For the desert environment with complex terrain and wide range, the current map model occupies too much storage space. At the same time, in complex terrain, the current full coverage path planning algorithm consumes a lot of energy and is not suitable for online conditions. Aiming at these problems, an on-line fully coverage path planning algorithm and its map model is proposed. Firstly, a variable resolution 3D grid map model is introduced. Then, the energy consumption of a robot in the full coverage task in non-planar environment is analyzed, and the most energy-saving coverage mode is obtained. In the coverage of flat terrain, based on the idea of priority coverage, the traditional boustrophedon fully coverage algorithm is improved by being expanded into 8 directions. Then, an on-line terrain oriented region decomposition method is proposed for non-flat terrain. In the process of full coverage, the special terrain region is decomposed by height and covered separately. In the sub region, the slope model is abstracted from the special terrain, the terrain change function is introduced to form a new priority traversal method, and a targeted obstacle avoidance strategy is designed to further reduce energy consumption. Simulation verification and experiment results show that compared with other algorithms, this algorithm can significantly reduce the repetition rate and total energy consumption of robots in the process of full coverage.