It has been noted that the motion control of a hydraulic robotic excavator has some difficulties in excavator mechanical structure variations, disturbance, non-linearity of complex dynamics of the hydraulic manipulator, and so on. In this paper, a new discrete model-free robust controller is proposed for robotic excavator motion control based on the time delay control (TDC) combined with terminal sliding mode control (TSMC). The proposed controller formulation consists of TDC without acceleration information and TSMC with nonlinear desired error dynamics. Less computational effort and sensing signals are required with this controller, which can decrease the influence of noise by eliminating the acceleration information. Furthermore, the designed terminal sliding error dynamics provide robotic excavator motion control with high position tracking accuracy. The proposed controller was implemented on a 30 ton Volvo hydraulic robotic excavator, and its effectiveness was verified. The achieved end-effector position tracking accuracy was within 2 cm for a curved surface.