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This paper proposes a kinematic modeling method for robotic manipulators by extracting the modified Denavit–Hartenberg (MDH) parameters using line geometry. For single-branched manipulators, various joint axes can be represented as lines using Plücker coordinates. The forward kinematics is derived by performing the product of matrices which are the exponential maps lifted from two kinds of exponential coordinates using the MDH parameters. For extracting MDH parameters, line geometry systematically analyzes the following: (1) the closest point between a point and line, (2) the closest distance and twist angle between two lines, (3) the common perpendicular line and its intersection points, and (4) classifies line relationships into collinear, distant parallel, intersected, and skewed cases. For each case, five parameters including twist angle, closest distance, common perpendicular direction vector, and both feet on a common perpendicular line are sequentially computed as results of the line geometry block. Finally, the aforementioned line geometry blocks are utilized to extract the four MDH parameters according to their definitions. The effectiveness of the proposed algorithm is verified by four examples including a typical Selective Compliance Assembly Robot Arm (SCARA) robot and three different commercial manipulators.

We propose a new paradigm for modelling and calibrating laser scanners with rotation symmetry, as is the case for lidars or for galvanometric laser systems with one or two rotating mirrors. Instead of bothering about the intrinsic parameters of a physical model, we use the geometric properties of the device to model it as a specific configuration of lines, which can be recovered by a line-data-driven procedure. Compared to universal data-driven methods that train general line models, our algebraic-geometric approach only requires a few measurements. We elaborate the case of a galvanometric laser scanner with two mirrors, that we model as a grid of hyperboloids represented by a grid of 3×3 lines. This provides a new type of look-up table, containing not more than nine elements, lines rather than points, where we replace the approximating interpolation with exact affine combinations of lines. The proposed method is validated in a realistic virtual setting. As a collateral contribution, we present a robust algorithm for fitting ruled surfaces of revolution on noisy line measurements.

Hirsch, Devaney, and Smale's classic Differential Equations, Dynamical Systems, and an Introduction to Chaos has been used by professors as the primary text for undergraduate and graduate level courses covering differential equations. It provides a theoretical approach to dynamical systems and chaos written for a diverse student population among the fields of mathematics, science, and engineering. Prominent experts provide everything students need to know about dynamical systems as students seek to develop sufficient mathematical skills to analyze the types of differential equations that arise in their area of study. The authors provide rigorous exercises and examples clearly and easily by slowly introducing linear systems of differential equations. Calculus is required as specialized advanced topics not usually found in elementary differential equations courses are included, such as exploring the world of discrete dynamical systems and describing chaotic systems. Classic text by three of the world's most prominent mathematicians Continues the tradition of expository excellenceContains updated material and expanded applications for use in applied studies

We consider a curve of Fredholm pairs of Lagrangian subspaces in a fixed Banach space with continuously varying As an application, we consider curves of elliptic operators which have varying principal symbol, varying maximal domain and are not necessarily of Dirac type. For this class of operator curves, we derive a desuspension spectral flow formula for varying well-posed boundary conditions on manifolds with boundary and obtain the splitting formula of the spectral flow on partitioned manifolds.

The close relation between spatial kinematics and line geometry has been proven to be fruitful in surface detection and reconstruction. However, methods based on this approach are limited to simple geometric shapes that can be formulated as a linear subspace of line or line element space. The core of this approach is a principal component formulation to find a best-fit approximant to a possibly noisy or impartial surface given as an unordered set of points or point cloud. We expand on this by introducing the Gaussian process latent variable model, a probabilistic non-linear non-parametric dimensionality reduction approach following the Bayesian paradigm. This allows us to find structure in a lower dimensional latent space for the surfaces of interest. We show how this can be applied in surface approximation and unsupervised segmentation to the surfaces mentioned above and demonstrate its benefits on surfaces that deviate from these. Experiments are conducted on synthetic and real-world objects.

