The virtual decomposition control (VDC) is an efficient tool suitable to deal with the full-dynamics-based control problem of complex robots. However, the regressor-based adaptive control used by VDC to control every subsystem and to estimate the unknown parameters demands specific knowledge about the system physics. Therefore, in this paper, we focus on reorganizing the equation of the VDC for a serial chain manipulator using the adaptive function approximation technique (FAT) without needing specific system physics. The dynamic matrices of the dynamic equation of every subsystem (e.g. link and joint) are approximated by orthogonal functions due to the minimum approximation errors produced. The control, the virtual stability of every subsystem and the stability of the entire robotic system are proved in this work. Then the computational complexity of the FAT is compared with the regressor-based approach. Despite the apparent advantage of the FAT in avoiding the regressor matrix, its computational complexity can result in difficulties in the implementation because of the representation of the dynamic matrices of the link subsystem by two large sparse matrices. In effect, the FAT-based adaptive VDC requires further work for improving the representation of the dynamic matrices of the target subsystem. Two case studies are simulated by Matlab/Simulink: a 2-R manipulator and a 6-DOF planar biped robot for verification purposes.
Las diferencias entre el pretérito perfecto simple y el imperfecto son uno de los temas más complejos de la lengua española, no sólo para el estudiante, sino para el profesor, puesto que sistematizar los casos y hacerlos fácilmente comprensibles al alumno es tarea difícil. Los profesores de lengua, cuyas investigaciones han dado lugar a una serie de teorías y de corrientes metodológicas y didácticas que permiten enfocar la enseñanza de una lengua extranjera de manera muy distinta a como se hacía tradicionalmente. Vamos a repasar muy brevemente cuáles son estas teorías.
En primer lugar es necesario señalar en qué consiste el aprendizaje de una segunda lengua:
"El aprendizaje de una segunda lengua (L2) es el
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The study is conducted by the use of the modern Russian and Arabic dictionary, specifically, (Intermediate lexicon Dictionary
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