The motion planning problem can be formulated as a Markov decision process (MDP), if the uncertainties in the robot motion and environments can be modeled probabilistically. The complexity of solving these MDPs grow exponentially as the dimension of the problem increases and hence, it is nearly impossible to solve the problem even without constraints. Using hierarchical methods, these MDPs can be transformed into a semi-Markov decision process (SMDP) which only needs to be solved at certain landmark states. In the deterministic robotics motion planning community, sampling based algorithms like probabilistic roadmaps (PRM) and rapidly exploring random trees (RRTs) have been successful in solving very high dimensional deterministic problem. However they are not robust to system with uncertainties in the system dynamics and hence, one of the primary objective of this work is to generalize PRM/RRT to solve motion planning with uncertainty. We first present generalizations of randomized sampling based algorithms PRM and RRT, to incorporate the process uncertainty, and obstacle location uncertainty, termed as "generalized PRM" (GPRM) and "generalized RRT" (GRRT). The controllers used at the lower level of these planners are feedback controllers which ensure convergence of trajectories while mitigating the effects of process uncertainty. The results indicate that the algorithms solve the motion planning problem for a single agent in continuous state/control spaces in the presence of process uncertainty, and constraints such as obstacles and other state/input constraints. Secondly, a novel adaptive sampling technique, termed as "adaptive GPRM" (AGPRM), is proposed for these generalized planners to increase the efficiency and overall success probability of these planners. It was implemented on high-dimensional robot n-link manipulators, with up to 8 links, i.e. in a 16-dimensional state-space. The results demonstrate the ability of the proposed algorithm to handle the motion planning problem for highly non-linear systems in very high-dimensional state space. Finally, a solution methodology, termed the "multi-agent AGPRM" (MAGPRM), is proposed to solve the multi-agent motion planning problem under uncertainty. The technique uses a existing solution technique to the multiple traveling salesman problem (MTSP) in conjunction with GPRM. For real-time implementation, an ?inter-agent collision detection and avoidance? module was designed which ensures that no two agents collide at any time-step. Algorithm was tested on teams of homogeneous and heterogeneous agents in cluttered obstacle space and the algorithm demonstrate the ability to handle such problems in continuous state/control spaces in presence of process uncertainty.

La problématique étudiée dans cette thèse concerne le maintien de l’intégrité de robots mobiles en milieux naturels. L’objectif est de fournir des lois de commande permettant de garantir l’intégrité d’un véhicule lors de déplacements autonomes en milieux naturels à vitesse élevée (5 à 7 m.s -1 ) et plus particulièrement dans le cadre de l’agriculture de précision. L’intégrité s’entend ici au sens large. En effet, l’asservissement des déplacements d’un robot mobile peut générer des consignes nuisant à son intégrité physique, ou à la réalisation de sa tâche (renversement, tête-à-queue, stabilité des commandes, maintien de la précision, etc.). De plus, le déplacement en milieux naturels amène des problématiques liées notamment à des conditions d’adhérence variables et relativement faibles (d’autant plus que la vitesse du véhicule est élevée), ce qui se traduit par de forts glissements des roues sur le sol, ou encore à des géométries de terrains non traversables par le robot. Aussi, cette thèse vise à déterminer en temps réel l’espace de stabilité en terme de commandes admissibles permettant de modérer les actions du robot. Après une présentation des modélisations existantes, et des observateurs permettant l’exploitation de ces modélisations pour la mise en place de loi de commande prédictive en braquage pour le suivi de trajectoire, une nouvelle méthode d’estimation des glissements basé sur une observation cinématique est proposée. Celle-ci permet de répondre aux problématiques de vitesse variable (et notamment du passage de la vitesse par des valeurs nulles) du véhicule et d’observation lors d’un déplacement sans trajectoire de référence. Ce nouvel observateur est primordial pour la suite des développements de cette thèse, puisque la suite des travaux s’intéresse à la modulation de la vitesse du véhicule. Ainsi, dans la suite des travaux, deux lois de