to this paper we investigate the problem of finding an algorithm for the movement of a vehicle under the nonholonomic constraint to track a given directed 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, and positional difference. We call this function 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. Numerous simulation results are included to show the effectiveness of this method.
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