A Twisted String Actuator-Driven SoftRobotic Manipulator

David Bombara1 ∗ Ryan Coulter1 ∗ Revanth Konda1 ∗

Jun Zhang ∗

∗ University of Nevada, Reno, NV 89557 USA (e-mail: {dbombara,rcoulter, rkonda}@nevada.unr.edu, jun@unr.edu)

Abstract: To make robots more ubiquitous, robotic structures that are compliant, lightweight,and low-cost are desired. Soft robots, which are fabricated using compliant materials and softactuators, are ideal for such applications. However, producing high-performance soft robots ischallenging due to the lack of systematic procedures and availability of standard components. Inthis paper, a soft robotic manipulator powered by twisted string actuators (TSAs) is presented.Although TSAs have been widely adopted in multiple robotic applications, their inclusion insoft robots has been limited. Due to their tendon-based (muscle-like) linear actuation, high forcegeneration, and high operational bandwidth, TSAs are highly suitable to actuate soft roboticdevices with advantages over other soft actuators. The design of the proposed soft roboticmanipulator was presented. The performance of the manipulator was analyzed by experimentallycharacterizing and modeling the correlations between (1) the bending angle and motor rotationsand (2) the tip force and motor rotations. Furthermore, closed-loop control was successfullyemployed to control the bending angle of the manipulator. Through experiments, the proposedrobotic manipulator was found to exhibit a maximum bending angle of 97.4°and exerted a forceof nearly 500 mN.

Keywords: Soft robot, Soft manipulator, Soft gripper, Twisted string actuator

1. INTRODUCTION

To make robots more ubiquitous in scenarios where safeinteraction with humans is demanded, it is highly desirablebut challenging to realize robotic devices that are com-pliant, lightweight, low-cost, and generate sufficient forceto perform useful tasks. Unlike traditional rigid robots,soft robots—those fabricated using soft materials andactuators—are ideal for such applications (Schmitt et al.(2018); Rich et al. (2018)). Different useful motions suchas grasping, crawling, twisting, and swimming have beenachieved using soft robots (Zhou et al. (2016); Almubarakand Tadesse (2017); Pawlowski et al. (2019); Chen et al.(2020)). However, realizing soft robots is challenging incomparison to traditional robotic devices because softrobots lack a wide availability of standard components(Tang et al. (2019)) and can be difficult to analyze.

Artificial muscles are a special class of soft actuators whichare widely adopted as driving mechanisms in numeroussoft robots (Zhang et al. (2019)). Artificial muscles gener-ate motion by varying their shape due to external stimuli,such as voltage or temperature (Mirvakili and Hunter(2017); Ye and Chen (2019)). Unlike traditional rigidactuators, artificial muscles exhibit desirable propertiessuch as compliance, high power-to-weight ratio, and lowmass (Mirvakili and Hunter (2017); Zhang et al. (2019)),thereby exhibiting strong potential as driving mechanismsfor advanced robotic and mechatronic applications (Sridar

? 1 Authors D. Bombara, R. Coulter, and R. Konda contributedequally to this work.

(a) (b)

Fig. 1. The twisted string actuator (TSA) in the (a) fullyuntwisted state and (b) twisted (actuated) state.

et al. (2020); Ho et al. (2015); Laschi et al. (2016)). Mostof the existing soft robots are moved by different artificialmuscles such as pneumatic actuators (Zhou et al. (2016);Tang et al. (2020)), shape memory alloy (SMA) actuators(Rodrigue et al. (2017)), and twisted and coiled actuators(TCAs) (Tang et al. (2019)).

