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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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Robotic mechanisms control
Mareček, Tomáš ; Hrdina, Jaroslav (referee) ; Vašík, Petr (advisor)
The aim of this thesis is to discuss kinematic models, their properties and control. For this task, we chose a geometric control theory approach. For a predescribed trajectory of the gripper, a straight path in particular, motion planning algorithm for the UR5e robotic arm from Universal Robots is implemented. For the description of motion, the concept of conformal geometric algebra is used. Properties of the algebra objects were thoroughly described and consequently used to propose a model of forward and reverse kinematics of UR5e. Gains and losses of this approach were discussed. The algorithms are implemented in CLUViz 7.0.
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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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Applications of fractional calculus in control theory
Kiša, Daniel ; Nechvátal, Luděk (referee) ; Kisela, Tomáš (advisor)
Tato bakalářská práce se zabývá matematickou teorií zlomkového kalkulu a jeho aplikacemi v oblasti teorie řízení. V první části jsou uvedeny základy řízení lineárních časově invariantních systémů, a jsou dále diskutovány tři klasické úlohy, a to určení stability, řiditelnosti a pozorovatelnosti. V druhé části je zaveden Riemann-Liouvillův a Caputův diferintegrál a jsou formulovány výše zmíněné problémy pro lineární časově invariantní systém zlomkého řádu. Opět jsou diskutována řešení a jejich odvození.
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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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Control theory in robotics
Bartoňová, Ludmila ; Hrdina, Jaroslav (referee) ; Vašík, Petr (advisor)
This thesis deals with the local control of a snake robot. The model control system is derived from kinematic equations and local controllability is investigated by means of Lie brackets. Then we describe some elementary motions along flow of the controlling vector fields and show the meaning of a periodic input. Another control model is formed by an approximation of the first system. Afterwards, both systems are compared by means of sub-Riemannian metric and thus the qualitative analysis is made.
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