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Geometric approach in robotic snake motion control
Vechetová, Jana ; Hrdina, Jaroslav (oponent) ; Vašík, Petr (vedoucí práce)
This thesis deals with the description of controllability of a specific robotic snake named trident snake robot. This robot is classified as a nonholonomic system. The kinematics model is converted into the language of differential geometry and controlled by vector fields and their operation Lie bracket. Approximation of the controlling distribution is also considered. Next, vector field motions are described and also their combinations which provide basic planar surface motions (rotation and translation). Finally, these motions caused by vector fields are simulated in V-REP.
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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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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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Geometric control of nonholonomic systems
Ramasubramaniyan, Sri Ram Prasath ; Vašík, Petr (oponent) ; Návrat, Aleš (vedoucí práce)
This thesis focuses on a mathematical model for a three-body space robot with the objective of reconfiguring its structure using only internal joint torques. The aim is to minimize fuel consumption and achieve efficient reconfiguration without relying on external actuators. The system exhibits one holonomic and non-holonomic constraint, making the analysis and control design challenging. To address the complexity of the non-holonomic system, the local behavior is studied through the nilpotent approximation. The thesis emphasizes understanding the nilpotent approximation and constructing the nilpotent system of the space robot using algebraic coordinates, along with transforming them into exponential coordinates within the Maple environment.
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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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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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Geometric approach in robotic snake motion control
Vechetová, Jana ; Hrdina, Jaroslav (oponent) ; Vašík, Petr (vedoucí práce)
This thesis deals with the description of controllability of a specific robotic snake named trident snake robot. This robot is classified as a nonholonomic system. The kinematics model is converted into the language of differential geometry and controlled by vector fields and their operation Lie bracket. Approximation of the controlling distribution is also considered. Next, vector field motions are described and also their combinations which provide basic planar surface motions (rotation and translation). Finally, these motions caused by vector fields are simulated in V-REP.
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