On the Controllers Based on Time Delay Estimation for Robotic Manipulators

TL;DR

This paper critically examines controllers based on time delay estimation for robotic manipulators, revealing flaws in existing proofs and proposing corrected versions with rigorous stability guarantees.

Contribution

It challenges previous claims about the stability of TDE-based controllers and introduces modified controllers with valid proofs for robotic manipulators.

Findings

Previous stability proofs are incorrect.

Modified controllers with rigorous proofs are proposed.

The new controllers ensure asymptotic trajectory tracking.

Abstract

Assurance of asymptotic trajectory tracking in robotic manipulators with a smooth control law in the presence of unmodeled dynamics or external disturbance is a challenging problem. Recently, it is asserted that it is achieved via a rigorous proof by designing a traditional model-free controller together with time delay estimation (TDE) such that neither dynamical parameters nor conservative assumptions on external disturbance are required. The purpose of this note is to show that this claim is not true and the stability proof of the method is incorrect. Finally, some modified versions of this controller with rigorous proof is presented for robotic manipulators.