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

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.