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.
Current robotic navigation algorithms rely on a dense environment representation for safe navigation. Occupancy grid maps are the standard way of environment representation in robotics and are the natural choice for online implementations @cite_4 @cite_32 @cite_7 @cite_42 @cite_22 . However, they simplify the mapping problem to a set of independent cells and estimate the probability of occupancy for each cell by ignoring the correlation between them. The map posterior is then approximated as the product of its marginals.
@cite_4 @cite_22 @cite_7 @cite_42 @cite_32
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Occupancy grids have been a popular mapping technique in mobile robotics for nearly 30 years. Occupancy grids offer a discrete representation of the world and seek to determine the occupancy probability of each cell. Traditional occupancy grid mapping methods make two assumptions for computational efficiency and it has been shown that the full posterior is computationally intractable for real-world mapping applications without these assumptions. The two assumptions result in tuning parameters that control the information gained from each distance measurement. In this paper, several tuning parameters found in the literature are optimized against the full posterior in 1D. In addition, this paper presents a new parameterization of the update function that outperforms existing methods in terms of capturing residual uncertainty. Capturing the residual uncertainty better estimates the position of obstacles and prevents under- and over-confidence in both the occupied and unoccupied cells. The paper concludes by showing that the new update function better captures the residual uncertainty in each cell when compared to an offline mapping method for realistic 2D simulations. In this paper we provide an overview of a new framework for robot perception, real-world modelling, and navigation that uses a stochastic tesselated representation of spatial information called the Occupancy Grid. The Occupancy Grid is a multi-dimensional random field model that maintains probabilistic estimates of the occupancy state of each cell in a spatial lattice. Bayesian estimation mechanisms employing stochastic sensor models allow incremental updating of the Occupancy Grid using multi-view, multi-sensor data, composition of multiple maps, decision-making, and incorporation of robot and sensor position uncertainty. We present the underlying stochastic formulation of the Occupancy Grid framework, and discuss its application to a variety of robotic tusks. These include range-based mapping, multi-sensor integration, path-planning and obstacle avoidance, handling of robot position uncertainty, incorporation of pre-compiled maps, recovery of geometric representations, and other related problems. The experimental results show that the Occupancy Grid approach generates dense world models, is robust under sensor uncertainty and errors, and allows explicit handling of uncertainty. It supports the development of robust and agile sensor interpretation methods, incremental discovery procedures, and composition of information from multiple sources. Furthermore, the results illustrate that robotic tasks can be addressed through operations performed di- rectly on the Occupancy Grid, and that these operations have strong parallels to operations performed in the image processing domain. 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. This article describes a new algorithm for acquiring occupancy grid maps with mobile robots. Existing occupancy grid mapping algorithms decompose the high-dimensional mapping problem into a collection of one-dimensional problems, where the occupancy of each grid cell is estimated independently. This induces conflicts that may lead to inconsistent maps, even for noise-free sensors. This article shows how to solve the mapping problem in the original, high-dimensional space, thereby maintaining all dependencies between neighboring cells. As a result, maps generated by our approach are often more accurate than those generated using traditional techniques. Our approach relies on a statistical formulation of the mapping problem using forward models. It employs the expectation maximization algorithm for searching maps that maximize the likelihood of the sensor measurements.