artikel haptic simulink

7/29/2019 Artikel Haptic Simulink

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A Haptic Interface Using MATLAB/Simulink

Magnus G. Eriksson and Jan Wikander

Mechatronics Lab, Department of Machine DesignThe Royal Institute of Technology

Stockholm, Sweden

[email protected], [email protected]

Abstract The concept of a new haptic system based on a low level interface for

MATLAB/Simulink is presented. The interface enables users to connect

dismantled, re-constructed or self-developed haptic devices without any

commercial drivers or APIs for verification and further development. A virtual

environment is easily created and connected to the Simulink models, whichrepresent haptic algorithms and real time communication. The paradigm shift to

start using MATLAB/Simulink with model based programming instead of the

commonly used C++ programming language for haptic applications will attract

new users. Users from other scientific areas, e.g. mechatronics, can bring new

knowledge into the haptic topic and solve control-engineering issues that will

give the users even more realistic haptic feedback in future applications.

Keywords Haptic system, real time programming, MATLAB/Simulink, virtual

reality, force algorithm, control engineering

1. Introduction

The work presented in this paper is done in the context of developing haptic and

visual simulation of surgical procedures [1]. Haptic is the sense of touching

something and get tactile and kinestic force feedback. A haptic device is connected to

a virtual world for enabling touch of 3D modeled objects. If there is a collision in the

virtual world between a tool and the object, the device provides force feedback to the

user.

The conventional way of creating these haptic systems is to use a commercial haptic

device including drivers and Application Programming Interfaces (APIs) in

conjunction with available haptic libraries (HLibs). The devices cannot be used

without the licensed drivers and APIs, which limits the freedom of developing haptic

systems and applications.

The HLibs used today put high demands on the user skills in the C++ programming

language. The HLibs are built up with C++ and the implementation of self-developed

haptic applications must be done in this language.

There are several HLibs presented on the haptic market. The CHAI libraries [2], the

eTouch API [3] and the H3DAPI [4] are three C++ based open source alternatives.

The benefits of using an open source library is firmly the enabling of access to low

level details; such as adding an arbitrary haptic device or control your own haptic


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force effects. OpenHaptics [5] and the Reachin API [6] are examples of commercial

available HLibs.

The most haptic devices are constructed to have 3-6 Degrees Of Freedom (DOF)

input sensor signals and 3-6 DOF output actuator signals. Some commonly used

devices are the Sensables PHANTOM series [7], the Novint Falcon [8], the

Delta/Omega devices from Force Dimension [9] and the Freedom6S device fromMPB Technologies [10]. Each one of them is introduced with their own commercial

licensed drivers.

In this paper we present a new haptic system set up; where a Sensable PHANTOM

Omni haptic device is dismantled and in low level directly connected to

MATLAB/Simulink [11]. Simulink enables model based programming instead of

using the C++ programming language. This paradigm shift in haptics will admit new

users and extend the haptic topic into new scientific areas. Where the users can be

more into mathematics and control system engineering than programming experts.

This will enable further development of the haptic topic, since there are still many

control-engineering issues to be solved to give realistic haptic feedback to the user.The area of using MATLAB for haptic applications is quite young and unexplored;

hence, it is difficult to find published information about other systems elsewhere in

literature. However, Handshake VR Inc. [12] has developed a commercial

MATLAB/Simulink interface for the Sensable Omni haptic device. In that case the

OpenHaptics API drivers still need to be used. By using pre-defined haptic Simulink

blocks which directly is connected to the OpenHaptics API they enable higher level of

programming with the application. However, our system differs in the way that the

low level connection to the haptic device conveys use of self-developed control

algorithms and haptic feedback without any required drivers and APIs. All the

kinematics, transformations, collision detection and force feedback is modeled by the

user through real time communication with the sensors and actuators of the device.

Thus, implementation and verification of self modified or constructed haptic devices

is possible in this system. Systems based on haptic drivers and APIs do not have this

flexibility and easy compatibility.

This system also gives an extra input for education and greater understanding in

haptics for beginners. Often when conventional graphical-based haptic development

APIs and environments are used the subjects have problem to separate visualization

and haptics. They create a 3D object and add a haptic surface to it. In this system all

the haptic algorithm information is built up in Simulink separately from the graphics.

The 3D rendering is an extra shell added in the end for nice visualization of the haptic

collision and movements of the haptic devices. To create it in this way increases theknowledge of the separation between haptic and graphic rendering.

