Multi-path planning and multi-body constrained attitude control

Okoloko, Innocent (2012-12)

Thesis (PhD)--Stellenbosch University, 2012.


ENGLISH ABSTRACT: This research focuses on the development of new efficient algorithms for multi-path planning and multi-rigid body constrained attitude control. The work is motivated by current and future applications of these algorithms in: intelligent control of multiple autonomous aircraft and spacecraft systems; control of multiple mobile and industrial robot systems; control of intelligent highway vehicles and traffic; and air and sea traffic control. We shall collectively refer to the class of mobile autonomous systems as “agents”. One of the challenges in developing and applying such algorithms is that of complexity resulting from the nontrivial agent dynamics as agents interact with other agents, and their environment. In this work, some of the current approaches are studied with the intent of exposing the complexity issues associated them, and new algorithms with reduced computational complexity are developed, which can cope with interaction constraints and yet maintain stability and efficiency. To this end, this thesis contributes the following new developments to the field of multipath planning and multi-body constrained attitude control: • The introduction of a new LMI-based approach to collision avoidance in 2D and 3D spaces. • The introduction of a consensus theory of quaternions by applying quaternions directly with the consensus protocol for the first time. • A consensus and optimization based path planning algorithm for multiple autonomous vehicle systems navigating in 2D and 3D spaces. • A proof of the consensus protocol as a dynamic system with a stochastic plant matrix. • A consensus and optimization based algorithm for constrained attitude synchronization of multiple rigid bodies. • A consensus and optimization based algorithm for collective motion on a sphere.

AFRIKAANSE OPSOMMING: Hierdie navorsing fokus op die ontwikkeling van nuwe koste-effektiewe algoritmes, vir multipad-beplanning en veelvuldige starre-liggaam beperkte standbeheer. Die werk is gemotiveer deur huidige en toekomstige toepassing van hierdie algoritmes in: intelligente beheer van veelvuldige outonome vliegtuig- en ruimtevaartuigstelsels; beheer van veelvuldige mobiele en industrile robotstelsels; beheer van intelligente hoofwegvoertuie en verkeer; en in lug- en see-verkeersbeheer. Ons sal hier “agente” gebruik om gesamentlik te verwys na die klas van mobiele outonome stelsels. Een van die uitdagings in die ontwikkeling en toepassing van sulke algoritmes is die kompleksiteit wat spruit uit die nie-triviale agentdinamika as gevolg van die interaksie tussen agente onderling, en tussen agente en hul omgewing. In hierdie werk word sommige huidige benaderings bestudeer met die doel om die kompleksiteitskwessies wat met hulle geassosieer word, bloot te l^e. Verder word nuwe algoritmes met verminderde berekeningskompleksiteit ontwikkel. Hierdie algoritmes kan interaksie-beperkings hanteer, en tog stabiliteit en doeltreffendheid behou. Vir hierdie doel dra die proefskrif die volgende nuwe ontwikkelings by tot die gebied van multipad-beplanning van multi-liggaam beperkte standbeheer: • Die voorstel van ’n nuwe LMI-gebasseerde benadering tot botsingsvermyding in 2D en 3D ruimtes. • Die voorstel van ’n konsensus-teorie van “quaternions” deur “quaternions” vir die eerste keer met die konsensusprotokol toe te pas. • ’n Konsensus- en optimeringsgebaseerde padbeplanningsalgoritme vir veelvoudige outonome voertuigstelsels wat in 2D en 3D ruimtes navigeer. • Die bewys van ’n konsensusprotokol as ’n dinamiese stelsel met ’n stochastiese aanlegmatriks. • ’n Konsensus- en optimeringsgebaseerde algoritme vir beperkte stand sinchronisasie van veelvoudige starre liggame. • ’n Konsensus- en optimeringsgebaseerde algoritme vir kollektiewe beweging op ’n sfeer.

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