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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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Automatic robot path planning tool
Rotrekl, Tomáš ; Zechmeister, Jaroslav (referee) ; Kadlec, Petr (advisor)
This bachelor’s thesis deals with the issue of robot path planning. The aim of the work is to get acquainted with the principles of robot path planning as is the creation of mazes with obstacles, expanding those obstacles, describing the environment of the maze, and using different ways to solve those mazes using the Dijkstra algorithm, A star algorithm, and the Variable Number of Dimensions Differential Evolution (VND-DE) algorithm. These algorithms are then implemented is independent toolbox created in programming language MATLAB. This tool allows as to create test tasks (mazes) and solve them using the mentioned algorithms.
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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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