Optimization of interval type-2 fuzzy logic controllers for a perturbed autonomous wheeled mobile robot using genetic algorithms
Introduction
Mobile robots have attracted considerable interest in the robotics and control research community, because they have non-holonomic properties caused by non-integrable differential constrains [16], [19]. The motion of non-holonomic mechanical systems [15] is constrained by its own kinematics, so the control laws are not derivable in a straightforward manner (Brockett’s condition [6]).
Furthermore, most reported designs rely on intelligent control approaches such as fuzzy logic control (FLC) [4], [25], [34], [38], [39], [45], [46] and neural networks [15], [43]. However the majority of the publications mentioned above, have concentrated on kinematics models of mobile robots, which are controlled by the velocity input, while less attention has been paid to the control problems of non-holonomic dynamic systems, where forces and torques are the true inputs: Bloch and Drakunov [5], [13] and Chwa [10], used a sliding mode control to the tracking control problem.
This paper is organized as follows: Section 2.1 presents an introductory explanation of type-2 fuzzy logic, Section 2.2 presents the basics of genetic fuzzy systems, Section 2.3 presents the problem statement and the kinematic and dynamic models of the unicycle mobile robot. Section 3 introduces the posture and velocity control design where a genetic algorithm is used to select the parameters of the posture controller. Robustness properties of the closed-loop system are achieved with a type-2 fuzzy logic velocity control system using a Takagi–Sugeno model where the wheel input torques, linear velocity, and angular velocity will be considered as linguistic variables. Section 4 provides a simulation study of the unicycle mobile robot using the controller described in Section 3. Finally, Section 5 presents the conclusions.
Section snippets
Theoretical basis and problem statement
This section describes the theoretical basis of the paper as well as the problem definition. Some basics about type-2 fuzzy systems and genetic fuzzy systems are first presented [8].
Fuzzy logic control design
This section illustrates the framework to achieve stabilization of a unicycle mobile robot around a desired path. The stabilizing control law for the system (17), (18) can be designed using the backstepping approach [24] since the kinematics subsystem (18) is controlled indirectly through the velocity vector v. The procedure to design the overall controller consists of two steps:
- (1)
Design a virtual velocity vector ϑr = ϑ such that the kinematic model (18) be uniformly asymptotically stable.
- (2)
Design a
Simulation results
In this section, we evaluate, through computer simulations performed in MATLAB® and SIMULINK®, the ability of the proposed controller to stabilize the unicycle mobile robot, defined by (17), (18) where the matrix valueswhere taken from [14].
The desired trajectory is the following one:and was chosen in terms of its corresponding desired linear vd and angular velocities wd, subject to
Conclusions
We have designed a trajectory tracking controller taking into account the kinematics and the dynamics of the autonomous mobile robot using type-2 fuzzy logic and genetic algorithms.
Genetic algorithms are used for the optimization of the constants for the trajectory tracking and also for the optimization of the parameters of membership functions for fuzzy logic control.
Currently, the design of a type-2 fuzzy logic controller has been tested under a perturbed autonomous wheeled mobile robot, but
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