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Stabilizing the relative position of millirobots inside an MRI scanner considering magnetic interaction forces

The concept of navigating groups of magnetically propelled particles through the fluid-filled passageways of the body provides the potential to perform highly localized diagnostic and therapeutic procedures. The use of MRI scanners to both navigate and propel millimeter-scale robots has received recent attention. MRI-based motion planning and control laws have been proposed that can achieve independent position control of multiple robots despite the system being underactuated, i.e., the same magnetic gradients are experienced by all the robots. To date, however, these analyses have neglected the magnetic interaction forces and torques between these robots. Thus, the question of whether or not the relatively weak gradients can stabilize the particles as they approach each other has remained open. This paper investigates this question by analyzing interaction forces and torques experienced inside an MRI scanner. It is shown that interaction torques can be neglected in the presence of the strong central field of the scanner. Using the reduced force-based model, a lower bound on separation distance is derived and it is shown that this bound could be achieved if the system was fully actuated. Considering underactuation, simulation demonstrates that Model Predictive Control can stabilize pairs of robots at separation distances 2.5-3 times the lower bound on separation distance.