Peristaltic locomotion with antagonistic actuators in soft robotics

Sangok Seok, Cagdas D. Onal, Robert Wood, Daniela Rus, and Sangbae Kim

Abstract— This paper presents a soft robotic platform thatexhibits peristaltic locomotion. The design principle is basedon the unique antagonistic arrangement of radial/circularand longitudinal muscle groups of Oligochaeta. Sequentialantagonistic motion is achieved in a flexible braided mesh-tubestructure with NiTi coil actuators. A numerical model for themesh structure describes how peristaltic motion induces robustlocomotion and details the deformation by the contractionof NiTi actuators. Several peristaltic locomotion modes aremodeled, tested, and compared on the basis of locomotionspeed. The entire mechanical structure is made of flexiblemesh materials and can withstand significant external impactsduring locomotion. This approach can enable a completely softrobotic platform by employing a flexible control unit and energysources.

I. INTRODUCTION

Peristalsis is common in small limbless invertebrates suchas Oligochaeta (worms). Oligochaeta need to deform theirbody to create the essential processes of locomotion (en-gagement, propulsion, and detachment) in contrast to leggedlocomotion which involves legs for the same functions. Bydeforming their body, worms can modulate friction forcesof ground contact points at the body. For applications thatrequire operation in limited space, peristalsis can enablerobust locomotion without the need for complicated limbstructures.

Several worm-like platforms have been developed foroperation in confined spaces, such as with endoscopy. Serialconfigurations of pneumatic actuators generated peristalticlocomotion for an endoscope that maneuvers inside a smalltube [4]. Alternatively, moving magnetic fields can drivesequential expansion of each segment when filled with amagnetic fluid [8]. Piezoelectric actuators have demonstratedreciprocal motion of two halves of the platform with direc-tional skin [2]. Finally, NiTi actuators have been used tocontract each elastic segment and then extend by releasingthe stored elastic energy in the structure [5].

This paper presents peristaltic locomotion using the uniquecharacteristics of a mesh-tube driven by antagonistic circularand longitudinal NiTi muscle groups. The body structureconsists of an elastic fiber mesh tube, which enables theantagonistic arrangement between radial/circular muscle andlongitudinal muscle [3]. The kinematic model of mesh tube

Sangok Seok, Cagdas D. Onal, Sangbae Kim, and Daniela Rus are,respectively, a graduate student, a post doctoral fellow, and faculty membersin Massachusetts Institute of Technology, Cambridge, MA 02139, USAsangok@mit.edu

Robert Wood is a faculty member in School of Engineering and AppliedSciences at Harvard University, Cambridge, MA 02138, USA

This work is supported in part by Defense Advanced Research ProjectsAgency (DARPA) grant W911NF-08-C-0060 (Chemical Robots)

longitudinalmusclefibers

circularmusclefibers

Oligochaetamusclestructure

coelom

20mlofpayload

MicroNiTicoilactuators

Fig. 1. Oligochaeta utilize antagonistic radial and longitudinal deformationof the body. The meshworm prototype exhibits peristaltic locomotioninduced by a similar antagonistic configuration.

Longitudinalmuscle

Circumferen3almuscle

θ

Fig. 2. The mesh structure can transmit power from the longitudinaldirection to the radial direction and vice versa.

deformation describes how peristaltic contraction enableslocomotion of the platform. To ensure a minimum numberof actuators, induced antagonistic actuation is introduced andexperimentally validated. Multiple gait modes are chosen andtested on the prototype and analyzed to determine locomotionspeed and efficiency.

II. ANTAGONISTIC ACTUATION IN SOFT BODIES

Natural muscles generate power in contraction. Vertebratesattain flexion and extension motions from intricate kine-matics of rigid bones, joints with cartilage, and contract-ing muscles in antagonistic arrangements. In invertebrates,a hydrostatic skeleton enables shape change and stiffnessmodulation. Oligochaeta, in particular, employ an antago-nistic pairing of radial muscles and longitudinal muscles.Figure 1 shows the arrangement of muscle groups found inOligochaeta.

Antagonistic circular or radial muscles and longitudinalmuscles control movements of the hydrostatic bodies ofearthworms [6]. Coelom in each septum contains liquid thatworks as fluidic transmission between the longitudinal andradial directions. With this divided cavity filled with fluid,

Fig. 3. Comparison between hydrostatic cylindrical deformation found innature and deformation in fiber mesh-tube.

e Mesh-fibers

Projection of e

Radius of the crossing point

e

e : Length of equilateral parallelogram

Fig. 4. The projection of an individual fiber in the mesh structure to theplane perpendicular to the axis of the mesh-tube. The length of a spiralstrand does not change over antagonistic deformation but changes radiusand height.

each segment of the worm can deform with a constantvolume constraint [1], [6]. The hydrostatic skeleton can bethought of as an elastic cylindrical container that variesradius and length subject to fixed internal volume.

