Page 23 - Read Online

Blewitt et al. Soft Sci 2024;4:13 https://dx.doi.org/10.20517/ss.2023.49 Page 5 of 26

the robot will be better known which is vital for mapping and navigation.

Mesh worms are a type of earthworm robot made from a single piece of mesh as opposed to a series of
actuators. Such materials, akin to those seen in McKibben Actuators, elongate when their diameter is
shortened due to the nature of their geometry. Mesh worms can use soft actuators such as Shape Memory
Alloys and nickel-titanium wrapped around a mesh tube to create a smaller diameter and, hence, elongation
[22]
at points along the mesh . The sequence of this actuation around the mesh creates a peristaltic locomotion.
Other mesh worms, such as the Compliant Modular Mesh Worm (CMMWorm) presented in Figure 3B
[23]
and Softworm presented in Daltorio et al., make use of traditional actuators such as servomotors which use
a cable-driven mechanism to contract the mesh . Softworm was actuated using 12 hoop actuators pulled
[24]
by a single motor. The hoop actuator contracts sections of a helical mesh which is reinforced with
longitudinal springs to return it to its initial state after contraction. Daltorio et al. model each segment as a
rhombus to calculate the lengthening under actuation whilst also using a spring-mass model to determine
[24]
the forces acting on the pipe . The size of the motors and mesh structures mean they are more suited for
medium-sized pipes (> 75 mm Ø); CMMWorm was demonstrated for use in a 152 mm Ø pipe .
[23]
Wall-press ability
In pipe inspection robotics, the robot’s capability to create sufficient friction with the pipe walls is called
wall-press ability, which is vitally important for load carrying and vertical climbing. Ideally, a robot would
be able to create enough force to carry its own weight and an additional extra load. Dai et al. developed an
earthworm made from tensegrity structures that were actuated using linear solenoids which bent the
structures to create a force on the pipes, with the resulting earthworm mechanism capable of traversing 155
[25]
to 195 mm pipes with a gripping force of 55 N in the 155 m pipes and 30 N in the 195 mm pipe . Dai
demonstrated the robot’s ability to carry an 850 g load in a 195 mm pipe. It is more common for earthworm
robots to be made from pneumatic actuators such as PAMs akin to the one developed by Sato et al.
[26]
[Figure 3C]. Sato et al. used axially reinforced PAMs where a single unit is capable of a 300 N traction force
in a 102 mm pipe . The robot, by contrast, only weighed 6.3 kg, and thus, it could carry a load vertically.
[26]
However, creating as much traction force in smaller pipe diameters is more difficult as friction is
proportional to contact area and smaller actuators in smaller pipes will create less contact area. One way to
enhance wall-press ability in smaller earthworm robots is to increase the number of units contracted at a
time. However, this action can affect the robot motion by decreasing its speed.

Motion
When considering peristaltic motion in earthworm mechanisms, speed is not just a question of fast
actuation but also of optimising the motion. For an Earthworm mechanism, the motion can be defined in
terms of “Wavelength”, “Propagation speed” and “Number of waves” [Figure 4]. At any time within a
peristaltic Earthworm mechanism cycle, some number of units will be elongated, with this number referred
to as “Wavelength” (l). To move, the number of units gripping the pipe will shift back by a set number of
units referred to as the “Propagation Speed” (s). Lastly, an Earthworm mechanism can have more than one
group of gripping units actuated at a time, a number referred to as “Number of Waves” (n). By convention,
an Earthworm motion pattern can be described by l-n-s [20,21,27] . For example, the motion pattern in Figure 4
may be described as 4-1-1.

We can use these values to calculate the speed of the robot. If we know the length of contraction of a single
unit r, and the time each unit takes to contract t, then for N unit-long robots, the distance moved is d . As a
w
wave of gripping units propagates from head to tail, d and the time taken T can be given by Equations (1)
w
w
and (2).