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A target-capturing problem based on a cyclic  pursuit strategy.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2011 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

A consensus problem is best described as a situation where multiple agents need to come

to an agreement based on information gathered by all agents. However, each agent only

has information from a few other agents. Applications for this could, for instance, be any

kind of situation where you have autonomous agents that need to cooperate. This could be

agreeing upon a rendezvous time or maintaining a formation.

In this thesis a specic kind of consensus problem is considered and expanded upon,

namely a target pursuit problem where a number of agents want to approach a target and

assume a formation around it. In our case the agents will only get information from their

next neighbour with respect to the angle around the target, which makes it a cyclic pursuit.

We will show that if a directed communication graph, representing the network, contains

a rooted directed spanning tree the agents will reach consensus. We also construct a

simulation of an introductory problem, examine what makes it work and verify convergence

and collision avoidance. The problem will be modied by making the agents converge to an

arbitrary plane instead of the xy-plane as presented in the original setup. Basic concepts of

matrix and graph theory and zero-order hold sampling will be explained.

Abstract [sv]

Konsensusproblem kan beskrivas som situationer dar ett ertal agenter behover komma till

ett gemensamt beslut baserat pa information inhamtad fran alla agenter. Varje agent kan

dock bara hamta information fran ett fatal andra agenter. Tillampningar pa detta ar, till

exempel, situationer dar autonoma agenter behover samarbeta. Detta kan bland annat galla

att bibehalla en formation eller att bestamma tid for en rendezvous.

I denna uppsats behandlas och utvecklas ett grundproblem, namligen scenariot dar ett

antal agenter vill narma sig ett mal och anta en cirkelformation runt det med hjalp av en

cyklisk konsensusalgoritm.

Vi visar att om den riktade graf som representerar kommunikationsnatverket innehaller

ett rotat riktat uppspannande trad sa konvergerar konsensusproblemet. Vi konstruerar aven

en simulering av grundproblemet samt undersoker konvergensen och visar att kollisioner inte

kan intraa. Detta problemet modieras sedan genom att lata agenterna konvergera mot

ett godtyckligt plan istallet for xy-planet. For att forsta problemet kravs en del kunskap

om graf- och matristeori samt kannedom om zero-order hold sampling, vilket kommer att

gas igenom.

Place, publisher, year, edition, pages
2011. , 31 p.
National Category
Engineering and Technology
URN: urn:nbn:se:kth:diva-105809OAI: diva2:572275
Available from: 2012-11-27 Created: 2012-11-27 Last updated: 2013-02-18Bibliographically approved

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