A Dynamic Boundary Guarding Problem with Translating Targets

We introduce a problem in which a service vehicle seeks to guard a deadline (boundary) from dynamically arriving mobile targets. The environment is a rectangle and the deadline is one of its edges. Targets arrive continuously over time on the edge opposite the deadline, and move towards the deadline at a fixed speed. The goal for the vehicle is to maximize the fraction of targets that are captured before reaching the deadline. We consider two cases; when the service vehicle is faster than the targets, and; when the service vehicle is slower than the targets. In the first case we develop a novel vehicle policy based on computing longest paths in a directed acyclic graph. We give a lower bound on the capture fraction of the policy and show that the policy is optimal when the distance between the target arrival edge and deadline becomes very large. We present numerical results which suggest near optimal performance away from this limiting regime. In the second case, when the targets are slower than the vehicle, we propose a policy based on servicing fractions of the translational minimum Hamiltonian path. In the limit of low target speed and high arrival rate, the capture fraction of this policy is within a small constant factor of the optimal.Comment: Extended version of paper for the joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conferenc

Job Selection in a Network of Autonomous UAVs for Delivery of Goods

This article analyzes two classes of job selection policies that control how a network of autonomous aerial vehicles delivers goods from depots to customers. Customer requests (jobs) occur according to a spatio-temporal stochastic process not known by the system. If job selection uses a policy in which the first job (FJ) is served first, the system may collapse to instability by removing just one vehicle. Policies that serve the nearest job (NJ) first show such threshold behavior only in some settings and can be implemented in a distributed manner. The timing of job selection has significant impact on delivery time and stability for NJ while it has no impact for FJ. Based on these findings we introduce a methodological approach for decision-making support to set up and operate such a system, taking into account the trade-off between monetary cost and service quality. In particular, we compute a lower bound for the infrastructure expenditure required to achieve a certain expected delivery time. The approach includes three time horizons: long-term decisions on the number of depots to deploy in the service area, mid-term decisions on the number of vehicles to use, and short-term decisions on the policy to operate the vehicles

Stabilizing Queuing Networks with Model Data-Independent Control

Classical queuing network control strategies typically rely on accurate knowledge of model data, i.e., arrival and service rates. However, such data are not always available and may be time-variant. To address this challenge, we consider a class of model data-independent (MDI) control policies that only rely on traffic state observation and network topology. Specifically, we focus on the MDI control policies that can stabilize multi-class Markovian queuing networks under centralized and decentralized policies. Control actions include routing, sequencing, and holding. By expanding the routes and constructing piecewise-linear test functions, we derive an easy-to-use criterion to check the stability of a multi-class network under a given MDI policy. For stabilizable multi-class networks, we show that a centralized, stabilizing MDI policy exists. For stabilizable single-class networks, we further show that a decentralized, stabilizing MDI policy exists. In addition, for both settings, we construct explicit policies that attain maximal throughput and present numerical examples to illustrate the results.Comment: Accepted by IEEE Transactions on Control of Network System

Application of Genetic Algorithms to Solve MTSP Problems with Priority (Case Study at the Jakarta Street Lighting Service)

Transportation is one thing that is very important and is the highest cost in the supply chain. One way to reduce these costs is to optimize vehicle routes. The Multiple Traveling Salesman Problem (MTSP) and Capacitated Vehicle Routing Problem (CVRP) are models that have been extensively researched to optimize vehicle routes. In its development based on actual events in the real world, some priorities must be visited first in optimizing vehicle routes. Several studies on MTSP and CVRP models have been conducted with exact solutions and algorithms. In a real case in the Jakarta City Street Lighting Section, the problem of determining the route in three shifts is a crucial problem that must be resolved to increase worker productivity to improve services. Services in MCB (Miniature Circuit Breaker) installation and maintenance activities for general street lights and priority is given to light points that require replacement. Because, in this case, the delivery capacity is not taken into account, the priority of the lights visited is random, and the number of street light points is enormous, in this study, we use the MTSP method with priority and solve by a genetic algorithm assisted by the nearest neighbor algorithm. From the resolution of this problem, it was found that the travel time reduction was 32 % for shift 1, 24 % for shift 2, and 23 % for shift 3. Of course, this time reduction will impact worker productivity so that MCB installation can be done faster for all lights and replace a dead lamp

