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Mechanics–Based Virtual Prototypingof Robots with Deformable
Bodies and
Flexible Joints
Stanislao Grazioso(B), Giuseppe Di Gironimo, and Antonio
Lanzotti
Fraunhofer Joint Lab IDEAS, Dipartimento di Ingegneria
Industriale,Università degli Studi di Napoli Federico II,
P.le Tecchio 80, 80125 Naples,
Italy{stanislao.grazioso,giuseppe.digironimo,antonio.lanzotti}@unina.it
Abstract. This paper describes a mechanics–based framework for
vir-tual prototyping of soft robots, i.e. robots with deformable
bodies andflexible joints. The framework builds on top of the screw
theory, and usesgeometrically exact nonlinear beam models for
describing the behavior ofdeformable bodies, aswell as the finite
elementmethod for space discretiza-tion.The computer implementation
of this framework results in SimSOFT,a physics engine for soft
robots. The capabilities of the framework are illus-trated with one
general example, an articulated chain of rigid and soft
linksconnected through rigid and flexible joints. Furthermore,
several case stud-ies are shown for industrial and medical
applications.
Keywords: Virtual prototyping · Design methods · Soft robotics
·Continuum mechanics · Multibody dynamics
1 Introduction
The standard hypothesis underlying robot modeling, simulation
and control isthat manipulators consist of a discrete set of rigid
bodies connected by joints;this is valid for most of industrial
robots working at slow motion and with smallinteraction forces [1].
However, in real conditions, mechanical flexibility can arisedue to
the particular geometric configuration and external loads that the
robotsundergone during operations, or it is introduced on purpose
to let the robothaving a more compliant behavior. With this
respect, the need for developinghuman–friendly and collaborative
robots has led to the introduction of flexibleelements inside the
joints: the literature refers to these systems as soft
articulatedrobots [2]. A different strategy is to move the
mechanical flexibility along themanipulator’s structure, through
slender concept designs and lightweight mate-rials applied to the
links. This design approach generates internal deformations,which
in most of cases are limited to the linear domain. Since these
deformationsin the past were seen as undesired, the most diffused
paradigm was to design
c© Springer Nature Switzerland AG 2020C. Rizzi et al. (Eds.):
ADM 2019, LNME, pp. 444–457,
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Virtual Prototyping of Soft Robots 445
control algorithms to avoid and suppress them. Conversely, a
recent trend is toexploit (large) internal deformations to provide
robotic systems novel capabilitieswith respect to traditional
robots, such as increased safety in cooperating withhuman beings
and morphological adaptation to complex environments.
Robotsdeliberately made with a continuously deformable body (but
without joints) arereferred to as soft continuum robots or
soft–bodied robots [3,4]. In the litera-ture, soft articulated
robots and soft continuum robots are generically namedsoft
robots.
Robotic systems made of deformable bodies and/or flexible joints
are becom-ing pervasive in several applications, including
medicine, rehabilitation, manu-facturing, inspection and
maintenance, remote explorations. However, despitethe recent
growing interest in soft robotics, most of existing applications
arelimited to laboratories.
In order to further advance the development of soft robots
towards commer-cially available solutions, it is important to put a
great effort in their designphase; in this respect, their effective
development should be based on robust andefficient virtual
prototyping techniques [5]. Due to the mechanical structure ofsoft
robots, it is clear that such virtual prototyping techniques should
be basedon continuum mechanics and multibody dynamics theories.
Therefore, compu-tational tools with the ability to handle finite
deformations, multi–joint systems,linear and nonlinear materials
are highly desired in this context.
Virtual prototyping tools for soft robots would have impact in
variousdomains: (i) aiding the first phases of concept design; (ii)
analysis of mecha-nisms; (iii) testing and verification of geometry
and materials; (iv) simulation ofcomplex motions; (v) development
of model–based controllers; (vi) planning ofinput trajectories.
