2024 7th International Conference on Soft Robotics (RoboSoft)San Diego, CA, USA. April 14-17, 2024

Interaction Behaviors of a Vine Robot in a Pipe T-Junction

2024 IEEE 7th International Conference on Soft Robotics (RoboSoft) | 979-8-3503-8181-8/24/$31.00 ©2024 IEEE | DOI: 10.1109/ROBOSOFT60065.2024.10522034

Lily Behnke1 , Brian H. Do1 , Sophia Eristoff1 , and Rebecca Kramer-Bottiglio1

Abstract— Continuous advances in soft robotic technologies have promoted the feasibility of exploration of complex
environments and terrains. One prominent example is theclass of tip-everting “vine” robots, which have enabled a
new set of real-world applications. Vine robots navigate theirenvironment through growth and have recently been used inpractice for in-pipe inspection, maintenance, and exploration.
While locomotion through these directed cylindrical systems is
simplified by a vine robot’s growth, there are challenges withnavigation. In complex pipe networks with many junctions,
one question is how a vine can navigate around its own bodyduring exploration. For example, a vine may navigate a pipe
network that forces the robot to traverse a section of a pipe it
already traversed in the opposite direction. This work presents
an experimental approach to investigating and characterizing
the interaction of a vine with its own body inside of a pipe
T-junction. The results of this work provide initial design
recommendations for facilitating the successful navigation ofa vine robot in a T-junction.

Fig. 1. A pipe network with a magnified inset of the T-junction along avine robot trajectory. The two schematics indicate two potential outcomesof the vine robot coming into contact with its own body: one that allows
continued locomotion and one that stalls locomotion.

is their ability to easily interact with their environments andleverage these interactions, previous work has only characterized vine robot interactions with rigid environments andobstacles [11]–[13]. Vine robot interactions with compliant
or compliance-matched objects, such as its own body, havebeen much less studied.
To exemplify the relevance of pipe navigation as a grandchallenge in soft robotics, the 2023 IEEE International
Conference on Soft Robotics (RoboSoft) held a competition
on “in-pipe locomotion,” featuring a mazelike pipe network
for robots to autonomously navigate [14]. This challenge
mimicked a real-world scenario where the task completion
required navigating through a T-junction as shown in Fig. 1.
A vine robot was indeed used in the competition and won
third place, although failed to navigate through the T-junction
to complete the course. This prior Robosoft competition
result further motivated the work herein.
In this work, we characterize passive vine robot selfinteraction behavior inside a pipe T-junction. We also explore
the capabilities of vine robots to locomote through a pipe andenvironments with self-constrained boundaries. The resultsof this study aim to provide insight into basic design parameters that promote successful continued locomotion for vine
robots that intersect their own bodies inside pipe T-junctions.

I. INTRODUCTION
Exploring confined environments and complex terrain isa major goal in robotics, but navigation in confined, complex, or viscous spaces is difficult for traditional gait-based
systems [1]. While soft robots aim to accomplish tasks
such as search and rescue, ecological monitoring, medical
intervention, and industrial maintenance, challenges still exist
for navigation of the aforementioned environments [2]–[4].
As such, a class of soft robots known as vine robots that
locomote through growth has been leveraged to address thelimitations of other robots in exploration [5].
One application that necessitates such exploration is inpipe inspection and maintenance [6]. Pipes and pipelike
structures are ubiquitous in modern society, ranging fromoil and water pipelines to air ducts. Research into in-pipe
locomoting robots extends back decades, but navigating
through variable diameter pipes and complex pipe networks
involving T-junctions remains challenging [6].
Vine robots are especially well-suited for such applications. One of the most applied use cases for vine robots
has been the exploration of networks such as electricalconduits, tunnels, and pipes [7]–[10]. However, since vine
robots move through the growth of their own bodies, tunnel
or pipe environments with loops or intersecting branches, avine robot may have to navigate around its own body forcontinued locomotion. While a key advantage of soft robots