With mesh tubes, a similar antagonistic configuration hasbeen previously demonstrated [3]. The mesh tube structureis composed of multiple spiral polymeric fibers woven into atube shape. An increase in the pitch of the individual spiralfiber results in a reduction of its radius and decrease in pitchexpands the radial dimension of the spiral. Figure 3 showsthe relationship between length and radius in earthworms(constant volume) and in the mesh-tube. In a constantvolume cylinder, the relationship between radius and lengthof the cylinder follows (1). In a mesh-tube structure, therelationship between radius and length follows (2).

r2l = Constant (1)Ar2 + l2 = Constant (2)

where r is radius and l is length of the cylinder and where Ais characteristic coefficient of the cylinder. Correspondingly,parabolic and circular curves are found in Figure 3.

(b) (a) (c) (d)

Fig. 5. (a) One spiral strand shown in 3D space. Mesh-tube is woven frommultiple strands of these polymeric spirals. (b) Projection of an individualspiral to any plane which contains the worm’s longitudinal axis is a sinusoid.(c) Recreation of the mesh-tube on a 2D surface is a combination ofsinusoidal curves. (d) Simulated deformation.

(a)

(b)

(c)

Fig. 6. Simulation results show three different actuation mode. (a)The 2ndactuator is actuated. (b)The 2nd and the 3rd actuators are actuated. (c)The1st and the 3rd actuator are actuated.

III. PERISTALTIC LOCOMOTION

A. Simulation

The mesh-tube structure consists of multiple spirals. Eachspiral is kinematically identical to a stretched spring. Understress, the tube deforms in a antagonistic regime with aconstraint given in (2). The basic element is an rhombus.Mathematically, we can assume the mesh-tube is composedof a number of rhombi, shown in figure 4 using a cylindricalcoordinate. The lengths of each side are assumed to beequal and remain constant under deformation. Also, eachrhombus can bend out of plane along the diagonal lineperpendicular to the longitudinal axis of the tube. In otherwords, each rhombus can create two equilateral triangles andthe two triangles can bend within a limited angle. In figure4, e remains constant and the radii of mesh crossing pointschanges depending on the deformation. Also, θ in this caseremains constant since the number of mesh crossing pointsalong the perimeter remains constant.

r2n+1(sinθ)2 + (rn − rn+1(cosθ)

2 = e2(cosβn)2 (3)

β = cos−1

(√r2n+1 + r2n − 2rn+1rncosθ

e

)(4)

zn+1 = esinβn (5)

Through (3) (5), we can calculate zn+1 as a function ofrn. Once the radius profile as a function of z of the tube isknown, we can obtain geometrical configuration of the entiremesh structure. The radius profile is experimentally verified

0 50 100 150 200 250 -10 0 10

-10 0 10

-10 0 10

(b) (a)

Ist segment contraction

2nd segment contraction

Fig. 7. The red solid lines represent mesh-tube deformation in the sagittalplane (left). Magnification of the trajectory of the black point (right). Theblack point travels through the air during the contraction wave passes.

Contact

Contrac)ngsegment

1 2

1

1

1

1

2

2

2

2

3 4

3 4

3 4

3 4

3 4

Longitudinaltendon

Relaxedsegment

δ

Fig. 8. An example of peristaltic locomotion sequence by inducedantagonism in the sagittal plane. Dotted red line represent contact with theground. Longitudinal tendons keep the body length constant. Contraction ofradial actuators induces radial expansion of adjacent segments.

since the stress-strain analysis of the weave of the elasticstrands becomes excessively complicated.