Currently, the design and development of soft robots relies on
the subsequentuse of computer aided design (CAD) software for
design of the undeformed con-figuration of the system, and computer
aided engineering (CAE) software formultibody and structural
analyses. With this respect, a major problem is in thedata exchange
process between different software tools. Generically, the CAEphase
involves the combined use of multibody systems (MBS) packages
withfinite element (FE) analysis tools. First, a FE model is
created from the CADmodel; then, the FE solver generates an input
model for the MBS software,and in the latter the multibody analyses
are performed. To implement this pro-cess, commercial available
software solutions are: ABAQUS and SIMPACK fromDassault Systèmes1;
NASTRAN/PATRAN and ADAMS from MSC Software.2
This approach presents two major limitations: (1) the overall
motion of a flexiblesystems is usually seen as a superposition of a
local motion (available from amodal analysis) to a mean rigid body
motion; thus, the geometrically nonlineareffects of deformations
are not captured [6]; (2) it is time expensive, since a FEexpert
and a MBS expert are required for developing two different models,
andsince the solutions of these two models are usually
computationally expensive.
1 https://www.3ds.com/.2 https://www.mscsoftware.com/.
https://www.3ds.com/https://www.mscsoftware.com/
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446 S. Grazioso et al.
In order to overcome the second issue, RecurDyn from
Functionbay3 integratesmultibody dynamics analysis with non–linear
finite element analysis. Examplesof using RecurDyn for compliant
mechanisms can be found in [7], where theauthors modeled the
flexible members via a series of rigid links connected
byspring–loaded joints. However, the models developed using
commercially avail-able solutions are still heavy from the
computational point of view, and thusthey can be used only for
simulation purposes (not for real–time control appli-cations).
Furthermore, as a manageable mathematical model is not available
inthis case, the development of model–based controllers is not
possible.
An ideal solution for rapid and effective product development of
soft robotswould foresee a unique software environment where it is
possible to integratestructural and multibody analyses, together
with planning and control algo-rithms. With this respect, it has
also been pointed out that integrating thegeometry of soft
mechanisms with their analysis is a major challenge in the
softrobotics community [8]. Such environment should be based on
models which,from one side, are able to capturing all the
nonlinearities of the problem, andfrom the other side, are
computationally efficient in order to get simulationscloser to
real–time. Furthermore, in order to use this environment for
controlpurposes, the models should be control–oriented.
Existing mathematical formulations are well–known for soft
articulatedrobots [9]. The literature on modeling of soft continuum
robots is more recent,and the most promising approaches are those
based on geometrically exact the-ories from continuum mechanics
[10–13]. To date, there is not yet an establishedmathematical
framework which can accommodate the simulation and control ofrobots
made of both deformable bodies and flexible joints, i.e. multi–link
soft–bodied robots. One of the first attempt in developing such
kind of mathematicalframework can be found in our past works [14].
In the rest of this paper, weshow how this framework can be used
for mechanics–based virtual prototypingof generically complex soft
robots.
2 The Mechanics–Based Method for Virtual Prototypingof Soft
Robots
The virtual simulation workflow for mechanical systems used in
this work is illus-trated in Fig. 1. First, the system is designed
using classic CAD software. Then,the CAD model is translated in a
simulation model for performing both struc-tural and multibody
analyses. In this phase (called also pre–processing phase),the
simulation engineer has to: (1) extract the geometric topology of
the systemfrom the CAD model; (2) assign the physical behavior to
the elements involvedin the model (i.e. rigid and/or soft bodies);
(3) define the kinematic joints; (4)define the boundary conditions.
Hence, the model is ready for the analyses, madethrough a proper
solver engine, which has to solve the equations of motion of
thesystem according to the input trajectories and control
algorithms. At the end,
3 https://functionbay.com/.
https://functionbay.com/
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Virtual Prototyping of Soft Robots 447
Fig. 1. Mechanics–based virtual simulation workflow for
mechanical systems.
the solver generates output files for post–processing purposes
(positions, veloci-ties and accelerations of joints and bodies;
forces and torques at boundaries andjoint location; stresses and
strains of the deformable elements; animations).
