Design and Analytical Modeling of a Dumbbell-Shaped Balloon Anchoring Actuator for Safe and Efficient Locomotion Inside Gastrointestinal Tract

Abstract

Colorectal cancer stands as one of the most prevalent cancers globally, representing 9.8% of total cases and contributing to 9.2% of mortalities annually. Robotic “front-wheel” navigating colonoscopes mitigate aggressive stretching against the long and tortuous colonic wall, alleviating associated discomfort and pain typically experienced by patients inspected by conventional “back-wheel” navigating colonoscopes. The anchoring unit of most “front-wheel” navigating colonoscopes plays a crucial role in ensuring effective locomotion by preventing slipping during elongation/contraction of the central actuation part. The soft balloon anchoring actuator emerges as a promising solution due to its high compliance. This study introduces a dumbbell-shaped balloon anchoring actuator (DBAA) integrating an “inflation and suction” mechanism to address the inherent conflict between achieving sufficient anchoring force and minimizing expansion and potential trauma of the colonic wall, commonly encountered in current balloon anchoring actuators. Analytical modeling of DBAA and soft external lumen, encompassing geometric deformation and anchoring force, were proposed to characterize the actuator and provide guidelines for designing and controlling DBAA in further applications, enabling autonomous anchoring within different diameter lumens and achieving the expected anchoring force. A comprehensive set of validation experiments was conducted, and the outcomes revealed high consistency with analytical predictions, confirming the effectiveness of the proposed analytical modeling approach. Furthermore, the results demonstrated a significant enhancement in anchoring force with the proposed actuator and corresponding mechanism while concurrently maintaining low-lumen expansion. For instance, in a lumen sample with $R_{i n} = 15 m m, Λ_{2} = 105 %,$ the anchoring force reaches 14.5 N with 50 kPa negative pressure, which is 12.4 times of the force (1.17 N) observed without applying negative pressure.

Introduction

Colorectal cancer (CRC) is one of the most common cancers worldwide accounting for more than 1.85 million cases (9.8% of total cancer cases) and 850 thousand deaths (9.2% of total mortalities) annually.¹ Moreover, CRC incidence continues to rise steadily, with an estimated 3.2 million new cases annually in 2040 on a global scale.² Implementing early-stage screening presents a significant opportunity to reduce CRC incidence and mortality, increasing 5-year survival rate from 64% to 90%.³ Colonoscopy, utilizing conventional colonoscopes, is widely recognized as the gold standard clinical methodology for CRC screening.⁴ However, these conventional passive devices face challenges navigating the long and tortuous colonic lumen, particularly at splenic and hepatic flexures,⁵ since it is difficult to transmit movement in sharp turns with a “back-wheel” manual navigation. In addition, possible pushing/stretching against colonic wall often causes invasiveness to patients,^6,7 which is aggravated by the looping phenomenon.⁸

Therefore, robotic colonoscopes, integrating “front-wheel” navigation mechanism, which can move forward and drag posterior tether, were developed to mitigate aforementioned issues.^9–11 Among these, robots endowed with autonomous or teleoperated locomotion ability control^12–14 exhibit greater promise compared with those reliant on external actuation systems.^15,16 The former offers the advantage of reduced accessories and costs. Self-propelled robots typically adhere to an earthworm-like movement principle,¹⁴ incorporating both a central component for locomotion and front and rear anchoring parts for adhesion with colonic wall.

The anchoring part plays a crucial role in ensuring effective locomotion by preventing slipping during elongation/contraction of central component. Fundamental requirements for anchoring modules are (1) accommodating a wide deformation range adapting to the colonic lumen with varying diameters, (2) providing a substantial anchoring force to avoid slippage, and (3) exhibiting low invasiveness to colon tissue. While several anchoring methods have been developed to fulfill these requirements, some inherent drawbacks still hinder their broader applications. For instance, anchoring actuators activated by shape memory alloy face challenges related to low response efficiency and a limited expandable range in radial direction.¹⁷ Other methods, such as integration of expandable legs¹⁸ or spiral legs,¹⁹ exhibited insufficient anchoring force due to the limited contacting area. Considering the soft nature of colonic wall, one possible solution lies in the use of expandable soft balloons, known for their high tactile comfortability against tissue.^14,20–22 Nevertheless, a conflict arises between achieving robust anchoring force and minimizing invasiveness to human tissue since the anchoring force, derived by friction, is almost determined by compressed force between anchoring module and colonic wall. Excessive compression may lead to substantial deformation of colonic lumen, resulting in increased invasiveness and potential trauma to patients. In contrast to radial expansion of the actuator, anchoring can be also achieved through the deflation of colonic lumen under negative pressure, thereby preventing excessive deformation of colonic tissue²³; however, this approach presents a challenge, as entire colonic tract becomes deflated, resulting in immobilization of actuation part and hindering elongation capabilities.

