Task-space Control of Robots Using an Adaptive Taylor Series Uncertainty Estimator Revisited

This paper presents an improved version of the article “task-space control of robots uses an adaptive Taylor series uncertainty estimator” by designing a more general framework for dealing with actuator saturation. There are four important issues about the aforementioned article. Firstly, the saturated and unsaturated regions have been discussed separately in that article, while this paper presents a unified approach for stability analysis. Secondly, the linear parameterization of unknown multi-variable vector-valued nonlinearities represented in the aforementioned article is not true. Consequently, it will affect the stability analysis significantly and the obtained results are doubtful. Thirdly, although the tracking error is bounded in the saturated area, it may be unacceptable due to undesirable performance. Thus, performance evaluation is needed to verify the satisfactory operation of the control system. However, in the aforementioned article, performance evaluation has not been presented. Fourthly, the aforementioned paper applies the Taylor series as a universal approximator without verifying the conditions of the universal approximation theorem. This paper proves that the Taylor series can satisfy the conditions of this theorem. All these four important issues are addressed in this paper and a modified version of the aforementioned article is presented.