Stochastic Force-Based Insertion Depth and Tip Position Estimations of Flexible FBG-Equipped Instruments in Robotic Retinal Surgery

Vitreoretinal surgery is among the most delicate surgical tasks during which surgeon hand tremor may severely attenuate surgeon performance. Robotic assistance has been demonstrated to be beneficial in diminishing hand tremor. Among the requirements for reliable assistance from the robot is to provide precise measurements of system states, e.g., sclera forces, tool tip position, and tool insertion depth. Providing this and other sensing information using existing technology would contribute toward development and implementation of autonomous robot-assisted tasks in retinal surgery such as laser ablation, guided suture placement/assisted needle vessel cannulation, among other applications. In this article, we use a state-estimating Kalman filtering (KF) to improve the tool tip position and insertion depth estimates, which used to be purely obtained by robot forward kinematics (FWK) and direct sensor measurements, respectively. To improve tool tip localization, in addition to robot FWK, we also use sclera force measurements along with beam theory to account for tool deflection. For insertion depth, the robot FWK is combined with sensor measurements for the cases where sensor measurements are not reliable enough. The improved tool tip position and insertion depth measurements are validated using a stereo camera system through preliminary experiments and a case study. The results indicate that the tool tip position and insertion depth measurements are significantly improved by 77% and 94% after applying KF, respectively.