Controlling magnetic microswimmers toward 3-D manipulation tasks has received considerable attention. Although related studies on manipulating helical microswimmers have been developed, stable closed-loop controls and accuracy swimming models should be still investigated. This article addresses the problem of 3-D path following for magnetically driven helical microswimmers with an adaptive-compensation scheme. The orientation-compensation model in the global coordinate frame is learned by radial basis function (RBF) networks trained with backpropagation algorithms, which is used to express the motion of the helical microswimmer in the presence of the weight of the swimmer and lateral disturbances from the boundary effects. A proxy-based sliding-mode control (PSMC) approach is developed to design stable controllers based on the kinematic error model. The effects of variable parameters and boundary effects are also considered. Experimental results including different paths in 3-D space validated the path following with submillimeter accuracy using the helical microswimmer. Note to Practitioners —This article is motivated by the issue of the following predefined paths for magnetically driven helical microswimmers in 3-D space. The proposed closed-loop controller employs the error model in 3-D space to formulate the control law according to an orientation-compensation model learned by neural networks. It is demonstrated that the helical microswimmer is able to follow different paths in 3-D space with submillimeter accuracy using the proposed control scheme.

中文翻译：

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带有自适应方向补偿模型的螺旋微泳器的3D路径跟随

控制磁性微游泳器执行3-D操作任务已引起了广泛的关注。尽管已经开发了有关操纵螺旋微游泳器的相关研究，但仍应研究稳定的闭环控制和精确游泳模型。本文针对具有自适应补偿方案的磁驱动螺旋微扫描器的3-D路径跟踪问题。通过使用反向传播算法训练的径向基函数（RBF）网络学习全局坐标系中的方向补偿模型，该网络用于在游泳者的体重和来自游泳者的横向干扰的情况下表达螺旋微游泳器的运动。边界效应。开发了一种基于代理的滑模控制（PSMC）方法，以基于运动学误差模型设计稳定的控制器。还考虑了可变参数的影响和边界影响。实验结果包括在3-D空间中的不同路径，使用螺旋微扫描仪以亚毫米精度验证了该路径。执业者注意 —本文的灵感来自于3-D空间中磁驱动螺旋微扫描器的以下预定义路径问题。所提出的闭环控制器根据神经网络学习的定向补偿模型，利用3-D空间中的误差模型来制定控制律。事实证明，使用所提出的控制方案，螺旋微扫描器能够以亚毫米级的精度在3-D空间中遵循不同的路径。