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Control theory in robotics
Bartoňová, Ludmila ; Hrdina, Jaroslav (referee) ; Vašík, Petr (advisor)
This thesis deals with the local control of a snake robot. The model control system is derived from kinematic equations and local controllability is investigated by means of Lie brackets. Then we describe some elementary motions along flow of the controlling vector fields and show the meaning of a periodic input. Another control model is formed by an approximation of the first system. Afterwards, both systems are compared by means of sub-Riemannian metric and thus the qualitative analysis is made.
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Algebra of dual quaternions in image analysis
Hrubý, Jan ; Návrat, Aleš (referee) ; Hrdina, Jaroslav (advisor)
This work has two goals. Firstly it is to acquaint the reader with the classical use of quaternions and dual quaternions in geometry. Secondly the generalization of the Fourier transform into the set of dual quaternions. At first it goes into algebraic properties and structure of quaternions and ways of their inscriptions. Later dual numbers are introduced and consecutively with their help dual quaternions. Then the work deals with description of rotations and translations using quaternions and dual quaternions, that enable their easy description. Finally the discreet dual quaternion Fourier transform is defined, and for its effective calculation the algorithm is derived, which is then brought into effect as a code in program environment MATLAB.
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Application of cooperative game theory in Cournot oligopoly
Eryganov, Ivan ; Mazal,, Jan (referee) ; Hrdina, Jaroslav (advisor)
This Master’s thesis deals with the application of cooperative game theory for solving the problems of Cournot's oligopolies. The knowledge of oligopoly theory and game theory has been elaborated to build a model describing the behavior of companies at a market that meets the preconditions of Cournot's oligopoly. The definition of cooperative game is based on the -characteristic function, which takes into account, compared to classical methods, that companies which are not in the coalition are pursuing their own profits, not suppressing coalition positions. The properties of the resulting cooperative games are examined in detail, focusing on monotony and convexity. Several theorems about these properties have been derived and their economic interpretations are given. Also, the question of calculation of the -characteristic function using the best-reply dynamics algorithm is being solved, and its convergence for a given type of games is justified. The model is applied to data from the oil market, which is further characterized by the results of the cooperative game.
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Two person quantum game theory
Krajný, Matěj ; Vašík, Petr (referee) ; Hrdina, Jaroslav (advisor)
This thesis presents introductuion to mathematical notation of quantum states, furthermore foucuses on deeper understanding of their representation. We broaden a clasical game of two players Prisoners dilema by adding quantum strategies. And we observe changes of equilibrium in comparison to clasical game.
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Geometric control of a snake-like robot
Jašek, Dominik ; Hrdina, Jaroslav (referee) ; Návrat, Aleš (advisor)
This thesis deals with the nonholonomic mechanics, description of nonholonomic constraints and the control algorithms. In particular it focuses on snake with 4 links. From kinematic equations we derive elementary vector fields, later four more are added thanks to Lie bracket. Using these vector fields we are able to devise an algorithm for controling the snake. Furthermore, the thesis also includes a serpenoid input applicated in the simulation enviroment V-REP.
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Voronoi cell constructions on the map
Čermák, Jan ; Hrdina, Jaroslav (referee) ; Pavlík, Jan (advisor)
This bachelor’s thesis deals with study of Voronoi cell and its representation in Voronoi diagrams and their construction on the model of Earth’s surface. At first, Voronoi diagrams and their characteristics are explained in a plane, we describe their construction using Fortune’s algorithm, then spherical geometry is explained. Then we take a look at some equations that are useful for calculating on a sphere, and we use them for calculating distances on Earth, which we approximate with a sphere. Finally we apply Fortune’s algorithm on a sphere, we explain the principles of construction of Voronoi diagrams with this algorithm on a sphere and changes compared to the planar case that must be taken care of. The goal of the thesis is to display Voronoi diagram on Google maps, thus we work with Google Maps API.
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Matrices, Determinant and Body Volume
Šomplák, Radovan ; Hrdina, Jaroslav (referee) ; Vašík, Petr (advisor)
In his thesis describes the basic properties of matrices, determinants and their use in display issues between vector spaces. In the final chapters devoted to determinants and its applications, which indicates the relation between determinants and calculation of volume. Subsequently determinanti describes how to use in calculating the elements using multiple integrals. Another possible application is the so-called Cramerovo rule which allows us to solving systems of linear equations.
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Image corrections by CGA
Machálek, Lukáš ; Hrdina, Jaroslav (referee) ; Vašík, Petr (advisor)
This thesis deals with conformal geometric algebra (CGA) in image processing. We focus on correct definitions of notions in geometric algebra, which we use for correcting image defects. First, the concepts of vector space are mentioned, then, the properties of geometric algebra are observed. Consequently, the 3D point is conformaly embedded into CGA, thereafter, another geometric objects are described with their representations in null spaces. In the end, the thesis deals with object transformation and with image defects correction.
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General Codes with m Marks
Holešovský, Jan ; Hrdina, Jaroslav (referee) ; Skula, Ladislav (advisor)
This bachelor's thesis is concerned with results of error-correcting codes theory, which deals with detection and correction of errors, that arise during communication by means of these codes. The aim of this thesis is the explanation of the theory above in absolute generality, followed by detail view of some significant codes. Using linear algebra over finite fields, we will introduce an error-corecting code like a set with structure, whose characters considerably simplify the detection and correction of errors. The knowledge, that was acquired for general codes, is applied to well-known binary codes at the end of the thesis (ie. Hamming codes and Golay code). With these codes are demonstrated their properties, that sort these codes to the most important binary codes.
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