  Currently used wireless capsule endoscopy (WCE) is limited in terms of
inspection time and flexibility since the capsule is passively moved by
peristalsis and cannot be accurately positioned. Different methods have been
proposed to facilitate active locomotion of WCE based on simultaneous magnetic
actuation and localization technologies. In this work, we investigate the
trajectory following problem of a robotic capsule under rotating magnetic
actuation in a tubular environment, in order to realize safe, efficient and
accurate inspection of the intestine at given points using wireless capsule
endoscopes. Specifically, four trajectory following strategies are developed
based on the PD controller, adaptive controller, model predictive controller
and robust multi-stage model predictive controller. Moreover, our method takes
into account the uncertainty in the intestinal environment by modeling the
intestinal peristalsis and friction during the controller design. We validate
our methods in simulation as well as in real-world experiments in various
tubular environments, including plastic phantoms with different shapes and an
ex-vivo pig colon. The results show that our approach can effectively actuate a
reciprocally rotating capsule to follow a desired trajectory in complex tubular
environments, thereby having the potential to enable accurate and repeatable
inspection of the intestine for high-quality diagnosis.
