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An engineering vector-like approach to attitude kinematics & nominal attitude state tracking control

In dealing with rigid body three-dimensional rotational motion, one is inevitably led to face the fact that rotations are not vector quantities. They may, however, be treated as such when the angle of rotation is (very) small. In this context, i.e. the infinitesimal case analysis, the time derivativ...

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Autor principal:	Pece, Carlos Alessandro Zanetti
Formato:	Tese
Idioma:	Inglês
Publicado em:	Instituto Tecnológico de Aeronáutica 2013
Assuntos:	Métodos de simulação Cálculo vetorial Cinemática das máquinas Engenharia mecânica Teoria dos erros Simulation methods Vector analysis Machinery, Kinematics of Mechanical engineering Error analysis (Mathematics)
Acesso em linha:	http://repositorio.utfpr.edu.br/jspui/handle/1/481
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spelling	riut-1-4812015-03-07T06:09:29Z An engineering vector-like approach to attitude kinematics & nominal attitude state tracking control Pece, Carlos Alessandro Zanetti Almeida, Sérgio Francisco Müller de Métodos de simulação Cálculo vetorial Cinemática das máquinas Engenharia mecânica Teoria dos erros Simulation methods Vector analysis Machinery, Kinematics of Mechanical engineering Error analysis (Mathematics) In dealing with rigid body three-dimensional rotational motion, one is inevitably led to face the fact that rotations are not vector quantities. They may, however, be treated as such when the angle of rotation is (very) small. In this context, i.e. the infinitesimal case analysis, the time derivatives of the rotation variables hold simple (sometimes vector-like) relationships to the components of the angular velocity vector. Conventionally, this distinctive characteristic cannot be associated with general moderate-to-large rotations. In this thesis, it is demonstrated that the kinematical differential relationship between the rotation vector and the angular velocity vector may, in fact, be expressed in terms of a mere time derivative, provided that the angle of rotation is kept within moderate bounds. The key to achieve such simplicity in the kinematical equation (linear attitude kinematics) within moderate angles of rotation is a judicious choice of the basis from which the time derivative is observed. This result is used to advantage within a generalised version of Euler’s motion equations to construct a simple control law, which nominally realises both linear attitude tracking and linear angular velocity tracking (nominal linear attitude state tracking), within moderate attitude tracking errors. The analytical work presented here is unique in the sense that it combines attitude kinematics, dynamics and control in such a way that nominal linearity between the attitude state error variables is achieved within moderate attitude tracking errors. For the first time, an attitude control law explicitly enables the nominal closed-loop attitude state error dynamics to be chosen and motivated by useful physical concepts from linear control theory. The text also includes numerical simulations that validate and illustrate the theoretically achieved results. CAPES, Fundação Casimiro Montenegro Filho No tratamento do movimento rotacional tridimensional de corpos rígidos é inevitável lidar-se com o fato de que rotações não são quantidades vetoriais. Elas podem, no entanto, ser tratadas como tais quando o ângulo de rotação é (muito) pequeno. Neste contexto, ou seja, o da análise infinitesimal, as derivadas temporais das variáveis de rotação mantêm um relacionamento simples (às vezes mesmo do tipo vetorial) com os componentes do vetor velocidade angular. Convencionalmente, esta distinta característica não pode ser associada a rotações grandes, nem mesmo medianas. Nesta tese é demonstrado que a relação diferencial entre o vetor rotação e o vetor velocidade angular pode, na realidade, ser expressa em termos de uma simples derivada temporal, desde que o ângulo de rotação seja mantido numa faixa moderada. O artifício permitindo tal simplicidade na equação cinemática (cinemática linear de atitude) com um ângulo de rotação moderado é a escolha criteriosa da base a partir da qual a derivada temporal é observada. Este resultado é utilizado vantajosamente em conjunto com uma versão generalizada das equações de movimento de Euler na construção de uma lei de controle simples. Essa lei realiza, concomitantemente, o rastreamento linear nominal de atitude e o rastreamento linear nominal de velocidade angular (rastreamento linear nominal de estado rotacional), dentro de uma faixa moderada de erro de rastreamento de atitude. O trabalho analítico apresentado é único no sentido em que este combina cinemática rotacional, dinâmica rotacional e controle de forma tal que linearidade nominal entre as variáveis de erro de estado é atingida mesmo para erros moderados de rastreamento de atitude. Pela primeira vez, uma lei de controle permite explicitamente que a dinâmica de erro de estado rotacional em malha fechada seja escolhida e motivada por conceitos físicos úteis da teoria linear de controle. O texto também inclui simulações numéricas que validam e ilustram os resultados teóricos obtidos. 