Gaussian process modeling of large‐scale terrain

Abstract

Building a model of large-scale terrain that can adequately handle uncertainty and incompleteness in a statistically sound way is a challenging problem. This work proposes the use of Gaussian processes as models of large-scale terrain. The proposed model naturally provides a multiresolution representation of space, incorporates and handles uncertainties aptly, and copes with incompleteness of sensory information. Gaussian process regression techniques are applied to estimate and interpolate (to fill gaps in occluded areas) elevation information across the field. The estimates obtained are the best linear unbiased estimates for the data under consideration. A single nonstationary (neural network) Gaussian process is shown to be powerful enough to model large and complex terrain, effectively handling issues relating to discontinuous data. A local approximation method based on a "moving window" methodology and implemented using k-dimensional (KD)-trees is also proposed. This enables the approach to handle extremely large data sets, thereby completely addressing its scalability issues. Experiments are performed on large-scale data sets taken from real mining applications. These data sets include sparse mine planning data, which are representative of a global positioning system-based survey, as well as dense laser scanner data taken at different mine sites. Further, extensive statistical performance evaluation and benchmarking of the technique has been performed through cross-validation experiments. They conclude that for dense and/or flat data, the proposed approach will perform very competitively with grid-based approaches using standard interpolation techniques and triangulated irregular networks using triangle-based interpolation techniques; for sparse and/or complex data, however, it would significantly outperform them. C 2009 Wiley Periodicals, Inc.

Efficient motion planning for manipulation robots in environments with deformable objects

“…A good introduction into GPs can be found in [17]. In robotics, GPs have been used for terrain modeling [20], for occupancy mapping [16], for estimating gas distributions [19], learning motion and observation models [12] and several other problems. In some parts, the approach of Vasudevan et al [20] is similar to our method.…”

“…In robotics, GPs have been used for terrain modeling [20], for occupancy mapping [16], for estimating gas distributions [19], learning motion and observation models [12] and several other problems. In some parts, the approach of Vasudevan et al [20] is similar to our method. To model large outdoor terrain structures, they perform a nearest neighbor query on measured elevation data and consider only inputs in the local neighborhood of the query point.…”

Efficient Non-Parametric Surface Representations Using Active Sampling for Push Broom Laser Data

“…In this context, GP models are particularly favoured for their ability to handle incomplete data in a principled probabilistic fashion. Examples of such approaches include [9], [19], [30], although they were first introduced to the geostatistics field under the name kriging many years previously by [11] amongst others. While these approaches differ in their choice of (non-stationary) covariance function and GP sparsification method, they adopt the same parameterisation of the problem -that is they model a function f : R 2 → R which associates a single elevation value z with any given position (x, y) in 3D Euclidean space.…”

“…We explicitly account for noise in the training observations r through an additive white noise process of strength σ m along the diagonal entries of K 2 . The derivation of the mean E[r * ] and covariance V[r * ] of the predictive distribution p(r * |q * , D) for a deterministic µ(q) = 0 (as is commonly used [30]) are standard and can be found, for example, in [21] …”

Building Fuzzy Elevation Maps from a Ground-Based 3D Laser Scan for Outdoor Mobile Robots

“…In mobile robotics, elevation grids have been processed with fuzzy rules to assess traversability [18,19]. Gaussian processes have also been proposed to model terrain from uncertain and incomplete sensor data [20]. Adaptive Network-based Fuzzy Inference Systems (ANFIS) [21] has been employed to recognize objects like trees and buildings from aerial stereo images [22].…”