Inverse kinematics of a 3 DOF parallel manipulator: A conformal geometric algebra approach

2016 ◽  
Author(s):  
O. Carbajal-Espinosa ◽  
F. Izar-Bonilla ◽  
M. Diaz-Rodriguez ◽  
E. Bayro-Corrochano
Keyword(s):  
Geometric Algebra ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Conformal Geometric Algebra ◽  
Algebra Approach

Feature preserving multiresolution subdivision and simplification of point clouds: A conformal geometric algebra approach

2017 ◽  
Vol 41 (11) ◽  
pp. 4074-4087 ◽  
Author(s):  
Shuai Yuan ◽  
Shuai Zhu ◽  
Dong-Shuang Li ◽  
Wen Luo ◽  
Zhao-Yuan Yu ◽  
...  
Keyword(s):  
Geometric Algebra ◽  
Point Clouds ◽  
Conformal Geometric Algebra ◽  
Algebra Approach ◽  
Feature Preserving

Differential and inverse kinematics of robot devices using conformal geometric algebra

Robotica ◽  
2006 ◽  
Vol 25 (1) ◽  
pp. 43-61 ◽  
Author(s):  
Eduardo Bayro-Corrochano ◽  
Julio Zamora-Esquivel
Keyword(s):  
Stereo Vision ◽  
Geometric Algebra ◽  
Inverse Kinematics ◽  
Three Dimensional ◽  
Conformal Geometric Algebra ◽  
Robot Arm ◽  
Standard Formulation ◽  
Visually Guided ◽  
Interesting Application ◽  
Differential Control

In this paper, the authors use the conformal geometric algebra in robotics. This paper computes the inverse kinematics of a robot arm and the differential kinematics of a pan–tilt unit using a language of spheres showing how we can simplify the complexity of the computations.This work introduces a new geometric Jacobian in terms of bivectors, which is by far more effective in its representation as the standard Jacobian because its derivation is done in terms of the projections of the involved points onto the line axes. Furthermore, unlike the standard formulation, our Jacobian can be used for any kind of robot joints.In this framework, we deal with various tasks of three-dimensional (3D) object manipulation, which is assisted by stereo-vision. All these computations are carried out using real images captured by a robot binocular head, and the manipulation is done by a five degree of freedom (DOF) robot arm mounted on a mobile robot. In addition to this, we show a very interesting application of the geometric Jacobian for differential control of the binocular head. We strongly believe that the framework of conformal geometric algebra can generally be of great advantage for visually guided robotics.

scholarly journals Evaluating a Semiautonomous Brain-Computer Interface Based on Conformal Geometric Algebra and Artificial Vision

2019 ◽  
Vol 2019 ◽  
pp. 1-19
Author(s):  
Mauricio Adolfo Ramírez-Moreno ◽  
David Gutiérrez
Keyword(s):  
Process Control ◽  
Geometric Algebra ◽  
Inverse Kinematics ◽  
Brain Computer Interface ◽  
Conformal Geometric Algebra ◽  
Artificial Vision ◽  
Computer Interface ◽  
Proof Of Concept ◽  
Goal Selection ◽  
Pick And Place

In this paper, we evaluate a semiautonomous brain-computer interface (BCI) for manipulation tasks. In such a system, the user controls a robotic arm through motor imagery commands. In traditional process-control BCI systems, the user has to provide those commands continuously in order to manipulate the effector of the robot step-by-step, which results in a tiresome process for simple tasks such as pick and replace an item from a surface. Here, we take a semiautonomous approach based on a conformal geometric algebra model that solves the inverse kinematics of the robot on the fly, and then the user only has to decide on the start of the movement and the final position of the effector (goal-selection approach). Under these conditions, we implemented pick-and-place tasks with a disk as an item and two target areas placed on the table at arbitrary positions. An artificial vision (AV) algorithm was used to obtain the positions of the items expressed in the robot frame through images captured with a webcam. Then, the AV algorithm is integrated into the inverse kinematics model to perform the manipulation tasks. As proof-of-concept, different users were trained to control the pick-and-place tasks through the process-control and semiautonomous goal-selection approaches so that the performance of both schemes could be compared. Our results show the superiority in performance of the semiautonomous approach as well as evidence of less mental fatigue with it.

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