Design of Fuzzy Logic Control System for Segway Type Mobile Robots
Design of Fuzzy Logic Control System for Segway Type Mobile Robots
International Journal of Fuzzy Logic and Intelligent Systems. 2015. Jun, 15(2): 126-131
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
• Received : April 23, 2015
• Accepted : June 25, 2015
• Published : June 30, 2015
PDF
e-PUB
PPT
Export by style
Article
Author
Metrics
Cited by
TagCloud
Sangfeel, Kwak
Byung-Jae, Choi

Abstract
Studies on the control of inverted pendulum type systems have been widely reported. This is because this type of system is a typical complex nonlinear system and may be a good model to verify the performance of a proposed control system. In this paper, we propose the design of two fuzzy logic control systems for the control of a Segway mobile robot which is an inverted pendulum type system. We first introduce a dynamic model of the Segway mobile robot and then analyze the system. We then propose the design of the fuzzy logic control system, which shows good performance for the control of any nonlinear system. In this paper, we here design two fuzzy logic control systems for the position and balance control of the Segway mobile robot. We demonstrate their usefulness through simulation examples. We also note the possibility of simplifying the design process and reducing the computational complexity. This possibility is the result of the skew symmetric property of the fuzzy rule tables of the system.
Keywords
1. Introduction
Studies on the control of inverted pendulum type systems have been widely reported. This is because this type of system is a good model to verify the performance of a proposed controller for such a system, which is inherently a nonlinear. An inverted pendulum type mobile robot system adds mobility to the utilization of a mechanical function that balances the inverted pendulum system [1] . Furthermore, it is similar to the control scheme of a biped robot which is modelled after the human form and is supported by two feet.
Segway type mobile robots operate based on the dynamics of the inverted pendulum system. They are capable of forward, backward, and turning motions, and these are the only possible movements of the body. Unlike scooters whose two interdependent wheels are in series, Segway mobile robots have two wheels connected in a parallel configuration. Thus, Segway mobile robots allow the construction of a mobile platform that can travel smoothly to a small area by reducing the migration area. However, a mobile robot employing an inverted pendulum mechanism as its mobile platform requires an additional controller design to maintain the balance of the body, as its balancing ability is generally not good under excessive disturbances.
In this paper, we propose the design of a fuzzy logic control system for the position and balance control of an inverted pendulum type Segway mobile robot. We first introduce a dynamic model of the Segway mobile robot and analyze it. We then design two fuzzy logic control systems based on our analysis. Their usefulness is verified by simulation examples. Based on the skew symmetry property of the rule table for the fuzzy logic control system, we also present a possibility for a reduction in the computational complexity and the simplification of the design of the fuzzy logic control system.
The remainder of the paper is organized as follows. In Section 2, we describe the introduction of the dynamic model of the Segway mobile robot. The design of two fuzzy logic control systems for the Segway mobile robot is presented in Section 3. In Section 4, we present the results of simulation examples and explain their relevance. Concluding remarks are given in Section 5.
2. Dynamics of Segway Mobile Robot
Segway type mobile robots are composed of two wheels and a pole between them. The angle of the pole is measured by a gyro, tilt or acceleration sensor, and is maintained at zero degrees.
In this section, we introduce the dynamics of the Segway type mobile robot which is an inverted pendulum type mobile robot. Schematics of this robot are shown in Figure 1 .
PPT Slide
Lager Image
Schematics of Segway type mobile robot.
The main parameters used in Figure 1 are presented in Table 1 .
Definitions of Segway robot Parameters
PPT Slide
Lager Image
Definitions of Segway robot Parameters
As shown in Figure 1 , the mobile robot can be divided into two parts. The wheel part and the pole part, which consists of a pole and a driving motor to support the body over the wheel and maintain the balance of the robot.
We first introduce equations associated with the wheel part of the robot, which is shown in Figure 1 (b) . The following equations of motion are derived from the moment of inertia of the wheel of the driving shaft and the reaction forces of the horizontal and vertical axes of the pole:
PPT Slide
Lager Image
PPT Slide
Lager Image
The rotational angle of the wheel and the displacement of the robot have the following relationship.
PPT Slide
Lager Image
From Eqs. (2) and (3), the horizontal reaction force of the wheels is derived from the displacement and the driving torque as
PPT Slide
Lager Image
The following equation can be obtained from Eqs. (1) and (4).
