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UNIVERSIDADE FEDERAL DE SANTA CATARINA DEPARTAMENTO DE ENGENHARIA MECÂNICA Anelize Zomkowski Salvi ENUMERATING and ASSEMBLING C

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UNIVERSIDADE FEDERAL DE SANTA CATARINA DEPARTAMENTO DE ENGENHARIA MECÂNICA Anelize Zomkowski Salvi ENUMERATING and ASSEMBLING C UNIVERSIDADE FEDERAL DE SANTA CATARINA DEPARTAMENTO DE ENGENHARIA MECÂNICA Anelize Zomkowski Salvi ENUMERATING AND ASSEMBLING CONFIGURATIONS WITH MODULAR ROBOTS. Florianópolis 2018 Anelize Zomkowski Salvi ENUMERATING AND ASSEMBLING CONFIGURATIONS WITH MODULAR ROBOTS. Tese submetida ao Programa de Pós- Graduação em Engenharia Mecânica para a obtenção do grau de Doutor em Engenharia Mecânica. Orientador: Henrique Simas, PhD Coorientador: Roberto Simoni, PhD Florianópolis 2018 Ficha de identificação da obra elaborada pelo autor, através do Programa de Geração Automática da Biblioteca Universitária da UFSC. Salvi, Anelize Zomkowski Enumerating and assembling configurations with modular robots / Anelize Zomkowski Salvi ; orientador, Henrique Simas, coorientador, Roberto Simoni, 2018. 224 p. Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós Graduação em Engenharia Mecânica, Florianópolis, 2018. Inclui referências. 1. Engenharia Mecânica. 2. enumeration. 3. modular robots. 4. assemble sequence planning. 5. metamorphic robots. I. Simas, Henrique . II. Simoni, Roberto . III. Universidade Federal de Santa Catarina. Programa de Pós-Graduação em Engenharia Mecânica. IV. Título. Anelize Zomkowski Salvi ENUMERATING AND ASSEMBLING CONFIGURATIONS WITH MODULAR ROBOTS. Esta Tese foi julgada aprovada para a obtenção do Título de “Doutor em Engenharia Mecânica”, e aprovada em sua forma final pelo Programa de Pós-Graduação em Engenharia Mecânica. Florianópolis, 07 de Maio 2018. Jonny Carlos da Silva, PhD Coordenador do Curso Roberto Simoni, PhD Coorientador Banca Examinadora: Henrique Simas, PhD Presidente Tarcisio Antonio Hess Coelho, PhD Relator Clovis Sperb De Barcellos, PhD Fábio Baldissera, PhD Luís Paulo Laus, PhD Marcelo Sobottka, PhD To my husband. AGRADECIMENTOS I would like to thank my supervisor, Prof. Henrique Simas, and my co-supervisor, Prof. Roberto Simoni, for the patient guidance, en- couragement, advice and friendship throughout all my time as a stu- dent. They have been crucial to this work and to my formation as a scientist. Special thanks to my committee, Prof. Tarcisio Antonio Hess Coelho, Prof. Clovis Sperb De Barcellos, Prof. Fábio Baldissera, Prof. Luís Paulo Laus and Prof. Marcelo Sobottka for their guidance and suggestions which have strongly contributed to this work. All colleagues of UFSC, for their support, encouragement and friendship. I am grateful to institutions that have supported my work: UFSC (Federal University of Santa Catarina); CAPES (Coordenação de Aper- feiçoamento de Pessoal de Nível Superior) and CNPQ (National Coun- sel of Technological and Scientific Development). I wish to thank my family, my mother, brother, stepfather and parents in law, for their support and encouragement throughout all these years. I am specially thankful to my husband, Andrea Piga Car- boni, whose love and encouragement cannot be measured. You are my life. Wisdom begins in wonder. Socrates RESUMO Esta tese apresenta novas contribuições para dois problemas forte- mente relacionados: a enumeração e o sequenciamento da montagem de configurações (Assembly Sequence Planning - ASP) constituídas por robôs modulares. Ferramentas matemáticas, mais especificamente, fer- ramentas de Teoria dos Grafos, são largamente empregadas no trata- mento desses dois problemas. Em sua primeira parte, a tese aborda o problema de enumeração, fornecendo um novo método que permite enumerar as configurações não-isomórficas de robôs modulares com mó- dulos cúbicos. Este método é baseado em trabalhos anteriores do autor para robôs modulares com módulos planares. O método foi imple- mentado em C++, fornecendo a enumeração de configurações com até 10 módulos cúbicos. Este resultado constitui um avanço em relação ao número de módulos alcançados na literatura. Em sua segunda parte, a tese introduz três novos ASP para robôs modulares que tratam classes de configurações em aberto na literatura. Esta tese é o primeiro tra- balho a resolver os seguintes problemas: Como montar configurações compostas por sistemas de robôs modulares; como montar configura- ções com corredores estreitos; como montar configurações com furos internos; como montar configurações sem furos internos nem corredores estreitos, mas escolhendo o ponto de partida do ASP e como montar estruturas planares verticais. Todos os ASP obedecem a condição de acessibilidade, ou seja, nenhum módulo pode passar por um corredor entre dois robôs que estejam na estrutura, se este corredor for tão es- treito quanto o lado de um módulo. Como resultado complementar, esta tese apresenta novas contribuições ao ASP para estrutura maríti- mas de Seo, Yim