To make this workflow effective, solver engines with the
following capabili-ties are required: (i) simulation of rigid and
deformable bodies; (ii) modeling ofall kind of joints and external
boundary conditions; (iii) modeling of serial andparallel kinematic
chains; (iv) modeling of multiple actuation sources, in termsof
motion and forces; (v) planning of input trajectories from a set of
motionprimitives; (vi) providing of control algorithms. It is
important that such solverengine would balance the trade–off
between accuracy of the solution and compu-tational efficiency, in
view of possible real–time applications related to simulationand
control of deformable–based robots.
In the following we describe the basis of a mechanics framework
whose com-puter implementation might result in a solver engine with
the desirable featuresreported above.
2.1 The Geometric Finite Element Approach for Modeling of
SoftArticulated and Soft–Bodied Robots
The mechanics–based framework for soft articulated and
soft–bodied robots isbased on three main pillars:
– Differential geometry of Lie groups and Lie algebras. The use
of geometrictechniques allow to capture in an elegant way the most
salient physical fea-tures of a robot [15].
– Cosserat rod theory. In robotics, we usually deal with solids
in which onedimension is predominant over the two others.
Therefore, we need to refer tobeam theories from computational
mechanics. Since soft–bodied robots areusually subject to finite
deformations, we need to refer to nonlinear geometri-cally exact
beam theories. From those, one of the most appealing for
roboticsapplications in the Cosserat rod theory [16,17].
– Finite element method. This method is a spatial discretization
technique forsolving partial differential equations (PDE) – which
in this case describe thebehavior of deformable bodies.
Furthermore, due to its assembly process, itallows to simulate both
serial and/or parallel chains of soft bodies.
In the following, we report the equations of motion of a generic
soft robot.
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448 S. Grazioso et al.
2.2 Equations of Motion
A generic soft robot is composed by rigid/soft bodies connected
throughrigid/flexible joints. The effects of the joints connecting
the bodies are takeninto account by imposing a set of algebraic
constraints, which prevent the non–allowed motion as imposed by the
joint. A single rigid body is described by themotion of one node in
its center of gravity, to which a frame HCoG ∈ SE(3) (spe-cial
Euclidean group) is attached; a soft body is described by the
motion of twoextreme nodes, to which two frames HA ∈ SE(3) and HB ∈
SE(3) are attachedand connected through an helical shape function
[18]. Indeed, the relative motionbetween two nodes 1 and 2,
belonging to two different bodies, can be described bya relative
frame HJ,I ∈ Lie subgroup of SE(3) as H2 = H1HJ,I [19,20].
Collect-ing the motion variables in the matrix H = diag(H1, . . .
,Hn,HJ,1, . . . ,HJ,k),with n the number of nodes and k the number
of joints of the system, the strongform for the global dynamic
equilibrium of the system take the form
M(H)η̇ − C(H)η + f int(H) + fϕ(H,λ) = fext(H) (1)
where η contains the absolute and relative velocities of the
nodes and joints ofthe system, M and C are the global discretized
mass and velocity matrices;f int are the discretized global
internal forces, including elastic forces of the softbodies as well
as elastic and dissipative forces of the flexible joints; fϕ are
thediscretized constraint forces, with λ the Lagrange multiplier
vector; fext are thediscretized global external forces, including
also gravity. An algebraic constraintequation ϕ(H) = 0 must be
append to the differential system (1) to definea
differential-algebraic equation (DAE) system that must be solved
for (H, λ).Finally, a geometric implicit integration scheme and a
Newton-Raphson iterativemethod are used to numerically solve the
DAE system [21].
3 Example
As an illustrative example of the capabilities of the method, in
this section weshow the dynamic analysis of a generic robotic
mechanism (GRM). The GRMis composed by rigid and soft bodies,
articulated in a kinematic chain with onebranched tree and one
closed loop, according to the topology shown in Fig. 2.
