International Journal on Mechanical Engineering and Robotics (IJMER)
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Trajectory Tracking of Differential Drive Wheeled Mobile Robot
Ekta A.Mishra
Instrumentation dept/DYPIET pimpri / Pune University , India
Email:
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ISSN (Print) : 2321-5747, Volume-2, Issue-2,2014
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International Journal on Mechanical Engineering and Robotics (IJMER)
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Abstract -In this paper wall following differential drive wheeled mobile robot is presented. Differential drive wheeled mobile robot is non-holonomic mechanical system that is subjected to non-holonomic constraints. They are the constraints on velocity which cannot be integrated to the position constraints. In this project two different type of controllers are examined. First one is Fuzzy logic controller and second is Fuzzy sliding mode controller. Both controllers are able to control a non-holonomic mobile robot to track the desired trajectory. All simulations are performed using SIMULINK/MATLAB.
Keywords -constraints, non-holonomic, differential drive
I. INTRODUCTION
Mobile robots are mechanical devices that are equipped with an on-board power source, computational resources, sensors and actuators. They are able to move autonomously and freely to perform their task. These mobile vehicles can be operated in large buildings (such as shopping centre, hospital and warehouse), nuclear waste facility, security and defense industry, transportation sector, inspection process and planetary exploration. The interest in investigating and developing mobile robots has become increasingly relevant and beneficial to human society and industry. There has been active and rapid development in this area pertaining to its research and implementation. Recent advances in computer and sensor technologies have made it feasible and practical to design and develop new and innovative mobile robots that can effectively serve as utility vehicles and material transporters.
One of the important aspects of the mobile robot systems is related to its motion or navigation control. The issue of control problem is not only dependent on the kinematics and dynamics of the mobile robot system but also the actual individual elements of the control itself. Without a good control system, a mobile robot is practically useless and ineffective. Therefore, the development of a mobile robot is significantly influenced by the proper design of the control system. A variety of theoretical and applied control problems of mobile robot system have been studied and proposed such as kinematics control, dynamic control, intelligent control, adaptive control, and robust control.
Mobile robots are mechanical devices capable of moving in an environment with a certain degree of autonomy. Autonomous navigation is associated to the availability of external sensors that capture information of the environment through visual images or distance or proximity measurements. The most common sensors are distance sensors (ultrasonic, laser, etc) capable of detecting obstacles and of measuring the distance to walls close to the robot path. When advanced autonomous robots navigate within indoor environments (industrial or civil buildings), they have to be endowed the ability to move through corridors, to follow walls, to turn corners and to enter open areas of the rooms. In attempts to formulate approaches that can handle real world uncertainty, researches are frequently faced with the necessity of considering tradeoffs between developing complex cognitive systems that are difficult to control, or adopting a host of assumptions that lead to simplified models which are not sufficiently representative of the system or the real world. The latter option is a popular one which often enables the formulation of viable control laws. However, these control laws are typically valid only for systems that comply with imposed assumptions, and further more, only in neighborhoods of some nominal state. The option that involves complex systems has been less prevalent due to that lack of analytical methods that can adequately handle uncertainty and concisely represent knowledge in practical control systems. Recent research and application employing non-analytical methods of computing such as fuzzy logic, evolutionary computation, and neural networks have demonstrated the utility and potential of these paradigms for intelligent control of complex systems. In particular, fuzzy logic has proven to be a convenient tool for handling real world uncertainty and knowledge representation.The motion planning objective is to transfer a system from a specified initial state to a specified final state while motion control is to solve the three basic navigation problems; tracking a reference trajectory, path following and stabilization about a desired posture.
In this paper, a study on kinematics modeling and a design of two stable tracking controllers of non-holonomic wheeled mobile robot is used. The two controller are fuzzy logic controller and fuzzy sliding mode controller.Then both controllers will be discussed in terms of their advantages and disadvantages.
1. Model and control design of robot
1.1 Mathematical robot model
The kinematics and dynamic equations of the wheeled mobile robot of the differential drive type and formulates the problem of controlling it to a point with a desired orientation. The vehicle has two identical parallel, non-deformable rear wheels which are controlled by two independent motors, and a front caster wheel. It is assumed that the plane of each wheel is perpendicular to the ground and the contact between the wheels and the ground is pure rolling and non-slipping, i.e., the velocity of the center of mass of the robot is orthogonal to the rear wheels’ axis. It is further assumed that the masses and inertias of the wheels are negligible and that the center of mass of the mobile robot is located in the middle of the axis connecting the rear wheels.
