Real-time fractional-order control of electrically driven flexible-joint robots has been addressed in this article. An important contribution of this article is that the control law is designed based on the Fourier series that eliminates the need for computation of regressor matrix. Moreover, the nonlinear effects of actuator saturation are considered in the control law. The lumped uncertainty can be approximated using Fourier series with unknown coefficients. Then, the unknown coefficients are estimated using the adaptation law obtained in the stability analysis. The overall closed-loop system is proven to be robust and bounded-input bounded-output stable. In addition, it has been shown that the joint-position errors are uniformly bounded based on Lyapunov’s stability concept. The satisfactory performance of the proposed control scheme is verified by experimental results. To highlight the superiority of the proposed method, experimental results of two voltage-based controllers are also presented.

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.

In this paper, fractional-order observer/controller design for flexible-joint robots is developed. In order to eliminate the need for obtaining the regressor matrix, the Fourier series expansion is applied for uncertainty estimation. Voltage saturation nonlinearities are compensated in the control law; hence, knowledge of the actuator/manipulator dynamics model is not required in the proposed method. Uniformly ultimately boundedness of observer estimation error and joint position tracking error are guaranteed through Lyapunov stability concept. The case study is a single-link flexible-joint robot actuated by permanent magnet DC motors. Experimental results are presented to emphasize the successful practical implementation of the proposed algorithm. Based on the experimental results, the proposed controller considerably outperforms some previous related works using various criteria.

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SummaryThis paper presents a robust tracking controller for electrically driven robots, without the need for velocity measurements of joint variables. Many observers require the system dynamics or nominal models, while a model-free observer is presented in this paper. The novelty of this paper is presenting a new observer–controller structure based on function approximation techniques and Stone–Weierstrass theorem using differential equations. In fact, it is assumed that the lumped uncertainty can be modeled by linear differential equations. Then, using Stone–Weierstrass theorem, it is verified that these differential equations are universal approximators. The advantage of proposed approach in comparison with previous related works is simplicity and reducing the dimensions of regressor matrices without the need for any information of the systems’ dynamic. Simulation results on a 6-degrees of freedom robot manipulator driven by geared permanent magnet DC motors indicate the satisfactory performance of the proposed method in overcoming uncertainties and reducing the tracking error. To evaluate the performance of proposed controller in practical implementations, experimental results on an SCARA manipulator are presented.