A note on the ‘task-space control of robots using an adaptive Taylor series uncertainty estimator’

Abstract

This note points out some errors in the above paper that presents an indirect adaptive Taylor series control approach for the asymptotic tracking task-space control of electrically driven robots. In the proposed approach, Taylor series estimator is designed to approximate the lumped uncertainties (a real-valued function of several variables) in a decentralised form. However, in this note, it is proven that according to Stone–Weierstrass theorem, such an approximation is not technically true, and consequently, the obtained results in the above-mentioned paper are not correct.