Nature provides a wide range of inspiration for building mobile micromachines that can navigate through confined heterogenous environments and perform minimally invasive environmental and biomedical operations. For example, microstructures fabricated in the form of bacterial or eukaryotic flagella can act as artificial microswimmers. Due to limitations in their design and material properties, these simple micromachines lack multifunctionality, effective addressability and manoeuvrability in complex environments. Here we develop an origami-inspired rapid prototyping process for building self-folding, magnetically powered micromachines with complex body plans, reconfigurable shape and controllable motility. Selective reprogramming of the mechanical design and magnetic anisotropy of body parts dynamically modulates the swimming characteristics of the micromachines. We find that tail and body morphologies together determine swimming efficiency and, unlike for rigid swimmers, the choice of magnetic field can subtly change the motility of soft microswimmers.

The goal of this article is to provide a thorough introduction to the state of the art in magnetic methods for remote-manipulation and wireless-actuation tasks in robotics. The article synthesizes prior works using a unified notation, enabling straightforward application in robotics. It begins with a discussion of the magnetic fields generated by magnetic materials and electromagnets, how magnetic materials become magnetized in an applied field, and the forces and torques generated on magnetic objects. It then describes systems used to generate and control applied magnetic fields, including both electromagnetic and permanent-magnet systems. Finally, it surveys work from a variety of robotic application areas in which researchers have utilized magnetic methods, including microrobotics, medical robotics, haptics, and aerospace.

The dipole approximation for magnetic fields has become a common simplifying assumption in magnetic-manipulation research when dealing with permanent magnets because the approximation provides convenient analytical properties that are a good fit at large distances. What is meant by “good fit at large distances” is generally not quantified in the literature. By using a parameterized multipole expansion and collaborating finite-element analysis (FEA) simulations to represent the magnet's field, we quantify the error associated with the dipole approximation as a function of distance from the permanent magnet. Using this expression, we find cylindrical, washer, and rectangular-cross-section bar permanent-magnet aspect ratios that minimize the error of the dipole approximation. For cylinders and rectangular-cross-section bars, these aspect ratios are a diameter-to-length ratio of √{4/3} and a cube, respectively.

In this paper we apply Cosserat rod theory to catheters with permanent magnetic components that are subject to spatially varying magnetic fields. The resulting model formulation captures the magnetically coupled catheter behavior and provides numerical solutions for rod equilibrium configurations in real-time. The model is general, covering cases with different catheter geometries, multiple magnetic components, and various boundary constraints. The necessary Jacobians for quasi-static, closed-loop control using an electromagnetic coil system and a motorized advancer are derived and incorporated into a visual-feedback controller. We address the issue of solution bifurcations caused by the magnetic field by proposing an additional, stabilizing control method that makes use of system redundancies. We demonstrate the effectiveness of the model by performing 3D tip-position trajectories with root-mean-square distance errors of 2.7 mm in open-loop, 0.30 mm in closed-loop, and 0.42 mm in stabilizing closed-loop modes. The stabilizing controller achieved on average a factor of 1.6 increase in the restoring wrenches for the least stable direction.

Numerous magnetic-manipulation systems have been developed to control objects in relatively large workspaces. These systems vary in their number of electromagnets, their configuration, and their limitations. To date, no attempt has been made to rigorously quantify how many electromagnets are required to perform a given magnetic manipulation task. For some tasks, such as controlling the field at a point, the answer is clear: the same number as dimension of control. For tasks that apply magnetic forces on an object, the answer is less clear, and some systems, which have more control magnets than kinematic degrees of freedom (DOFs), have demonstrated unexpected singularities that only arise at specific object orientations. This paper provides a general analysis for static electromagnetic systems rooted in the governing magnetic equations and proves an unintuitive result. That is, if only magnetic fields and forces are used to control an unconstrained magnetic object, four magnetic sources are required for 3-DOF force control and eight magnetic sources are required for orientation-independent 5-DOF force and heading control.