Zero dynamics and off-tracking bounds for the path following problem of wheeled vehicles

By off-tracking bound it is meant the minimal clearance needed around a given path in order for the same to be physically feasible in avoiding possible obstacles. It depends on the path following criterion adopted and, for smooth paths and perfect tracking, it can be intended as the maximum of the off-tracking envelope given by the integral curves of the zero dynamics of the system corresponding to the tracking error zeroing manifold. Such a bound is compared with a slightly more conservative one which can be obtained from more intuitive geometric considerations