Meeting in a Polygon by Anonymous Oblivious Robots

The Meeting problem for $k\geq 2$ searchers in a polygon $P$ (possibly with holes) consists in making the searchers move within $P$, according to a distributed algorithm, in such a way that at least two of them eventually come to see each other, regardless of their initial positions. The polygon is initially unknown to the searchers, and its edges obstruct both movement and vision. Depending on the shape of $P$, we minimize the number of searchers $k$ for which the Meeting problem is solvable. Specifically, if $P$ has a rotational symmetry of order $\sigma$ (where $\sigma=1$ corresponds to no rotational symmetry), we prove that $k=\sigma+1$ searchers are sufficient, and the bound is tight. Furthermore, we give an improved algorithm that optimally solves the Meeting problem with $k=2$ searchers in all polygons whose barycenter is not in a hole (which includes the polygons with no holes). Our algorithms can be implemented in a variety of standard models of mobile robots operating in Look-Compute-Move cycles. For instance, if the searchers have memory but are anonymous, asynchronous, and have no agreement on a coordinate system or a notion of clockwise direction, then our algorithms work even if the initial memory contents of the searchers are arbitrary and possibly misleading. Moreover, oblivious searchers can execute our algorithms as well, encoding information by carefully positioning themselves within the polygon. This code is computable with basic arithmetic operations, and each searcher can geometrically construct its own destination point at each cycle using only a compass. We stress that such memoryless searchers may be located anywhere in the polygon when the execution begins, and hence the information they initially encode is arbitrary. Our algorithms use a self-stabilizing map construction subroutine which is of independent interest.Comment: 37 pages, 9 figure

Multi Robot Intruder Search

The aim of this work is the development and analysis of methods and algorithms to allow a multi robot system to cooperatively search a closed, 2-dimensional environment for a human intruder. The underlying problem corresponds to the game-theoretic concept of a classical pursuit evasion game, whereas the focus is set to the generation of plans for the group of pursuers. While the main aspect of of this work lies in the field of probabilistic robotics, concepts and ideas are incorporated from differential game theory, algorithmic geometry and graph theory. The probabilistic basis allows the integration of sensor error as well as nondeterministic robot motion. The main contributions of this work can be divided into three major parts: The first part deals with the development and implementation of probabilistic human models. Depending on the specific behavior of an intruder, ranging from uncooperative to unaware, different classes of intruders are identified. Models are proposed for two of these classes. For the case of a clever and uncooperative intruder who actively evades detection, we propose a model based on the concept of contamination. The second class corresponds to a person who is unaware of the pursuit. We show that simple Markov models, which are often proposed in literature, are not suited for modeling realistic human motion and develop advanced Markov models, which conform to random waypoint motion models. The second part, which is also the most extensive part of this work, deals with the problem of finding an uncooperative and clever