In the work [Chua, 1992], a deep intuition of its author gave rise to the choice of singularities corresponding to Chua's circuit. Therefore, it is the only one probably exhibiting three saddle points named Chua's singularities in this paper. One of the singularities is a saddle in forward time (dt > 0) of integration, whereas the other two are saddles in backward time (dt < 0) of integration. In the following, the term Chua's Chaos denotes chaos related to Chua's singularities. These singularities are the source of all special surfaces that are the subject of this contribution. We named the surface to which all other surfaces are bound as the Double-Arm Stable Manifold (DASM). The beauty and multifunctionality of this surface represents the unfathomable Intelligence in the sense of [Tolle, 2003]. The presence of the DASM in the state space is a sufficient condition for the generation of Chua's chaos or corresponding periodic windows. Since Chua's singularities are not limited by circuit morphology or the order of state equations, the research on Chua's chaos seems to be still very promising.
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.
The issue of navigation methods is being continuously developed globally. The aim of this article is to test the fuzzy control algorithm for track finding in mobile robotics. The concept of an autonomous mobile robot EN20 has been designed to test its behaviour. The odometry navigation method was used. The benefits of fuzzy control are in the evidence of mobile robot's behaviour. These benefits are obtained when more physical variables on the base of more input variables are controlled at the same time. In our case, there are two input variables -heading angle and distance, and two output variables -the angular velocity of the left and right wheel. The autonomous mobile robot is moving with human logic.
The paper deals with comparing electricity power consumption of various control algorithms by simulating differential mobile robot motion control in a vineyard row. In field of autonomous mobile robotics, the quality of control is a crucial aspect. Besides the precision of control, the energy consumption for motion is becoming an increasingly demanding characteristic of a controller due to the increasing costs of fossil fuels and electricity. A simulation model of a differential drive mobile robot motion in a vineyard row was created, including robot dynamics for evaluating motion consumption, and there were implemented commonly used PID, Fuzzy, and LQ control algorithms, the task of which was to navigate the robot through the centre of vineyard row section by measuring distances from trellises on both robot sides. The comparison was carried out using Matlab software and the best results in terms of both power consumption and control accuracy were achieved by LQI controller. The designed model for navigating the robot through the vineyard row centre and optimized controllers were implemented in a real robot and tested under real conditions.
The numerical mathematical theory provides a few ways of numerical integration with different errors. It is necessary to make use of the most exact method with respect to the computing power for a majority of microprocessors, because errors are integrated within them due to the algorithm. In our contribution, trapezoidal rule and Romberg's method of numerical integration are compared in the velocity calculation algorithm of the strapdown inertial navigation. The sample frequency of acceleration and angular velocity measurement was 816.6599 Hz. Inertial navigation velocity was compared with precise incremental encoder data. Trapezoidal method velocity error in this example was 1.23 × 10 -3 m/s in the fifteenth-second measurement. Romberg's method velocity error was 0.16 × 10 -3 m/s for the same input data.
Driving wheel operation is characterized by force interactions with the ground, manifested in the form of vibrations. Signals generated by driving wheels can be analyzed in the frequency spectrum of tractor drawbar pull. The paper presents the analysis of a drawbar pull signal generated by a tractor equipped with two types of special driving wheels and standard tires. Beside the evaluation of special driving wheels’ properties according to drawbar power, the frequency spectra of measured signals were analyzed using a fast Fourier transformation. The model spectrum intervals for the standard tires, spike tires, and blade wheels were calculated according to the number of rubber lugs, blades, or spikes and compared with the experimental results. The results showed that the specific frequencies typical for blades and spikes were identified in model spectrum intervals. In the case of standard tires, the spectrum components typical for rubber lugs of the tire tread pattern were not identified. The highest amplitude of the typical frequency component was detected in the case of blades wheels, which showed the highest difference in drawbar power in comparison with the standard tires. Smaller dimensions of spikes resulted in lower amplitude and lower difference in drawbar power in comparison with the standard tires.
The application of intelligent control algorithms in the field of autonomous mobile robotics enables effective control of mobile robots with a minimal possible error. At present, most of commonly used systems to control an autonomous mobile robot are, however, too complicated to design. Our goal was to design a fuzzy controller with an optimal number of inference rules in a way to achieve the best possible level of quality of mobile robot control. The proposed controller was implemented in the mobile robot EN20, where the time of regulation and the absolute and the quadratic control surface were used to evaluate quality parameters. The analysis of the quality of control was performed with the use of a fuzzy controller with 9, 25 and 49 inference rules. We found from the results of modelling that the greatest influence on the quality of control of a mathematical model of the mobile robot had the number of inference rules of the fuzzy controller. Mathematical and graphical dependence of the quality of control on the number of inference rules was calculated from the parameters of the quality of control. The results of the research are equations of the curves of the individual parameters of control of quality, which show that for the control of the autonomous mobile robot EN 20, that the optimal fuzzy controller has 49 inference rules, triangular functions of the pertinence of individual linguistic values and it is defuzzificated by Centroid method.
Due to expansion of utilisation of photovoltaics in ordinary households, the question arises how this phenomenon affects the electric power of photovoltaic modules. The article deals with the electric power analysis of photovoltaic modules as a function of two very important factors. The first examined factor was partial shading, and the second factor was the intensity of reflected radiation. In order to determine the dependence of module power on the aforementioned parameters, a measurement system under laboratory conditions has been prepared. For identification of the reflected radiation effect on the power of the photovoltaic module, a series of measurements was performed on 7 different surfaces with the same radiation source. It is evident from obtained experimental result that the ratio of reflected irradiation on the solar module power is 1.29%. By simulation of partial shading of photovoltaic module, the decrease of 86.15% in its output power was identified.
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