This paper presents a fault-tolerant control (FTC) based on impedance control and full state feedback backstepping sliding mode control (FBSMC) algorithm for an n degree of freedoms (n-DOF) serial hydraulic manipulator under the presence of matched and mismatched uncertainties and sensor faults in the constrained framework. These faulty signals, generated from unknown constant or time-variant offset values, happen on both manipulator joint angles and force sensors; thereby degrading the system performance. Therefore, to address both matched and mismatched uncertainties and signal faults, the system dynamics subjects to the sensor faults is mathematically modeled. Then, the robust fault estimation algorithm based on extended state observer (ESO) is proposed to estimate the system state and faulty signals for the FTC design to achieve the force and position tracking performance. System stability of the proposed control scheme is theoretically proven by performing Lyapunov theorems. Finally, comparative simulation results are given on a 3-DOF serial hydraulic manipulator to evaluate the effectiveness of the proposed fault estimation and FTC methodology.