Lagrangian Duality in 3D SLAM: Verification Techniques and Optimal Solutions

State-of-the-art techniques for simultaneous localization and mapping (SLAM) employ iterative nonlinear optimization methods to compute an estimate for robot poses. While these techniques often work well in practice, they do not provide guarantees on the quality of the estimate. This paper shows that Lagrangian duality is a powerful tool to assess the quality of a given candidate solution. Our contribution is threefold. First, we discuss a revised formulation of the SLAM inference problem. We show that this formulation is probabilistically grounded and has the advantage of leading to an optimization problem with quadratic objective. The second contribution is the derivation of the corresponding Lagrangian dual problem. The SLAM dual problem is a (convex) semidefinite program, which can be solved reliably and globally by off-the-shelf solvers. The third contribution is to discuss the relation between the original SLAM problem and its dual. We show that from the dual problem, one can evaluate the quality (i.e., the suboptimality gap) of a candidate SLAM solution, and ultimately provide a certificate of optimality. Moreover, when the duality gap is zero, one can compute a guaranteed optimal SLAM solution from the dual problem, circumventing non-convex optimization. We present extensive (real and simulated) experiments supporting our claims and discuss practical relevance and open problems.Comment: 10 pages, 4 figure

Infecting capitalism with the common: The class process, communication, and surplus * *

abstract This paper makes two moves in considering the question of the communism of capital. First, it draws upon diverse economies scholarship to conceptualize class as the process of creating, appropriating, and distributing surplus labor. Second, the paper relies upon autonomist Marxism to conceptualize communication as an instance of the common informing immaterial labor. These two moves situate communication as an intervention into the class process, offering new avenues for the production of capitalist surplus value. In so doing, however, capital does not capture the common. Rather, communication infects capitalism with non-capitalist practices and values. To support this argument, this paper analyzes field data from a job-training program for economically dislocated workers. The analysis highlights unexpected outcomes, including varying routes to the creation of surplus value, differing notions of value, and possibilities to rethink and restructure capitalism. The call for this special issue poses the communism of capital as a question, a matter open to investigation as well as the possibilities of the imagination. At the same time, there seems to be a belief that we have witnessed the capture of the common by capitalis

Boundary Spanners as Bridges of Student and School Discourses in an Urban Science and Mathematics High School

A key to improving urban science and mathematics education is to facilitate the mutual understanding of the participants involved and then look for strategies to bridge differences. Educators need new theoretical tools to do so. In this paper the argument is made that the concept of “boundary spanner” is such a tool. Boundary spanners are individuals, objects, media, and other experiences that link an organization to its environment. They serve critical communicative roles, such as bridges for bringing distinct discourses together, cultural guides to make discourses of the “other” more explicit, and change agents for potentially reshaping participants' discourses. This ethnographic study provides three examples of boundary spanners found in the context of an urban public high school of science, mathematics, and technology: boundary media, boundary objects, and boundary experiences. The analysis brings to the foreground students' and teachers' distinct discourses about “good student identity,”“good student work,” and “good summer experience” and demonstrates how boundary spanners shaped, were shaped by, and sometimes brought together participants' distinct discourses. An argument is made for boundary spanners' practical and theoretical utility: practically, as a tool for enhancing meaning-making between diverse groups, and theoretically, as a heuristic tool for understanding the reproductive and transformative aspects of urban science education

SE-Sync: a certifiably correct algorithm for synchronization over the special Euclidean group

Many important geometric estimation problems naturally take the form of synchronization over the special Euclidean group: estimate the values of a set of unknown group elements (Formula presented.) given noisy measurements of a subset of their pairwise relative transforms (Formula presented.). Examples of this class include the foundational problems of pose-graph simultaneous localization and mapping (SLAM) (in robotics), camera motion estimation (in computer vision), and sensor network localization (in distributed sensing), among others. This inference problem is typically formulated as a non-convex maximum-likelihood estimation that is computationally hard to solve in general. Nevertheless, in this paper we present an algorithm that is able to efficiently recover certifiably globally optimal solutions of the special Euclidean synchronization problem in a non-adversarial noise regime. The crux of our approach is the development of a semidefinite relaxation of the maximum-likelihood estimation (MLE) whose minimizer provides an exact maximum-likelihood estimate so long as the magnitude of the noise corrupting the available measurements falls below a certain critical threshold; furthermore, whenever exactness obtains, it is possible to verify this fact a posteriori, thereby certifying the optimality of the recovered estimate. We develop a specialized optimization scheme for solving large-scale instances of this semidefinite relaxation by exploiting its low-rank, geometric, and graph-theoretic structure to reduce it to an equivalent optimization problem defined on a low-dimensional Riemannian manifold, and then design a Riemannian truncated-Newton trust-region method to solve this reduction efficiently. Finally, we combine this fast optimization approach with a simple rounding procedure to produce our algorithm, SE-Sync. Experimental evaluation on a variety of simulated and real-world pose-graph SLAM datasets shows that SE-Sync is capable of recovering certifiably globally optimal solutions when the available measurements are corrupted by noise up to an order of magnitude greater than that typically encountered in robotics and computer vision applications, and does so significantly faster than the Gauss–Newton-based approach that forms the basis of current state-of-the-art techniques

