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In this work we present the first initialization methods equipped with explicit performance guarantees adapted to the pose-graph simultaneous localization and mapping (SLAM) and rotation averaging (RA) problems. SLAM and rotation averaging are typically formalized as large-scale nonconvex point estimation problems, with many bad local minima that can entrap the smooth optimization methods typically applied to solve them; the performance of standard SLAM and RA algorithms thus crucially depends upon the quality of the estimates used to initialize this local search. While many initialization methods for SLAM and RA have appeared in the literature, these are typically obtained as purely heuristic approximations, making it difficult to determine whether (or under what circumstances) these techniques can be reliably deployed. In contrast, in this work we study the problem of initialization through the lens of spectral relaxation. Specifically, we derive a simple spectral relaxation of SLAM and RA, the form of which enables us to exploit classical linear-algebraic techniques (eigenvector perturbation bounds) to control the distance from our spectral estimate to both the (unknown) ground-truth and the global minimizer of the estimation problem as a function of measurement noise. Our results reveal the critical role that spectral graph-theoretic properties of the measurement network play in controlling estimation accuracy; moreover, as a by-product of our analysis we obtain new bounds on the estimation error for the maximum likelihood estimators in SLAM and RA, which are likely to be of independent interest. Finally, we show experimentally that our spectral estimator is very effective in practice, producing initializations of comparable or superior quality at lower computational cost compared to existing state-of-the-art techniques.

2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) October 23-27, 2022, Kyoto, Japan, Simultaneous localization and mapping (SLAM) is a critical capability in autonomous navigation, but in order to scale SLAM to the setting of "lifelong" SLAM, particularly under memory or computation constraints, a robot must be able to determine what information should be retained and what can safely be forgotten. In graph-based SLAM, the number of edges (measurements) in a pose graph determines both the memory requirements of storing a robot's observations and the computational expense of algorithms deployed for performing state estimation using those observations; both of which can grow unbounded during long-term navigation. To address this, we propose a spectral approach for pose graph sparsification which maximizes the algebraic connectivity of the sparsified measurement graphs, a key quantity which has been shown to control the estimation error of pose graph SLAM solutions. Our algorithm, MAC (for "maximizing algebraic connectivity"), which is based on convex relaxation, is simple and computationally inexpensive, and admits formal post hoc performance guarantees on the quality of the solutions it provides. In experiments on benchmark pose-graph SLAM datasets, we show that our approach quickly produces high-quality sparsification results which retain the connectivity of the graph and, in turn, the quality of corresponding SLAM solutions, as compared to a baseline approach which does not consider graph connectivity.

2023 IEEE International Conference on Robotics and Automation (ICRA 2023) May 29 - June 2, 2023. London, UK, We present a novel initialization technique for the range-aided simultaneous localization and mapping (RASLAM) problem. In RA-SLAM we consider measurements of point-to-point distances in addition to measurements of rigid transformations to landmark or pose variables. Standard formulations of RA-SLAM approach the problem as nonconvex optimization, which requires a good initialization to obtain quality results. The initialization technique proposed here relaxes the RA-SLAM problem to a convex problem which is then solved to determine an initialization for the original, non-convex problem. The relaxation is a second-order cone program (SOCP), which is derived from a quadratically constrained quadratic program (QCQP) formulation of the RASLAM problem. As a SOCP, the method is highly scalable. We name this relaxation Second-order COnic RElaxation for RASLAM (SCORE). To our knowledge, this work represents the first convex relaxation for RA-SLAM. We present real-world and simulated experiments which show SCORE initialization permits the efficient recovery of quality solutions for a variety of challenging single- and multi-robot RA-SLAM problems with thousands of poses and range measurements.