commande prédictives agissant sur la vitesse du véhicule ont été mises en place. La première apporte une solution à la problématique de la saturation des actionneurs en braquage, lorsque la vitesse ou les glissements rendent la trajectoire à suivre inadmissible vis-à-vis des capacités physiques du véhicule. La deuxième répond à la problématique de la garantie de la précision du suivi de trajectoire (maintien du véhicule dans un couloir de déplacement). Dans les deux cas la stratégie de commande est similaire : on prédit l’état futur du véhicule en fonction de ses conditions d’évolution actuelle et de conditions d’évolutions futures simulées (obtenues grâce à la simulation de l’évolution d’un modèle dynamique du véhicule) afin de déterminer la valeur de la vitesse optimale pour que les variables cibles (dans un cas la valeur du braquage et dans l’autre l’écart à la trajectoire) respectent les conditions imposées (non-dépassement d’une valeur cible). Les résultats présentés dans ce mémoire ont été réalisés soit en simulations, soit en conditions réelles sur des plateformes robotiques. Il en découle que les algorithmes proposés permettent dans un cas de réduire la vitesse du véhicule pour éviter la saturation du braquage et donc les phénomènes de sur et sous virage qui en découlerait et donc permet de conserver la commandabilité du véhicule. Et dans l’autre cas de garantir que l’écart à la trajectoire reste sous une valeur cible. / This thesis focused on the issue of the preseving of the integrity of mobile robots in off-road conditions. The objective is to provide control laws to guarantee the integrity of a vehicle during autonomous displacements in natural environments at high speed (5 to 7 m.s -1 ) and more particularly in The framework of precision farming. Integrity is here understood in the broad sense. Indeed, control of the movements of a mobile robot can generate orders that affect its physical integrity, or restrains the achievement of its task (rollover, spin, control stability, maintaining accuracy , etc.). Moreover, displacement in natural environments leads to problems linked in particular to relatively variable and relatively low adhesion conditions (especially since the speed of the vehicle is high), which results in strong sliding of wheels on the ground, or to ground geometries that can not be crossed by the robot. This thesis aims to determine in real time the stability space in terms of permissible controls allowing to moderate the actions of the robot. After a presentation of the existing modelings and observers that allow the use of these modelizations for the implementation of predictive control law for trajectory tracking, a new method of estimation of side-slip angles based on a kinematic observation is proposed. It permit to address the problem of variable speed of the vehicle (and in particular the case of zero values) and also to allow the observation during a displacement without reference trajectory. This new observer is essential for the further development of this thesis, since the rest of the work is concerned with the modulation of the speed of the vehicle. So, in the further work, two predictive control laws acting on the speed of the vehicle have been set up. The first one provides a solution to the problem of the saturation of steering actuators, when the speed or side-slip angles make the trajectory inadmissible to follow with respect to the physical capacities of the vehicle. The second one adress the problem of guaranteeing the accuracy of trajectory tracking (keeping the vehicle in a corridor of displacement). In both cases, the control strategy is similar: the future state of the vehicle is predicted according to the current conditions of evolution and the simulated one for the future evolution (obtained by simulating the evolution of dynamics models of the vehicle) in order to determine the value of the optimum speed so that the target variables (in one case the value of the steering and in the other the lateral deviation from the trajectory) comply with the imposed conditions (not exceeding a target value). The results presented in this thesis were realized either in simulations or in real conditions on robotic platforms. It follows that the proposed algorithms make it possible : in one case to reduce the speed of the vehicle in order to avoid the saturation of the steering actuator and therefore the resulting over and under steering phenomena and thus make it possible to preserve the vehicle’s controllability. And in the other case, to ensure that the lateral deviation from the trajectory remains below a target value.

Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-11T16:01:13Z No. of bitstreams: 1 arquivototal.pdf: 1341956 bytes, checksum: 725d00067ec252af7f139395f2803b1b (MD5) / Made available in DSpace on 2017-08-11T16:01:13Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1341956 bytes, checksum: 725d00067ec252af7f139395f2803b1b (MD5) Previous issue date: 2015-12-15 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work develops the theories of local cohomology and local homology with respect to an arbitrary set of ideals and generalises most of the important results from the classical theories. It also introduces the category of quasi-holonomic D-modules and proves some finiteness properties of local cohomology modules which generalise Lyubeznik's results in some sense. / Este trabalho desenvolve as teorias de cohomologia e homologia locais com respeito a um conjunto arbitrário de ideais e generaliza vários dos resultados importantes das teorias clássicas. Também, introduz a categoria dos D-módulos quase-holônomos e prova alguns resultados de finitude de cohomologia local que generalizam, em algum sentido, os resultados de G. Lyubeznik.

This thesis deals with the theory of geometric control of the trident robot. The thesis describes the basic concepts of differential geometry and control theory, which are subsequently used for describing various mechanisms. Finally, the thesis proposes the management using inferred results.

With the development of technology and availability of data, it is sometimes easier to learn the control policies directly from the data, rather than modeling a plant and designing a controller. Modeling a plant is not always possible due to the complexity of the plant. Data-enabled predictive control (DeePC) is a recently proposed approach that combines system identification, estimation, and control in a single optimization problem. DeePC is primarily designed for LTI systems. The purpose of this thesis is to extend the application of DeePC to nonlinear systems with a particular focus on a non-holonomic ground robot. To reach this goal, we decompose the system states into different working modes where each mode can be linearly approximated. Furthermore, the data collection policies were also evaluated to conclude how they affect the performance of the DeePC. We identified several key challenges in this direction, namely: data-demanding structure, high computational complexity, and performance deterioration with increased non-linearity. While these challenges prohibited the application of DeePC to the ground robot system; we successfully applied the method to a benchmark non-linear system, the inverted pendulum on cart problem, and studied the effect of various design choices on control performance. Our observations indicate potential areas of improvement toward enabling DeePC for highly nonlinear systems. / Med utvecklingen av teknik och tillgänglighet av data är det ibland enklare att lära sig styrpolicyerna direkt från data, snarare än att modellera ett system och designa en styrenhet. Att modellera ett system är inte alltid möjligt på grund av systemets komplexitet. Data aktiverad prediktiv kontroll (DeePC) är en nyligen föreslagen metod som kombinerar systemidentifiering, uppskattning och kontroll i ett enda optimeringsproblem. DeePC är främst designad för LTI-system. Syftet med denna avhandling är att utöka tillämpningen av DeePC till icke-linjära system med särskilt fokus på en icke-holonomisk markrobot. För att nå detta mål delar vi upp systemtillstånden i olika arbetslägen där varje läge kan approximeras linjärt. Dessutom utvärderades datainsamlingspolicyerna för att dra slutsatser om hur de påverkar DeePCs prestation. Vi identifierade ett antal nyckelutmaningar i denna riktning, nämligen: datakrävande struktur, hög beräkningskomplexitet och prestandaförsämring med ökad icke-linjäritet. Även om de utmaningerna hindrade tillämpningen av DeePC på markrobot systemet; har vi framgångsrikt tillämpat metoden på ett benchmark icke-linjärt system, problemet med inverterad pendel på vagn, och studerade effekten av olika designval på kontrollprestanda. Våra observationer indikerar potentiella förbättringsområden för att möjliggöra DeePC för mycket olinjära system.

