This work concerns the class of wheeled mobile robots with single axis front steering. Because of the relatively low speed of these vehicles their dynamic properties have little effect on their path tracking behaviour. Their motion is, moreover, on a flat environment and can be assumed two dimensional.
The kinematics of motion of such a vehicle can be utilized for design of control strategies for maintaining path following stability. In this paper, optimal control technique is implemented to such a system. First, the state space equations governing the motion are derived. The orientation error and the offset from a path form the states and the steering angle is the control input to the system. An optimal controller to minimize the two errors and the steering angle is then sought. The conditions for the existence of the feedback matrix are discussed. The controller structure is defined in terms of the forward speed of the vehicle and, thus, has the advantage of being flexible for speed changes. Numerical illustrative examples, however, demonstrate that variation of the speed has no effect on the controller structure.
