Estimación de la función de distribución no paramétrica de tiempos de reconfiguración de los controladores de un prototipo de un robot planar.

Abstract

In this study, the estimation of the nonparametric density function of the controller reconfiguration times of a planar robot prototype was investigated. There is a planar robot model designed to solve inverse kinematics, which has two controllers to provide the solution to the approach of four trajectories designed for the research, so that if the main controller fails the other controller is able to resume control of the robot prototype and solve the trajectory in progress, in that process a certain amount of time is invested, this process is known as reconfiguration. It is intended to determine a density function capable of characterizing the behavior of the reconfiguration times used in each of the trajectories. The same that has been determined by the kernel or kernel method, the solution has been implemented in an automated way in Matlab so to determine the best estimate were used the kernels of: Epanechnikov, Triangular, Quartic and Normal or Gaussian, the kernels need a bandwidth, the same that has been used under the Silverman parameter. The selection of the best kernel for estimation is based on the mean square error criterion, the best kernel for estimation being the Gaussian kernel with a mean square error of 2.9085% in trajectory 1, 3.4843% in trajectory 2, 2.3345% in trajectory 3 and 2. 4747% in trajectory 4, in addition the reliability at 95% per trajectory was determined as a function of the reconfiguration time giving as a result: 1.036 s in trajectory 1, 0.9601 s in trajectory 2, 09729 s in trajectory 3 and 1.002 s in trajectory 4. It is recommended to perform statistical tests relevant to the treatment of non-normal datasets.