Model Predictive Control of Magnetic Helical Swimmers in Two-Dimensional Plane

Abstract

Magnetic micro/mini-swimmers have a great potential application in biomedical research and have gained broad attention. Recent research studies focus on the automatic control methods of magnetic micro/mini-swimmers, such as artificial intelligence methods. However, their autonomous manipulation remains a challenge since they are subject to various disturbances from the external environment and model uncertainties. The current methods employ a status observer to estimate these disturbances and uncertainties. In this paper, we apply a data-driven technique that utilizes the nonlinear approximation ability of neural networks (NNs). To be specific, a flexible structure of NNs, Broad Learning System (BLS), is employed to model the input-output mapping relationship between the direction of the rotating magnetic field and the swimming direction of the helical miniature swimmer. Then, according to the dual-variable decoupling control, a levitation controller is formulated and a path following controller is proposed based on a planar three-degree-of-freedom model of magnetic helical swimmers, which is inspired by the model of wheeled mobile robots. Simulations and experiments are conducted to quantitatively validate the proposed control method using different planar paths. The experiment results show that the mean absolute error of the path following control is about 3 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\%$</tex-math> </inline-formula> of the body length which is less than 0.5 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$mm$</tex-math> </inline-formula> . Our proposed control method provides a preliminary study to alleviate the impact of disturbances and uncertainties on the control performance of magnetic micro/mini-swimmers. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is mainly motivated by the potential application of artificial intelligence methods in magnetic micro/mini-robot community, especially for the applications that reject disturbances and uncertainties. In practice, a path planner is employed to compute a pre-defined reference path that connects the start and the targeted locations. Then our control method is applied to the magnetic helical swimmer and it is guided to follow the reference path. Tackling external disturbances and model uncertainties is still challenging during the control progress. Neural network-based technique is an intuitive approach since their nonlinear modeling ability and generalization are suitable for estimating these disturbances and uncertainties. As for training the neural-network model, the training data about the angle parameters should be recorded by manual control of the helical swimmer. These angle parameters define the rotating axis of the uniform rotating magnetic field and the self-rotating axis of the magnetic helical swimmer. According to the planar motion model, the optimal controller is formulated using the feedback distance error and angle error, and the sum of the control signal and the prediction of the compensating model is used as the final control input. Our electromagnetic coil system features easy operation and configuration of cameras or other sensors. Simulations and experiments validate the performance of the neural network-based compensating method and the proposed optimal control method using magnetic micro/mini-swimmers.