Abstract

We consider a kinematic model of a mobile robot with a trailer moving on a homogeneous plane. The robot can move back and forth and make a pivot turn. For this model, we pose the following optimal control problem: transfer the “robot–trailer” system from an arbitrarily given initial configuration into an arbitrarily given final configuration so that the amount of maneuvering is minimal. By a maneuver we mean a functional that defines a trade-off between the linear and angular robot motion. Depending on the trailer–robot coupling, this problem corresponds to a two-parameter family of optimal control problems in the 4-dimensional space with a 2-dimensional control.

We propose a nilpotent approximation method for the approximate solution of the problem. A number of iterative algorithms and programs have been developed that successfully solve the posed problem in the ideal case, namely, with no state constraints. Based on these algorithms, we propose a dedicated reparking algorithm that solves a particular case of the problem where the initial and final robot position coincide and takes into account a state constraint on the trailer’s turning angle occurring in real systems.

中文翻译：

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基于幂等逼近的带拖车移动机器人控制

摘要

我们考虑带有在均匀平面上移动的拖车的移动机器人的运动学模型。机器人可以来回移动并旋转。对于此模型，我们提出了以下最佳控制问题：将“机器人-拖车”系统从任意给定的初始配置转换为任意给定的最终配置，以使操纵量最小。操纵是指定义线性和角度机器人运动之间的权衡的功能。根据挂车与机器人的耦合关系，该问题对应于带有二维控制的4维空间中的最优控制问题的两参数系列。

对于该问题的近似解，我们提出了一种幂等近似方法。已经开发了许多迭代算法和程序，它们在理想情况下，即没有状态约束，成功地解决了所提出的问题。基于这些算法，我们提出了一种专用的重新停车算法，该算法解决了机器人初始位置和最终位置重合的问题的特殊情况，并考虑了在实际系统中出现的对拖车转弯角度的状态约束。