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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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Foundations of geometric control theory
Čulák, Michal ; Hrdina, Jaroslav (referee) ; Vašík, Petr (advisor)
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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Finding a mechanism with (4, 7) filtration corresponding to the path geometry
Rajsiglová, Eva ; Zalabová,, Lenka (referee) ; Hrdina, Jaroslav (advisor)
The subject of this Bachelor's thesis is control theory of mechanism, the so-called trident snake robot. From a viewpoint of control theory, it is classified as a nonholonomic system whose controllability is determined by vector fields. In this thesis, input vector fields are obtained from the system of nonholonomic equations. The Lie bracket operation is applied on this vector fields. On the basis of an analysis of the results of the Lie bracket operation, the fulfillment of the definition of the generalized path geometry is verified for the particular models of the trident snake robot. Finally, Hamiltonian function and Christoffel symbols, needed to compile equations of geodesics, are calculated.
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Control Theory of robotic snakes with more than three links
Tejkal, Martin ; Návrat, Aleš (referee) ; Hrdina, Jaroslav (advisor)
The subject of this Bachelor's thesis is control theory of mechanism that simulates snake's movement. From a viewpoint of control theory the robot is classified as nonholonomic system, controllability of which is determined by vector fields. Based on nonholomic constrain a set of input vector fields is obtained from a system of nonholonomic equations. The other vector fields that are necessary for controllability of the system are derived from the set of input vector fields by application of Lie bracket operation on two input fields. This set of vector fields is further analysed in particular points of the configuration space. Finally we discuss changes that need to be done in order to describe a mechanism created by adding one, or more new links.
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Control Theory of robotic snakes with missing wheels
Reichmanová, Barbora ; Vašík, Petr (referee) ; Hrdina, Jaroslav (advisor)
This thesis looks into the mathematical description of a three-sectional robot. The thesis deals with cases of wheels missing either on the middle or the last section or solely on the middle section. At first theoretical basis is mentioned including the terms such as vector and affinne space, Lie algebra, distribution or controllable system. Subsequently, there is presented formulation of equations describing a snake robot with missing wheels, solutions of equations, calculation of Lie brackets and discussion of controllability. The calculations are demonstrated on examples of various configurations of the robot.
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Geometric optimal control of a snake robot
Vechetová, Jana ; Hrdina, Jaroslav (referee) ; Vašík, Petr (advisor)
This thesis deals with the description of robotic snake the trident snake robot. From a viewpoint of control theory the robot is classified as a nonholonomic system whose controllability is determined by vector fields. We use the operation Lie bracket to create other necessary control vector fields to ensure local controllability of this system. Then we propose the motion planning algorithm. Finally some of the motions caused by the control vector fields are verified in a simulation environment called V-rep.
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Foundations of geometric control theory
Čulák, Michal ; Hrdina, Jaroslav (referee) ; Vašík, Petr (advisor)
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 (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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