

A(X , Y , Z )

BBB

B(X , Y , Z )

EEE

E(X , Y , Z )

Figure 2: The angles of the passive Cardan joint: φ, θ.

The implicit functions equation system, which

has been obtained from the kinematic model, are:

() ()

() ()

()

⎪

⎪

⎪

⎩

⎪

⎪

⎪

⎨

⎧

=−≡

=⋅

⎥

⎦

⎤

⎢

⎣

⎡

−−+−≡

=⋅

⎥

⎦

⎤

⎢

⎣

⎡

−−+−≡

0qZq,Zf

0qsinqqdbYq,q,q,Yf

0qcosqqdbXq,q,q,Xf

1A1E3

3

2

12

2

A321E2

3

2

12

2

A321E1

(1)

With the notations:

[][]

T

321

T

EEE

q,q,qq,Z,Y,XX ==

&

&

(2)

Through derivation of the relations (1), it yields:

0qBXA =⋅+⋅

&

&

(3)

where A is the Jacobian matrix of the direct

kinematics and B is the Jacobian matrix of the

inverse kinematics, x the vector of end-effecter

coordinates and q the vector of generalized

coordinates of the actuators.

The form of the A and B matrices are:

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎣

⎡

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

=

E

3

E

3

E

3

E

2

E

2

E

2

E

1

E

1

E

1

Z

f

Y

f

X

f

Z

f

Y

f

X

f

Z

f

Y

f

X

f

A

(4)

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎣

⎡

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

∂

=

3

3

2

3

1

3

3

2

2

2

1

2

3

1

2

1

1

1

q

f

q

f

q

f

q

f

q

f

q

f

q

f

q

f

q

f

B

(5)

3.1 Singularities Analysis

An important problem for the parallel robots is to

identify and avoid singularities, ensuring the system

stability and kinematic accuracy. Physically, these

singular positions lead to an instantaneous change in

the system number of degree of freedom and hence

loss of controllability and degradation of the natural

stiffness. Therefore it is important to identify

singular configurations at the design stage in order

to improve the system performance. For an optimal

robot control these positions should be identified and

avoided from the robot workspace.

A number of papers have studied the singularity

problem for close kinematic chains (Merlet, 2005),

(Sefrioui, 1992), (Park, 1999), (Romdahne, 2002).

The used algorithm for the PARAMIS structure

singularity analysis is based on the deriving the

determinants for the two Jacobian matrices derived

from the inverse and the direct geometric model.

Singularities of Type I. First type of singularities

occurs when the determinant of the Jacobian matrix

B is zero.

Using (1), it yields:

()

()

⎥

⎦

⎤

⎢

⎣

⎡

−−+⋅

−−

−

=

2

12

2

2

12

2

12

qqdb

qqd

qq

)Bdet(

(6)

If det(B)=0, physically, the parallel robot looses

one or more degrees of freedom.

Case 1

.

21

qq

=

- The mechanisms is locked.

The situation corresponds to the positioning on the

horizontal plane of the rod of length d (the first

extreme position).

Solution

. Constructively, the mechanical

structure of the robot will impose

21

qq <

Case 2

.

(

)

12

2

12

2

qqdqqd −=≡−=

- The

mechanisms is locked.

This situation corresponds to

the positioning on the vertical axis of the rod of

length d (the second extreme position).

Solution. Constructively, the structure of the

robot will not allow displacements so long as the rod

of length d to reach a vertical position.

MODELING AND SIMULATION OF A NEW PARALLEL ROBOT USED IN MINIMALLY INVASIVE SURGERY

197

Case 3.

() ()

0qqd0b0qqdb

2

12

2

2

12

2

>−−>=−−+

is impossible (as they represent lengths of

mechanical components).

Singularities of Type II. Second type of

singularities appears when the determinant of the

Jacobian matrix A is zero.

Using (1), it yields:

()

2

1

h

h

1Adet

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

−=

If det(A)=0, the system gains one or more

degrees of freedom.

Case 1

.

1

hh = it yields a point where the robot

cannot be controlled. In case of the point A will

superpose over point B.

Solution.

The attachment mechanism of surgical

instruments on the robot and the shape of the trocar

will not allow point A to superpose over point B. (In

this situation the instrument or laparoscope will be

situated entirely in the patient).

