Three-dimensional independent control of multiple magnetic microrobots via inter-agent forces

This article presents a method to independently control the position of multiple microscale magnetic robots in three dimensions, operating in close proximity to each other. Having multiple magnetic microrobots work together in close proximity is difficult due to magnetic interactions between the robots, and here we aim to control those interactions for the creation of desired multi-agent formations in three dimensions. Based on the fact that all magnetic agents orient to the global input magnetic field, the local attraction-repulsion forces between nearby agents can be regulated. For the first time, 3D manipulation of two microgripping magnetic microrobots is demonstrated. We also mathematically and experimentally prove that the center-of-mass external magnetic pulling of the multi-agent system is possible in three dimensions with an underactuated magnetic field generator. Here we utilize the controlled interaction magnetic forces between two spherical agents to steer them along two prescribed paths. We apply our method to independently control the motion of a pair of magnetic microgrippers as functional microrobot candidates each equipped with a five-degree-of-freedom motion mechanism and a grasp-release mechanism for targeted cargo delivery. A proportional controller and an optimization-based controller are introduced and compared, with potential to control more than two magnetic agents in three dimensions. Average tracking errors of less than 141 and 165 micrometers are accomplished for the regulation of agents' positions using optimization-based and proportional controllers, respectively, for spherical agents with approximate nominal radius of 500 micrometers operating within several body-lengths of each other.