Polynomial-Based Robust Adaptive Impedance Control of Electrically Driven Robots

SUMMARY This paper presents a robust adaptive impedance controller for electrically driven robots using polynomials of degree N as a universal approximator. According to the universal approximation theorem, polynomials of degree N can approximate uncertainties including un-modeled dynamics and external disturbances. This fact is completely discussed and proved in this paper. The polynomial coefficients are estimated based on the adaptive law calculated in the stability analysis. A performance evaluation has been carried out to verify satisfactory performance of the controller. Simulation results on a two degree of freedom manipulator have been presented to guarantee its successful implementation.

Bi-Level Adaptive Computed-Current Impedance Controller for Electrically Driven Robots

SUMMARY This paper presents a bi-level adaptive computed-current impedance controller for electrically driven robots. This study aims to reduce calculation complexities by utilizing the electrical equations of actuators, instead of the entire model of the electromechanical system. Moreover, taking the dynamical effects of mechanical parts into account through the current’s feedback, external disturbances are compensated. In order to handle uncertainties, a bi-level optimization problem is formulated to obtain guaranteed stability besides the estimation convergence. An adaptation rule and its optimal tuning gain are achieved. The proposed method is applied to control of a rehabilitation robot to evaluate its performance.

Tracking Control of Electrically Driven Robots Using a Model-free Observer

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.

Robust task-space control of robot manipulators using differential equations for uncertainty estimation

SUMMARYMost control algorithms for rigid-link electrically driven robots are given in joint coordinates. However, since the task to be accomplished is expressed in Cartesian coordinates, inverse kinematics has to be computed in order to implement the control law. Alternatively, one can develop the necessary theory directly in workspace coordinates. This has the disadvantage of a more complex robot model. In this paper, a robust control scheme is given to achieve exact Cartesian tracking without the knowledge of the manipulator kinematics and dynamics, actuator dynamics and nor computing inverse kinematics. The control design procedure is based on a new form of universal approximation theory and using Stone–Weierstrass theorem, to mitigate structured and unstructured uncertainties associated with external disturbances and actuated manipulator dynamics. It has been assumed that the lumped uncertainty can be modeled by linear differential equations. As the method is Model-Free, a broad range of manipulators can be controlled. Numerical case studies are developed for an industrial robot manipulator.