Annotation. This article discusses different types of roller wheels, their location methods. There are two main types of roller wheels, such as omnidirectional and a mecanum wheels. The existing types of omnidirectional mobile platforms are indicated. The analysis of the scientific literature devoted to the study of control methods of mobile roller platforms, methods of dynamic description and control of the movement of platforms with roller wheels has been carried out. Maggi and Appel equations are used to describe the dynamics of the mobile platform. It is also noted that consideration of issues of mechanics and control of mobile platforms with roller bearing wheels, frictional forces acting on shafts and axles of mechanical wheel gears. Today, the most relevant area of research is the development and construction of mobile platform control systems using artificial intelligence methods. The control algorithm based on odd logic with slip detection for a mobile platform is proposed. Thus, the use of information technology provides an expansion of the technological and functional capabilities of the mobile platform.
Keywords: mobile platform, roller wheels, mathematical model, control system, artificial intelligence, neural network.
Today, there are a large number of different design variants of mobile wheeled platforms, which are used to move cargo or survey the terrain, and are also widely used in limited conditions in warehouses or production facilities, etc. The most interesting is a mobile platform with roller wheels, the main feature of which is high manoeuvrability. A mobile platform with roller wheels can at any moment change the trajectory of its movement to a certain angle without turning or changing the direction of the wheels. To carry out manoeuvres, translational and rotational movements should be combined. The main element of such a platform is a roller wheel.
Wheel types. A roller wheel is a wheel with rollers installed around the circumference of the wheel at an angle of 90о or 45о to the direction of movement, with the help of which the mobile robot can move in any direction, combining linear and rotational movements. There are two main types of roller bearing wheels - an omni-wheel and a mecanum-wheel. (Fig. 1 a, b).
If the axes of the rollers located on the outer circle of the disk lie in the plane of the wheel, then this is an omni-wheel or a classical omnidirectional wheel. And if the axes of the rollers cross the axis of the wheel at an angle of 45 о, then it is a mecanum-wheel or a Swedish wheel [1].
Figure 1 – The main types of roller wheels: omni-wheel (a) and mecanum-wheel (b)
The rollers of an omnidirectional wheel are located so that their axes of rotation are tangent to the wheel circle, so the movement of the wheel is the result of two movements – movement along the rotation of the disk and movement along the rotation of the passive roller. The design of such wheels allows the platform to rotate in place with minimal friction and low torque [2].
Platform types. Mobile platforms differ in the number of wheels and the way they are placed. The typical omni-wheel platform configuration is a three-wheeled platform, although other solutions are available. The most common are three- or six-wheel platforms with omni-wheels (Fig. 2 a) and four-, six- or eight-wheel platforms with mecanum wheels (Fig. 2 b).
Figure 2 – Mobile platforms with roller wheels
The use of omni-wheels results in each wheel developing a tractive force directed approximately along the axis of the roller in contact with the support. Thus, by changing the speed and direction of rotation of each wheel, it is possible to ensure that the platform moves like a typical four-wheeled platform. It also allows you to implement translational movement of the platform or its arbitrary rotation and turns. It is possible to implement, for example, the transverse movement of the platform, combinations of wheel movements allow you to build movement in any direction with any rotation. A significant number of omni- and mecanum-wheel platforms have already been developed [2-3].
Dynamic description methods. Papers [4-6] and others are devoted to the study of the dynamics and motion control of platforms with omnidirectional wheels. Rollers are fixed on the wheels of the platform of this design, the axes of rotation of which lie in the plane of the wheels, which allows movement in any direction without prior turning, which significantly increases the platform's manoeuvrability. The wheels are driven independently of the DC motors.
Maggi and Appel equations are used to describe the dynamics of the mobile platform. However, it should be noted that for the implementation of control algorithms, it is also necessary to identify the values of the coefficients for the components of the mobile platform. The paper [7] is dedicated to obtaining estimates of the parameters of real mechanical and mechatronic systems.
