Balaji R. Sharma

An ant colony optimization technique for solving min–max Multi-Depot Vehicle Routing Problem

Abstract The Multi-Depot Vehicle Routing Problem (MDVRP) involves minimizing the total distance traveled by vehicles originating from multiple depots so that the vehicles together visit the specified customer locations (or cities) exactly once. This problem belongs to a class of Nondeterministic Polynomial Hard (NP Hard) problems and has been used in literature as a benchmark for development of optimization schemes. This article deals with a variant of MDVRP, called min–max MDVRP, where the objective is to minimize the tour-length of the vehicle traveling the longest distance in MDVRP. Markedly different from the traditional MDVRP, min–max MDVRP is of specific significance for time-critical applications such as emergency response, where one wants to minimize the time taken to attend any customer. This article presents an extension of an existing ant-colony technique for solving the Single Depot Vehicle Routing Problem (SDVRP) to solve the multiple depots and min–max variants of the problem. First, the article presents the algorithm that solves the min–max version of SDVRP. Then, the article extends the algorithm for min–max MDVRP using an equitable region partitioning approach aimed at assigning customer locations to depots so that MDVRP is reduced to multiple SDVRPs. The proposed method has been implemented in MATLAB for obtaining the solution for the min–max MDVRP with any number of vehicles and customer locations. A comparative study is carried out to evaluate the proposed algorithms performance with respect to a currently available Linear Programming (LP) based algorithm in literature in terms of the optimality of solution. Based on simulation studies and statistical evaluations, it has been demonstrated that the ant colony optimization technique proposed in this article leads to more optimal results as compared to the existing LP based method.

Cyclic pursuit in a multi-agent robotic system with double-integrator dynamics under linear interactions

We investigate the controlled realization of a stable circular pursuit model in a multi-agent robotic system described by double-integrator dynamics with homogeneous controller gains. The dynamic convergence of the system starting from a randomly chosen, non-overlapping initial configuration to a sustained, stable pursuit configuration satisfying velocity matching and uniform inter-agent separation is demonstrated using the proposed control framework. The cyclic pursuit configuration emerges from local, linear, inter-agent interactions and is shown to be robust under stochastic perturbations of small and moderate intensities. The stability criterion discussed in this work is independent of the number of agents, permitting dynamic addition/deletion of agents without affecting overall system stability. Experimental results that validate the key theoretical results are also presented. Potential applications of the results obtained include cooperative perimeter tracking and resource distribution applications such as border patrol and wildfire monitoring.

A Hierarchical Market Solution to the Min-Max Multiple Depots Vehicle Routing Problem

The problem of assigning a group of Unmanned Aerial Vehicles (UAVs) to perform spatially distributed tasks often requires that the tasks will be performed as quickly as possible. This problem can be defined as the Min–Max Multiple Depots Vehicle Routing Problem (MMMDVRP), which is a benchmark combinatorial optimization problem. In this problem, UAVs are assigned to service tasks so that each task is serviced once and the goal is to minimize the longest tour performed by any UAV in its motion from its initial location (depot) to the tasks and back to the depot. This problem arises in many time-critical applications, e.g. mobile targets assigned to UAVs in a military context, wildfire fighting, and disaster relief efforts in civilian applications. In this work, we formulate the problem using Mixed Integer Linear Programming (MILP) and Binary Programming and show the scalability limitation of these formulations. To improve scalability, we propose a hierarchical market-based solution (MBS). Simulation results demonstrate the ability of the MBS to solve large scale problems and obtain better costs compared with other known heuristic solution.

A Proper Orthogonal Decomposition based algorithm for smoke filtering in videos

Wildfires exhibit threats of all magnitudes and types to life and property. Past records suggest inevitable need of complete situational awareness and importance of the use of Unmanned Aerial Systems (UAS) to improve the wildland fire management by using onboard digital cameras. A major issue is the presence of smoke that occludes the hot spots in videos taken from such cameras. This research work focuses on reconstructing images from video of scenes occluded by thick smoke and a method for filtering smoke occlusions in fire image streams using Proper Orthogonal Decomposition (POD). Assuming that the image of the wildfire is taken from a static camera, the smoke will be moving over a stream of images or a video but the background will be static. Using POD, the smoke is filtered out of the video and clear background with fire can be seen in the output images. It provides an efficient way of capturing the dominant components of an infinite-dimensional process with only a finite number of “modes”. The technique is applied to a number of sample videos and it is demonstrated at the smoke is sufficiently removed from the video with the background information intact.

