  The paper considers a motion control problem for kinematic models of
nonholonomic wheeled systems. The class of maneuverable wheeled systems is
defined consisting of systems that can follow any sufficiently smooth non-stop
trajectory on the plane. A sufficient condition for maneuverability is
obtained. The design of control law that stabilizes motion along the desired
trajectory on the plane is performed in two steps. On the first step the
trajectory on the configuration manifold of the system and the input function
are constructed that ensure the exact reproduction of the desired trajectory on
the plane. The second step is the stabilization of the constructed trajectory
on the configuration manifold of the system. For this purpose a recursive
procedure is used that is a version of backstepping algorithm meant for
non-stationary systems nonlinearly depending on input. The procedure results in
the continuous memoryless feedback that stabilizes the trajectory on the
configuration manifold of the system. As an example the motion control problem
for a truck with multiple trailers is considered. It is shown that the proposed
control law stabilizes the desired trajectory of the vehicle on the plane for
all initial states of the system from some open dense submanifold of the
configuration manifold, i.e., almost globally. The statement takes place both
for a truck pulling any number of trailers in a forward direction and for a
truck pushing any number of trailers in a backward direction. The latter result
is the solution of the intuitively hard problem of the road train reverse
motion control. The effectiveness of the proposed control is demonstrated by
simulation. Animated examples are presented at Sergei V. Gusev Web Page.