In this study, the authors present a novel dumbbell-shaped balloon anchoring actuator (DBAA) and investigate the corresponding “inflation and suction” mechanism (ISM) to address the conflict (sufficient anchoring force and low lumen’s deformation) related to the expandable balloons and immobilization of actuation part associated with the complete suction of whole lumen. The new anchoring method is achieved through both the contact between two inflated chambers and tissue, and the subsequent partial suction of the cavity formed by balloons and lumen. While the inflated chambers can expand the colon and seal the space between colon and the suction cavity, DBAA can generate larger anchoring force with vacuum effect instead of depending on friction by large expansion against the colon wall. The anchoring force experiences a substantial enhancement under negative pressure applied to the cavity. To better understand this method, we introduce analytical modeling including geometric deformation and anchoring force, building upon our previous work. The modeling is rigorously validated through experimental procedures. The deformation analysis establishes a reasonable range to prevent excessive expansion of colon. Simultaneously, the force analysis validates the effectiveness of the newly proposed anchoring actuator and mechanism, offering valuable insights into controllability of anchoring force.

Materials and Methods

Working principle of the DBAA

The anchoring actuator (Fig. 1A) comprises two identical inflatable balloon chambers separated by a middle-undeformed segment (MUS). In Figure 1B, four stages are depicted to show working mechanism when DBAA is within a tubular environment: (1) initial states; (2) inflation of chambers in free space before contacting lumen; (3) constrained inflation of chambers after contact, forming a ring-shaped sealed cavity in between; and (4) suction of the sealed cavity while the chambers maintain inflation. It is essential to note that the primary purpose of chamber’s inflation is to establish a sealed cavity, rather than to generate majority of the anchoring force. Therefore, lumen’s outward deformation can keep low level. The anchoring force is predominantly obtained through local suction of the sealed cavity, leveraging on negative pressure is safer than a positive pressure on the tissue which potentially causes perforation of colon. The expansive radial deformation range of balloon, coupled with the modest outward deformation of lumen, and the anchoring force primarily generated by local suction, collectively ensure DBAA’s robust anchoring in various colonic lumen diameters while minimizing deformation of colonic wall and following pain to patients.²³ Figure 1C shows the application of the earthworm-like robot, involving DBAA with ISM, inside colonic lumen. The snapshots and Supplementary Video S1 indicate that the robots could realize the anchoring and locomotion a colon simulator²⁴ holding the similar geometry with the human colon. The feasibility of anchoring is also validated in an extreme condition where the colon has the exaggerated haustra (Supplementary Fig. S1 and Video S2).

FIG. 1.

(A) Components of the dumbbell-shaped balloon anchoring actuator (DBAA); (B) various stages of DBAA and external lumen showing the working principle, including initial state, inflation of DBAA in free space, outward deformation of lumen, and inward deformation of cavity; and (C) the potential application scenario of the earthworm-like robot integrating DBAA in colonoscopy with (C-I) the schematic layout of the robot inside the colonic lumen and (C-II) snapshots demonstrating the locomotion process.

Analytical modeling of the inflation of DBAA’s chambers in free space

The activated DBAA, shown in Figure 2A, presents a dumbbell shape. An analytical modeling of the inflation of chambers in free space is explored to characterize the relationship between inner pressure and chamber’s deformation. This characterization serves as a guide for determining the required pressure to initiate contact between DBAA and lumens of various diameters (mimicking different segments of colonic lumen), since the primary purpose of chamber inflation is to construct the sealed cavity. To describe the structure, a polar coordinate system is employed due to the axial symmetry of dumbbell, only one of the two identical chambers is investigated, where position of arbitrary point can be represented as (r, δ, x). The schematic diagrams of the section view and rendering of DBAA and lumen in different states are depicted in Figure 2B–E. The original state of DBAA is shown in Figure 2B, in which original outer radius is r, original lengths of chamber and MUS are $2 l_{0}$ and $2 {l l}_{0}$ , respectively, and original wall thickness of chamber is h. Regarding the inflated chamber, in Figure 2C, the meridian with a radius of m is the intersecting line between inflated chamber and plane passing through the axis of DBAA, arc length of inflated chamber is defined as s, and $φ$ denotes half of arc’s central angle. The latitude, on the contrary, is the intersecting line between inflated surface and plane perpendicular to the axis, where $r^{*}$ donates the maximum radius of inflated chamber in latitudinal direction. The wall thickness of inflated chamber is represented by $h^{*}$ , u is distance between arc center and DBAA’s original edge, and $r^{m}$ is the radius of arc center in latitudinal direction. Consequently, $φ = π - 2 \tan^{- 1} (\frac{l_{0}}{r^{*} - r})$ (1) $m = \frac{l_{0}}{\sin φ}$ (2) $u = \frac{l_{0}}{\tan φ}$ (3) $r^{m} = r - u$ (4) $s = 2 m φ$ (5)