intruder. A solution is presented, which projects the problem on a graph structure, which is then searched by a highly optimized A* planner. The solution for the corresponding graph problem is afterwards projected back to the original search space and can be executed by the robotic pursuers. By means of the models proposed in the first part, the performance and correctness of the method is shown. We present experiments in simulation as on real robots to show the practicability and efficiency of the method. The third part deals with the problem of finding an intruder who is unaware of the search. Based on the advanced Markov model previously discussed, a greedy algorithm is proposed, which aims at maximizing the probability to find the intruder in the near future. Experimental results for this method are shown and comparisons to simpler methods are given.Mehrroboter-Eindringlings-Suche Ziel dieser Arbeit ist die Entwicklung und Analyse von Methoden und Algorithmen, die einem kooperativen Mehrrobotersystem erlauben nach einem Eindringling in einer zweidimensionalen, geschlossenen Umgebung zu suchen. Das dem zugrunde liegende Problem entspricht dem spieltheoretischen Konzept eines Suche und Ausweichen Spieles (pursuit evasion game), wobei der Fokus auf der Generierung von Plänen für die Verfolger liegt. Der Hauptaspekt dieser Arbeit liegt dabei im Feld der probabilistischen Robotik, wobei Konzepte und Ideen aus dem Gebiet der differentiellen Spieltheorie, der algorithmischen Geometrie und der Graph Theorie verwendet werden. Die probabilistische Modellierung erlaubt dabei die Integration von Sensorfehlern wie auch nichtdeterministische Roboter-Bewegung. Die Arbeit gliedert sich in drei Hauptteile: Der erste Teil beschäftigt sich mit dem Entwurf und der Implementierung von probabilistischen Modellen für menschliche Bewegung. Abhängig vom angenommenen Verhalten eines Eindringlings, von aktiv ausweichend bis zu ignorant, werden verschiedene Klassen von menschlichem Verhalten unterschieden. Für zwei dieser Klassen stellen wir Modelle auf: Für den Fall einer intelligenten und aktiv ausweichenden Person, generieren wir ein Modell basierend auf dem Konzept von Kontamination. Das zweite Modell entspricht einem Eindringling, der sich der Suche nach ihm nicht bewusst ist. Wir zeigen, dass einfache Markov-Modelle, wie sie in der Vergangenheit oft vorgeschlagen worden sind, ungeeignet sind, um realistische Bewegung zu abzubilden und entwickeln entsprechend erweiterte Markov-Modelle für eine realistischere Modellierung. Der zweite Teil der Arbeit beschäftigt sich mit der Frage, wie man einen intelligente und aktiv ausweichenden Eindringling aufspüren kann. Die vorgestellte Lösung basiert auf der Projektion des Problems auf einen Graphen, der anschließend von einem hoch optimierten A*-Planungsalgorithmus durchsucht werden kann. Diese Lösung kann anschließend auf den ursprünglichen Raum rückprojeziert werden und kann als direkter Plan von den verfolgenden Robotern ausgeführt werden. Mittels der Modelle aus dem ersten Teil wird die Korrektheit und Effizienz der Lösung gezeigt. Der letzte Teil befasst sich mit der Frage, wie ein Eindringling gefunden werden kann, der sich neutral zur Suche verhält. Basierend auf den erweiterten Markov-Modellen aus dem ersten Teil, wird eine Lösung durch gierige Suche präsentiert, die die Wahrscheinlichkeit eine Person im nächsten Zeitschritt aufzuspüren, maximiert. Wie im zweiten Teil werden Experimente diskutiert und diese mit der Proformanz simplerer Methoden verglichen