Unifying geometric, probabilistic, and potential field approaches to multi-robot deployment

This paper unifies and extends several different existing strategies for deploying groups of robots in an environment. A cost function is proposed that can be specialized to represent widely different multi-robot deployment tasks. It is shown that geometric and probabilistic deployment strategies that were previously seen as distinct are in fact related through this cost function, and differ only in the value of a single parameter. These strategies are also related to potential field-based controllers through the same cost function, though the relationship is not as simple. Distributed controllers are then obtained from the gradient of the cost function and are proved to converge to a local minimum of the cost function. Three special cases are derived as examples: a Voronoi-based coverage control task, a probabilistic minimum variance task, and a task using artificial potential fields. The performance of the three different controllers are compared in simulation. A result is also proved linking multi-robot deployment to non-convex optimization problems, and multi-robot consensus (i.e. all robots moving to the same point) to convex optimization problems, which implies that multi-robot deployment is inherently more difficult than multi-robot consensus.United States. Office of Naval Research. Multidisciplinary University Research Initiative. Smarts (Grant N00014-09-1-1051)United States. Army Research Office. Multidisciplinary University Research Initiative. Scalable Swarms of Autonomous Robots and Mobile Sensors Project (Grant W911NF-05-1-0219)National Science Foundation (U.S.) (Grant IIS-0513755)National Science Foundation (U.S.) (Grant IIS-0426838)National Science Foundation (U.S.) (Grant CNS-0520305)National Science Foundation (U.S.) (Grant CNS-0707601)National Science Foundation (U.S.) (Grant EFRI-0735953

Distributed and Adaptive Algorithms for Vehicle Routing in a Stochastic and Dynamic Environment

In this paper we present distributed and adaptive algorithms for motion coordination of a group of m autonomous vehicles. The vehicles operate in a convex environment with bounded velocity and must service demands whose time of arrival, location and on-site service are stochastic; the objective is to minimize the expected system time (wait plus service) of the demands. The general problem is known as the m-vehicle Dynamic Traveling Repairman Problem (m-DTRP). The best previously known control algorithms rely on centralized a-priori task assignment and are not robust against changes in the environment, e.g. changes in load conditions; therefore, they are of limited applicability in scenarios involving ad-hoc networks of autonomous vehicles operating in a time-varying environment. First, we present a new class of policies for the 1-DTRP problem that: (i) are provably optimal both in light- and heavy-load condition, and (ii) are adaptive, in particular, they are robust against changes in load conditions. Second, we show that partitioning policies, whereby the environment is partitioned among the vehicles and each vehicle follows a certain set of rules in its own region, are optimal in heavy-load conditions. Finally, by combining the new class of algorithms for the 1-DTRP with suitable partitioning policies, we design distributed algorithms for the m-DTRP problem that (i) are spatially distributed, scalable to large networks, and adaptive to network changes, (ii) are within a constant-factor of optimal in heavy-load conditions and stabilize the system in any load condition. Simulation results are presented and discussed.Comment: Paper to be submitted to IEEE Transactions on Automatic Contro

Persistent Robotic Tasks: Monitoring and Sweeping in Changing Environments

In this paper, we present controllers that enable mobile robots to persistently monitor or sweep a changing environment. The environment is modeled as a field that is defined over a finite set of locations. The field grows linearly at locations that are not within the range of a robot and decreases linearly at locations that are within range of a robot. We assume that the robots travel on given closed paths. The speed of each robot along its path is controlled to prevent the field from growing unbounded at any location. We consider the space of speed controllers that are parametrized by a finite set of basis functions. For a single robot, we develop a linear program that computes a speed controller in this space to keep the field bounded, if such a controller exists. Another linear program is derived to compute the speed controller that minimizes the maximum field value over the environment. We extend our linear program formulation to develop a multirobot controller that keeps the field bounded. We characterize, both theoretically and in simulation, the robustness of the controllers to modeling errors and to stochasticity in the environment

