mechanics–based virtual prototyping of robots with deformable bodies...

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, 2020.https://doi.org/10.1007/978-3-030-31154-4_38

http://crossmark.crossref.org/dialog/?doi=10.1007/978-3-030-31154-4_38&domain=pdfhttps://doi.org/10.1007/978-3-030-31154-4_38

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/

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/


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.


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.


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.


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


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.


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).


(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/


(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


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


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)


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

mechanics–based virtual prototyping of robots with deformable bodies...

Documents