Embossing is a functional and strategic process for creating high-quality multi-sensory tissue-paper products. Embossing modifies the sheet surface by generating hill and/or valley designs, changing the third-dimension z with a compressive die. This research work specifically concerns the impact study of the engraving finishing geometry on the final properties of tissue paper. This work led us to conclude that, even though the sheets individually present a higher hand-feel (HF) value for the straight finishing geometry, the highest softness was obtained in the two-ply prototype for the round finishing geometry. Moreover, this study confirmed that the HF value reduces with the increase of the bulk, being more accentuated for the micropattern. Relevant differences could not be seen in the spreading kinetics of the liquid droplets over time. Thus, the finishing geometry of the 3D plates did not impact the absorption kinetics on these samples. The finite element model allows us to understand the effect of the plate pattern and its finishing geometry on the paper, and the simulation results were in accordance with the experimental results, showing the same trend where patterns with a round finishing geometry marked the tissue-paper sheet more than patterns with a straight finishing did.

Introducción al Álgebra Lineal es un material de apoyo y referencia dirigido a los profesores y estudiantes del curso Álgebra Lineal, en el que se desarrolla el enfoque didáctico para el estudio, la enseñanza y el aprendizaje de esta área. El contenido está dividido en seis capítulos, en los cuales abarca temas como matrices, sistemas de ecuaciones lineales, determinantes, álgebra vectorial, espacios vectoriales, transformaciones y valores y vectores propios.El libro tiene como objetivo principal mejorar los recursos disponibles para los profesores y facilitar el aprendizaje de los estudiantes en Álgebra Lineal. Además, se enfoca en promover un método didáctico que va más allá de la transferencia de información, fomentando el análisis de problemas, la organización de secuencias de aprendizaje, la resolución de problemas y la evaluación del proceso educativo.Cada capítulo comienza con una sección introductoria y objetivos de estudio, seguido de varias secciones específicas que cubren temas como coordenadas cartesianas, vectores, rectas y planos, acompañados de situaciones problema para concretar los conceptos. Por lo tanto, el libro se destina a ser utilizado como texto guía o de consulta en cursos de Álgebra Lineal en programas de ingeniería, tecnología, matemáticas, así como en licenciaturas en matemáticas y física en universidades.

It is generally accepted that visual illusions affect line bisection in the predicted direction. However, it has been reported an illusionary bias which seems questioning such general view. In a previous study, participants bisected lines flanked at both ends by two pairs of arrows, pointing in the same direction. The medialmost vertices of one pair converged on the line (converging arrows), whereas those of the other pair did not (non-converging arrows). Participants bisected lines toward the base of the arrows, i.e., toward the wider end of the stimulus and in the direction opposite to that predicted by the Baldwin illusion. However, the bisection bias was also directed away from the location of the converging arrows. We investigated what is the main factor affecting line bisection: arrows orientation, as previously suggested, or interference effects related to the location of converging arrows. In experiment 1, participants bisected lines flanked by converging versus non-converging arrows. Results confirmed the presence of a bisection bias directed not only toward the base of the converging arrows but also away from their location. In experiment 2, the arrows were located more internally, so that their medialmost vertices always converged on the line. Results showed that the bisection bias was directed away from the location of the arrows regardless of their orientation. It is suggested that the previously reported bisection bias did not depend on arrows orientation, but rather on interference effects related to converging arrows position. The theoretical implications of the results are discussed.

Autonomous unmanned air vehicles (UAVs) are critical to current and future military, civil, and commercial operations. Despite their importance, no previous textbook has accessibly introduced UAVs to students in the engineering, computer, and science disciplines--until now. Small Unmanned Aircraft provides a concise but comprehensive description of the key concepts and technologies underlying the dynamics, control, and guidance of fixed-wing unmanned aircraft, and enables all students with an introductory-level background in controls or robotics to enter this exciting and important area. The authors explore the essential underlying physics and sensors of UAV problems, including low-level autopilot for stability and higher-level autopilot functions of path planning. The textbook leads the student from rigid-body dynamics through aerodynamics, stability augmentation, and state estimation using onboard sensors, to maneuvering through obstacles. To facilitate understanding, the authors have replaced traditional homework assignments with a simulation project using the MATLAB/Simulink environment. Students begin by modeling rigid-body dynamics, then add aerodynamics and sensor models. They develop low-level autopilot code, extended Kalman filters for state estimation, path-following routines, and high-level path-planning algorithms. The final chapter of the book focuses on UAV guidance using machine vision. Designed for advanced undergraduate or graduate students in engineering or the sciences, this book offers a bridge to the aerodynamics and control of UAV flight.

Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than 200 exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers. Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics. The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to 600 references from books and journals from a wide variety of disciplines.