The requirements of a haptic system that are fulfilled in this work are a minimum

updating frequency of the haptic loop at 1000 Hz and real time graphic rendering of

the 3D object to be visualized at 30 Hz [13].

The paper is organized as follows. Section 2 describes the components used for

creating the haptic system in MATLAB. Section 3 gives an overview of haptic

modeling and implementation. In section 4 test results and verification of a specific

application is presented. Finally, section 5 gives some conclusions and a glance into

possible future work.


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2. System Components

In this section the components used for the running a haptic application on MATLAB

are presented. Each component is relevant to fulfill the development of a complete

system. The main components are: the development platform, the real-time control

tool, the graphic rendering interface and the haptic device.

2.1 MATLAB / Simulink / Real Time Workshop

The mathematical-based programming language MATLAB is used as a base for

development of the haptic interface. MATLAB is an easy to use program for

development, analysis and visualization of algorithms and numerical computations.

Simulink is a block library that runs on MATLAB. It provides a model based

programming language for simulation and analysis. The programming takes place in a

graphical environment where the algorithms can be simulated and tested for relevant

data. Simulink is a useful tool to avoid experimental set up and fast simulated results.

The Real Time Workshop [14] is a plug-in to Simulink, which is building code from

the blocks during a simulation. The code can then be used for real time applications in

conjunction with the algorithms created by blocks in Simulink.

In this research, all the developed algorithms are implemented in Simulink and

compiled with the Real Time Workshop.

2.2 dSPACE

dSPACE [15] is a real-time tool for control prototyping and verification ofmechatronic systems. The compiled code from the Real Time Workshop is

downloaded to the dSPACE platform, where it will be driven in real time on the

dSPACE CPU. The basic function of dSPACE is to read sensor signals from some

external device, manage the signals with the downloaded algorithms, and send

relevant signals back to the actuators of the device.

Here the signals of the encoders and potentiometers from the haptic device are read

and PWM-signals are sent to the motors.

2.3 Virtual Reality Toolbox

The Virtual Reality (VR) Toolbox [16] for MATLAB is used for 3D rendering of

simulated objects. It can either be implemented as a Simulink block or in low level

MATLAB programming.

The virtual environment is built up with the VRML-editor V-Realm Builder [17].

Each geometrical object is defined as a node in the VRML scene graph. Each node

contains fields, which can be reached from MATLAB. E.g. a sphere is a node that

contains the field translation. To this field a signal can be sent in from

MATLAB/Simulink to perform graphic rendering of real time translation of the

sphere, that is how we did it in this project. The VR Toolbox is usually used to

demonstrate simulated signals from Simulink as 3D objects. But in our case, real time

signals are used instead of simulated ones. Therefore dSPACE MLIB-functions areused to take real time signals from the dSPACE platform to MATLAB workspace. A


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script in the MATLAB workspace transfers the signals with the VR Toolbox to the

virtual environment. The Blaxxun VRML-viewer [18] enables 3D visualization of the

rendered objects. The user can explore the virtual environment with several functions

of the VRML-viewer; such as zoom, rotation and translation.

2.4 Sensable PHANTOM Omni Haptic Device

The Sensable PHANTOM Omni haptic device is used as implementation for haptic

feedback to the user when manipulating virtual objects. Commonly the OpenHaptics

drivers needs for the device to work with haptic applications. The drivers are not used

in this project, just the hardware. The haptic device is dismantled and the sensors and

actuators are low level connected to dSPACE. There are six input signals (3 encoders

+ 3 potentiometers) and three output signals (3 dc motors). Sensor and actuator

signals are connected to the dSPACE system that also controls timing in the system.

The device can be seen as an inverted robot arm, where the algorithm reads the

position and calculates a force feedback to the user if collision in the virtualenvironment occurs. The mechanical construction of the arm consists of a three linked

robot arm, three dc motors that strengthen wires between the joints and six sensors to

calculate the position and orientation of the end effector (x, y, z, yaw, pitch and roll).

There are also two buttons on the device and a pre-defined position location that

enables calibration. Figure 1 is showing the dismantled PHANTOM Omni haptic

device.

Figure 1. The dismantled PHANTOM Omni haptic device.

2.5 Drivers

Since the haptic device is dismantled; new drivers are created for easy

implementation. Motor drivers are used to convert the PWM-signals from dSPACE

when collision to relevant motor voltage. To enable the whole working range of the

motor 18V supply is used, which gives a feeling of high stiffness in the haptic

feedback.

