Simulation of A Differential-Drive Wheeled Mobile Lego Robot Mindstorms NXT.
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!
Huaqiao University, Ministry of Education Engineering Research Center for Brittle Materials Machining;
Xiamen, China, 361021;
!
University of Applied Sciences of Southern Switzerland, Dynamat Laboratory; Via Trevano P.o. Box 12,
Canobbio, 6952, Switzerland;
Harbin Institute of Technology, School of Materials Science and Technology; P.O. Box 435, Harbin,
China, 150001;
Yurga Institute of Technology of National Research Tomsk Polytechnic University; Leningradskaya
Street, 26, Yurga, Russian Federation, 652055;
Slovak University of Technology in Bratislava, Faculty of Materials Science and Technology in Trnava;
Bottova 25, Trnava, 917 24, Slovakia;
Gheorghe Asachi Technical University of IaHi, Department of Machine Manufacturing Technology; D.
Mangeron Blvd, 39A, IaHi, 700050, Romania;
Clermont Université, Pascal Institute; UMR 6602 CNRS/UBP/IFMA, BP10448, Clermont'Ferrand, F'
63000, France;
!
Technical University of Kosice, Department of Production Systems and Robotics, Faculty of Mechanical
Engineering; Letná 9, Kosice, 042 00, Slovakia;
"
#
!
Université de Toulouse, INPT ' Ecole Nationale d’Ingénieurs de Tarbes (ENIT), LGP (Laboratoire Génie
de Production); 47 Avenue d’Azereix, BP1629, Tarbes Cedex, 65016, France;
"
$ %
Technical University of Kosice, Faculty of Mechanical Engineering, Department of Production Systems
and Robotics; Nemcovej 32, Kosice, 042 00, Slovakia;
"
& ' (
Technical University of Košice, Department of Technical Devices Design; Štúrova 31, Prešov, 08001,
Slovakia;
% &
!
University of Glasgow, Department of Mechanical Engineering; Glasgow, United Kingdom, G12 8QQ;
!
!
Malaysian Nuclear Agency Bangi, Materials Technology Group (MTEC), Industrial Technology Division;
Kajang, Malaysia, 43000;
Politehnica University of Bucharest; Splaiul Independentei 313. Sector VI, Bucharest, 060042,
Romania;
#
&
TU Kosice, Faculty of Manufacturing Technologies; Bayerova 1, Presov, 08001, Slovakia;
)
*"
Friedrich'Alexander'Universität Erlangen'Nürnberg, Institute for Factory Automation and Production
Systems; Egerlandstraße 7'9, Germany;
+
(
AGH University of Science and Technology, Department of Robotics and Mechatronics, Faculty of
Mechanical Engineering and Robotics; Al. Mickiewicza 30, Krakow, 30'059, Poland;
,
Universiti Kebangsaan Malaysia, Department of Mechanical and Materials Engineering, Faculty of
Engineering and Built Environment, Centre for Automotive Research, Faculty of Engineering and Built
Environment; Bangi, Malaysia, 43600;
CONTENTS
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Simulation of a Differential'Drive Wheeled Mobile Lego Robot Mindstorms
NXT
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model of a mobile Lego robot Mindstorm NXT. The...
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Applied Mechanics and Materials Vol. 776 (2015) pp 319-324
© (2015) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/AMM.776.319
Submitted: 2015-02-19
Accepted: 2015-04-10
Simulation of A Differential-Drive Wheeled Mobile
Lego Robot Mindstorms NXT
I Wayan Widhiada1,a, Cok. Gd. Indra Partha2,b, Wayan Reza Yuda A.P3,c
1,3
Teknik Mesin, Fakultas Teknik, Universitas Udayana, Indonesia
2
Teknik Elektro, Fakultas Teknik, Universitas Udayana, Indonesia
a
widhiwyn@yahoo.com, bcokindra@ee.unud.ac.id ,c wayan_unnes@yahoo.co.id
Keywords: Differential-drive robot, Lego Mindstorms NXT, Simulation
Abstract. The aim of this paper is to model and simulate kinematics motion using the differential
drive model of a mobile Lego robot Mindstorm NXT. The author’s use integrated two software as a
method to solve the simulation of mobile lego robot mindstorms NXT using Matlab/Simulink and
Solidworks software. These softwares are enable easier 3D model creation for both simulation and
hardware implementation. A fundamental of this work is the use of Matlab/Simulink Toolboxes to
support the simulation and understanding of the various kinematics systems and in particular how
the SimMechanics toolbox is used to interface seamlessly with ordinary Simulink block diagrams to
enable the mechanical elements and its associated control system elements to be investigated in one
common environment. The result of simulation shows the mobile robot movement control based on
decentralized point algorithm to follow the precision x and y references that has been specified. The
design of the mobile robot is validated in simulation results as proof that this design can achieve the
good performance.
