In this paper, an adaptive impedance control combined with disturbance observer (DOB) is developed for a general class of uncertain robot manipulators in discrete time. The impedance control is applied to realize the interaction force control of robot manipulators in unknown, time-varying environments. The optimal reference trajectory is produced by impedance control, and the impedance parameters are achieved using Q-learning technique, which is implemented based on trajectory tracking errors. The position control with DOB of robot manipulators is implemented to track the virtual desired trajectory, and the DOB is designed to compensate for unknown compounded disturbance function by bounding both tracking error inputs and compounded disturbance inputs in a permitted control region, of which the compounded disturbance function is taken into account of all uncertain terms and external disturbances. The appropriate DOB parameters are selected applying linear matrix inequalities (LMIs) method. Both the impedance control and the bounded DOB control can well guarantee semiglobal uniform boundness of the closed-loop robot systems based on Lyapunov analysis and Schur complement theory. Simulation results are performed to test and verify effectiveness of the investigated combining adaptive impedance control with DOB