Other drivers are also created for indication of the buttons and the calibration position

location. These drivers are switches that give 5V/0V when a button is pushed/not

pushed. The high or low values give 1/0 to the slave bit in channels on the dSPACEplatform.


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3. System Overview

The system overview is presented in figure 2. The haptic interface of using

MATLAB/Simulink is shortly described as follows. A PHANTOM Omni haptic

device is dismantled and the sensors and actuators are low level connected to

dSPACE. The signals are transferred from dSPACE to MATLAB/Simulink (runningon a PC) by MLIB-functions. A virtual reality scene is built up in the MATLAB VR

Toolbox. The procedure of the algorithm is as follows (inertia is assumed to be

neglected):

Read the encoders and use direct kinematics position of the end effector.Check collision detection.If no collision: No signals to the motors.If collision: Calculate a force and transform it to motor torques. Send PWM-signals

from dSPACE to the motors based on the torques. A PI-controller is used to control

the motor current.

Graphic rendering of the tool object and a virtual scene for interaction.

Figure 2. System overview of the MATLAB/Simulink haptic interface.

The following subsections are in detail describing the systems functionality.

VRML Viewer

VR Toolbox

Matlab Script

Simulink Models

Real Time Workshop

dSPACE CPU

Haptic Device

Motor drivers

Virtual environment

Sphere translation

Position end effectorwith MLIB

Compile

Download code

3 PWM-signals

3 Motor voltages

3 Encodersignals

3 Potentiometersignals

MATLAB

1000 Hz

30 Hz


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3.1 Kinematic Model

A direct kinematic model has been developed for the PHANTOM Omni haptic

device. The six sensor signals (3 encoders + 3 potentiometers) can be reached from

the dSPACE CPU and the position and orientation of the end effector (x, y, z, yaw,

pitch and roll) can be calculated. But for the collision detection and haptic algorithmthe position of the end effector is the only parameter of interest. Therefore only the

three encoder signals are used in the kinematic model to calculate the correct position.

For the graphic rendering it can be useful with all the six sensors to enable depicting

of the end effectors rotation.

The well known Denawit-Hartenberg [19] convention is adopted to define each link

and frame of the open chain manipulator. The sensor signals and lengths of the links

are the necessary joint and rigid body variables for an unambiguous solution. See

figure 3 for a sketch of the links, joints and variables for the PHANTOM Omni.

Figure 3. A sketch of the links, joints and variables for the PHANTOM Omni.

All the joints are revolute; hence 1, 2 and 3 will be the controlling variables in thedirect kinematic model. The base frame is O0 and the end effector frame is Oe. Theestablished Denawit-Hartenberg link parameters are specified in table 1.

Link (Li) Frame (Oi) ai i di iL0 O0 - - - -

L1 O1 0 /2 0 1L2 O2 a2 0 0 2L3 O3 a3 0 0 3

Table 1. The established Denawit-Hartenberg link parameters for the PHANTOM Omni.

a2

a3

1

2

3z0

z1

z2

z3

y1

y2

y3

x0,x1

x2

x3

O0,O1O2

O3=Oe


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On the basis of the parameters in table 1, the homogenous transformation matrix to go

from one frame to another can be described as follows. )(1 ii

iA is the matrix, i is the

variable and i is frame 0..n.

=

1000

cossin0

sinsincoscoscossin

cossinsincossincos

)(1

iii

iiiiiii

iiiiiii

i

i

id

a

a

A

Eq. 1

For the PHANTOM Omni haptic device n=3 and gives the following transformation

matrices between all frames.

=

1000

0010

0cos0sin

0sin0cos

)(11

11

101

A Eq. 2

=

1000

0100

sin0cossin

cos0sincos

)(2222

2222

2

1

2

a

a

A Eq. 3

=

1000

0100

sin0cossincos0sincos

)(3333

3333

3

2

3

aa

A Eq. 4

Based on these matrices the homogenous transformation matrix 0eT is computed,

which yields the position and orientation of the end effector with respect to the base

frame 0. (Frame 3 is equal to the frame of the end effector).

++++

+

+

=

===

1000

0

)()()(

2232323332323232

212321332131321321321321

212213332131231321321321

3

2

32

1

21

0

1

0

3

0

sascascaccsssccs

csasssacssaccsssssssscss

ccascsacccassccsccssccccAAATTe

Eq. 5

Where c1 indicates cos(1), s2 indicates sin(2) and so on. In the derivedtransformation matrix the three first rows of the last column give the global position

of the end effector.


