Closed Loop Control of a Tethered Magnetic Capsule Endoscope

Abstract

Magnetic field gradients have repeatedly been shown to be the most feasible mechanism for gastrointestinal capsule endoscope actuation. An inverse quartic magnetic force variation with distance results in large force gradients induced by small movements of a driving magnet; this necessitates robotic actuation of magnets to implement stable control of the device. A typical system consists of a serial robot with a permanent magnet at its end effector that actuates a capsule with an embedded permanent magnet. We present a tethered capsule system where a capsule with an embedded magnet is closed loop controlled in 2 degree-of-freedom in position and 2 degree-of-freedom in orientation. Capitalizing on the magnetic field of the external driving permanent magnet, the capsule is localized in 6-D allowing for both position and orientation feedback to be used in a control scheme. We developed a relationship between the serial robot's joint parameters and the magnetic force and torque that is exerted onto the capsule. Our methodology was validated both in a dynamic simulation environment where a custom plug-in for magnetic interaction was written, as well as on an experimental platform. The tethered capsule was demonstrated to follow desired trajectories in both position and orientation with accuracy that is acceptable for colonoscopy.

Autonomous Retroflexion of a Magnetic Flexible Endoscope

“…However, owing to the nature of the dipole field, consideration must be made as to what is the best way to apply a magnetic torque between dipoles. Past works, such as [13], [15], [18], set desired infinitesimal torque directions about ϕ̂ ; however, we now demonstrate that this is typically not the most effective axis to apply torque about. We show that one must take into account the relative poses of the magnetic fields when determining how a heading error should be minimized.…”

“…The linearizations of magnetic force and torque that the EPM exerts onto the capsule, or in our case onto the tip of the endoscope, have been analytically derived and explicitly presented in our previous work [13]. Hereafter, bold letters indicate vectors ( v ), a dot above a letter indicates a time derivative ( v̇ ), a hat over a bold letter indicates a unit vector ( v̂ ), and an uppercase letter indicates a matrix ( M ).…”

“…Rotation about the x axis is fruitless owing to axial symmetry of the magnets, and we are left with either a y or z rotation, or a combination of the two. We are interested in which rotation has the largest magnitude of δτ m which is defined as follows [13]:…”

“…avoiding collision with the patient's body) exist. Further, in our previous work [13], [15], the error term for the closed-loop orientation controller was defined by the cross product of the current and desired heading vectors. While this error term describes the shortest angular path between the heading vectors, it is not necessarily the most efficient for magnetic manipulation.…”

Nonholonomic closed-loop velocity control of a soft-tethered magnetic capsule endoscope

“…Since Gazebo does not yet have the capability to simulate continuum objects, the tether was modelled with a large number of short links joined by 2-DoF universal joints. Additionally, we have built a custom plugin to simulate magnetic interaction [10]. Support between Gazebo and ROS allows for Gazebo to emulate a node, and thus all code, excluding the magnetic localization algorithm, is executed identically whether running a simulation or on the physical platform.…”