Composite direct adaptive Taylor series – fuzzy controller for the robust asymptotic tracking control of flexible-joint robots

Abstract

Recent developments in the use of Taylor series-based controllers have increased the need for utilizing Taylor series system for complex nonlinear systems. This research aims at developing a direct adaptive controller for the tracking control of electrically-driven flexible-joint robotic manipulators. In our direct adaptive method, the decentralized controller benefits by two control terms, namely a Taylor series estimator to approximate an ideal controller for the diminution of joint tracking error in the presence of lumped uncertainty and also a fuzzy estimator to compensate an approximation error. The joint tracking error and its time derivatives up to the second order are guaranteed to converge asymptotically to zero by means of the stability analysis. To obtain better control performance, the particle swarm optimization is used for selecting the control parameters. Simple and accurate design, small joint tracking error and no need of bounding functions are the main advantages of proposed control method. Finally, numerous simulation studies are included to verify the efficiency of the controller.

A finite‐time adaptive Taylor series tracking control of electrically‐driven wheeled mobile robots

“…Utilizing Taylor series as universal approximators, one can design ψ ∈ ℝ 2×1 to approximate the uncertain non-linear function, 𝝍, which can be formulated via [63]…”

“…T ∈ ℝ 6×1 is the vector of regressors. On the other hand, one can formulate 𝝍 via [63] 𝝍 = 𝒫 T Y + 𝜺 a (55) in which 𝜺 a ∈ ℝ 2×1 denotes the approximation error. Let us introduce the upper bound of approximation error, 𝛿, as…”

“…Utilizing Taylor series as universal approximators, one can design $${\hat{\bm{\psi }}} \in {\mathbb{R}^{2 \times 1}}$$ to approximate the uncertain non‐linear function, ψ , which can be formulated via [63] $$\begin{equation} \widehat{\bm{\psi}}={\widehat{\mathcal{P}}}^{T}\ \bm{{\rm Y}} \end{equation}$$where $${\hat{\bm{\psi }}}$$ is the Taylor polynomial, $$ {\widehat{\mathcal{P}}}^{T} = \left[ \def\eqcellsep{&}\begin{array}{ll} {\widehat{\mathcal{P}}}_{1}\in {\mathbb{R}}^{1\ensuremath{\times{}}3} &\quad {\bm 0} \in {\mathbb{R}}^{1\ensuremath{\times{}}3}\\ {\bm 0} \in {\mathbb{R}}^{1\ensuremath{\times{}}3} &\quad {\widehat{\mathcal{P}}}_{2}\in {\mathbb{R}}^{1\ensuremath{\times{}}3} \end{array} \right] \in {\mathbb{R}}^{2\ensuremath{\times{}}6}$$ is the vector of coefficients, and …”

A state augmented adaptive backstepping control of wheeled mobile robots

“…This paper designs a Taylor series system to approximate H i in the tracking error space as (Ahmadi and Fateh, 2018a, 2018b, 2019)…”

Observer-based robust control for flexible-joint robot manipulators: A state-dependent Riccati equation-based approach

“…A robust Lyapunov-based controller for EFJRs utilizing VCS has been designed which is free from the mechanical dynamics of the actuator (Izadbakhsh, 2016; Izadbakhsh and Fateh, 2014). A direct adaptive controller has been developed utilizing a composition of Taylor series and a fuzzy estimator for EFJRs (Ahmadi and Fateh, 2019). An observer-based output feedback control scheme has been investigated under the framework of the backstepping design for EFJRs (Chang et al, 2017).…”