# Supervised Learning of Natural-Terrain Traversability with Synthetic 3D Laser Scans
## 2 Traversability-Labeling of 3D laser scans  
This section overviews how synthetic 3D laser scans of the mobile robot Andabata on natural environments can be labelled automatically [15]. Andabata is a ground vehicle for outdoor navigation, which is 0.67 m long, 0.54 m wide and 0.81 m high [23]. This skid-steered robot carries a 3D laser rangefinder on top and centered (see Figure 1), which is based on the unrestrained rotation of a commercial two-dimensional (2D) laser scanner around its optical centre [25].  
The vertical and horizontal fields of view of the 3D sensor are 270\({}^{\circ}\) and 360\({}^{\circ}\), respectively. The 3D sensor has inherited from the 2D scanner its vertical resolution of 0.25\({}^{\circ}\), its \(\pm\)3 cm accuracy and its range of measurements from 0.1 m to 15 m under direct sunlight [25]. The horizontal resolution of the 3D rangefinder depends on the turns performed by the entire 2D sensor and its turning speed. Once mounted on Andabata, the blind region of the 3D sensor is a cone that begins at its optical centre (0.723 m above the ground) and encompasses all the vehicle below [23].  
Figure 1: Andabata mobile robot equipped with its 3D laser scanner on the upper end.  
The robotic simulator Gazebo [22] can be employed to obtain realistic point clouds of rough terrain from 3D rangefinders [3; 19]. Figure 2 shows a general view of the natural environment generated with Gazebo, whose maximum dimensions are 150 m long, 150 m wide and 20 m high [15]. It contains natural elements like uneven ground, grass, bushes, rocks, trees and water. However, it also has artificial elements like tables, benches, fences, power lines and pavement. Five different zones can be distinguished inside: hills (A), a cave (B), a forest (C), a lake (D) and a park (E).  
Apart from modelling the natural environment, Gazebo simulates the range and intensity measurements of the 2D laser scanner [22]. Successive rotations are applied to the 2D sensor around its optical center to obtain a full 3D scan [15]. The ranges are employed to calculate the 3D Cartesian coordinates of detected objects. Moreover, by taking into account the pitch and roll angles on the terrain [15], the whole point cloud is levelled to operate as Andabata does [23]. Besides, the intensity measurements are used to label each 3D point distinctively by assigning different reflectivity values to each natural or artificial element. In addition, points from the water element are removed from the 3D point cloud to emulate laser beam deflections [15].  
Three laser scans with a horizontal resolution of \(1^{\circ}\) have been obtained for each zone of the natural environment by placing Andabata on different spots on the ground. Then, these synthetic scans are binarized in the following way; those points that belong to the ground, pavement and low grass (with a maximum height of 5 cm) are labelled as traversable and the rest as non-traversable. In addition, the inclination of every traversable point is estimated by computing the normal of the local plane fitted with the twenty nearest traversable neighbours. Finally, all the points with a slope greater than \(20^{\circ}\) (maximum inclination that Andabata can navigate) are re-labelled as non-traversable.  
Figure 3 summaries the different stages required for labelling traversability:  
1. [label=()]
2. Represents a view of the hills zone (A) built with Gazebo [22].
3. Shows a simulated 3D scan acquired with Andabata. The empty circle on the ground at the center of the laser scan corresponds to the blind area of the 3D sensor.
4. Represents the previous scan once it has been levelled and its 3D points tagged with different colours according to their intensity values [15].
5. Shows the traversable points of the laser scan in green colour, and the rest in red. In this case, non-traversable points originate from trees, bushes, the electric line and very sloped terrain.  
Figure 2: Overview of the natural environment built with Gazebo. Five different zones are marked with capital letters.