Comparative evaluation of the consistency of three-dimensional spatial representations used in autonomous robot navigation

An increasing number of robots for outdoor applications rely on complex three-dimensional (3D) environmental models. In many cases, 3D maps are used for vital tasks, such as path planning and collision detection in challenging semistructured environments. Thus, acquiring accurate three-dimensional maps is an important research topic of high priority for autonomously navigating robots. This article proposes an evaluation method that is designed to compare the consistency with which different representations model the environment. In particular, the article examines several popular (probabilistic) spatial representations that are capable of predicting the occupancy of any point in space, given prior 3D range measurements. This work proposes to reformulate the obtained environmental models as probabilistic binary classifiers, thus allowing for the use of standard evaluation and comparison procedures. To avoid introducing localization errors, this article concentrates on evaluating models constructed from measurements acquired at fixed sensor poses. Using a cross-validation approach, the consistency of different representations, i.e., the likelihood of correctly predicting unseen measurements in the sensor field of view, can be evaluated. Simulated and real-world data sets are used to benchmark the precision of four spatial models - occupancy grid, triangle mesh, and two variations of the three-dimensional normal distributions transform (3D-NDT) - over various environments and sensor noise levels. Overall, the consistency of representation of the 3D-NDT is found to be the highest among the tested models, with a similar performance over varying input data.