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Local control based on chosen symmetries of carnot group
Frolík, Stanislav ; Galaev, Anton (oponent) ; Zelenko, Igor (oponent) ; Hrdina, Jaroslav (vedoucí práce)
We study the control theory on a specific Carnot group from geometric viewpoint. As an example, we introduce a new class of planar mechanisms, named robotic worms. These mechanisms brings a new class of control problems to the non–holonomic mechanics. We study the first nontrivial instance, which is the 2–link case. From the control theory viewpoint we study a Carnot group equipped with a (4,6) filtration. To solve the optimal control problem we introduce our own design of control. This method is based on a choice of an additional geometric structure on top of the control algebra, mainly CR-structure. Then we can choose an initial class of geodesics to be extended to the whole configuration space.
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