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Geometric control of nonholonomic systems
Ramasubramaniyan, Sri Ram Prasath ; Vašík, Petr (referee) ; Návrat, Aleš (advisor)
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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Numerical solution of a stochastic model of a ball-type vibration absorber
Fischer, Cyril ; Náprstek, Jiří
The mathematical model of a ball-type vibration absorber represents a non-linear differential system which includes non-holonomic constraints. When a random ambient excitation is taken into account, the system has to be treated as a stochastic deferential equation. Depending on the level of simplifcation, an analytical solution is not practicable and numerical solution procedures have to be applied. The contribution presents a simple stochastic analysis of a particular resonance effect which can negatively influence efficiency of the absorber.
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