Distributed memoryless point convergence algorithm for mobile robots with limited visibility
01 Dec 1999-Vol. 15, Iss: 5, pp 818-828
TL;DR: The results of computer simulation under a more realistic model give convincing indication that the algorithm, if implemented on physical robots, will be robust against sensor and control error.
Abstract: We present a distributed algorithm for converging autonomous mobile robots with limited visibility toward a single point. Each robot is an omnidirectional mobile processor that repeatedly: 1) observes the relative positions of those robots that are visible; 2) computes its new position based on the observation using the given algorithm; 3) moves to that position. The robots' visibility is limited so that two robots can see each other if and only if they are within distance V of each other and there are no other robots between them. Our algorithm is memoryless in the sense that the next position of a robot is determined entirely from the positions of the robots that it can see at that moment. The correctness of the algorithm is proved formally under an abstract model of the robot system in which: 1) each robot is represented by a point that does not obstruct the view of other robots; 2) the robots' motion is instantaneous; 3) there are no sensor and control error; 4) the issue of collision is ignored. The results of computer simulation under a more realistic model give convincing indication that the algorithm, if implemented on physical robots, will be robust against sensor and control error.
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05 Mar 2007
TL;DR: A theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees is provided.
Abstract: This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions. Simulation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multivehicle formations
9,715 citations
Cites background from "Distributed memoryless point conver..."
...4) Rendezvous in Space: Another common form of consensus problems is rendezvous in space [ 90 ], [91]....
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07 Aug 2002
TL;DR: In this paper, the authors describe decentralized control laws for the coordination of multiple vehicles performing spatially distributed tasks, which are based on a gradient descent scheme applied to a class of decentralized utility functions that encode optimal coverage and sensing policies.
Abstract: This paper describes decentralized control laws for the coordination of multiple vehicles performing spatially distributed tasks. The control laws are based on a gradient descent scheme applied to a class of decentralized utility functions that encode optimal coverage and sensing policies. These utility functions are studied in geographical optimization problems and they arise naturally in vector quantization and in sensor allocation tasks. The approach exploits the computational geometry of spatial structures such as Voronoi diagrams.
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TL;DR: This paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies which are adaptive, distributed, asynchronous, and verifiably correct.
Abstract: This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.
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...Consider HV a cost function to be minimized and impose that the location pi follows a gradient descent....
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26 Jul 2009
TL;DR: This self-contained introduction to the distributed control of robotic networks offers 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.
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
1,166 citations
Cites background or methods or result from "Distributed memoryless point conver..."
...This law was introduced by Ando et al. (1999) and later studied by Lin et al. (2007a) and Cortés et al. (2006)....
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...…algorithms 8 4.3 Rendezvous algorithms 17 4.4 Simulation results 26 4.5 Notes 27 4.6 Proofs 29 4.7 Exercises 41 Algorithm Index 49 Subject Index 51 Symbol Index 53 share May 20, 2009 share May 20, 2009 Chapter Four Connectivity maintenance and rendezvous The aims of this chapter are twofold....
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...The rendezvous problem and the circumcenter algorithm were originally introduced by Ando et al. (1999)....
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...Regarding Theorem 4.16, the results on Sdisk appeared originally in Ando et al. (1999); the results on SLD and on S∞-disk appeared originally in Cortés et al. (2006) and in Mart́ınez et al. (2007), respectively....
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...The results presented in this section start with the original idea introduced by Ando et al. (1999) for first-order robots communicating along the edges of a disk graph, that is, for the network described in Example 3.4....
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TL;DR: It is proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node.
Abstract: The feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control. The directed graph defined by the information flow plays a key role. It is proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node. A similar result is given for formation stabilization to a line and to more general geometric arrangements.
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References
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TL;DR: The design of a machine which is composed of homogeneous mechanical units, and the control software of the unit which realizes "self-assembly," one of the basic functions of this machine is developed.
