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Unlike some other reproductions of classic texts (1) We have not
used OCR(Optical Character Recognition), as this leads to bad
quality books with introduced typos. (2) In books where there are
images such as portraits, maps, sketches etc We have endeavoured to
keep the quality of these images, so they represent accurately the
original artefact. Although occasionally there may be certain
imperfections with these old texts, we feel they deserve to be made
available for future generations to enjoy.
Nonholonomic systems are control systems which depend linearly on
the control. Their underlying geometry is the sub-Riemannian
geometry, which plays for these systems the same role as Euclidean
geometry does for linear systems. In particular the usual notions
of approximations at the first order, that are essential for
control purposes, have to be defined in terms of this geometry. The
aim of these notes is to present these notions of approximation and
their application to the motion planning problem for nonholonomic
systems.
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