IEEE Robotics & Automation Magazine - September 2023 - 107

rather than real mechanical systems. TMTDyn is a geometrically
exact package based on the parametrization of positions
and orientations rather than strains. Within this scenario, we
present SoRoSim, which is a MATLAB toolbox based on the
GVS approach and that directly extends rigid robot modeling
techniques to soft and hybrid systems while maintaining
a high level of accuracy. The toolbox takes advantage of the
high fidelity of the Cosserat rod approach and the simplifying
assumptions of the GVS approach that minimize the number
of DoF required to represent the system and provide a geometrically
exact framework, leading to accurate, fast, and
computationally less expensive results. We implement a new
computational approach based on a nested Gaussian quadrature
scheme to solve the GVS formulation.
The SoRoSim toolbox allows the user to define and manipwrite
robot-specific scripts for the simulation, design optimization,
and model-based control of specific manipulators by
providing user-friendly, accurate, fast, and reliable algorithms.
Popular examples of such platforms include, Soft Motion
(SoMo) [4], a Python-based toolbox to simulate continuum
manipulators as approximated spring mass systems, and Simulation
Open Framework Architecture (SOFA) [5], a simulation
tool that employs simplified FEMs. Toolboxes such as
ChainQueen [6] and SimSOFT [7] also employ FEM-based
modeling techniques to simulate soft robots. Titan [8], which
is a GPU-accelerated C++ library, is another example of a
simulator that models soft robots as a spring mass system.
Toolboxes based on DERs include Elastica [9], which employs
the Cosserat rod theory to model and control slender bodies
with a finite number of lumped DoF, and Volume Invariant
Position-based Elastic Rods (VIPER) [10], which uses a volume-invariant
position-based elastic rods model to simulate
the behavior of muscular hydrostats (muscle-like). Finally, the
MATLAB package TMT Dynamics (TMTDyn) [11] uses discretized
lumped systems and reduced-order models to control
and analyze hybrid rigid-soft robots.
The majority of the available toolboxes for soft robotics
modeling are based on FEM and lumped mass systems.
These are theoretically simple but computationally heavy
approaches, with a lot of nodes and DoF, designed for generalpurpose
simulation instead of analysis and control. Most of the
DER-based simulators are oriented toward computer graphics
ulate links (rigid and soft) and robotic systems (linkages) using
user-friendly GUIs and the MATLAB workspace. The GUIs
assist the definition of links, the links' assembly, the definition
of the links' DoF, the assignment of constraints as closed-loop
joints, and the application of external and actuation forces.
A variety of typical external forces and actuation inputs are
handled by GUIs, which provides a black-box experience,
allowing users from all backgrounds to easily use the toolbox
to perform static and dynamic analyses. The toolbox provides
specific MATLAB files that the user can edit to input customized
values of external and actuation forces as functions
of joint coordinates, their derivatives, positions, velocities,
and so on. Moreover, as a MATLAB toolbox, it can be used
alongside built-in functions; add-ons, such as the Optimization
Toolbox; and user-written codes to further facilitate the analysis
and control of robotic systems. The intrinsic limitation
of the toolbox is that it can model soft links only as Cosserat
rods. However, rigid links can be modeled with no limitation
on geometry and DoF. Figure 1 shows a small subset of robotic
systems the toolbox can analyze. The SoRoSim toolbox package
and user manual are available for free on [15]. The " Toolbox
Design and Structure " section provides details on various
aspects of SoRoSim toolbox, including its design, structure,
and workflow.
We perform several toolbox sanity tests by comparing the
toolbox's analysis results with published data and commercial
software output. We compare the static equilibrium results with
published solutions and ANSYS workbench results. We study
the dynamic simulation of a flexible flying rod and compared it
with existing literature. We also investigate the energy transfer
among the kinetic, gravitational potential, and elastic potential
energy of a cantilever beam under gravity. We discuss these
validation studies in the " Toolbox Validation " section. In addition
to validation, in the " Modeling Applications " and " Design
Analysis and Control Applications " sections, we demonstrate
four innovative applications where the soft robotics community
can use the toolbox. The examples include the analysis of
the static equilibrium and contact dynamics of hybrid robotic
arms, an underwater locomotor, a design optimization problem,
and a study of two cases of inverse dynamic control problems.
Finally, in the " Discussion and Conclusion " section we
SEPTEMBER 2023 IEEE ROBOTICS & AUTOMATION MAGAZINE
107
IEEE Robotics & Automation Magazine - September 2023

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