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Lie groups from the point of view of kinematics and applications in robotics
Kalenský, Jan ; Kureš, Miroslav (referee) ; Tomáš, Jiří (advisor)
This diploma thesis deals with the kinematic and robotic implications of Lie theory. In the introductory section, a manifold is defined as a basic element of configuration space. The main body of the thesis deals with the definition of a structure in the configuration space - Lie group. Tangent space with vector field including a structure of Lie algebra is defined to represent velocity. These two structures are connected using exponential mapping. The conclusion of the thesis focuses on fibre space, especially considering principal bundle and principal connection. Throughout the thesis, numerous examples are presented to illustrate the terms used.
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Properties examination of complete matrix and its cofactors for symbolic calculations
Kalenský, Jan ; Krejsa, Jiří (referee) ; Březina, Tomáš (advisor)
This thesis is focused on the characteristics of a complete matrix, its application in physical analogies and exploration of suitable methods of computer generation of its cofactors. The opening section covers the key elements of matrix algebra, emphasising cofactors, and their attributes. The next segment examines the generalization of circuit theory for the purposes of multidisciplinary modeling and detailed analysis of a complete matrix and its properties. Finally, the previous findings and the characteristics of a complete matrix and its cofactors are applied to the deduction of elementary transfers, explained on examples and symbolically utilised in computer generation.
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Lie groups from the point of view of kinematics and applications in robotics
Kalenský, Jan ; Kureš, Miroslav (referee) ; Tomáš, Jiří (advisor)
This diploma thesis deals with the kinematic and robotic implications of Lie theory. In the introductory section, a manifold is defined as a basic element of configuration space. The main body of the thesis deals with the definition of a structure in the configuration space - Lie group. Tangent space with vector field including a structure of Lie algebra is defined to represent velocity. These two structures are connected using exponential mapping. The conclusion of the thesis focuses on fibre space, especially considering principal bundle and principal connection. Throughout the thesis, numerous examples are presented to illustrate the terms used.
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Properties examination of complete matrix and its cofactors for symbolic calculations
Kalenský, Jan ; Krejsa, Jiří (referee) ; Březina, Tomáš (advisor)
This thesis is focused on the characteristics of a complete matrix, its application in physical analogies and exploration of suitable methods of computer generation of its cofactors. The opening section covers the key elements of matrix algebra, emphasising cofactors, and their attributes. The next segment examines the generalization of circuit theory for the purposes of multidisciplinary modeling and detailed analysis of a complete matrix and its properties. Finally, the previous findings and the characteristics of a complete matrix and its cofactors are applied to the deduction of elementary transfers, explained on examples and symbolically utilised in computer generation.
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