The paper presents a strategy for robotic exploration problems using Space-Filling curves (SFC). The region of interest is first tessellated, and the tiles/cells are connected using some SFC. A robot follows the SFC to explore the entire area. However, there could be obstacles that block the systematic movement of the robot. We overcome this problem by providing an evading technique that avoids the blocked tiles while ensuring all the free ones are visited at least once. The proposed strategy is online, implying that prior knowledge of the obstacles is not mandatory. It works for all SFCs, but for the sake of demonstration, we use Hilbert curve. We present the completeness of the algorithm and discuss its desirable properties with examples. We also address the non-uniform coverage problem using our strategy.