Systems and methods for determining instrument position in the presence of backlash

A robotically-assisted manipulator system, comprising:

• an instrument including a first instrument driver and a second instrument driver, wherein the first and second instrument drivers are coupled such that movement of the first instrument driver causes movement of the second instrument driver;
• an instrument manipulator including a first carriage driver, a second carriage driver, and a sensor configured to monitor a position of the second carriage driver, wherein the first carriage driver is configured to couple to the first instrument driver and the second carriage driver is configured to couple to the second instrument driver;
• and
• a controller in operative communication with the instrument manipulator, the controller being configured to:
• apply a first torque to the first carriage driver, the first carriage driver configured to impart motion to the first instrument driver to cause movement of the instrument in a degree-of-freedom;
• apply a second torque to the second carriage driver;
• adjust a magnitude of the first torque to cause a desired degree of movement of the instrument in the degree-of-freedom, wherein the magnitude of the first torque compensates for at least one of an external force on the instrument or the second torque;
• receive a sensor signal from the sensor indicating a position of the second carriage driver;
• and
• determine, based on the position of the second carriage driver, a current instrument position in the degree-of-freedom.