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

Implementation and evaluation of medical imaging techniques based on conformal geometric algebra

Medical imaging tasks, such as segmentation, 3D modeling, and registration of medical images, involve complex geometric problems, usually solved by standard linear algebra and matrix calculations. In the last few decades, conformal geometric algebra (CGA) has emerged as a new approach to geometric computing that offers a simple and efficient representation of geometric objects and transformations. However, the practical use of CGA-based methods for big data image processing in medical imaging requires fast and efficient implementations of CGA operations to meet both real-time processing constraints and accuracy requirements. The purpose of this study is to present a novel implementation of CGA-based medical imaging techniques that makes them effective and practically usable. The paper exploits a new simplified formulation of CGA operators that allows significantly reduced execution times while maintaining the needed result precision. We have exploited this novel CGA formulation to re-design a suite of medical imaging automatic methods, including image segmentation, 3D reconstruction and registration. Experimental tests show that the re-formulated CGA-based methods lead to both higher precision results and reduced computation times, which makes them suitable for big data image processing applications. The segmentation algorithm provides the Dice index, sensitivity and specificity values of 98.14%, 98.05% and 97.73%, respectively, while the order of magnitude of the errors measured for the registration methods is 10-5

Design and implementation of an embedded coprocessor with native support for 5D, quadruple-based Clifford algebra

Geometric or Clifford algebra (CA) is a powerful mathematical tool that offers a natural and intuitive way to model geometric facts in a number of research fields, such as robotics, machine vision and computer graphics. Operating in higher-dimensional spaces, its practical use is hindered, however, by a significant computational cost, only partially addressed by dedicated software libraries and hardware/software codesigns. For low dimensional algebras, several dedicated hardware accelerators and coprocessing architectures have been already proposed in literature. This paper introduces the architecture of CliffordALU5, an embedded coprocessing core conceived for native execution of up to five-dimensional (5D) CA operations. CliffordALU5 exploits a novel, hardware-oriented representation of the algebra elements that allows for faster execution of Clifford operations. In this paper, a prototype implementation of a complete SoC based on CliffordALU5 is presented. This prototype integrates an embedded processing soft-core based on the PowerPC 405 and a CliffordALU5 coprocessor on a Xilinx XUPV2P FPGA board. Test results show a 5 7 average speedup for 4D Clifford products and a 4 7 average speedup for 5D Clifford products against the same operations in Gaigen 2, a CA software library generator running on the general-purpose PowerPC processor. The paper also presents an execution analysis of three different applications in three diverse domains, namely inverse kinematics of a robot, optical motion capture, and raytracing, showing an average speedup between 3 7 to 4 7 with respect to the baseline Gaigen 2 implementation. Lastly, a multi-core approach to higher dimensional CA based on CliffordALU5 is discussed

Studies related to the process of program development

The submitted work consists of a collection of publications arising from research carried out at Rhodes University (1970-1980) and at Heriot-Watt University (1980-1992). The theme of this research is the process of program development, i.e. the process of creating a computer program to solve some particular problem. The papers presented cover a number of different topics which relate to this process, viz. (a) Programming methodology programming. (b) Properties of programming languages. aspects of structured. (c) Formal specification of programming languages. (d) Compiler techniques. (e) Declarative programming languages. (f) Program development aids. (g) Automatic program generation. (h) Databases. (i) Algorithms and applications