Introduction
During the last three decades, the application of robotic has commonly developed in the
world of industry and education. Robotics research in the world of education is very rarely done by
the students, because the robot modeling and control techniques have a high degree of difficulty.
Therefore, the author’s submitted a research paper on " Simulation of a differential-drive wheeled
mobile lego robot mindstorms NXT".
The design of the robot is a difficult enough task with some considerations such as the
geometry of the robot and the complexity of the mechanism [1]. Traditionally, in need of physical
prototypes to test the robot's ability to perform his duties, but it would spend a lot of cost and time.
Therefore, to reduce the cost and time, the simulation technique is used as a first step by a designer
to model the kinematic and dynamic of mobile robot. Simulation has been known as a powerful tool
to support the design, planning and analysis of the dynamic behavior of a robot [2]. Currently,
Matlab / Simulink is a very popular software for control engineers, and often implicitly suggest that
colleges use this software as a tool to design a controller. The students are familiar with Matlab /
Simulink, it obviously would be a significant advantage in program control system. Typically, such
real-time interaction between the system and the computer on which Matlab / Simulink has been
installed require additional expensive hardware and software [3].
The driver for this research study arose from the limitation of students to understand the
robotic course in mechanical engineering of Udayana university. In this paper, the author’s has
focused to shows how to easy to model and simulate kinematics motion using the differential drive
model in the mobile Lego robot Mindstorm NXT, so it would be expected that students who
followed the robot course in a class will be able to make the simulation robot, the robot is able to
make a control technique using the Matlab programming language / Simulink.
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans
Tech Publications, www.ttp.net. (ID: 120.174.198.61-10/07/15,15:51:50)
320
Recent Decisions in Technologies for Sustainable Development
Simulation Technique
Simulation has been identified as a significantstudy tool for robotic systems since the early of the
20th century [4] and now simulation methods area powerful tool supporting the design, planning,
analysis, and decisions in different areas of research and development. The Simulink extension to
Matlab was identified in 1990 [5], permitting users to establish continuous a causal design
graphically without the need of writing code. Now, Simulink has developed in many directions:
adding more blocks, built-in algebraic loop solving, and a physical modeling of toolboxes.
Simscape is a toolbox for physical modelling developed by the Mathworks for interfacing
with Simulink and it has been available since version R2007A of the Matlab suite [6]. It includes a
foundation library, which contains basic components for electrical, hydraulic, mechanical and
thermal systems. There are also more specialized toolboxes for physical modelling that now are
considered as parts of the Simscape product family. A virtue of this modeling software for
mechanical systems is that it provides a single simulation environment for the construction of
reliable mechanical and controller models. These models can be reused by converting them into
compact, efficient C code for embedded controller implementations [7]. SimMechanics also
includes a computer aided design (CAD) to SimMechanics translator that facilities the automatic
creation of SimMechanics models from Solidworks software packages.According to Goncalves, the
realistic simulation of Lego Mindstorms NXT is presented approach does not replace the training
with hardware but an important complement, since it allows to develop robot software without
accessing to the real hardware [8].
The author has shown through the demonstration of simulation that it is suitable for the
fundamental building of mechanical systems. A fundamental of this work is the use of
Matlab/Simulink Toolboxes to support the simulation and understanding of the various dynamics
systems and in particular how the SimMechanics toolbox is used to interface seamlessly with
ordinary Simulink block diagrams to enable the mechanical elements and its associated control
system elements to be investigated in one common environment.
Creating and Modelling Mobile Lego Mindstorms NXT
The design and 3D modelling of a mobile Lego Mindstorms NXT are worked using
Solidworks 2013 as CAD software. This software enables easier 3D model creation for both
simulation and hardware implementation. Mobile robot has two wheels on left and right with
separately driven is called differentially driven mobile robot (DDMR) which is showed in Figure 1.
In general, the determination of a models position, orientation, and visualization of the body
use transformation matrices. However, when confronted with a complex model with the multidegree of freedom mechanism analytic solutions are tedious to determine. The software package
Solidworks and Matlab/SimMechanics provides an easier method to analyse physical models.
