In this work, we introduce a generalization methodology for the automatic selection of the activation functions inside a neural network, taking advantage of concepts defined in fractional calculus. This methodology enables the neural network to search and optimize its own activation functions during the training process, by defining the fractional order of the derivative of a given primitive activation function. This fractional order is tuned as an additional training hyper-parameter a for intrafamily selection and b for cross family selection. By following this approach, the neurons inside the network can adjust their activation functions, e.g. from MLP to RBF networks, to best fit the input data, and reduce the output error. The experimental results obtained show the benefits of using this technique implemented on a ResNet18 topology, by outperforming the accuracy of a ResNet100 trained with CIFAR10 and Improving 1% ImageNet reported in the literature.

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.

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.

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

This paper presents an approach to deal with standard tasks of computer animations and robotics based on Conformal Geometric Algebra. We will show that this algebra is very well suitable for applications of all kind of robot manipulator kinematics, representation and visualization and object robot manipulation. Due to its geometric intuitiveness and simplicity Conformal Geometric Algebra appears to be a promising mathematical tool for building intelligent man-machine interfaces.

In this paper the authors introduce the conformal geometric algebra in the field of visually guided robotics. As opposite to the standard projective geometry, we can deal simultaneously with incidence algebra operations and conformal transformations. As a result this framework appears promising for dealing with kinematics, dynamics and projective geometry problems without the need to abandon the mathematical system (as current approaches). Using this framework the authors compute the inverse kinematics of a robot arm and a pan-tilt unit and solve a problem of visually guided grasping.