Local geometric control of a certain mechanism with the growth vector (4,7)
Jaroslav Hrdina, Lenka Zalabova
TL;DR
This paper investigates the local controllability and extremal trajectories of a (4,7) growth vector mechanism using nilpotent approximation, contributing to control theory on Lie groups.
Contribution
It provides solutions and examples of extremal trajectories for the (4,7) mechanism, advancing understanding of control on Lie groups.
Findings
Characterization of controllability for the (4,7) mechanism
Explicit solutions for extremal trajectories
Illustrative examples demonstrating control properties
Abstract
We study local control of the mechanism with the growth vector (4,7). We study controllability and extremal trajectories on the nilpotent approximation as an example of the control theory on Lie group. We give solutions of the system an show examples of local extremal trajectories.
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