Fig. 1(a) and 1(b) show the assembly of mobile Lego Mindstorm NXT parts and the
complete model respectively. SimMechanics tool provides a reserve to deriving equations and
performing them with base blocks. To create a SimMechanics model, the mechanical system should
be break down into the building blocks. Ground block place point is at position [0 0 0] in the World
CS (coordinate system).
Fig. 1(a). Assembly of mobile Lego Mindstorm NXT parts and 1(b) complete model
Applied Mechanics and Materials Vol. 776
321
The body of mobile robot is connected to revolute joint. Joint sensor is connected to revolute
joint to measure its physical properties such as angular position and angular velocity of the revolute
joint. The joint initial condition is used to adjust the initial position of the wheel mobile robot.
Actuator Modelling
The mobile Lego Mindstorms NXT provides two servomotors with built in rotation sensor
and a gear ratio. A Lego Mindstorms NXT servomotor is shown in Fig. 2.
Fig. 2 Lego Mindstorms NXT servomotor and DC motor circuit
Speed of motor in robotic is able to change in accessible parameter of source voltage. Motor
speed control is required to obtain the various rotation methods and trajectory control. Driving
servo dc motor lego robot has two direction, forward and reverse. H-Bridge circuit is required as a
methods to determine the position of mobile robot [9].
The following of armature control DC servomotor with the load will be presented using an
algorithm. Consider the DC servomotor armature, where in the armature current is constant. In this
system transfer function can be written as shown in Fig. 4 as follows:
( )
=
( )
[
Trajectory Line
+
+
]
=
(
+ 1)
(1)
The trajectory planning is necessary to generate the reference inputs to the motion control
system, which ensures that the mobile robot executes the planned trajectories.The minimal set of
requirement for a mobile robot is to be able to run from an initial position to a final assigned
position.
The input of trajectory planning algorithm is the path description, the path constraints, and
the constraints imposed by a robot gripper dynamics, whereas the outputs are the joint trajectories in
terms of a time sequence of the values attained by position, velocity and acceleration.
Position control is used when the robot finger must be moved with or without load along a
prescribed trajectory through the mobile robot workspace. The control system of mobile robot is
merely a collection of joint controllers each of which is presented to a single joint to drive it
individually. The reference signals for these controllers are supplied by a joint trajectory generator
determining the desired joint trajectory from the desired trajectory of the mobile robot.
Kinematics mobile robot
According to Valera, Mobile robot control education provides a motivating subject for the
students due to the practical work that it involves and present different activities based on Lego
NXT developed for teaching Control Engineering. The tasks that the students must do during this
course deal with system identification, dynamic control of the robot’s wheels, kinematic control of
the mobile robot, path generation etc [10].
A differential-drive motor robot has two wheel is located in left side and right side. Robot is
assumed into 2D domain of XY Cartesian coordinates. In analysis of kinematics robot is assumed
drive relatively slowly and wheels are not slippery on the road surface. From the eq. (7) shows the
number of degree of freedom in kinematics control is three coordinates which is ( , , ). These
322
Recent Decisions in Technologies for Sustainable Development
parameters are needed to control as simultaneously to obtain non-holonomic motion. The average of
velocity is shown in the eq. (2) and eq. (3) is the angular velocity of the wheels.
Fig. 3 DDMR in 2D Cartesian coordinates
−
=
+
2
=
(2)
(3)
The parameter of coordinates are provided by eq. (4), and (5) and the position of the mobile robot is
calculated by eq. (6).
=
=
=
(4)
.
(5)
(6)
Commonly, the equation of differential–drive motor robot is obtained in eq. (7). TNH is nonholonomic transformation matrices. The variables of ,
are the radial speed left wheel and right
wheel respectively.
=
(7)
The mathematic model of a differential drive mobile robot is provided in Fig. 4. It is created in
block diagram in Matlab/Simulink. A differential drive mobile robot is controlled in closed loop
system. The speed of servomotor is used to drive the wheels and created using constant input
references. The body of mobile robot is created in block physical model in Matlab/Simmechanics
block.
Fig. 4 Mathematics modeling of Mobile robot with MATLAB/Simulink
Result and Discussion
The physical model of the mobile robot is built using SimMechanics software and the
application SimMechanics has also been verified with identical outputs when compared with
Simulink simulations. The result for mobile robot simulation is shown in Fig. 5, 6 and 7. Fig. 5
Applied Mechanics and Materials Vol. 776
323
shows an example of the mobile robot movement control based on decentralized point algorithm. It
can be appreciated that mobile robot can follow with precision the x and y references that has been
specified. The desired input velocity right wheel and left wheel mobile robot are provided with the
different value parameters, 15 rpm and 10 rpm respectively. Therefore the right wheel rotated
quickly than left wheel and the mobile robot moved rotation shown in Fig. 6. The mobile robot
started a initial position of (0,0) cm, an initial orientation of zero degrees, a final position of mobile
robot in coordinates (30000, 6000) cm and a final orientation of zero degrees. The times depicted in
the figure is to=0 seconds, t1=200 seconds.
