arXiv subjects

Vijay Kumar

Publications and source records attributed to Vijay Kumar.

At least 235 records · Page 13Linked to original sources

arXiv2017

A Macroscopic Model for Differential Privacy in Dynamic Robotic Networks

The increasing availability of online and mobile information platforms is facilitating the development of peer-to-peer collaboration strategies in large-scale networks. These technologies are being leveraged by networked robotic systems to provide applications of automated transport, resource redistribution (collaborative consumption), and location services. Yet, external observations of the system dynamics may expose sensitive information about the participants that compose these networks (robots, resources, and humans). In particular, we are concerned with settings where an adversary gains access to a snapshot of the dynamic state of the system. We propose a method that quantifies how easy it is for the adversary to identify the specific type of any agent (which can be a robot, resource, or human) in the network, based on this observation. We draw from the theory of differential privacy to propose a closed-form expression for the leakage of the system when the snapshot is taken at steady-state, as well as a numerical approach to compute the leakage when the snapshot is taken at any given time. The novelty of our approach is that our privacy model builds on a macroscopic description of the system's state, which allows us to take account of protected entities (network participants) that are interdependent. Our results show how the leakage varies, as a function of the composition and dynamic behavior of the network; they also indicate design rules for increasing privacy levels.

cs.RO↗

arXiv2016

Algorithms for Visibility-Based Monitoring with Robot Teams

We study the problem of planning paths for a team of robots for visually monitoring an environment. Our work is motivated by surveillance and persistent monitoring applications. We are given a set of target points in a polygonal environment that must be monitored using robots with cameras. The goal is to compute paths for all robots such that every target is visible from at least one path. In its general form, this problem is NP-hard as it generalizes the Art Gallery Problem and the Watchman Route Problem. We study two versions: (i) a geometric version in \emph{street polygons} for which we give a polynomial time $4$--approximation algorithm; and (ii) a general version for which we present a practical solution that finds the optimal solution in possibly exponential time. In addition to theoretical proofs, we also present results from simulation studies.

cs.RO↗

arXiv2016

DimensionApp : android app to estimate object dimensions

In this project, we develop an android app that uses on computer vision techniques to estimate an object dimension present in field of view. The app while having compact size, is accurate upto +/- 5 mm and robust towards touch inputs. We use single-view metrology to compute accurate measurement. Unlike previous approaches, our technique does not rely on line detection and can be generalize to any object shape easily.

cs.CV↗

arXiv2016

Toward a Science of Autonomy for Physical Systems: Aerial Earth Science

Unmanned Aerial Vehicles (UAVs) equipped with LiDAR, electro-optical and infrared cameras, SAR and atmospheric sensors have transformed the way we acquire high spatio-temporal resolution data. For example, UAVs equipped with these sensors have been able to obtain topography at resolutions of less than one meter, revolutionizing earth sciences. Surface processes act at spatial scales on the order of a meter to produce intricate landforms and UAVs equipped with these sensors are able to measure the three dimensional spatio-temporal geometry of the earths surface and overlying anthropogenic features and vegetation at resolutions appropriate to document these processes. In addition, surface changes due to erosion, transport and sedimentation, as well as earthquakes, landslides, volcanoes can be quantified with this data.

cs.CY↗

arXiv2016

Next Generation Robotics

The National Robotics Initiative (NRI) was launched 2011 and is about to celebrate its 5 year anniversary. In parallel with the NRI, the robotics community, with support from the Computing Community Consortium, engaged in a series of road mapping exercises. The first version of the roadmap appeared in September 2009; a second updated version appeared in 2013. While not directly aligned with the NRI, these road-mapping documents have provided both a useful charting of the robotics research space, as well as a metric by which to measure progress. This report sets forth a perspective of progress in robotics over the past five years, and provides a set of recommendations for the future. The NRI has in its formulation a strong emphasis on co-robot, i.e., robots that work directly with people. An obvious question is if this should continue to be the focus going forward? To try to assess what are the main trends, what has happened the last 5 years and what may be promising directions for the future a small CCC sponsored study was launched to have two workshops, one in Washington DC (March 5th, 2016) and another in San Francisco, CA (March 11th, 2016). In this report we brief summarize some of the main discussions and observations from those workshops. We will present a variety of background information in Section 2, and outline various issues related to progress over the last 5 years in Section 3. In Section 4 we will outline a number of opportunities for moving forward. Finally, we will summarize the main points in Section 5.