Many publications are devoted to the study of kinematics, dynamics, motion control algorithms and practical application of mobile platforms with roller wheels [8-14]. Publications [8-11] consider some features of the contact of roller wheels with the surface. In article [8], the dynamics of a platform with omni-wheels is considered, taking into account their slippage, and in article [9], the main attention is paid to the modelling of devices with omni-wheels, taking into account the visco-elastic properties of the roller material. The article [10] proposes a control algorithm based on odd logic with slip detection for a mobile platform with mecanum wheels. The paper [11] describes the development of an adaptive control system for an omnidirectional platform with mecanum wheels on a surface with unknown terrain.
Publications [12-14] are devoted to special issues of motion control of omnidirectional mobile platforms. The article [12] proposes an algorithm for suboptimal speed control of a mobile platform with omni-wheels that takes into account its dynamics and limited contact friction forces. The paper [13] is devoted to the synthesis of the law of control of a mobile robot with omni-wheels with stabilization of the program trajectory by the method of Lyapunov functions, taking into account restrictions on the magnitude of angular velocities of the wheels. The paper [14] describes the problem of controlling a mobile platform with omni-wheels with stabilization of the program trajectory and heading angle is solved, taking into account the dynamics of the tracking drives and limitations on the angular velocity of the wheels. Identification of the parameters of the discrete mathematical model of the wheel drives was carried out.
In the mentioned publications, which deal with the mechanics and control of mobile platforms with roller wheels, the frictional forces acting on the shafts and axles of mechanical wheel gears are either ignored or grouped with control moments.
Artificial Intelligence. Artificial intelligence, namely the neural network, is becoming increasingly interesting. Of course, certain studies have already been carried out on this topic by foreign experts. It should be noted that in paper [15] was investigated how the development of dynamics in periodic neural networks is used to control a mobile platform. An approach to motion control based on a new recurrent neural network has been developed. The advantage of this approach is that it does not require any information about the dynamic model. The article [16] investigates the adaptive sliding mode using the radial basis of a functional neural network, and also proposes an online training algorithm for adjusting the controller parameters in accordance with the variation characteristics of nonlinear dynamics.
The self-learning ability of neural networks eliminates the need to use complex mathematical analysis. In recent years, much attention has been paid to the analytical study of an adaptive nonlinear control system using a radial basis function (RBF) neural network as a universal approximator. The RBF network is a special form of artificial neural network, the advantages of which are simple structure, faster algorithms and better approximation to the nonlinear system.
The structure of a typical three-level RBF neural network is shown in Fig. 3. There is an input vector in the RBF neural network x=x Ti . Assuming that there are neural networks m th and the radial basis vector function in the hidden layer RBF is h=hTi, where hi is the value of the Gaussian function for the neural network j in the hidden layer, so  .
The RBF weight value is: w=w1, ..., wTm . The output of the RBF neural network
is:
Figure 3 – Structure of RBF neural network
The article [17] demonstrates the performance of the main modules of the system in the computer vision field, a new colour calibration method based on the rapidly random-exploring tree (RRT) neural network algorithm, with additional rules that allow controlling the approach angle of the robot. In paper [18], a neural network with basic sigmoidal functions is used to compensate for nonlinearity and variable operating conditions of a mobile robot with mecanum wheels. The Lyapunov stability theory is used, including the Hamilton-Jacobi inequality.
Due to the nonlinearity, as well as the complexity of the structure of the dynamic equations of motion of mobile wheeled platforms and the need to include a mathematical model in the motion control algorithms for these objects, the application of the theory of artificial neural networks is an alternative approach to solving such problems. From the point of view of control theory, the ability to approximate nonlinear mappings is the most important property of neural networks. These properties will be used in the synthesis of control of neural networks for tracking the movement of the system.
Thus, the use of information technology provides the expansion of technological and functional capabilities of the mobile platform.
Reference
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