---
kind: concept
slug: magnetic-actuation
title: Magnetic actuation
summary: >-
  Moving a small body with an external magnetic field instead of onboard power. A rotating field makes a magnetized millirobot roll, flip, swim or steer, and a short pulse makes it jump. A haptic loop lets an operator feel a field-driven micro-robot. The trade-off: the body must respond to the field, and its motion follows the field.
tags: [robotics, magnetic-actuation, locomotion, drug-delivery, micromanipulation, haptics]
papers: ["2203.10122", "2412.06917"]
related: [teleoperation, haptic-feedback-rendering]
status: draft
updated_at: 2026-10-25
---

## Overview

Magnetic actuation drives a body from outside. A magnetized part of the body
responds to an applied field B. For a permanently magnetized plate with volume
V and magnetization M, the torque is T = V(M × B), which rotates M toward B
[arxiv:2203.10122 p. 4]. A rotating field therefore gives continuous rotation,
and the way the field's rotation plane sits relative to the body decides how
the body moves [arxiv:2203.10122 p. 4, fig. 1E-G]. Paramagnetic microparticles
also respond to a field, but they take their magnetization from the field
rather than carrying a permanent one [arxiv:2412.06917 p. 10-11]. The torque
formula above does not describe them, and the haptic paper gives no force law
for its actuation term [arxiv:2412.06917 eq. 1].

Its main appeal for very small devices is that the power source sits outside
the body. Nothing has to be on board except the magnetic part. This is why the
field is the control input for the whole design: the same field that rolls the
robot on ground can also make it swim, jump or pump, depending on how it is
aimed, how strong it is and how it changes in time [arxiv:2203.10122 p. 6-8].

Two papers cover this page. The Kresling origami millirobot is a single
robot whose results are author-reported, mostly from bench tests and ex vivo
pig stomach experiments [arxiv:2203.10122 p. 17-18]. The haptic chapter is a
teleoperation framework for magnetically guided micro-robots, tested in three
single-trial lab experiments [arxiv:2412.06917 p. 11-13]. The variants below
are modes of the first robot, plus one control setup from the second.

## Variants

### Rotation-axis locomotion (rolling, flipping, swimming, steering)

A rotating field in a plane perpendicular to the body's long axis makes the
robot roll on ground. A plane parallel to the long axis makes it flip. In water,
spinning about the long axis turns the tilted panels into propeller blades and
drives it forward. Tilting the field's rotation axis steers the robot, since M
follows B within the rotation plane [arxiv:2203.10122 p. 3-4, fig. 1E-H]. The
paper reports rolling and flipping at 10 mT and 4 Hz on the ground, and a
self-adaptive switch from rolling to flipping when an obstacle blocks the
robot, with the field left unchanged [arxiv:2203.10122 p. 6, fig. 2A-B].
Card: [Spinning-enabled Wireless Amphibious Origami Millirobot](/papers/2203.10122).

### Impulsive jump

A short, strong field pulse pulls the magnetized plate around. Jump height and
distance depend on the field strength and on the angle theta between the field
and the plate's magnetization. The paper reports a 23.5 mm high and 56.2 mm
long jump at 40 mT and 120 degrees. Its sweep over theta shows that this single
angle is not the robot's general jump performance [arxiv:2203.10122 p. 7,
fig. 2E-F]. The pulse duration is not stated [arxiv:2203.10122 p. 7].

### Cyclic folding for liquid release

Two magnetic plates sit on opposite ends of a hollow body, with their
magnetizations at 90 degrees to each other. The sum of the two is the net
magnetization. A field along that sum twists the body one way and then the
other, and the inner cavity shrinks and pushes liquid out through cuts in the
wall. Repeating the fold and unfold releases liquid in steps. The paper reports
this at 200 mT [arxiv:2203.10122 p. 7-8, fig. 2G-H]. It gives no volume per
cycle, no dose accuracy and no residual volume, so the "controlled dose" claim
has no number behind it [arxiv:2203.10122 p. 8].

### Floating at the air-water interface

A captured air bubble lowers the robot's effective density so that it floats. A
field perpendicular to the surface releases the bubble [arxiv:2203.10122 p. 12,
fig. 3I]. The bubble holding depends on a surface treatment whose details sit
in the paper's supplementary material, not in the main text [arxiv:2203.10122
p. 12, p. 17].

### Haptic bilateral teleoperation of a field-driven micro-robot

A person moves a handheld haptic device, the master, and a magnetic field moves
the micro-robot, the slave, to follow. Motion is scaled down on the way to the
tool, and the interaction force is scaled up on the way back to the device, so
the operator can feel forces that are too small to feel directly [arxiv:2412.06917
p. 2, p. 8-9] [fig. 1]. A PI force loop compares the desired force with a
predicted one and can cancel the operator's input when the force would exceed
the allowed limit [arxiv:2412.06917 eq. 3] [p. 8-9]. The chapter reports three
single-trial experiments: an 8 µm steady-state tracking error for a microbead
[arxiv:2412.06917 p. 11] [fig. 4], a 0.4 µN force during cell penetration
[fig. 5] [p. 12], and a qualitative gas-bubble trial [p. 11-13]. The scale
factors, the gains and the sampling rate are not stated. The abstract promises
closed-loop stability, but no stability analysis appears in the text [p. 1,
p. 13]. Card: [Haptics in Micro- and Nano-Manipulation](/papers/2412.06917).

