A circle tracking method for nonholonomic vehicles

In this paper a circle tracking algorithm is proposed for vehicles under the nonholonomic constraint using the curvature controlling principle. The algorithm is derived for controlling the movement of the vehicle to track a given directed circle without allowing any spinning motion. The derivative of path curvature is computed as a linear function of the current vehicle path curvature, vehicle orientation, and positional difference. This function is called a steering function. This is a generalization of the algorithm that has been previously developed by the authors for the straight line tracking problem. By linearization an optimal selection of parameters is found for critically damped motions and a single parameter <(sigma)over cap> for tracking is obtained called smoothness. This method is simple and is applicable to numerous motion control problems. To verify the effectiveness and usefulness of this steering function method for tracking a circular path, numerous simulation results are presented.