Six-degree-of-freedom Localization Under Multiple Permanent Magnets Actuation

Localization of magnetically actuated medical robots is essential for accurate actuation, closed loop control and delivery of functionality. Despite extensive progress in the use of magnetic field and inertial measurements for pose estimation, these have been either under single external permanent magnet actuation or coil systems. With the advent of new magnetic actuation systems comprised of multiple external permanent magnets for increased control and manipulability, new localization techniques are necessary to account for and leverage the additional magnetic field sources. In this letter, we introduce a novel magnetic localization technique in the Special Euclidean Group SE(3) for multiple external permanent magnetic field actuation and control systems. The method relies on a milli-meter scale three-dimensional accelerometer and a three-dimensional magnetic field sensor and is able to estimate the full 6 degree-of-freedom pose without any prior pose information. We demonstrated the localization system with two external permanent magnets and achieved localization errors of 8.5 ? 2.4 mm in position norm and 3.7 ? 3.6? in orientation, across a cubic workspace with 20 cm length.

Independent Control of Two Magnetic Robots using External Permanent Magnets: A Feasibility Study

The ability to have multiple magnetic robots operate independently in the same workspace would increase the clinical potential of these systems allowing collaborative operation. In this work, we investigate the feasibility of actuating two magnetic robots operating within the same workspace using external permanent magnets. Unlike actuation systems based on pairs of electromagnetic coils, the use of multiple permanent magnets comes with the advantage of a large workspace which better suits the clinical setting. In this work, we present an optimization routine capable of generating the required poses for the external magnets in order to control the position and orientation of two magnetic robots. We show that at a distance of 15cm, minimal coupling between the magnetic robots can be achieved (3.9\% crosstalk) each embedded with 5mm diameter, 5mm length NdFeB magnets. At smaller distances, we observe that the ability to independently control the robot torques decreases, but forces can still achieve independent control even with alignment of the robots. We test our developed control system in a simulation of two magnetic robots following pre-planned trajectories in close proximity (60 mm) showing a mean positional error of 8.7 mm and mean angular error of 16.7 degrees.