Planejamento periódico de trajetórias de sistemas afins sem arrasto em grupos de Lie compactos / Periodic motion planning of trajectories for control-affine driftless systems in compact Lie groups
AUTOR(ES)
Gabriel Cueva Candido Soares de Araujo
FONTE
IBICT - Instituto Brasileiro de Informação em Ciência e Tecnologia
DATA DE PUBLICAÇÃO
08/03/2012
RESUMO
We treat the periodic motion planning problem: given a periodic trajectory of a control-affine driftless system in a compact and connected Lie group G and an initial condition in G, find another trajectory of the same system satisfying the initial condition given and that asymptotically tracks the periodic trajectory. We solve this problem locally (for initial conditions in a neighborhood of some point of the periodic trajectory) when G is semisimple and the system is Lie-determined (i.e. controllable), and only for a class of periodic trajectories (which we call \"regular\"). Finally we present a set of sufficient conditions to ensure the existence of such trajectories.
ASSUNTO(S)
compact lie groups control-affine driftless systems grupos de lie compactos rastreamento de trajetórias sistemas afins sem arrasto trajectory tracking
