Material-based modeling for continuum soft robots

In Industry 4.0, a collaboration between humans and robots within a shared workspace marks a signif-
icant change concerning automated working environments where robots are completely separate from
humans. This innovative industrial concept necessitates fostering safe and sophisticated interactions be-
tween human workers and robotic counterparts. A groundbreaking solution to this requirement has been
developing new robotic mechanisms and manipulation devices. These devices are constructed from soft
polymeric materials, leading to their categorization as soft robots.
Soft robotics represents a burgeoning field of research that pioneers the use of flexible, compliant ma-
terials in constructing robotic structures. This new typology of robots stands out for their exceptional
dexterity and adaptability. It is paramount for efficiently navigating through and interacting with their
environments or precisely grasping and manipulating various objects. The inspiration behind the design
of soft robots stems from the natural world, drawing from the complex shapes and geometries found
in various animals and plants. This approach aims to replicate the innate efficiency and versatility ob-
served in nature, thereby enhancing the robots’ functionality and interaction capabilities. The research
community within this domain is deeply invested in advancing the principle of bio-inspiration in soft
robotics. This principle also spurs the development of smart materials that closely mimic the properties
and functionalities of biological tissues found in nature. These innovative materials significantly enrich
the overall design of soft robots, imbuing them with capabilities that allow for more natural and intuitive
interactions with their human counterparts and the environment. However, integrating these materials
also introduces substantial complexity to the modeling and control of soft robotic systems. Due to their
continuum structures, soft robots exhibit infinite passive degrees of freedom. This characteristic poses a
formidable challenge in creating accurate models and formulating effective control strategies that aptly
characterize the robots’ performance in terms of kinematics and dynamics.
As researchers strive to overcome these challenges, they are exploring sophisticated computational mod-
els and control algorithms that can adequately capture the unique behaviors of soft robots. This entails a
multi-disciplinary effort, combining insights from materials science, mechanical engineering, and com-
puter science to unlock the full potential of soft robots. In doing so, soft robotics promises to revolutionize
industrial processes and extend its benefits to other domains such as healthcare, search and rescue opera-
tions, and assistive technologies, where soft robots’ adaptive nature can make a significant impact.
The principal goal of this research is to have a modeling method that can accurately describe the mechan-
ical behavior of soft actuators in quasi-static and dynamic conditions. To achieve this, a methodology
that integrates advanced consideration of the mechanical properties of the elastomers into the procedure
is followed. In particular, the case studies this thesis considers are pneumatic actuators made up totally
or partially of self-healing polymers, a particular kind of smart material able to recover severe damage
to the structure. These materials are chosen because they allow the creation of bio-inspired soft contin-
uum structures that are less susceptible to occasional damage that usually occurs during tasks (like cuts,
penetration, tearing, and so on). Furthermore, these elastomers are recyclable, making their production
sustainable at a large scale. However, apart from the particular use case, the modeling approach presented
in this thesis can be applied to any elastomers used in soft robotics, which have non-linear constitutive
equations for elasticity and are afflicted by viscous effects in dynamic conditions that influence the soft
actuators’ mechanical performances. Hence, this dissertation stresses the soft robotic research commu-
nity’s need to link and consider the complicated mechanical properties of the elastomers in the modeling
process, defining the choice to use and following the material-based methodology. This methodology
aims to bridge the materials’ mechanical properties investigated through mechanical tests to the mechan-
ical performances of soft robotic actuators. More precisely, a constitutive equation is retrieved from the
tests that resume the material’s mechanical properties, catching the non-linearities and the viscous effects
of elastomer mechanics. Then, the equation is inserted in a finite element analysis simulation where the
model of the soft continuum actuator is produced. The finite element model is validated with experi-
mental tests on the prototyped actuator. Eventually, the model can be used to build a control scheme
involving the continuum mechanics equations and finite element analysis. Hence, this work results in
a multi-disciplinary procedure that unifies concepts from scientific fields like material science, robotics,
and computational mechanics. The FEA simulator used in this thesis is called Software Open Framework
Architecture (SOFA). It is an open-source simulator developed by the researchers of Institut National de
Recherche en sciences et Technologies du numérique (INRIA) in 2006. This simulator is chosen because
it can ensure fast and interactive simulations that properly deal with contact and collisions. Furthermore,
it is sustained by an active community to which the candidate became an active contributor during his
year of the PhD.
This thesis aims to answer several research questions to address the research work. Which steps compose
the material-based methodology, and how is the link made between the material and actuator levels? How
is this methodology adapted for quasi-static and dynamic conditions, and how do we behave concerning
multi-material actuators? Hence, it will be shown how the same methodology has been employed and
adapted for any showcase.
The first part of this dissertation tries to answer the first and second research questions by describing
one of the principal steps of material-based modeling: the material testing executed on self-healing elas-
tomers. In particular, uniaxial compression and tension tests are executed in quasi-static and dynamic
tests to adapt the material test condition to the soft actuator application conditions.
Based on the material analysis, the second part of this thesis tries to demonstrate that the materials’
specific non-linear mechanical properties and viscous effects in quasi-static and dynamic conditions are
reflected at the actuator level, resulting in one of this work’s main novelties. Hence, stressing the knowl-
edge of the material’s mechanical properties leads to a general modeling method independent of the
design geometry and the actuation and applicable to any elastomer used in soft robotics.