The synthesis control problem for the plane motion of a wheeled robot with con-
strained control resource is studied. The goal of the control is to bring the robot to an assigned
curvilinear trajectory and to stabilize its motion along it. A new change of variable is suggested
that reduces the problem of stabilizing robot’s motion to that of stabilizing the zero solution in
the form that admits feedback linearization. A control law stabilizing robot’s motion along an
arbitrary curvilinear target trajectory is synthesized. For a straight target path, the closed-loop
system is shown to be asymptotically stable for any initial conditions except for the case where
the initial direction of motion is perpendicular to the target path.