A reconstruction of admissible reference signals for the inner dynamics upon a prescribed output reference of a dynamical system is a one of the key problems stated in the control theory. We address this problem with respect to a class of driftless dynamical systems representing nonholonomic kinematics of the N-trailers equipped with the on-axle and off-axle hitching, including difficult cases of the differentially non-flat and nonminimum-phase kinematics. Given a prescribed admissible reference path or trajectory for the last trailer’s posture (treated as a reference output), we analyse possible solutions to the reconstruction problem for different types of the reference output. We propose a computational procedure to reconstruct the corresponding references (in a continuous domain of some parametrizing variable) for the joint angles of the N-trailer vehicles comprising an arbitrary number of segments interconnected by any type of hitching. In particular, we show how to find an admissible solution to the reconstruction problem, that is, the one which does not exhibit a jackknife effect, by appropriate searching in a set of all the possible (at least $2^N$) solutions. The proposed computational method is formally explained and numerically verified for the 3-trailer kinematics equipped with various types of hitching.

在控制系统中提出的关键问题之一是在动力学系统的规定输出参考下重建内部动力学的允许参考信号。我们针对一类无漂移动力系统解决了这个问题，该系统代表装备有轴上和轴外挂接的N挂车的非完整运动学，包括非平坦和非最小相位运动学的困难情况。给定最后一个拖车的姿势的规定允许参考路径或轨迹（作为参考输出），我们分析了针对不同类型参考输出的重构问题的可能解决方案。我们提出了一种计算程序，以重新构造N挂车车辆的关节角的相应参考（在一些参数化变量的连续域中），该N挂车的关节角包括通过任意类型的挂钩相互连接的任意数量的路段。特别是，我们展示了如何找到通过适当地搜索所有可能的集合（至少是不出现折刀效应的重建问题）的一种可接受的解决方案$2^{ñ}$）解决方案。对于配备有各种类型的挂钩的三轮拖车运动学，该提议的计算方法已得到正式解释和数值验证。