Modeling and control of magnetically actuated micro/milli robots position under laminar flow

The goal of this study is to model and control the position of micro- and milli-scale robots (MMRs) under laminar flow for multiscale robotic applications. A conceptual design depending on Lagrange point-based manipulation of the MMRs is proposed. The design includes a channel between two cylindrical permanent magnets that are used as the magnetic actuator. Spherical magnetic MMRs are placed in this channel with a diameter range of 0.25–1 mm. First, an analytical permanent magnet model is implemented. Following this, an adaptive mathematical model is built considering the dynamic magnetic forces on the MMRs. The position of the MMRs is analyzed for different parameters such as the channel dimension, the magnet diameter and distance, the type of the surrounding liquid, and the Re number. It is observed that there are considerable fluctuations during the positioning. Also, there is a deviation from the Lagrange point due to the significant drag forces caused by the laminar flow. To overcome these fluctuations and the deviation, an I-PD controller is implemented. Then, the position of the MMRs is analyzed with similar parameters in the presence of the controller. Results indicated that it is possible to control the MMR position at the Lagrange point by the I-PD controller, with a 14 % maximum overshoot.