This paper attempts to uncover one possible method for the IMR (indoor mobile robot) to perform indoor exploration associated with SLAM (simultaneous localization and mapping) using LiDAR. Specifically, the IMR is required to construct a map when it has landed on an unexplored floor of a building. We had implemented the e-SLAM (exploration-based SLAM) using the coordinate transformation and the navigation prediction techniques to achieve that purpose in the engineering school building which consists of many 100-m2 labs, corridors, elevator waiting space and the lobby. We first derive the LiDAR mesh for the orthogonal walls and filter out the static furniture and dynamic humans in the same space as the IMR. Then, we define the LiDAR pose frame including the translation and rotation from the orthogonal walls. According to the MSC (most significant corner) obtained from the intersection of the orthogonal walls, we calculate the displacement of the IMR. The orientation of the IMR is calculated from the alignment of orthogonal walls in the consecutive LiDAR pose frames, which is also assisted by the LQE (linear quadratic estimation) method. All the computation can be done in a single processor machine in real-time. The e-SLAM technique leads to a potential for the in-house service robot to start operation without having pre-scan LiDAR maps, which can save the installation time of the service robot. In this study, we use only the LiDAR and compared our result with the IMU to verify the consistency between the two navigation sensors in the experiments. The scenario of the experiment consists of rooms, corridors, elevators, and the lobby, which is common to most office buildings.