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 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.
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.
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