Fig, 5 Animation of Mobile robot in
Fig. 6 Result of tracking wheel mobile
of right
wheel mobile robot
2000
1000
0
0
3000
50
100
150
t, s ec onds
the average veloc ity
1000
0
50
t,
100
s ec onds
150
200
of left
wheel mobile robot
2000
1500
1000
500
0
200
2000
0
Veloc ity
2500
v
,s
p
e
e
d
o
fle
f
tw
h
e
e
l(
V
L
)
Veloc ity
3000
robot in coordinate x, y
v
,a
n
g
u
la
rv
e
lo
c
t
y
(
w
)
v
,a
v
e
r
a
g
e
s
p
e
e
d
(
V
r
t
)
v
,s
p
e
e
d
o
fr
ig
h
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h
e
e
l(
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R
)
MATLAB/Simmechanics
0
50
0
50
15
100
150
t, s ec onds
angular veloc ity
200
10
5
0
t,
100
s ec onds
150
200
Fig. 7 The simulation results of differential drive mobile robot
Mobile robot is completed with 2 DC servomotors to drive wheels. Fig. 7 shows the
simulation results of differential drive mobile robot. The right wheel mobile robot speed rotated
from 0 to 3000 rpm and the left wheel mobile robot speed rotated from 0 to 2000 rpm. Therefore
mobile robot moved rotation to right direction because the desired speed input in right wheel is
bigger than speed in the left wheel and the time simulation is stopped at 200 seconds. The average
speed model moved as a linear function and achieved in 2500 rpm at 200 seconds. The maximum
angular speed is achieved in 14.5 rpm at 200 seconds.
Conclusion
The application of simulation techniques is presented to support the students in mechanical
engineering of Udayana university into design, analysis and control of a differential-drive wheeled
mobile robot base on algorithm through integrations both MATLAB and Solidworks. This paper is
to model and simulate kinematics motion using the differential drive model of mobile Lego robot
Mindstorm NXT. The author’s use integrated two software to solve the simulation of mobile lego
robot mindstorms NXT using Matlab/Simulink and Solidworks.
The mobile robot movement has been controlled based on decentralized point algorithm to
follow the precision x and y references that has been specified. The design of the mobile robot is
validated in simulation results as proof that this design can achieve the good performance. The
kinematics control method was extended to control of the trajectory mobile robot.
324
Recent Decisions in Technologies for Sustainable Development
Acknowledge
We are deeply and invaluable gratitude a Department of Research and Community Service (LPPM)
Udayana University for supporting and finding this Fundamental research Grant though Letter of
assignment in the contract of implementation of decentralization research Grant (BOPTN) Fiscal
year 2014 No:104.8/UN14.2/PNL.01.03.00/2014
References
[1] Andrew, T Miller “A Versatile Simulator for Grasp Analysis”PhD thesis,Department of
Computer Science Columbia University, New York, NY 10027.
[2] Zlajpah, L., Robot Simulation for Control Design. Robot Manipulators Trends and
Development.ISBN 978-953-307-073-5, Slovenia
[3] Yoonso, 2011, Control Systems Lab Using a LEGO Mindstorms NXT Motor System, IEEE
transactions on education, vol. 54, no. 3, August 2011
[4] Zlajpah, L. “Simulation in robotics” Mathematics and Computers in Simulation, Slovenia,
Vol.79, no.4.
[5] Moler, C., The growth of MATLAB and The MathWorks over two decades.The
MathWorks.com: News and Notes, Jan. 2010
[6] Matlab and Simulink. MathWorks, June 1, 2014, Available: http://www.mathworks.com
[7] Ledin, J. M., Dickens and Sharp, J. Single Modelling Environment for Constructing HighFidelity Plant and Controller Models, American Institute of Astronautics, 2004.
[8] Goncaves, Jos´e Lima, Paulo Malheiros and Paulo Costa, Realistic simulation of a Lego
Mindstorms NXT based robot, 18th IEEE International Conference on Control Applications Part of
2009 IEEE Multi-conference on Systems and Control Saint Petersburg, Russia, July 8-10, 2009
[9] John Iovine, Robots, androids, and animatrons, McGraw-Hill, 2001
[10] A. Valera†, M. Vallés†, L. Marín†, A. Soriano†, A. Cervera†, A. Giret‡, Application and
evaluation of Lego NXT tool for Mobile Robot Control, 18th IFAC World Congress Milano (Italy)
2011
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!
