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Complex environments pose great challenges for autonomous mobile robot navigation. In this study, we address the problem of autonomous navigation in 3D environments with staircases and slopes. An integrated system for safe mobile robot navigation in 3D complex environments is presented and both the perception and navigation capabilities are incorporated into the modular and reusable framework. Firstly, to distinguish the slope from the staircase in the environment, the robot builds a 3D OctoMap of the environment with a novel Simultaneously Localization and Mapping (SLAM) framework using the information of wheel odometry, a 2D laser scanner, and an RGB-D camera. Then, we introduce the traversable map, which is generated by the multi-layer 2D maps extracted from the 3D OctoMap. This traversable map serves as the input for autonomous navigation when the robot faces slopes and staircases. Moreover, to enable robust robot navigation in 3D environments, a novel camera re-localization method based on regression forest towards stable 3D localization is incorporated into this framework. In addition, we utilize a variable step size Rapidly-exploring Random Tree (RRT) method which can adjust the exploring step size automatically without tuning this parameter manually according to the environment, so that the navigation efficiency is improved. The experiments are conducted in different kinds of environments and the output results demonstrate that the proposed system enables the robot to navigate efficiently and robustly in complex 3D environments.