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Local controllability of trident snake robot based on sub-Riemannian extremals


Abstract


To solve trident snake robot local controllability by differential geometry tools, we construct a privileged system of coordinates with respect to the distribution given by Pffaf system based on local nonholonomic conditions and, furthermore, we construct a nilpotent approximation of the transformed distribution with respect to the given filtration. We compute normal extremals of sub-Riemanian structure, where the Hamiltonian point of view was used. We demonstrated that the extremals of sub-Riemannian structure based on this distribution play the similar role as classical periodic imputs in control theory with respect of our mechanism.

DOI Code: 10.1285/i15900932v37suppl1p93

Keywords: local controllability; nonholonomic mechanics; planar mechanisms; sub-Riemannian geometry; differential geometry

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