Huaqiao University, Ministry of Education Engineering Research Center for Brittle Materials Machining;
Xiamen, China, 361021;
!
University of Applied Sciences of Southern Switzerland, Dynamat Laboratory; Via Trevano P.o. Box 12,
Canobbio, 6952, Switzerland;
Harbin Institute of Technology, School of Materials Science and Technology; P.O. Box 435, Harbin,
China, 150001;
Yurga Institute of Technology of National Research Tomsk Polytechnic University; Leningradskaya
Street, 26, Yurga, Russian Federation, 652055;
Slovak University of Technology in Bratislava, Faculty of Materials Science and Technology in Trnava;
Bottova 25, Trnava, 917 24, Slovakia;
Gheorghe Asachi Technical University of IaHi, Department of Machine Manufacturing Technology; D.
Mangeron Blvd, 39A, IaHi, 700050, Romania;
Clermont Université, Pascal Institute; UMR 6602 CNRS/UBP/IFMA, BP10448, Clermont'Ferrand, F'
63000, France;
!
Technical University of Kosice, Department of Production Systems and Robotics, Faculty of Mechanical
Engineering; Letná 9, Kosice, 042 00, Slovakia;
"
#
!
Université de Toulouse, INPT ' Ecole Nationale d’Ingénieurs de Tarbes (ENIT), LGP (Laboratoire Génie
de Production); 47 Avenue d’Azereix, BP1629, Tarbes Cedex, 65016, France;
"
$ %
Technical University of Kosice, Faculty of Mechanical Engineering, Department of Production Systems
and Robotics; Nemcovej 32, Kosice, 042 00, Slovakia;
"
& ' (
Technical University of Košice, Department of Technical Devices Design; Štúrova 31, Prešov, 08001,
Slovakia;
% &
!
University of Glasgow, Department of Mechanical Engineering; Glasgow, United Kingdom, G12 8QQ;
!
!
Malaysian Nuclear Agency Bangi, Materials Technology Group (MTEC), Industrial Technology Division;
Kajang, Malaysia, 43000;
Politehnica University of Bucharest; Splaiul Independentei 313. Sector VI, Bucharest, 060042,
Romania;
#
&
TU Kosice, Faculty of Manufacturing Technologies; Bayerova 1, Presov, 08001, Slovakia;
)
*"
Friedrich'Alexander'Universität Erlangen'Nürnberg, Institute for Factory Automation and Production
Systems; Egerlandstraße 7'9, Germany;
+
(
AGH University of Science and Technology, Department of Robotics and Mechatronics, Faculty of
Mechanical Engineering and Robotics; Al. Mickiewicza 30, Krakow, 30'059, Poland;
,
Universiti Kebangsaan Malaysia, Department of Mechanical and Materials Engineering, Faculty of
Engineering and Built Environment, Centre for Automotive Research, Faculty of Engineering and Built
Environment; Bangi, Malaysia, 43600;
CONTENTS
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The Significant Importance to Measure Road Safety
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Abstract:Although road safety is a huge problem in develop and developing countries, road safety
measures are not implemented seriously yet,...
Accessibility to Location of Activities in Denpasar City, Bali'Indonesia
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Chapter 1: Technologies of Sustainable Development in Civil Engineering, Transportation and Urban
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Determining Passenger Car Equivalent for Motorcycle at Mid'Block of
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Readiness Criteria: Indonesias’ New Initiative to Ensure Sustainable
Development Program
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Conceptual Framework of Bidding Strategy in Order to Improve Construction
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The Conceptual Framework of Design Change Effects in Some Project
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An Identification of Construction Project Overheads for Sustainable Cost
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Abstract:Project overheads are allocated on a percentage basis to project costs and common to
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Simulation of a Differential'Drive Wheeled Mobile Lego Robot Mindstorms
NXT
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Chapter 3: Advanced Decisions in Mechanical Engineering
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of Components
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Abstract:Every manufacturer requires plant maintenance. Knowing that an effective maintenance
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Model of Carbon Dioxide (CO2) Emission from Motorcycle to the
Manufactures, Engine Displacement, Service Life and Travel Speed
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Experimental Study of Heat Transfer Characteristics of Condensed Flow on
the Vertical Wave Plates
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Forces Analysis on a Spherical Shaped Delivery Valve of Hydram Pump
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Chapter 3: Advanced Decisions in Mechanical Engineering
Abstract:Hydram pump has been found more than two centuries ago, and has been widely developed
and operated to this day. However, constraints...
