Six-Dimensional Localization of a Robotic Capsule Endoscope Using Magnetoquasistatic Field

This study presents a six-dimensional (6D) localization method and theoretical analysis for a robotic capsule endoscope (RCE). Herein, the challenge of implementing 6D localization for an RCE, with the simultaneous localization of 3D position and 3D orientation, is resolved using optimization with an induced magnetostatic field and RCE kinematics. The optimization is achieved using three transmitting coils (Txs) that are placed in a foundation bed to generate the magnetoquasistatic field and three orthogonal receiving coils (Rxs) that are embedded in the RCE, which is aligned with a capsule coordinate system (CCS), to detect the magnetoquasistatic field. For the 3D position estimation, a nonlinear net magnetic field model is linearized, and a polynomial equation optimization is formulated. The local existence and uniqueness of the solution in the region of interest (ROI) are proved based on the model and simulation. For the 3D orientation estimation, a rotation matrix describing the RCE orientation is computed using the measured magnetic field at the three orthogonal Rxs, and the orthogonality of the rotation matrix is enhanced by using the polar coordinate decomposition. Both simulations and experiments verify the suitability of the proposed method. The maximum error for position and orientation are 1.68+/−0.76 mm and 1.74+/−1.06°, respectively, under a 5 Hz sampling rate in an applicable spherical ROI with a diameter of 10 cm.