The decomposition and classification of radiant affine 3-manifolds

An affine manifold is a manifold with torsion-free flat affine connection. A geometric topologist's definition of an affine manifold is a manifold with an atlas of charts to the affine space with affine transition functions; a radiant affine manifold is an affine manifold with holonomy consisting of affine transformations fixing a common fixed point. We decompose an orientable closed radiant affine 3-manifold into radiant 2-convex affine manifolds and radiant concave affine 3-manifolds along mutually disjoint totally geodesic tori or Klein bottles using the convex and concave decomposition of real projective $n$-manifolds developed earlier. Then we decompose a 2-convex radiant affine manifold into convex radiant affine manifolds and concave-cone affine manifolds. To do this, we will obtain certain nice geometric objects in the Kuiper completion of holonomy cover. The equivariance and local finiteness property of the collection of such objects will show that their union covers a compact submanifold of codimension zero, the complement of which is convex. Finally, using the results of Barbot, we will show that a closed radiant affine 3-manifold admits a total cross section, confirming a conjecture of Carri\`ere, and hence every radiant affine 3-manifold is homeomorphic to a Seifert fibered space with trivial Euler number, or a virtual bundle over a circle with fiber homeomorphic to a torus.Comment: Some notational mistakes fixed, and the appendix rewritte

Perception Based Navigation for Underactuated Robots.

Robot autonomous navigation is a very active field of robotics. In this thesis we propose a hierarchical approach to a class of underactuated robots by composing a collection of local controllers with well understood domains of attraction. We start by addressing the problem of robot navigation with nonholonomic motion constraints and perceptual cues arising from onboard visual servoing in partially engineered environments. We propose a general hybrid procedure that adapts to the constrained motion setting the standard feedback controller arising from a navigation function in the fully actuated case. This is accomplished by switching back and forth between moving "down" and "across" the associated gradient field toward the stable manifold it induces in the constrained dynamics. Guaranteed to avoid obstacles in all cases, we provide conditions under which the new procedure brings initial configurations to within an arbitrarily small neighborhood of the goal. We summarize with simulation results on a sample of visual servoing problems with a few different perceptual models. We document the empirical effectiveness of the proposed algorithm by reporting the results of its application to outdoor autonomous visual registration experiments with the robot RHex guided by engineered beacons. Next we explore the possibility of adapting the resulting first order hybrid feedback controller to its dynamical counterpart by introducing tunable damping terms in the control law. Just as gradient controllers for standard quasi-static mechanical systems give rise to generalized "PD-style" controllers for dynamical versions of those standard systems, we show that it is possible to construct similar "lifts" in the presence of non-holonomic constraints notwithstanding the necessary absence of point attractors. Simulation results corroborate the proposed lift. Finally we present an implementation of a fully autonomous navigation application for a legged robot. The robot adapts its leg trajectory parameters by recourse to a discrete gradient descent algorithm, while managing its experiments and outcome measurements autonomously via the navigation visual servoing algorithms proposed in this thesis.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/58412/1/glopes_1.pd

Sliding Mode Control

The main objective of this monograph is to present a broad range of well worked out, recent application studies as well as theoretical contributions in the field of sliding mode control system analysis and design. The contributions presented here include new theoretical developments as well as successful applications of variable structure controllers primarily in the field of power electronics, electric drives and motion steering systems. They enrich the current state of the art, and motivate and encourage new ideas and solutions in the sliding mode control area

Dynamic path following controllers for planar mobile robots

In the field of mobile robotics, many applications require feedback control laws that provide perfect path following. Previous work has shown that transverse feedback linearization is an effective approach to designing path following controllers that achieve perfect path following and path invariance. This thesis uses transverse feedback linearization and augments it with dynamic extension to present a framework for designing path following controllers for certain kinematic models of mobile robots. This approach can be used to design path following controllers for a large class of paths. While transverse feedback linearization makes the desired path attractive and invariant, dynamic extension allows the closed-loop system to achieve the desired motion along the path. In particular, dynamic extension can be used to make the mobile robot track a desired velocity or acceleration profile while moving along a path

Underwater Vehicles

For the latest twenty to thirty years, a significant number of AUVs has been created for the solving of wide spectrum of scientific and applied tasks of ocean development and research. For the short time period the AUVs have shown the efficiency at performance of complex search and inspection works and opened a number of new important applications. Initially the information about AUVs had mainly review-advertising character but now more attention is paid to practical achievements, problems and systems technologies. AUVs are losing their prototype status and have become a fully operational, reliable and effective tool and modern multi-purpose AUVs represent the new class of underwater robotic objects with inherent tasks and practical applications, particular features of technology, systems structure and functional properties

Research on a semiautonomous mobile robot for loosely structured environments focused on transporting mail trolleys

In this thesis is presented a novel approach to model, control, and planning the motion of a nonholonomic wheeled mobile robot that applies stable pushes and pulls to a nonholonomic cart (York mail trolley) in a loosely structured environment. The method is based on grasping and ungrasping the nonholonomic cart, as a result, the robot changes its kinematics properties. In consequence, two robot configurations are produced by the task of grasping and ungrasping the load, they are: the single-robot configuration and the robot-trolley configuration. Furthermore, in order to comply with the general planar motion law of rigid bodies and the kinematic constraints imposed by the robot wheels for each configuration, the robot has been provided with two motorized steerable wheels in order to have a flexible platform able to adapt to these restrictions. [Continues.

