Nancy Arana-Daniel

Clifford Support Vector Machines for Classification, Regression, and Recurrence

This paper introduces the Clifford support vector machines (CSVM) as a generalization of the real and complex-valued support vector machines using the Clifford geometric algebra. In this framework, we handle the design of kernels involving the Clifford or geometric product. In this approach, one redefines the optimization variables as multivectors. This allows us to have a multivector as output. Therefore, we can represent multiple classes according to the dimension of the geometric algebra in which we work. We show that one can apply CSVM for classification and regression and also to build a recurrent CSVM. The CSVM is an attractive approach for the multiple input multiple output processing of high-dimensional geometric entities. We carried out comparisons between CSVM and the current approaches to solve multiclass classification and regression. We also study the performance of the recurrent CSVM with experiments involving time series. The authors believe that this paper can be of great use for researchers and practitioners interested in multiclass hypercomplex computing, particularly for applications in complex and quaternion signal and image processing, satellite control, neurocomputation, pattern recognition, computer vision, augmented virtual reality, robotics, and humanoids.

Geometric preprocessing, geometric feedforward neural networks and Clifford support vector machines for visual learning

This paper shows the design and use of feed-forward neural networks and the support vector machines (SVM) in the coordinate-free mathematical system of the Clifford geometric algebra. We compare the McCulloch-Pitts neuron and the geometric neuron. An interesting case of the geometric neuron is the conformal neuron which can be used for RBF networks and SVM. The paper presents the generalization of the real- and complex-valued multilayer perceptron (MLP) to the Clifford valued multilayer perceptron. The paper studies also the multivector support vector machines (MSVM) which are SVMs for processing multivectors. For that we design kernels involving Clifford products. The resultant kernel resembles a sort of polynomial kernel using a multivector representation. In the context of SVMs an important contribution of the paper is the generalization of the real- and complex-valued SVM classifiers over the hyper-complex numbers. This Clifford valued SVM accepts multiple multivector inputs and it is a multi-class classifier. For the preprocessing the authors introduce a promising geometric method utilizing Clifford moments. This method is applied together with geometric MLPs for tasks of 2D pattern recognition. The experimental part shows applications of SVM using the conformal neuron and Clifford kernels. We include challenging applications of the Clifford SVM classifier for nonlinear separable problems. The authors believe that the use of the MLPs and SVMs in the geometric algebra framework expands their sphere of applicability for multivector learning in graded spaces.

Stability of nonlinear teleoperators using PD controllers without velocity measurements

This paper presents two Proportional-Derivative (PD) like controllers for nonlinear bilateral teleoperation systems. Compared to previous controllers of this kind, these schemes do not make use of velocity measurements. Under the assumptions that the human operator and the environment define passive maps from velocity to force, both controllers can ensure boundedness of velocities and position error. Moreover, in the case that the human and environment forces are zero, the controllers ensure velocity and position synchronization. Furthermore, the paper also presents a generalization to the case of teleoperation of networks of multiple robots. Simulations and real experiments, comparing the performance on free motion and interacting with a stiff wall, support the performance of the reported schemes. The experiments have been performed using two 3-degree-of-freedom nonlinear manipulators.

Smooth global and local path planning for mobile robot using particle swarm optimization, radial basis functions, splines and Bézier curves

An approach to plan smooth paths for mobile robots using a Radial Basis Function (RBF) neural network trained with Particle Swarm Optimization (PSO) was presented in [1]. Taking the previous approach as an starting point, in this paper it is shown that it is possible to construct a smooth simple global path and then modify this path locally using PSO-RBF, Ferguson splines or Bézier curves trained with PSO, in order to describe more complex paths in partially known environments. Experimental results show that our approach is fast and effective to deal with complex environments.

Bacterial foraging optimization algorithm to improve a discrete-time neural second order sliding mode controller

This paper deals with design parameter selection of a discrete-time neural second order sliding mode controller for unknown nonlinear systems, based on bacterial foraging optimization. First, a neural identifier is proposed in order to obtain a mathematical model for the unknown discrete-time nonlinear systems, then a novel second order sliding mode controller is proposed. Finally, both, the neural identifier and the controller are optimized using bacterial foraging algorithm. In order to illustrate the applicability of the proposed scheme, simulation results are included for a Van der Pol oscillator.

Discrete super twisting control algorithm for the nonholonomic mobile robots tracking problem

The tracking control of nonholonomic mobile robots has been an important class of control problems. This paper deals with the design and real-time implementation of a discrete-time super twisting control algorithm for nonholonomic wheeled mobile robots, without the previous knowledged of the plant model or its parameters. In order to show the effectiveness of the proposed controller experimental results are included for a nonholonomic mobile robot QBot®3.

Neural identifier for unknown discrete-time nonlinear delayed systems

This work proposes a discrete-time nonlinear neural identifier based on a recurrent high-order neural network trained with an extended Kalman filter-based algorithm for discrete-time deterministic multiple-input multiple-output systems with unknown dynamics and time-delay. To prove the semi-globally uniformly ultimately boundedness of the proposed neural identifier, the stability analysis based on the Lyapunov approach is included. Applicability of the proposed identifier is shown via simulation and experimental results, all of them performed under the presence of unknown external and internal disturbances as well as unknown time-delays.

Neural-PSO second order sliding mode controller for unknown discrete-time nonlinear systems

This paper deals with adaptive tracking for unknown discrete-time MIMO nonlinear systems in presence of disturbances. A Particle Swarm Optimization (PSO) is used to improve a discrete-time neural second order sliding mode controller for unknown discrete-time nonlinear systems. In order to show the applicability of the proposed scheme, simulation results are included for a Van der Pol oscillator.

Real-time neural identification and inverse optimal control for a tracked robot

This work presents the implementation in real-time of a neural identifier based on a recurrent high-order neural network which is trained with an extended Kalman filter–based training algorithm and an inverse optimal control applied to a tracked robot. The recurrent high-order neural network identifier is developed without the knowledge of the plant model or its parameters; on the other hand, the inverse optimal control is designed for tracking velocity references. This article includes simulation and real-time results, both using MATLAB®, and also the experimental tests use a modified HD2® Treaded ATR Tank Robot Platform with wireless communication.

Image Classification Using PSO-SVM and an RGB-D Sensor

Image classification is a process that depends on the descriptor used to represent an object. To create such descriptors we use object models with rich information of the distribution of points. The object model stage is improved with an optimization process by spreading the point that conforms the mesh. In this paper, particle swarm optimization (PSO) is used to improve the model generation, while for the classification problem a support vector machine (SVM) is used. In order to measure the performance of the proposed method a group of objects from a public RGB-D object data set has been used. Experimental results show that our approach improves the distribution on the feature space of the model, which allows to reduce the number of support vectors obtained in the training process.