We present a novel LIDAR streaming architecture for real-time, on-board processing using unmanned robots. We propose a two-level 3D data structure that allows pipelined and streaming processing of the 3D data as it arrives from a moving robot: (i) at the coarse level, the incoming 3D scans are stored in memory in a dense 3D voxel grid with a relatively large voxel size - this ensures buffering of the most recent data and the availability of sufficient 3D measurements within a specific processing volume at the next level; (ii) at the fine level, we employ a data chunking mechanism guided by the movement of the robot and a rolling dense 3D voxel grid for processing the data in the immediate vicinity of the robot, which enables reuse of previously computed features. The architecture proposed requires a very small memory footprint, minimal data copying, and allows a fast spatial access for 3D data, even at the finest resolutions. We illustrate the proposed streaming architecture on a real-time 3D structure characterization task for detecting doors and stairs in indoor environments and show qualitative results demonstrating the effectiveness of our approach.