# Supervised Learning of Natural-Terrain Traversability with Synthetic 3D Laser Scans
## 1 Introduction  
Traversability is a key issue for motion planning of ground vehicles on unstructured terrain that has been addressed in different ways [1]. Among them, this relevant analysis can also be carried out with three-dimensional (3D) point clouds acquired at the ground level with stereo vision [2] or laser scanners [3].  
3D laser scanners are of common use when moving on rough surfaces because they offer a great quantity of reliable information of the surroundings [4]. However, the resulting scans often have a complex structure and an uneven point density that decays with the distance to the sensor [5]. Nevertheless, these problems have not hindered autonomous navigation by processing raw point clouds directly [6; 7].  
Ground extraction is a process very related with traversability assessment, which is commonly performed just before scene segmentation [8]. Instead of designing specific segmentation procedures for floor detection [9], different machine learning techniques can be trained with spatial features computed right from the 3D point cloud [10; 11].  
Supervised learning usually employs hand-labelled points to obtain predictive models that can be applied to new data [12]. In this way, the Classification Learner App of Matlab has been employed to extract ground from 3D point clouds of an urban dataset [13]. Accordingly, a support vector machine was used to detect urban and rural roads with stereo vision [14].  
However, tagging point by point real 3D data from ground vehicles on natural environments requires a laborious and error-prone effort [15]. In addition, to the best knowledge of the authors, there are no tagged repositories with this kind of data. As an alternative to manually-labelled data, learning from demonstration with 3D point clouds acquired from a teleoperated vehicle on traversable zones can be employed by a Positive Naive Bayes classifier [16], a Gaussian Process [17], or a support vector machine [18].  
Moreover, synthetic depth data offers interesting opportunities for training traversability [19]. In this sense, virtual Lidar data generated with Matlab has been employed to build a neural network that classifies traversable terrain of planetary surfaces [20]. Similarly, in [21], a convolutional neural network has been trained to distinguish traversable patches from heightmap images obtained by the robotic simulator Gazebo [22].  
To obtain natural-terrain traversability classifiers for 3D point clouds acquired by the mobile robot Andabata [23] on non-slippery solid ground, this paper develops the following main contributions.  
* Synthetic 3D point clouds from Gazebo, that were previously labelled without errors [15], are employed for training and validation.
* The performance of seven potent supervised learning techniques from the free software _Scikit-learn_ library [24] of the Python programming language is evaluated.
* The resulting classifiers are also tested with real data acquired, whereas Andabata was teleoperated on natural terrain.  
The rest of the paper is organised as follows. The following section overviews the procedure used to obtain synthetic 3D laser scans with point traversability labels. Section 3 presents the training of various classifiers with these labelled point clouds. Then, Sections 4 and 5 contain validation results for both simulated and real data, respectively. The paper ends with conclusions, acknowledgements and references.