  Automation of surgical subtasks using cable-driven robotic surgical
assistants (RSAs) such as Intuitive Surgical's da Vinci Research Kit (dVRK) is
challenging due to imprecision in control from cable-related effects such as
cable stretching and hysteresis. We propose a novel approach to efficiently
calibrate such robots by placing a 3D printed fiducial coordinate frames on the
arm and end-effector that is tracked using RGBD sensing. To measure the
coupling and history-dependent effects between joints, we analyze data from
sampled trajectories and consider 13 approaches to modeling. These models
include linear regression and LSTM recurrent neural networks, each with varying
temporal window length to provide compensatory feedback. With the proposed
method, data collection of 1800 samples takes 31 minutes and model training
takes under 1 minute. Results on a test set of reference trajectories suggest
that the trained model can reduce the mean tracking error of the physical robot
from 2.96 mm to 0.65 mm. Results on the execution of open-loop trajectories of
the FLS peg transfer surgeon training task suggest that the best model
increases success rate from 39.4 % to 96.7 %, producing performance comparable
to that of an expert surgical resident. Supplementary materials, including code
and 3D-printable models, are available at
https://sites.google.com/berkeley.edu/surgical-calibration