PPT Slide
Lager Image
We then derive the dynamic equations of the pole. The force acting the pole is shown in Figure 1 (c) . Then the horizontal displacement of the center of gravity of the pole is
PPT Slide
Lager Image
Eq. (6) can be expressed in an acceleration form as
PPT Slide
Lager Image
Eq. (7) can be expressed as an equation of motion with respect to the axis of the center of gravity of the pole as
PPT Slide
Lager Image
PPT Slide
Lager Image
Next, the vertical displacement of the center of gravity of the pole is
PPT Slide
Lager Image
Eq. (10) can be expressed in the form of an acceleration equation as
PPT Slide
Lager Image
Eq. (11) can be expressed as an equation of motion with respect to the y axis of the center of gravity of the pole as
PPT Slide
Lager Image
PPT Slide
Lager Image
The following equation is derived from Eqs. (5) and (9).
PPT Slide
Lager Image
The moment of inertia of the center of gravity of the pole is
PPT Slide
Lager Image
The following equation is derived from Eqs. (9), (13) and (15).
PPT Slide
Lager Image
The dynamic model of the Segway robot is expressed by Eqs. (14) and (16).
3. Design of Fuzzy Logic Control Systems
Two fuzzy logic control (FLC) systems are required to control the Segway robot: the Distance FLC and the Balance FLC for position and balance control, respectively.
The Distance FLC to control the position of the robot is designed first. It has two input variables, edist and dedist, which are the error signal between the set position and the current position of the robot and its change signal, respectively. It also has one output variable, AddAngle, which is the weight of the angle error of the pole.
The membership functions of the input and output variables of the Distance FLC are shown in Figures 2 , 3 , and 4 .
PPT Slide
Lager Image
Membership functions of input variable, edist, for Distance FLC.
PPT Slide
Lager Image
Membership functions of input variable, dedist, for Distance FLC.
PPT Slide
Lager Image
Membership functions of output variable, AddAngle, for Distance FLC.
The control rule table for the Distance FLC is given in Table 2 .
Rule table for Distance FLC
PPT Slide
Lager Image
Rule table for Distance FLC
We then design the Balance FLC for the control of the balance of the robot. Its input variables are etheta and detheta, which represent the angle of the pole and the output of the Distance FLC. Its output variable is the torque.
The membership functions of the input and output variables of the Balance FLC are shown in Figures 5 , 6 , and 7 .
PPT Slide
Lager Image
Membership functions of input variable, etheta, for Balance FLC.
PPT Slide
Lager Image
Membership functions of input variable, detheta, for Balance FLC.
PPT Slide
Lager Image
Membership functions of output variable, torque, for Balance FLC.
The Z membership function for the output variable, torque, was widely set. The shapes of the membership functions of PLO and NLO are sharper than that of Z membership function. This can reduce the vibration of the output variable and make the output of the system converge to a steady state.
The control rule table for the Balance FLC is given in Table 3 .
IRule table for Balance FLC
PPT Slide
Lager Image
IRule table for Balance FLC
4. Simulation Examples
In this section, we simulate the position and balance control of the Segway mobile robot using the two proposed fuzzy logic control systems. We first set θ ,
PPT Slide
Lager Image
, and τ as
PPT Slide
Lager Image
And some parameters of the Segway mobile robot are as follows [2] :
PPT Slide
Lager Image
The AND and OR operations for the fuzzy logic control system are min and max, respectively. Additionally, Mamdani reasoning and the defuzzification method for the center of gravity are used in this simulation.
The results of the weight of the angle error of the pole, the torque, the displacement, the change in the displacement, the angle of the pole, and the change in this angle are shown in Figures 8 , 9 , 10 , 11 , 12 , and 13 respectively. The initial conditions are as follows: the angle of the pole = 1 [radian], the target position is 10 [m].
PPT Slide
Lager Image
PPT Slide
Lager Image
Simulation results of torque.
PPT Slide
Lager Image
Simulation results of displacement of robot.
PPT Slide
Lager Image
Simulation results of velocity of robot.
PPT Slide
Lager Image
Simulation results of angle of pole.
PPT Slide
Lager Image
Simulation results of angular velocity of pole.