A twisted string actuator (TSA) is an artificial musclethat consists of two or more strings connected to anelectric motor at one end and a load at the other end(Gaponov et al. (2014)). As shown in Fig. 1, actuation isrealized by twisting the strings with a motor to shortenthe strings’ length and linearly displace the attached load

(Gaponov et al. (2014)). TSAs typically generate strains ofapproximately 30–40% of their untwisted length, exhibithigh energy efficiency, and can exert more stress thanskeletal muscles (Gaponov et al. (2014)). Although TSAshave been widely employed in multiple robotic applicationssuch as tensegrity robots, robotic gloves, robotic hands,and exoskeletons (Gaponov et al. (2017); Muller et al.(2015); Bombara et al. (2021)), their application in softrobots has been limited. This is because TSAs are oftenincorrectly considered to be stiff and non-compliant. Al-though the strings used in traditional TSAs are not largelystretchable, their flexibility could be sufficient for theiradoption in soft robots. Powering soft robots with TSAscould present its own advantages over soft robots enabledby other actuators (Tang et al. (2019); Pawlowski et al.(2019); Shih et al. (2017)). These advantages are due toTSAs’ large linear strain generation, wide range of forcegeneration, high operating frequency, and compactness incomparison to other commonly-used soft actuators (Zhanget al. (2019)). For example, although pneumatic actuatorsexhibit appreciable strain and force generations, adoptingthem in robotic devices demands the inclusion of pumpsor compressors (Shih et al. (2017); Tang et al. (2020)).Similarly, the thermal actuation of SMA actuators andTCAs not only results in low-bandwidth and low-forcegeneration (Zhang et al. (2018)), but also could be po-tentially dangerous and cause damage to the soft roboticdevices in which they are employed. TSAs are sometimesconsidered to be stiff because they require a rigid motorand can possess non-stretchable strings. However, TSAscould potentially be employed in soft robotic devices byembedding them in soft material similar to the work byTang et al. (2019).

In this paper, we present a multi-degrees of freedom (DOF)soft robotic manipulator powered by TSAs. This is the firststudy on the inclusion of TSAs to enable soft robotic de-vices (Tang et al. (2019); Shih et al. (2017)). The design ofthe soft manipulator is presented. This design was similarto previous works by Tang et al. (2019) and Shih et al.(2017) for soft robot modules. However, the employmentof TSAs meant that the soft body could be larger inscale and act as an arm rather than a finger. To ensurecompactness of the proposed robotic device, thin (1-mm-diameter) strings and small (20-mm-diameter, 46-g) DCmotors were used to operate the TSAs. The performanceof the robotic device was demonstrated by analyzing themanipulator’s force-generation capabilities and bendingangle caused by the TSAs. The main contributions of thispaper are:

• Design and fabrication of a general multi-DOF softrobotic device powered by TSAs.• Modeling of the force generation and bending angle,

and control of the bending angle of the proposed softrobotic manipulator.

2. DESIGN AND FABRICATION

2.1 Soft Arm

The design of the soft arm was biomimetic and inspiredby an elephant trunk. The design of the soft arm usedthree TSAs in conjunction to bend, retract, and orient the

Top cap with end-effector

fixture

Soft robotic arm

Base housing the

motors

Channels in which TSAs are placed

Fig. 2. Model of the soft arm.

end point of the manipulator in multiple directions. At thetime of this writing, a soft and compliant robotic elephanttrunk-inspired arm powered by TSAs has not yet beenstudied. The natural compliance of the soft robot wouldallow for safe human-robot interaction.

The soft arm, as shown in Fig. 2, was constructedfrom Smooth-On Ecoflex™00-50 silicone via a three-dimensionally (3D) printed mold. The mold was designedto be printed quickly and be disposable. The walls of eachmold part were 0.8-mm thick—twice the nozzle diameterof the 3D printer—to optimize slicing and printing. Thethin walls also allowed for the model to be quickly brokenapart to retrieve the cast arm. The soft arm was 175-mm long and utilized three internal channels to housethe TSAs’ strings. The channels were placed evenly atangles 120° from each other near the circumference of thearm. A channel was also provided in the center of the armthat contained the wires of the inertial measurement unit(IMU).