Case 2

. 0h

1

= , correponds to the situation when

the laparoscope is positioned completely out of the

surgical field, with

BE ≡ situation which will be

impossible to attain with the robot, as the insertion

and removel of the laparoscope is done manually by

the surgeon.

The Third Type of Singularities so called

“architectural singularities” takes place when both

Jacobian determinants are zero.

Superposing the cases when the two

determinants are equal with zero, it can be easily

seen that in none of the above situations the

determinants cannot be null in the same time. In

conclusion, from the constructive point of view, for

the functioning conditions imposed, there are no

singularity points of type III.

These types of singularities can be easily

avoided in the design stage.

Based on the fact that the only singularity cases

appear in areas where the positions that the robot

cannot attain it can be concluded that, in the working

space of the robot, there are no points where the

robot cannot be controlled.

4 WORKSPACE MODELING

For the geometrical determination of the working

space of point E (the laparoscope extremity where

the camera is placed) the first step is the

determination of the working space of point A and

its projection, keeping in mind that for on the

segment ABE the point B is fixed in space and AE

has a constant length.

The working space of point A can be easily

determined, by determining the cross-sections within

the working space in a parallel plane with OXY

which for the limits imposed for

1

q and

2

q will

have the same shape for any position of the Z axis.

Figure 3: Motion of point A in a parallel plane with OXY

(horizontal).

The hatched area in Figure 3, represents all the

possible coordinates that point A can attain in a

horizontal plane. Generating the three-dimensional

working space it results the shape presented in

Figure 4.

Figure 4: The workspace of point A.

For the workspace generation for point E has to

be considered that the laparoscope (or any other

surgical instrument) has a constant length and will

always pass through a fixed point in space. The

working space of point E by generating two

intermediate working spaces whose intersection will

represent the effective working space. The first

intermediate working space is generated by

projecting the point A from sections parallel with

OXY plane. The second one is generated from

sections of the working space of point A

perpendicular on the plane OXY.

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The intersection of the two intermediary

volumes will result in the working space of point E

presented in Figure 5.

Figure 5: The workspace of point E.

5 SIMULATION PROGRAM FOR

PARAMIS PARALLEL ROBOT

A complex simulation program was developed in

order to study the geometric, kinematic and dynamic

characteristics of parallel robots with different

degrees of freedom (Pisla, 2001), (Pisla, 2005).

This simulation system consists of the following

modules:

-the geometrical module (GM) defines the robot

geometric structure;

-the kinematic module (KM) defines the parallel

kinematic structure. The KM consists of: the

algorithms for the kinematics, the algorithms for

workspace generation and for singularities

identification;

-the modeler (MM) represents the combination

of the geometrical representations, kinematic

descriptions and the adequate disposition of different

objects;

-the simulator (SM) has the main task to

compute the current state of the parallel robot with

respect to certain instructions such as: the robot

source program or signals which are generated by

sensors;

-the graphical module (GPM) is responsible with

the simulated robot transformations and screen

graphical visualization.

The simulator is interactively achieved such as

the user could influence the simulation parameters

and could be informed about the possible errors

during the simulation process.

The simulator determinates the next robot state,

independent of the input mode. If an error appears,

the user is informed through an error message with

its type and elimination way. The simulator is

interactively achieved such as the user could

influence the simulation parameters and could be

informed about the possible errors during the

simulation process.

The data exchange between simulation system

modules is achieved through data files, which allow

future module integration in the existing system and

makes easy the data exchange with another off-line

programming systems.

For the graphical modeling of the parallel

structures it was used Solid Edge

©

, one of the most

advanced software for computer aided design,

available on the market (www.solidedge.com). This

program was selected especially for its outstanding

performances in terms of stability and user-friendly

interface, and even more for its total compatibility

with Visual Basic.Within the simulation system the

virtual graphical model of parallel structures has

been created.

The geometric parameters of the parallel

structure can be modified within the 3D modeling

software (Solid Edge Assembly) influencing the

simulation environment. The assembly relations

between parts, between subassemblies or between

parts and subassemblies can be also modified (Pisla,

2001), (Pisla, 2004).

The program has the possibility to select the

parallel structure from a list in accordance with the

class of the mechanism and its degree of freedom.

The parallel structure parameterization enables

the possibility to develop a study regarding the

geometric optimization and the robot workspace

shape.

The results obtained are useful for the designers

not only to understand the distribution of

characteristics of the workspaces for various

geometrical parameters of parallel structures, but

also to optimize the parallel robots.

