A surgical robotic system automatically calibrates tubular and flexible surgical tools such as endoscopes. By compensating for unideal behavior of an endoscope, the surgical robotic system can accurately model motions of the endoscope and navigate the endoscope while performing a surgical procedure on a patient. During calibration, the surgical robotic system moves the endoscope to a target position and receives data describing an actual position and/or orientation of the endoscope. The surgical robotic system determines gain values based at least on the discrepancy between the target position and the actual position. The endoscope can include tubular components referred to as a sheath and leader. An instrument device manipulator of the surgical robotic system actuates pull wires coupled to the sheath and/or the leader, which causes the endoscope to articulate.