A new line tracking method for nonholonomic vehicles

We investigate the problem of finding an algorithm for the movement of a vehicle under the nonholonomic constraint to track a given directed straight line without allowing any spinning motion. We propose a new principle of computing the derivative of path curvature as a linear combination of the current vehicle path curvature, vehicle orientation error, and positional error. We call this function the steering function. By linearization we find an optimal selection of parameters for critically damped motions and obtain a single parameter, σ, for tracking, which we call smoothness. The uniform asymptotic stability of the feedback rule is proved through a Lyapunov function. Numerous simulation results as well as experimental results obtained on the autonomous robot Yamabico at the Naval Postgraduate School are included to show the effectiveness of this method