scispace - formally typeset
Search or ask a question

Showing papers by "Swaroop Darbha published in 2009"


Proceedings ArticleDOI
10 Jun 2009
TL;DR: This paper presents a transformation of a Heterogeneous, Multiple Depot, Multiple Traveling Salesman Problem (HMDMTSP) into a single, Asymmetric, Traveling salesman problem (ATSP), and results show that good quality solutions can be obtained for the HMD MTSP relatively fast.
Abstract: Unmanned aerial vehicles (UAVs) are being increasingly used for surveillance missions in civil and military applications. These vehicles can be heterogeneous in the sense that they can differ either in their motion constraints or sensing/attack capabilities. Given a surveillance mission that require a group of heterogeneous UAVs to visit a set of targets, this paper addresses a resource allocation problem of finding the optimal sequence of targets for each vehicle such that 1) each target is visited at least once by some vehicle, and 2) the total cost travelled by all the vehicles is minimized. This problem can be posed as a Heterogeneous, Multiple Depot, Multiple Traveling Salesman Problem (HMDMTSP). This paper presents a transformation of a Heterogeneous, Multiple Depot, Multiple Traveling Salesman Problem (HMDMTSP) into a single, Asymmetric, Traveling Salesman Problem (ATSP). As a result, algorithms available for the single salesman problem can be used to solve the HMDMTSP. To show the effectiveness of the transformation, the well known Lin-Kernighan-Helsgaun heuristic was applied to the transformed ATSP. Computational results show that good quality solutions can be obtained for the HMDMTSP relatively fast.

61 citations


Journal ArticleDOI
TL;DR: In this article, the authors considered the problem of motion planning of m Dubins' vehicles through n points in a plane, where the initial location and heading of the vehicles are specified and are assumed to be distinct for each vehicle.
Abstract: In this manuscript, we consider the problem of motion planning of m Dubins’ vehicles through n points in a plane. The initial location and heading of the vehicles is specified and is assumed to be distinct for each vehicle. A motion plan for a vehicle is given by the sequence of points and the corresponding angles at which each point must be visited by the vehicle. We require that each vehicle return to the same initial location (depot) at the same heading after visiting the points. The objective of the motion planning problem is to choose at most q ( ≤ m ) Dubins’ vehicles and find their motion plans so that all the points are visited and the total cost of the tours of the chosen vehicles is a minimum amongst all the possible choice of vehicles and their tours. This problem is a generalization of the Multiple Depot, Multiple Traveling Salesmen Problem (MDMTSP) in two directions — the problem involves the determination of choice of vehicles and their respective headings at each of their assigned points. This problem is NP-hard. We propose a two step approach to solve this problem — (1) The combinatorial problem of choosing the vehicles and their associated tours is based on Euclidean distances between points and (2) Once the sequence of points to be visited is found, the heading at each point is determined based on a Dynamic Programming scheme. The solution to the first step is based on a generalization of Held–Karp’s method for the MDMTSP. We modify the Lagrangian heuristics, in the literature, for finding a close primal solution from the Held–Karp’s (dual) solution. Empirical results indicate that this scheme seems to provide primal solutions which are within 5 % of the optimum in the span of 25 dual iterations for instances which have about 45 points to visit and 6 vehicles.

44 citations


Proceedings ArticleDOI
10 Jun 2009
TL;DR: In this paper, a Multiple Depot, Multiple Traveling Salesman Problem is transformed into a Single, Asymmetric Traveling salesman Problem if the cost of the edges satisfy the triangle inequality.
Abstract: In this paper, a Multiple Depot, Multiple Traveling Salesman Problem is transformed into a Single, Asymmetric Traveling Salesman Problem if the cost of the edges satisfy the triangle inequality. This improves on the previously known transformation for a 2-Depot, Multiple Traveling Salesman Problem in the literature. To test the effectiveness of the transformation, some computational results are presented by applying the well known LKH heuristic on the transformed problem for instances involving Dubins vehicles. Results show that the transformation is effective and high quality solutions can be found for large instances in a relatively short time.

