In this paper, we study extensions to the Gaussian processes (GPs) continuous occupancy mapping problem. There are two classes of occupancy mapping problems that we particularly investigate. The first problem is related to mapping under pose uncertainty and how to propagate pose estimation uncertainty into the map inference. We develop expected kernel and expected submap notions to deal with uncertain inputs. In the second problem, we account for the complication of the robot's perception noise using warped Gaussian processes (WGPs). This approach allows for non-Gaussian noise in the observation space and captures the possible nonlinearity in that space better than standard GPs. The developed techniques can be applied separately or concurrently to a standard GP occupancy mapping problem. According to our experimental results, although taking into account pose uncertainty leads, as expected, to more uncertain maps, by modeling the nonlinearities present in the observation space WGPs improve the map quality.
Kernel methods in the form of Gaussian processes (GPs) framework @cite_34 are non-parametric regression and classification techniques that have been used to model spatial phenomena @cite_41 . The development of GPOM is discussed in @cite_14 @cite_23 . The incremental GP map building using the Bayesian Committee Machine (BCM) technique @cite_29 is developed in @cite_11 @cite_2 @cite_18 @cite_27 and for online applications in @cite_24 . @cite_12 , the Hilbert maps technique is proposed and is more scalable. However, it is an approximation for continuous occupancy mapping and produces maps with less accuracy than GPOM.
@cite_18 @cite_14 @cite_41 @cite_29 @cite_24 @cite_27 @cite_23 @cite_2 @cite_34 @cite_12 @cite_11
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In this paper, a novel solution for autonomous robotic exploration is proposed. We model the distribution of information in an unknown environment as an unsteady diffusion process, which can be an appropriate mathematical formulation and analogy for expanding, time-varying, and dynamic environments. This information distribution map is the solution of the diffusion process partial differential equation, and is regressed from sensor data as a Gaussian Process. Optimization of the process parameters leads to an optimal frontier map which describes regions of interest for further exploration. Since the presented approach considers a continuous model of the environment, it can be used to plan smooth exploration paths exploiting the structural dependencies of the environment whilst handling sparse sensor measurements. The performance of the approach is evaluated through simulation results in the well-known Freiburg and Cave maps. In this paper we introduce a new statistical modeling technique for building occupancy maps. The problem of mapping is addressed as a classification task where the robot's environment is classified into regions of occupancy and unoccupancy. Our model provides both a continuous representation of the robot's surroundings and an associated predictive variance. This is obtained by employing a Gaussian process as a non-parametric Bayesian learning technique to exploit the fact that real-world environments inherently possess structure. This structure introduces a correlation between points on the map which is not accounted for by many common mapping techniques such as occupancy grids. Using a trained neural network covariance function to model the highly non-stationary datasets, it is possible to generate accurate representations of large environments at resolutions which suit the desired applications while also providing inferences into occluded regions, between beams, and beyond the range of the sensor, even with relatively few sensor readings. We demonstrate the benefits of our approach in a simulated data set with known ground-truth, and in an outdoor urban environment covering an area of 120,000 m2. 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. © 2009 Wiley Periodicals, Inc. The Bayesian committee machine (BCM) is a novel approach to combining estimators that were trained on different data sets. Although the BCM can be applied to the combination of any kind of estimators, the main foci are gaussian process regression and related systems such as regularization networks and smoothing splines for which the degrees of freedom increase with the number of training data. Somewhat surprisingly, we find that the performance of the BCM improves if several test points are queried at the same time and is optimal if the number of test points is at least as large as the degrees of freedom of the estimator. The BCM also provides a new solution for on-line learning with potential applications to data mining. We apply the BCM to systems with fixed basis functions and discuss its relationship to gaussian process regression. Finally, we show how the ideas behind the BCM can be applied in a non-Bayesian setting to extend the input-dependent combination of estimators. We present a novel algorithm to produce descriptive online 3D occupancy maps using Gaussian processes (GPs). GP regression and classification have met with recent success in their application to robot mapping, as GPs are capable of expressing rich correlation among map cells and sensor data. However, the cubic computational complexity has limited its application to large-scale mapping and online use. In this paper we address this issue first by proposing test-data octrees, octrees within blocks of the map that prune away nodes of the same state, condensing the number of test data used in a regression, in addition to allowing fast data retrieval. We also propose a nested Bayesian committee machine which, after new sensor data is partitioned among several GP regressions, fuses the result and updates the map with greatly reduced complexity. Finally, by adjusting the range of influence of the training data and tuning a variance threshold implemented in our method's binary classification step, we are able to control the richness of inference achieved by GPs - and its tradeoff with classification accuracy. The performance of the proposed approach is evaluated with both simulated and real data, demonstrating that the method may serve both as an improved-accuracy classifier, and as a predictive tool to support autonomous navigation. An information-driven autonomous robotic explo- ration method on a continuous representation of unknown envi- ronments is proposed in this paper. The approach conveniently handles sparse sensor measurements to build a continuous model of the environment that exploits structural dependencies without the need to resort to a fixed resolution grid map. A gradient field of occupancy probability distribution is regressed from sensor data as a Gaussian process providing frontier boundaries for further exploration. The resulting continuous global frontier surface completely describes unexplored regions and, inherently, provides an automatic stop criterion for a desired sensitivity. The performance of the proposed approach is evaluated through simulation results in the well-known Freiburg and Cave maps. We introduce a new statistical modelling technique for building occupancy maps. The problem of mapping is addressed as a classification task where the robot's environment is classified into regions of occupancy and free space. This is obtained by employing a modified Gaussian process as a non-parametric Bayesian learning technique to exploit the fact that real-world environments inherently possess structure. This structure introduces dependencies between points on the map which are not accounted for by many common mapping techniques such as occupancy grids. Our approach is an 'anytime' algorithm that is capable of generating accurate representations of large environments at arbitrary resolutions to suit many applications. It also provides inferences with associated variances into occluded regions and between sensor beams, even with relatively few observations. Crucially, the technique can handle noisy data, potentially from multiple sources, and fuse it into a robust common probabilistic representation of the robot's surroundings. We demonstrate the benefits of our approach on simulated datasets with known ground truth and in outdoor urban environments. In this paper, a novel solution for autonomous robotic exploration is proposed. We model the distribution of information in an unknown environment as an unsteady diffusion process, which can be an appropriate mathematical formulation and analogy for expanding, time-varying, and dynamic envi- ronments. This information distribution map is the solution of the diffusion process partial differential equation, and is regressed from sensor data as a Gaussian Process. Optimization of the process parameters leads to an optimal frontier map which describes regions of interest for further exploration. Since the presented approach considers a continuous model of the environment, it can be used to plan smooth exploration paths exploiting the structural dependencies of the environment whilst handling sparse sensor measurements. The performance of the approach is evaluated through simulation results in the well- known Freiburg and Cave maps. Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics.The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes. This paper proposes a new method for occupancy map building using a mixture of Gaussian processes. We consider occupancy maps as a binary classification problem of positions being occupied or not, and apply Gaussian processes. Particularly, since the computational complexity of Gaussian processes grows as O(n3), where n is the number of data points, we divide the training data into small subsets and apply a mixture of Gaussian processes. The procedure of our map building method consists of three steps. First, we cluster acquired data by grouping laser hit points on the same line into the same cluster. Then, we build local occupancy maps by using Gaussian processes with clustered data. Finally, local occupancy maps are merged into one by using a mixture of Gaussian processes. Simulation results will be compared with previous researches and provided demonstrating the benefits of the approach.