II. BEHAVIOR CHARACTERIZATION
A. Experimental Setup
To characterize the behavior of a vine robot in a pipe Tjunction, an experimental setup consisting of an inlet, loop,
and T-junction was constructed from clear 6.35 cm diameter
pipes (Jumpanny). Vine robots were fabricated from 1.3 ozsilicone-impregnated ribstop nylon (Seattle Fabrics) and were
each 150 cm in length with varying diameters. A Nikon

1 Schoolof Engineering and Applied Sciences, Yale University,
New Haven, CT, USA email:{lily.behnke, brian.do,

sophia.eristoff, rebecca.kramer}@yale.edu
L.B. was supported by the National Science Foundation Graduate Research Fellowship (DGE-2139841). B.H.D. was supported by the National
Science Foundation under grant no. IIS-1955225. S.E. was supported by theNASA NSTGRO fellowship (80NSSC21K1269).

979-8-3503-8181-8/24/$31.00 ©2024 IEEE

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Fig. 2. Still images of the behaviors demonstrated by a Dr /D p = 0.68 vine robot in a pipe T-junction for self and rigid rod collisions with accompanying
schematic visual representations. Bar chart showing the outcome percentage of each behavior across both collision types (rigid and self) for all vine robot
diameters and operating pressures. The red and green coloring separates the behaviors into whether locomotion continued successfully or failed.

camera was positioned above the T-junction to record thevine interaction and trajectory. For each trial, the vine robot
was placed at the inlet and pressurized to begin tip eversion.
The robot traversed through the base of the T-junction before
looping around to the top of the T-junction via three pipe
elbows, ultimately directing the vine to contact itself.
A similar setup was made using a rigid rod as an obstaclein the T-junction. This rigid interaction was used as a control
since the interactions of vine robots with rigid structures are
more defined in literature [11]–[13]. For each vine tested, a
PLA rod of the same diameter was placed in the T-junction
base during testing. The vine robots were pressurized from an
inlet point after the T-junction base and then passed throughthree pipe elbows to approach the T-junction and interact
with the rigid rod.
Each self-interaction and interaction with a rigid rod was
carried out at five different pressures (50, 70, 90, 110, and130 kPa) and four vine diameters (2.25, 3.25, 4.25, and5.25 cm). Diameter and pressure were investigated because
they are two universally controllable design parameters forvine robots. For each interaction at a given diameter andpressure, 10 interactions were recorded; in total, there were
200 trials for both the rigid and self characterizations.
Figure 2 shows segmented still images of the resulting vine
robot behaviors and success vs. failure characterizations withrespect to continued locomotion through the T-junction.

one of five behaviors: When successful, the vine either 1) hit
the body and then bent left or right to continue locomotionor 2) moved past the body and hit the wall to then bend leftor right. When unsuccessful, the vine either 3) got stuck on
the body it collided with, 4) moved past the body and got
stuck on the wall, or 5) looped around the body to continue
locomotion in the direction of approach.
It was hypothesized that a vine colliding with its own
body would pose a treacherous obstacle due to the matchedcompliance of the bodies. However, it can be observed inFig. 2 that a vine colliding with its own body showed
greater success than a vine interacting with a rigid rod. In
fact, self-interaction behavior demonstrates greater successthan interaction with a rigid rod in both success categories.
Furthermore, it was observed that failure due to the vine
looping around the rigid rod was the most common outcome across all experiments; this is consistent with priorwork on vine robot interactions with rigid barriers [11].
Generally, the outcomes in Fig. 2 demonstrate that contact
with a compliance-matched body better facilitates T-junction
navigation compared to with a rigid body.
III. SELF-CONTACT OUTCOMES
After observing that the self-contact of a vine robot facilitates successful T-junction navigation, we further investigatedthis behavior. We characterized each instance where thevine was observed hitting its own body, buckling, and thensuccessfully continuing locomotion, which occurred in 53
out of the 200 tests conducted. We then performed motion
tracking of the vine self-contact in post-processing (Tracker
Inc.). The pose of the approaching vine tip to the stationaryvine body was tracked throughout the buckling behavior, andthe contact angle between the bodies was calculated. The
initial time stamp for the analysis was when the vine robot
first made contact with its own body, and the final time stamp
was marked just after the vine robot buckled and the axial
portion of the vine above the buckle point stabilized.

