Most metal parts made by machining operations contain burrs, which can be removed by robotic manipulators. Modeling a deburring robot on unknown contours is a relatively difficult task. In this study, we present a novel compliant motion controller that uses a modified on-line rule self-regulating fuzzy control (RSFC) and depends on no mathematical models. In the proposed controller, a Cartesian robot on which a grinding tool is mounted rigidly performs edge following (precision deburring) and chamfering on unknown contours. The manipulator is controlled along the tangential direction of a constrained surface and its cutting force is maintained at a desired level. Experimental results demonstrate the effectiveness of this control strategy in terms of automatically deburring the edges of parts with an unknown geometrical configuration.