Design and modeling of a novel soft parallel robot driven by endoskeleton pneumatic artificial muscles

doi:10.1007/s11465-022-0678-2

Front. Mech. Eng.

2022, Vol. 17

Issue (2) : 22 https://doi.org/10.1007/s11465-022-0678-2

RESEARCH ARTICLE

Design and modeling of a novel soft parallel robot driven by endoskeleton pneumatic artificial muscles

Peng CHEN^1,^2,³, Tingwen YUAN⁴, Yi YU^1,^2,³, Yuwang LIU^1,²(

)

¹. State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016, China
². Institutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences, Shenyang 110169, China
³. University of Chinese Academy of Sciences, Beijing 100049, China
⁴. School of Mechanical Engineering, Northeastern University, Shenyang 110000, China

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Abstract

Owing to their inherent great flexibility, good compliance, excellent adaptability, and safe interactivity, soft robots have shown great application potential. The advantages of light weight, high efficiency, non-polluting characteristic, and environmental adaptability provide pneumatic soft robots an important position in the field of soft robots. In this paper, a soft robot with 10 soft modules, comprising three uniformly distributed endoskeleton pneumatic artificial muscles, was developed. The robot can achieve flexible motion in 3D space. A novel kinematic modeling method for variable-curvature soft robots based on the minimum energy method was investigated, which can accurately and efficiently analyze forward and inverse kinematics. Experiments show that the robot can be controlled to move to the desired position based on the proposed model. The prototype and modeling method can provide a new perspective for soft robot design, modeling, and control.

Keywords pneumatic artificial muscles soft robot modeling approach principle of virtual work external load

Corresponding Author(s): Yuwang LIU

About author:

Tongcan Cui and Yizhe Hou contributed equally to this work.

Just Accepted Date: 15 April 2022 Issue Date: 16 June 2022

Cite this article:

Peng CHEN,Tingwen YUAN,Yi YU, et al. Design and modeling of a novel soft parallel robot driven by endoskeleton pneumatic artificial muscles[J]. Front. Mech. Eng., 2022, 17(2): 22.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-022-0678-2
https://academic.hep.com.cn/fme/EN/Y2022/V17/I2/22

Fig.1 Developed soft robot.

Fig.2 Relative deflection of adjacent modules.

Fig.3 Pneumatic artificial muscles with different numbers of creases. (a) Few numbers of creases, (b) appropriate number of creases, and (c) large number of creases.

Fig.4 (a) Relationship between

P i n

d a

, and

F c

; (b) relationship between muscle length, inflation time, and deflation time.

Fig.5 (a) PAM stiffness measured method; (b) experimental results of PAM configuration with different lengths.

Parameter	Value
Robot length, L	1000 mm
Robot diameter, $d r$	40 mm
Elastic rod diameter, d	2.5 mm
Young’s modulus, E	6.2 MPa
Shear modulus, G	2.4 MPa
Robot gravity, $f g$	4 N

Tab.1 Parameters of the soft parallel robot

Fig.6 (a) Prototype of the designed soft parallel robot; (b) control module of the robot.

Fig.7 Soft robot prototype bending in 3D space (with and without load).

Fig.8 Force on the micro element arc segment of the backbone.

Fig.9 Experiment 1: The endpoint trajectory is circular. (a) Spatial configuration of soft robot endpoints with different constraints, (b)

η O ζ

projection view, (c)

η O ξ

projection view, and (d) comparison of endpoint simulation and experimental position.

Fig.10 Position errors of robot endpoints in Experiment 1.

Fig.11 Experiment 2: The endpoint trajectory is square. (a) Spatial configuration of soft robot endpoints with different constraints, (b)

η O ζ

projection view, (c)

η O ξ

projection view, and (d) comparison of endpoint simulation and experimental position.

Fig.12 Position errors of robot endpoints in Experiment 2.

Fig.13 Experiment 3: The endpoint trajectory is a heart-shaped curve. (a) Spatial configuration of soft robot endpoints with different constraints, (b)

ξ O ζ

projection view, (c)

ξ O η

projection view, and (d) comparison of endpoint simulation and experimental position.

Fig.14 Position errors of robot endpoints in Experiment 3.