5. Concluding Remarks
In this paper, we analyzed the dynamics of the Segway mobile robot which has nonlinear properties, and designed two fuzzy logic control systems for the control of the position of the Segway mobile robot and the balance of the pole part of the robot. First, we designed the Distance FLC for the position control. The two input variables of the Distance FLC are the error signal between the set position and the current position of the robot and its change signal, the output variable is the weight of the angle error of the pole. We then designed the Balance FLC for the control of the balance of the pole. Its input variables of the Balance FLC are the angle of the pole and the output of the Distance FLC, and the output variable is the torque. The control rule table indicates that the control rules for the two fuzzy logic control systems are the skew symmetric [3] .
This can simplify the control rule table to a single dimensional case with a small number of input variables and control rules. This in turn simplifies the design of the overall control system. This will be studied in future work with the implementation of an embedded board based system.
Acknowledgements
This research was supported by the Daegu University Research Scholarship Grants.
BIO
Sangfeel Kwak is a Ph.D candidate at the College of Information, Communication, and Computer Engineering, Daegu University. He received the M.S. degree in Electronics Engineering from Daegu University, Korea. Currently, his main research interests include intelligent control and systems.
Byung-Jae Choi is a professor at the College of Information, Communication, and Computer Engineering, Daegu University. He received the Ph.D. degree in Electrical Engineering from KAIST, Korea. Currently, his main research interests include intelligent control and systems.
References
The SEGWAY website [Online]. Available:
Lee S.-H. , Rhee S.-Y. 2012 “Dynamic modelling of a wheeled inverted pendulum for inclined road and changing its center of gravity,” J. of Korean Institute of Intelligent Systems 22 (1) 69 - 74    DOI : 10.5391/JKIIS.2012.22.1.69
Choi B.-J. , Jin S. 2012 “Design of Simple-structured Fuzzy Logic System based Driving Controller for Mobile Robot,” J. of Korean Institute of Intelligent Systems 22 (1)
Kim H. W. , Jung S. 2012 “Fuzzy Logic Application to a Two-wheel Mobile Robot for Balancing Control Performance,” Int. J. of Fuzzy Logic and Intelligent Systems 12 (2)
Park J. H. 2003 “Fuzzy-logic zero-moment-point trajectory generation for reduced trunk motion of biped robots,” Fuzzy Set Techniques for Intelligent Robotic Systems 134 (1) 189 - 203
Ha H. , Lee J. 2010 “A control of mobile inverted pendulum using single accelerometer,” J. of Institute of Control, Robotics and Systems 16 (5)
Nawawi S. W. , Ahmad M. N. , Osman J. H. S. 2006 “Control of two-wheels inverted pendulum mobile robot using full order sliding mode control,” Proc. of International Conference on Man-Machine System Lankawi, Malaysia
Axelsson P. , Jung Y. 2011 Lego Segway Project Report, Technical Report Automatic Control at Linkopings Universitet, Division of Automatic Control
Noh J. S. , Lee G. H. , Jung S. 2010 “Position control of amobile inverted pendulum system using radial basis function network,” Int. J. of Control Automation and Systems 8 (1)
Huang J. , Guan Z. , Matsuno T. , Fukuda T. , Sekiyama K. 2010 “Sliding-Mode Velocity Control of Mobile WheeledInverted-Pendulum Systems,” IEEE Trans. on Robotics 26 (4)
Jin T. 2012 “Obstacle Avoidance of Mobile Robot Based on Behavior Hierarchy by Fuzzy Logic,” Int. J. of Fuzzy Logic and Intelligent Systems 12 (3)
Mao L. , Huang J. , Ding F. , Wang Y. 2013 “Velocity control of mobile wheeled inverted pendulum,” Int. J. of Modelling Identification and Control 19 (1)
Xiong X. , Choi B.-J. 2013 “Comparative Analysis of Detection Algorithms for Corner and Blob Features in Image Processing,” Int. J. of Fuzzy Logic and Intelligent Systems 13 (4)
Kim B.-H. 2013 “Analysis of Balance of Quadrupedal Robotic Walk using Measure of Balance Margin,” Int. J. of Fuzzy Logic and Intelligent Systems 13 (2)
Do K. D. , Seet G. 2010 “Motion Control of a Two-Wheeled Mobile Vehicle with an Inverted Pendulum,” J. of Intelligent and Robotic Systems 60 (3-4)
Nguyen H.-G. , Kim W.-H. , Shin J.-H. 2010 “A Study on an Adaptive Robust Fuzzy Controller with GAs for Path Tracking of a Wheeled Mobile Robot,” Int. J. of Fuzzy Logic and Intelligent Systems 10 (1)