Simulation of A Differential-Drive Wheeled Mobile Lego Robot Mindstorms NXT
I Wayan Widhiada
1,a, Cok. Gd. Indra Partha
2,b, Wayan Reza Yuda A.P
3,c1,3Teknik Mesin, Fakultas Teknik, Universitas Udayana, Indonesia
2Teknik Elektro, Fakultas Teknik, Universitas Udayana, Indonesia
a[email protected], b[email protected] ,c [email protected]
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.
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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 multi- degree 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
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:
( )
( ) = [ + + ] = ( + 1) (1)
Trajectory Line
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
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 non- holonomic 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
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 MATLAB/Simmechanics robot in coordinate x, y
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.
0 50 100 150 200
0 1000 2000 3000
Veloc ity of right wheel mobile robot
t, s ec onds
v, speed of right wheel(VR)
0 50 100 150 200
0 500 1000 1500 2000 2500
V eloc ity of left wheel mobile robot
t, s ec onds
v, speed of left wheel(VL)
0 50 100 150 200
0 1000 2000 3000
the average veloc ity
t, s ec onds
v, average speed(Vrt)
0 50 100 150 200
0 5 10 15
angular veloc ity
t, s ec onds
v, angular velocty(w)
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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