872 research outputs found
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
Visual Servoing and Robust Object Manipulation Using Symmetries and Conformal Geometric Algebra
Object tracking and manipulation is an important process for many applications in robotics and computer vision. A novel 3D pose estimation of objects using reflectionally symmetry formulated in Conformal Geometric Algebra (CGA) is proposed in this work. The synthesis of the kinematics model for robots and a sliding mode controller using the CGA approach is described. Real time implementation results are presented for the pose estimation of object using a stereo vision system.ITESO, A.C.CINVESTA
Robust Pose Control of Robot Manipulators Using Conformal Geometric Algebra
A controller, based on sliding mode control, is proposed for the n-link robotic manipulator pose tracking problem. The point pair (a geometric entity expressed in geometric algebra) is used to represent position and orientation of the end-effector of a manipulator. This permits us to express the direct and differential kinematics of the endeffector of the manipulator in a simple and compact way. For the control, a sliding mode controller is designed with the following properties: robustness against perturbations and parameter variations, finite time convergence, and easy implementation. Finally, the application, of the proposed controller in a 6 DOF robotic manipulator is presented via simulation.Consejo Nacional de Ciencia y Tecnologí
Robust Tracking of Bio-Inspired References for a Biped Robot Using Geometric Algebra and Sliding Modes
Controlling walking biped robots is a challenging
problem due to its complex and uncertain dynamics. In order
to tackle this, we propose a sliding mode controller based on a
dynamic model which was obtained using the conformal
geometric algebra approach (CGA). The CGA framework
permits us to use lines, points, and other geometric entities, to
obtain the Lagrange equations of the system. The references
for the joints of the robot were bio-inspired in the kinematics of
a walking human body. The first and second derivatives of the
reference signal were obtained through an exact robust
differentiator based on high order sliding modes. The
performance of the proposed control scheme is illustrated
through simulation.CINVESTA
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