  Accurate kinematic models are essential for effective control of surgical
robots. For tendon driven robots, which is common for minimally invasive
surgery, intrinsic nonlinearities are important to consider. Traditional
analytical methods allow to build the kinematic model of the system by making
certain assumptions and simplifications on the nonlinearities. Machine learning
techniques, instead, allow to recover a more complex model based on the
acquired data. However, analytical models are more generalisable, but can be
over-simplified; data-driven models, on the other hand, can cater for more
complex models, but are less generalisable and the result is highly affected by
the training dataset. In this paper, we present a novel approach to combining
analytical and data-driven approaches to model the kinematics of nonlinear
tendon-driven surgical robots. Gaussian Process Regression (GPR) is used for
learning the data-driven model and the proposed method is tested on both
simulated data and real experimental data.
