The inverse kinematics problem (IKP) is fundamental in robotics, but it gets harder to solve as the complexity of the mechanisms increases. For that reason, several approaches have been applied to solve it, including metaheuristic algorithms. This work presents a proposal for solving the IKP of a doubly articulated kinematic chain by means of a modified differential evolution (DE) algorithm. The novelty of the proposal is both in the modeling of the problem and the modification to the DE for solving it. The modeling is inspired by a technique used in animation software to recreate movements by dividing the complete trajectory in a number of segments. Each segment represents a single optimization problem linked to the IKP as a sequence that is solved by the modified DE where the initial population for each single problem is biased by using the solution of the previous one. The approach produces solutions for positioning the end effector in a specific point within the work space while minimizing the angular displacement between the initial and final poses. The proposal was able to obtain solutions requiring a fewer total execution cycles compared to the usual approach of solving only one optimization problem related to the inverse kinematics. Different trajectories were used to test the solutions generated by the proposed approach, and the set of conditions that must be covered to apply it to solve the IKP of a particular mechanism are presented.
This paper shows a proposal for a control scheme for the trajectory tracking problem in a Two Degree of Freedom Helicopter (2DOFH). For this purpose, a control scheme based on a feedback linearization combined with a Generalized Proportional Integral (GPI) controller is used. In order to implement linearization by feedback, it is required to know and have access to all the physical 2DOFH parameters, however, angular velocity and viscous friction are often not available. Commonly, state observers are used to know the angular velocity, however, estimating friction results out to be more complex. Therefore, we propose the use of a Convolutional Neural Network (CNN) to estimate viscous friction and angular velocity. The variables estimated by the CNN are entered into both the GPI and feedforward controllers. Thus, the system is brought to a linear representation that directly relates the GPI control to the dynamics of perturbations and non-model parameters. Finally, results of numerical simulations are shown that validate the robustness of our scheme in the presence of disturbances in the tail rotor, as well as the advantages of using a feedforward control based on a CNN. INDEX TERMSFriction estimation, Neural networks, Non-linear system, Tail rotor disturbance, Two degrees of freedom helicopter. Hence, different experimental prototypes have been developed to study helicopter dynamics [13]-[15]. One of the most popular consists of a Two Degree of Freedom Helicopter (2DOFH), which recreates the dynamic behavior of the helicopter in its pitch (θ) and yaw (ψ) rotations [15], [16].
En este trabajo se propuso la aplicacion de un método de sintonización en línea basado en redes neuronales para un controlador PID que regula el flujo en una bomba centrífuga. Se llevo a cabo la implementación de un algoritmo de retropropagación modificado estable en el sentido de estabilidad de entrada a estado para actualizar los pesos de una red neuronal. Se empleó la energía consumida por la bomba para mantener un determinado flujo en la tuber´ía de una a estación experimental como indicador para evaluar la eficiencia del controlador. Se llevaron a cabo diferentes pruebas experimentales para mostrar el rendimiento del controlador propuesto en diferentes condiciones, tales como ausencia de perturbaciones, perturbaciones constantes y perturbaciones dependientes del tiempo. Se implementó una v´álvula proporcional para generar las perturbaciones en el sistema. El controlador se comparó con un controlador PID clasico y un método de ajuste en línea basado en redes neuronales para un controlador PID con algoritmo de retropropagacion sin modificación. Los resultados mostraron que el método de ajuste en línea basado en redes neuronales con un algoritmo de aprendizaje estable produjo un menor consumo de energía en la bomba centrífuga de hasta 4 Watt-hora de acuerdo con los resultados reportados.
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