Sensorless Estimation of the Planar Distal Shape of a Tip-Actuated Endoscope

Abstract

Traditional endoscopes consist of a flexible body and a steerable tip with therapeutic capability. Although prior endoscopes have relied on operator pushing for actuation, recent robotic concepts have relied on the application of a tip force for guidance. In such case, the body of the endoscope can be passive and compliant; however, the body can have significant effect on mechanics of motion and may require modeling. As the endoscope body s shape is often unknown, we have developed an estimation method to recover the approximate distal shape, local to the endoscope s tip, where the tip position and orientation are the only sensed parameters in the system. We leverage a planar dynamic model and extended Kalman filter to obtain a constant-curvature shape estimate of a magnetically guided endoscope. We validated this estimator in both dynamic simulations and on a physical platform. We then used this estimate in a feed-forward control scheme and demonstrated improved trajectory following. This methodology can enable the use of inverse-dynamic control for the tip-based actuation of an endoscope, without the need for shape sensing.