SE-Sync: A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group

Many important geometric estimation problems naturally take the form of synchronization over the special Euclidean group: estimate the values of a set of unknown poses given noisy measurements of a subset of their pairwise relative transforms. Examples of this class include the foundational problems of pose-graph simultaneous localization and mapping (SLAM) (in robotics), camera motion estimation (in computer vision), and sensor network localization (in distributed sensing), among others. This inference problem is typically formulated as a nonconvex maximum-likelihood estimation that is computationally hard to solve in general. Nevertheless, in this paper we present an algorithm that is able to efficiently recover certifiably globally optimal solutions of the special Euclidean synchronization problem in a non-adversarial noise regime. The crux of our approach is the development of a semidefinite relaxation of the maximum-likelihood estimation whose minimizer provides an exact MLE so long as the magnitude of the noise corrupting the available measurements falls below a certain critical threshold; furthermore, whenever exactness obtains, it is possible to verify this fact a posteriori, thereby certifying the optimality of the recovered estimate. We develop a specialized optimization scheme for solving large-scale instances of this semidefinite relaxation by exploiting its low-rank, geometric, and graph-theoretic structure to reduce it to an equivalent optimization problem defined on a low-dimensional Riemannian manifold, and then design a Riemannian truncated-Newton trust-region method to solve this reduction efficiently. Finally, we combine this fast optimization approach with a simple rounding procedure to produce our algorithm, SE-Sync. Experimental evaluation on a variety of simulated and real-world pose-graph SLAM datasets shows that SE-Sync is capable of recovering certifiably globally optimal solutions when the available measurements are corrupted by noise up to an order of magnitude greater than that typically encountered in robotics and computer vision applications, and does so more than an order of magnitude faster than the Gauss-Newton-based approach that forms the basis of current state-of-the-art techniques

Manifestations of Neoliberal Discourses Within a Local Job-Training Program

The purpose of conducting this study was to understand how neoliberal discourses manifest within the local context of a short-term, job-training program offered at a two-year college in the USA. Ethnographic data were collected at the local site through interviews, observations and document analysis. We then situated these data within a global context represented by a corpus of purposively selected national and international policy texts. Focusing on three components of discourse as social action—genres, representations and identities—the data analysis illuminated three interrelated themes relating to how institutional actors translated neoliberal discourses available at the global scale into practice. The ideological consequences for learners as well as examples of counter-hegemonic resistance are discussed

Silicon communication: A reply and case study

In their contributions to this forum, Nadesan, Cloud, and Weaver have critiqued and extended our argument for the benefits of collaboration between organizational communication and cultural studies. Originally (Carlone & Taylor, 1998), we argued that communication scholars should integrate the resources of these fields to fashion new ways of engaging the convergence of organization and culture in the post-industrial, hyper-capitalist new economy. In response, Nadesan has distinguished a variety of arguments concerning the nature and consequences of “post-Fordism,” Cloud has asserted the enduring relevance of materiality and class, and Weaver has called for public relations practitioners and scholars to reflect on the “worldly” affiliations of their work with the hegemonic interests of profit, efficiency, and progress. In this short article, we address these responses and advance our project through a case study of a particular object

The ambiguous nature of a management guru lecture: Providing answers while deepening uncertainty

Each year, managers and employees spend billions of dollars retaining management consultants, buying business books, and attending seminars to regain certainty. Some of this quest occurs in the lectures of star management consultants, such as Stephen R. Covey. For his audience, a Covey lecture is a liminoid event, that is, a middle phase in a secular rite of passage from “ineffective” to “effective.” Viewed through the lens of liminoidity, the lecture (a) disrupts the ontology of business subjects, (b) gains force by blending sacred wisdom and technical instruction, (c) makes permanent a transitional stage, and (d) situates the lecturer as guru and audience members as neophytes through their interaction with one another. Despite the quest for certainty, Covey?s lectures simultaneously ease and deepen uncertainty and anxiety

Meaningful work and organizational communication: Questioning boundaries, positionalities and engagements

As organizational communication scholars, we routinely orient ourselves to organizations as places of work while often ignoring the diverse forms of communicative work and communication about our working lives that underpin such locales. In this essay, we consider how the study of meaningful work problematizes the boundaries of organizational communication. Specifically, we reflect on how definitions of meaningful work are very much caught up in our contemporary milieu. Organizational communication scholars, then, must be willing and able to work within and across traditional boundaries, perhaps redefining them in the process. We illustrate these claims in three parts. In the first part, we consider the rise of communication work and how it calls into question common notions of meaningful work. In our second section, we argue that what counts as meaningful work often stems from the raced, classed, and gendered assumptions guiding our practice. Finally, in part three, and with these elements of our milieu in mind, we describe ways in which scholars can begin to investigate meaningful work by examining tensions between description and prescription and microlevels and macrolevels of discourse and experience to uncover the strategies and tactics available to individuals as they craft meaningful working lives