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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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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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Robotic mechanisms control
Mareček, Tomáš ; Hrdina, Jaroslav (referee) ; Vašík, Petr (advisor)
The aim of this thesis is to discuss kinematic models, their properties and control. For this task, we chose a geometric control theory approach. For a predescribed trajectory of the gripper, a straight path in particular, motion planning algorithm for the UR5e robotic arm from Universal Robots is implemented. For the description of motion, the concept of conformal geometric algebra is used. Properties of the algebra objects were thoroughly described and consequently used to propose a model of forward and reverse kinematics of UR5e. Gains and losses of this approach were discussed. The algorithms are implemented in CLUViz 7.0.
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Nonholonomic mechanisms control
Mareček, Tomáš ; Hrdina, Jaroslav (referee) ; Vašík, Petr (advisor)
This thesis deals with a control theory of nonholonomic mechanisms. Examples explaining the application of dierential geometry notions are provided. More precisely, the area of Lie groups and Lie algebras is employed. Kinematic equations are constructed for a 3-link snake-like robot and a nonholonomic control system is derived in terms of vector felds. Additional vector felds are created by the Lie bracket operation to prove local controllability of the nonholonomic system. Finally, the snake-like robot’s moves are animated in MATLAB software.
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Geometric approach in robotic snake motion control
Vechetová, Jana ; Hrdina, Jaroslav (referee) ; Vašík, Petr (advisor)
Tato diplomová práce se zabývá popisem řiditelnosti specifického robotického hada, který se nazývá trident snake robot. Tento robot je řazen mezi neholonomní systémy. Model je převeden do jazyka diferenciální geometrie a řízen pomocí vektorových polí a operace na nich zavedené (Lieova závorka). Je také uvažována aproximace řídicí distribuce. Dále jsou formulovány pohyby hada ve směru vektorových polí a jejich kombinace, které zajišťují základní pohyby v prostoru (rotace a translace). Tyto pohyby jsou na závěr simulovány v prostředí V-REP.
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Nonholonomic mechanisms geometry
Bartoňová, Ludmila ; Návrat, Aleš (referee) ; Vašík, Petr (advisor)
Tato diplomová práce se zabývá popisem kinematického modelu řízení neholonomního mechanismu, konkrétně robotického hada. Model je zkoumán prostředky diferenciální geometrie. Dále je odvozena jeho nilpotentní aproximace. Lokální říditelnost je zjištěna pomocí dimenze Lieovy algebry generované řídícími vektorovými poli a jejich Lieovými závorkami. V závěru jsou navrženy dva jednoduché řídící algoritmy, jeden pro globální a druhý pro lokální řízení, a poté následuje srovnání jednotlivých modelů.
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