A semi-implicit homogeneous discretized differentiator based on two projectors: experimental validation on a cable-driven parallel robot

¹ Nantes Université, École Centrale de Nantes, CNRS, LS2N, UMR 6004, F-44000 Nantes, France
² QUARTZ EA 7393, ENSEA, Cergy-Pontoise, France, France

^* e-mail: yannick.aoustin@univ-nantes.fr

Received: 22 February 2023
Accepted: 24 January 2024

Abstract

This work is dedicated to the application of a semi-implicit homogeneous differentiator to estimate the angular velocity and the angular acceleration of each of the eight electric motors of the CRAFT cable-driven parallel robot from the recording of the angular position of their respective output shaft. These motors drive the winding or unwinding of eight cables to move the robot moving-platform. The results show that this differentiator, whose the definition is respectively based on two projectors, is an extremely efficient tool for estimating the angular velocities and accelerations of the eight motors. These estimated velocities and accelerations are much less noisy than their reference signals obtained by backward difference. Moreover, the estimated quantities obtained with this differentiator are successfully compared to those obtained by a non-linear observer based on the interpolation and numerical difference of the measured position variable. Those promising results will definitely contribute to a better control of the CRAFT robot.