The soft arm utilized three TSAs to enable bending inall directions, thereby providing the robot with multipleDOF. The arm functioned by actuating the TSAs, whereeach TSA could be actuated at varying levels in conjunc-tion with one another to bend in any direction in therange of the TSA pair. The bending angle of the armwas varying by varying the twists in any TSA. The baseof the arm housed the motors to actuate the TSAs andencoders to measure the number of twists. The electronicswere placed outside of the robot and were wired to themotors and encoders. The three elements of the basesection were also designed using a peg-and-slot systemto be printed separately and efficiently, reducing supportmaterial, printing time, and printing cost. Leading up tothe arm, the topmost base section utilized friction to gripthe outer diameter of the arm so that it did not fall off ofthe base. The axial forces exerted by the TSAs fixed thearm to the base.

The top caps, where the ends of the TSAs attached, wereattached to the silicone both by friction (by following theinner diameter of the center channel) and axial force ofthe twisted strings. Additionally, the simple design of theend piece could allow for any type of end-effector to beattached. All rigid parts of the arm were 3D printed on a

traditional fused deposition modeling (FDM) printer fromacrylonitrile butadiene styrene (ABS) plastic.

2.2 TSAs

This study utilized two strings with the same lengthand material properties to construct each TSA. Morestrings with different material properties could also beused (Gaponov et al. (2014)). The strings were hungvertically in tension with one end attached to the motorshaft. The free end of the strings was attached to thetop cap of the arm and was constrained such that thearm bent due to the motor’s rotation. More informationon the design and assembly of TSAs can be found inGaponov et al. (2014). The TSAs were realized using ultra-high molecular-weight polyethylene (UHMWPE) stringswith diameters of 1.0 mm. This material and diameterwere chosen due to their repeated usage in previousstudies (Gaponov et al. (2014)). Brushed DC motors(Metal Gearmotor 20Dx44L, Pololu), with 125:1 gear ratiotwisted the pairs of strings to realize the TSAs. EachDC motor utilized a dual-channel Hall-effect sensor boardto track the motor rotations. Accounting for the gearratio, the encoders enabled 625 counts per revolution(CPR). 625 CPR corresponded to 0.58°-resolution sensingof the angle of the motor output shaft. With a 12-Vinput, each motor was able to output 7.8 kg·cm of torquebefore stalling, but each motor had a mass of only 46 g.A microcontroller based on the ATmega2560 microchip(MEGA 2560 R3 Board, Elegoo) with brushed DC motordrivers (DRV8871, Adafruit) controlled the robot.

2.3 Inertial Measurement Unit

An IMU (VR IMU Breakout - BNO080, Sparkfun) wasutilized to measure the bending angle of the soft TSA-driven arm. According to the manufacturer, the maximumerror of the angle of the IMU was 3.5°. Although themeasurement uncertainty may have been greater thanother devices, its low cost (approximately 35 USD) keptthe overall cost of the robot low. The IMU returned theorientation in terms of quaternions which were convertedinto roll, pitch, and yaw angles (Euler angles) for modelingpurposes.

3. EXPERIMENTAL CHARACTERIZATION

Firstly, the TSA-driven arm was studied for the correlationbetween the bending angle and motor rotations. Thearm was studied in the range of [0, 22] motor rotations.The bending angle was measured about the axis normalto the actuating motor shaft. The motor rotations wereapplied in monotonically increasing, then monotonicallydecreasing steps for two complete cycles. The motor wasactuated in steps of 1 rotation and paused for 6 s to ensurethe motor angle and bending angle became steady. Thisinput sequence is shown in Fig. 3(a). The correspondingmeasurements of bending angle are shown in Fig. 3(b).As expected, mild hysteresis was observed, which wascommonly observed in TSAs in previous work (Bombaraet al. (2021)). In addition, experimental results appearedto be less noisy at a higher number of rotations. When theTSA was twisted for less than 5 rotations, the strings may

