Magnetic actuation

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 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 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 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 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 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 2203.10122 p. 17-18. The haptic chapter is a teleoperation framework for magnetically guided micro-robots, tested in three single-trial lab experiments 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 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 2203.10122 p. 6, fig. 2A-B. Card: Spinning-enabled Wireless Amphibious Origami Millirobot.

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 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 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 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 2412.06917 eq. 3 p. 8-9. The chapter reports three single-trial experiments: an 8 µm steady-state tracking error for a microbead 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.

When to use which

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 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 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.

# 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)

# 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 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 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: 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: a bilateral haptic teleoperation framework for magnetically guided micro-robots, with a PI force controller and three single-trial lab experiments.