A 5-D Localization Method for a Magnetically Manipulated Untethered Robot Using a 2-D Array of Hall-Effect Sensors

This paper introduces a new 5-D localization method for an untethered meso-scale magnetic robot, which is manipulated by a computer-controlled electromagnetic system. The developed magnetic localization setup is a 2D array (8 × 8) of mono-axial Hall-effect sensors, which measure the perpendicular magnetic fields at their given positions. We introduce two steps for localizing a magnetic robot more accurately. First, the dipole-modeled magnetic field of the electromagnet is subtracted from the measured data in order to determine the robot's magnetic field. Second, the subtracted magnetic field is twice differentiated in the perpendicular direction of the array, so that the effect of the electromagnetic field in the localization process is minimized. Five variables regarding the position and orientation of the robot are determined by minimizing the error between the measured magnetic field and the modeled magnetic field in an optimization method. The resulting position error is 2.1 ± 0.8 mm and angular error is 6.7 ± 4.3° within the applicable range (5 cm) of magnetic field sensors at 200 Hz. The proposed localization method would be used for the position feedback control of untethered magnetic devices or robots for medical applications in the future.