Fast Global Optimality Verification in 3D SLAM

J. Briales, J. Gonzalez-Jimenez, "Fast Global Optimality Verification in 3D SLAM", in Int. Conf. on Intelligent Robots and Systems (IROS), Daejeon, Korea, IEEE/RSJ, pp. 4630-4636, 2016Graph-based SLAM has proved to be one of the most effective solutions to the Simultaneous localization and Mapping problem. This approach relies on nonlinear iterative optimization methods that in practice perform both accurately and efficiently. However, due to the non-convexity of the problem, the obtained solutions come with no guarantee of global optimality and may get stuck in local minima. The application of SLAM to many real-world applications cannot be conceived without additional control tools that detect possible suboptimalities as soon as possible in order to take corrective action and avoid catastrophic failure of the entire system. This paper builds upon the state-of-the-art framework [1] in verification for this problem and introduces a novel superior formulation that leads to a much higher efficiency. While retaining the same high effectiveness, the verification times of our proposal reduce up to >50x, paving the way for faster verification in critical real applications or in embedded low-power systems.We support our claims with extensive experiments with real and simulated data.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Spanish grant program FPU14/06098 and the project PROMOVE (DPI2014-55826-R), funded by the Spanish Government and the "European Regional Development Fund"

Global Optimality via Tight Convex Relaxations for Pose Estimation in Geometric 3D Computer Vision

In this thesis, we address a set of fundamental problems whose core difficulty boils down to optimizing over 3D poses. This includes many geometric 3D registration problems, covering well-known problems with a long research history such as the Perspective-n-Point (PnP) problem and generalizations, extrinsic sensor calibration, or even the gold standard for Structure from Motion (SfM) pipelines: The relative pose problem from corresponding features. Likewise, this is also the case for a close relative of SLAM, Pose Graph Optimization (also commonly known as Motion Averaging in SfM). The crux of this thesis contribution revolves around the successful characterization and development of empirically tight (convex) semidefinite relaxations for many of the aforementioned core problems of 3D Computer Vision. Building upon these empirically tight relaxations, we are able to find and certify the globally optimal solution to these problems with algorithms whose performance ranges as of today from efficient, scalable approaches comparable to fast second-order local search techniques to polynomial time (worst case). So, to conclude, our research reveals that an important subset of core problems that has been historically regarded as hard and thus dealt with mostly in empirical ways, are indeed tractable with optimality guarantees.Artificial Intelligence (AI) drives a lot of services and products we use everyday. But for AI to bring its full potential into daily tasks, with technologies such as autonomous driving, augmented reality or mobile robots, AI needs to be not only intelligent but also perceptive. In particular, the ability to see and to construct an accurate model of the environment is an essential capability to build intelligent perceptive systems. The ideas developed in Computer Vision for the last decades in areas such as Multiple View Geometry or Optimization, put together to work into 3D reconstruction algorithms seem to be mature enough to nurture a range of emerging applications that already employ as of today 3D Computer Vision in the background. However, while there is a positive trend in the use of 3D reconstruction tools in real applications, there are also some fundamental limitations regarding reliability and performance guarantees that may hinder a wider adoption, e.g. in more critical applications involving people's safety such as autonomous navigation. State-of-the-art 3D reconstruction algorithms typically formulate the reconstruction problem as a Maximum Likelihood Estimation (MLE) instance, which entails solving a high-dimensional non-convex non-linear optimization problem. In practice, this is done via fast local optimization methods, that have enabled fast and scalable reconstruction pipelines, yet lack of guarantees on most of the building blocks leaving us with fundamentally brittle pipelines where no guarantees exist

Rotation Averaging and Strong Duality

In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of computer vision applications. In its conventional form, rotation averaging is stated as a minimization over multiple rotation constraints. As these constraints are non-convex, this problem is generally considered challenging to solve globally. We show how to circumvent this difficulty through the use of Lagrangian duality. While such an approach is well-known it is normally not guaranteed to provide a tight relaxation. Based on spectral graph theory, we analytically prove that in many cases there is no duality gap unless the noise levels are severe. This allows us to obtain certifiably global solutions to a class of important non-convex problems in polynomial time. We also propose an efficient, scalable algorithm that out-performs general purpose numerical solvers and is able to handle the large problem instances commonly occurring in structure from motion settings. The potential of this proposed method is demonstrated on a number of different problems, consisting of both synthetic and real-world data

Bayesian Pose Graph Optimization via Bingham Distributions and Tempered Geodesic MCMC

We introduce Tempered Geodesic Markov Chain Monte Carlo (TG-MCMC) algorithm for initializing pose graph optimization problems, arising in various scenarios such as SFM (structure from motion) or SLAM (simultaneous localization and mapping). TG-MCMC is first of its kind as it unites asymptotically global non-convex optimization on the spherical manifold of quaternions with posterior sampling, in order to provide both reliable initial poses and uncertainty estimates that are informative about the quality of individual solutions. We devise rigorous theoretical convergence guarantees for our method and extensively evaluate it on synthetic and real benchmark datasets. Besides its elegance in formulation and theory, we show that our method is robust to missing data, noise and the estimated uncertainties capture intuitive properties of the data.Comment: Published at NeurIPS 2018, 25 pages with supplement

A Compositional Approach to Verifying Modular Robotic Systems

Robotic systems used in safety-critical industrial situations often rely on modular software architectures, and increasingly include autonomous components. Verifying that these modular robotic systems behave as expected requires approaches that can cope with, and preferably take advantage of, this inherent modularity. This paper describes a compositional approach to specifying the nodes in robotic systems built using the Robotic Operating System (ROS), where each node is specified using First-Order Logic (FOL) assume-guarantee contracts that link the specification to the ROS implementation. We introduce inference rules that facilitate the composition of these node-level contracts to derive system-level properties. We also present a novel Domain-Specific Language, the ROS Contract Language, which captures a node's FOL specification and links this contract to its implementation. RCL contracts can be automatically translated, by our tool Vanda, into executable monitors; which we use to verify the contracts at runtime. We illustrate our approach through the specification and verification of an autonomous rover engaged in the remote inspection of a nuclear site, and finish with smaller examples that illustrate other useful features of our framework.Comment: Version submitted to RA