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Dynamics of Snake Robots
Kubiena, Jaromír ; Doupovec, Miroslav (referee) ; Návrat, Aleš (advisor)
In this thesis, we deal with the mathematical description of the kinematics and the dynamics of mechanical systems. Then we focus on the particular mechanical system which is the Square robot with four legs with active joints and passive wheels, which moves on horizontal plane. The kinematics of the mechanical system is described by the control matrix, then we use it to express the equations of motion. We compute the dynamics the robot by using Lagrange equations. We verify that the mechanical system is nonholonomic constrained and we verify controllability by using Lie bracket and distribution. We find the singular postures 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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Lie groups and their physical applications
Kunz, Daniel ; Kureš, Miroslav (referee) ; Tomáš, Jiří (advisor)
In this thesis I describe construction of Lie group and Lie algebra and its following usage for physical problems. To be able to construct Lie groups and Lie algebras we need define basic terms such as topological manifold, tensor algebra and differential geometry. First part of my thesis is aimed on this topic. In second part I am dealing with construction of Lie groups and algebras. Furthermore, I am showing different properties of given structures. Next I am trying to show, that there exists some connection among Lie groups and Lie algebras. In last part of this thesis is used just for showing how this apparat can be used on physical problems. Best known usage is to find physical symmetries to establish conservation laws, all thanks to famous Noether theorem.
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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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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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Geometric control of a snake-like robot
Jašek, Dominik ; Hrdina, Jaroslav (referee) ; Návrat, Aleš (advisor)
This thesis deals with the nonholonomic mechanics, description of nonholonomic constraints and the control algorithms. In particular it focuses on snake with 4 links. From kinematic equations we derive elementary vector fields, later four more are added thanks to Lie bracket. Using these vector fields we are able to devise an algorithm for controling the snake. Furthermore, the thesis also includes a serpenoid input applicated in the simulation enviroment V-REP.
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The Frölicher-Nijenhuis bracket and its applications in geometry and calculus of variations
Šramková, Kristína ; Tomáš, Jiří (referee) ; Kureš, Miroslav (advisor)
This Master's thesis clarifies the significance of Frölicher-Nijenhuis bracket and its applications in problems of physics. The basic apparatus for these applications is differential geometry on manifolds, tensor calculus and differential forms, which are contained in the first part of the thesis. The second part summarizes the basic theory of calculus of variations on manifolds and its selected applications in the field of physics. The last part of the thesis is devoted to the applications of Frölicher-Nijenhuis bracket in the derivation of Maxwell's equations and to the description of the geometry of ordinary differential equations.
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