A control synthesis problem for planar motion of a wheeled robot is considered. The control goal is to bring the robot to a given path and to stabilize motion of a certain target point along it. The trajectory is assumed to be an arbitrary smooth curve with bounded curvature. A simple actuator is introduced into the vehicle model, and the rate of angular rotation of the steering wheels is taken as the control, which is subject to two-sided constraints. In addition, because of phase constraints, the system under consideration is hybrid: at different stages of its motion, it is governed by different systems of differential equations. A control law is synthesized for an arbitrary target path. Qualitative analysis of the straight line case is given. Results of numerical experiments are presented.