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++

+

+

=

22323233

21232133213

21221333213

__sinsincossincos

cossinsinsinsincossinsin

coscossincossincoscoscos

aaa

aaa

aaa

z

y

x

effectorendpos

Eq. 6

The expression of the end effectors position is built up in Simulink by connectingblocks and signals to create an algorithm of the kinematics.

3.2 Collision Detection Algorithm

The pre-defined workspace of the virtual environment gives virtual boundaries that

limit the free space movements. In our case, the workspace is created as a bounding

box showed in figure 4.

The position of the end effector is calculated by the kinematic algorithm and thelocations of the virtual walls are pre-defined. By checking the xyz-coordinates of the

end effector in relation to the boundaries collision detection is performed in real time

on the dSPACE CPU. The collision detection algorithm is built up with blocks in

Simulink as presented in figure 5.

ymin

zmax

xmax

ymax

zmin

xmin

z

x

y

posend_effector

Figure 4. Workspace in the virtual environment is pre-defined as a bounding box.


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Figure 5. The collision detection algorithm for xyz-coordinates created in Simulink.

3.3 Haptic Feedback

If the collision detection algorithm finds collision between the sphere, which

illustrates the depicted position and movements of the end effector, and the virtual

walls a haptic feedback will be sent to the user. The force feedback gives the user a

sense of touching the virtual walls and the sphere can be dragged along theboundaries.

The basic idea with the haptic algorithm is based on the well known proxy-probe

method. The probe position is equal to the global position of the end effector

independent if collision or not. The proxy position is the position on the boundary

where collision occurs. The force algorithm is a modified spring-damper model

edcedkF += , where the spring constant, k, and the damper constant, c, arearbitrary chosen. d is the distance between the proxy and the probe and e is thenormalized gradient to the collided surface. See figure 6.

Figure 6. The haptic algorithm when collision occurs in the virtual environment.

F

d

e Probe

Proxy

Free Workspace

Boundary


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The motivation of using the spring-damper model as a relevant haptic algorithm is as

follows. Assume that the probe and the proxy are two dynamical masses that moves in

relation to each other connected by a spring and a damper. The derivation and

motivation is based on the approximations proved in figure 7.

Figure 7. Approximations used for derivation of using the spring-damper model as a haptic algorithm.

Based on the approximations from figure 7 the following derivation shows that

spring-damper model gives a relevant haptic feedback for the probe-proxy case.

Newtons second law gives: =

xmFx

Eq. 7xmFgmxcxk probeexternalprobe =++ Eq. 8

The probe is assumed to be weightless by motivation from above = 0probem

=+ 0externalFxcxk Eq. 9

xcxkFexternal += Q.E.D.

mproxy

mprobe

Approximate the proxy witha wall that not moves.

mprobe

The probe can be assumed tobe weightless; since if noexternal force (no collision):Equilibrium and probe=proxy atthe wall or in free workspace.

Probe=Proxy

If there is collision detected: Anexternal force is applied basedon the spring-damper model.

mprobe

Fexternal

Create a free body diagram inequilibrium of the probe object.

x=the distance the probe hasbeen moved from the proxy (wall)

by the external force.gmprobe

xk xc

externalF

x


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3.4 Motor Torques

The force that occurs if collision is detected must be transformed to corresponding

motor torques for the three motors. Inertia, and hence dynamic impacts, is assumed to

be neglected; therefore will not the motor torques be dependent of velocity and

acceleration. The mechanical construction of the PHANTOM Omni gives that two ofthe motors rotate around the global x-axis and one motor rotates around the global z-

axis. See figure 8.

Figure 8. Relevant parameters for the torque algorithm.

The torque algorithm is described in relation to the information given in figure 8. The

three known positions from the origin 1p , 2p and endp give the corresponding vector

directions of the links 1L , 2L and 3L . The three dimensional force vector is

determined from the haptic algorithm and located at the position of the end effector.

The algorithm gives the torques 1T , 2T and 3T in three dimensions for each motor, but

T1z, T2x and T3x are the only used components.

011= pL Eq. 10

122 ppL = Eq. 11

23 ppL end = Eq. 12

( ) zTkjiFLLLT 13211 ......... +=++= Eq. 13( ) xTkjiFLLT 2322 ......... +=+= Eq. 14

xTkjiFLT 333 ......... +== Eq. 15

F

1L

2L

3L

1p

2p

endp

0

zT1

xT2

xT3 x

y

z


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3.5 PWM-signals

A PWM-signal must be sent to control a motor from the dSPACE CPU. Hence, the

above mentioned motor torques is changed to currents based on gear ratio and motor

type. The currents (one for each motor) are normalized to relevant PWM-signals (0-

1). The PWM signals are sent to the motors that strengthen the wires of the hapticdevice and give the user a feeling of force feedback when collision is detected in the

virtual environment.