1.2 Differential Drive
Kinematics is the study of the mathematics of motion without considering the forces that affect the motion. It deals with the geometric relationships that govern the system. It develops a relationship between control parameters and the parameters and the behavior of a system in space. The model of the robot is as shown in Figure 1
Fig 1 Kinematic Model of the Robot
1.3 Equations Defining the Robot For a differential drive the kinematics equations in the world frame are as follows
Vr(t)= linear velocity of right wheel
Vl(t)= linear velocity of left wheel
ωr(t)= angular velocity of right wheel
ωl(t) = angular velocity of left wheel
r = nominal radius of each wheel
L = distance between the two wheels
R = instantaneous curvature radius of the robot trajectory, relative to the mid-point axis
ICC = Instantaneous Center of Curvature
R-L/2= curvature radius of trajectory described by left wheel
R+L/2== Curvature radius of trajectory described by right wheel
With respect to ICC the angular velocity of the robot is given as follows
The instantaneous curvature radius of the robot trajectory relative to the mid-point axis is given as
The above equations can also be represented in the following form
In this paper only kinematics model is considered, which represents the relationship between postures and velocities of the described non-holonomic wheeled mobile robot. The dynamic model is not considered in order to simplify the analysis. It is known that this simplification is acceptable when the system velocities are low, as is in most mobile robot applications .
These are the equations that are used to build a model of the robot. These equations were used to simulate the robot in MATLAB Simulink. The fuzzy logic controller and fuzzy sliding mode control were tested, as well as compared with each other controllers for optimum results.
II. FUZZY LOGIC CONTROLLER DESIGN
The processing time required when using fuzzy logic control depends upon the number of rules that must be evaluated. Large systems with many rules would require very powerful and fast processors to compute in real time. The smaller the rule base, the less computational power needed. To reduce processing time, a static lookup table can be used to generate FLC control action. In some applications, that can greatly reduce processing time compared to performing fuzzy inference
2.1 Rule Base
2.2Linguistic Variable and Membership function
The linguistic variables are error in angle et , error in distance ex and change in angular velocities of the two wheels wr and wl . The error in distance and error in angle are rounded off as the sensor outputs a value rounded to the nearest inch.
2.3 Fuzzy Logic Controller tunning
Tuning an FLC is a daunting task as there are many parameters that can be adjusted. These include the rules, membership functions and any other gains within the control system. The overall FLC tuning process consists of the following two steps:-
Gross adjustment of the system is done by iteratively adjusting rules, membership functions and number of variables needed.
Once gross tuning is accomplished, the FLC is fine tuned. This involves slight adjustments of individual membership functions and their ranges.
III. SLIDING MODE CONTROLLER DESIGN
The control objective is to steer the mobile robot so as to follow the desired trajectory, which can be represented in polar coordinates.
The kinematic equations in Cartesian coordinates corresponding
Based on the above representation, the sliding surface Ѕ is chosen for >1
Even when decreases to zero, is well defined and the resulting controller can be free from the problem of singularity around the origin
IV. RESULT
4.1.Simulation Model of fuzzy Logic Controller
The mathematical modeling of the robot was discussed in detail. Using the kinematic and dynamic equations of the robot a Simulink model was developed to test the feasibility of using a controller The fuzzy block in the Simulink model is a customized MATLAB M-file function block replacing the fuzzy logic toolbox. The measurement noise observed in the sensors is shown in the Simulink block diagram as white noise, with a standard deviation of 1 inch. The error in angle is measured as the difference between the two sensors on the side of the robot; hence it is measured in inches. This was done as calculating the actual angle would require use of trigonometric functions which would take a long time to calculate or require large memory space.
4.2 Simulation Model for Fuzzy sliding mode Controller
The output variables X, Y, and T are the two Cartesian coordinates of the robot position, along with its angular orientation. The Xref input (step input) is intended to keep the robot a certain distance away from the wall which it is following. The Tref input(constant input) is zero, as it is intended that the orientation of the robot be maintained at a zero angle relative to the wall
4.3 Comparison of results
Simulation result obtained by using fuzzy logic controllerSimulation results obtained using fuzzy sliding mode controllercomparison of results
V. CONCLUSION
Main objective was to develop an optimal path controller for an autonomous mobile robot. The first step in approaching this problem was to build the highly nonlinear dynamic model of the mobile robot. This was done using the Simulink toolbox available in MATLAB. The next step is to implement Fuzzy logic controller. Since the two controller are fuzzy logic controller and fuzzy sliding mode controller
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ISSN (Print) : 2321-5747, Volume-2, Issue-2,2014
1
International Journal on Mechanical Engineering and Robotics (IJMER)
______
______
ISSN (Print) : 2321-5747, Volume-2, Issue-2,2014
1