arXiv subjects

Matthew Giamou

Publications and source records attributed to Matthew Giamou.

26 records · Page 2Linked to original sources

arXiv2020

Certifiably Globally Optimal Extrinsic Calibration from Per-Sensor Egomotion

We present a certifiably globally optimal algorithm for determining the extrinsic calibration between two sensors that are capable of producing independent egomotion estimates. This problem has been previously solved using a variety of techniques, including local optimization approaches that have no formal global optimality guarantees. We use a quadratic objective function to formulate calibration as a quadratically constrained quadratic program (QCQP). By leveraging recent advances in the optimization of QCQPs, we are able to use existing semidefinite program (SDP) solvers to obtain a certifiably global optimum via the Lagrangian dual problem. Our problem formulation can be globally optimized by existing general-purpose solvers in less than a second, regardless of the number of measurements available and the noise level. This enables a variety of robotic platforms to rapidly and robustly compute and certify a globally optimal set of calibration parameters without a prior estimate or operator intervention. We compare the performance of our approach with a local solver on extensive simulations and multiple real datasets. Finally, we present necessary observability conditions that connect our approach to recent theoretical results and analytically support the empirical performance of our system.

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arXiv2020

Probabilistic Regression of Rotations using Quaternion Averaging and a Deep Multi-Headed Network

Accurate estimates of rotation are crucial to vision-based motion estimation in augmented reality and robotics. In this work, we present a method to extract probabilistic estimates of rotation from deep regression models. First, we build on prior work and argue that a multi-headed network structure we name HydraNet provides better calibrated uncertainty estimates than methods that rely on stochastic forward passes. Second, we extend HydraNet to targets that belong to the rotation group, SO(3), by regressing unit quaternions and using the tools of rotation averaging and uncertainty injection onto the manifold to produce three-dimensional covariances. Finally, we present results and analysis on a synthetic dataset, learn consistent orientation estimates on the 7-Scenes dataset, and show how we can use our learned covariances to fuse deep estimates of relative orientation with classical stereo visual odometry to improve localization on the KITTI dataset.

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arXiv2019

PROBE: Predictive Robust Estimation for Visual-Inertial Navigation

Navigation in unknown, chaotic environments continues to present a significant challenge for the robotics community. Lighting changes, self-similar textures, motion blur, and moving objects are all considerable stumbling blocks for state-of-the-art vision-based navigation algorithms. In this paper we present a novel technique for improving localization accuracy within a visual-inertial navigation system (VINS). We make use of training data to learn a model for the quality of visual features with respect to localization error in a given environment. This model maps each visual observation from a predefined prediction space of visual-inertial predictors onto a scalar weight, which is then used to scale the observation covariance matrix. In this way, our model can adjust the influence of each observation according to its quality. We discuss our choice of predictors and report substantial reductions in localization error on 4 km of data from the KITTI dataset, as well as on experimental datasets consisting of 700 m of indoor and outdoor driving on a small ground rover equipped with a Skybotix VI-Sensor.

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arXiv2019

Sparse Bounded Degree Sum of Squares Optimization for Certifiably Globally Optimal Rotation Averaging

Estimating unknown rotations from noisy measurements is an important step in SfM and other 3D vision tasks. Typically, local optimization methods susceptible to returning suboptimal local minima are used to solve the rotation averaging problem. A new wave of approaches that leverage convex relaxations have provided the first formal guarantees of global optimality for state estimation techniques involving SO(3). However, most of these guarantees are only applicable when the measurement error introduced by noise is within a certain bound that depends on the problem instance's structure. In this paper, we cast rotation averaging as a polynomial optimization problem over unit quaternions to produce the first rotation averaging method that is formally guaranteed to provide a certifiably globally optimal solution for \textit{any} problem instance. This is achieved by formulating and solving a sparse convex sum of squares (SOS) relaxation of the problem. We provide an open source implementation of our algorithm and experiments, demonstrating the benefits of our globally optimal approach.

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arXiv2018

Entropy-Based $Sim(3)$ Calibration of 2D Lidars to Egomotion Sensors

This paper explores the use of an entropy-based technique for point cloud reconstruction with the goal of calibrating a lidar to a sensor capable of providing egomotion information. We extend recent work in this area to the problem of recovering the $Sim(3)$ transformation between a 2D lidar and a rigidly attached monocular camera, where the scale of the camera trajectory is not known a priori. We demonstrate the robustness of our approach on realistic simulations in multiple environments, as well as on data collected from a hand-held sensor rig. Given a non-degenerate trajectory and a sufficient number of lidar measurements, our calibration procedure achieves millimetre-scale and sub-degree accuracy. Moreover, our method relaxes the need for specific scene geometry, fiducial markers, or overlapping sensor fields of view, which had previously limited similar techniques.

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arXiv2018

Near-Optimal Budgeted Data Exchange for Distributed Loop Closure Detection

Inter-robot loop closure detection is a core problem in collaborative SLAM (CSLAM). Establishing inter-robot loop closures is a resource-demanding process, during which robots must consume a substantial amount of mission-critical resources (e.g., battery and bandwidth) to exchange sensory data. However, even with the most resource-efficient techniques, the resources available onboard may be insufficient for verifying every potential loop closure. This work addresses this critical challenge by proposing a resource-adaptive framework for distributed loop closure detection. We seek to maximize task-oriented objectives subject to a budget constraint on total data transmission. This problem is in general NP-hard. We approach this problem from different perspectives and leverage existing results on monotone submodular maximization to provide efficient approximation algorithms with performance guarantees. The proposed approach is extensively evaluated using the KITTI odometry benchmark dataset and synthetic Manhattan-like datasets.

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arXiv2018

Talk Resource-Efficiently to Me: Optimal Communication Planning for Distributed Loop Closure Detection

Due to the distributed nature of cooperative simultaneous localization and mapping (CSLAM), detecting inter-robot loop closures necessitates sharing sensory data with other robots. A na\"ıve approach to data sharing can easily lead to a waste of mission-critical resources. This paper investigates the logistical aspects of CSLAM. Particularly, we present a general resource-efficient communication planning framework that takes into account both the total amount of exchanged data and the induced division of labor between the participating robots. Compared to other state-of-the-art approaches, our framework is able to verify the same set of potential inter-robot loop closures while exchanging considerably less data and influencing the induced workloads. We develop a fast algorithm for finding globally optimal communication policies, and present theoretical analysis to characterize the necessary and sufficient conditions under which simpler strategies are optimal. The proposed framework is extensively evaluated with data from the KITTI odometry benchmark datasets.

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arXiv2016

Information-based Active SLAM via Topological Feature Graphs

Active SLAM is the task of actively planning robot paths while simultaneously building a map and localizing within. Existing work has focused on planning paths with occupancy grid maps, which do not scale well and suffer from long term drift. This work proposes a Topological Feature Graph (TFG) representation that scales well and develops an active SLAM algorithm with it. The TFG uses graphical models, which utilize independences between variables, and enables a unified quantification of exploration and exploitation gains with a single entropy metric. Hence, it facilitates a natural and principled balance between map exploration and refinement. A probabilistic roadmap path-planner is used to generate robot paths in real time. Experimental results demonstrate that the proposed approach achieves better accuracy than a standard grid-map based approach while requiring orders of magnitude less computation and memory resources.

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