Controllability and control synthesis of underactuated magnetic microrobots

The control of multiple magnetic microrobots is of particular interest for therapeutic applications. Yet the controllability of such a system is not straightforward since, on most of such systems designs, there is only a single control input per axis. The paper addresses the controllability and control synthesis for several magnetic microrobots navigating in blood vessels. First, controllability requires the microrobots to magnetically interact in order to achieve trajectory tracking along an admissible reference trajectory, whether swimming at low or high Reynolds. Then the resulting nonlinear system is shown to be diffeomorphic to different nonlinear canonical forms depending on the choice of the microrobots, so that the stabilization of the system along any admissible reference trajectory can be achieved using a backstepping controller synthesis, yet sometimes at the price of a zero dynamics stability analysis. Simulation results illustrate the efficiency of the proposed approach.