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Stochastic Models, Information Theory, and Lie Groups, Volume 1
This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises and motivating examples make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.
Harmonic Analysis for Engineers and Applied Scientists
Although the Fourier transform is among engineering's most widely used mathematical tools, few engineers realize that the extension of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. This self-contained approach, geared toward readers with a standard background in engineering mathematics, explores the widest possible range of applications to fields such as robotics, mechanics, tomography, sensor calibration, estimation and control, liquid crystal analysis, and conformational statistics of macromolecules. Harmonic analysis is explored in terms of particular Lie groups, and the text deals with only a limited number of proofs, focusing instead on specific applications and fundamental mathematical results. Forming a bridge between pure mathematics and the challenges of modern engineering, this updated and expanded volume offers a concrete, accessible treatment that places the general theory in the context of specific groups.
Engineering Applications of Noncommutative Harmonic Analysis
The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is sti
Stochastic Models, Information Theory, and Lie Groups, Volume 2
This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises, motivating examples, and real-world applications make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.
Essays on Mathematical Robotics
The chapters in this book present an excellent exposition of recent developments in both robotics and nonlinear control centering around "hyper-redundancy", highly oscillatory inputs, optimal control, exterior differential systems, and the use of generic loops. The principal topics covered in the book are: adaptive control for a class of nonlinear systems, event-based motion planning, nonlinear control synthesis and path planning in robotics with special emphasis on nonholonomic and "hyper-redundant" robotic systems, control design and stabilization of driftless affine control systems (of the type arising in the kinematic control of nonholonomic robotic systems), control design methods for Hamiltonian systems and exterior differential systems. The chapter covering exterior differential systems contains a detailed introduction to the use of exterior differential methods, including the Goursat and extended Goursat normal forms and their application to path planning for nonholonomic systems.
Algorithmic Foundations of Robotics VIII
This book contains selected contributions to WAFR, the highly-competitive meeting on the algorithmic foundations of robotics. They address the unique combination of questions that the design and analysis of robot algorithms inspires.
Redundancy in Robot Manipulators and Multi-Robot Systems
The trend in the evolution of robotic systems is that the number of degrees of freedom increases. This is visible both in robot manipulator design and in the shift of focus from single to multi-robot systems. Following the principles of evolution in nature, one may infer that adding degrees of freedom to robot systems design is beneficial. However, since nature did not select snake-like bodies for all creatures, it is reasonable to expect the presence of a certain selection pressure on the number of degrees of freedom. Thus, understanding costs and benefits of multiple degrees of freedom, especially those that create redundancy, is a fundamental problem in the field of robotics. This volume ...
Frontiers
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Modern Signal Processing
A description of the mathematical basis of signal processing, and many areas of application.
Robotics: The Algorithmic Perspective
This volume gathers together cutting-edge research from the Third Workshop on Algorithmic Foundations of Robotics and gives a solid overview of the state of the art in robot algorithms. The papers cover core problems in robotics, such as motion planning, sensor-based planning, manipulation, and assembly planning. They also examine the application o
