Navigation functions provide both path and motion planning, which can be used to ensure obstacle avoidance and convergence in the sphere world. When dealing with complex and realistic scenarios, constructing a transformation to the sphere world is essential and, at the same time, challenging. This work proposes a novel transformation termed the conformal navigation transformation to achieve collision-free navigation of a robot in a workspace populated with obstacles of arbitrary shapes. The properties of the conformal navigation transformation, including uniqueness, invariance of navigation properties, and no angular deformation, are investigated, which contribute to the solution of the robot navigation problem in complex environments. Based on navigation functions and the proposed transformation, feedback controllers are derived for the automatic guidance and motion control of kinematic and dynamic mobile robots. Moreover, an iterative method is proposed to construct the conformal navigation transformation in a multi-connected workspace, which transforms the multi-connected problem into multiple single-connected problems to achieve fast convergence. In addition to the analytic guarantees, simulation studies verify the effectiveness of the proposed methodology in workspaces with non-trivial obstacles.

翻译：导航功能提供路径和运动规划,可用于确保在球体世界中避免和融合障碍。在应对复杂和现实的情景时,构建向球体世界的转型至关重要,同时也具有挑战性。这项工作提议进行新的转变,称为在工作空间实现不碰撞导航的同步导航转换,在工作空间中,机器人有任意形状障碍,实现无碰撞导航。对一致性导航转换的特性,包括独一性、航行特性的不稳定性以及没有角形变形,都进行了调查,这有助于解决复杂环境中的机器人导航问题。根据导航功能和拟议变形,为运动和动态移动机器人的自动导航和运动控制提供了反馈控制。此外,还提议了一种迭接方法,在多连接的工作空间中构建一致性导航转换,将多连接的问题转化为多连接的单一问题,以便快速融合。除了分析保证外,模拟研究还核实了在非三重障碍的工作场所拟议方法的有效性。