38 citations


Journal ArticleDOI
TL;DR: This paper critically review mathematical models for the flow of traffic that treat traffic as a continuum and provides a discussion of their shortcomings and a spatially discrete traffic flow model that does not suffer from such shortcomings and provides recently collected, corroborating data for a trip-time estimation scheme based on the spatially separate model.
Abstract: In this paper, we critically review mathematical models for the flow of traffic that treat traffic as a continuum and provide a discussion of their shortcomings We also review a spatially discrete traffic flow model that does not suffer from such shortcomings and provide recently collected, corroborating data for a trip-time estimation scheme based on the spatially discrete model

19 citations


Journal ArticleDOI
TL;DR: In this paper, the authors studied the response of a linearized elastic solid whose material properties change due to the diffusion of a chemical, and they found that the response characteristics of such structures that are exposed to the environment changes due to its impact such as oxidation due to moisture.
Abstract: Many structures are made of concrete and steel. The response characteristics of such structures that are exposed to the environment change due to its impact such as oxidation due to moisture. Usually the structural element “degrades” in that the load bearing capacity decreases; it also decreases due to “aging”. On the other hand, chemicals are infused into biological systems in order to enhance their strength. Thus far, not much attention has been paid to studying such problems. In this investigation, we study the response of a linearized elastic solid whose material properties change due to the diffusion of a chemical.

11 citations


Proceedings ArticleDOI
10 Aug 2009
TL;DR: This paper addresses a base perimeter patrol scenario where alerts are generated from a set of stations at random intervals and a stochastic control optimization problem is developed to determine the optimal loiter time.
Abstract: This paper addresses a base perimeter patrol scenario where alerts are generated from a set of stations at random intervals. A Unmanned Aerial Vehicle patrols the perimeter and responds to alerts. After arriving at an alert site, the vehicle loiters for a time to enable the operator to determine if the alert is a nuisance trip or an actual threat. The false alarms are modeled as a Poisson process. A stochastic control optimization problem is developed to determine the optimal loiter time. The optimal length of time that a vehicle can dwell at an alert site while minimizing the expected service time is a function of the size of the alert queue and the alert rate. Results from where the algorithm was ∞ight tested as part of a base defense scenario is presented.

10 citations


Proceedings ArticleDOI
10 Jun 2009
TL;DR: This paper provides necessary and sufficient conditions for a rational proper stable transfer function to have a non-negative impulse response and proposes an outer approximation of the feasible set of matrix inequalities using Lasserre's moment method.
Abstract: Practical problems require the synthesis of a set of stabilizing controllers that guarantee transient performance specifications such as a bound on the overshoot of its closed loop step response. A majority of these specifications for Linear Time Invariant (LTI) systems can be converted to the requirement of synthesizing a set of stabilizing controllers guaranteeing the non-negative impulse response of an appropriate transfer function whose coefficients are functions of the controller parameters. The main topic of investigation of this paper is to find a bound for the set of control parameters, K, so that a rational, proper transfer function, N (z, K)/D (z, K) has a decaying, non-negative impulse response. For Single Input Single Output (SISO) LTI systems, one may assume that the coefficients of the polynomials N (z, K) and D (z, K) are affine in K. An earlier result by the authors provides an approximation of the set of stabilizing controller parameters in terms of unions of polyhedral sets. In this paper, we provide necessary and sufficient conditions for a rational proper stable transfer function to have a non-negative impulse response. For the synthesis problem, we show that these conditions translate into a sequence of polynomial matrix inequalities in K using Markov-Lucaks' theorem. We propose an outer approximation of the feasible set of matrix inequalities using Lasserre's moment method.

9 citations


Proceedings ArticleDOI
10 Jun 2009
TL;DR: A mathematical model for an air brake system in the presence of leaks is presented with a view towards developing a diagnostic system based on this model in the near future and a simple leak detection scheme is provided.
Abstract: Brake systems in trucks are crucial for ensuring the safety of vehicles and passengers on the roadways. Most trucks in the US are equipped with S-cam drum brake systems and they are sensitive to maintenance. Brake defects such as leaks are a major cause of accidents involving trucks. Leaks in the air brake systems affect braking performance drastically by decreasing the maximum braking pressure and also increasing the time required to attain the same, thereby resulting in longer stopping distances. In this paper, we present a mathematical model for an air brake system in the presence of leaks with a view towards developing a diagnostic system based on this model in the near future. The model that has been developed builds on earlier research at Texas A&M University in which the pressure evolution in the brake chamber was determined as a function of the brake pedal input in the absence of any leaks in the air brake system. A leak may be characterized by its location and size. Since the connecting pipes are short, the location of the leak does not significantly affect the evolution in the brake pressure as much as its size. We provide a constitutive relationship for the leak and we estimated the associated parameter, namely, the “effective area” of the leak from the experimental data. The supply pressure and effective area of leak comprised the inputs to the model along with the displacement of the brake pedal (treadle valve plunger). We also provide a simple leak detection scheme and estimates of the severity of the leak in terms of the mass flow rate of leaking air based on the input measurements of brake pressure for a full application of the brake pedal and the supply pressure. This scheme can be implemented using a simple look-up table.

