In this study, an existing superfinishing method used for polishing glass surfaces was refined using a five-joint closed-link compact robot with fixed abrasive grains. In previous studies, a voice coil motor was used to control the constant-pressure pressing force while maintaining the polishing force for a relatively short period. However, maintaining the polishing force for long periods is imperative for achieving a high-quality polished surface. Thus, in this study, a strain gauge load cell was adopted in addition to a conventional piezoelectric force sensor to maintain the polishing force for a long period. First, the amounts of DC drift of the piezoelectric force sensor and strain gauge type load cell were compared to confirm the necessity of signal processing as well as the compatibility of long-term force measurement and high-frequency vibration measurement by application. Further, a method was proposed in which the change in the pressing force was recorded from the connected sensor; when the pressing force fluctuated, chatter vibrations were determined to occur, and the pressing force was temporarily set to 0 N. This method could obtain a better polished surface than the proportional-integral-differential (PID) control, which simply controls the pressing force at a constant value. Finally, chatter vibrations could be determined by detecting high-frequency sounds using a sound level meter. Notably, a finely polished surface could be obtained.