B. Characterization
Figure 2 shows the characterized behaviors and frequency
for both interaction types, also categorizing the behaviors asa success or failure. Success was defined as the vine robot
continuing locomotion to the completion of its length, leftor right, after colliding with the body in the junction, andany other outcome was defined as a failure. The images tothe left of the plot show stills of each behavior for both self
and rigid interactions and schematics of the behavior. Duringlocomotion inside the T-junction, the vine robot exhibited
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angle and the onset of buckling differs by about 15◦ . Thissuggests that repositioning is required by larger-diametervines to achieve buckling during a self-interaction. Moreover,
the angle at the completion of buckling also differs between
small and large-diameter vines. As shown in the still images
for the Dr /D p = 0.36 vine, buckling occurs further in thepositive y-direction from the contact point and causes thevine to buckle to 0 degrees relative to the stagnant partof the body parallel to the x-axis. This buckling behavior
is reflected in the large difference between the onset andcompletion of buckling angles. However, for larger diametervines, Fig. 3 shows that the difference between the onsetof and completion of buckling is more narrow. This can beobserved by the corresponding sequence of images for the
Dr /D p = 0.68 vine, where buckling occurs at the tip of theapproaching body where the contact takes place.
IV. DESIGN PARAMETER INVESTIGATIONIn this section, we analyze how three design parameters—
diameter, pressure, and stiffness—affect successful vine
robot traversal in a T-junction. We also relate results fromempirical tests, summarized in Fig. 4, to interaction models.
A. DiameterAs shown in Fig. 3, vine robot diameter plays a criticalrole in the buckling progression of the robot. Since buckling
is a vine robot’s key mode of enabling locomotion when
encountering a barrier, it was anticipated that vine-robot
locomotion in a T-junction would be diameter-dependent.
Figure 4 demonstrates this diameter dependency on the
success mode and frequency in a T-junction as well as
the relationship between compressive modulus and diameter. In Fig. 4 (a)-(e), the results from the self-interaction
experiments are plotted as a function of Dr /D p for thefive pressures tested. The points in Fig. 4 (a)-(e) show
the total success percentage of each diameter vine robot
across the five tested internal pressures. The bars under eachpoint represent the contribution of each successful behavior
toward the total. The two behaviors categorized as successfulnavigation are illustrated by the schematics in Fig. 4 (f) and(g), respectively.
We observed that smaller diameter vine robots are more
successful than larger diameters ones at navigating a Tjunction. The smallest diameter vine robot (Dr /D p = 0.36)
was the most successful for 4 of the 5 operating pressures,as shown in Fig. 4 ((a)-(e)). This trend further extends to thesecond smallest vine robot diameter tested (Dr /D p = 0.52)
which was the second most successful diameter with all thepressures considered.
Smaller vine diameters are less likely to come into
contact with their own bodies in the T-junction. From
Greer et al. [11], when the tip of the vine robot is in contact
with a rigid obstacle and free growth is possible, the robot
tip will move parallel to the obstacle surface, pivoting about
the last previous point of contact. The reaction force fromthe obstacle will cause the vine robot to buckle about thatpivot point, allowing the robot to move around that obstacle.

Fig. 3. Top: Still images showing contact angle during initial contact at
the onset of buckling and at the completion of buckling for small and large
diameter vine robots. Bottom: Graph of contact angles vs diameters. The
scatter plot points represent the angle for each occurrence of the behavior
for the respective vine diameter while the line represents the average.