The GRM comprises six rigid bodies, each one with the following
mass androtation inertia properties: m = 0.15 kg; Jxx = Jyy = Jzz =
1 × 10−4 kgm2.Indeed, the cross sections of the soft bodies have
the mass and stiffness matrices
M = diag(0.1 kgm−1, 0.1 kgm−1, 0.1 kgm−1, 0.5 kg m, 0.5 kg m,
0.5 kg m) (2)K = diag(1 × 106 N, 1 × 106 N, 1 × 106 N, 1Nm2, 1Nm2,
1Nm2) (3)
The initial configuration of the GRM is given in Table 1, while
the jointsare defined in Table 2. There are a total of eight
joints: four passive and fouractuated. All joints are revolute
about the z–axis, except joint 5 which rotatesabout x–axis and
joint 3 which is prismatic.
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Virtual Prototyping of Soft Robots 449
Table 1. Initial configuration of the GRM.
Point x [m] y [m] z [m] Point x [m] y [m] z [m]
0 0 0 0 4 0.5 1.3 0.2
0 0.2 0.6 0 5 0.8 1.6 0.2
2′ 1 1 0 6 1 1.8 0.3
3′ 1.2 0 0 7 1.2 2 0.4
2 0 1 0 8 1.4 2.2 0.5
3 0.2 1.5 0
Table 2. Kinematic joint definition of the GRM. A = actuated; P
= passive. c = cos;s = sin. au, aω = displacement and rotation
parts of the relative motion.
Joint au aω A/P Joint au aω A/P
0 03×1 [0 0 1]T A 2 03×1 [0 0 1]T A
1 03×1 [0 0 1]T P 3 [c(1.1903) s(1.1903) 0]T 03×1 A
2′ 03×1 [0 0 1]T P 4 03×1 [0 0 1]T P
3′ 03×1 [0 0 1]T P 5 03×1 [1 0 0]T A
Table 3. (Left) Point-to-point motion of the actuated joint with
bang-bang accelera-tion profiles. qi, qf = initial, final values.
(Right) Point-to-point actuation forces withS−shaped force
profiles. fi, ff = initial, final values.
Joint q0 q2 q3 q5 Act. force f1x f1y f2x f2y f3x f3y
qi [m] or [rad] 0 0 0 0 fi [N] 0 0 0 0 0 0
qf [m] or [rad] π/6 π/6 0.75 π/3 ff [N] 100 −100 −100 100 100
−100q̈ [ms−2] or [rads−2] 2/3π 2/3π 3 4π/3 f̈ [Ns−2] 400 −400 −400
400 400 −400
The GRM is subject to: (1) prescribed joint motion to the four
actuatedjoints and actuation forces on three points on the system.
The active joints areactuated with a bang–bang acceleration profile
(triangular velocity profile) for1 s, according to the data given
in Table 3. Three actuation forces are applied onthe system at
points 6, 7 and 8. These forces follow a S−shaped profile for 1
s(see Table 3). The system is subject to gravity downward
z−direction.
The dynamic simulations are performed using SimSOFT, our physics
enginefor soft robots. Snapshots of the simulation are shown in
Fig. 3a–d. As output,we plot in Fig. 4 the 3D displacements,
velocities and accelerations of the tip ofthe GRM (point 8) as well
as of the free joint (4). A total of three simulations
areperformed, each one with the assumption of: (i) rigid joints;
(ii) soft joints withinternal stiffness K = 10 Nm−1 for the
prismatic joint and K = 10 Nmrad−1
for the revolute joints; (iii) soft joints with internal
stiffness (same as before)and damping D = 5Nsm−1 for the prismatic
joint and D = 5Nmsrad−1 for therevolute joints.