Environment Characterization for Non-Recontaminating Frontier-Based Robotic Exploration

This paper addresses the problem of obtaining a concise description of a physical environment for robotic exploration. We aim to determine the number of robots required to clear an environment using non-recontaminating exploration. We introduce the medial axis as a configuration space and derive a mathematical representation of a continuous environment that captures its underlying topology and geometry. We show that this representation provides a concise description of arbitrary environments, and that reasoning about points in this representation is equivalent to reasoning about robots in physical space. We leverage this to derive a lower bound on the number of required pursuers. We provide a transformation from this continuous representation into a symbolic representation. Finally, we present a generalized pursuit-evasion algorithm. Given an environment we can compute how many pursuers we need, and generate an optimal pursuit strategy that will guarantee the evaders are detected with the minimum number of pursuers.Singapore-MIT Alliance for Research and Technology Center (Future Urban Mobility Project)United States. Air Force Office of Scientific Research (Award FA9550-08-1-0159)National Science Foundation (U.S.) (Award CNS-0715397)National Science Foundation (U.S.) (Award CCF-0726514)National Science Foundation (U.S.) (Grant 0735953

Deployment algorithms for multi-agent exploration and patrolling

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 80-85).Exploration and patrolling are central themes in distributed robotics. These deployment scenarios have deep fundamental importance in robotics, beyond the most obvious direct applications, as they can be used to model a wider range of seemingly unrelated deployment objectives. Deploying a group of robots, or any type of agent in general, to explore or patrol in dynamic or unknown environments presents us with some fundamental conceptual steps. Regardless of the problem domain or application, we are required to (a) understand the environment that the agents are being deployed in; (b) encode the task as a set of constraints and guarantees; and (c) derive an effective deployment strategy for the operation of the agents. This thesis presents a coherent treatment of these steps at the theoretical and practical level. First, we address the problem of obtaining a concise description of a physical environment for robotic exploration. Specifically, we aim to determine the number of robots required to be deployed to clear an environment using non-recontaminating exploration. We introduce the medial axis as a configuration space and derive a mathematical representation of a continuous environment that captures its underlying topology and geometry. We show that this representation provides a concise description of arbitrary environments, and that reasoning about points in this representation is equivalent to reasoning about robots in physical space. We leverage this to derive a lower bound on the number of required pursuers. We provide a transformation from this continuous representation into a symbolic representation. We then present a Markov-based model that captures a pickup and delivery (PDP) problem on a general graph. We present a mechanism by which a group of robots can be deployed to patrol the graph in order to fulfill specific service tasks. In particular, we examine the problem in the context of urban transportation, and establish a model that captures the operation of a fleet of taxis in response to incident customer arrivals throughout the city. We consider three different evaluation criteria: minimizing the number of transportation resources for urban planning; minimizing fuel consumption for the drivers; and minimizing customer waiting time to increase the overall quality of service. Finally, we present two deployment algorithms for multi-robot exploration and patrolling. The first is a generalized pursuit-evasion algorithm. Given an environment we can compute how many pursuers we need, and generate an optimal pursuit strategy that will guarantee the evaders are detected with the minimum number of pursuers. We then present a practical patrolling policy for a general graph. We evaluate our policy using real-world data, by comparing against the actual observed redistribution of taxi drivers in Singapore. Through large-scale simulations we show that our proposed deployment strategy is stable and improves substantially upon the default unmanaged redistribution of taxi drivers in Singapore.by Mikhail Volkov.S.M

Mobile robotic network deployment for intruder detection and tracking

This thesis investigates the problem of intruder detection and tracking using mobile robotic networks. In the first part of the thesis, we consider the problem of seeking an electromagnetic source using a team of robots that measure the local intensity of the emitted signal. We propose a planner for a team of robots based on Particle Swarm Optimization (PSO) which is a population based stochastic optimization technique. An equivalence is established between particles generated in the traditional PSO technique, and the mobile agents in the swarm. Since the positions of the robots are updated using the PSO algorithm, modifications are required to implement the PSO algorithm on real robots to incorporate collision avoidance strategies. The modifications necessary to implement PSO on mobile robots, and strategies to adapt to real environments are presented in this thesis. Our results are also validated on an experimental testbed. In the second part, we present a game theoretic framework for visibility-based target tracking in multi-robot teams. A team of observers (pursuers) and a team of targets (evaders) are present in an environment with obstacles. The objective of the team of observers is to track the team of targets for the maximum possible time. While the objective of the team of targets is to escape (break line-of-sight) in the minimum time. We decompose the problem into two layers. At the upper level, each pursuer is allocated to an evader through a minimum cost allocation strategy based on the risk of each evader, thereby, decomposing the agents into multiple single pursuer-single evader pairs. Two decentralized allocation strategies are proposed and implemented in this thesis. At the lower level, each pursuer computes its strategy based on the results of the single pursuer-single evader target-tracking problem. We initially address this problem in an environment containing a semi-infinite obstacle with one corner. The pursuer\u27s optimal tracking strategy is obtained regardless of the evader\u27s strategy using techniques from optimal control theory and differential games. Next, we extend the result to an environment containing multiple polygonal obstacles. We construct a pursuit field to provide a guiding vector for the pursuer which is a weighted sum of several component vectors. The performance of different combinations of component vectors is investigated. Finally, we extend our work to address the case when the obstacles are not polygonal, and the observers have constraints in motion

