Automated Control of Microparticle Swarm in a Rotating Gradient-Based Magnetic Field

The magnetic micromanipulation of swarm microparticles has attracted considerable attention because of its advantages of non-invasiveness, high drug-carrying capacity, and easy observation in the targeted delivery in in-vivo environments. This paper presents an automated control scheme for the magnetic micromanipulation of microswarms in a rotating gradient-based field. Different from the rotating uniform magnetic field generated by Helmholtz coils, the rotating gradient-based field is a type of convergent field established by sequentially powering each coil of the electromagnetic coil system. By changing the coil currents, the field can rotate while driving the microswarm to a pre-determined position, facilitating the swarm localization and tracking. According to the preliminary motion characterization of the swarm in the rotating gradient-based field, an intuitive trapping dynamic model which can simplify the analysis of swarm dynamics is established to facilitate controller design. Based on this model, a super-twisting sliding mode estimator is first designed to estimate the position of the microswarm as well as the disturbances caused by parameter variations and unmodeled dynamics. A robust controller is then developed based on the estimator. In this way, closed-loop manipulation of the microswarm to follow a desired trajectory in the rotating gradient-based field is realized, and the system's behavior has been significantly improved due to the capability to estimate disturbances. The proposed control scheme for the rotating gradient-based field has the potential to avoid volume loss and unexpected drug diffusion of the swarm when facing complex in-vivo environments. The stability of the control scheme is proved by the Lyapunov approach. Experiments are finally performed to demonstrate the effectiveness of the proposed control approach in a collision-free environment and in a simulated channel. Note to Practitioners-The motivation of this study is to realize automated feedback control of the microparticle swarm in a rotating gradient-based magnetic field. The rotating gradient-based magnetic field is a type of convergent field that can rotate while driving the microswarm to a pre-determined position. This magnetic actuation method facilitates microswarm tracking and enables microagents to overcome static friction with the bottom substrate by rotating them, thereby inducing movement. However, existing research on the rotating gradient-based magnetic field concentrates on moving the microswarm to the targeted position without real-time visual guidance in an open-loop manner, which provides less reliability and convenience compared to real-time closed-loop control. Moreover, it will result in unavoidable volume loss when collisions happen in the complicated environments. In addition, the existing swarm dynamics in such a field need to be simplified to apply in controller design. To solve the above problems, an automated point-to-point navigation control scheme is proposed in this study. An intuitive trapping model is first established to simplify the swarm dynamics. Then, a robust controller with a super-twisting algorithm-based estimator is designed based on the model to manipulate the microswarm. Experimental results have shown that the proposed method can successfully control the microparticle swarm in collision-free environments and a simulated channel with considerable accuracy in the rotating gradient-based magnetic field. The proposed control scheme has the potential to avoid volume loss and unexpected drug diffusion of the swarm when facing complex in-vivo vascular environments, particularly those involve fluids with completely different directions in a bifurcation, such as the vascular network of lymphatic vessels and blood vessels.