9 citations


Proceedings ArticleDOI
10 Jun 2009
TL;DR: This paper presents the first approximation algorithm for a 2-Depot, Heterogeneous Vehicle Routing Problem when the cost of direct travel between any pair of locations is no costlier than thecost of travel between the same locations and going through any intermediate location.
Abstract: Routing problems involving heterogeneous vehicles naturally arise in several civil and military applications due to fuel and motion constraints of the vehicles. These vehicles can differ either in their motion constraints or sensing capabilities. Approximation algorithms are useful for solving these routing problems because they produce solutions that can be efficiently computed and are relatively less sensitive to the noise in the data. In this paper, we present the first approximation algorithm for a 2-Depot, Heterogeneous Vehicle Routing Problem when the cost of direct travel between any pair of locations is no costlier than the cost of travel between the same locations and going through any intermediate location.

6 citations


Proceedings ArticleDOI
01 Jan 2009
TL;DR: In this article, the authors considered the problem of decentralized control of a collection of homogeneous vehicles trying to maintain a rigid formation and showed that if there are two or more vehicles in the collection that are adjacent to other vehicles, then the motion of the collection will be unstable if the size of the aggregate collection exceeds a certain threshold.
Abstract: In this paper, we consider the problem of decentralized control of a collection of homogeneous vehicles trying to maintain a rigid formation. Each vehicle attempts to maintain a specified constant safe distance from its adjacent vehicles in the collection. We consider an identical structure for each decentralized controller so that it is simpler from an implementation viewpoint as it does not depend on collection size or vehicle indices. We call a vehicle B adjacent to vehicle A if the relative position of vehicle B is known to vehicle A either by communication or by sensing. In this paper, we only consider undirected information flow graphs, i.e., graphs where vehicle A is adjacent to vehicle B if and only if vehicle B is adjacent to vehicle A. We consider a point mass model for each vehicle and assume the actuation transfer function, which relates the control input to the force supplied to the vehicle, to be a strictly proper rational transfer function. It is known that spacing errors due to disturbances amplify if the reference vehicle information is not available to Ω (n) vehicles, n being the size of the collection [1]. In this paper, we generalize this result to show the following: If there are two or more vehicles in the collection that are adjacent to Ω (n) vehicles, then there is a critical size N* so that the motion of the collection will be unstable if the size of the collection exceeds N*. Practical issues of fault tolerance indicate that there be at least two vehicles that are adjacent to Ω (n) vehicles in the collection. We also further show that the use of a kinematic vehicle model for analysis of disturbance propagation yields results which may not agree with what is observed in practice and hence are inappropriate.Copyright © 2009 by ASME

1 citations


Proceedings ArticleDOI
01 Jan 2009
TL;DR: In this paper, the authors considered a combinatorial motion planning problem of finding a shortest tour for a Dubins' vehicle that must visit a given set of targets and return to its initial depot while satisfying the motion constraints of the vehicle and the precedence constraints.
Abstract: This paper considers a combinatorial motion planning problem of finding a shortest tour for a Dubins’ vehicle that must visit a given set of targets and return to its initial depot while satisfying the motion constraints of the vehicle and the precedence constraints. Precedence constraints restrict the sequence in which a Dubins’ vehicle visits the given set of targets by imposing a partial ordering on the sequence in which the targets must be visited. This problem arises in applications involving fixed wing, Unmanned Aerial Vehicles (UAVs) where the vehicles have fuel and motion constraints. A fixed wing UAV may be modeled as a Dubins’ vehicle that can travel at a constant speed and has an upper bound on its turning rate. This is a difficult problem because it couples the combinatorial problem of optimally visiting a set of targets with the path planning problem of finding the shortest path that satisfies the motion constraints given the sequence in which the targets must be visited. In this paper, the sequence in which the targets must be visited is obtained by solving the combinatorial problem using a split dual algorithm. Using this sequence, the path planning problem is solved using Dynamic Programming. Computational results are given to corroborate the performance of the algorithms.Copyright © 2009 by ASME

Posted Content
TL;DR: In this article, the authors consider the vibratory motions of lumped parameter systems where the components of the system cannot be described by constitutive expressions for the force in terms of appropriate kinematical quantities.
Abstract: In this paper, we consider the vibratory motions of lumped parameter systems wherein the components of the system cannot be described by constitutive expressions for the force in terms of appropriate kinematical quantities. Such physical systems reduce to a system of differential-algebraic equations, which invariably need to be solved numerically. To illustrate the issues with clarity, we consider a simple system in which the dashpot is assumed to contain a "Bingham" fluid for which one cannot describe the force in the dashpot as a function of the velocity. On the other hand, one can express the velocity as a function of the force.