The presented simulation system enables the

motion visualization, it is valid for any structure of

parallel robot enabling to introduce the kinematic

model over the virtual robot the single foreseen limit

being the hardware computing capacity. The

introduction of extra conditions related to any

element, joint or overall behaviour of the robot is

possible with a small number of actions.

These facilities of the simulation software enable

the possibility to develop a complex study about the

kinematics and dynamics in order to optimize the

parallel structure.

MODELING AND SIMULATION OF A NEW PARALLEL ROBOT USED IN MINIMALLY INVASIVE SURGERY

199

Figure 6: Simulation of the PARAMIS parallel structure.

In Figure 6 is presented the graphical interface for

graphical modeling for different parallel structures.

The kinematic algorithms have been implemented in

the kinematical module (Kinematics). In the

simulation is included the parallel robot with the

instrument and the virtual human body.

Within the simulation system (Figure 6) the

virtual graphical model was created. The 3D

functional model of the parallel structure allows the

designer to understand better its form and its

functionality. Using the Solid Edge Assembly

module it is possible to impose the assembling

conditions between the components including the

mounting possibilities and the tolerance for and

between the parts.

Figure 7: The PARAMIS robotic system.

The simulations were performed using the

parallel robot presented in figure 7 which

manipulates the laparoscope in the virtual human

model to ensure also the fixed point in the working

space of the robot (point B from Figure 1).

The virtual model was used for the validation of

the geometrical model. For that, the robot was

placed in an arbitrary position and all its parameters

measured, including the point B (Figure 1). The

second step was the computation of the coordinates

of the point E in parallel with their measurement on

the virtual model (Figure 8).

The calculated results based on the equations

matched 100% with the ones given by the virtual

model.

Figure 8: Validation of the geometric model.

The second goal concerning the virtual model

was its use for the simulation of the robotic structure

in the medical environment created. In this stage it

was important to achieve proper motions for

different commands in the active joints. Solid Edge

allows a the definition of motion trajectories in

terms of displacements, speeds and accelerations as

points, lines or equations implemented in the active

joints, as shown in figure 9.

Figure 9: Input of motion trajectory in a module.

The simulation enabled the validation of the

structure from the points of view of both engineers

and surgeons and opened the way for the next step in

the PARAMIS robotic design evolution, the

construction of an experimental model.

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6 CONCLUSIONS

Modeling and simulation are important and essential

stages in the engineering design and problem solving

process because it allows to prevent the risks and to

lower the costs that appear with the design,

construction and testing stage of a new robot. Since

parallel mechanisms have a complex structure, using

the proposed approached of modeling and

simulation will lead to an increased efficiency in

developing new structures.

In the paper the modelling and simulation of the

PARAMIS new parallel robot is presented. The

simulations results obtained with the developed

simulation system for parallel robots allow a

structure verification before a parallel robot is built.

The developed simulation system for the parallel

robots offer multiple advantages: modularity of the

simulation system for parallel robots; friendly

graphical user interface of the simulation system;

possibility for parallel structure parameterization;

possibility to generalize some parallel structures;

Identification of singularities; possibility to identify

the optimal working zone; workspace generation:

the structures verification before a parallel robot is

built.

In this case, the contribution is the use a virtual

reality definition system to create the virtual objects

(bodies) that includes shape, dimensions, mass and

center of mass, surface characteristics and the

deviations from these characteristics may be also

considered. Between the virtual objects are defined

the appropriate structure joints. The type of joint,

their constructive dimensions, together with the

actuating define the motion restrictions that are

encapsulated within the subassemblies.

Over the predefined virtual structure is applied

the kinematic model using a programming interface

in Visual Basic ensuring the PTP or the path control

motion.

The presented simulation system enables the

motion visualization, enabling to introduce the

kinematic model over the virtual robot the single

foreseen limit being the hardware computing

capacity. The introduction of extra conditions related

to any element, joint or overall behavior of the robot

is possible with a small number of actions. The up-

to-date results validated the solution creating the

premises for the next step, the construction of the

experimental model for the PARAMIS robot.

ACKNOWLEDGEMENTS

This research was financed from the research grants

awarded by the Romanian Ministry of Education and

Research and the “Institutional Academic

Cooperation Research Grant” between the Technical

University of Braunschweig, Germany and the

Technical University of Cluj-Napoca, Romania,

awarded by Alexander von Humboldt foundation.

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