Figure 3 shows the resulting progression of the contact
angle throughout this self-intersection behavior as a functionof vine diameter. The plot’s x-axis represents the ratio Dr /D pof the vine robot diameter Dr to the diameter of the pipe
D p . The three lines on the plot represent key events in thismotion: initial contact, buckling onset, and completion ofbuckling; stills of these events are shown in Fig. 3.
The initial contact angle (orange) was similar for all vine
robot diameters, ranging between 75◦ and 90◦ , indicating
this initial contact angle may be required for self-intersection
behavior. Furthermore, for small-diameter vines (Dr /D p =0.36 and 0.52), only a marginal difference exists between theinitial contact angle (orange) and the onset of buckling angle(blue). However, for larger diameter vines (Dr /D p = 0.68
and 0.84), the average difference between the initial contact
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Fig. 4. a-e) Frequency of successful navigation of a pipe T-junction for a vine robot as a function of pressure and diameter. f-g) Schematics of successfulnavigation modes corresponding to the bar chart compositions in a-e. h) Compressive modulus of a vine robot of constant diameter (Dr /D p = 0.68) asa function of pressure. i) Compressive modulus of a vine robot of constant pressure (90 kPa) as a function of diameter. j) Success frequency of threecase studies where a Dr /D p = 0.84 vine approaches itself (compliance-matching; green), a rigid rod (orange), and a soft foam cylinder (blue) in a pipe
T-junction.

the vine robot applies to its environment. In the T-junction,
when the robot hits its body head-on, it must undergo axial
buckling before continuing to traverse the pipe network.
From Fichter [15], the critical force for axial buckling is:2
EI πL2 PA + π2 GDr t
(1)
Fcr =
2
EI πL2 + PA + π2 GDr t

For smaller diameter vines, this obstacle interaction dominates as the vine either misses its body and simply slides
along the inside of the T-junction wall or slides around its
body before proceeding to the wall. The tip of the robot
will slide as it pivots about the top of the T junction until
it undergoes transverse buckling and completes the 90◦ turnto the other branches of the pipe network.
However, this trend does not extend to larger vine diameters, where the primary success mode was throughself-contact. The data in Fig. 4 (a)-(e) show each successmode’s frequency. Besides the smallest vine robot diameter(Dr /D p = 0.36), successful navigation due to self-contacts
was more frequent than successful navigation from a wallcontact because large diameter vines have less free spacewithin the T-junction and thus must interact themselves.

where E, G, and t are Young’s modulus, shear modulus, andthickness of the wall material, respectively; I is the beam
second moment of area; P is the internal pressure; A is the
cross-sectional area; and L is the length of the robot body.
When interacting with its environment, the vine robot
is subject to a reaction force F = PA resulting from its
attempted growth. If F > Fcr , the robot will buckle. If theforce is not high enough to cause immediate buckling, therobot may end up getting stuck on its body or slipping around
its body and failing to buckle to successfully navigate the Tjunction. This explains why increasing P promotes buckling,
as it can increase F so that F > Fcr .
Equation 1 can be rewritten to explicitly solve for thecritical pressure Pcr for buckling. Substituting Fcr = Pcr A into
Eq. 1 and solving for Pcr , we find that increasing Dr increases
the required Pcr and Fcr for buckling.
One key difference between this work and past work isthat the vine robot interacts with a compliant obstacle—its
own body. When the vine robot hits its body, both the tip
and the body deform. This deformation plays a key rolein keeping the robot tip perpendicular to the body until
wrinkling propagates around the circumference of the body,enabling self-buckling and successful traversal of the Tjunction. At larger diameters, the vine robot always hits its
own body, and this compliant interaction is key in successful
traversal. Modeling this compliant interaction is complex andwill be addressed in future work.