not have been in sufficient tension. This meant that smallchanges in motor angle did not cause consistent changes inthe bending angle. However, at greater than 5 rotations,the tension in the strings was sufficiently high such that theaforementioned noise in the bending angle decreased. Thesoftness of the silicone in the arm caused the bending angleto slightly oscillate due to the acceleration of the motorshaft and strings. However, these oscillations eventuallydecayed to a negligible amplitude while the TSA was atrest. The maximum bending angle achieved by the softarm was 97.4°at 35 motor rotations, as shown in Fig.3(c). The maximum bending angle was dependent on (1)the toughness of the silicone and (2) maximum attainabletwists in the strings. Although it was physically possibleto bend beyond 97.4°, the silicone risked breakage due tothe high forces exerted by the strings on the inner walls ofthe channels in the arm.

Secondly, the force exerted perpendicular to the height ofthe TSA-driven arm was correlated with the actuation ofthe TSA in the range of [0, 15] motor rotations. At 15rotations, the robot began to bend into an “S” shape dueto the forces holding it in place at the top and bottomof the robot. To prevent potential damage to the robot’ssilicone body, the actuation was limited to 15 rotations—not 22 rotations as in the bending angle experiments. Theforce measurements were recorded using an LSP-2 loadcell. The motor rotation input sequence and correspondingforce data versus time is shown in Figs. 3(d) and (e),respectively. The force–motor rotations correlation wasobserved to be hysteretic; the force during twisting wasgreater than the force during untwisting. At the startingand ending motor rotations, the forces during twisting anduntwisting were approximately equivalent. At 15 motorrotations, the TSA-driven arm exerted a force of 508 mN.

4. MODELING

A polynomial was utilized to model the relationship be-tween the (1) motor rotations versus bending angle and(2) motor rotations versus force output of the robot. Themodel took the following form:

y =

n∑i=0

aixi, (1)

where x is the number of rotations of the motor shaft, andy is the output variable of interest—either the bendingangle θ or force output f of the robot. Constants to beidentified are ai, i = 0, 1, 2, ..., n. The error in the modelwas defined as

Ey,k = |yk,exp − yk,model|, (2)

where Ey,k is the error of the kth point. yexp and ymodel

are respectively the experimentally-obtained and modeledoutputs of the system. By replacing ymodel with ydes, thisdefinition was also utilized to evaluate the control errormagnitude in Section 5, where ydes is the desired outputof the system.

4.1 Bending Angle

To model the bending angle θ, n = 2 was chosen for highaccuracy yet low computational complexity. A third-order

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Fig. 3. The results for the experimental characterization and modeling of the TSA-driven soft robot. (a) The motorrotation input sequence versus time and (b) the corresponding bending angle versus time. (c) The TSA-driven softarm at its maximum bending angle, 97.4°. (d) The input sequence of motor rotations to measure the force of therobot. (e) The force of the robot versus time. (f) The experimental results and model of bending angle versus motorrotations. (g) The error magnitude of the bending angle–motor rotations correlation. (h) The correlation betweenmotor rotations and force of the robot. (i) The error magnitude of the force–rotations correlation.

polynomial (n = 3) was also tested but was found toproduce negligibly different accuracy. Note that the modelin (1) was obtained during the actuation of a single motor.In this study, multiple motors did not actuate simultane-ously during the modeling and control experiments. Usingthe Matlab function polyfit, the following model wasobtained:

θ(x) = (0.188x2 − 1.748x+ 4.780)◦/rev. (3)

where “rev” denotes a single revolution of the motor shaft(1 rev = 360°). Fig. 3(f) shows the identified model ontop of the experimental results. The corresponding errorEθ is shown in Fig. 3(g), in which the maximum andaverage errors were 3.04°and 1.08 °, respectively. This erroris within the uncertaintly region of the IMU (3.5 °).