FIG. 2.

(A) General schematic illustration of DBAA in activated condition; parameter setting for DBAA and lumen in different states: (B) the initial state of DBAA, (C) the inflation of DBAA in free space, (D) the outward deformation of lumen under the actuation of DBAA, and (E) the inward deformation of lumen under suction.

In the polar coordinate system, the principal directions at any point (r, δ, x) coincide with meridian, latitude, and normal directions of deformed surface. Then principal strains of the point (r*,0,0) in these three directions are defined as follows: $λ_{1} = \frac{d s}{d x}, λ_{2} = \frac{r^{*}}{r}, λ_{3} = \frac{h^{*}}{h} = \frac{1}{λ_{1} λ_{2}}$ (6)

In the context provided, the strains in the meridional, latitudinal, and radial directions are denoted as $λ_{1}$ , $λ_{2}$ , $λ_{3}$ , respectively. Following the nonlinear elastic membrane theory proposed by Green and Adkin,²⁵ in the axially symmetrical deformed structure, the force equilibrium of a unit volume element at point (r*,0,0) can be formulated as follows: $\begin{matrix} \frac{d}{d s} (t_{1} r^{*}) = t_{2} \frac{d r^{*}}{d s} \end{matrix}$ (7) $\frac{t_{1}}{m} + \frac{t_{2}}{r^{*}} = P_{i n - b} - P_{atm}$ (8)

Here, $t_{1}$ and $t_{2}$ represent the stress per unit length in meridional and latitudinal directions, respectively; $P_{i n - b}$ is the pressure inside chamber, and $P_{atm}$ is the atmosphere pressure. Referring to authors’ previous work²⁶: $t_{1} = h^{*} λ_{1} \frac{\partial w}{\partial λ_{1}}$ (9) $t_{2} = h^{*} λ_{2} \frac{\partial w}{\partial λ_{2}}$ (10)

where $w$ represents the strain energy density function. Yeoh hyperelastic elastomer modeling is adopted to describe the strain energy density, $C_{i}$ denotes the material constants in this model, and $I_{1}$ is the first invariant of three principal stretch ratios. Then the equation can be derived as follows: $w (λ_{1}, λ_{2}) = \sum_{i}^{3} C_{i} (I_{1} - 3)^{i}$ $= \sum_{i}^{3} C_{i} (λ_{1}^{2} + λ_{2}^{2} + (λ_{1} λ_{2})^{- 2} - 3)^{i}$ (11)

Therefore, $\frac{\partial w}{d λ_{1}} = \sum_{i}^{3} {i C}_{i} (2 λ_{1} - 2 λ_{1}^{- 3} λ_{2}^{- 2}) {(λ}_{1}^{2} + λ_{2}^{2} + (λ_{1} λ_{2})^{- 2} - 3)^{i - 1}$ (12) $\frac{\partial w}{d λ_{2}} = \sum_{i}^{3} {i C}_{i} (2 λ_{2} - 2 λ_{1}^{- 2} λ_{2}^{- 3}) {(λ}_{1}^{2} + λ_{2}^{2} + (λ_{1} λ_{2})^{- 2} - 3)^{i - 1}$ (13)

Combining equations (8–13), the relationship between $P_{i n - b}$ and deformation can be derived as follows: $P_{i n - b} - P_{atm} = \frac{h}{m λ_{2}} \sum_{i}^{3} {i C}_{i} (2 λ_{1} - 2 λ_{1}^{- 3} λ_{2}^{- 2}) {(λ}_{1}^{2} + λ_{2}^{2} + (λ_{1} λ_{2})^{- 2} - {3)}^{i - 1} + \frac{h}{r^{*} λ_{1}} \sum_{i}^{3} {i C}_{i} (2 λ_{2} - 2 λ_{1}^{- 2} λ_{2}^{- 3}) {\times (λ}_{1}^{2} + λ_{2}^{2} + ({λ_{1} λ_{2})}^{- 2} - 3)^{i - 1}$ (14)

