In this paper, a new adaptive control strategy, based on the Modified Function Approximation Technique, is proposed for a manipulator robot with unknown dynamics. This novel strategy benefits from the backstepping control approach and the use of state and output feedback. Unlike the conventional Function Approximation Technique approach, the use of basis functions to approximate the dynamic parameters is completely eliminated in the proposed scheme. Another improvement is eliminating the need to measure velocity by means of integrating a high-order sliding mode observer. Furthermore, utilizing the Lyapunov function theory, it is demonstrated that all controller signals are uniformly ultimately bounded in the closed-loop form. Lastly, simulation and comparative studies are carried out to validate the effectiveness of the proposed control approach.

Joint flexibility introduces additional degrees of freedom and vibration modes, thus limiting the performance of the manipulator. To improve control bandwidth, this paper proposes an enhanced two-stage state feedback (SFB) controller, which combines two parts. The first is a SFB loop, which considers the motor position as a virtual control input for the link side dynamics. The second is a disturbance-state observer, which compensates disturbances and reconstructs indirect measurements. Experimental results show the effectiveness of the proposed controller in terms of position tracking, link vibration, and rejection of the kinematic error from the joint’s harmonic drive reducer.

Singular systems simultaneously capture the dynamics and algebraic constraints in many practical applications. Output feedback admissible control for singular systems through a delta operator method is considered in this article. Two novel admissibility conditions, derived for the singular delta operator system (SDOS) from a singular continuous system through sampling, can not only produce unified admissibility for both continuous and discrete singular systems but also practical procedures. To solve the problem of output feedback admissible control for the SDOS, an existence condition and design procedure is given for the determination of a physically realisable observer for the state estimation, and then a suitable state-feedback-like admissible controller design based on the observer is developed. All of the conditions presented are necessary and sufficient, involving strict linear matrix inequalities (LMI) with feasible solutions obtained with low computational costs. Numerical examples illustrate our approach.

Observer-based two-time scale robust control is proposed for free-flying flexible-joint space manipulators with unknown payload parameters and bounded disturbances. The dynamic equations of a free-flying space manipulator with two flexible revolute joints were derived by the momentum conservation law and the Lagrange equations. A flexibility compensator was introduced to make the equivalent joint stiffness large enough, which made traditional singular perturbation approach applicable. Then, a singular perturbation model was formulated and a reduced-order controller is proposed. This controller consisted of a slow sub-controller and a fast flexible-joint sub-controller. To the slow subsystem, a sliding observer based robust slow sub-controller was proposed. By optimal linear quadratic regulator method, the fast sub-controller was designed with the estimated velocity by linear observer. This fast sub-controller could stabilize the fast subsystem around the equilibrium trajectory created by the slow subsystem under the effect of the slow control. Finally the numerical simulations were carried out, which showed that elastic joint vibrations had been stabilized effectively and good tracking performances had been achieved.

The uncalibrated robotic hand–eye coordination problem is firstly modeled by a dynamic system, where the unknown hand–eye relationship is regarded as the system's unmodeled dynamics. A state observer is then designed to estimate impacts of this modeling error together with the system's external disturbances. With the estimation results as the compensation, the system control is thus accomplished based on a nonlinear combination of the system state errors. Convergence analysis of the whole system under the proposed control scheme is emphasized. Simulations and experiment results are presented to verify the performance of the proposed approach.