$a t, i$	Position coordinates of the ith muscle endpoint in the tth soft module
d	Elastic rod diameter
$d a$	Side length of the airbag
$d r$	Robot diameter
e	Robot endpoint position error
E	Young’s modulus
$E e$	Elastic strain energy
$E p$	External force potential energy
$E t$	Total elastic potential energy
$e 1, e 2, e 3$	Unit vectors of the x, y, and z axes, respectively
$f g$	Robot gravity
F_c	Load carrying capacity of PAM
$f i$	External force of the ith discretized nodes $N i$
F	Internal force
$k 1, k 2$	Flexural stiffnesses of the x and y axes, respectively
$k 3$	Torsional stiffness of the z axis
l_p	Pneumatic artificial muscle length
L	Robot length
$N i$	Theith discretized nodes
P	Simulation position of the robot endpoint
$P a$	Experimental position of the robot endpoint
$P i n$	Air pressure inside the PAM
$P o u t$	Atmospheric pressure
$r c$	Constraint disk radius
r	Position vector of the robot discrete nodes
$(P 1, P 2, P 3)$	Position of the desired point
(α,β,θ)	Euler angles
$ϕ$	Relative rotation angle of adjacent coordinate systems
$ω$	Derivative of $ϕ$ with respect to arc coordinate s

