Artificial Potential Fields (APFs) constitute an intuitive tool for designing autonomous robot navigation control schemes, though they generally suffer from the existence of local minima which may trap the robot away from its desired configuration, an issue usually addressed by appropriate offline 'tuning' of the potential field's parameters. On the other side, most APF based approaches rely on a diffeomorphism to sphere worlds to handle realistic scenarios, which may be either costly to compute (e.g., conformal mappings) or requires some sort of preconditioning of the workspace (e.g., decomposition of complex geometries to simple elementary components). In this work, we first propose a constructive procedure to map multiply connected compact 2D workspaces to one or more punctured disks based on harmonic maps. Subsequently, we design an APF based control scheme along with an adaptive law for its parameters that requires no offline tuning to guarantee safe convergence to its goal configuration. Finally, an extensive simulation study is conducted to demonstrate the efficacy of the proposed control scheme.