## When to use which

| Situation | Use | Why |
|---|---|---|
| Robot must move on ground and in water with one body | Rotation-axis locomotion, with the field's axis switched between modes | The paper's single body does both, at 10 mT and 4 Hz on ground and up to 81.2 mm/s swimming at 10 mT and 30 Hz [arxiv:2203.10122 p. 6, p. 10] |
| Robot must cross an obstacle without a change to the field | Self-adaptive switching between rolling and flipping | The paper reports this switch with one fixed field, and reports climbing stairs, a 30 degree incline and column arrays of about robot size [arxiv:2203.10122 p. 6-7, fig. 2C] |
| Robot must clear a gap or step in one move | Impulsive jump | The paper reports a 23.5 mm jump at 40 mT and 120 degrees, but only for one angle and one robot size [arxiv:2203.10122 p. 7, fig. 2E-F] |
| Robot must release a stored liquid in doses | Cyclic folding | The paper shows release by repeated folding at 200 mT [arxiv:2203.10122 p. 8, fig. 2H], with no dose or volume numbers to design against |
| Robot must work in a viscous fluid such as stomach-like liquid | Rotation-axis swimming at higher field and frequency | The paper's swimming demo in 12 mPa·s fluid uses 12 mT and 24 Hz, tested once [arxiv:2203.10122 p. 14, fig. 4H] |
| Operator must feel forces on a micro-robot that carries no sensor | Haptic bilateral teleoperation | The chapter scales the tool force up to the haptic device, but gives no scale factor or gains, and its experiments are single trials [arxiv:2412.06917 p. 2, p. 11-13] |
| Operator push must be limited so the robot does not overload tissue | PI force cancellation inside the haptic loop | The chapter describes the cancel rule [arxiv:2412.06917 eq. 3] [p. 8-9], but gives no gain values and does not show the stability it claims [p. 1, p. 13] |
| Robot must be fully free of batteries and wires | Any variant above | The only power input is the external field; the paper's coil setup covers a 160 x 120 x 80 mm workspace [arxiv:2203.10122 p. 17], and the haptic chapter uses four electromagnetic coils for its cell experiments [arxiv:2412.06917 p. 12] |

Real-world use outside a lab setting is not shown. All biomedical results are
ex vivo, and the coil setup is a small Helmholtz arrangement, not a clinical
system [arxiv:2203.10122 p. 8, p. 14, p. 17]. The haptic chapter's experiments
are in vitro or ex vivo, and it names in vivo use as a future goal
[arxiv:2412.06917 p. 13].

## Implementation sketch

Language-agnostic pseudocode of the common core: the torque from a magnetized
part in an applied field, and how the field's rotation plane selects the mode.
Thresholds in the mode rule are not from the paper.

```pseudocode
# Torque on a magnetized part in an applied field  [arxiv:2203.10122 p. 4]
# Input:  volume (scalar), magnetization (3,), field (3,)
# Output: torque (3,)

def plate_torque(volume, magnetization, field):
    # Torque is volume times the cross product of magnetization and field
    return volume * cross(magnetization, field)
```

```pseudocode
# Mode from the field's rotation plane  [arxiv:2203.10122 p. 4, fig. 1E-G]
# Input:  plane_normal (unit vector normal to the rotation plane),
#         long_axis (unit vector along the body), medium
# Output: mode name

def mode(plane_normal, long_axis, medium):
    # Spinning about the long axis in water gives propulsion [fig. 1G]
    if medium == "water":
        return "swimming"
    # Plane perpendicular to the long axis gives rolling [fig. 1E]
    # (the 0.99 cut-off is an implementation choice, not from the paper)
    if dot(plane_normal, long_axis) > 0.99:
        return "rolling"
    # Plane parallel to the long axis gives flipping [fig. 1F]
    return "flipping"
```

The paper does not give the magnetic moment of its plate, the mapping from
coil current to field, or the field's time profile [arxiv:2203.10122 p. 6].
Any controller built from this sketch has to measure or calibrate those
itself.

The mode rule covers only the rotating-field robot. The haptic chapter's
control loop needs a dynamics model, but it leaves the actuation, drag and
contact terms unspecified [arxiv:2412.06917 eq. 1] [p. 9], so a force loop
built on it has to take those terms from elsewhere.

## Contradictions

The two papers measure different things, so their numbers do not conflict.
Within the haptic chapter, the timings disagree. The Fig. 2 frame labelled
91.0 s does not match the 64 s engulfment time in the text [fig. 2] [p. 12],
and the Fig. 5 caption puts cell penetration at 21 s while the text gives about
66 s for uptake [fig. 5] [p. 12]. The chapter also says the force is scaled up
by about six orders of magnitude [p. 12], but its plots show the haptic-side
force in µN [fig. 4] [fig. 7]. Six orders of magnitude from µN would reach N,
and the plots do not show that. The scale factor is not given [p. 9] [p. 13].
Neither side is resolved here.

## Papers

- [Spinning-enabled Wireless Amphibious Origami Millirobot](/papers/2203.10122): a magnetically driven Kresling-origami millirobot that rolls, flips, swims, jumps, pumps and carries cargo under one rotating field.
- [Haptics in Micro- and Nano-Manipulation](/papers/2412.06917): a bilateral haptic teleoperation framework for magnetically guided micro-robots, with a PI force controller and three single-trial lab experiments.