Recently, ferromagnetic soft continuum robots – a type of slender, thread-like robots that can be steered magnetically – have demonstrated the capability to navigate through the brain's narrow and winding vasculature, offering a range of captivating applications such as robotic endovascular neurosurgery. Composed of soft polymers with embedded hard-magnetic particles as distributed actuation sources, ferromagnetic soft continuum robots produce large-scale elastic deflections through magnetic torques and/or forces generated from the intrinsic magnetic dipoles under the influence of external magnetic fields. This unique actuation mechanism based on distributed intrinsic dipoles yields better steering and navigational capabilities at much smaller scales, which differentiate them from previously developed continuum robots. To account for the presence of intrinsic magnetic polarities, this emerging class of magnetic continuum robots provides a new type of active structure – hard-magnetic elastica – which means a thin, elastic strip or rod with hard-magnetic properties. In this work, we present a nonlinear theory for hard-magnetic elastica, which allows accurate prediction of large deflections induced by the magnetic body torque and force in the presence of an external magnetic field. From our model, explicit analytical solutions can be readily obtained when the applied magnetic field is spatially uniform. Our model is validated by comparing the obtained solutions with both experimental results and finite element simulations. The validated model is then used to calculate required magnetic fields for the robot's end tip to reach a target point in space, which essentially is an inverse problem challenging to solve with a linear theory or finite-element simulation. Providing facile routes to analyze nonlinear behavior of hard-magnetic elastica, the presented theory can be used to guide the design and control of the emerging class of magnetically steerable soft continuum robots.

最近，铁磁软连续体机器人一种纤细的，可以像电磁一样操纵的线状机器人，已经展示了在大脑狭窄而弯曲的脉管系统中导航的能力，提供了一系列引人入胜的应用，例如机器人血管内神经外科手术。铁磁软连续介质机器人由具有嵌入的硬磁颗粒作为分布的致动源的软聚合物组成，通过外部磁场的作用下，由固有磁偶极子产生的磁转矩和/或力产生大规模的弹性变形。这种基于分布式固有偶极子的独特致动机制可以在更小的范围内产生更好的操纵和导航功能，从而使其与先前开发的连续介质机器人区分开来。考虑到本征磁极性的存在，硬磁弹性–表示具有硬磁特性的细的弹性条或棒。在这项工作中，我们提出了一种用于硬磁弹性的非线性理论，该理论可以准确预测在存在外部磁场的情况下由磁体转矩和力引起的大挠度。根据我们的模型，当施加的磁场在空间上均匀时，可以轻松获得明确的解析解。通过将获得的解与实验结果和有限元模拟进行比较来验证我们的模型。然后，将经过验证的模型用于计算机器人的末端达到空间目标点所需的磁场，这本质上是一个逆向问题，要用线性理论或有限元仿真来解决。