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450 S. Grazioso et al.
x
zy
6
g1(t)
g2(t)
g3(t)
q4(t)
q3′(t)
q2′(t)
q1(t)
q0(t)
q2(t)
q3(t)q5(t)
7
8
soft jointsoft body
rigid body
rigid joint
rigid constraint
actuation forcenodal frame
additional nodal frame
relative frame
helical shape function
(1 for rigid bodies; 2 for soft bodies)
Fig. 2. Geometric description of the GRM.
(a) t = 0 s (b) t = 0.33 s (c) t = 0.66 s (d) t = 1 s
Fig. 3. Snapshots of the GRM in SimSOFT
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Virtual Prototyping of Soft Robots 451
Fig. 4. Displacements, velocities and accelerations of the tip
(8) and of the free joint(4) of the GRM.
4 Applications
We present here some models and simulations developed using the
mechanics–based virtual prototyping framework described in this
paper. These case studiesillustrate the diversity and the
flexibility of this framework to handle differentkind of
mechanisms.
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452 S. Grazioso et al.
4.1 Serial/Parallel Soft Articulated Robot for
RemoteTransportation of Large Payloads
The Hybrid Kinematic Mechanism (HKM) is the current proposal for
remotetransportation of breeder blanket segments for the DEMO
reactor [22].It includes a parallel and serial kinematic structure.
The parallel section com-prises three elastic prismatic joints
which position the mechanism in space. Then,a serial section
composed by three revolute joints orientate the mechanism. Allthe
links of the HKM are modeled as rigid bodies, while the joints as
flexible ele-ments with internal stiffness. A rigid payload is
attached to the tip of the HKM.Figure 5a shows the CAD model of the
HKM, while Fig. 5b the simulation modelin our simulation
environment. For the complete description of this case study,the
reader can refer to the work in [23].
(a) CAD model (b) Simulation model
Fig. 5. HKM.
4.2 Hyper–redundant Soft Articulated Robot for RemoteInspection
and Maintenance
The Telescopic Articulated Remote Manipulator (TARM) is a 9
joints hyper–redundant robot, used for testing remote inspection
and maintenance operationsinside nuclear reactors. In order to test
how a payload can eventually deform duringthe maintenance
procedures, a special end–effector has been developed and hereit is
attached to the TARM (see Fig. 6a). The simulation model in Fig. 6b
consid-ers rigid links, elastic joints and a flexible payload
modeled as a nonlinear beamelement. This case study is described in
our previous works [24,25].
4.3 Soft Continuum Robot for Intravascular Shaping
Operations
Soft continuum robots are used in minimally invasive surgery, as
they can exploittheir internal deformations to access in anatomical
sites through one single inci-sion on the patient’s body [26]. In
this context, it is important to predict thereal shapes that these
systems undergone when subject to actuation and exter-nal loads.
One commercial surgical continuum instrument is the Magellan
R©10FrRobotic Catheter from Hansen Medical (Auris Health Inc.,
Redwood City, CA).
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Virtual Prototyping of Soft Robots 453
(a) CAD model (b) Simulation model
Fig. 6. TARM with flexible payload.
Fig. 7. Magellan R©10Fr Robotic Catheter
(https://www.aurishealth.com/hansen-medical)
(a) t = 1 s (b) t = 0.66 s (c) t = 0.33 s (d) t = 0 s
Fig. 8. Snapshots of the soft continuum robot in SimSOFT
Fig. 9. Soft bending actuator
(https://softroboticstoolkit.com/)
https://www.aurishealth.com/hansen-medicalhttps://www.aurishealth.com/hansen-medicalhttps://softroboticstoolkit.com/
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454 S. Grazioso et al.
(a) t = 0 s (b) t = 0.33 s (c) t = 0.66 s (d) t = 1 s
Fig. 10. Snapshots of the soft actuator in SimSOFT
This instrument is composed by a guide and a robotically
steerable inner leader;both the guide and leader have the
possibility to bend (see, e.g. Fig. 7). Whenthe leader is in its
minimal extension, the instrument is composed of two con-secutive
bendable elements, which we have modeled as active nonlinear
beamelements. The time evolution of the shape of these two
elements, subject tospecific actuation loads, is given in Fig.