B. Pressure
We also investigated the effect of the vine robot’s internal pressure. Each plot in Fig. 4 (a)-(e) also presents therelationship between pressure and navigation success. At an
operation pressure of 50 kPa, no vine robot was notably more
successful in navigating the pipe T-junction, indicating that
this pressure did not produce the critical force for the vine
robot to consistently buckle. However, at 70 kPa (Fig. 4 (b)),
overall success increases for all tested diameters. Aside from
50 kPa, the total success rates of smaller diameter vine robots
were consistent. However, at larger vine robot diameters
there is an increase in vine robot success as a function ofpressure. Specifically, for Dr /D p = 0.84, there is a steadyincrease in success due to self-contact from 50-130 kPa.
The vine robot can be modeled as an inflated beam. Whenthe vine robot operates in a constrained environment, such asa pipe network, it navigates by reconfiguring its body. This
reconfiguration occurs through buckling caused by the forces
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Figure 2 (j) implies that for matched compliance interactions, successful buckling and continued locomotion are
facilitated by increased stiffness. However, for mismatchedcompliance vine interactions, collisions with soft bodies
produces greater success for continued trajectory comparedto rigid bodies. Very rigid objects act as rigid obstacles
which often deflect the robot around them, leading the vine
robot to loop around rather than self-buckle. Meanwhile,
very compliant objects are compressed by the vine robot andconform to the T-junction interior walls or are simply pushed
out of the way. Afterwards, the typical vine interactions inconstrained environments occur and the vine tip slides along
the surface until it buckles and exits the T-junction.

C. Stiffness
Prior work has shown that variable stiffness can facilitatevine robot shape change [16], [17]. Our observation ofincreased navigation success with increased pressure forlarge diameter vines prompted a deeper investigation into
the relationship between stiffness and navigation success.
1) Compressive Modulus: We tested how the vine robot’s
compressive modulus varies with diameter and pressure. We
conducted compression tests on representative inflated beams
for a constant pressure (90 kPa) with varied diameter and fora constant diameter (Dr /D p = 0.68) with varied pressure.
Using a universal testing machine (Instron 3345), samples
were loaded transversely on a flat plate and compressed to
50% displacement at a rate of 5 mm/s. The resulting stressvs. strain curves were obtained, and their slopes were used
to obtain the compressive modulus. Each sample was tested
5 times at each condition. Figure 4 (h)-(i) show the results.
Increasing compressive modulus increases navigation success. Figure 4 (h) presents the relationship of inflated beamcompressive modulus with pressure. The inflated beam compressive modulus increases as a function of input pressure
for the tested range (50-130 kPa).
Figure 4 (i) presents the relationship between compressive
modulus and inflated beam diameter. Inflated beam diameteris reported as a ratio with respect to pipe diameter forconsistency. The results show that inflated beam compressive
modulus increases as a function of diameter. For larger
diameter vines, increased pressures resulted in a greater
propensity for successful T-junction navigation (Fig. 4 (a)(e)). Larger diameters guarantee vine contact in a T-junction,
resulting in a dependence on this material interaction.
2) Compliance Mismatch: When changing pressure alone,
the stiffness of the entire vine increases together; the tip
and body compliance are matched. To further investigate theeffect of stiffness on vine interactions, we also looked atcases of large compliance mismatch between the vine tip
and the body it interacted with. We conducted three casestudies for a constant Dr /D p (0.84): a vine colliding with 1)
its own body, 2) a rigid PLA body, and 3) a soft foam body;tests were performed for a constant diameter over a rangeof pressures. The ratio between the compressive modulus of
the stagnant body and the approaching body was reported
as a compliance ratio as denoted by Cr in Fig. 4 (j). Case 2
and 3 act as bounding controls for compliance mismatchedcollisions, while case 1 reflects the work observed thus far.
The same experimental procedure outlined in Sec. II wasused for each case, and the results are shown in Fig. 4 (j).
Figure 4 (j) shows that all cases at low pressures (<90 kPa)
have relatively similar success rates. However, at higher
pressures (>90 kPa), the success rates diverge. For case 2,
where the robot encounters a rigid rod, there is a low successrate, which follows the observations shown in Fig. 2. For
case 1 an increase in pressure (and therefore compressive
modulus) facilitates success. Finally, case 3, where the morerigid vine robot encounters the soft foam cylinder, shows thehighest success rate.