3.6 PI-control of the Current

An error is established by comparing the measured actual motor currents and the

calculated motor currents. A PI-controller is implemented to reduce the errors of the

algorithm that calculates the motor currents. The integration part of the controller is

removing the static error and summing the current difference every time a PWM-

signal is sent to the motors. Hence, after a while the errors are reduced. The P-factor

is tested and verified for a specific constant value. The control signal of the current is

sent back to the motor. See figure 9.

Figure 9. Simulink model of the PI-controller for one motor.

The real current in the motor is measured by using an operational amplifier (Opamp).

A resistor is mounted in serial connection with the motor, and the Opamp is

measuring the voltage drop over the resistor when activating the motor. The voltage

drop is taken in to the dSPACE platform. The motor current is received by dividing

the voltage drop with the resistor value.

3.7 Graphic Rendering

To do the haptic feedback more understandable a 3D virtual environment is built up

and visualized. The collision detection is based on max/min- boundaries along the

xyz-axes, which easily is rendered as a virtual cube having the walls at the given

boundary values. A small sphere is graphic rendered to illustrate the movements of

the end effector of the haptic device. The sphere follows the movements of the end

effector in real time at 30 Hz, which enables visualization of the collision with thevirtual walls. There are no deformations of the collided walls; hence just the


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translation of the sphere needs to be updated in the graphics loop since the other

objects are static unchanged. The virtual environment presented in figure 10 is

rendered using the MATLAB VR Toolbox.

Figure 10. The virtual environment including the walls and the sphere.

The work presented in sub-sections 3.1-3.6 is implemented and built up in Simulink

and by using the real time workshop it is compiled and downloaded to the dSPACE

processor. All the collision detection and haptic feedback is performed on the

dSPACE platform at 20 kHz in real time. To extend the solution with 3D visualization

a virtual environment is created and connected to the system through the MATLAB

VR Toolbox, which is running on the PC. The position of the end effector is in real

time transferred with MLIB functions from the dSPACE CPU to the PC forvisualization. The translation of the small sphere in the virtual environment directly

follows the position of the end effector in real time.

4. Test Results and Verification

In this paper some early test results and verification of the haptic algorithm is

presented. The test is based on the application described above with the small sphere

that collides with the walls in the virtual environment.

4.1 Product Specification

A Pentium D 2.8 GHz with 2.0 GB RAM desktop PC was used for this application.

The graphic card is an Intel 82945G Express. A dismantled Sensable PHANTOM

Omni is used as a haptic device. No drivers or API components are required since

direct connection to low-level sensors and dc-motors. The dSPACE CPU platform is

used for real time controlling and routing of signals. MATLAB 7.2 and Simulink 6.4

were used with the Real Time Workshop. The MATLAB Virtual Reality Toolbox 4.0

was used for graphic rendering.


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4.2 The Application

A 3D rendered small sphere is following the movements of the end effector and

collision detection is performed against pre-defined virtual walls. The virtual

environment is created in the V-Realm Builder VRML-editor. A MATLAB m-file

consisting of all variables must be updated before compiling the Simulink model anddownload it to the dSPACE platform for every new application.

4.3 Test Procedure and Results

The developed haptic platform described above has been tested and verified for the

basic application of the sphere colliding with virtual walls along the global xyz-axes.

A user is holding the haptic device and manipulating the virtual objects. A haptic

feedback is sent to the device when the operator moves the sphere so it collides with

the walls, which gives the user a sense of kinestic and tactile feedback. Test data has

been logged from a specific test, where the user is dragging the sphere against one

wall and relevant data are saved. The logged data are the position of the probe relative

to the wall, the calculated force, the torques and the PWM-signals for the three

motors. See figure 11-14. The globally defined boundary conditions of the walls and

the pre-defined spring and damper constants of the force algorithm were also used for

the analysis of the system. The test procedure took place for one certain case of pre-

defined parameters and logged data. The stiffness constant in the haptic algorithm was

set to a high value to give the user a sense of collision between two rigid materials. As

mentioned above the virtual scene was 3D rendered for visual feedback.

Figure 11. Position of the sphere relative to

the wall.

Figure 13. The modeled torques for the three

motors.

Figure 12. The magnitude of the calculated

force.

