Broad area/overview

The purpose of this paper is to present an overview of theoretical elements and practical uses of consensus algorithms, and to demonstrate the close relation of seemingly different consensus algorithms.

Consensus Algorithms

A consensus algorithm is a set of rules that specifies the information between an agent and its neighbors in a network. This includes how to interact when one agent encounters another, as well as processing interactions with external stimuli.

Applications of Consensus Algorithms

• Synchronization of Coupled Oscillators

  • Happens when two oscillators sync to the same frequency.

  • Has many uses in fields of physics, biology, engineering.

• Flocking Theory

  • When self-propelled individuals organize into ordered motion.

• Fast Consensus in Small Worlds

• Rendezvous in Space

  • Matching of orbital velocities of multiple agents in space.

• Distributed Sensor Fusion in Sensor Networks

• Distributed Formation Control

  • Multi vehicle control based on vectors of relative positions of neighboring vehicles.

Cooperation in Consensus

Not all consensus problems require cooperation between agents. For example, an unconstrained consensus problem may only require that all agents reach a similar value. In this case, one or more of the agents could be unwilling to cooperate with the others, and the consensus problem may be solved. Whereas a constrained case where all agents must meet a particular value requires that all agents be willing to cooperate and follow commands to reach the desired value.

Comments

• This paper is incredibly thorough in its review and analysis of the types of consensus algorithms and their many practical uses in a diverse range of subjects.

• While someone lacking a background in matrix and graph theory may have difficulty in interpreting much of the material covered in this review, it nonetheless provides a good introduction to a concept that spans many fields of study.