8a–d.
4.4 Soft Actuators for Rehabilitation Robots
Soft actuators are used in the development of soft othoses
and/or prostheses [27].In this context, dynamic analyses using a
fast finite element solver which usesmono–dimensional elements
could play an essential role in the first design phasesof the
robotic system, when we are interested in the simulation of the
overallmotion of the actuator. A typical circumstance could be the
one involved inrobust design optimization, i.e. how changing the
design parameters regardingthe topology and the geometry of the
actuator, could affect the motion per-formance of the system. In
this case, a fast physics engine could predict theresulting motion
in short time, if compared to classic finite element software
asABAQUS. After, once defined the overall parameters of the
actuator, one could,eventually, optimize the internal design of the
actuator’s chambre by using finiteelement meshes with
three–dimensional solids, available in commercial software.A
typical example of a soft actuator is shown in Fig. 9, with some
snapshots ofits motion shown in Fig. 10a–d.
5 Three Major Challenges
Research on virtual prototyping techniques for soft robotics is
still in its earlystage. In order to facilitate the design and
fabrication of soft robotic systems,three grand challenges are in
the development of: (1) Conceptual design tools;(2) Integrated
software tools for design, analysis and control; (3) Interactive
andreal–time virtual simulation tools.
5.1 Conceptual Design Tools
Virtual prototyping tools usually deal with analysis and
verification of systems,when a detailed CAD model is already
available. This strategy can result in
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Virtual Prototyping of Soft Robots 455
wasted time and effort for detailed designs which may not work.
A special effort isworth to be made towards the development of
computer aided conceptual designtools specifics for soft robots.
Indeed, model–based conceptual design tools mightspeed up the
development of effective soft robots, by providing non–experts
keydesign parameters of the systems according to their specific
application.
5.2 Integrated Software Tools for Design, Analysis and
Control
Virtual prototyping tools for soft robots should foresee a
unique software environ-ment where the integration of geometry and
analysis of soft mechanisms is natu-ral. As a soft robot usually
works in its deformed configuration, it is necessary tohave an
environment where the CAD geometry follows the real physics
behaviorof the manipulator during the working trajectories. Such
integrated environmentshould provide multiple material models,
multibody dynamics, computationalmechanics and (eventually)
computational fluid dynamics capabilities (the lat-ter is required
for flying and underwater soft robots). Furthermore,
effectivevirtual prototyping tools for soft robots should foresee
the possibility to testcontrol algorithms and different input
trajectories. To this end, models specif-ically developed for
control purposes and not only for simulation purposes arerequired.
However, having an integrated software environment for design,
anal-ysis and control of soft robots is still hard to achieve. A
first effort could bedone in developing software tools for
automatically generating input files fromthe CAD model to an
existing solver engine for analysis and control purposes.Another
aspect which is worth to be investigated is in the development of
aunique product design representation of soft robots.
5.3 Interactive and Real–Time Virtual Simulation Tools
Interactive and real–time virtual simulation tools [28],
together with advancedinterface devices might allow engineers and
users to moving closer to a bettermodel viewing, manipulation and
feedback on the design for soft robotics. To dothat, the following
features are needed: (i) rapid computational mechanics toolsbased
on efficient dynamic models; (ii) integration of graphics and
mechanics;(iii) interface devices with mapping algorithms able to
move a distributed systemas a soft robot with few inputs.
