An Optimized Architecture for CGA Operations and Its Application to a Simulated Robotic Arm

Conformal geometric algebra (CGA) is a new geometric computation tool that is attracting growing attention in many research fields, such as computer graphics, robotics, and computer vision. Regarding the robotic applications, new approaches based on CGA have been proposed to efficiently solve problems as the inverse kinematics and grasping of a robotic arm. The hardware acceleration of CGA operations is required to meet real-time performance requirements in embedded robotic platforms. In this paper, we present a novel embedded coprocessor for accelerating CGA operations in robotic tasks. Two robotic algorithms, namely, inverse kinematics and grasping of a human-arm-like kinematics chain, are used to prove the effectiveness of the proposed approach. The coprocessor natively supports the entire set of CGA operations including both basic operations (products, sums/differences, and unary operations) and complex operations as rigid body motion operations (reflections, rotations, translations, and dilations). The coprocessor prototype is implemented on the Xilinx ML510 development platform as a complete system-on-chip (SoC), integrating both a PowerPC processing core and a CGA coprocessing core on the same Xilinx Virtex-5 FPGA chip. Experimental results show speedups of 78x and 246x for inverse kinematics and grasping algorithms, respectively, with respect to the execution on the PowerPC processor

Compiling Geometric Algebra Computations into Reconfigurable Hardware Accelerators

Geometric Algebra (GA), a generalization of quaternions and complex numbers, is a very powerful framework for intuitively expressing and manipulating the complex geometric relationships common to engineering problems. However, actual processing of GA expressions is very compute intensive, and acceleration is generally required for practical use. GPUs and FPGAs offer such acceleration, while requiring only low-power per operation. In this paper, we present key components of a proof-of-concept compile flow combining symbolic and hardware optimization techniques to automatically generate hardware accelerators from the abstract GA descriptions that are suitable for high-performance embedded computing

Reductions in computational complexity using Clifford algebras

International audienceA number of combinatorial problems are treated using properties of abelian nilpotent- and idempotent-generated subalgebras of Clifford algebras. For example, the problem of deciding whether or not a graph contains a Hamiltonian cycle is known to be NP-complete. By considering entries of $\Lambda^k$, where $\Lambda$ is an appropriate nilpotent adjacency matrix, the $k$-cycles in any finite graph are recovered. Within the algebra context (i.e., considering the number of multiplications performed within the algebra), these problems are reduced to matrix multiplication, which is in complexity class $P$. The Hamiltonian cycle problem is one of many problems moved from classes NP-complete and $\sharp P$-complete to class $P$ in this context. Other problems considered include the set covering problem, counting the edge-disjoint cycle decompositions of a finite graph, computing the permanent of an arbitrary matrix, computing the girth and circumference of a graph, and finding the longest path in a graph

\u201cA Sliced Coprocessor for Native Clifford Algebra Operations\u201d

Computer graphics applications require efficient tools to model geometric objects. The traditional approach based on compute-intensive matrix calculations is error-prone due to a lack of integration between geometric reasoning and matrix-based algorithms. Clifford algebra offers a solution to these issues since it permits specification of geometry at a coordinate-free level. The best way to exploit the symbolic computing power of geometric (Clifford) algebra is supporting its data types and operators directly in hardware. This paper outlines the architecture of S-CliffoSor (Sliced Clifford coprocessor), a parallelizable embedded coprocessor that executes native Clifford algebra operations. S-CliffoSor is a sliced coprocessor that can be replicated for parallel execution of concurrent Clifford operations. A single slice has been designed, implemented and tested on the Celoxica Inc. RC1000 board. The experimental results show the potential to achieve a 3times speedup for Clifford sums and 4times speedup for Clifford products compared to against the analogous operations in the software library generator GAIGE

Understanding Quantum Technologies 2022

Understanding Quantum Technologies 2022 is a creative-commons ebook that provides a unique 360 degrees overview of quantum technologies from science and technology to geopolitical and societal issues. It covers quantum physics history, quantum physics 101, gate-based quantum computing, quantum computing engineering (including quantum error corrections and quantum computing energetics), quantum computing hardware (all qubit types, including quantum annealing and quantum simulation paradigms, history, science, research, implementation and vendors), quantum enabling technologies (cryogenics, control electronics, photonics, components fabs, raw materials), quantum computing algorithms, software development tools and use cases, unconventional computing (potential alternatives to quantum and classical computing), quantum telecommunications and cryptography, quantum sensing, quantum technologies around the world, quantum technologies societal impact and even quantum fake sciences. The main audience are computer science engineers, developers and IT specialists as well as quantum scientists and students who want to acquire a global view of how quantum technologies work, and particularly quantum computing. This version is an extensive update to the 2021 edition published in October 2021.Comment: 1132 pages, 920 figures, Letter forma

NASA Tech Briefs, July 1993

Topics include: Data Acquisition and Analysis: Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Computer Programs; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences; Life Sciences

Spinoff, 1994

This publication is intended to foster the aim of the NASA Technology Transfer Program by heightening awareness of the NASA technology available for reapplication and its potential for public benefit. The publication is organized in three main sections. The first section, Aerospace Aims, is an illustrated summary of NASA's major aeronautical and space programs, their goals and directions, their contributions to American scientific and technological growth, and their potential for practical benefit. The second section, Technology Twice Used, is a representative selection of new products and processes adapted from technology originally developed for NASA mainline programs, underlying the broad diversity of spinoff applications and the social/economic benefits they provide. The third section, Technology Transfer, is a description of the mechanisms employed to encourage and facilitate practical application of new technologies developed in the course of NASA activities

1990-1995 Brock Campus News

A compilation of the administration newspaper, Brock Campus News, for the years 1990 through 1995. It had previously been titled The Blue Badger

XX Workshop de Investigadores en Ciencias de la Computación - WICC 2018 : Libro de actas

Actas del XX Workshop de Investigadores en Ciencias de la Computación (WICC 2018), realizado en Facultad de Ciencias Exactas y Naturales y Agrimensura de la Universidad Nacional del Nordeste, los dìas 26 y 27 de abril de 2018.Red de Universidades con Carreras en Informática (RedUNCI