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Robotic Networks, Distributed Algorithms for

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Encyclopedia of Complexity and Systems Science

Definition of the Subject

The study of distributed algorithms for robotic networks is motivated by the recentemergence of low-power, highly-autonomous devices equipped with sensing, communication,processing, and control capabilities. In the near future, cooperative robotic sensor networkswill perform critical tasks in disaster recovery, homeland security, and environmentalmonitoring. Such networks will require efficient and robust distributed algorithms withguaranteed quality-of-service. In order to design coordination algorithms with thesedesirable capabilities, it is necessary to develop new frameworks to design and formalize theoperation of robotic networks and novel tools to analyze their behavior.

Introduction

Distributed algorithms are a classic subject of study for networks composed ofindividual processors with communication capabilities. Within the automata-theoreticliterature, important research topics on distributed algorithms include the introduction ofmathematical models...

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Notes

  1. 1.

    Note that the description of the LCR algorithm given here is slightly different from the classic one as presented in [57].

Abbreviations

Cooperative control :

In recent years, the study of groups of robots and multi-agent systems has received a lot of attention. This interest has been driven by the envisioned applications of these systems in scientific and commercial domains. From a systems and control theoretic perspective, the challenges in cooperative control revolve around the analysis and design of distributed coordination algorithms that integrate the individual capabilities of the agents to achieve a desired coordination task.

Distributed algorithm :

In a network composed of multiple agents, a coordination algorithm specifies a set of instructions for each agent that prescribe what to sense, what to communicate and to whom, how to process the information received, and how to move and interact with the environment. In order to be scalable, coordination algorithms need to rely as much as possible on local interactions between neighboring agents.

Complexity measures :

Coordination algorithms are designed to enable networks of agents achieve a desired task. Since different algorithms can be designed to achieve the same task, performance metrics are necessary to classify them. Complexity measures provide a way to characterize the properties of coordination algorithms such as completion time, cost of communication, energy consumption, and memory requirements.

Averaging algorithms :

Distributed coordination algorithms that perform weighted averages of the information received from neighboring agents are called averaging algorithms. Under suitable connectivity assumptions on the communication topology, averaging algorithms achieve agreement, i.?e., the state of all agents approaches the same value. In certain cases, the agreement value can be explicitly determined as a function of the initial state of all agents.

Leader election :

In leader election problems, the objective of a network of processors is to elect a leader. All processors have a variable “leader” initially set to unknown. The leader-election task is solved when only one processor has set the variable “leader” to true, and all other processors have set it to false.

LCR algorithm :

The classic Le Lann–Chang–Roberts (LCR) algorithm solves the leader election task on a static network with the ring communication topology. Initially, each agent transmits its unique identifier to its neighbors. At each communication round, each agent compares the largest identifier received from other agents with its own identifier. If the received identifier is larger than its own, the agent declares itself a non-leader, and transmits it in the next communication round to its neighbors. If the received identifier is smaller than its own, the agent does nothing. Finally, if the received identifier is equal to its own, it declares itself a leader. The LCR algorithm achieves leader election with linear time complexity and quadratic total communication complexity, respectively.

Agree-and-pursue algorithm :

Coordination algorithms for robotic networks combine the features of distributed algorithms for networks of processors with the sensing and control capabilities of the robots. The agree-and-pursue motion coordination algorithm is an example of this fusion. Multiple robotic agents moving on a circle seek to agree on a common direction of motion while at the same achieving an equally-spaced distribution along the circle. The agree-and-pursue algorithm achieves both tasks combining ideas from leader election on a changing communication topology with basic control primitives such as “follow your closest neighbor in your direction of motion.”

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Acknowledgments

This material is based upon worksupported in part by NSF CAREER Award CMS-0643679, NSF CAREER Award ECS-0546871, andAFOSR MURI Award FA9550-07-1-0528.

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  1. Department of Mechanical Engineering, University of California, Santa Barbara, USA

    Francesco Bullo

  2. Department of Mechanical and Aerospace Engineering, University of California, San Diego, USA

    Jorge Cortés & Sonia Martínez

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Bullo, F., Cortés, J., Martínez, S. (2009). Robotic Networks, Distributed Algorithms for. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_457

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