The model was valid in the domain of 5 ≤ x ≤ 22 rota-tions. The domain was restricted to x ≥ 5 motor rotationsto ensure the strings actuated in sufficient tension. x ≤ 22rotations was chosen to limit the highest forces exertedby the TSA’s strings on the soft silicone inside the arm.At 22 rotations, the TSA’s strings visibly bulged from theouter surface of the soft arm. Repeatedly actuating thearm beyond 22 rotations might have damaged the sili-cone, although the bending angle would have significantlyincreased.

The relationship between x and θ was parabolic due tothe nonlinear gear ratio of the TSA. For a TSA whosestrings are inextensible, the relationship between the linearcontraction of the strings and the motor shaft angle is

(a) (b) (c)

Fig. 4. The control performance of the TSA-driven soft robot. (a) The setpoint and steady-state error of the closed-loopbending angle controller and (b) corresponding steady-state error. (c) The step-response of the bending angle withclosed-loop control for two different setpoints.

also parabolic (Gaponov et al. (2014)). In (3), increasingx implied dθ/dx would also increase. For a given constantrotational speed, dx/dt,

{dx/dt = v, dθ/dx > 0} =⇒ d2θ/dt2 > 0, (4)

where v > 0 is a constant. In other words, the bendingangle of the arm accelerated if the strings in the TSA weretwisted at a constant angular velocity.

4.2 Force Output

Although the relationship between output force and mo-tor rotations was hysteretic, a polynomial based on (1)approximated the correlation with reasonable accuracy.Using the Matlab function polyfit and an order of n = 3,the following equation was obtained:

f(x) = (0.267x3−1.852x2+0.557x+10.391)mN/rev, (5)

where f is the output force at the top of the arm, inunits of mN. The modeling results are shown with theexperimental data in Fig. 3(h). The error Ef is providedin Fig. 3(i), with maximum and average errors of 51.00 mNand 18.46 mN, respectively. This slightly large error wasdue to the polynomial’s inability to model the hysteresisin the motor rotations–force relationship.

5. CONTROL

A closed-loop proportional control strategy was developedto obtain desired bending angles of the arm. The speedsof the motors were adjusted by varying the duty cyclesof pulse-width modulated (PWM) 12-V signals. The in-put voltage Vm to the motor was bounded such that2.4 V < Vm < 12 V. The upper bound was the nominalvoltage of the motor that was provided by the manu-facturer. The lower bound was the minimum voltage atwhich the motor produced sufficient torque to twist theTSA’s strings and bend the robot’s body. In addition,a control board was fabricated to independently actuateeach motor using push-buttons and to set the motors’speeds using four potentiometers. Two buttons each cor-responded to each of the four motors: one button spun themotor clockwise whereas the other button spun the motorcounterclockwise. In closed-loop control, the bending angleof the arm was measured by the IMU to directly obtain

the error between the desired bending angle and the actualbending angle. This error was utilized to determine thecontrol input. The duty cycle of Vm was proportional tothe bending angle error. The proportional gain, K = 5,was determined experimentally. The lower bound of 2.4 Vmeant that, even when K decreased, the input voltageto the motor remained at 2.4 V for |θ − θdes| < 10°.K ≤ 5 prevented overshoot of the motor rotation angle.The steady-state closed-loop control performance is shownin Fig. 4(a). The experimental procedure consisted ofstep reference signals whose amplitudes were uniformly-distributed random floating point numbers in the rangeof [0◦, 60◦]. The error magnitude, Eθ, of the controller isshown in Fig. 4(b), in which the maximum and averageerrors were 0.82°and 0.38°, respectively.

