A medical instrument system includes actuators, a medical instrument, and a control system operably connected to the actuators. The medical instrument includes an end portion and transmission systems, each of which couples the end portion to an actuator of the actuators such that the actuators are operable to drive the transmission systems to move the end portion. The control system is configured to execute operations including determining a difference between a current configuration of the end portion and a desired configuration of the end portion, and operating the actuators to apply tensions to the transmission systems based on the difference and based on constant offset tensions. The constant offset tensions are independent of current tensions experienced by the transmission systems.