1,177 research outputs found
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
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
Computational neural learning formalisms for manipulator inverse kinematics
An efficient, adaptive neural learning paradigm for addressing the inverse kinematics of redundant manipulators is presented. The proposed methodology exploits the infinite local stability of terminal attractors - a new class of mathematical constructs which provide unique information processing capabilities to artificial neural systems. For robotic applications, synaptic elements of such networks can rapidly acquire the kinematic invariances embedded within the presented samples. Subsequently, joint-space configurations, required to follow arbitrary end-effector trajectories, can readily be computed. In a significant departure from prior neuromorphic learning algorithms, this methodology provides mechanisms for incorporating an in-training skew to handle kinematics and environmental constraints
Development of Artificial Intelligent Techniques for Manipulator Position Control
Inspired by works in soft computing this research applies the constituents of soft
computing to act as the "brain" that controls the positioning process of a robot
manipulator's tool. This work combines three methods in artificial intelligence: fuzzy
rules, neural networks, and genetic algorithm to form the soft computing plant
uniquely planned for a six degree-of-freedom serial manipulator. The forward
kinematics of the manipulator is made as the feedforward control plant while the soft
computing plant replaces the inverse kinematics in the feedback loop. Fine
manipulator positioning is first achieved from the learning stage, and later execution
through forward kinematics after the soft computing plant proposes inputs and the
iterations. It is shown experimentally that the technique proposed is capable of
producing results with very low errors. Experiment A for example resulted the
position errors onpx: 0.004%;py: 0.006%; andpz: 0.002%
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
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
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
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