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Aeronautics and Astronautics at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2023., Simultaneous localization and mapping (SLAM) is the process by which a robot constructs a global model of an environment from local observations of it; this is a fundamental perceptual capability supporting planning, navigation, and control. We are interested in improving the expressiveness and operational longevity of SLAM systems. In particular, we are interested in leveraging state-of-the-art machine learning methods for object detection to augment the maps robots can build with object-level semantic information. To do so, a robot must combine continuous geometric information about its trajectory and object locations with discrete semantic information about object classes. This problem is complicated by the fact that object detection techniques are often unreliable in novel environments, introducing outliers and making it difficult to determine the correspondence between detected objects and mapped landmarks. For robust long-term navigation, a robot must contend with these discrete sources of ambiguity. Finally, even when measurements are not corrupted by outliers, long-term SLAM remains a challenging computational problem: typical solution methods rely on local optimization techniques that require a good “initial guess,” and whose computational expense grows as measurements accumulate. The first contribution of this thesis addresses the problem of inference for hybrid probabilistic models, i.e., models containing both discrete and continuous states we would like to estimate. These problems frequently arise when modeling e.g., outlier contamination (where binary variables indicate whether a measurement is corrupted), or when performing object-level mapping (where discrete variables may represent measurement-landmark correspondence or object categories). The former application is crucial for designing more robust perception systems. The latter application is especially important for enabling robots to construct semantic maps; that is, maps containing objects whose, This work was generously supported by the NSF Graduate Research Fellowship Program (GRFP), ONR Neuro-Autonomy MURI grant N00014-19-1-2571, ONR grant N00014-18-1-2832, and the MIT-Portugal Program Flagship Project: Knowledge to Data.

Submitted in partial fulfillment of the requirements for the degree of Master of Science in Aeronautics and Astronautics at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 2019., The recent success of object detection systems motivates object-based representations for robot navigation; i.e. semantic simultaneous localization and mapping (SLAM), in which we aim to jointly estimate the pose of the robot over time as well as the location and semantic class of observed objects. A solution to the semantic SLAM problem necessarily addresses the continuous inference problems where am I? and where are the objects?, but also the discrete inference problem what are the objects?. We consider the problem of semantic SLAM under non-Gaussian uncertainty. The most prominent case in which this arises is from data association uncertainty, where we do not know with certainty what objects in the environment caused the measurement made by our sensor. The semantic class of an object can help to inform data association; a detection classified as a door is unlikely to be associated to a chair object. However, detectors are imperfect, and incorrect classification of objects can be detrimental to data association. While previous approaches seek to eliminate such measurements, we instead model the robot and landmark state uncertainty induced by data association in the hopes that new measurements may disambiguate state estimates, and that we may provide representations useful for developing decisionmaking strategies where a robot can take actions to mitigate multimodal uncertainty. The key insight we leverage is that the semantic SLAM problem with unknown data association can be reframed as a non-Gaussian inference problem. We present two solutions to the resulting problem: we first assume Gaussian measurement models, and non-Gaussianity only due to data association uncertainty. We then relax this assumption and provide a method that can cope with arbitrary non-Gaussian measurement models. We show quantitatively on both simulated and real data that both proposed methods have robustness advantages as compared to traditional solutions when data associations are uncertai, This work was partially supported by the Office of Naval Research under grants N00014-18-1-2832 and N00014-16-2628, as well as the National Science Foundation (NSF) Graduate Research Fellowship.

The 2018 National Defense Strategy describes the worldwide threat environment as one in which our military advantage is eroding and where interstate competition is now the most prevalent threat. Reducing the time needed to deploy forces to counter these threats is essential to national security. A key enabler of this is the operational readiness of the force. The Marine Corps’ Readiness and Availability Tool (RAT) provides insight to Marine Corps leadership on the effects of readiness policies and world events on operational readiness. This thesis uses large-scale simulation and design of experiments to methodically explore the dynamic interactions of the RAT and provide insight on the key factors, critical readiness decision thresholds and model interactions. Analysis of 1200 simulated readiness timelines highlights the critical importance of not focusing on any one aspect of readiness planning, but rather considering the interactions between force structure, deployment-demand, and force-generation-timeline decisions when developing a force-wide readiness strategy for the Marine Corps. Home-station readiness levels were found to be deficient as a stand-alone metric of success for tracking the Marine Corps’ readiness capacity to meet demand. The author used a multiple-objective analysis to better understand readiness capacity by exploring the trade-off between the level of home-station readiness maintained and the quantifying metric, risk of deploying non-ready forces.

Lightweight ceramic-metal combinations are one option for advanced vehicle and other structural applications. These structures can require the fabrication of large area arrays of ceramic tiles on a metallic backing. However, the process of fabricating a combination of lightweight ceramics and metals is complicated by the need to bond these very dissimilar materials together. For severe applications, a strong bond between the ceramic and metal is required. One option for achieving this strong bonding in ceramic-metal systems is active metal brazing. The active brazing alloys wet most materials (including ceramics and corrosion-resistant metals such as titanium alloys and stainless steels) and form strong, metallurgical bonds. However, the high processing temperatures result in large strain (stress) build-up from the inherent differences in coefficient of thermal expansion (CTE) of the substrates. There are some techniques available to alleviate the strains on the ceramic, such as using an interlayer, which either has an intermediate value (between the metal and ceramic) of CTE and/or is soft (plastically deforms). However, it is still extremely challenging to actively braze large specimens when there is a considerable CTE gradient. This study will introduce pyramidal core structures as one of many possible interlayers between ceramic tiles and metal substrates. The processing techniques to successfully fabricate lightweight, large area ceramic-metal arrays will also be discussed., The original document contains color images. IBSC 2012: Proceedings From the 5th International Brazing and Soldering Conference, Las Vegas, NV, 22 25 April 2012.