The motion of the system was simulated using a numericalmodel for the mesh-tube structure. Figure 6 shows thesimulated deformation of the mesh-tube. Sequential radialcontractions of the segments result in peristalsis. Figure 7shows how sequential contraction of segments can inducerobust locomotion. The red solid lines represent body defor-mation in several time sequences between first and secondcontractions. The dotted blue line represents the trajectory ofa point of the skin contacting the ground periodically whensegments contract radially and expand axially. Assumingthat the ground is flat, the contact point releases from theground with radial contractions and travels through a swingphase forward of the initial contact point. If trajectories of anumber of points along the tube are considered, they createa traveling wave. This resembles leg trajectories found insmall arthropods, which create a couple of waves of trajec-tories of legs instead of body deformation. The trajectorydepends on the relative position relative to the segmentborder. However, if the segments are small enough to createa pseudo-continuous wave in the body deformation, everypoint will detach from the ground, progress, and land on theground. This simulation shows how a peristaltic wave createdby antagonistic radial and longitudinal actuators can createeffective locomotive without legs.

B. Induced antagonism

Two different arrangements of NiTi actuators were con-sidered for the mesh-tube prototype. The first arrangement

lw

1 2 … Nw

Fig. 9. A general expression of all possible gaits.Nw represents the numberof gaits and lw represents the number of contracted segments (length ofwave)

consists of a series of individual active antagonistic seg-ments with both longitudinal and radial actuators. In thiscase, each segment can independently contract in radialor longitudinal directions. This enables independent con-trol for various gaits but introduces high complexities infabrication and in synchronizing multiple NiTi actuatorsin order to create effective gaits. In particular, NiTi issensitive to heat dissipation and thus it becomes challengingto synchronize multiple actuators in phase. The secondmethod utilizes induced antagonistic actuators. Instead ofadding longitudinal actuators at each segment, flexible butinextensible tendons are attached through the body alongthe longitudinal direction. The longitudinal tendon keeps thebody length constant, thus any local longitudinal expansioncreates other sections’ longitudinal contraction. The constantlength constraint forces neighboring segments to contractlongitudinally and expand radially, hence the antagonism.Figure 8 shows how the length constraint enables coupledbehavior among segments. Consider the bottom sequence inFigure 8. The radial actuators in the first segment contractradially and expand in the longitudinal direction. This alsoinduces reduction of last segment’s length because of thetotal length restriction by the tendons. This method enablesinduced antagonism between deformation in longitudinal andradial direction without a passive spring return, which causesa significant bandwidth limitation. A prototype using thesecond method is described in section IV. Quillin expressesthe speed of the worms by protrusion times and stancetime [7] with stride length. His analysis includes the totallength change in worms. Assuming the total number of bodysegments is large enough, which is consistent with worms’case, a general expression for all the gaits available using thisapproach is shown in Figure 9 Thus, the theoretical speed ofthe locomotion is,

Speed = δ ×Nw × lw × f (6)

where δ is the length change of each segment, Nw isnumber of waves of contraction, lw is a number of segmentscontracted in single wave, and f is the frequency of thewaves.

IV. EXPERIMENTAL RESULTS

A. Controller

A key goal of the experiments has been to test andmeasure the effectiveness of several locomotion gaits for theMeshworm. We developed a gait controller using LabVIEWsoftware and NI Single-Board RIO (NI sbRIO-9642). Figure

10 shows a screenshot of the control panel. This experimentalsetup allows various actuation sequences, the number ofactive segments and duration.

For a standalone implementation of the Meshworm, weused a custom PCB as an embedded controller. Figure 11shows the control board which has a very small form-factorthat easily fit inside the robot body. Equipped with an AT-mega88PA microcontroller, the PCB has eight digital outputsthat are used to drive eight MOSFETs, which are connectedto a separate power line to protect the microcontroller fromlarge currents. Actuation power is supplied by an on-boardstep-up regulator. Using the digital outputs, we can regulatepower to the individual NiTi coils to produce different gaits.In addition, the board has eight 10 bit A/D channels forclosed-loop implementation.

We built an experimental prototype using a polyesterbraided mesh tube. The tube is approximately 22mm indiameter and each strand is 0.25mm in diameter. The lengthof the tube is approximately 20cm in the unloaded state.The unloaded state is created by annealing the polyestermesh-tube held with a metal pipe with the desired diameter.The annealing temperature is approximately 125◦C and theduration is 10 min. Since polyester is a thermoplastic, theunloaded state can be reconfigurable with different sizes ofthe metal pipe. NiTi coil actuators introduced in [3] are used.The wire diameter is 100 µm and the coil diameter is 400µm. Five NiTi actuators are wrapped around the tube.

