Identification of Dynamics of Movement of the Differential Mobile Robotic Platform Controlled by Fuzzy Controller

Abstract

Mobile robots with differential chassis are very often used because of simple construction and a smaller number of drive and sensors elements. For practical applications, it is necessary to know the kinematic and dynamic structure of the differential mobile robot. This paper deals with identification of the dynamics of the differential robotic platform, using differential kinematics. Electro-optical rpm sensors obtain required values such as speed of the driven wheels. Identification of dynamic system is used to determine the dynamic characteristics of power subsystem of developed EN 20 robot, whose control subsystem is created by single-chip microcontroller. Response of the dynamic system is monitored along with the peripheral velocity of the right and left drive wheels. Incremental encoders that work on optics principle measure the speeds of both wheels. It was necessary to calibrate the sensors and obtain constants for precise speed determination. The monitored system with the dumped oscillation characteristic is approximated by a system with the inertia of the 2 nd order. Dynamic system parameters are found. The system approximation is suitable for given evolution of circumferential speeds of the right and left wheels. This is confirmed by the quantitative determination coefficients R 2. The equations for calculating peripheral velocities of driving wheels are applied to the system of the differential equations for the differential chassis. A mathematical model of the mobile robot EN20 was obtained for testing control algorithms, where a robot is equipped with sensory systems and it is designed for interior conditions. Fuzzy controller with 49 interference rules is used to control the mobile robot. The real mobile robot path matches the path determined according to simulation model.

Approximation Possibilities of Fuzzy Control Surfaces for Purpose of Implementation into Microcontrollers

“…The movement can be described as a movement along the arcs around the instant center of rotation (ICR) with the radius of R. From Figure 1, the simplest will be to calculate the position of the chassis relative to the P point, which lies in the center of the wheel axis. Angular velocity of the robot ωP is calculated from the difference in the speeds of the left and right wheel from (1) [27]:…”

“…where L is track width, VP and VL is peripheral velocity of right VP and left VL wheels are given in (2) [27]:…”

“…Based on the distance of the mobile robot from the target position D and the angle of deflection of the mobile robot from the target position of the mobile robot δ, the task of a fuzzy controller is to control the speed of the right and left wheel of the EN20 mobile robot Angular velocity of the robot ω P is calculated from the difference in the speeds of the left and right wheel from (1) [27]:…”

“…where R is radius to the instant center of rotation. To determine tangential speed V TP of the chassis at the point P from the peripheral velocities of wheels we simply calculate their mean value (3) [27]:…”

“…where x(k), y(k) is current sample of the x and y mobile robot coordinates, x(k − 1) and y(k − 1) is the previous sample of the x and y mobile robot coordinates, Θ(k) is current angle of the robot, Θ(k − 1) is the previous angle of the robot, V P (k) and V L (k) is current sample of the right and left wheel peripheral velocity and T is the sampling period [27].…”