Considered is the quazi-optimal control design problem for planar motion of a wheeled
robot. The control objective is to place the reference point in the prespecied trajectory
and to stabilize the motion of the reference point along this trajectory. The trajectory
is a line. In the mathematical model under consideration, the current curvature of the
trajectory of the reference point is taken as control. The control is subject to two-sided
constraints due to limitations on the steering angle of the front wheels. For the control law
proposed, the attraction domain in the space distance to the trajectoryangle deviation
is constracted. For all initial points from the interior region of this domain to assure xed
time stability. Numerical examples are given to illustrate the theoretical results.