This paper brings together the concepts of navigation transformation and harmonic functions to form navigation functions that are correct-by-construction in the sense that no tuning is required. The form of the navigation function is explicitly related to the number of obstacles in the environment. This enables application of navigation functions for autonomous robot navigation in partially or fully unknown environments, with the capability of on-the-fly adjustment of the navigation function when new obstacles are discovered by the robot. Appropriate navigation controllers, applicable to robots with local, sector bounded sensing, are presented and analyzed for a~kinematic point-mass robot and then for the dynamic point-mass robot system. The closed form nature of the proposed navigation scheme provides for online, fast-feedback based navigation. In addition to the analytic guarantees, simulation studies are presented to verify the effectiveness of the methodology.