  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.