6 Conclusions
Mechanics–based virtual prototyping techniques can play a
relevant role in thedevelopment of robust and effective designs for
soft robots. As a matter of fact,currently, soft robots are more
widespread in laboratories and only few examplesof commercial
solutions exist. In this work we have presented a modeling
frame-work which can be eventually used for different virtual
prototyping applicationsrelated to soft articulated and soft–bodied
robots: design optimization, designanalysis and verification,
simulation of motion. Due to its good balance between
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456 S. Grazioso et al.
accuracy (below 5% according to experimental trials in previous
papers) andcomputation time (average of 2 s of computer time for
simulating 1 s of motion)for simulation of such kind of complex
systems, this framework can be the basisfor the development of
conceptual design tools, integrated software tools fordesign,
analysis and control, as well as interactive and real–time virtual
simu-lation tools, tailored for soft robots. However, the
integration of multiple toolsto create a robust virtual prototyping
simulation software for soft robots stillremains an open topic.
References
1. De Luca, A., Book, W.J.: Robots with flexible elements. In:
Springer Handbook ofRobotics, pp. 243–282. Springer (2016)
2. Della Santina, C., Bianchi, M., Grioli, G., Angelini, F.,
Catalano, M., Garabini, M.,Bicchi, A.: Controlling soft robots:
balancing feedback and feedforward elements.IEEE Robot. Autom. Mag.
24(3), 75–83 (2017)
3. Trivedi, D., Rahn, C.D., Kier, W.M., Walker, I.D.: Soft
robotics: biological inspi-ration, state of the art, and future
research. Appl. Bionics Biomech. 5(3), 99–117(2008)
4. Majidi, C.: Soft robotics: a perspective-current trends and
prospects for the future.Soft Robot. 1(1), 5–11 (2014)
5. Zorriassatine, F., Wykes, C., Parkin, R., Gindy, N.: A survey
of virtual prototypingtechniques for mechanical product
development. Proc. Inst. Mech. Eng., Part B:J. Eng. Manuf. 217(4),
513–530 (2003)
6. Wasfy, T.M., Noor, A.K.: Computational strategies for
flexible multibody systems.Appl. Mech. Rev. 56(6), 553–613
(2003)
7. Bilancia, P., Berselli, G., Bruzzone, L., Fanghella, P.: A
CAD/CAE integrationframework for analyzing and designing spatial
compliant mechanisms via pseudo-rigid-body methods. Robot.
Comput.-Integr. Manuf. 56, 287–302 (2019)
8. Shabana, A.A.: Continuum-based geometry/analysis approach for
flexible and softrobotic systems. Soft Robot. 5(5), 613–621
(2018)
9. Albu-Schaffer, A., Eiberger, O., Grebenstein, M., Haddadin,
S., Ott, C., Wimbock,T., Wolf, S., Hirzinger, G.: Soft robotics.
IEEE Robot. Autom. Mag. 15(3), 20–30(2008)
10. Trivedi, D., Lotfi, A., Rahn, C.D.: Geometrically exact
models for soft roboticmanipulators. IEEE Trans. Robot. 24(4),
773–780 (2008)
11. Rucker, D.C., Jones, B.A., Webster III, R.J.: A
geometrically exact model forexternally loaded concentric-tube
continuum robots. IEEE Trans. Robot. 26(5),769 (2010). A
Publication of the IEEE Robotics and Automation Society
12. Renda, F., Boyer, F., Dias, J., Seneviratne, L.: Discrete
cosserat approach formultisection soft manipulator dynamics. IEEE
Trans. Robot. 34(6), 1518–1533(2018)
13. Grazioso, S., Di Gironimo, G., Siciliano, B.: A
geometrically exact model for softcontinuum robots: the finite
element deformation space formulation. Soft Robot.(2018)
14. Grazioso, S.: Geometric soft robotics: a finite element
approach. Ph.D. thesis, Uni-versity of Naples Federico II
(2018)
15. Lynch, K.M., Park, F.C.: Modern Robotics. Cambridge
University Press, New York(2017)
-
Virtual Prototyping of Soft Robots 457
16. Simo, J.C., Vu-Quoc, L.: A three-dimensional finite-strain
rod model. Part II:computational aspects. Comput. Methods Appl.
