Swaroop Darbha

Bio: Swaroop Darbha is an academic researcher from Texas A&M University. The author has contributed to research in topics: Travelling salesman problem & Approximation algorithm. The author has an hindex of 28, co-authored 162 publications receiving 3767 citations. Previous affiliations of Swaroop Darbha include Air Force Research Laboratory & University of California, Berkeley.

Combinatorial Motion Planning of Multiple Vehicle Systems

Abstract: In this paper, we are concerned with the development of approximation algorithms for the combinatorial motion planning of a collection of m vehicles. Specifically, we consider the following multiple depot, generalized multiple traveling salesmen problem (GMTSP). We are given m vehicles that start at possibly different locations and n targets that must be visited. The problem is to choose at most p les m vehicles so that (1) each target is visited by exactly one of the chosen vehicles and (2) the cost of the tours of the chosen vehicles is a minimum among all possible choices and their corresponding tours of vehicles. The criteria for the cost of tours considered is the total distance (total cost of edges) traveled by the entire collection. This problem is a generalization of the symmetric traveling salesman problem (TSP) and is NP-hard. We show that there is a 2-approx algorithm for this problem. We also provide a branch and bound procedure for this problem

Computation of lower bounds for a multiple depot, multiple vehicle routing problem with motion constraints

Abstract: In this paper, the problem of planning paths for a collection of vehicles passing through a set of targets is considered. Each vehicle starts at a specified location (called a depot) and it is required that each target be on the path of at least one vehicle. Every vehicle has a motion constraint and the path of each vehicle must satisfy that constraint. In this article, we developed a method to compute lower bounds to this path planning problem by relaxing some of the constraints and posing it as a standard multiple traveling salesmen problem. For those problem instances where the distance between every pair of targets is at least 4 units, another method is developed to compute a lower bound using the convexity property of the length of such paths. The proposed bounds are numerically corroborated.

Persistent Monitoring of Dynamically Changing Environments Using an Unmanned Vehicle.

Abstract: We consider the problem of planning a closed walk $\mathcal W$ for a UAV to persistently monitor a finite number of stationary targets with equal priorities and dynamically changing properties. A UAV must physically visit the targets in order to monitor them and collect information therein. The frequency of monitoring any given target is specified by a target revisit time, $i.e.$, the maximum allowable time between any two successive visits to the target. The problem considered in this paper is the following: Given $n$ targets and $k \geq n$ allowed visits to them, find an optimal closed walk $\mathcal W^*(k)$ so that every target is visited at least once and the maximum revisit time over all the targets, $\mathcal R(\mathcal W(k))$, is minimized. We prove the following: If $k \geq n^2-n$, $\mathcal R(\mathcal W^*(k))$ (or simply, $\mathcal R^*(k)$) takes only two values: $\mathcal R^*(n)$ when $k$ is an integral multiple of $n$, and $\mathcal R^*(n+1)$ otherwise. This result suggests significant computational savings - one only needs to determine $\mathcal W^*(n)$ and $\mathcal W^*(n+1)$ to construct an optimal solution $\mathcal W^*(k)$. We provide MILP formulations for computing $\mathcal W^*(n)$ and $\mathcal W^*(n+1)$. Furthermore, for {\it any} given $k$, we prove that $\mathcal R^*(k) \geq \mathcal R^*(k+n)$.

Efficient Computation of Optimal UAV Routes for Persistent Monitoring of Targets

Abstract: In this article, we consider a routing problem that arises in the scenario of persistently monitoring a set of targets using an unmanned vehicle. A UAV is tasked with monitoring a set of targets, by frequently visiting them for data collection. The UAV has a limited fuel capacity, which is specified in terms of the number of visits it makes, at the end of which it must be recharged at a depot. The problem considered here is to plan an optimal sequence of visits (to targets) for the UAV, such that the maximum time between consecutive revisits to the targets is minimized. The problem is a generalization of the Traveling Salesman Problem (TSP) and is computationally challenging; It is significantly difficult to compute optimal solutions using standard formulations. However, the authors recently developed a set of theoretical results characterizing the structure of optimal solutions for this problem. Using these results, in this article, we propose a new formulation to solve the problem. Extensive numerical simulations suggest that the average computation time required to solve the problem using the proposed formulation is within a fraction of a second on a standard laptop (here, a MacBook Pro with Intel Core i7 processor and 16 GB RAM was used).

Optimal Cooperative Pursuit on a Manhattan Grid

Abstract: The optimal control of two pursuers searching for a slower moving evader on a Manhattan grid road network is considered. The pursuers do not have on-board capability to detect the evader and rely instead on Unattended Ground Sensors (UGSs) to locate the evader. We assume that all the intersections in the road network have been instrumented with UGSs. When an evader passes by an UGS location, it triggers the UGS and this time-stamped information is stored by the UGS. When a pursuer arrives at an UGS location, the UGS informs the pursuer if and when the evader passed by. When the evader and a pursuer arrive at an UGS location simultaneously, the UGS is triggered and this information is instantly relayed to the pursuer, thereby enabling “capture”. We derive exact values for the minimum time guaranteed capture of the evader on the Manhattan grid and the corresponding pursuit policy.

Multi-messenger observations of a binary neutron star merger

Abstract: On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of $\sim 1.7\,{\rm{s}}$ with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg2 at a luminosity distance of ${40}_{-8}^{+8}$ Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 $\,{M}_{\odot }$. An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at $\sim 40\,{\rm{Mpc}}$) less than 11 hours after the merger by the One-Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ~10 days. Following early non-detections, X-ray and radio emission were discovered at the transient's position $\sim 9$ and $\sim 16$ days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC 4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta.

Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms

Abstract: This self-contained introduction to the distributed control of robotic networks offers a distinctive blend of computer science and control theory. The book presents a broad set of tools for understanding coordination algorithms, determining their correctness, and assessing their complexity; and it analyzes various cooperative strategies for tasks such as consensus, rendezvous, connectivity maintenance, deployment, and boundary estimation. The unifying theme is a formal model for robotic networks that explicitly incorporates their communication, sensing, control, and processing capabilities--a model that in turn leads to a common formal language to describe and analyze coordination algorithms.Written for first- and second-year graduate students in control and robotics, the book will also be useful to researchers in control theory, robotics, distributed algorithms, and automata theory. The book provides explanations of the basic concepts and main results, as well as numerous examples and exercises.Self-contained exposition of graph-theoretic concepts, distributed algorithms, and complexity measures for processor networks with fixed interconnection topology and for robotic networks with position-dependent interconnection topology Detailed treatment of averaging and consensus algorithms interpreted as linear iterations on synchronous networks Introduction of geometric notions such as partitions, proximity graphs, and multicenter functions Detailed treatment of motion coordination algorithms for deployment, rendezvous, connectivity maintenance, and boundary estimation

Masses, Radii, and the Equation of State of Neutron Stars

Abstract: We summarize our current knowledge of neutron-star masses and radii. Recent instrumentation and computational advances have resulted in a rapid increase in the discovery rate and precise timing of radio pulsars in binaries in the past few years, leading to a large number of mass measurements. These discoveries show that the neutron-star mass distribution is much wider than previously thought, with three known pulsars now firmly in the 1.9–2.0-M⊙ mass range. For radii, large, high-quality data sets from X-ray satellites as well as significant progress in theoretical modeling led to considerable progress in the measurements, placing them in the 10–11.5-km range and shrinking their uncertainties, owing to a better understanding of the sources of systematic errors. The combination of the massive-neutron-star discoveries, the tighter radius measurements, and improved laboratory constraints of the properties of dense matter has already made a substantial impact on our understanding of the composition and bulk p...

Short-Duration Gamma-Ray Bursts

Abstract: Gamma-ray bursts (GRBs) display a bimodal duration distribution with a separation between the short- and long-duration bursts at about 2 s. The progenitors of long GRBs have been identified as massive stars based on their association with Type Ic core-collapse supernovae (SNe), their exclusive location in star-forming galaxies, and their strong correlation with bright UV regions within their host galaxies. Short GRBs have long been suspected on theoretical grounds to arise from compact object binary mergers (neutron star–neutron star or neutron star–black hole). The discovery of short GRB afterglows in 2005 provided the first insight into their energy scale and environments, as well as established a cosmological origin, a mix of host-galaxy types, and an absence of associated SNe. In this review, I summarize nearly a decade of short GRB afterglow and host-galaxy observations and use this information to shed light on the nature and properties of their progenitors, the energy scale and collimation of the relativistic outflow, and the properties of the circumburst environments. The preponderance of the evidence points to compact object binary progenitors, although some open questions remain. On the basis of this association, observations of short GRBs and their afterglows can shed light on the on- and off-axis electromagnetic counterparts of gravitational wave sources from the Advanced LIGO/Virgo experiments.

Origin of the heavy elements in binary neutron-star mergers from a gravitational-wave event

Abstract: Modelling the electromagnetic emission of kilonovae enables the mass, velocity and composition (with some heavy elements) of the ejecta from a neutron-star merger to be derived from the observations. Merging neutron stars are potential sources of gravitational waves and have long been predicted to produce jets of material as part of a low-luminosity transient known as a 'kilonova'. There is growing evidence that neutron-star mergers also give rise to short, hard gamma-ray bursts. A group of papers in this issue report observations of a transient associated with the gravitational-wave event GW170817—a signature of two neutron stars merging and a gamma-ray flash—that was detected in August 2017. The observed gamma-ray, X-ray, optical and infrared radiation signatures support the predictions of an outflow of matter from double neutron-star mergers and present a clear origin for gamma-ray bursts. Previous predictions differ over whether the jet material would combine to form light or heavy elements. These papers now show that the early part of the outflow was associated with lighter elements whereas the later observations can be explained by heavier elements, the origins of which have been uncertain. However, one paper (by Stephen Smartt and colleagues) argues that only light elements are needed for the entire event. Additionally, Eleonora Troja and colleagues report X-ray observations and radio emissions that suggest that the 'kilonova' jet was observed off-axis, which could explain why gamma-ray-burst detections are seen as dim. The cosmic origin of elements heavier than iron has long been uncertain. Theoretical modelling1,2,3,4,5,6,7 shows that the matter that is expelled in the violent merger of two neutron stars can assemble into heavy elements such as gold and platinum in a process known as rapid neutron capture (r-process) nucleosynthesis. The radioactive decay of isotopes of the heavy elements is predicted8,9,10,11,12 to power a distinctive thermal glow (a ‘kilonova’). The discovery of an electromagnetic counterpart to the gravitational-wave source13 GW170817 represents the first opportunity to detect and scrutinize a sample of freshly synthesized r-process elements14,15,16,17,18. Here we report models that predict the electromagnetic emission of kilonovae in detail and enable the mass, velocity and composition of ejecta to be derived from observations. We compare the models to the optical and infrared radiation associated with the GW170817 event to argue that the observed source is a kilonova. We infer the presence of two distinct components of ejecta, one composed primarily of light (atomic mass number less than 140) and one of heavy (atomic mass number greater than 140) r-process elements. The ejected mass and a merger rate inferred from GW170817 imply that such mergers are a dominant mode of r-process production in the Universe.