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This work proposes a novel transformation termed the conformal navigationtransformation to achieve collision-free navigation of a robot in a workspacepopulated with arbitrary polygonal obstacles. The properties of the conformalnavigation transformation in the polygonal workspace are investigated in thiswork 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 complexpolygonal environments. %which facilitates the navigation of robots in complexenvironments. The definition of the navigation function is generalized toaccommodate non-smooth obstacle boundaries. Based on the proposedtransformation and the generalized navigation function, a provably correctfeedback controller is derived for the automatic guidance and motion control ofthe kinematic mobile robot. Moreover, an iterative method is proposed toconstruct the conformal navigation transformation in a multi-connectedpolygonal workspace, which transforms the multi-connected problem into multiplesingle-connected problems to achieve fast convergence.In addition to theanalytic guarantees, the simulation study verifies the effectiveness of theproposed methodology in a workspace with non-trivial polygonal obstacles.

Mobile Robot Navigation in Complex Polygonal Workspaces Using Conformal Navigation Transformations