Scale-inspired programmable robotic structures with concurrent shape morphing and stiffness variation

1 Working principle #

SAILS is a base layer with a row of scales attached to it, both printed from TPU and covered with PTFE tape to reduce friction. Each scale is bonded to the base layer on one side, and the whole structure is sealed between two latex films. With no pressure applied, the scales and the base layer are barely coupled, so the structure can be rolled up or sag under its own weight. A negative pressure of 90 kPa presses the patterned surfaces together until they interlock: the structure takes the shape its patterns were designed for and becomes stiff.

The patterns come from the target shape itself, by a method the paper calls layered tessellation. A sinusoidal cutting surface drawn along the middle of the target splits it into two layers. Each layer is divided into small units and flattened by rotating them, a thin supporting sheet is added to its back, and the upper layer is cut into scales short enough that their patterns still match the base layer when the structure lies flat. Pressed back together, the patterns mesh fully only in the shape they were cut from, which is why the structure returns to it.

1  Print

2  Deburr

3  Tape

4  Bond

5  Seal

6  Trim and test

2 Programmed shapes #

The same method programs many shapes. For surfaces that can be flattened without stretching, the target shapes, the finite element simulations and the experiments agree within a root mean square error of about 5%: a hook whose curvature grows toward its free end, a wave, a helix, which needs the patterns turned to 70.62°, and two surfaces defined by splines.

A single structure bends in only one direction, so domes and saddles are approximated with three-by-three meshes, to within about 10% of the target. The dome unfolds from a folded state and then holds 50 g, more than four times its own weight.

TargetSimulationExperimentDistance from target

Hook

Wave

Helix

Spline 1

Spline 2

TargetSimulationExperimentDistance from target

Dome

Saddle

3 Stiffness variation #

In three-point bending, a 2 mm thick structure with four scales stiffens as the pressure rises. Its apparent bending modulus goes from 9.8 MPa with no pressure to 36.8 MPa at 5 kPa and 58.7 MPa at 90 kPa, about six times, and it is similar whether the scales face up or down.

Thicker structures stiffen much more. From 1 to 6 mm, the modulus at 90 kPa grows from a few times to 53 times the modulus with no pressure, more than the 10 to 26 times of many jamming-based structures, while SAILS stays among the thinnest of them.

More scales make a structure softer but let it reach its target shape more closely, and changing the material's stiffness or the friction between the layers shows the same trade-off. The finite element models behind these results, in Abaqus/Explicit, are 3D for the shapes above and 2D plane strain for the bending tests. They treat the printed TPU as linear elastic (55.7 MPa) and the latex as neo-Hookean (1.1 MPa), use friction coefficients measured on an inclined plane, and reproduce both the bending tests and the morphed shapes.

4 An amphibious soft robot #

Three segments of SAILS, each with a chamber on either side, make a soft robot that moves like an eel or a snake. Actuating the chamber on one side or the other bends a segment up or down. A Raspberry Pi switches six solenoid valves on a vacuum pump. Actuating the chambers in turn, with each segment a quarter period behind the last, sends a wave along the body that drives the robot forward on ground; the reversed sequence makes it swim.

The robot climbs a 10 mm obstacle and crosses from land into water, squeezes through gaps that narrow from 20 to 8 mm, carries 50 g, nearly twice its own weight, and climbs a 22° slope. It is fastest at 0.56 Hz on ground and 1.25 Hz in water, where it reaches 0.34 body lengths per second, and models of both cases match the measured speeds.

5 A bridge and a shield #

A larger robot, twice as thick and as wide and about twice as long, puts the stiffness to work. After crawling over an obstacle, it stiffens into a bridge for a toy car. It covers a quail egg and shields it from a falling 50 g ball that breaks the egg without protection, and it carries 1.26 kg, seven times its own weight.

6 Adaptive landing gear for a drone #

Hook-shaped landing gear made of SAILS turns its stiffness into adjustable impact protection. A Raspberry Pi, a vacuum pump, valves and a pressure gauge on the drone set the gear's pressure.

In drop tests, a stiffer gear gives a higher peak force when the drone falls 3 cm, but a lower one when it falls 20 cm. Simulations of the gear under compression explain why: at low pressure the soft gear collapses until its fixed end hits the ground, while the gear at 90 kPa does not. The gear deploys in flight before landing, and it also works as a gripper, lifting a 225 g load that the drone then carries off.

BibTeX #

@article{chen2024scale,
  title = {Scale-inspired programmable robotic structures with concurrent shape morphing and stiffness variation},
  author = {Chen, Tianyu and Yang, Xudong and Zhang, Bojian and Li, Junwei and Pan, Jie and Wang, Yifan},
  journal = {Science Robotics},
  volume = {9},
  number = {92},
  pages = {eadl0307},
  year = {2024},
  doi = {10.1126/scirobotics.adl0307}
}