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.

The solution of the inverse kinematics of mobile manipulators is a fundamental capability to solve problems such as path planning, visual-guided motion, object grasping, and so on. In this article, we present a metaheuristic approach to solve the inverse kinematic problem of mobile manipulators. In this approach, we represent the robot kinematics using the Denavit–Hartenberg model. The algorithm is able to solve the inverse kinematic problem taking into account the mobile platform. The proposed approach is able to avoid singularities configurations, since it does not require the inversion of a Jacobian matrix. Those are two of the main drawbacks to solve inverse kinematics through traditional approaches. Applicability of the proposed approach is illustrated using simulation results as well as experimental ones using an omnidirectional mobile manipulator.

In this paper, an adaptive single neuron Proportional–Integral–Derivative (PID) controller based on the extended Kalman filter (EKF) training algorithm is proposed. The use of EKF training allows online training with faster learning and convergence speeds than backpropagation training method. Moreover, the propose adaptive PID approach includes a back-calculation anti-windup scheme to deal with windup effects, which is a common problem in PID controllers. The performance of the proposed approach is shown by presenting both simulation and experimental tests, giving results that are comparable to similar and more complex implementations. Tests are performed for a four wheeled omnidirectional mobile robot. Tests show the superiority of the proposed adaptive PID controller over the conventional PID and other adaptive neural PID approaches. Experimental tests are performed on a KUKA^® Youbot^® omnidirectional platform.

In recent years, unmanned aerial vehicles (UAVs) have gained significant attention. However, we face two major drawbacks when working with UAVs: high nonlinearities and unknown position in 3D space since it is not provided with on-board sensors that can measure its position with respect to a global coordinate system. In this paper, we present a real-time implementation of a servo control, integrating vision sensors, with a neural proportional integral derivative (PID), in order to develop an hexarotor image based visual servo control (IBVS) that knows the position of the robot by using a velocity vector as a reference to control the hexarotor position. This integration requires a tight coordination between control algorithms, models of the system to be controlled, sensors, hardware and software platforms and well-defined interfaces, to allow the real-time implementation, as well as the design of different processing stages with their respective communication architecture. All of these issues and others provoke the idea that real-time implementations can be considered as a difficult task. For the purpose of showing the effectiveness of the sensor integration and control algorithm to address these issues on a high nonlinear system with noisy sensors as cameras, experiments were performed on the Asctec Firefly on-board computer, including both simulation and experimenta results.