e Kumar. Palavras-chave: enumeração, robôs modulares, robôs metamórficos, sequência de montagem (ASP). RESUMO EXPANDIDO Introdução Robôs modulares reconfiguráveis são robôs constituídos de módulos independentes que podem ser homogêneos ou heterogêneos em suas formas e funcionalidades. Cada módulo possui atuadores, sensores, processadores de energia, memória, além de maneiras de se comunicar e de se conectar a outros módulos. Se um robô modular reconfigurável pode mudar de forma autônoma as conexões de seus módulos, o robô é chamado de robô modular auto-reconfigurável (MSR). Em outras palavras, um MSR é capaz de modificar de maneira autônoma o seu formato rearranjando as conexões entre seus módulos. Um MSR pode modificar seu formato para efetuar determinada tarefa, seja ela transpor um buraco, rolar adotando a forma de um aro, cons- truir uma forma complexa com muitos braços ou ainda utilizar a re- configuração para locomoção. O crescente interesse neste tipo de robôs deve-se justamente à capacidade de auto-reconfiguração, pois esta ca- racterística confere aos robôs adaptabilidade a novas circunstâncias e tarefas, bem como a capacidade de recuperação de falhas mecânicas, como, por exemplo, a perda da funcionalidade de um módulo. Visto que é a capacidade de assumir diferentes configurações que torna estes robôs versáteis, é necessário que eles possam ser operados no maior número de configurações diversas. Portanto, é importante conhecer as configurações que um dado conjunto de módulos pode assumir, assim como determinar uma sequência correta de montagem para cada con- figuração. A enumeração de configurações e a montagem de configurações são pro- blemas fortemente relacionados. De fato, para que uma configuração seja montada, é necessário escolhê-la do conjunto de todas as configura- ções possíveis para um dado número de módulos. Além disto, escolhida a configuração desejada, é importante determinar que sequência de ope- rações leva à correta montagem da configuração. Estes dois problemas são tratados nesta tese que apresenta um novo método de enumeração para configurações não-isomórficas de robôs modulares com módulos cúbicos e novas estratégias de montagem para configurações planares compostas por módulos retangulares ou cúbicos. Objetivos gerais Os objetivos gerais desta tese são desenvolver métodos de enumera- ção e de montagem para configurações de robôs modulares. Objetivos específicos: problema de enumeração Os objetivos específicos relativos à enumeração de configurações para robôs modulares são: desenvolver um método de enumeração para con- figurações compostas por módulos cúbicos e desenvolver um método simples para capturar as simetrias deste tipo de configuração. Objetivos específicos: problema de montagem O objetivo específico relativo à montagem de configurações para robôs modulares é atingir classes de configurações não tratadas na literatura, como por exemplo: estruturas compostas de substruturas previamente montadas e estruturas que apresentem corredores estreitos, i.e. espaços que são demasiado estreitos para que um módulo possa atravessá-los ou ainda estruturas planares verticais. Metodologia A tese trata o problema de enumeração e de montagem em capítu- los distintos. Porém, ferramentas de teoria dos grafos são largamente utilizadas no tratamento de ambos os problemas e fornecem uma base comum para o desenvolvimento da tese. Metodologia: problema de enumeração Em trabalhos anteriores [15–17], o autor propôs técnicas de enume- ração para robôs modulares. Uma destas técnicas, chamada Método Orbital [16, 17], foi desenvolvida para robôs com módulos quadrados. A tese estende o Método Orbital para configurações compostas por módulos cúbicos. Para efetuar esta extensão, ferramentas de teoria dos grafos e dos gru- pos são largamente empregadas e uma nova modelagem que permite detectar as simetrias das configurações é apresentada. Além disto, dois resultados apresentados pelo autor [15] para robôs com módulos qua- drados são estendidos para o caso cúbico. Assim, um método completo para enumeração de configurações não-isomórficas compostas de mó- dulos cúbicos e um teste para checagem de simetrias deste tipo de configuração são obtidos e são melhor discutidos na seção Resultados e Discussão. Metodologia: problema de montagem Para atingir diferentes classes de configurações, a tese introduz três novos ASP. Estes ASP são baseados em teoria dos grafos, mais especi- ficamente em algoritmos de busca em grafos. Além disso estes ASP são modelados para obedecer a condição de aces- sibilidade proposta por Paulos et al.[2]: “Qualquer módulo retangular não pode passar por um espaço entre dois módulos da estrutura final, se este espaço for tão pequeno quanto o lado do módulo.” Nos ASP propostos, a estrutura é modelada por um grafo não direci- onado, apresentado na forma de sua lista de adjacência. Estes ASP são estruturados com um algoritmo principal que apresenta uma
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