Abstract: The design of a machine which is composed of homogeneous mechanical units is described. We show the design of both hardware and control software of the unit. Each unit can connect with other units and change the connection by itself. In spite of its simple mechanism, a set of these units realizes various mechanical functions. We developed the control software of the unit which realizes "self-assembly," one of the basic functions of this machine. A set of these units can form a given shape of the whole system by themselves. The units exchange information about local geometric relation by communication, and cooperate to form the whole shape through a diffusion-like process. There is no upper level controller to supervise these units, and the software of each unit is completely the same. Three actual units have been built to test the basic movements, and the function of self-assembly has been verified by computer simulation. >
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"Distributed memoryless point conver..." refers methods in this paper
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...Distributed autonomous robot systems have rapidly attracted interest in recent years (e.g., the Cellular Robotic System [7], the Swarm Intelligence [2], the Self-Assembling Machine [9], and others [1], [8], [16]), where one of the main issues is the study of cooperative behavior of autonomous robots that operate under distributed control....
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TL;DR: A sufficient condition for the stability of a desired formation pattern for a fleet of robots each equipped with the navigation strategy based on nearest neighbor tracking is developed and simple navigation strategies for robots moving in formation are derived.
Abstract: The problem of deriving navigation strategies for a fleet of autonomous mobile robots moving in formation is considered. Here, each robot is represented by a particle with a spherical effective spatial domain and a specified cone of visibility. The global motion of each robot in the world space is described by the equations of motion of the robot's center of mass. First, methods for formation generation are discussed. Then, simple navigation strategies for robots moving in formation are derived. A sufficient condition for the stability of a desired formation pattern for a fleet of robots each equipped with the navigation strategy based on nearest neighbor tracking is developed. The dynamic behavior of robot fleets consisting of three or more robots moving in formation in a plane is studied by means of computer simulation.
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TL;DR: In this article, four closely related minimax location problems are considered, each involves locating a point in the plane to minimize the maximum distance (plus a possible constant) to a given finite set of points.
Abstract: Four closely related minimax location problems are considered. Each involves locating a point in the plane to minimize the maximum distance (plus a possible constant) to a given finite set of points. The distance measures considered are the Euclidean and the rectilinear. In each case efficient, finite solution procedures are given. The arguments are geometrical.
347 citations
"Distributed memoryless point conver..." refers background in this paper
...We omit the proof of the following well-known property [5]....
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TL;DR: It turns out that in many cases most robots execute an identical, simple algorithm, and a method for controlling a group of mobile robots in a distributed manner is discussed.
Abstract: We discuss a method for controlling a group of mobile robots in a distributed manner. The method is distributed in the sense that all robots, or most of the robots in some cases, plan their motion individually based upon the given goal of the group and the observed positions of other robots. We illustrate the method by showing how a large number of robots can form an approximation of a circle, a simple polygon, or a line segment in the plane. We also show how the robots can distribute themselves nearly uniformly within a circle or a convex polygon in the plane. Finally, we show how the robots can be divided into two or more groups. It turns out that in many cases most robots execute an identical, simple algorithm. The performance of the method is demonstrated by simulation. © 1996 John Wiley & Sons, Inc.
274 citations
"Distributed memoryless point conver..." refers background in this paper
...The importance of formation problems was first recognized by Sugihara and Suzuki [10], [11]....
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05 Sep 1990
TL;DR: A new method for controlling a group of mobile robots is presented, and it turns out that in many cases most robots execute an identical simple algorithm.
Abstract: A new method for controlling a group of mobile robots is presented. The method is fully distributed in the sense that each robot plans its motion individually on the basis of a given goal of the group and the observed positions of other robots. The method is illustrated by showing how a large number of robots can form an approximation of a circle, a simple polygon, or a line segment in the plane. It is also shown how the robots can distribute themselves nearly uniformly within a circle or a convex polygon in the plane. A method of dividing the robots into two or more groups is presented. It turns out that in many cases most robots execute an identical simple algorithm. The performance of the method is demonstrated by simulation. >
181 citations
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...The importance of formation problems was first recognized by Sugihara and Suzuki [10], [11]....
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...Mr. Suzuki is a member of the IEEE Computer Society and the Association for Computer Machinery....
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...[10] K. Sugihara and I. Suzuki, “Distributed motion coordination of multiple mobile robots,” inProc....
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...Ichiro Suzuki (M’99) received the D.E. degree in information and computer science from Osaka University, Osaka, Japan, in 1983....
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