FAT-Based Robust Adaptive Control of Electrically Driven Robots in Interaction with Environment

Abstract

SummaryThis paper presents a robust adaptive impedance controller for robot manipulators using function approximation techniques (FAT). Recently, FAT-based robust impedance controllers have been presented using Fourier series expansion for uncertainty estimation. In fact, sinusoidal functions can approximate nonlinear functions with arbitrary small approximation error based on the orthogonal functions theorem. The novelty of this paper in comparison with previous related works is that the number of required regressor matrices in this paper has been reduced. This superiority becomes more dominant when the manipulator degrees of freedom (DOFs) are increased. First, the desired signals for motor currents are calculated, and then the desired voltages are obtained. In the proposed approach, only a simple model of the actuator and manipulator dynamics is used in the controller design and all the rest dynamics are treated as external disturbance. The external disturbances can then be approximated by Fourier series expansion. The adaptation laws for Fourier series coefficients are derived from a Lyapunov-based stability analysis. Simulation results on a 2-DOF planar robot manipulator including the actuator dynamics indicate the efficiency of proposed method.

Polynomial-Based Robust Adaptive Impedance Control of Electrically Driven Robots

“…This problem has been improved in ref. [32]. In the next section, we present a simpler FAT-based adaptive impedance controller, for rigid-link electrically driven robot interacting with the environment.…”

Observer-based adaptive control of robot manipulators using reinforcement learning and the Fourier series expansion

“…Due to the excellent uncertainty approximation ability of function approximation techniques such as the Fourier series (FS) (Izadbakhsh et al, 2019), Szász–Mirakyan operator (Izadbakhsh et al, 2020), and Legendre polynomials (Zarei and Khorashadizadeh, 2019) much interest has been generated in this area (Chien and Huang, 2012; Kai and Huang, 2013). Similar to other estimators such as fuzzy systems and NNs, a function can be expanded by an FS.…”

Robust adaptive control of robot manipulators using Bernstein polynomials as universal approximator

“…To cope with these problems, function approximation techniques (FATs) have been proposed whereas; FAT‐based estimators have simpler structures and fewer tuning parameters. Some robust adaptive controllers for robots using the Fourier series and Legendre Polynomials as universal approximator have been proposed in Reference . A third order Taylor series‐based uncertainty estimator for electrically driven robots in the presence of nonlinearities associated with actuator input constraint has been presented in Reference .…”