1	D Rus, M T Tolley. Design, fabrication and control of soft robots. Nature, 2015, 521( 7553): 467– 475 https://doi.org/10.1038/nature14543
2	T L Liu, W F Xu, T W Yang, Y M Li. A hybrid active and passive cable-driven segmented redundant manipulator: design, kinematics, and planning. IEEE/ASME Transactions on Mechatronics, 2021, 26( 2): 930– 942 https://doi.org/10.1109/TMECH.2020.3013658
3	Q H Guan, J Sun, Y J Liu, N M Wereley, J S Leng. Novel bending and helical extensile/contractile pneumatic artificial muscles inspired by elephant trunk. Soft Robotics, 2020, 7( 5): 597– 614 https://doi.org/10.1089/soro.2019.0079
4	C A Aubin, S Choudhury, R Jerch, L A Archer, J H Pikul, R F Shepherd. Electrolytic vascular systems for energy-dense robots. Nature, 2019, 571( 7763): 51– 57 https://doi.org/10.1038/s41586-019-1313-1
5	Y Kim, H Yuk, R K Zhao, S A Chester, X H Zhao. Printing ferromagnetic domains for untethered fast-transforming soft materials. Nature, 2018, 558( 7709): 274– 279 https://doi.org/10.1038/s41586-018-0185-0
6	G R Li, X P Chen, F H Zhou, Y M Liang, Y H Xiao, X N Cao, Z Zhang, M Q Zhang, B S Wu, S Y Yin, Y Xu, H B Fan, Z Chen, W Song, W J Yang, B B Pan, J Y Hou, W F Zou, S P He, X X Yang, G Y Mao, Z Jia, H F Zhou, T F Li, S X Qu, Z B Xu, Z L Huang, Y W Luo, T Xie, J Gu, S Q Zhu, W Yang. Self-powered soft robot in the Mariana Trench. Nature, 2021, 591( 7848): 66– 71 https://doi.org/10.1038/s41586-020-03153-z
7	S J Park, M Gazzola, K S Park, S Park, V Di Santo, E L Blevins, J U Lind, P H Campbell, S Dauth, A K Capulli, F S Pasqualini, S Ahn, A Cho, H Y Yuan, B M Maoz, R Vijaykumar, J W Choi, K Deisseroth, G V Lauder, L Mahadevan, K K Parker. Phototactic guidance of a tissue-engineered soft-robotic ray. Science, 2016, 353( 6295): 158– 162 https://doi.org/10.1126/science.aaf4292
8	M Wehner, R L Truby, D J Fitzgerald, B Mosadegh, G M Whitesides, J A Lewis, R J Wood. An integrated design and fabrication strategy for entirely soft, autonomous robots. Nature, 2016, 536( 7617): 451– 455 https://doi.org/10.1038/nature19100
9	M J Zhu, T N Do, E Hawkes, Y Visell. Fluidic fabric muscle sheets for wearable and soft robotics. Soft Robotics, 2020, 7( 2): 179– 197 https://doi.org/10.1089/soro.2019.0033
10	L Cappello, K C Galloway, S Sanan, D A Wagner, R Granberry, S Engelhardt, F L Haufe, J D Peisner, C J Walsh. Exploiting textile mechanical anisotropy for fabric-based pneumatic actuators. Soft Robotics, 2018, 5( 5): 662– 674 https://doi.org/10.1089/soro.2017.0076
11	M T Tolley, R F Shepherd, B Mosadegh, K C Galloway, M Wehner, M Karpelson, R J Wood, G M Whitesides. A resilient, untethered soft robot. Soft Robotics, 2014, 1( 3): 213– 223 https://doi.org/10.1089/soro.2014.0008
12	R K Katzschmann, A D Marchese, D Rus. Autonomous object manipulation using a soft planar grasping manipulator. Soft Robotics, 2015, 2( 4): 155– 164 https://doi.org/10.1089/soro.2015.0013
13	B N Peele, T J Wallin, H C Zhao, R F Shepherd. 3D printing antagonistic systems of artificial muscle using projection stereolithography. Bioinspiration & Biomimetics, 2015, 10( 5): 055003 https://doi.org/10.1088/1748-3190/10/5/055003
14	S Terryn, J Brancart, D Lefeber, G Van Assche, B Vanderborght. Self-healing soft pneumatic robots. Science Robotics, 2017, 2( 9): eaan4628 https://doi.org/10.1126/scirobotics.aan4268
15	S Y Li, K W Wang. Fluidic origami: a plant-inspired adaptive structure with shape morphing and stiffness tuning. Smart Materials and Structures, 2015, 24( 10): 105031 https://doi.org/10.1088/0964-1726/24/10/105031
16	M A Robertson, J Paik. New soft robots really suck: vacuum-powered systems empower diverse capabilities. Science Robotics, 2017, 2( 9): eaan6357 https://doi.org/10.1126/scirobotics.aan6357
17	B Gorissen, D Reynaerts, S Konishi, K Yoshida, J W Kim, M De Volder. Elastic inflatable actuators for soft robotic applications. Advanced Materials, 2017, 29( 43): 1604977 https://doi.org/10.1002/adma.201604977
18	W Kim, J Byun, J K Kim, W Y Choi, K Jakobsen, J Jakobsen, D Y Lee, K J Cho. Bioinspired dual-morphing stretchable origami. Science Robotics, 2019, 4( 36): eaay3493 https://doi.org/10.1126/scirobotics.aay3493
19	R V Martinez, C R Fish, X Chen, G M Whitesides. Elastomeric origami: programmable paper-elastomer composites as pneumatic actuators. Advanced Functional Materials, 2012, 22( 7): 1376– 1384 https://doi.org/10.1002/adfm.201102978
20	D Yang, M S Verma, J H So, B Mosadegh, C Keplinger, B Lee, F Khashai, E Lossner, Z G Suo, G M Whitesides. Buckling pneumatic linear actuators inspired by muscle. Advanced Materials Technologies, 2016, 1( 3): 1600055 https://doi.org/10.1002/admt.201600055
21	Z D Jiao, C Ji, J Zou, H Y Yang, M Pan. Vacuum-powered soft pneumatic twisting actuators to empower new capabilities for soft robots. Advanced Materials Technologies, 2019, 4( 1): 1800429 https://doi.org/10.1002/admt.201800429