cs.CY↗

arXiv2016

Toward a Science of Autonomy for Physical Systems

Our lives have been immensely improved by decades of automation research -- we are more comfortable, more productive and safer than ever before. Just imagine a world where familiar automation technologies have failed. In that world, thermostats don't work -- you have to monitor your home heating system manually. Cruise control for your car doesn't exist. Every elevator has to have a human operator to hit the right floor, most manufactured products are assembled by hand, and you have to wash your own dishes. Who would willingly adopt that world -- the world of last century -- today? Physical systems -- elevators, cars, home appliances, manufacturing equipment -- were more troublesome, ore time consuming, less safe, and far less convenient. Now, suppose we put ourselves in the place someone 20 years in the future, a future of autonomous systems. A future where transportation is largely autonomous, more efficient, and far safer; a future where dangerous occupations like mining or disaster response are performed by autonomous systems supervised remotely by humans; a future where manufacturing and healthcare are twice as productive per person-hour by having smart monitoring and readily re-tasked autonomous physical agents; a future where the elderly and infirm have 24 hour in-home autonomous support for the basic activities, both physical and social, of daily life. In a future world where these capabilities are commonplace, why would someone come back to today's world where someone has to put their life at risk to do a menial job, we lose time to mindless activities that have no intrinsic value, or be consumed with worry that a loved one is at risk in their own home? In what follows, and in a series of associated essays, we expand on these ideas, and frame both the opportunities and challenges posed by autonomous physical systems.

cs.CY↗

arXiv2015

Ecosystem: A Characteristic Of Crowdsourced Environments

The phenomenal success of certain crowdsourced online platforms, such as Wikipedia, is accredited to their ability to tap the crowd's potential to collaboratively build knowledge. While it is well known that the crowd's collective wisdom surpasses the cumulative individual expertise, little is understood on the dynamics of knowledge building in a crowdsourced environment. A proper understanding of the dynamics of knowledge building in a crowdsourced environment would enable one in the better designing of such environments to solicit knowledge from the crowd. Our experiment on crowdsourced systems based on annotations shows that an important reason for the rapid knowledge building in such environments is due to variance in expertise. First, we used as our test bed, a customized Crowdsourced Annotation System (CAS) which provides a group of users the facility to annotate a given document while trying to understand it. Our results showed the presence of different genres of proficiency amongst the users of an annotation system. We observed that the ecosystem in crowdsourced annotation system comprised of mainly four categories of contributors, namely: Probers, Solvers, Articulators and Explorers. We inferred from our experiment that the knowledge garnering mainly happens due to the synergetic interaction across these categories. Further, we conducted an analysis on the dataset of Wikipedia and Stack Overflow and noticed the ecosystem presence in these portals as well. From this study, we claim that the ecosystem is a universal characteristic of all crowdsourced portals.

cs.CY↗

arXiv2015

Clustering by transitive propagation

We present a global optimization algorithm for clustering data given the ratio of likelihoods that each pair of data points is in the same cluster or in different clusters. To define a clustering solution in terms of pairwise relationships, a necessary and sufficient condition is that belonging to the same cluster satisfies transitivity. We define a global objective function based on pairwise likelihood ratios and a transitivity constraint over all triples, assigning an equal prior probability to all clustering solutions. We maximize the objective function by implementing max-sum message passing on the corresponding factor graph to arrive at an O(N^3) algorithm. Lastly, we demonstrate an application inspired by mutational sequencing for decoding random binary words transmitted through a noisy channel.

cs.LG↗

arXiv2015

Experimental Characterization of a Bearing-only Sensor for Use With the PHD Filter

This report outlines the procedure and results of an experiment to characterize a bearing-only sensor for use with PHD filter. The resulting detection, measurement, and clutter models are used for hardware and simulated experiments with a team of mobile robots autonomously seeking an unknown number of objects of interest in an office environment.

