This paper studies the position tracking control problem of nonlinear robotic system subject to time-varying state delay and input dead-zone. The input dead-zone and unknown external disturbance are regarded as the lumped disturbance and a sliding mode disturbance observer is designed. In order to ensure the stability of the robotic system with time-varying state delay, a position tracking controller based on auxiliary position tracking error functions is designed. Considering the estimated error of the sliding mode disturbance observer, a gain adaptive law is designed to further improve the position tracking accuracy of the system. The stability of the proposed controller is theoretically proved by Lyapunov-Krasovskii function method, and the effectiveness of the controller is verified by comparative simulations. The proposed control method can achieve stable and accurate position tracking of the robotic system with simultaneous time-varying state delay and input dead-zone.

For nonlinear teleoperation system with time delay, a control scheme based on force estimation is proposed. Since the force signals in teleoperation system are difficult to measure, a force estimation algorithm is designed to estimate the force signals. Using the estimated force signals and time delayed position error signals, two backstepping controllers are designed for teleoperation system. The performance of position tracking and force reflection of the system is analyzed, and the effectiveness of the proposed method is verified by simulations. The results show that the proposed control method can accurately estimate the force signals, and improve the performance of position tracking and force reflection while maintaining the stabilization of the robotic system.

For accurate position tracking of robotic system subject to payload presence and payload variation, an adaptive time delay controller is proposed. First, the conventional time delay control (TDC) which is simple in structure and does not depend on the model of the system is employed to offset all the nonlinear terms in the dynamic model of the robotic system. Next, using a sliding variable, a payload adaptive law is designed to adapt to the payload presence and payload variation in the robotic system. Furthermore, a time delay estimation (TDE) error adaptive law is designed to suppress the TDE error caused by the conventional TDC. Finally, since two control gains in the conventional TDC need to be chosen, a control gain adaptive law is designed to adjust one control gain automatically. The stability of the closed-loop system is proved via Lyapunov stability synthesis and simulations are conducted on a 2-DOF robot. With the proposed adaptive time delay controller, position tracking performance of the robotic system can be achieved even there exits payload presence and payload variation. Meanwhile, it can effectively suppress the TDE error and it only needs to adjust one control gain.

To improve the trajectory tracking performance of a complex nonlinear robotic system, a velocity-free adaptive time delay control is proposed. First, considering that conventional time delay control (TDC) may cause large time delay estimation (TDE) error under nonlinear friction, a TDC with gradient estimator is designed. Next, since it is complicated and time-consuming to adjust gains manually, an adaptive law is designed to estimate the gain of the gradient. Finally, in order to avoid the measurement of velocity and acceleration in the controller while enabling the robot to implement position tracking, an observer is designed. The proposed control can not only offset the nonlinear terms in the complex dynamics of the robotic system but also reduce the TDE error, estimate the gain of the gradient online, and avoid the measurement of velocity and acceleration. The stability of the system is analyzed via Lyapunov function. Simulations are conducted on a 2-DOF robot to verify the effectiveness of the proposed control.