2013-06-14T21:29:44Z 2013-06-14T21:29:44Z 2002-10 doctoralThesis PECE, Carlos Alessandro Zanetti. An engineering vector-like approach to attitude kinematics & nominal attitude state tracking control. 2002. 154 f. Tese (Doutorado em Engenharia Aeronáutica e Mecânica) - Instituto Tecnológico de Aeronáutica, São José dos Campos, 2002. http://repositorio.utfpr.edu.br/jspui/handle/1/481 eng http://www.bd.bibl.ita.br/tde_busca/arquivo.php?codArquivo=204 application/pdf Instituto Tecnológico de Aeronáutica Curitiba Programa de Pós-Graduação em Engenharia Aeronáutica e Mecânica
institution	Universidade Tecnológica Federal do Paraná
collection	RIUT
language	Inglês
topic	Métodos de simulação Cálculo vetorial Cinemática das máquinas Engenharia mecânica Teoria dos erros Simulation methods Vector analysis Machinery, Kinematics of Mechanical engineering Error analysis (Mathematics)
spellingShingle	Métodos de simulação Cálculo vetorial Cinemática das máquinas Engenharia mecânica Teoria dos erros Simulation methods Vector analysis Machinery, Kinematics of Mechanical engineering Error analysis (Mathematics) Pece, Carlos Alessandro Zanetti An engineering vector-like approach to attitude kinematics & nominal attitude state tracking control
description	In dealing with rigid body three-dimensional rotational motion, one is inevitably led to face the fact that rotations are not vector quantities. They may, however, be treated as such when the angle of rotation is (very) small. In this context, i.e. the infinitesimal case analysis, the time derivatives of the rotation variables hold simple (sometimes vector-like) relationships to the components of the angular velocity vector. Conventionally, this distinctive characteristic cannot be associated with general moderate-to-large rotations. In this thesis, it is demonstrated that the kinematical differential relationship between the rotation vector and the angular velocity vector may, in fact, be expressed in terms of a mere time derivative, provided that the angle of rotation is kept within moderate bounds. The key to achieve such simplicity in the kinematical equation (linear attitude kinematics) within moderate angles of rotation is a judicious choice of the basis from which the time derivative is observed. This result is used to advantage within a generalised version of Euler’s motion equations to construct a simple control law, which nominally realises both linear attitude tracking and linear angular velocity tracking (nominal linear attitude state tracking), within moderate attitude tracking errors. The analytical work presented here is unique in the sense that it combines attitude kinematics, dynamics and control in such a way that nominal linearity between the attitude state error variables is achieved within moderate attitude tracking errors. For the first time, an attitude control law explicitly enables the nominal closed-loop attitude state error dynamics to be chosen and motivated by useful physical concepts from linear control theory. The text also includes numerical simulations that validate and illustrate the theoretically achieved results.
format	Tese
author	Pece, Carlos Alessandro Zanetti
author_sort	Pece, Carlos Alessandro Zanetti
title	An engineering vector-like approach to attitude kinematics & nominal attitude state tracking control
title_short	An engineering vector-like approach to attitude kinematics & nominal attitude state tracking control
title_full	An engineering vector-like approach to attitude kinematics & nominal attitude state tracking control
title_fullStr	An engineering vector-like approach to attitude kinematics & nominal attitude state tracking control
title_full_unstemmed	An engineering vector-like approach to attitude kinematics & nominal attitude state tracking control
title_sort	engineering vector-like approach to attitude kinematics & nominal attitude state tracking control
publisher	Instituto Tecnológico de Aeronáutica
publishDate	2013
citation	PECE, Carlos Alessandro Zanetti. An engineering vector-like approach to attitude kinematics & nominal attitude state tracking control. 2002. 154 f. Tese (Doutorado em Engenharia Aeronáutica e Mecânica) - Instituto Tecnológico de Aeronáutica, São José dos Campos, 2002.
url	http://repositorio.utfpr.edu.br/jspui/handle/1/481
_version_	1805307764059144192
score	10,814766

An engineering vector-like approach to attitude kinematics & nominal attitude state tracking control

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