Spectral Sparsification for Communication-Efficient Collaborative Rotation and Translation Estimation

We propose fast and communication-efficient optimization algorithms for multi-robot rotation averaging and translation estimation problems that arise from collaborative simultaneous localization and mapping (SLAM), structure-from-motion (SfM), and camera network localization applications. Our methods are based on theoretical relations between the Hessians of the underlying Riemannian optimization problems and the Laplacians of suitably weighted graphs. We leverage these results to design a collaborative solver in which robots coordinate with a central server to perform approximate second-order optimization, by solving a Laplacian system at each iteration. Crucially, our algorithms permit robots to employ spectral sparsification to sparsify intermediate dense matrices before communication, and hence provide a mechanism to trade off accuracy with communication efficiency with provable guarantees. We perform rigorous theoretical analysis of our methods and prove that they enjoy (local) linear rate of convergence. Furthermore, we show that our methods can be combined with graduated non-convexity to achieve outlier-robust estimation. Extensive experiments on real-world SLAM and SfM scenarios demonstrate the superior convergence rate and communication efficiency of our methods.Comment: Revised extended technical report (37 pages, 15 figures, 6 tables

Pose-graph neural network classifier for global optimality prediction in 2D SLAM

The ability to decide if a solution to a pose-graph problem is globally optimal is of high significance for safety-critical applications. Converging to a local-minimum may result in severe estimation errors along the estimated trajectory. In this paper, we propose a graph neural network based on a novel implementation of a graph convolutional-like layer, called PoseConv, to perform classification of pose-graphs as optimal or sub-optimal. The operation of PoseConv required incorporating a new node feature, referred to as cost, to hold the information that the nodes will communicate. A training and testing dataset was generated based on publicly available bench-marking pose-graphs. The neural classifier is then trained and extensively tested on several subsets of the pose-graph samples in the dataset. Testing results have proven the model's capability to perform classification with 92 - 98% accuracy, for the different partitions of the training and testing dataset. In addition, the model was able to generalize to previously unseen variants of pose-graphs in the training dataset. Our method trades a small amount of accuracy for a large improvement in processing time. This makes it faster than other existing methods by up-to three orders of magnitude, which could be of paramount importance when using computationally-limited robots overseen by human operators

Research on 2D general feature based SLAM algorithm for mobile robot

University of Technology Sydney. Faculty of Engineering and Information Technology.Simultaneous Localization and Mapping (SLAM) is a fundamental research problem for autonomous robot navigation and map construction. This thesis studied the problem of improving the performance of localization and mapping for mobile robots, including pre-fitting features with ellipse representation, representing features with implicit functions, parameterization in Fourier series, and submap joining. The main contributions include three aspects: (1) a SLAM algorithm with pre-fitted conic features via 2D lidar is presented, which is named as Pre-fit SLAM and can be adapted to an open environment nicely; (2) a post-count framework for 2D lidar SLAM with implicit functions on general features is studied; (3) a 2D laser SLAM approach with Fourier series based feature parameterization (called Fourier-SLAM) and submap joining is studied

Synchronization Problems in Computer Vision

The goal of \u201csynchronization\u201d is to infer the unknown states of a network of nodes, where only the ratio (or difference) between pairs of states can be measured. Typically, states are represented by elements of a group, such as the Symmetric Group or the Special Euclidean Group. The former can represent local labels of a set of features, which refer to the multi-view matching application, whereas the latter can represent camera reference frames, in which case we are in the context of structure from motion, or local coordinates where 3D points are represented, in which case we are dealing with multiple point-set registration. A related problem is that of \u201cbearing-based network localization\u201d where each node is located at a fixed (unknown) position in 3-space and pairs of nodes can measure the direction of the line joining their locations. In this thesis we are interested in global techniques where all the measures are considered at once, as opposed to incremental approaches that grow a solution by adding pieces iteratively

Patterns and Pattern Languages for Mobile Augmented Reality

Mixed Reality is a relatively new field in computer science which uses technology as a medium to provide modified or enhanced views of reality or to virtually generate a new reality. Augmented Reality is a branch of Mixed Reality which blends the real-world as viewed through a computer interface with virtual objects generated by a computer. The 21st century commodification of mobile devices with multi-core Central Processing Units, Graphics Processing Units, high definition displays and multiple sensors controlled by capable Operating Systems such as Android and iOS means that Mobile Augmented Reality applications have become increasingly feasible. Mobile Augmented Reality is a multi-disciplinary field requiring a synthesis of many technologies such as computer graphics, computer vision, machine learning and mobile device programming while also requiring theoretical knowledge of diverse fields such as Linear Algebra, Projective and Differential Geometry, Probability and Optimisation. This multi-disciplinary nature has led to a fragmentation of knowledge into various specialisations, making it difficult to integrate different solution components into a coherent architecture. Software design patterns provide a solution space of tried and tested best practices for a specified problem within a given context. The solution space is non-prescriptive and is described in terms of relationships between roles that can be assigned to software components. Architectural patterns are used to specify high level designs of complete systems, as opposed to domain or tactical level patterns that address specific lower level problem areas. Pattern Languages comprise multiple software patterns combining in multiple possible sequences to form a language with the individual patterns forming the language vocabulary while the valid sequences through the patterns define the grammar. Pattern Languages provide flexible generalised solutions within a particular domain that can be customised to solve problems of differing characteristics and levels of iii complexity within the domain. The specification of one or more Pattern Languages tailored to the Mobile Augmented Reality domain can therefore provide a generalised guide for the design and architecture of Mobile Augmented Reality applications from an architectural level down to the ”nuts-and-bolts” implementation level. While there is a large body of research into the technical specialisations pertaining to Mobile Augmented Reality, there is a dearth of up-to-date literature covering Mobile Augmented Reality design. This thesis fills this vacuum by: 1. Providing architectural patterns that provide the spine on which the design of Mobile Augmented Reality artefacts can be based; 2. Documenting existing patterns within the context of Mobile Augmented Reality; 3. Identifying new patterns specific to Mobile Augmented Reality; and 4. Combining the patterns into Pattern Languages for Detection & Tracking, Rendering & Interaction and Data Access for Mobile Augmented Reality. The resulting Pattern Languages support design at multiple levels of complexity from an object-oriented framework down to specific one-off Augmented Reality applications. The practical contribution of this thesis is the specification of architectural patterns and Pattern Language that provide a unified design approach for both the overall architecture and the detailed design of Mobile Augmented Reality artefacts. The theoretical contribution is a design theory for Mobile Augmented Reality gleaned from the extraction of patterns and creation of a pattern language or languages