tracking control of robots revisited based on taylor series and asymptotic expansion

This paper points out some errors based on the one-dimensional taylor series for a multi-dimensional function that is used for robots manufacturing. it is argued that the proof of theorem 1 is not mathematically true, and consequently, the obtained results cannot be correct. in addition to this, the stability analysis presented in the paper does not address the saturated area properly. therein, stability is analyzed separately in saturated and unsaturated operation areas. however, the stability of the closed-loop system may not be guaranteed through these separate analyses, since transitions from saturation area to unsaturated area and vice versa are neglected. this work is an extension of the above paper, based on the revised taylor series and considering actuator saturation limit in both controller design and stability analysis.