Applied Mechanics and Materials Vol. 776 (2015) pp 319-324
© (2015) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/AMM.776.319
Submitted: 2015-02-19
Accepted: 2015-04-10
Simulation of A Differential-Drive Wheeled Mobile
Lego Robot Mindstorms NXT
I Wayan Widhiada1,a, Cok. Gd. Indra Partha2,b, Wayan Reza Yuda A.P3,c
1,3
Teknik Mesin, Fakultas Teknik, Universitas Udayana, Indonesia
2
Teknik Elektro, Fakultas Teknik, Universitas Udayana, Indonesia
a
widhiwyn@yahoo.com, bcokindra@ee.unud.ac.id ,c wayan_unnes@yahoo.co.id
Keywords: Differential-drive robot, Lego Mindstorms NXT, Simulation
Abstract. The aim of this paper is to model and simulate kinematics motion using the differential
drive model of a mobile Lego robot Mindstorm NXT. The author’s use integrated two software as a
method to solve the simulation of mobile lego robot mindstorms NXT using Matlab/Simulink and
Solidworks software. These softwares are enable easier 3D model creation for both simulation and
hardware implementation. A fundamental of this work is the use of Matlab/Simulink Toolboxes to
support the simulation and understanding of the various kinematics systems and in particular how
the SimMechanics toolbox is used to interface seamlessly with ordinary Simulink block diagrams to
enable the mechanical elements and its associated control system elements to be investigated in one
common environment. The result of simulation shows the mobile robot movement control based on
decentralized point algorithm to follow the precision x and y references that has been specified. The
design of the mobile robot is validated in simulation results as proof that this design can achieve the
good performance.
Introduction
During the last three decades, the application of robotic has commonly developed in the
world of industry and education. Robotics research in the world of education is very rarely done by
the students, because the robot modeling and control techniques have a high degree of difficulty.
Therefore, the author’s submitted a research paper on " Simulation of a differential-drive wheeled
mobile lego robot mindstorms NXT".
The design of the robot is a difficult enough task with some considerations such as the
geometry of the robot and the complexity of the mechanism [1]. Traditionally, in need of physical
prototypes to test the robot's ability to perform his duties, but it would spend a lot of cost and time.
Therefore, to reduce the cost and time, the simulation technique is used as a first step by a designer
to model the kinematic and dynamic of mobile robot. Simulation has been known as a powerful tool
to support the design, planning and analysis of the dynamic behavior of a robot [2]. Currently,
Matlab / Simulink is a very popular software for control engineers, and often implicitly suggest that
colleges use this software as a tool to design a controller. The students are familiar with Matlab /
Simulink, it obviously would be a significant advantage in program control system. Typically, such
real-time interaction between the system and the computer on which Matlab / Simulink has been
installed require additional expensive hardware and software [3].
The driver for this research study arose from the limitation of students to understand the
robotic course in mechanical engineering of Udayana university. In this paper, the author’s has
focused to shows how to easy to model and simulate kinematics motion using the differential drive
model in the mobile Lego robot Mindstorm NXT, so it would be expected that students who
followed the robot course in a class will be able to make the simulation robot, the robot is able to
make a control technique using the Matlab programming language / Simulink.
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans
Tech Publications, www.ttp.net. (ID: 120.174.198.61-10/07/15,15:51:50)
320
Recent Decisions in Technologies for Sustainable Development
Simulation Technique
Simulation has been identified as a significantstudy tool for robotic systems since the early of the
20th century [4] and now simulation methods area powerful tool supporting the design, planning,
analysis, and decisions in different areas of research and development. The Simulink extension to
Matlab was identified in 1990 [5], permitting users to establish continuous a causal design
graphically without the need of writing code. Now, Simulink has developed in many directions:
adding more blocks, built-in algebraic loop solving, and a physical modeling of toolboxes.
Simscape is a toolbox for physical modelling developed by the Mathworks for interfacing
with Simulink and it has been available since version R2007A of the Matlab suite [6]. It includes a
foundation library, which contains basic components for electrical, hydraulic, mechanical and
thermal systems. There are also more specialized toolboxes for physical modelling that now are
considered as parts of the Simscape product family. A virtue of this modeling software for
mechanical systems is that it provides a single simulation environment for the construction of
reliable mechanical and controller models. These models can be reused by converting them into
compact, efficient C code for embedded controller implementations [7]. SimMechanics also
includes a computer aided design (CAD) to SimMechanics translator that facilities the automatic
creation of SimMechanics models from Solidworks software packages.According to Goncalves, the
realistic simulation of Lego Mindstorms NXT is presented approach does not replace the training
with hardware but an important complement, since it allows to develop robot software without
accessing to the real hardware [8].