cs.RO↗

arXiv2014

New Methods for Characterizing Phases of 2D Supersymmetric Gauge Theories

We study the physics of two-dimensional N=(2,2) gauged linear sigma models (GLSMs) via the two-sphere partition function. We show that the classical phase boundaries separating distinct GLSM phases, which are described by the secondary fan construction for abelian GLSMs, are completely encoded in the analytic structure of the partition function. The partition function of a non-abelian GLSM can be obtained as a limit from an abelian theory; we utilize this fact to show that the phases of non-abelian GLSMs can be obtained from the secondary fan of the associated abelian GLSM. We prove that the partition function of any abelian GLSM satisfies a set of linear differential equations; these reduce to the familiar A-hypergeometric system of Gel'fand, Kapranov, and Zelevinski for GLSMs describing complete intersections in toric varieties. We develop a set of conditions that are necessary for a GLSM phase to admit an interpretation as the low-energy limit of a non-linear sigma model with a Calabi-Yau threefold target space. Through the application of these criteria we discover a class of GLSMs with novel geometric phases corresponding to Calabi-Yau manifolds that are branched double-covers of Fano threefolds. These criteria provide a promising approach for constructing new Calabi-Yau geometries.

hep-th↗

arXiv2014

Generation of isolated asymmetric umbilics in light's polarization

Polarization-singularity C-points, a form of line singularities, are the vectorial counterparts of the optical vortices of spatial modes and fundamental optical features of polarization-spatial modes. Their generation in tailored beams has been limited to lemon and star C-points that contain symmetric dislocations in state-of-polarization patterns. In this article we present the theory and laboratory measurements of two complementary methods to generate isolated asymmetric C-points in tailored beams, of which symmetric lemons and stars are limiting cases; and we report on the generation of monstars, an asymmetric C-point with characteristics of both lemons and stars.

physics.optics↗

arXiv2013

Two-Sphere Partition Functions and Gromov-Witten Invariants

Many N=(2,2) two-dimensional nonlinear sigma models with Calabi-Yau target spaces admit ultraviolet descriptions as N=(2,2) gauge theories (gauged linear sigma models). We conjecture that the two-sphere partition function of such ultraviolet gauge theories -- recently computed via localization by Benini et al. and Doroud et al. -- yields the exact Kähler potential on the quantum Kähler moduli space for Calabi-Yau threefold target spaces. In particular, this allows one to compute the genus zero Gromov-Witten invariants for any such Calabi-Yau threefold without the use of mirror symmetry. More generally, when the infrared superconformal fixed point is used to compactify string theory, this provides a direct method to compute the spacetime Kähler potential of certain moduli (e.g., vector multiplet moduli in type IIA), exactly in α'. We compute these quantities for the quintic and for Rødland's Pfaffian Calabi-Yau threefold and find agreement with existing results in the literature. We then apply our methods to a codimension four determinantal Calabi-Yau threefold in P^7, recently given a nonabelian gauge theory description by the present authors, for which no mirror Calabi-Yau is currently known. We derive predictions for its Gromov-Witten invariants and verify that our predictions satisfy nontrivial geometric checks.

hep-th↗

arXiv2013

Technical Report: Cooperative Multi-Target Localization With Noisy Sensors

This technical report is an extended version of the paper 'Cooperative Multi-Target Localization With Noisy Sensors' accepted to the 2013 IEEE International Conference on Robotics and Automation (ICRA). This paper addresses the task of searching for an unknown number of static targets within a known obstacle map using a team of mobile robots equipped with noisy, limited field-of-view sensors. Such sensors may fail to detect a subset of the visible targets or return false positive detections. These measurement sets are used to localize the targets using the Probability Hypothesis Density, or PHD, filter. Robots communicate with each other on a local peer-to-peer basis and with a server or the cloud via access points, exchanging measurements and poses to update their belief about the targets and plan future actions. The server provides a mechanism to collect and synthesize information from all robots and to share the global, albeit time-delayed, belief state to robots near access points. We design a decentralized control scheme that exploits this communication architecture and the PHD representation of the belief state. Specifically, robots move to maximize mutual information between the target set and measurements, both self-collected and those available by accessing the server, balancing local exploration with sharing knowledge across the team. Furthermore, robots coordinate their actions with other robots exploring the same local region of the environment.

cs.RO↗

arXiv2012

Nonabelian 2D Gauge Theories for Determinantal Calabi-Yau Varieties

The two-dimensional supersymmetric gauged linear sigma model (GLSM) with abelian gauge groups and matter fields has provided many insights into string theory on Calabi--Yau manifolds of a certain type: complete intersections in toric varieties. In this paper, we consider two GLSM constructions with nonabelian gauge groups and charged matter whose infrared CFTs correspond to string propagation on determinantal Calabi-Yau varieties, furnishing another broad class of Calabi-Yau geometries in addition to complete intersections. We show that these two models -- which we refer to as the PAX and the PAXY model -- are dual descriptions of the same low-energy physics. Using GLSM techniques, we determine the quantum Kähler moduli space of these varieties and find no disagreement with existing results in the literature.

