  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.
