A robotic surgical system configured to perform minimally invasive surgical procedures. In one variation, this robotic surgical system includes an instrument driver configured to steer an elongate instrument of an instrument assembly in one or more degrees of motion. A drape is disposed between the instrument driver and the instrument assembly. A drive interface apparatus is operatively coupled to the drape. The drape and drive interface apparatus may form a fluid barrier between the instrument driver and the instrument assembly. Drive interface apparatus may be disposed on a top surface of the instrument driver and on a bottom surface of the instrument assembly. The drive interface apparatus may transmit torque from the instrument driver to the instrument assembly. The input torque drives a pulley in the instrument assembly that operates one or more control wires to steer an elongate instrument of the instrument assembly for performing minimally invasive surgical procedures.