hep-th↗

arXiv2012

Invariants for Homology Classes with Application to Optimal Search and Planning Problem in Robotics

We consider planning problems on a punctured Euclidean spaces, $\mathbb{R}^D - \widetilde{\mathcal{O}}$, where $\widetilde{\mathcal{O}}$ is a collection of obstacles. Such spaces are of frequent occurrence as configuration spaces of robots, where $\widetilde{\mathcal{O}}$ represent either physical obstacles that the robots need to avoid (e.g., walls, other robots, etc.) or illegal states (e.g., all legs off-the-ground). As state-planning is translated to path-planning on a configuration space, we collate equivalent plannings via topologically-equivalent paths. This prompts finding or exploring the different homology classes in such environments and finding representative optimal trajectories in each such class. In this paper we start by considering the problem of finding a complete set of easily computable homology class invariants for $(N-1)$-cycles in $(\mathbb{R}^D - \widetilde{\mathcal{O}})$. We achieve this by finding explicit generators of the $(N-1)^{st}$ de Rham cohomology group of this punctured Euclidean space, and using their integrals to define cocycles. The action of those dual cocycles on $(N-1)$-cycles gives the desired complete set of invariants. We illustrate the computation through examples. We further show that, due to the integral approach, this complete set of invariants is well-suited for efficient search-based planning of optimal robot trajectories with topological constraints. Finally we extend this approach to computation of invariants in spaces derived from $(\mathbb{R}^D - \widetilde{\mathcal{O}})$ by collapsing subspace, thereby permitting application to a wider class of non-Euclidean ambient spaces.

math.AT↗

arXiv2012

Freedom and Constraints in the K3 Landscape

We consider "magnetized brane" compactifications of the type I/heterotic string on K3 with U(1) background fluxes. The nonabelian gauge group and matter content of the resulting six-dimensional vacua are parameterized by a matrix encoding a lattice contained within the even, self-dual lattice Gamma^{3,19}. Mathematical results of Nikulin on lattice embeddings make possible a simple classification of such solutions. This approach makes it possible to explicitly and efficiently construct models in this class with a particular allowed gauge group and matter content, so that one can immediately "dial-a-model" with desired properties.

hep-th↗

arXiv2012

Mapping 6D N = 1 supergravities to F-theory

We develop a systematic framework for realizing general anomaly-free chiral 6D supergravity theories in F-theory. We focus on 6D (1, 0) models with one tensor multiplet whose gauge group is a product of simple factors (modulo a finite abelian group) with matter in arbitrary representations. Such theories can be decomposed into blocks associated with the simple factors in the gauge group; each block depends only on the group factor and the matter charged under it. All 6D chiral supergravity models can be constructed by gluing such blocks together in accordance with constraints from anomalies. Associating a geometric structure to each block gives a dictionary for translating a supergravity model into a set of topological data for an F-theory construction. We construct the dictionary of F-theory divisors explicitly for some simple gauge group factors and associated matter representations. Using these building blocks we analyze a variety of models. We identify some 6D supergravity models which do not map to integral F-theory divisors, possibly indicating quantum inconsistency of these 6D theories.

hep-th↗

arXiv2011

N=1 Sigma Models in AdS_4

We study sigma models in AdS_4 with global N=1 supersymmetry and find that they differ significantly from their flat-space cousins -- the target space is constrained to be a Kahler manifold with an exact Kahler form, the superpotential transforms under Kahler transformations, the space of supersymmetric vacua is generically a set of isolated points even when the superpotential vanishes, and the R-symmetry is classically broken by the cosmological constant. Remarkably, the exactness of the Kahler class is also required for the sigma model to arise as a decoupling limit of N=1 supergravity, and ensures the vanishing of gravitational anomalies. As simple applications of these results, we argue that fields with AdS_4 scale masses are ubiquitous in, for example, type IIB N=1 AdS_4 vacua stabilized near large volume; we also show that the Affleck-Dine-Seiberg runaway of N_f < N_c SQCD is regulated by considering the theory in AdS_4.

hep-th↗