Julio Zamora-Esquivel

Conformal Geometric Algebra for Robotic Vision

In this paper the authors introduce the conformal geometric algebra in the field of visually guided robotics. This mathematical system keeps our intuitions and insight of the geometry of the problem at hand and it helps us to reduce considerably the computational burden of the problems.As opposite to the standard projective geometry, in conformal geometric algebra we can deal simultaneously with incidence algebra operations (meet and join) and conformal transformations represented effectively using spinors. In this regard, this framework appears promising for dealing with kinematics, dynamics and projective geometry problems without the need to resort to different mathematical systems (as most current approaches do). This paper presents real tasks of perception and action, treated in a very elegant and efficient way: body–eye calibration, 3D reconstruction and robot navigation, the computation of 3D kinematics of a robot arm in terms of spheres, visually guided 3D object grasping making use of the directed distance and intersections of lines, planes and spheres both involving conformal transformations. We strongly believe that the framework of conformal geometric algebra can be, in general, of great advantage for applications using stereo vision, range data, laser, omnidirectional and odometry based systems.

Kinematics and diferential kinematics of binocular robot heads

This paper presents an analysis of the kinematics of a binocular head, and a new formulation of its differential kinematics using the conformal geometric algebra framework. The experimental part includes the smooth visual tracking of 3D objects

Differential and inverse kinematics of robot devices using conformal geometric algebra

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.

Parallel forward Dynamics: A geometric approach

The authors present a new algorithm to compute the forward Dynamics of n degrees of freedom serial kinematic chains, which is faster than the classical approaches. This algorithm was created rewriting the Lagrange equation in terms of lines and points in the framework of conformal geometric algebra, which allows having a new equation to compute the dynamics with less number of products. This algorithm not only performs less computations but it also takes the advantages of the newest multi core architectures by computing the dynamics in parallel.

KINEMATICS AND GRASPING USING CONFORMAL GEOMETRIC ALGEBRA

In this paper we introduce the conformal geometric algebra in the field of robot grasping. It help us to tackle problems of object modelling, hand kinematics and vision system using a unifying geometric language. We present an grasp algorithm using velocity control.

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.

Visually Guided Robotics Using Conformal Geometric Computing

1. Abstract Classical Geometry, as conceived by Euclid, was a plataform from which Mathematics started to build its actual form. However, since the XIX century, it was a language that was not evolving as the same pase as the others branches of Physics and Mathematics. In this way, analytic, non-Euclidean and projective geometries, matrix theory, vector calculus, complex numbers, rigid and conformal transformations, ordinary and partial differential equations, to name some, are different mathematical tools which are used nowadays to model and solve almost any problem in robotic vision, but the presence of the classical geometric theory in such solutions is only implicit. However, over the last four decades a new mathematical framework has been developed as a new lenguage where not only the classical geometry is included, but where many of these mathematical systems will be embedded too. Instead of using different notation and theory for each of those systems, we will simplify the whole study introducing the CGA, a unique mathematical framework where all those systems are embedded, gaining in principle clarity and simplicity. Moreover, incidence algebra operations as union and intersection of subspaces, are also included in this system through the meet and join operations. In this regard, CGA appears promising for dealing with kinematics, dynamics and projective geometric problems in one and only one mathematical framework. In this chapter we propose simulated and real tasks for perception-action systems, treated in a unify way and using only operations and geometrical entities of this algebra. We propose applications to follow geometric primitives or ruled sufaces with an arm’s robot for shape understanding and object manipulation, as well as applications in visual grasping. But we believe that the use of CGA can be of great advantage in visually guided robotics using stereo vision, range data, laser, omnidirectional or odometry based systems.

Geometric techniques for visually guided grasping

In this paper the authors propose geometric techniques to deal with the problem of grasping of the objects relaying on their mathematical models. For that we use the geometric algebra framework to formulate the kinematics of a three linger robotic hand. Our main objective is by formulating a kinematic control law to close the loop between perception and actions. This allows us to perform a smooth visually guided object grasping.

Detection and classification of intra boby acoustic wave signals for wearable applications

Wearable Devices (WD) are systems designed to do a specific task, these system are embedded in daily life personal objects. Usual transducers in wearable devices involve accelerometers gyroscopes, cameras etc. In WD is required to design efficiently in terms of power. Therefore, a new trend incorporates acoustic transducer that does not need a power supply to sense. They are very cheap and easy to replace. In WD, these transducers detect acoustic wave signals traveling in human tissue and bones. The processing of these kind of signals is related with many areas such as medical, gesture recognition, haptics etc. The proposed system uses a set of three sensors to capture Intra Body Acoustic Wave Signals (IBAWS) from the wrist of the right hand. A signal database is constructed using 18 users repeating 30 times each one of five gestures proposed. The patterns are composed by six features per sensor, including Spectral Flux, Spectral Centroid and Short Time Energy. Complete proposed patterns contains 18 features. Classifiers results shown 75.37% of accuracy using Bayesian classifier with Gaussian Kernel, 80% of accuracy using Knn classifier, and 85.56% of accuracy with Artificial Neural Networks. All this for a set of 18 users, supporting the hypothesis that classify IBAWS is independent from the user and could be generalized to use them in WD.

Humanoid egomotion using planes

When dealing with humanoid vision, it is very important to take into account the velocity and complexity of the algorithms. This paper presents an efficient combination of basic algorithm with quadratic complexity. Our real time procedure gives an excellent representation of the 3D scene. This 3D reconstruction allows the humanoid to maneuver, as well as the robotic manipulation of objects.