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An simulation of the robot in webots and ROS
Musílek, Miloš ; Lázna, Tomáš (referee) ; Burian, František (advisor)
This work deals with the creation of a simulated manipulator with six degrees of freedom. The thesis describes simulation tools webots and Gazebo and the ROS system. The practical part deals with the creation of a simulation with a robot model and a simple environment. Subsequently, the simulated robot is coupled with the ROS system to create a controller that mimics real manipulators. The result is shown by moving an object using a set of instructions.
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Lipschitz mappings in the plane
Kaluža, Vojtěch ; Matoušek, Jiří (advisor) ; Šámal, Robert (referee)
In this thesis we consider an open question of Feige that asks whether there always exists a constantly Lipschitz bijection of an n2 -point subset of Z2 onto a regular grid [n] × [n] for every n ∈ N. We relate this question to an already resolved problem of the existence of a bounded positive measurable density in R2 that is not the Jacobian of any bilipschitz map. This problem was resolved by Burago and Kleiner [1], and independently, by McMullen [12]. We present the work of Burago and Kleiner, analyze its relation to Feige's problem and sug- gest a continuous formulation of Feige's question in a special case. Then we present the Burago-Kleiner density, make several observation about the properties of this density, and after that we construct a density that is everywhere nonrealizable as the Jacobian of a bilipschitz map. Subsequently, we discuss our continuous variant of Feige's question, provide several observation concerning it, and finally, we try to use the everywhere nonrealizable density constructed before to answer our continuous variant of Feige's question. However, this last task still remains incomplete. 1
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