Analytical modeling of lumen’s outward deformation under the actuation of the DBAA

In addition to the exact contact between DBAA and lumen, the chamber needs further deformation to ensure sealing of the cavity. Besides, the contact pressure between them is also the resource of anchoring force, as presented in common balloon anchoring actuators.^12,14 Therefore, the required pressure for enabling lumen’s outward deformation is analyzed in this section to guarantee construction of the cavity and to figure out the contact pressure. In this analysis, we consider the soft tubular environment as external constraint: its deformable structure introduces more challenges compared with rigid tubular. We assume that lumen is sufficiently soft, and then lumen’s deformation conforms to chamber’s deformation after their contact. Figure 2D illustrates the parameters of DBAA and lumen after contacting. Similar to modeling of the inflation of DBAA chamber in free space, the principal strains of point ( $R^{*}$ ,0,0) are derived as follows: $Λ_{1} = \frac{d S}{d x}, Λ_{2} = \frac{R^{*}}{R}, Λ_{3} = \frac{H^{*}}{H} = \frac{1}{Λ_{1} Λ_{2}}$ (15)

where $Λ_{1}$ , $Λ_{2}$ , and $Λ_{3}$ represent lumen’s strains in meridional, latitudinal, and radial directions, respectively. R is the lumen’s original outer radius, and $R^{'}$ is the lumen’s maximum outer radius in latitudinal direction. S is the arc meridional arclength of inflated lumen. H and $H^{*}$ denote the lumen’s wall thickness in undeformed and inflated states, respectively. Lumen’s two axial ends are free to move rather than fixed, thus assuming ${H = H}^{*}$ . Then: $M_{i} = m + H^{*} = m + H$ (16) $R^{*} = r^{*} + H^{*} = r^{*} + H$ (17)

Here, $M_{i}$ is the radius of inflated lumen in meridional direction. By adopting the same principle as that in the inflation modeling in free space, the following equations can be derived as follows: $P_{i n - b t} - P_{contact - I} = \frac{t_{1}}{m} + \frac{t_{2}}{r^{*}}$ (18) $P_{contact - I} - P_{atm} = \frac{T_{1}}{M} + \frac{T_{2}}{R^{*}}$ (19)

That is, $P_{i n - b t} - P_{atm} = \frac{h}{m λ_{2}} \sum_{i}^{3} {i C}_{i} (2 λ_{1} - 2 λ_{1}^{- 3} λ_{2}^{- 2}) {\times (λ}_{1}^{2} + λ_{2}^{2} + (λ_{1} λ_{2})^{- 2} - 3)^{i - 1} + \frac{h}{r^{*} λ_{1}} \sum_{i}^{3} {i C}_{i} \times (2 λ_{2} - 2 λ_{1}^{- 2} λ_{2}^{- 3}) {(λ}_{1}^{2} + λ_{2}^{2} + (λ_{1} λ_{2})^{- 2} - 3)^{i - 1} + \frac{H}{M Λ_{2}} \sum_{i}^{3} {i C}_{i} (2 Λ_{1} - 2 Λ_{1}^{- 3} Λ_{2}^{- 2}) {(Λ}_{1}^{2} + Λ_{2}^{2} + (Λ_{1} Λ_{2})^{- 2} - 3)^{i - 1} + \frac{H}{R^{*} Λ_{1}} \sum_{i}^{3} {i C}_{i} (2 Λ_{2} - 2 Λ_{1}^{- 2} Λ_{2}^{- 3}) \times (Λ_{1}^{2} + Λ_{2}^{2} + {(Λ_{1} Λ_{2})}^{- 2} - 3)^{i - 1}$ (20)

where $P_{i n - b t}$ and $P_{contact - I}$ are the pressure inside chamber, and contact pressure between chamber and lumen, respectively. $T_{1}$ and $T_{2}$ are the stress per unit length of lumen in meridional and latitudinal directions, respectively.

