 
Summary: A matrix Lie group of Carnot type for filiform
subRiemannian structures and its application
to control systems in chained form
Claudio Altafini \Lambda
Optimization and Systems Theory
Royal Institute of Technology
SE10044, Stockholm, Sweden
tel. +46 8 790 7507
fax +46 8 225 320
altafini@math.kth.se
March 13, 2000
Abstract
A Carnot group G is a simply connected graded nilpotent Lie group
endowed a leftinvariant distribution generating the Lie algebra g of G.
Here we show that the quotient manifold of a filiform Carnot group by
the subgroup generated by its characteristic line field is projectively
abelian. The result is used to show how a class of bilinear control
systems have an intrinsic linear behavior.
1 Introduction and motivation
The kinematic model of an ntrailer i.e. a carlike vehicle pulling an arbitrary