The step response of the closed-loop system for two dif-ferent step reference signals is shown in Fig. 4(c). Therise time Tr for a desired bending angle θdes = 32◦ wasTr = 8.03 s. Tr is defined as the time in which the bendingangle of the arm changes from 10% to 90% of θdes. Therise time could be decreased by (1) using a motor with alower gear ratio, or (2) using strings with larger diame-ters. Decreasing the gear ratio would increase the angularspeed of the motor without increasing the size or mass ofthe motors, but the motor’s smaller torque output maydecrease the maximum bending angle. Although larger-diameter strings would increase the contraction speed ofthe TSA, the minimum required torque from the motorwould also increase, as shown in the model developedby Nedelchev et al. (2020). Because the motor’s mostlyoperated at the saturation voltage, increasing Kp may notsignificantly decrease the rise time.

5.1 Discussion

The closed-loop controller drove the bending angles ofthe robot to desired values with small steady-state errors.The control board provided a simple interface to actuatethe robot. The disadvantage of the control board wasthat the signal controlled by the buttons did not directlycorrespond to the desired output variable. For example,a human operator is likely interested in controlling thebending angle of the robot, which can be difficult andtedious to obtain by manually actuating the TSAs. Infuture work, a more intuitive control interface may be

developed. For example, a joystick could be utilized to setthe top end of robot to a desired position in 3D-space.

6. CONCLUSION AND FUTURE WORK

In this paper, the development of a soft robotic manipula-tor powered by TSAs was presented. Firstly, the designand fabrication of the manipulator was discussed. Sec-ondly, the performance of the manipulator was studied byexperimentally analyzing the bending angle and the tipforce of the soft arm with respect to the number of twists(motor rotations) of the TSAs. Thirdly, the relationshipsbetween the motor rotations versus (1) bending angleand (2) output force were modeled using polynomials.Finally, a closed-loop controller was designed to controlthe bending angle of the manipulator. The experimentalresults confirmed the high performance of the manipulator.Despite the capabilities of the robot in this study, furtherimprovements can be made. Firstly, the traditional TSAscould be replaced by compliant TSAs that use conductivesupercoiled polymer (SCP) strings to realize strain self-sensing. Secondly, a physics-based dynamic model couldbe developed to capture the position of the free end ofthe manipulator as a function of the twisting angles of theTSAs. Finally, other soft robotic devices such as contin-uum robots and crawling robots could be realized usingTSAs.

ACKNOWLEDGEMENTS

The authors would like to thank Edwin Casildo Rios atthe University of Nevada, Reno, for his assistance in thereview of literature and selection of components.

REFERENCES

Almubarak, Y. and Tadesse, Y. (2017). Twisted and coiledpolymer (TCP) muscles embedded in silicone elastomerfor use in soft robot. International Journal of IntelligentRobotics and Applications, 1(3), 352–368.

Bombara, D., Konda, R., and Zhang, J. (2021). Experi-mental characterization and modeling of the self-sensingproperty in compliant twisted string actuators. IEEERobotics and Automation Letters, 6(2), 974–981.

Bombara, D., Fowzer, S., and Zhang, J. (2021). Compliant,large-strain, and self-sensing twisted string actuators.Soft Robotics. doi:10.1089/soro.2020.0086.

Chen, S., Cao, Y., Sarparast, M., Yuan, H., Dong, L.,Tan, X., and Cao, C. (2020). Soft crawling robots:Design, actuation, and locomotion. Advanced MaterialsTechnologies, 5(2), 1900837.

Gaponov, I., Popov, D., and Ryu, J.H. (2014). Twistedstring actuation systems: A study of the mathe-matical model and a comparison of twisted strings.IEEE/ASME Transactions on Mechatronics, 19(4),1331–1342.

Gaponov, I., Popov, D., Lee, S.J., and Ryu, J.H. (2017).Auxilio: A portable cable-driven exosuit for upper ex-tremity assistance. International Journal of Control,Automation and Systems, 15(1), 73–84.

Ho, M., Kim, Y., Cheng, S.S., Gullapalli, R., and Desai,J.P. (2015). Design, development, and evaluation of anMRI-guided SMA spring-actuated neurosurgical robot.International Journal of Robotics Research, 34(8), 1147–1163.