Roadmap-Based Techniques for Modeling Group Behaviors in Multi-Agent Systems

Simulating large numbers of agents, performing complex behaviors in realistic environments is a difficult problem with applications in robotics, computer graphics and animation. A multi-agent system can be a useful tool for studying a range of situations in simulation in order to plan and train for actual events. Systems supporting such simulations can be used to study and train for emergency or disaster scenarios including search and rescue, civilian crowd control, evacuation of a building, and many other training situations. This work describes our approach to multi-agent systems which integrates a roadmap-based approach with agent-based systems for groups of agents performing a wide range of behaviors. The system that we have developed is highly customizable and allows us to study a variety of behaviors and scenarios. The system is tunable in the kinds of agents that can exist and parameters that describe the agents. The agents can have any number of behaviors which dictate how they react throughout a simulation. Aspects that are unique to our approach to multi-agent group behavior are the environmental encoding that the agents use when navigating and the extensive usage of the roadmap in our behavioral framework. Our roadmap-based approach can be utilized to encode both basic and very complex environments which include multi- level buildings, terrains and stadiums. In this work, we develop techniques to improve the simulation of multi-agent systems. The movement strategies we have developed can be used to validate agent movement in a simulated environment and evaluate building designs by varying portions of the environment to see the effect on pedestrian flow. The strategies we develop for searching and tracking improve the ability of agents within our roadmap-based framework to clear areas and track agents in realistic environments. The application focus of this work is on pursuit-evasion and evacuation planning. In pursuit-evasion, one group of agents, the pursuers, attempts to find and capture another set of agents, the evaders. The evaders have a goal of avoiding the pursuers. In evacuation planning, the evacuating agents attempt to find valid paths through potentially complex environments to a safe goal location determined by their environmental knowledge. Another group of agents, the directors may attempt to guide the evacuating agents. These applications require the behaviors created to be tunable to a range of scenarios so they can reflect real-world reactions by agents. They also potentially require interaction and coordination between agents in order to improve the realism of the scenario being studied. These applications illustrate the scalability of our system in terms of the number of agents that can be supported, the kinds of realistic environments that can be handled, and behaviors that can be simulated

Decentralized Collision-Free Control of Multiple Robots in 2D and 3D Spaces

Decentralized control of robots has attracted huge research interests. However, some of the research used unrealistic assumptions without collision avoidance. This report focuses on the collision-free control for multiple robots in both complete coverage and search tasks in 2D and 3D areas which are arbitrary unknown. All algorithms are decentralized as robots have limited abilities and they are mathematically proved. The report starts with the grid selection in the two tasks. Grid patterns simplify the representation of the area and robots only need to move straightly between neighbor vertices. For the 100% complete 2D coverage, the equilateral triangular grid is proposed. For the complete coverage ignoring the boundary effect, the grid with the fewest vertices is calculated in every situation for both 2D and 3D areas. The second part is for the complete coverage in 2D and 3D areas. A decentralized collision-free algorithm with the above selected grid is presented driving robots to sections which are furthest from the reference point. The area can be static or expanding, and the algorithm is simulated in MATLAB. Thirdly, three grid-based decentralized random algorithms with collision avoidance are provided to search targets in 2D or 3D areas. The number of targets can be known or unknown. In the first algorithm, robots choose vacant neighbors randomly with priorities on unvisited ones while the second one adds the repulsive force to disperse robots if they are close. In the third algorithm, if surrounded by visited vertices, the robot will use the breadth-first search algorithm to go to one of the nearest unvisited vertices via the grid. The second search algorithm is verified on Pioneer 3-DX robots. The general way to generate the formula to estimate the search time is demonstrated. Algorithms are compared with five other algorithms in MATLAB to show their effectiveness

Conference on Intelligent Robotics in Field, Factory, Service, and Space (CIRFFSS 1994), volume 1

The AIAA/NASA Conference on Intelligent Robotics in Field, Factory, Service, and Space (CIRFFSS '94) was originally proposed because of the strong belief that America's problems of global economic competitiveness and job creation and preservation can partly be solved by the use of intelligent robotics, which are also required for human space exploration missions. Individual sessions addressed nuclear industry, agile manufacturing, security/building monitoring, on-orbit applications, vision and sensing technologies, situated control and low-level control, robotic systems architecture, environmental restoration and waste management, robotic remanufacturing, and healthcare applications