Gregory S. Chirikjian - Böcker

First published in 2001. 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 still no place they can turn to for a clear presentation of the background they need to apply the concept to engineering problems.Engineering Applications of Noncommutative Harmonic Analysis brings this powerful tool to the engineering world. Written specifically for engineers and computer scientists, it offers a practical treatment of harmonic analysis in the context of particular Lie groups (rotation and Euclidean motion). It presents only a limited number of proofs, focusing instead on providing a review of the fundamental mathematical results unknown to most engineers and detailed discussions of specific applications.Advances in pure mathematics can lead to very tangible advances in engineering, but only if they are available and accessible to engineers. Engineering Applications of Noncommutative Harmonic Analysis provides the means for adding this valuable and effective technique to the engineer's toolbox.

First published in 2001. 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 still no place they can turn to for a clear presentation of the background they need to apply the concept to engineering problems.Engineering Applications of Noncommutative Harmonic Analysis brings this powerful tool to the engineering world. Written specifically for engineers and computer scientists, it offers a practical treatment of harmonic analysis in the context of particular Lie groups (rotation and Euclidean motion). It presents only a limited number of proofs, focusing instead on providing a review of the fundamental mathematical results unknown to most engineers and detailed discussions of specific applications.Advances in pure mathematics can lead to very tangible advances in engineering, but only if they are available and accessible to engineers. Engineering Applications of Noncommutative Harmonic Analysis provides the means for adding this valuable and effective technique to the engineer's toolbox.

Tools and methods from stochastic processes, information theory, and Lie groups are used in a wide variety of problems in engineering and the physical sciences. Featuring extensive exercises and applications, this two-volume set presents these topics in a uniquely unified setting.

This two-volume set covers stochastic processes, information theory and Lie groups in a unified setting, bridging topics rarely studied together. The emphasis is on using stochastic, geometric, and group-theoretic concepts for modeling physical phenomena.

By the dawn of the new millennium,robotics has undergonea major transformation in scope and dimensions. This expansion has been broughtabout by the maturity of the ?eld and the advances in its related technologies. From a largely dominant - dustrial focus, roboticshas been rapidly expandinginto the challengesof the human world.The new generationofrobotsis expectedto safely anddependablyco-habitat withhumansinhomes,workplaces,andcommunities,providingsupportinservices, entertainment, education, healthcare, manufacturing, and assistance. Beyond its impact on physical robots, the body of knowledge robotics has p- duced is revealing a much wider range of applications reaching across diverse research areas and scienti?c disciplines, such as: biomechanics, haptics, neu- sciences, virtual simulation, animation, surgery, and sensor networks among others. In return, the challenges of the new emerging areas are proving an abundant source of stimulation and insights for the ?eld of robotics. It is indeed at the intersection of disciplines that the most striking advances happen.The goal of the series of Springer Tracts in Advanced Robotics (STAR) is to bring, in a timely fashion, the latest advances and developments in robotics on the basis of their signi?cance and quality. It is our hope that the wider dissemination of research developmentswill stimulate more exchangesand collaborationsamongthe research community and contribute to further advancement of this rapidly growing ?eld. This volume is the outcome of the eight edition of the biennial Workshop Al- rithmic Foundations of Robotics (WAFR). Edited by G. Chirikjian, H. Choset, M.