A model-free adaptive robust control based on time delay estimation (TDE) is proposed for robot in the presence of disturbance and input saturation. TDE is utilized to estimate the complicated nonlinear terms of the robot including unknown dynamics and disturbance, and a TDE error observer is developed to estimate the inevitable TDE error. When the input torque of the robot exceeds the upper or lower limit of the input saturation, an auxiliary system and a saturation deviation boundary adaptive law are employed to mitigate the negative impact of input saturation on the position tracking. Finally, the robust control law is obtained by backstepping. The stability of the closed-loop system is proved by Lyapunov functions, and the validity of the proposed method is demonstrated by comparative simulations and experiments. Compared with the model-based controllers and other model-free controllers, the proposed method does not necessitate the accurate dynamic model of the complicated system and with lower computation. Moreover, it can guarantee the desired position tracking performance of the robot even subject to disturbance and input saturation simultaneously.

Reaction null space (RNS) planning and control of a planar three-link space manipulator’s pregrasping a spinning target are studied. First, the Lagrange dynamic model of the manipulator was established. Second, the RNS motion planning algorithm was derived, and the vector norm constraint algorithm of RNS planning was addressed to ensure certain joint angular acceleration constraints were satisfied. Furthermore, an augmented adaptive sliding mode controller based on time delay estimation (TDE) was proposed. This controller estimated the unknowns of the system by TDE technology, in which accurate and complete dynamics were not required, and an adaptive TDE was introduced to decrease the estimation errors and avoid serious chattering. Finally, numerical simulations were carried out to verify the effectiveness of the proposed RNS planning and control algorithm.

This paper investigates the passive and active control strategies to provide a physical assistance and rehabilitation by a 7-DOF exoskeleton robot with nonlinear uncertain dynamics and unknown bounded external disturbances due to the robot user's physiological characteristics. An Integral backstepping controller incorporated with Time Delay Estimation (BITDE) is used, which permits the exoskeleton robot to achieve the desired performance of working under the mentioned uncertainties constraints. Time Delay Estimation (TDE) is employed to estimate the nonlinear uncertain dynamics of the robot and the unknown disturbances. To overcome the limitation of the time delay error inherent of the TDE approach, a recursive algorithm is used to further reduce its effect. The integral action is employed to decrease the impact of the unmodeled dynamics. Besides, the Damped Least Square method is introduced to estimate the desired movement intention of the subject with the objective to provide active rehabilitation. The controller scheme is to ensure that the robot system performs passive and active rehabilitation exercises with a high level of tracking accuracy and robustness, despite the unknown dynamics of the exoskeleton robot and the presence of unknown bounded disturbances. The design, stability, and convergence analysis are formulated and proven based on the Lyapunov–Krasovskii functional theory. Experimental results with healthy subjects, using a virtual environment, show the feasibility, and ease of implementation of the control scheme. Its robustness and flexibility to deal with parameter variations due to the unknown external disturbances are also shown.