Analytical modeling of lumen’s inward deformation supported by inflated DBAA

The sealed cavity, formed by lumen and inflated DBAA, can be sucked when exposed to negative pressure, as shown in fourth state of Figure 1B. The required pressure to activate the inward deformation of the cavity is investigated in this section to pave the way for calculating anchoring force caused by the suction. A schematic diagram showing constitutive parameters is illustrated in Figure 2D and E. Assuming that two ends of middle part of lumen are fixed since they are anchored by two inflated chambers, the geometric relationship can be derived as follows: $θ = π - 2 \tan^{- 1} (\frac{L_{0}}{R - R^{* *}})$ (21) $U = \frac{L_{0}}{\tan θ}$ (22) $M_{d} = \frac{L_{0}}{\sin θ}$ (23)

Here, $θ$ is half of central angle of deflated lumen, $L_{0}$ is half of the distance between the edges of two chambers in lumen’s middle part, $R^{* *}$ is the minimum radius of vacuumed lumen in latitudinal direction, $M_{d}$ is the radius of deflated lumen in meridional direction, and U is the distance between arc central and lumen’s original edge.

The principal strains of point ( $R^{* *}$ ,0,0) are derived: $γ_{1} = \frac{d S}{d x}, γ_{2} = \frac{R}{R^{* *}}, γ_{3} = \frac{H^{* *}}{H} = \frac{1}{γ_{1} γ_{2}}$ (24)

where $γ_{1}$ , $γ_{2}$ , and $γ_{3}$ , are the lumen’s strains in meridional, latitudinal, and radial directions, respectively. $H^{* *}$ is the wall thickness of deflated middle part of lumen.

The relationship between pressure inside the cavity ( $P_{d e}$ ) and the deformation can be derived in a manner similar to the inflation of chambers: $P_{atm} - P_{d e} = \frac{H}{M γ_{2}} \sum_{i}^{3} {i C}_{i} (2 γ_{1} - 2 γ_{1}^{- 3} γ_{2}^{- 2}) {(γ}_{1}^{2} + γ_{2}^{2} + (γ_{1} γ_{2})^{- 2} - 3)^{i - 1} + \frac{H}{R^{* *} γ_{1}} \sum_{i}^{3} {i C}_{i} (2 γ_{2} - 2 γ_{1}^{- 2} γ_{2}^{- 3}) \times {(γ}_{1}^{2} + γ_{2}^{2} + (γ_{1} γ_{2})^{- 2} - 3)^{i - 1}$ (25)

Analytical modeling of the anchoring force without suction of the lumen

The anchoring force caused only by inflation of DBAA is analyzed in this section to characterize how the deformation affects the anchoring force and to investigate the conflict between firm anchoring and low deformation of colonic wall. The anchoring force, estimated by the friction force between inflated chambers and lumen, is determined by contact pressure ( $P_{contact - I}$ ), contact area ( $S_{contact - I}$ ), and friction coefficient $μ$ between chambers and lumen.

As shown in Figure 2D, in the polar coordinate system, contact area is confined to the boundary between inflated chambers and lumen. Here we defined the value of right boundary of right contact surface as $X_{bound - R}$ and corresponding central angle as $φ_{bound - R}$ . Then: $X_{bound - R} = \sqrt{m^{2} - (R - H - r^{m})^{2}}$ (26) $φ_{bound - R} = \sin^{- 1} \frac{X_{bound - R}}{m}$ (27)

In the unit region of the surface, the area can be calculated as follows: $d S = 2 π r_{dome} m \cdot d φ_{R}$ (28)

where $φ_{R}$ is the central angle of the unit contact region, the $r_{dome}$ denotes the radius of sectional circle in latitudinal direction, and $r_{dome} = r^{m} + m \cos φ_{R}$ (29)

Then the surface area of spherical dome (i.e., contact area caused by right chamber’s inflation) can be obtained as follows: $S_{contact - I R} = \int_{{- φ}_{bound - R}}^{φ_{bound - R}} 2 π (r^{m} + m \cos φ_{R}) m \cdot d φ_{R}$ (30)

The sliding friction force generated by the inflation of two chambers can be governed by Coulomb friction with the following formula: $F_{anchor - I} = 2 {μ P}_{contact - I} S_{contact - I R}$ (31)

Combining equations (19), (20), (30), and (31): $F_{anchor - I} = 2 μ (\frac{H}{M Λ_{2}} \sum_{i}^{3} {i C}_{i} (2 Λ_{1} - 2 Λ_{1}^{- 3} Λ_{2}^{- 2}) {\times (Λ}_{1}^{2} + Λ_{2}^{2} + {(Λ_{1} Λ_{2})}^{- 2} - 3)^{i - 1} + \frac{H}{R^{'} Λ_{1}} \sum_{i}^{3} {i C}_{i} \times (2 Λ_{2} - 2 Λ_{1}^{- 2} Λ_{2}^{- 3}) {(Λ}_{1}^{2} + Λ_{2}^{2} + (Λ_{1} Λ_{2})^{- 2} - 3)^{i - 1}) \int_{{- φ}_{bound - R}}^{φ_{bound - R}} 2 π (r^{m} + m \cos φ_{R}) m \cdot d φ_{R}$ (32)

