Adaptive Tracking Control of an Exoskeleton Robot With Uncertain Dynamics Based on Estimated Time-Delay Control

In this paper, we present a backstepping approach integrated with time-delay estimation to provide an accurate estimation of unknown dynamics and to compensate for external bounded disturbances. The control was implemented to perform passive rehabilitation movements with a 7-DOF exoskeleton robot named ETS-Motion Assistive Robotic-Exoskeleton for Superior Extremity. The unknown dynamics and external bounded disturbances can affect the robotic system in the form of input saturation, time-delay errors, friction forces, backlash, and different upper-limb's mass of each subject. The output of the time-delay estimator is coupled directly to the control input of the proposed adaptive tracking control through a feed-forward loop. In this case, the control system ensures a highly accurate tracking of the desired trajectory, while being robust to the uncertainties and unforeseen external forces, and flexible with variation of parameters. Due to the proposed strategy, the designed control approach does not require accurate knowledge of the dynamic parameters of the exoskeleton robot to achieve the desired performance. The stability of the exoskeleton robot and the convergence of its state errors are established and proved based on Lyapunov–Krasovskii functional theory. Experimental results and a comparative study are presented to validate the advantages of the proposed strategy.