NiTi actuation is based upon a solid-state phase transitioncontrolled by temperature changes. Since this is a ther-mal process, these actuators are typically rather inefficient.Greater efficiency can be achieved by rapid current pulsesas opposed to constant currents. Figure 12 compares radiuschanges with various current settings. Using a segment of themesh-tube and a circumferential actuator, the radius profileis plotted as a function of time. If the 400mA current withshorter pulse time is compared with 200mA current setting,it is clear that higher current with a shorter pulse durationresults in quicker and more energy efficient actuation. Thishigh current value, however, yields a steady-state temperatureabove the glass transition temperature of the body material

Segments

Tim

e St

eps

1 2 3 4 5

Actuated segments (Austenite state)

Passive segments (Martensite state)

Control Panel

Fig. 10. Control panel used for generating various gait for the meshwormprototype.

Fig. 11. A micro-controller prototype for gait generation and a Li-Polybattery.

0 0.5 1 1.5 2 2.519

19.5

20

20.5

21

21.5

22

22.5

time [sec]

Dia

met

er [m

m]

I = 400 mAI = 300 mAI = 200 mAI = 150 mASigmoid Fit

Fig. 12. Radius of the mesh as a function of time in different currentsettings on circumferential actuators.

and hence should be applied for short time intervals only.The given pulse consumes about 3.2 J of energy.

Additional experiments include measurements of thelength change of each segment, displacement of the mesh-tube, and overall locomotion speed. An external camerasystem (Microsoft LifeCam VX-3000) is used for capturingmotions of the prototype and the prototype has motiontracking markers at the borders between the segments. Asthe mesh-tube moves, the camera tracks the distance betweenthe markers and the head position of the tube for the overalltravel. The frame rate is 15 fps with 640 x480 resolution forlocomotion tests and 30 fps with 320x240 for contractionexperiments. The current applied to the actuators is 400mAwith 200ms duration.

We tested two different modes (gaits). The first mode isthe short-wave mode: Nw = 1, lw = 1. The second modeis the long-wave mode where two adjacent segments are

Short wave mode Long wave mode

Segments

Tim

e St

eps

1 2 3 4 5Segments

Tim

e St

eps

1 2 3 4 5

Fig. 13. Two different gaits were tested: short wave mode has one segmentcontracted at a time. Long wave mode have two segments contracted at atime.

Segment 1 Segment 2 Segment 3 Segment 4 Segment 5

Time (s)

Dis

plac

emen

t (m

m)

14

0

2

4

6

8

10

12

0 1 2 3 4 5 6

Fig. 14. Lengths of segments as a function of time. The data is filtered at5 Hz.

Time (s)

Velo

city

(m

m/s

)

-10

0

10

20

30

40

0 1 2 3 4 5 6 7 8 9 10 11 12

Time (s)

Dis

tanc

e (m

m)

70

0

10

20

30

40

50

60

0 1 2 3 4 5 6 7 8 9 10 11 12

Fig. 15. Displacement (top) and velocity (bottom) of the prototype usingthe short wave mode. The data is filtered at 5 Hz.

contracted at a time: Nw = 1, lw = 2. We figure thatthe distance between two waves in multi-wave mode shouldbe long enough because it needs cooling time. Therefore,the implementation of gaits with more than one waves forMeshworm which has only five segments results in inefficientlocomotion.

B. Closed-loop Control

The NiTi coil actuators are sensitive to environmentconditions (e.g. ambient temperature, air flow). This makesopen-loop control ineffective and inconsistent. For reliableactuation of NiTi, a feedback control is implemented usingsmall hall-effect sensor/magnet pairs that measure the radiusof a segment of the body. The desired radius can be achievedby controlling the time interval of current through the NiTicoils based on the signal from magnet sensor.

7

0

1

2

3

4

5

6

10 0 1 2 3 4 5 6 7 8 9 Time (s)

Dis

plac

emen

t (m

m)

Segment 1 Segment 2 Segment 3 Segment 4 Segment 5

Fig. 16. Using the long wave mode, five segments’ lengths are plotted asa function of time. The data is filtered at 5 Hz.

-15 -10 -5 0 5 10 15 20

13 0 1 2 3 4 5 6 7 8 9 10 11 12 Time (s)

Velo

city

(m

m/s

)

10

0

2

4

6

8

13 0 1 2 3 4 5 6 7 8 9 10 11 12

Time (s)

Dis

tanc

e (m

m)

Fig. 17. Displacement (top) and velocity (bottom) of the prototype usingthe long wave mode. The data is filtered at 5 Hz.

0 0.5 1 1.5 20

0.5

1

1.5

2

2.5

3

time [sec]

V

read [V]

δ [a.u.]E

nor = t/t

max

fobj

= (1−Enor

)δ

Fig. 18. Functions used to achieve the objective function. Voltage fromthe hall-effect sensors are converted to deflection data by δ = V −1/3−δ0.Energy consumption is normalized by a maximum time interval tmax = 2sec.

