This study considered the hybrid position/force control of robots with an oscillatory base. The objective when controlling such a system is to control the contact force between the environment and the object in the constrained directions. The auxiliary control input laws with the ANFIS tuning methodology were successfully applied to robot manipulators mounted on an oscillatory base to provide hybrid position/force control. Linguistic fuzzy information from human knowledge was incorporated into the fuzzy system, which was equipped with a training algorithm. The advantage of the proposed control scheme is that only select control inputs are needed to select control inputs for task space trajectory tracking. In other words, such a system does not require the redesign of the vibration damping controller. Tracking performance comparison is also presented for the proposed control scheme and the other existing control techniques. It is shown that the proposed fuzzy control scheme offers several implementation advantages such as less steady-state errors, reduced effect of overshoot, and a fast convergent rate in real-time verification. The experimental results of this study confirmed the efficiency of the proposed control design and its feasibility for use in various mechanical systems, including mobile robots, gantry cranes, underwater robots, and other dynamic systems mounted on oscillatory bases and used to perform constrained motion tasks.