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

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 Mode Control

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 mode. The performance of the proposed control schemes are illustrated through simulation.ITESO, A.C

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