A Novel Zeroing Neural Network for Solving Time-Varying Quadratic Matrix Equations against Linear Noises

The solving of quadratic matrix equations is a fundamental issue which essentially exists in the optimal control domain. However, noises exerted on the coefficients of quadratic matrix equations may affect the accuracy of the solutions. In order to solve the time-varying quadratic matrix equation problem under linear noise, a new error-processing design formula is proposed, and a resultant novel zeroing neural network model is developed. The new design formula incorporates a second-order error-processing manner, and the double-integration-enhanced zeroing neural network (DIEZNN) model is further proposed for solving time-varying quadratic matrix equations subject to linear noises. Compared with the original zeroing neural network (OZNN) model, finite-time zeroing neural network (FTZNN) model and integration-enhanced zeroing neural network (IEZNN) model, the DIEZNN model shows the superiority of its solution under linear noise; that is, when solving the problem of a time-varying quadratic matrix equation in the environment of linear noise, the residual error of the existing model will maintain a large level due to the influence of linear noise, which will eventually lead to the solution’s failure. The newly proposed DIEZNN model can guarantee a normal solution to the time-varying quadratic matrix equation task no matter how much linear noise there is. In addition, the theoretical analysis proves that the neural state of the DIEZNN model can converge to the theoretical solution even under linear noise. The computer simulation results further substantiate the superiority of the DIEZNN model in solving time-varying quadratic matrix equations under linear noise

A recurrent neural network applied to optimal motion control of mobile robots with physical constraints

Conventional solutions, such as the conventional recurrent neural network (CRNN) and gradient recurrent neural network (GRNN), for the motion control of mobile robots in the unified framework of recurrent neural network (RNN) are difficult to simultaneously consider both criteria optimization and physical constraints. The limitation of the RNN solution may lead to the damage of mobile robots for exceeding physical constraints during the task execution. To overcome this limitation, this paper proposes a novel inequality and equality constrained optimization RNN (IECORNN) to handle the motion control of mobile robots. Firstly, the real-time motion control problem with both criteria optimization and physical constraints is skillfully converted to a real-time equality system by leveraging the Lagrange multiplier rule. Then, the detailed design process for the proposed IECORNN is presented together with the neural network architecture developed. Afterward, theoretical analyses on the motion control problem conversion equivalence, global stability, and exponential convergence property are rigorously provided. Finally, two numerical simulation verifications and extensive comparisons with other existing RNNs, e.g., the CRNN and the GRNN, based on the mobile robot for two different path-tracking applications sufficiently demonstrate the effectiveness and superiority of the proposed IECORNN for the real-time motion control of mobile robots with both criteria optimization and physical constraints. This work makes progresses in both theory as well as practice, and fills the vacancy in the unified framework of RNN in motion control of mobile robots

Sistema de control cinemático guiado y colaborativo por percepción de las trayectorias de las extremidades superiores

This project studies the morphology of the human arm in order to build a robot capable of imitating the movements of the same, learning them and repeating them under a kinematic control routine, for this it was necessary to learn trajectories, which are obtained using artificial vision making use of the Kinect; from which the spatial coordinates of each joint are extracted, and subsequently processed by means of a mathematical model to obtain joint positions, calculate the kinematic model of the robot, and develop a routine for kinematic control that establishes the relationship between the speeds of the joints . The system allows the user to start learning their movements, and then simulate that learning on the virtual robot. As well as activating the physical robot to perform the learned movements. When comparing the results, it was determined that the standard deviation of the trajectories with and without control does not change to a greater extent; but the points that are within the deviation in the control part are more proportional, this because the stability of the trajectories improves when applying kinematic control.Este proyecto estudia la morfología del brazo humano con la finalidad de construir un robot capaz de imitar los movimientos del mismo, aprenderlos y repetirlos bajo una rutina de control cinemático, para esto fue necesario realizar un aprendizaje de trayectorias, las cuales se obtienen mediante visión artificial haciendo uso del Kinect; del cual se extraen las coordenadas espaciales de cada articulación, y posteriormente se procesan mediante un modelo matemático para obtener las posiciones articulares, calcular el modelo cinemático del robot, y desarrollar una rutina para el control cinemático que establece la relación entre las velocidades de las articulaciones. El sistema le permite al usuario poder iniciar un aprendizaje de sus movimientos, y posteriormente simular dicho aprendizaje en el robot virtual. Así como también activar el robot físico para que realice los movimientos aprendidos. Al comparar los resultados se determinó que la desviación estándar de las trayectorias con y sin control, no cambia en mayor medida; pero los puntos que se encuentran dentro de la desviación en la parte de control son más proporcionales, esto debido a que la estabilidad de las trayectorias mejora al aplicarle el control cinemático