Figure 14. The PWM-signals for the three

motors.


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The result from figure 11 indicates that the position of the sphere follows the position

of the wall very well, but follows the user movements into the material when applying

higher force. The surface is modeled to be quite stiff; therefore the probe is not deeper

in to the material which had been the case for a surface modeled with a lower spring

constant. From figure 12 it can be seen that the magnitude of the calculated force

directly follows the penetration distance of the surface: this is as expected. The forceis transformed to corresponding motor torques for the three motors. Figure 13 depicts

that the modeled torques (T1z, T2x and T3x) are varying as the user is dragging and

pushing the sphere along the surface of the wall. T1z is zero because no collision in the

y-direction. Any other conclusions are hard to draw. The PWM-signal sent from

dSPACE to each motor directly follows the torque, as illustrated in figure 14. It is

hereby verified that the force algorithm and the MATLAB/Simulink haptic system

works properly for this application.

There have also been blind tests with subjects that never tried haptics before; and they

recognize that you really get a realistic perception of touching the virtual objects.

5. Conclusion and Future Work

In this work a haptic interface for MATLAB/Simulink has been developed. A

PHANTOM Omni haptic device is dismantled and the sensors and actuators are low

level connected to a dSPACE platform for real time communication. The haptic

algorithm including kinematics, collision detection, force calculation, transformations

to motor torques and implementation of a PI controller is modelled in Simulink. The

developed algorithms built up of Simulink blocks are compiled with the Real Time

Workshop. A virtual reality scene is built up in the MATLAB VR Toolbox for realtime 3D visualization.

There are some major benefits to use this system:

MATLAB/Simulink enables model based programming instead of using theC++ programming language.

The low level connection to the haptic device conveys use of self-developedhaptic algorithms without any required drivers and APIs.

Easy implementation and verification of self modified or constructed hapticdevices is possible in this system.

In this system all the haptic algorithm information is built up in Simulink

separately from the graphics. To create it in this way increases the knowledgeof the separation between haptic and graphic rendering.

The developed haptic platform has been tested and verified for the basic application

of a 3D rendered small sphere that follows the movements of the end effector and

collision detection is performed against pre-defined virtual walls. By good results

from the tests it was hereby verified that the force algorithm and the

MATLAB/Simulink haptic system works properly for this application.

Possible future work could include some of the following suggestions:

To create other applications will include more advanced collision detectionalgorithms for arbitrary modeled 3D objects.


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U_drop Voltage drop [V]

x Spring length [m]x Change of spring length [m/s]

x Acceleration in x-direction [m/s2]

x,y,z Global coordinate system

xi,yi,zi Local coordinate system at Oi

References[1] Eriksson M.G., Haptic and Visual Simulation of a Material Cutting Process,

Licentiate Thesis, KTH Stockholm Sweden; 2006.

[2] CHAI 3D, http://www.chai3d.org.[3] eTouch API, http://www.ethouch3d.org.[4] H3DAPI, http://www.h3dapi.org.[5] OpenHaptics, http://www.sensable.com/products-openhaptics-toolkit.htm.[6] Reachin API, http://www.reachin.se.

[7] Sensable Inc. PHANTOM, http://www.sensable.com/products-haptic-devices.htm[8] Novin Falcon, http://home.novint.com/products/novint_falcon.php.[9] Force Dimension, http://www.forcedimension.com/fd/avs/home.

[10] MPB Technologies, http://www.mpb-technologies.ca/mpbt/haptics.[11] MATLAB/Simulink, http://www.mathworks.com/.

[12] Handshake VR Inc., http://www.handshakevr.com/.[13] Mark W.R., Randolph S.C., Finch M., Verth J., Adding force feedback to graphic

systems: issues and solutions, 23rd

Conference on computer graphics; 1996, pp. 447-52.[14] Real Time Workshop, http://www.mathworks.com/products/rtw/.[15] dSPACE, http://www.dspaceinc.com/ww/en/inc/home.cfm.[16] The Virtual Reality Toolbox, http://www.mathworks.com/products/virtualreality/.[17] V-Realm Builder, http://www.ligos.com/.[18] Blaxxun VRML-viewer, http://www.blaxxun.com/.[19] Sciavicco L., Siciliano B., Modeling and control of robot manipulators, 2nd edition,

Springer; 1999, pp. 39-77.

[20] Flemmer H., Control design and performance analysis of force reflective teleoperators a passivity based approach, Doctoral thesis, KTH Stockholm Sweden; 2004.

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