In multi-robot collaborative exploration tasks, it is essential to extract frontier points from a globally consistent map and allocate these points through a task allocation algorithm. Once a robot receives frontier points as task targets, it needs to perform obstacle-avoidance path planning on the globally consistent map. However, constructing a globally consistent point cloud map consumes significant communication resources and struggles to ensure real-time mapping. Therefore, based on the extended traversability map construction method, this paper proposes a method to construct a globally consistent extended traversability map. Subsequent processes such as frontier point clustering and path planning are based on this map. This paper employs a 3D LiDAR as the observation sensor to acquire point cloud models of the surrounding environment and analyzes the point cloud for traversability to obtain a traversability map. On the basis of the local extended traversability map, a globally consistent traversability map is established. This paper introduces the above process in detail: Sect. 2 introduces the design and calculation methods of the traversability map; Sect. 3 discusses the global fusion strategy of the traversability map; Sect. 4 verifies the effectiveness of the globally consistent traversability map in reflecting map accuracy and consistency in a simulation environment and KITTI seq-05.