The Mixed Kalman and H Infinity Filter Based Robust Model Following Control Algorithm for CABG Beating Heart Surgery

Abstract

In the CABG surgery the robot dynamically cancels the relative motion between the point of interest (POI) on the beating heart and robotic instruments, such that the surgeon can operate as if the heart is stationary. However, the highly nonlinear and non-stationary nature of the beating heart motion poses difficulties for robot to follow the characteristics of the beating heart motion. Furthermore, the surgery has potential safety risk if the robot system could not track the POI properly. Therefore, in order to minimize the effects caused by the uncertainty in the heart motion model during the surgery, a robust prediction based model following control algorithm is proposed here. The adaptive Autoregressive (AR) model integrated the mixed Kalman and H infinity filter to estimate the state of the beating heart motion in the sense of minimizing minimize both RMS motion estimation error and worst case motion estimation error. In addition, the linear quadratic optimal tracking theory was used to implement the model following controller. In such way a complicated heart motion tracking problem transformed to dynamic model following problem and the robust property of the tracking control is more effective. The method is verified by two prerecorded distinguished datasets on 3D test bed robotics.