Mech. Eng. 58(1), 79–116 (1986)
17. Sonneville, V., Cardona, A., Brüls, O.: Geometrically exact
beam finite elementformulated on the special euclidean group SE
(3). Comput. Methods Appl. Mech.Eng. 268, 451–474 (2014)
18. Grazioso, S., Di Gironimo, G., Siciliano, B.: From
differential geometry of curvesto helical kinematics of continuum
robots using exponential mapping. In: Interna-tional Symposium on
Advances in Robot Kinematics, pp. 319–326. Springer (2018)
19. Sonneville, V., Brüls, O.: A formulation on the special
Euclidean group for dynamicanalysis of multibody systems. J.
Comput. Nonlinear Dyn. 9(4), 041002 (2014)
20. Grazioso, S., Sonneville, V., Di Gironimo, G., Bauchau, O.,
Siciliano, B.: A non-linear finite element formalism for modelling
flexible and soft manipulators. In:2016 IEEE International
Conference on Simulation, Modeling, and Programmingfor Autonomous
Robots, pp. 185–190. IEEE (2016)
21. Brüls, O., Cardona, A., Arnold, M.: Lie group generalized-α
time integration ofconstrained flexible multibody systems. Mech.
Mach. Theory 48, 121–137 (2012)
22. Keep, J., Wood, S., Gupta, N., Coleman, M., Loving, A.:
Remote handling of demobreeder blanket segments: blanket
transporter conceptual studies. Fus. Eng. Des.124, 420–425
(2017)
23. Grazioso, S., Di Gironimo, G., Iglesias, D., Siciliano, B.:
Screw-based dynamics ofa serial/parallel flexible manipulator for
demo blanket remote handling. Fus. Eng.Des. 139, 39–46 (2019)
24. Grazioso, S., Di Gironimo, G., Siciliano, B.: Modeling and
vibration control of flex-ible mechanical systems for demo remote
maintenance: results from the flexARMproject. Fus. Eng. Des.
(2019)
25. Grazioso, S., Powell, R., Skilton, R., Di Gironimo, G.,
Siciliano, B.: Multibodysimulations of the telescopic articulated
remote manipulator with flexible payloadfor demo studies on remote
handling. Fus. Eng. Des. (2019)
26. Burgner-Kahrs, J., Rucker, D.C., Choset, H.: Continuum
robots for medical appli-cations: a survey. IEEE Trans. Robot.
31(6), 1261–1280 (2015)
27. Polygerinos, P., Correll, N., Morin, S.A., Mosadegh, B.,
Onal, C.D., Petersen,K., Cianchetti, M., Tolley, M.T., Shepherd,
R.F.: Soft robotics: review of fluid-driven intrinsically soft
devices; manufacturing, sensing, control, and applicationsin
human-robot interaction. Adv. Eng. Mater. 19(12), 1700016
(2017)
28. Di Gironimo, G., Lanzotti, A.: Designing in VR. Int. J.
Interact. Des. Manuf. 3(2),51–53 (2009)
Mechanics–Based Virtual Prototyping of Robots with Deformable
Bodies and Flexible Joints1 Introduction2 The Mechanics–Based
Method for Virtual Prototyping of Soft Robots2.1 The Geometric
Finite Element Approach for Modeling of Soft Articulated and
Soft–Bodied Robots2.2 Equations of Motion
3 Example4 Applications4.1 Serial/Parallel Soft Articulated
Robot for Remote Transportation of Large Payloads4.2
Hyper–redundant Soft Articulated Robot for Remote Inspection and
Maintenance4.3 Soft Continuum Robot for Intravascular Shaping
Operations4.4 Soft Actuators for Rehabilitation Robots
5 Three Major Challenges5.1 Conceptual Design Tools5.2
Integrated Software Tools for Design, Analysis and Control5.3
Interactive and Real–Time Virtual Simulation Tools
6 ConclusionsReferences