V. GUIDELINES AND DEMONSTRATION
1) Design Parameter Guidelines: In pipe exploration, Tjunctions are a complex boundary condition that will be
encountered by vine robots. As such, extensive characterization was performed to identify the passive behavior ofvine robots in a T-junction as a function of diameter andoperation pressure. It is understood that these variables play
an important role in dictating the material and geometricstate of a vine robot. Through analysis of the observed
outcomes, we drew insights into which parameters would aid
in facilitating a vine robot’s successful navigation through a
T-junction.
Throughout this study, we observed that small diametervines have the greatest success overall. By avoiding selfcontact, small diameter vines leverage rigid body interactions where they hit the wall and then bend for successful navigation. In contrast, larger diameter vines inherently
guarantee self-contact, and therefore are unable to isolate acompliance mismatch. These larger diameter vines demonstrated more successful navigation with increased operationpressure, which corresponds to an increase in compressive
modulus. Finally, we showed that the compliance mismatchin which the vine robot contacts a much softer foam bodyalso increased navigation success in a pipe T-junction.
2) Demonstrations: We can leverage the aforementioned
guidelines to enable vine robot traversal of network junctions. Three demonstrations were performed to show howchanging design parameters can promote the ability of avine robot to successfully navigate through a T-junction.
Figure 5 shows still images from a demonstration video
with methods for facilitating T-junction navigation. The top
left shows a failed condition where the vine robot becomes
stuck on itself. We showcase three modifications that canfacilitate successful navigation. In the first scenario (bottom
left), a variable diameter vine was created. The vine wasdesigned so that sections inside the T-junction had reduced
diameter. By reducing the diameter, the vine undergoes a
traditional wall interaction and does not pose as a barrier
to itself, resulting in successful navigation. In the second
scenario (top right), a varied stiffness patch was added tothe approaching part of a vine robot to induce a compliancemismatch in which the approaching body is stiffer than
the stagnant body resulting in a high frequency of success.
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underground, and through various media. By altering thediameter and operation pressure of a vine robot, greater
success for continued navigation within a pipe T-junction for
exploration could be realized. We foresee this work having
broader applications in the fields of pipe inspection andmaintenance where optimizing self-interaction will be criticalin the successful operation of vine robots, making them moreaccessible in real-world settings.
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Fig. 5. Still images from a demonstration detailing three design choicesthat facilitate the successful navigation of a vine robot in a pipe T-junction.

Finally, in the third scenario (bottom right), the operationpressure of the body was increased; for large values ofDr /D p , successful navigation of a T-junction when a vineinteracts with itself increases with operation pressure. Allof these design parameter changes facilitate successful Tjunction navigation.
VI. CONCLUSION
In this work, we characterized the interaction behaviors
of and provided design guidelines for successful vine robot
navigation in pipe junctions. The behaviors of vine selfinteraction and rigid rod interactions were investigated andcompared. The self-contact behavior, which resulted in avine robot hitting itself, buckling, and continuing locomotion
through a T-junction, was evaluated. The resulting successrate of vine robot self-contacts was then investigated withrespect to diameter and pressure. Geometrical properties
dominate vine robot success for small diameters wherecontact is not guaranteed for a vine robot with itself. In
contrast, at large diameters where vine robot contact is guaranteed within the T-junction, material properties dominate
the interaction behaviors. Furthermore, for larger diametercases where contact is guaranteed, it was observed thatthe frequency of successful navigation from self-contact isincreased by vine stiffness. Finally, we demonstrated how
insights from observations can be implemented in vine
robot designs—such as using a varied diameter, increased
operating pressure, or compliance mismatched vine robot—
to facilitate successful navigation through a T-junction.
The results of this study have introduced a need forfurther investigation into the characterization of vine robot
interactions with soft matter. Future work aims to introduce
mechanical models to elaborate upon the experimental findings in the work, such as precisely modeling the interactionof the vine robot with compliant objects. Additionally, work
remains to understand vine robot locomotion through avariety of complex applications systems such as in vivo,
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