Laschi, C., Mazzolai, B., and Cianchetti, M. (2016). Softrobotics: Technologies and systems pushing the bound-aries of robot abilities. Science Robotics, 1(1).

Mirvakili, S.M. and Hunter, I.W. (2017). Artificial mus-cles: Mechanisms, applications, and challenges. Ad-vanced Materials, 30(6), 1704407.

Muller, R., Hessinger, M., Schlaak, H., and Pott, P.(2015). Modelling and characterisation of twisted stringactuation for usage in active knee orthoses. IFAC-PapersOnLine, 48(20), 207–212. 9th IFAC Symposiumon Biological and Medical Systems BMS 2015.

Nedelchev, S., Gaponov, I., and Ryu, J.H. (2020). Ac-curate dynamic modeling of twisted string actuatorsaccounting for string compliance and friction. IEEERobotics and Automation Letters, 5(2), 3438–3443.

Pawlowski, B., Sun, J., Xu, J., Liu, Y., and Zhao, J. (2019).Modeling of soft robots actuated by twisted-and-coiledactuators. IEEE/ASME Transactions on Mechatronics,24(1), 5–15.

Rich, S.I., Wood, R.J., and Majidi, C. (2018). Untetheredsoft robotics. Nature Electronics, 1(2), 102.

Rodrigue, H., Wang, W., Han, M.W., Kim, T.J.Y., andAhn, S.H. (2017). An overview of shape memory alloy-coupled actuators and robots. Soft Robotics, 4(1), 3–15.

Schmitt, F., Piccin, O., Barbe, L., and Bayle, B. (2018).Soft robots manufacturing: A review. Frontiers inRobotics and AI, 5, 84.

Shih, B., Drotman, D., Christianson, C., Huo, Z., White,R., Christensen, H.I., and Tolley, M.T. (2017). Customsoft robotic gripper sensor skins for haptic object visu-alization. In 2017 IEEE/RSJ International Conferenceon Intelligent Robots and Systems (IROS), 494–501.

Sridar, S., Poddar, S., Tong, Y., Polygerinos, P., andZhang, W. (2020). Towards untethered soft pneumaticexosuits using low-volume inflatable actuator compos-ites and a portable pneumatic source. IEEE Roboticsand Automation Letters, 5(3), 4062–4069.

Tang, X., Li, K., Liu, Y., Zhou, D., and Zhao, J. (2019).A general soft robot module driven by twisted andcoiled actuators. Smart Materials and Structures, 28(3),035019.

Tang, Y., Chi, Y., Sun, J., Huang, T.H., Maghsoudi, O.H.,Spence, A., Zhao, J., Su, H., and Yin, J. (2020). Leverag-ing elastic instabilities for amplified performance: Spine-inspired high-speed and high-force soft robots. ScienceAdvances, 6(19).

Ye, Z. and Chen, Z. (2019). Modeling and controlof a 2-DOF dielectric elastomer diaphragm actua-tor. IEEE/ASME Transactions on Mechatronics, 24(1),218–227.

Zhang, J., Sheng, J., O’Neill, C., Walsh, C.J., Wood, R.J.,Ryu, J.H., Desai, J.P., and Yip, M.C. (2019). Roboticartificial muscles: Current progress and future perspec-tives for biomimetic actuators. IEEE Transactions onRobotics, 35(3), 761–781.

Zhang, J., Simeonov, A., and Yip, M.C. (2018). Three-dimensional hysteresis compensation enhances accuracyof robotic artificial muscles. Smart Mater. Struct., 27(3),035002.

Zhou, X., Teng, Y., and Li, X. (2016). Developmentof a new pneumatic-driven earthworm-like soft robot.In M2VIP 2016 - Proc. 23rd Int. Conf. MechatronicsMach. Vis. Pract., 1–5.