Spatio-Temporal Estimation of Wildfire Growth

This work presents a methodology for real-time estimation of wildland fire growth, utilizing afire growth model based on a set of partial differential equations for prediction, and harnessing concepts of space-time Kalman filtering and Proper Orthogonal Decomposition techniques towards low dimensional estimation of potentially large spatio-temporal states. The estimation framework is discussed in its criticality towards potential applications such as forest fire surveillance with unmanned systems equipped with onboard sensor suites. The effectiveness of the estimation process is evaluated numerically over fire growth data simulated using a well-established fire growth model described by coupled partial differential equations. The methodology is shown to be fairly accurate in estimating spatio-temporal process states through noise-ridden measurements for real-time deploy ability.© 2013 ASME

A Fuzzy Logic Based Image Processing Method for Automated Fire and Smoke Detection

Forest fires, and the scale of damage and destruction they leave in their wake, are well known and documented. With limitations in manual methods for fire monitoring, there is a strong need for developing automated methods for the same. In recent years, there has been considerable development in vision-based systems for fire detection. Forest fire tracking using visual sensors require the ability to identify fire regions in imagery, and a model for fire and smoke identification using Fuzzy Logic based image processing is presented in this paper. The model is tested on a wide range of images containing fire and smoke regions and its effectiveness is demonstrated.. The proposed model facilitates the development of a comprehensive fire and smoke detection system and is very attractive for military and civilian applications.

Perimeter tracking by multiple UAVs based on a cyclic-pursuit algorithm

This work is intended towards the development of an integrated controller for cooperative pursuit and perimeter tracking in a multi-UAV system around dynamic perimeters, for applications that include forest fires and oil spills, among others. The integrated controller proposed here consists of two orthogonal components, a radial component that acts on each agent facilitating perimeter tracking, and a tangential component acting along the curve that defines the interaction of each agent with its immediate neighboring agent further along the curve, facilitating cyclic pursuit along the closed perimeter. The control model assumes no prior knowledge of the curve, and perimeter tracking and cyclic pursuit implementations rely purely on local, instantaneous observations of the perimeter within each agent’s field of view. It is demonstrated through numerical simulations that the integrated controller is stable and allows for consistent perimeter tracking while ensuring uniform agent separations around the perimeter and uniform agent velocities.

Robot swarming over the Internet

We consider cooperative control of robots involving two different testbed systems in remote locations in different time zones, with communication on the internet. The goal is to have all robots properly follow a leader defined on one of the testbeds, while maintaining non-overlapping positions within each swarm and between swarms, assuming they are superimposed in the same virtual space. A dual-testbed design is developed involving real robots and remote network communication, performing a cooperative swarming algorithm based on a modified Morse Potential. Extensive experimental results were obtained with real internet communication and virtual testbeds running in each lab. The communication protocol was designed to minimize loss of packets, and average transfer delays are within tolerance limits for practical applications. We ran several experiments, with intentional packet loss, that illustrate the degradation of the results in the case of modest and severe packet loss. The novelty of this work is its experimental aspect involving long range network communication across a large distance via the internet. The work raises a series of interesting theoretical problems.

Distributed cyclic motion control of multiple UAVs for wildfire monitoring

This work focuses on the use of a swarm of unmanned aerial vehicles (UAVs) for fire front monitoring applications. Typically, fire monitoring relies on satellite imagery or manned aircraft missions for tracking fire spread. However, both methods have limitations in terms of accuracy and safety. In this paper the authors establish a framework for cooperative, persistent tracking of a dynamic perimeter using a swarm of UAVs with an emphasis on improved accuracy and reduced delays in the tracking process. The objective is to implement a coordinated, cyclic movement of the UAVs around the evolving fire perimeter thereby facilitating efficient tracking even with a limited number of agents. An expanding closed-curve model is introduced in order to represent a growing fire and the perimeter tracking process is demonstrated using numerical simulations. The control framework comprises of two aspects: (1) radial tracking of the perimeter by each UAV based on the fire boundary it perceives within its field of view, and (2) coordinated cyclic movement of the UAVs around the growing perimeter based on artificial potential functions that govern inter-UAV dynamics. Control vectors incorporating both the aspects are implemented in this study. It is demonstrated by means of simulation results that, interestingly, the multi-agent system of UAVs converges to stable configurations under both static and dynamic perimeter tracking scenarios. Additionally, the accuracy of perimeter tracking and spatial distribution while in cyclic pursuit is investigated. The article concludes with a discussion of directions of further research.Copyright

A Numerical Study of the Stochastic Cucker-Smale Flocking Model

We consider the influence of white noise on achieving consensus in a stochastic version of the well known Cucker-Smale model for flocking in multi-agent swarm systems. Our main results based on extensive numerical simulations suggest that while low intensity white noise has little appreciable effects on convergence to consensus in the system, the presence of high intensity white noise can fundamentally alter the flocking characteristics of the model. In particular, our results indicate that the numerical upper bound on a critical system parameter value that guarantees flocking in the deterministic model is no longer valid in the presence of high intensity white noise. In addition, the results also suggest that, interestingly, the influence of noise is independent of the number of agents in the swarm. Finally, we suggest a novel approach using the classical Fokker-Planck formalism as a direction of further analytical work aimed at validating our numerical results.Copyright