22	S G Li, D M Vogt, D Rus, R J Wood. Fluid-driven origami-inspired artificial muscles. PNAS, 2017, 114( 50): 13132– 13137 https://doi.org/10.1073/pnas.1713450114
23	A R Deshpande, Z T H Tse, H L Ren. Origami-inspired bi-directional soft pneumatic actuator with integrated variable stiffness mechanism. In: Proceedings of the 2017 18th International Conference on Advanced Robotics (ICAR). IEEE, 2017, 417– 421 https://doi.org/10.1109/ICAR.2017.8023642
24	J G Lee, H Rodrigue. Origami-based vacuum pneumatic artificial muscles with large contraction ratios. Soft Robotics, 2019, 6( 1): 109– 117 https://doi.org/10.1089/soro.2018.0063
25	F Renda, F Boyer, J Dias, L Seneviratne. Discrete Cosserat approach for multisection soft manipulator dynamics. IEEE Transactions on Robotics, 2018, 34( 6): 1518– 1533 https://doi.org/10.1109/TRO.2018.2868815
26	J Burgner-Kahrs, D C Rucker, H Choset. Continuum robots for medical applications: a survey. IEEE Transactions on Robotics, 2015, 31( 6): 1261– 1280 https://doi.org/10.1109/TRO.2015.2489500
27	R J III Webster, B A Jones. Design and kinematic modeling of constant curvature continuum robots: a review. The International Journal of Robotics Research, 2010, 29( 13): 1661– 1683 https://doi.org/10.1177/0278364910368147
28	M S Sofla, M J Sadigh, M Zareinejad. Design and dynamic modeling of a continuum and compliant manipulator with large workspace. Mechanism and Machine Theory, 2021, 164 : 104413 https://doi.org/10.1016/j.mechmachtheory.2021.104413
29	N Tan, X Y Gu, H L Ren. Design, characterization and applications of a novel soft actuator driven by flexible shafts. Mechanism and Machine Theory, 2018, 122 : 197– 218 https://doi.org/10.1016/j.mechmachtheory.2017.12.021
30	A Garriga-Casanovas, F Rodriguez y Baena. Complete follow-the-leader kinematics using concentric tube robots. The International Journal of Robotics Research, 2018, 37( 1): 197– 222 https://doi.org/10.1177/0278364917746222
31	L Schiller, A Seibel, J Schlattmann. A lightweight simulation model for soft robot’s locomotion and its application to trajectory optimization. IEEE Robotics and Automation Letters, 2020, 5( 2): 1199– 1206 https://doi.org/10.1109/LRA.2020.2966396
32	C H Yang, S N Geng, I Walker, D T Branson, J G Liu, J S Dai, R J Kang. Geometric constraint-based modeling and analysis of a novel continuum robot with shape memory alloy initiated variable stiffness. International Journal of Robotics Research, 2020, 39( 14): 1620– 1634 https://doi.org/10.1177/0278364920913929
33	W H Zeng, J Y Yan, K Yan, X Huang, X F Wang, S S Cheng. Modeling a symmetrically-notched continuum neurosurgical robot with non-constant curvature and superelastic property. IEEE Robotics and Automation Letters, 2021, 6( 4): 6489– 6496 https://doi.org/10.1109/LRA.2021.3094475
34	I Singh, Y Amara, A Melingui, P Mani Pathak, R Merzouki. Modeling of continuum manipulators using pythagorean hodograph curves. Soft Robotics, 2018, 5( 4): 425– 442 https://doi.org/10.1089/soro.2017.0111
35	I S Godage, G A Medrano-Cerda, D T Branson, E Guglielmino, D G Caldwell. Modal kinematics for multisection continuum arms. Bioinspiration & Biomimetics, 2015, 10( 3): 035002 https://doi.org/10.1088/1748-3190/10/3/035002
36	J Z Yang, H J Peng, W Y Zhou, J Zhang, Z G Wu. A modular approach for dynamic modeling of multisegment continuum robots. Mechanism and Machine Theory, 2021, 165 : 104429 https://doi.org/10.1016/j.mechmachtheory.2021.104429
37	H Yuan, L L Zhou, W F Xu. A comprehensive static model of cable-driven multi-section continuum robots considering friction effect. Mechanism and Machine Theory, 2019, 135 : 130– 149 https://doi.org/10.1016/j.mechmachtheory.2019.02.005
38	X J Huang, J Zou, G Y Gu. Kinematic modeling and control of variable curvature soft continuum robots. IEEE/ASME Transactions on Mechatronics, 2021, 26( 6): 3175– 3185 https://doi.org/10.1109/TMECH.2021.3055339
39	T M Bieze, F Largilliere, A Kruszewski, Z K Zhang, R Merzouki, C Duriez. Finite element method-based kinematics and closed-loop control of soft, continuum manipulators. Soft Robotics, 2018, 5( 3): 348– 364 https://doi.org/10.1089/soro.2017.0079
40	S M H Sadati, A Shiva, L Renson, C Rucker, K Althoefer, T Nanayakkara, C Bergeles, H Hauser, I D Walker. Reduced order vs. discretized lumped system models with absolute and relative states for continuum manipulators. In: Proceedings of Royal Statistics Society International Conference. Belfast, 2019, 1– 10
41	I S Godage, R Wirz, I D Walker, R J WebsterIII. Accurate and efficient dynamics for variable-length continuum arms: a center of gravity approach. Soft Robotics, 2015, 2( 3): 96– 106 https://doi.org/10.1089/soro.2015.0006

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