Warped Gaussian Processes Occupancy Mapping with Uncertain Inputs

© 2017 IEEE. 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

Gaussian processes for information-theoretic robotic mapping and exploration

University of Technology Sydney. Faculty of Engineering and Information Technology.This thesis proposes a framework for autonomous robotic mapping, exploration, and planning that uses Gaussian Processes (GPs) to model high-dimensional dense maps and solve the problem of infinite-horizon planning with imperfect state information. Robotic exploration is traditionally implemented using occupancy grid representations and geometric targets known as frontiers. The occupancy grid representation relies on the assumption of independence between grid cells and ignores structural correlations present in the environment. We develop an incremental GP occupancy mapping technique that is computationally tractable for online map building and represents a continuous model of uncertainty over the map spatial coordinates. The standard way to represent geometric frontiers extracted from occupancy maps is to assign binary values to each grid cell. We extend this notion to novel probabilistic frontier maps computed efficiently using the gradient of the GP occupancy map and propose a mutual information-based greedy exploration technique built on that representation. A primary motivation is the fact that high-dimensional map inference requires fewer observations, leading to a faster map entropy reduction during exploration for map building scenarios. The uncertainty from pose estimation is often ignored during current mapping strategies as the dense belief representation of occupancy maps makes the uncertainty propagation impractical. Additionally, when kernel methods are applied, such maps tend to model structural shapes of the environment with excessive smoothness. We show how the incremental GP occupancy mapping technique can be extended to accept uncertain robot poses and mitigate the excessive smoothness problem using Warped Gaussian Processes. This approach can model non-Gaussian noise in the observation space and capture the possible non-linearity in that space better than standard GPs. Finally, we develop a sampling-based information gathering planner, with an information-theoretic convergence, which allows dense belief representations. The planner takes the present uncertainty in state estimation into account and provides a general framework for robotic exploration in a priori unknown environments with an information-theoretic stopping criterion. The developed framework relaxes the need for any state or action space discretization and is a fully information-driven integrated navigation technique. The developed framework can be applied to a large number of scenarios where the robot is tasked to perform exploration and information gathering simultaneously. The developed algorithms in this thesis are implemented and evaluated using simulated and experimental datasets and are publicly available as open source libraries

Generalised Kernel Representations with Applications to Data Efficient Machine Learning

The universe of mathematical modelling from observational data is a vast space. It consists a cacophony of differing paths, with doors to worlds with seemingly diametrically opposed perspectives that all attempt to conjure a crystal ball of both intuitive understanding and predictive capability. Among these many worlds is an approach that is broadly called kernel methods, which, while complex in detail, when viewed from afar ultimately reduces to a rather simple question: how close is something to something else? What does it mean to be close? Specifically, how can we quantify closeness in some reasonable and principled way? This thesis presents four approaches that address generalised kernel learning. Firstly, we introduce a probabilistic framework that allows joint learning of model and kernel parameters in order to capture nonstationary spatial phenomena. Secondly, we introduce a theoretical framework based on optimal transport that enables online kernel parameter transfer. Such parameter transfer involves the ability to re-use previously learned parameters, without re-optimisation, on newly observed data. This extends the first contribution which was unable operate in real-time due to the necessity of reoptimising parameters to new observations. Thirdly, we introduce a learnable Fourier based kernel embeddings that exploits generalised quantile representations for stationary kernels. Finally, a method for input warped Fourier kernel embeddings is proposed that allows nonstationary data embeddings using simple stationary kernels. By introducing theoretically cohesive and algorithmically intuitive methods this thesis opens new doors to removing traditional assumptions that have hindered adoption of the kernel perspective. We hope that the ideas presented will demonstrate a curious and inspiring view to the potential of learnable kernel embeddings

Deep probabilistic methods for improved radar sensor modelling and pose estimation

Radar’s ability to sense under adverse conditions and at far-range makes it a valuable alternative to vision and lidar for mobile robotic applications. However, its complex, scene-dependent sensing process and significant noise artefacts makes working with radar challenging. Moving past classical rule-based approaches, which have dominated the literature to date, this thesis investigates deep and data-driven solutions across a range of tasks in robotics. Firstly, a deep approach is developed for mapping raw sensor measurements to a grid-map of occupancy probabilities, outperforming classical filtering approaches by a significant margin. A distribution over the occupancy state is captured, additionally allowing uncertainty in predictions to be identified and managed. The approach is trained entirely using partial labels generated automatically from lidar, without requiring manual labelling. Next, a deep model is proposed for generating stochastic radar measurements from simulated elevation maps. The model is trained by learning the forward and backward processes side-by-side, using a combination of adversarial and cyclical consistency constraints in combination with a partial alignment loss, using labels generated in lidar. By faithfully replicating the radar sensing process, new models can be trained for down-stream tasks, using labels that are readily available in simulation. In this case, segmentation models trained on simulated radar measurements, when deployed in the real world, are shown to approach the performance of a model trained entirely on real-world measurements. Finally, the potential of deep approaches applied to the radar odometry task are explored. A learnt feature space is combined with a classical correlative scan matching procedure and optimised for pose prediction, allowing the proposed method to outperform the previous state-of-the-art by a significant margin. Through a probabilistic consideration the uncertainty in the pose is also successfully characterised. Building upon this success, properties of the Fourier Transform are then utilised to separate the search for translation and angle. It is shown that this decoupled search results in a significant boost to run-time performance, allowing the approach to run in real-time on CPUs and embedded devices, whilst remaining competitive with other radar odometry methods proposed in the literature