Modeling EMI Resulting from a Signal Via Transition Through Power/Ground Layers

Signal transitioning through layers on vias are very common in multi-layer printed circuit board (PCB) design. For a signal via transitioning through the internal power and ground planes, the return current must switch from one reference plane to another reference plane. The discontinuity of the return current at the via excites the power and ground planes, and results in noise on the power bus that can lead to signal integrity, as well as EMI problems. Numerical methods, such as the finite-difference time-domain (FDTD), Moment of Methods (MoM), and partial element equivalent circuit (PEEC) method, were employed herein to study this problem. The modeled results are supported by measurements. In addition, a common EMI mitigation approach of adding a decoupling capacitor was investigated with the FDTD method

CONTINUOUS MEASUREMENTS AND NONCLASSICALITY AS RESOURCES FOR QUANTUM TECHNOLOGIES

This PhD thesis contains results about two different main topics. The first part deals with the application of continuously monitored quantum systems to high precision quantum metrology. A continuous in time measurement on a quantum system is a kind indirect measurement, which only weakly perturbs the system and leaves room for it to evolve under its dynamics. This time-continuous measurement allows one to collect information about some interesting parameter characterizing the dynamics. In this thesis we show how to apply the theory of quantum parameter estimation to continuously monitored quantum systems. In particular, we study the estimation of a magnetic field applied to an ensemble of two level atoms; we show that by continuously monitoring the system we can obtain a quadratic scaling of the precision with the number of atoms, in two different physical settings (dynamically generated entanglement or initial entanglement). In the second part we study different aspects of nonclassicality of continuous variable quantum systems (bosonic degree of freedoms). They can be described by distributions (in particular, the Wigner function) on a classical phase space, which however can take negative values, the hallmark of nonclassicality. In this context, states with a Gaussian distribution are very useful and very well studied; however, on a fundamental level they must be considered classical. We present several studies connected to the vast topic of non-Gaussian states, starting from an application to parameter estimation, as a link to the first part. We study the relationships between anharmonic Hamiltonians and the nonclassicality of their ground states; we also explore the connection between a quantum effect called `backflow of probability' and the negativity of the Wigner function. We end by showing that quantum operations made out of Gaussian building blocks give rise to a well-defined resource theory of Wigner negativity and non-Gaussianity

Performances and kinetic studies of hydrotreating of bio-oils in microreactor

Hydrotreating reaction of vegetable oil is an alternative method for the production of renewable biodiesel fuel. This reaction involves conversion of triglycerides into normal alkanes, leads to a deoxygenated and stable product, which is fully compatible with petroleum derived diesel fuel. The hydrotreating process uses hydrogen to remove oxygen from triglyceride molecules at elevated temperature in the presence of a solid catalyst. This work focused on the development of microtechnology-based chemical reaction process for liquid biofuel production from oil-based biofuel feedstock. A hydrotreating reaction of oleic acid and triolein as model compounds and jatropha oil as real feedstock was studied in a continuous flow microchannel reactor of inner diameter 500 μm and of varied length; 1.5 - 5 m. The microchannel reactor was fabricated from SS-316. The walls of the microreactor were coated with a thin Al₂O₃ film, which was then impregnated with Ni-Mo catalyst containing phosphorus as promoter. The reactions were carried out in the temperature range of 275-325 °C, residence time in the range of 11-40 s and at constant system pressure of 500 psig. The results showed that the microchannel reactor was suitable for the hydrotreating process. Complete conversion of the fatty acid hydrotreating reaction was achieved at a reaction temperature of 325 °C. Hydrotreating of fatty acids occurred primarily via hydrodeoxygenation and the main liquid products were octadecane and heptadecane. Fatty alcohol, fatty acid and long chain esters were formed as reaction intermediates. Hydrotreating of triglycerides proceeded via the hydrocracking of triglycerides into diglycerides, monoglycerides and fatty acids. Then fatty acids were subsequently deoxygenated to hydrocarbons. The conversion of fatty acids and triglycerides increased with increasing temperatures. A detailed mathematical model was developed to represent this two-phase chemical reaction process. The mathematical model was entirely based on first principles, i.e. no adjustable or correlation parameters were used. Kinetic parameter estimation was performed and the predicted results were in good agreement with experimental results

Advances in Evolutionary Algorithms

With the recent trends towards massive data sets and significant computational power, combined with evolutionary algorithmic advances evolutionary computation is becoming much more relevant to practice. Aim of the book is to present recent improvements, innovative ideas and concepts in a part of a huge EA field