Given a path of nonconstant curvature, local asymptotic stability can be proven for the general n trailer whenever the curvature can be considered as the output of an exogenous dynamical system. The controllers that provide convergence to zero of the tracking error chosen for the path-following problem are composed of a prefeedback that input-output linearizes the system, plus a linear controller.
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Claudio Altafini (2002) studied this question.
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