This work proposes a novel transformation termed the conformal navigation transformation to achieve collision-free navigation of a robot in a workspace populated with arbitrary polygonal obstacles. The properties of the conformal navigation transformation in the polygonal workspace are investigated in this work as well as its capability to provide a solution to the navigation problem. %The properties of the conformal navigation transformation are investigated, which contribute to the solution of the robot navigation problem in complex polygonal environments. %which facilitates the navigation of robots in complex environments. The definition of the navigation function is generalized to accommodate non-smooth obstacle boundaries. Based on the proposed transformation and the generalized navigation function, a provably correct feedback controller is derived for the automatic guidance and motion control of the kinematic mobile robot. Moreover, an iterative method is proposed to construct the conformal navigation transformation in a multi-connected polygonal workspace, which transforms the multi-connected problem into multiple single-connected problems to achieve fast convergence.In addition to the analytic guarantees, the simulation study verifies the effectiveness of the proposed methodology in a workspace with non-trivial polygonal obstacles.
翻译:这项工作提议了一种新型的转变,称为在拥有任意多边形障碍的工作场所对机器人进行不碰撞的导航转换,目的是实现一个机器人在具有任意多边形障碍的工作场所的无碰撞导航。在这项工作中,将调查多边形工作空间的一致导航转换的特性及其解决导航问题的能力。%对符合导航转换的特性进行了调查,这有助于解决复杂多边形环境中的机器人导航问题。%有助于在复杂的多边形环境中对机器人进行导航。导航功能的定义是通用的,以适应非单向障碍边界。根据拟议的转换和普遍导航功能,为运动式移动机器人的自动指导和运动控制,将产生一个可察觉到准确的反馈控制器。此外,还提议了一种迭接方法,在多连接的多连接多边形工作空间中,将多连接的问题转化为多个单一连接的问题,以便实现快速趋同。除了分析保证外,模拟研究还核实了在非三边形多边形多边形障碍的工作场所拟议方法的有效性。