Dynamic Vehicle Routing for Robotic Systems

Recent years have witnessed great advancements in the science and technology of autonomy, robotics, and networking. This paper surveys recent concepts and algorithms for dynamic vehicle routing (DVR), that is, for the automatic planning of optimal multivehicle routes to perform tasks that are generated over time by an exogenous process. We consider a rich variety of scenarios relevant for robotic applications. We begin by reviewing the basic DVR problem: demands for service arrive at random locations at random times and a vehicle travels to provide on-site service while minimizing the expected wait time of the demands. Next, we treat different multivehicle scenarios based on different models for demands (e.g., demands with different priority levels and impatient demands), vehicles (e.g., motion constraints, communication, and sensing capabilities), and tasks. The performance criterion used in these scenarios is either the expected wait time of the demands or the fraction of demands serviced successfully. In each specific DVR scenario, we adopt a rigorous technical approach that relies upon methods from queueing theory, combinatorial optimization, and stochastic geometry. First, we establish fundamental limits on the achievable performance, including limits on stability and quality of service. Second, we design algorithms, and provide provable guarantees on their performance with respect to the fundamental limits.United States. Air Force Office of Scientific Research (Award FA 8650-07-2-3744)United States. Army Research Office. Multidisciplinary University Research Initiative (Award W911NF-05-1-0219)National Science Foundation (U.S.) (Award ECCS-0705451)National Science Foundation (U.S.) (Award CMMI-0705453)United States. Army Research Office (Award W911NF-11-1-0092

Dynamic vehicle routing problems: Three decades and counting

Since the late 70s, much research activity has taken place on the class of dynamic vehicle routing problems (DVRP), with the time period after year 2000 witnessing a real explosion in related papers. Our paper sheds more light into work in this area over more than 3 decades by developing a taxonomy of DVRP papers according to 11 criteria. These are (1) type of problem, (2) logistical context, (3) transportation mode, (4) objective function, (5) fleet size, (6) time constraints, (7) vehicle capacity constraints, (8) the ability to reject customers, (9) the nature of the dynamic element, (10) the nature of the stochasticity (if any), and (11) the solution method. We comment on technological vis-à-vis methodological advances for this class of problems and suggest directions for further research. The latter include alternative objective functions, vehicle speed as decision variable, more explicit linkages of methodology to technological advances and analysis of worst case or average case performance of heuristics.© 2015 Wiley Periodicals, Inc

Data-driven task allocation for multi-robot deliveries

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 93-97).In this thesis, we present a distributed task allocation system for a team of robots serving queues of tasks in an environment. We consider how historical information about such a system's performance could be used to improve future allocations. Our model is representative of a multi-robot mail delivery service, in which teams of robots would have to cooperate to pick up and deliver packages in an environment. We provide a framework for task allocation, planning, and control of the system and analyze task switching as a method for improving a task allocation as the system is running. We first treat a system where robots exchange tasks as they encounter each other in the environment. We consider both cases where the number of robots matches the number of task queues being served and where it does not. Most importantly, for situations where an optimal task switching policy would be too computationally expensive, we provide heuristics that nonetheless guarantee task completion. Our simulations show that our heuristics also generally lower the costs of task completion. We incorporate historical data about system performance by looking at a spatial allocation of tasks to robots in the system. We propose an algorithm for partitioning the environment into regions of equal workload for the robots. In order to overcome communication constraints, we introduce hubs, locations where robots can pass tasks to each other. We simulate the system with this additional infrastructure and compare its performance to that without hubs. We find that hubs can significantly improve performance when the task queues themselves follow some spatial structure.by Cynthia Rueyi Sung.S.M