[pt] Robôs móveis autônomos são um grande foco de pesquisa devido à sua aplicabilidade e interdisciplinaridade. Robôs móveis com roda de direção diferencial, além de possuírem alta não-linearidade, detêm uma característica inerente à sua geometria: suas rodas só podem girar em torno de eixos fixos, sem esterçamento. Com isso, o deslizamento longitudinal e lateral é inevitável, principalmente quando o sistema está em movimento sob efeitos dinâmicos significativos. Controle Preditivo baseado em Modelo Não-Linear, Nonlinear Model Predictive Control (NMPC), é amplamente utilizado nesses casos, já que consegue lidar com sistemas com múltiplas restrições. O presente trabalho apresenta modelos matemáticos de um robô móvel com roda do tipo skidsteer, procedente da direção diferencial, incluindo o deslizamento longitudinal, aos quais o NMPC é empregado para seguimento de trajetória, obtendo trajetórias similares à de referência. Verificando que o custo de processamento de tais controladores pode ser muito alto para uso em tempo real, um controle hierárquico é desenvolvido otimizando as forças longitudinais entre as rodas e o solo para encontrar deslizamentos de referência para uma determinada trajetória a ser seguida. Como em um ambiente real nem todos os estados podem ser medidos, o controle necessita também estimar os estados não medidos. A Estimação de Estados por Horizonte Móvel, (Moving Horizon State Estimation (MHSE)), derivada dos fundamentos do NMPC, foi utilizada para realizar a estimativa, já que possui recursos para manter o sistema sob as restrições. Com o MHSE, o deslizamento do sistema pode ser calculado a partir dos estados estimados para as trajetórias obtidas com o Controle Preditivo baseado em Modelo, (Model Predictive Control (MPC)). Por fim, uma rede neural foi treinada com os estados preditos e estimados com o MHSE para que pudesse substituí-lo para que todo o controle fosse utilizado em tempo real. Com isso, o tempo computacional foi reduzido devido a substituição do MHSE. / [en] Autonomous mobile robots are a major focus of research due to their applicability and interdisciplinarity. Depending on the type of locomotion, the system’s controller needs to handle not only trajectory tracking but also the way the system interacts with the ground. Mobile robots with differential drive wheels, in addition to having high nonlinearity, possess an inherent characteristic due to their geometry: their wheels can only rotate around fixed axes, without steering. As a result, longitudinal and lateral slip is inevitable, especially when the system is in motion under significant dynamic effects. Nonlinear Model Predictive Control (NMPC) is widely used in these cases, as it can handle systems with multiple constraints. This work presents mathematical models of a skid-steer mobile robot, derived from differential drive, including longitudinal slip, to which NMPC is applied for trajectory tracking, achieving trajectories similar to the reference. Given that the processing cost of such controllers can be very high for real-time use, a hierarchical control is developed, optimizing the longitudinal forces between the wheels and the ground to find reference slips for a given trajectory to be followed. Since in a real environment not all states can be measured, the control also needs to estimate the unmeasured states. Moving Horizon State Estimation (MHSE), derived from the fundamentals of NMPC, was used to perform the estimation, as it has the resources to keep the system within the constraints. With MHSE, the system’s slip can be calculated from the estimated states for the trajectories obtained with Model Predictive Control (MPC). Finally, a neural network was trained with the predicted and estimated states using MHSE to replace it so that the entire control could be used in real-time. As a result, computational time was reduced due to the replacement of MHSE.