From Figure 12, we experimentally determined that thedeflection (δ) of a single segment can be described by ageneral sigmoid function and energy consumption is di-rectly proportional to time (E = I2Rt). Normalizing theenergy with the energy consumed at the maximum duration(I2Rtmax) yields Enor = t/tmax. The voltage reading fromthe hall-effect sensor has approximately an inverse cubicrelation with the deflection of the radius. This relation givesδ = V −1/3−δ0 in arbitrary units, where δ0 describes the ini-tial separation between the sensor and the magnet. Borrowingideas of optimization theory, we chose a steepest descentalgorithm on an objective function fobj = (1−Enor)δ, whichcorresponds to a metric that defines the trade-off betweenpower consumption and deflection as seen in Fig. 18. Usingthis method, an optimal current interval was experimentallyfound as shown in Fig. 19.

V. DISCUSSION

Figure 14 shows a plot of segment lengths as a function oftime. From this result, we can calculate theoretical speed dueto (6). δ average is 9.98 mm, f = 1/2.5 Hz, and Nw = Iw = 1,so theoretical speed becomes 3.99 mm/s. Also, actual speedcan be found from displacement plot in Figure 15. It is 3.47mm/s which is 13% lower than theoretical speed.

Unlike the ideal condition shown in Figure 8, the lengthchange does not complete at one step since a finite time(2seconds) is required for NiTi to shift its state from austenite

0 10 20 30 40 50 60 70 80400

450

500

550

600

650

700

Iteration

Tim

e S

tep

[mse

c]

Fig. 19. Experimental results using a steepest descent algorithm on fobj .Time steps gradually converge to an optimal value of τ ≈ 680 msec basedon this metric.

to martensite. When a radial actuator contracts, the corre-sponding segment elongates in the longitudinal direction.When the next segment contracts, it elongates and shortensthe previously elongated segment where the radial actuatorbecomes martensite and ready to detwine. The segment’slength does not become original length shown as the mini-mum value in Figure 14. This imperfection causes backwardmotion of the body in Figure 15. The long wave mode is notas efficient as the short wave mode in practice. Theoretically,the speed should be proportional to length of the wave. Sincethe total length of the prototype has only five segments, thereare only three unactuated segments. The mesh-tube couldnot hold the position very well with only three segmentsgrounded.

Variations in the change of length is caused by errors inthe manufacturing process. The short-wave mode is the mostreliable mode among gaits we have tried. When actuationshifts from one segment to adjacent one, three radially-expanded segments remain still holding the ground withfriction forces. As discussed in the peristaltic locomotionsection, the trajectory of points lift from the ground as thewave passes. However, in practice, the real trajectory tends toslide along the ground surface with several possible reasonssuch as imperfections in manufacturing, variation in actuatorstrength, and lack of friction between the body and theground.

VI. CONCLUSIONS AND FUTURE WORKS

Peristaltic locomotion by a soft bodied robot with antago-nistic actuation is successfully accomplished in this study.Speed and energy efficiency can be optimized by furtherinvestigation of gait generation and actuator fabrication.Additionally, more functions can be added by increasingin number of degrees of freedom. The mesh-tube prototypehas five segments whereas biological counterparts have closeto 100 of segments. The length of the each segments inthe mesh-tube is relatively longer compared to that of anearthworm. This prevents smooth wave travel through thebody and implementation of various gaits and functions. Thecurrent manufacturing process involves hand constructionand connections of the NiTi actuators to the mesh structure.For versatile performance of the platform, advances in the

Fig. 20. An experiment to verify the robustness of the mesh-tube platformis performed. During locomotion, a rubber hammer impacts the mesh tubeand the mesh tube experiences substantial amount of impact on the body.The results show that the mesh tube can continue locomotion after severalimpacts from the hammer.

fabrication methods will enable a greater number of segmentsin a given length, and hence smoother waves and moreefficient gaits. Direction changes introduced in [3] can beapplied to the mesh-tube platform to increase maneuverabil-ity. Since the platform contains no rigid components that mayfail by external impacts, this approach can open a new spaceof applications for robust morphable robots. With further de-velopment of a microprocessor and battery with flexible formfactors, this approach suggests a new paradigm of completelysoft robotic systems, that can demonstrate significant bodymorphing and versatile locomotion capabilities.

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