A teleoperated surgical system has an instrument manipulator that includes a first carriage driver and a second carriage driver that each provide independent rotary motion. Each carriage driver includes a first engagement feature. A surgical instrument includes two instrument drivers that each receive the rotary motion from one of the two carriage drivers. Each instrument driver includes a second engagement feature that engages the first engagement feature to positively couple the carriage driver to the instrument driver. The instrument drivers are rotationally coupled together. A manipulator controller controls rotation of the two carriage drivers and imparts a motion to the second carriage driver that is contrary to the rotation of the first carriage driver until the first engagement features positively engage the second engagement features. The surgical instrument may include an instrument shaft that can rotate indefinitely. The instrument drivers may be rotationally coupled to the instrument shaft.