The author has shown through the demonstration of simulation that it is suitable for the
fundamental building of mechanical systems. A fundamental of this work is the use of
Matlab/Simulink Toolboxes to support the simulation and understanding of the various dynamics
systems and in particular how the SimMechanics toolbox is used to interface seamlessly with
ordinary Simulink block diagrams to enable the mechanical elements and its associated control
system elements to be investigated in one common environment.
Creating and Modelling Mobile Lego Mindstorms NXT
The design and 3D modelling of a mobile Lego Mindstorms NXT are worked using
Solidworks 2013 as CAD software. This software enables easier 3D model creation for both
simulation and hardware implementation. Mobile robot has two wheels on left and right with
separately driven is called differentially driven mobile robot (DDMR) which is showed in Figure 1.
In general, the determination of a models position, orientation, and visualization of the body
use transformation matrices. However, when confronted with a complex model with the multidegree of freedom mechanism analytic solutions are tedious to determine. The software package
Solidworks and Matlab/SimMechanics provides an easier method to analyse physical models.
Fig. 1(a) and 1(b) show the assembly of mobile Lego Mindstorm NXT parts and the
complete model respectively. SimMechanics tool provides a reserve to deriving equations and
performing them with base blocks. To create a SimMechanics model, the mechanical system should
be break down into the building blocks. Ground block place point is at position [0 0 0] in the World
CS (coordinate system).
Fig. 1(a). Assembly of mobile Lego Mindstorm NXT parts and 1(b) complete model
Applied Mechanics and Materials Vol. 776
321
The body of mobile robot is connected to revolute joint. Joint sensor is connected to revolute
joint to measure its physical properties such as angular position and angular velocity of the revolute
joint. The joint initial condition is used to adjust the initial position of the wheel mobile robot.
Actuator Modelling
The mobile Lego Mindstorms NXT provides two servomotors with built in rotation sensor
and a gear ratio. A Lego Mindstorms NXT servomotor is shown in Fig. 2.
Fig. 2 Lego Mindstorms NXT servomotor and DC motor circuit
Speed of motor in robotic is able to change in accessible parameter of source voltage. Motor
speed control is required to obtain the various rotation methods and trajectory control. Driving
servo dc motor lego robot has two direction, forward and reverse. H-Bridge circuit is required as a
methods to determine the position of mobile robot [9].
The following of armature control DC servomotor with the load will be presented using an
algorithm. Consider the DC servomotor armature, where in the armature current is constant. In this
system transfer function can be written as shown in Fig. 4 as follows:
( )
=
( )
[
Trajectory Line
+
+
]
=
(
+ 1)
(1)
The trajectory planning is necessary to generate the reference inputs to the motion control
system, which ensures that the mobile robot executes the planned trajectories.The minimal set of
requirement for a mobile robot is to be able to run from an initial position to a final assigned
position.
The input of trajectory planning algorithm is the path description, the path constraints, and
the constraints imposed by a robot gripper dynamics, whereas the outputs are the joint trajectories in
terms of a time sequence of the values attained by position, velocity and acceleration.
Position control is used when the robot finger must be moved with or without load along a
prescribed trajectory through the mobile robot workspace. The control system of mobile robot is
merely a collection of joint controllers each of which is presented to a single joint to drive it
individually. The reference signals for these controllers are supplied by a joint trajectory generator
determining the desired joint trajectory from the desired trajectory of the mobile robot.
Kinematics mobile robot
According to Valera, Mobile robot control education provides a motivating subject for the
students due to the practical work that it involves and present different activities based on Lego
NXT developed for teaching Control Engineering. The tasks that the students must do during this
course deal with system identification, dynamic control of the robot’s wheels, kinematic control of
the mobile robot, path generation etc [10].
A differential-drive motor robot has two wheel is located in left side and right side. Robot is
assumed into 2D domain of XY Cartesian coordinates. In analysis of kinematics robot is assumed
drive relatively slowly and wheels are not slippery on the road surface. From the eq. (7) shows the
number of degree of freedom in kinematics control is three coordinates which is ( , , ). These
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Recent Decisions in Technologies for Sustainable Development
parameters are needed to control as simultaneously to obtain non-holonomic motion. The average of
velocity is shown in the eq. (2) and eq. (3) is the angular velocity of the wheels.
