IEEE Robotics & Automation Magazine - September 2023 - 117

modeled as rigid-soft hybrid robots with contact dynamics.
This example demonstrates that we can use the SoRoSim
toolbox to analyze robotic systems with collision and contact
events.
UNDERWATER ROBOTICS
Due to their compliant nature, soft robots pose no risk to underwater
habitats or organisms, making them an excellent choice to
employ in underwater exploration. Bacteria-inspired flagellate
propellers could be employed for the locomotion of robots
underwater. The idea of soft propellers is based on the observation
that an inclined rotation of a soft filament in a liquid environment
generates a helical filament shape, which produces
positive thrust for propulsion. An advanced version of an underwater
robot propelled by four soft flagellate modules is presented
in [14], with experimental validations of the dynamic
simulation. For those simulations, the authors used custommade
MATLAB codes with constant strain (order 0 strain polynomials)
approximations. Here, using the SoRoSim toolbox, we
demonstrate the variable-strain dynamics of a similar system
with a propeller consisting of three flagella [Figure 9(a)].
To rotate the filaments in an inclined fashion, we attach
them to the terminals of a rigid body, namely, the hook [the
inset in Figure 9(a)]. All hook terminals have an inclination
of 45º with the local x-axis. They are also separated by a
rotation of 120º with respect to one another. The hook is
connected to a motor shaft that provides the required torque.
Additional components, such as motors, electronics, the battery,
and balancing weights, are kept inside the spheroidal
shell of the robot. We create a SorosimLinkage consisting
of six links: the shell, shaft, hook, and three filaments.
The shell is modeled as a rigid link with an adjusted inertia
matrix to account for the internal components and spheroidal
(nondefault) shape. Its joint is a passive prismatic joint that
allows translation only along the x-axis. The shaft is modeled
as a cylindrical rigid link with an angle-controlled revolute
joint to simulate the motor's input to the propeller. The hook
is modeled as a fixed-joint rigid link with an adjusted inertia
matrix to account for its shape. Finally, we define the three
0.7-m-long soft filaments as fixed-joint soft links with linear
angular strains (torsion about the x-axis and bending about
the y- and z-axes). The dimensions and material properties of
these components are arbitrary but inspired by the proposed
design in [14].
To simulate the fluid-robot interaction forces described
in Figure 9(a), we need to include the external forces due to
the presence of the fluid (buoyancy, drag, and lift forces) and
the forces due to the volume of fluid moved by the propeller
(added mass), described in [14], that are not part of the default
force inputs during the SorosimLinkage creation. However,
this does not prevent the user from implementing them using
the " CustomExtForce.m " function.
By providing an actuation input of
ir2 t ,=
we run the
simulation to capture the system's dynamic response for the
first 5 s. Figure 9(b) presents superimposed images of the
motion of the robot, starting from rest to ..t 15 s=
In the inset,
we plot the robot's forward velocity as a function of time.
The combination of actuation and environmental interaction
leads to the emergence of intelligent helical deformations of
the filaments, which, in turn, cause a thrust that propels the
robot forward. This example emphasizes the usefulness of
the SoRoSim toolbox in modeling rigid-soft hybrid underwater
robots. The toolbox can model the robots mentioned
Figure 1(c) and (g) in a similar way.
DESIGN ANALYSIS AND CONTROL APPLICATIONS
In addition to static equilibrium analysis and dynamic simulations,
we can use the toolbox for design optimization,
inverse kinematics, and control applications. In this section,
we demonstrate examples of an optimization problem and
two control problems that can be solved using the SoRoSim
package and custom-made MATLAB codes.
DESIGN OPTIMIZATION
Here, we demonstrate the use of the toolbox in optimizing an
objective function based on the static equilibrium of a single
cable-actuated soft manipulator. We begin by defining a soft
0.5
0.4
0.3
0.2
0.1
-0.1
-0.2
-0.3
-0.4
0.4 0.2
Y (m)
Gravity
Drag
Lift
Drag
Buoyancy
0 -0.2 -0.4 0
(a)
0.4
0.2
t = 0 s
-0.2
-0.4
0.5
X (m)
-0.5
(b)
FIGURE 9. Underwater robotics. (a) The forces acting on the robot,
with an inset showing the hook geometry. (b) The motion of the
flagellate robot (superimposed images) due to the thrust generated
by the soft propeller, with an inset showing the robot's speed versus
time. Dotted lines show the tip trajectory of each soft filament.
SEPTEMBER 2023 IEEE ROBOTICS & AUTOMATION MAGAZINE
117
0.4 0.2
1.5 s
-0.2
Y (m)
0.2
0.6
0.4
0.2
02 4
Time (s)
0.4
X (m)
0.6
Z (m)
Z (m)
Velocity (m/s)
IEEE Robotics & Automation Magazine - September 2023

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