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

In this paper, we demonstrate velocity-level closed-loop control of a tethered magnetic capsule endoscope that is actuated via serial manipulator with a permanent magnet at its end-effector. Closed-loop control (2 degrees-of-freedom in position, and 2 in orientation) is made possible with the use of a real-time magnetic localization algorithm that utilizes the actuating magnetic field and thus does not require additional hardware. Velocity control is implemented to create smooth motion that is clinically necessary for colorectal cancer diagnostics. Our control algorithm generates a spline that passes through a set of input points that roughly defines the shape of the desired trajectory. The velocity controller acts in the tangential direction to the path, while a secondary position controller enforces a nonholonomic constraint on capsule motion. A soft nonholonomic constraint is naturally imposed by the lumen while we enforce a strict constraint for both more accurate estimation of tether disturbance and hypothesized intuitiveness for a clinician's teleoperation. An integrating disturbance force estimation control term is introduced to predict the disturbance of the tether. This paper presents the theoretical formulations and experimental validation of our methodology. Results show the system's ability to achieve a repeatable velocity step response with low steady-state error as well as ability of the tethered capsule to maneuver around a bend.