Fig. 3 DDMR in 2D Cartesian coordinates
−
=
+
2
=
(2)
(3)
The parameter of coordinates are provided by eq. (4), and (5) and the position of the mobile robot is
calculated by eq. (6).
=
=
=
(4)
.
(5)
(6)
Commonly, the equation of differential–drive motor robot is obtained in eq. (7). TNH is nonholonomic transformation matrices. The variables of ,
are the radial speed left wheel and right
wheel respectively.
=
(7)
The mathematic model of a differential drive mobile robot is provided in Fig. 4. It is created in
block diagram in Matlab/Simulink. A differential drive mobile robot is controlled in closed loop
system. The speed of servomotor is used to drive the wheels and created using constant input
references. The body of mobile robot is created in block physical model in Matlab/Simmechanics
block.
Fig. 4 Mathematics modeling of Mobile robot with MATLAB/Simulink
Result and Discussion
The physical model of the mobile robot is built using SimMechanics software and the
application SimMechanics has also been verified with identical outputs when compared with
Simulink simulations. The result for mobile robot simulation is shown in Fig. 5, 6 and 7. Fig. 5
Applied Mechanics and Materials Vol. 776
323
shows an example of the mobile robot movement control based on decentralized point algorithm. It
can be appreciated that mobile robot can follow with precision the x and y references that has been
specified. The desired input velocity right wheel and left wheel mobile robot are provided with the
different value parameters, 15 rpm and 10 rpm respectively. Therefore the right wheel rotated
quickly than left wheel and the mobile robot moved rotation shown in Fig. 6. The mobile robot
started a initial position of (0,0) cm, an initial orientation of zero degrees, a final position of mobile
robot in coordinates (30000, 6000) cm and a final orientation of zero degrees. The times depicted in
the figure is to=0 seconds, t1=200 seconds.
Fig, 5 Animation of Mobile robot in
Fig. 6 Result of tracking wheel mobile
of right
wheel mobile robot
2000
1000
0
0
3000
50
100
150
t, s ec onds
the average veloc ity
1000
0
50
t,
100
s ec onds
150
200
of left
wheel mobile robot
2000
1500
1000
500
0
200
2000
0
Veloc ity
2500
v
,s
p
e
e
d
o
fle
f
tw
h
e
e
l(
V
L
)
Veloc ity
3000
robot in coordinate x, y
v
,a
n
g
u
la
rv
e
lo
c
t
y
(
w
)
v
,a
v
e
r
a
g
e
s
p
e
e
d
(
V
r
t
)
v
,s
p
e
e
d
o
fr
ig
h
tw
h
e
e
l(
V
R
)
MATLAB/Simmechanics
0
50
0
50
15
100
150
t, s ec onds
angular veloc ity
200
10
5
0
t,
100
s ec onds
150
200
Fig. 7 The simulation results of differential drive mobile robot
Mobile robot is completed with 2 DC servomotors to drive wheels. Fig. 7 shows the
simulation results of differential drive mobile robot. The right wheel mobile robot speed rotated
from 0 to 3000 rpm and the left wheel mobile robot speed rotated from 0 to 2000 rpm. Therefore
mobile robot moved rotation to right direction because the desired speed input in right wheel is
bigger than speed in the left wheel and the time simulation is stopped at 200 seconds. The average
speed model moved as a linear function and achieved in 2500 rpm at 200 seconds. The maximum
angular speed is achieved in 14.5 rpm at 200 seconds.
Conclusion
The application of simulation techniques is presented to support the students in mechanical
engineering of Udayana university into design, analysis and control of a differential-drive wheeled
mobile robot base on algorithm through integrations both MATLAB and Solidworks. This paper is
to model and simulate kinematics motion using the differential drive model of mobile Lego robot
Mindstorm NXT. The author’s use integrated two software to solve the simulation of mobile lego
robot mindstorms NXT using Matlab/Simulink and Solidworks.
The mobile robot movement has been controlled based on decentralized point algorithm to
follow the precision x and y references that has been specified. The design of the mobile robot is
validated in simulation results as proof that this design can achieve the good performance. The
kinematics control method was extended to control of the trajectory mobile robot.
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Recent Decisions in Technologies for Sustainable Development
Acknowledge
We are deeply and invaluable gratitude a Department of Research and Community Service (LPPM)
Udayana University for supporting and finding this Fundamental research Grant though Letter of
assignment in the contract of implementation of decentralization research Grant (BOPTN) Fiscal
year 2014 No:104.8/UN14.2/PNL.01.03.00/2014
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