Optimization-based formation control of underactuated magnetic microrobots via inter-agent forces

This paper presents a new optimization-based method to control three micro-scale magnetic agents operating in close proximity to each other for applications in microrobotics. Controlling multiple magnetic microrobots close to each other is difficult due to magnetic interactions between the agents, and here we seek to control those interactions for the creation of desired multi-agent formations. Our control strategy arises from physics that apply force in the negative direction of states errors. The objective is to regulate the inter-agent spacing, heading and position of the set of agents, for motion in two dimensions, while the system is inherently underactuated. Simulation results on three agents and a proof-of-concept experiment on two agents show the feasibility of the idea to shed light on future micro/nanoscale multi-agent explorations. Average tracking error of less than 50 micrometers and 1.85 degrees is accomplished for the regulation of the inter-agent space and the pair heading angle, respectively, for identical spherical-shape agents with nominal radius less than of 250 micrometers operating within several body-lengths of each other.