Robot Navigation in Complex Polygonal Workspaces Using Conformal Navigation Transformations

Abstract

In this paper, a new transformation called the conformal navigation transformation is proposed to enable collision-avoidance navigation of the mobile robots on arbitrary polygonal environments. The properties of the proposed transformation and its ability to provide solutions to navigation problems for polygonal workspaces are studied. The definition of navigation functions is extended to workspaces with non-smooth boundary. Using the conformal navigation transformation and the extended navigation function, a provably correct feedback control law is derived for the motion control and obstacle avoidance of a kinematic mobile robot. In addition, a fast iterative construction method is presented to solve the proposed transformation on the complex polygonal workspaces, which reduces the multiply connected problem to multiple simply connected problems. Finally, the simulation study is presented to verify the effectiveness of the methodology.