Future lightweight military vehicles will demand increasingly mass-efficient structures to satisfy design requirements such as increased mobility and survivability. One possible family of lightweight structures entails sandwich panels consisting of solid facesheets and a low-density core. The sandwich structures can provide both structural strength and stiffness, with load-bearing potential. In this study, sandwich panels consisting of metallic facesheets and a pyramidal truss core manufactured from either 6061-T6 aluminum or 316L stainless steel are investigated. The structures were subjected to panel bending and in-plane compression testing to explore the effects of relative core density and process parameters. The mechanical response and failure mechanisms were categorized for the different structures and materials. The processing challenges associated with fabricating larger panels are also discussed., The original document contains color images.

Titanium is a candidate as a structural material for all new tactical and armored ground vehicles, because of its high strength-to-weight ratio, excellent corrosion resistance, and inherent ballistic resistance. However, titanium as a structural material is much less mature than both steel and aluminum alloys, especially in the area of joining. While welding is the typical joining method for titanium, vacuum brazing is an option in areas that are difficult to access for welding as well as areas near other nonmetallic materials, such as ceramics. This work focuses on vacuum brazing of titanium (both Ti-6Al-4V and commercially pure titanium) and the effect of processing changes (alloy, temperature, pressure), including post-braze hot isostatic pressing, on mechanical properties and microstructure. This study will examine the joining of both plate materials as well as lightweight, periodic pyramidal core structures. Shear and tensile testing is performed to determine the strength/ductility relationship to the various processing routes. Microscopy (optical and SEM) is employed to quantify the degree of bonding and to examine the microstructural changes, both within the base materials and at the bond line, associated with the process variations., The original document contains color images. Reprint from the Proceedings of the 3rd International Brazing and Soldering Conference, p268-273, San Antonio, TX, 24-26 Apr 2006.

Future military vehicles demand increasingly mass-efficient structural armor systems to satisfy design requirements of increased mobility and survivability. In order to fully realize lightweight solutions, sandwich plates consisting of monolithic facesheets and a low-density cellular core are targeted as an integral ingredient in these armor systems, providing both structural strength and stiffness via through-the-thickness load-bearing potential. In this study, sandwich plates consisting of thin facesheets and a periodic pyramidal core manufactured entirely from cold-rolled Grade 4 commercially-pure titanium (CP-1) are investigated. A plausible manufacturing route and its corresponding limitations are established, and analytical models for peak strength and effective stiffness for flatwise compression are presented. In addition, a strength-to-weight optimization technique is implemented, and model calibration experiments are conducted on the as-manufactured optimized plates. From these experiments, the model for peak strength was found to be a robust and accurate tool for depicting core performance. Although modeling effective stiffness was less successful, probable causes for reduced precision are presented. Also, the as-manufactured titanium plates are verified to be fully optimized from a strength-to-weight standpoint for flatwise compression., Reprinted from the Society for the Advancement of Material and Process Engineering [SAMPE] 2007 Conference Proceedings held Baltimore, MD on 3-7 Jun 2007. The original document contains color images.

The interaction between long rods and ceramics is only partially understood; however, this understanding is essential in the design of improved performance of impact-resistant materials and armor system design applications. The current work takes a preliminary look into the modem mythology surrounding the formation of radial cracking in ceramics during ballistic penetration. Tests were conducted using a 32-g tungsten alloy laboratory penetrator with a length to diameter ratio (L/D) = 20 at a nominal impact velocity of 1,600 m/s. Testing evaluated both prestressed and unstressed titanium diboride (TiB2) ceramic tiles. Evaluation of the damage included microstructural analysis using a scanning electron microscope (SEM) with a Robinson backscatter detector for surface structure, the x-ray computed tomography (CT) nondestructive technique to completely scan the interior of each disk, and limited analytical modeling of the stress state.