Autonomous navigation in unknown environments with the intent of exploring all traversable areas is a significant challenge for robotic platforms. In this paper, a simple yet reliable method for exploring unknown environments is presented based on bio-inspired reactive control and metric-topological planning. The reactive control algorithm is modeled after the spatial decomposition of wide and small-field patterns of optic flow in the insect visuomotor system. Centering behaviour and small obstacle detection and avoidance are achieved through wide-field integration and Fourier residual analysis of instantaneous measured nearness respectively. A topological graph is estimated using image processing techniques on a continuous occupancy grid. Node paths are rapidly generated to navigate to the nearest unexplored edge in the graph. It is shown through rigorous field-testing that the proposed control and planning method is robust, reliable, and computationally efficient.