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Nonholonomic mechanisms geometry
Bartoňová, Ludmila ; Návrat, Aleš (oponent) ; Vašík, Petr (vedoucí práce)
This master's thesis deals with a description of a kinematic control model of nonholonomic mechanism, namely the robotic snake. The model is analysed by means of differential geometry. Next, its nilpotent approximation is derived. Local controllability is checked by the dimension of Lie algebra generated by the controlling vector fields and their Lie brackets. In the end, two simple motion planning algorithms, one on global and one on local control, are proposed, and the comparison of models is discussed.
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Matematické metody zabezpečení přenosu digitálních dat
Bartušek, Petr ; Kureš, Miroslav (oponent) ; Vašík, Petr (vedoucí práce)
Tato diplomová práce se zabývá analýzou zabezpečení digitálních dat pomocí CRC. V práci je popsán princip bezpečnostního kódování, zejména pak zabezpečení dat pomocí CRC, u něhož je vysvětlen matematický princip zabezpečení, softwarová implementace a popis využívaných generujících polynomů. Hlavním cílem práce je pak testování nedetekovaných chyb a zjištění jejich počtu pro následný výpočet pravděpodobnosti vzniku nedetekované chyby. Práce je doplněna o několik programů naprogramovaných v prostředí Matlab.
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Geometrické struktury založené na kvaternionech.
Floderová, Hana ; Vašík, Petr (oponent) ; Hrdina, Jaroslav (vedoucí práce)
Geometrickou strukturou nazýváme dvojici (V, G), kde V je vektorový prostor a G je podgrupa GL(V), což je množina všech matic přechodu. V této práci klasifikujeme ty struktury, které jsou založeny na vlastnostech kvaternionů. Geometrické struktury založené na kvaternionech nazýváme trojné struktury. Jsou to čtyři struktury s vlastnostmi podobnými kvaternionům. Kvaterniony jsou vytvořeny z reálných čísel přidáním tří komplexních jednotek. Kvaterniony zapisujeme ve tvaru a+bi+cj+dk.
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Geodesic curves and their applications
Orgoník, Svetoslav ; Hrdina, Jaroslav (oponent) ; Vašík, Petr (vedoucí práce)
The aim of the thesis is to give a survey of basic results from the classical theory of curves. A special attention will be paid to geodesics and their properties. In particular, we treat geodesics on some special surfaces. We treat one application with animations. All examples will be illustrated by pictures, which were drawn by means of mathematical software.
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Foundations of geometric control theory
Čulák, Michal ; Hrdina, Jaroslav (oponent) ; Vašík, Petr (vedoucí práce)
This bachelor thesis deals with the description of algorithm for motion planning of trident snake robot. His model is created by means of differential geometry. The controllability of the robot is provided by Lie algebra, generated by elementary vector fields and their Lie bracket. The system is approximated by nilpotent approximation. In this thesis is proposed and described algorithm of motion planning with piecewise constant input. This algorithm is further derived for trident snake robot. Finally, selected motions of trident snake robot are simulated and portrayed in enviroment called MATLAB.
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Výpočty v geometrických algebrách
Tomešová, Tereza ; Vechetová, Jana (oponent) ; Vašík, Petr (vedoucí práce)
Tato práce se zabývá výpočty v geometrických algebrách, a jejich ukázkou v softwarovém prostředí CLUCalc na konkrétním příkladě. V prvé řadě seznamuje se základními pojmy a vlastnostmi vektorového prostoru, skalárního součinu a Cliffordovy algebry. Dále je zde zaveden pojem geometrická algebra, součiny a operace geometrické algebry. Tyto získané pojmy jsou poté demonstrovány na konkrétním příkladě, tj. na translaci a rotaci sféry po dané křivce, v softwarovém prostředí CLUCalc.
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Geometrically controlled snake-like robot model
Shehadeh, Mhd Ali ; Návrat, Aleš (oponent) ; Vašík, Petr (vedoucí práce)
This master’s thesis describes equations of motion for dynamic model of nonholonomic constrained system, namely the trident robotic snakes. The model is studied in the form of Lagrange's equations and D’Alembert’s principle is applied. Actually this thesis is a continuation of the study going at VUT about the simulations of non-holonomic mechanisms, specifically robotic snakes. The kinematics model was well-examined in the work of of Byrtus, Roman and Vechetová, Jana. So here we provide equations of motion and address the motion planning problem regarding dynamics of the trident snake equipped with active joints through basic examples and propose a feedback linearization algorithm.
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Game Theory in Waste Management
Osička, Ondřej ; Vašík, Petr (oponent) ; Hrdina, Jaroslav (vedoucí práce)
In this thesis, a game-theoretic model representing a decision-making situation in the waste management is created as a noncooperative game representing the conflict of waste processors and a cooperative game representing the conflict of waste producers. For the conflict of waste processors, the Nash equilibria are used to find stable strategies on gate fee values, which serve as a good prediction for the future. To specify the strategy sets, a lower bound and an upper bound are determined. For the conflict of waste producers, assuming a cooperation among all of them, a cost distribution is determined using the Shapley value and the nucleolus. For more producers, approximation algorithms for the Shapley value and the nucleolus are developed. These algorithms are based on an assumption that distant producers can not influence each other. The model is applied to a situation in the Czech Republic. For the conflict of waste processors, one Nash equilibrium is found. For the conflict of waste producers, some producers with high potential in cooperation are recognized.
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Geometric algebra applications
Machálek, Lukáš ; Návrat, Aleš (oponent) ; Vašík, Petr (vedoucí práce)
This diploma thesis deals with geometric algebra for conics (GAC) in autonomous navigation, presented on robot movement in a tube. First, the theoretical concepts are introduced. Consequently, the representations of conics in GAC are presented. Then an engine is implemented, which is capable of performing basic operations in GAC including displaying conics, which are entered in GAC context. In the end an algorithm is presented, which estimates the tube axis using points, placed into space from image, where we place center of an ellipse, which is obtained by image filter and fitting algorothm.
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