169 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
Geometric Algebra for Optimal Control with Applications in Manipulation Tasks
Many problems in robotics are fundamentally problems of geometry, which lead
to an increased research effort in geometric methods for robotics in recent
years. The results were algorithms using the various frameworks of screw
theory, Lie algebra and dual quaternions. A unification and generalization of
these popular formalisms can be found in geometric algebra. The aim of this
paper is to showcase the capabilities of geometric algebra when applied to
robot manipulation tasks. In particular the modelling of cost functions for
optimal control can be done uniformly across different geometric primitives
leading to a low symbolic complexity of the resulting expressions and a
geometric intuitiveness. We demonstrate the usefulness, simplicity and
computational efficiency of geometric algebra in several experiments using a
Franka Emika robot. The presented algorithms were implemented in c++20 and
resulted in the publicly available library \textit{gafro}. The benchmark shows
faster computation of the kinematics than state-of-the-art robotics libraries.Comment: 16 pages, 13 figures
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
Robot Object Manipulation Using Stereoscopic Vision and Conformal Geometric Algebra
This paper uses geometric algebra to formulate, in a single framework, the kinematics of a three finger robotic hand, a binocular robotic head, and the interactions between 3D objects, all of which are seen in stereo images. The main objective is the formulation of a kinematic control law to close the loop between perception and actions, which allows to perform a smooth visually guided object manipulation
Robot object manipulation using stereoscopic vision and conformal geometric algebra
Abstract. This paper uses geometric algebra to formulate, in a single framework, the kinematics of a three finger robotic hand, a binocular robotic head, and the interactions between 3D objects, all of which are seen in stereo images. The main objective is the formulation of a kinematic control law to close the loop between perception and actions, which allows to perform a smooth visually guided object manipulation
Extending the Cooperative Dual-Task Space in Conformal Geometric Algebra
In this work, we are presenting an extension of the cooperative dual-task
space (CDTS) in conformal geometric algebra. The CDTS was first defined using
dual quaternion algebra and is a well established framework for the simplified
definition of tasks using two manipulators. By integrating conformal geometric
algebra, we aim to further enhance the geometric expressiveness and thus
simplify the modeling of various tasks. We show this formulation by first
presenting the CDTS and then its extension that is based around a cooperative
pointpair. This extension keeps all the benefits of the original formulation
that is based on dual quaternions, but adds more tools for geometric modeling
of the dual-arm tasks. We also present how this CGA-CDTS can be seamlessly
integrated with an optimal control framework in geometric algebra that was
derived in previous work. In the experiments, we demonstrate how to model
different objectives and constraints using the CGA-CDTS. Using a setup of two
Franka Emika robots we then show the effectiveness of our approach using model
predictive control in real world experiments
Solution And Visualization 3D Plane Inverse Kinematics Method
The hyper-redundant type of robot is a type of robot that in carrying out its duties in the field of kinematics its degrees of freedom exceed the required minimum degrees. The advantage will be increased capability in operation and performance, if the degrees of freedom are excessive, even in unorganized and complex systems and environments. Algebraic approach method in inverse kinematics algorithm analysis can use; analytic algebra, jacobian basis, analytic KI, exponential multiplication, grobner, and conformal geometry. Iterative approach method in inverse kinematics algorithm analysis can use; genetic algorithm, fuzzy logic, ANFIS, and evolutionary algorithm. The geometric approach method in the inverse kinematics algorithm analysis can use; capital method. The purpose of this study is to analyze a virtual 2 arm robot, which will use axis manipulation in three dimensions using an inverse kinematics solution, using a geometric approach. How to step along on the z axis by rotating and using the reverse kinematics solution to the desired location. The visualization results will be repeated so as to ensure the effectiveness of the algorithm. As for this algorithm will provide a single solution, and this algorithm will prevent and reduce singularities if the link is lower
Research on dynamic performance and motion control of robot manipulator
Amongst the robotics and autonomous systems, robot manipulators have proven themselves to be of increasing importance and are widely adopted to substitute for human in repetitive and/or hazardous tasks. In this paper, the purpose is to research on dynamic performance and motion control of robot manipulator for the more precise, crucial and critical tasks in industry. Firstly, the forward and inverse kinematics was accurately described by obtaining the link transformation matrices from each joint in robot manipulator. To find admissible solutions along the path, the workspace of the manipulator was determined by joint limit condition and validated by actual measurement. And then, the dynamic performance of robot manipulator is researched by using the forming flexible multi-body system. Furthermore, the frequency response curves are obtained by exciting vibration simulation based on vibration model, which the predicted method was validated by comparing simulation and experimental results. Finally, the control system architecture was given and the grasping process was conducted by gripper based on motion trajectory control in the workspace
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