A key unsolved problem in tactile robotics is how to combine tactile perception and control to perform robust and general physical interaction with the surroundings. Here we focus on a prototypical task of tactile exploration over surface features such as edges or ridges, which is a principal exploratory procedure of humans to recognize object shape. The methods were adapted from an approach for biomimetic active touch that perceives the stimulus location and identity while controlling location based on the perception to aid perception; with minor modification to the control policy, to rotate the sensor to maintain a relative orientation and move tangentially (tactile servoing), the method applies also to tactile exploration. Robust exploratory tactile servoing is then attained over various 2D objects, ranging from the edge of a circular disk, a volute laminar, and circular or spiral ridges. Conceptually, the approach brings together active perception and haptic exploration as instantiations of a common active touch algorithm, and has potential to generalize to more complex tasks requiring the flexibility and robustness of human touch.