Made available in DSpace on 2015-05-14T12:14:06Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1577961 bytes, checksum: c71d976d783495df566e0fa6baadf8ca (MD5) Previous issue date: 2009-08-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / We start this work studying the appearance of geometric quantum phases as in the relativistic as in the non-relativistic quantum dynamics of a neutral particle with permanent magnetic and electric dipole moment which interacts with external electric and magnetic fields in the presence of linear topological defects. We describe the linear topological defects using the approach proposed by Katanaev and Volovich, where the topological defects in solids are described by line elements which are solutions of the Einstein's equations in the context of general relativity. We also analyze the in uence of non-inertial effects in the quantum dynamics of a neutral particle using two distinct reference frames for the observers: one is the Fermi-Walker reference frame and another is a rotating frame. As a result, we shall see that the difference between these two reference frames is in the presence/absence of dragging effects of the spacetime which makes its in uence on the phase shift of the wave function of the neutral particle. In the following, we shall use our study of geometric quantum phases to make an application on the Holonomic Quantum Computation, where we shall show a new approach to implement the Holonomic Quantum Computation via the interaction between the dipole moments of the neutral particle and external fields and the presence of linear topological defects. Another applications for the Holonomic Quantum Computation is based in the structure of the topological defects in graphene layers. In the presence of topological defects, a graphene layer shows two distinct phase shifts: one comes from the mix of Fermi points while the other phase shift comes from the topology of the defect. To provide a geometric description for each phase shift in the graphene layer, we use the Kaluza-Klein theory where we establish that the extra dimension describes the Fermi points in the graphene layer. Hence, we can implement the Holonomic Quantum Computation through the possibility to build cones and anticones of graphite in such way we can control the quantum uxes in graphene layers. In the last part of this work, we study the Landau quantization for neutral particles as in the relativistic dynamics and non-relativistic dynamics. In the non-relativistic dynamics, we study the Landau quantization in the presence of topological defects as in an inertial as in a non-inertial reference frame. In the relativistic quantum dynamics, we start our study with the Landau quantization in the Minkowisky considering two different gauge fields. At the end, we study the relativistic Landau quantization for neutral particles in the Cosmic Dislocation spacetime. / Neste trabalho estudamos inicialmente o surgimento de fases geometricas nas dinâmicas quânticas relativística e não-relativística de uma partícula neutra que possui momento de dipolo magnético e elétrico permanente interagindo com campos elétricos e magnéticos externos na presença de defeitos topológicos lineares. Para descrevermos defeitos topológicos lineares usamos a aproximação proposta por Katanaev e Volovich, onde defeitos lineares em sólidos são descritos por elementos de linha que são soluções das equações de Einstein no contexto da relatividade geral. Analisamos também a inuência de efeitos não-inerciais na dinâmica quântica de uma partícula neutra em dois tipos distintos de referenciais para os observadores: um é o referencial de Fermi-Walker e outro é um referencial girante. Vemos que a diferença entre dois referenciais está na presença/ausência de efeitos de arrasto do espaço-tempo que irá influenciar diretamente na mudança de fase na funçãao de onda da partícula neutra. Em seguida, usamos nosso estudo de fases geométricas para fazer aplicações na Computação Quântica Holonômica onde mostramos uma nova maneira de implementar a Computação Quântica Holonômica através da interação entre momentos de dipolo e campos externos e pela presença de defeitos topológicos lineares. Outra aplicação para a Computação Quântica Holonômica está baseada na estrutura de defeitos topológicos em um material chamado grafeno. Na presença de defeitos topológicos lineares, esse material apresenta duas fases quânticas de origens distintas: uma da mistura dos pontos de Fermi e outra da topologia do defeito. Para dar uma descrição geométrica para a origem de cada fase no grafeno usamos a Teoria de Kaluza-Klein, onde a dimensão extra sugerida por esta teoria descreve os pontos de Fermi no grafeno. Portanto, a implementação da Computação Quântica Holonômica no grafeno está baseada na possibilidade de construir cones e anticones de grafite de tal maneira que se possa controlar os fluxos quânticos no grafeno. Na última parte deste trabalho estudamos a quantização de Landau para partículas neutras tanto na dinâmica não-relativística quanto na dinâmica relativística. Na dinâmica não-relativítica, estudamos a quantização de Landau na presença de defeitos em um referecial inercial e, em seguida, em um referencial nãoo-inercial. Na dinâmica relativística, estudamos inicialmente a quantização de Landau no espaço-tempo plano em duas configurações de campos diferentes. Por fim, estudamos a quantização de Landau relativística para partículas neutras no espaço-tempo da deslocação cósmica.