Accurate kinematic models are essential for effective control of surgical robots. For tendon driven robots, which are common for minimally invasive surgery, the high nonlinearities in the transmission make modelling complex. Machine learning techniques are a preferred approach to tackle this problem. However, surgical environments are rarely structured, due to organs being very soft and deformable, and unpredictable, for instance, because of fluids in the system, wear and break of the tendons that lead to changes of the system’s behaviour. Therefore, the model needs to quickly adapt. In this work, we propose a method to learn the kinematic model of a redundant surgical robot and control it to perform surgical tasks both autonomously and in teleoperation. The approach employs Feedforward Artificial Neural Networks (ANN) for building the kinematic model of the robot offline, and an online adaptive strategy in order to allow the system to conform to the changing environment. To prove the capabilities of the method, a comparison with a simple feedback controller for autonomous tracking is carried out. Simulation results show that the proposed method is capable of achieving very small tracking errors, even when unpredicted changes in the system occur, such as broken joints. The method proved effective also in guaranteeing accurate tracking in teleoperation.