Analytical modeling of the anchoring force with suction of the lumen

The anchoring force can be enhanced when the cavity is vented to negative pressure. Notably, the anchoring force resulting from suction of the cavity can surpass that of chamber inflation as the safe negative pressure’s threshold is high. The relationship between the anchoring force and applied negative pressure is explored in this section to reveal the effect of suction and provide guidelines for effective and precise control of anchoring forces.

The suction of the cavity leads to two processes: (1) lumen’s deflation before the cavity is completely compressed, and subsequently (2) an increase in contact pressure with the application of negative pressure. Here we assumed that demarcation point between (1) and (2) is the meridional midpoint of deflated lumen contacts MUS of DBAA ( $R^{* *} = r$ ) since the contour constructed by inflated chambers and MUS approximates an arc conforming lumen’s deflation (referred to inset in Fig. 2E). Additionally, $L_{0}$ can be obtained through geometric relation between lumen and inflated chambers: $L_{0} = l_{0} + {l l}_{0} - X_{bound}$ (33)

Combining equations (21–25) and (33), the required negative pressure ( $P_{d e - r}$ ) to realize the complete deflation of the cavity can be derived. When input suction pressure ( $P_{d e}$ ) continues to increase, contact pressure ( $P_{contact - S}$ ) can be derived as follows: $P_{contact - S} = P_{d e} {- P}_{d e - r}$ (34)

With respect to the contact area under suction, it can be divided into two parts: (1) the arc part formed with inflated chambers and (2) the cylinder part formed with MUS of DBAA. The area of arc part ( $S_{contact - S A}$ ) and cylinder part ( $S_{contact - S C}$ ) can be derived as follows: $S_{contact - S A} = 2 \int_{- \sin^{- 1} \frac{l_{0}}{m}}^{- φ_{bound - R}} 2 π (r^{m} + m \cos φ_{R}) m \cdot d φ_{R}$ (35) $S_{contact - S C} = 4 π r {l l}_{0}$ (36)

The total area under suction can be obtained: $S_{contact - S} = S_{contact - S A} + S_{contact - S C}$ (37)

Consequently: $F_{anchor - S} = {μ P}_{contact - S} S_{contact - S}$ (38)

Furthermore, the total anchoring force is as follows: $F_{anchor - I S} = F_{anchor - I} + F_{anchor - S}$ (39)

Results and Discussion

Validation of the inflation of DBAA’s chambers in free space

To validate the analytical modeling of the chambers’ inflation in free space, in this study, the Eco-flex^TM 00-30 was adopted to fabricate DBAA. Yeoh hyperelastic elastomer model was characterized with $C_{1} = 17 kPa, C_{2} = - 0.2 kPa, C_{3} = 0.023 kPa .$ ²⁷ Considering the varying diameter of colonic lumen, ranging between 26 and 45 mm,²⁸ the external diameter of DBAA in default state was set to 25 mm (r =12.5 mm). Varied wall thicknesses of the chamber (h = 1/1.5/2/2.5 mm) were adopted. The experimental setup is shown in Figure 3A, and detailed description of geometric parameters and experiments can be found in Supplementary Data S1.

FIG. 3.

(A) Experimental setting for the validation of (A) the inflation of DBAA in free space, (B) the outward deformation of lumen under the actuation of DBAA, (C) the inward deformation of lumen under suction with (C-I) the inflation of the two balloons and (C-II) the suction of the sealed cavity, (D) the anchoring force without suction, and (E) the anchoring force with suction of the cavity.

Results are shown in Figure 4 with $r^{'}$ as the input dependent variable since it is the index to characterize the interaction between DBAA and lumen in the following sections. The error bar is standard deviation among three repeated tests of each sample. The experimental results show high consistency with the analytical one, and the analytical modeling effectively predicts relationship between $P_{i n - b}$ and $r^{*}$ of all the samples inflating in free space. When $λ_{2} < 1.6$ , the inflation is under the linear stage, $P_{i n - b}$ is approximately proportional to $r^{*}$ and $λ_{2}$ , which can be approximately expressed as $P_{i n - b} ≈ 2.25 λ_{2} h$ . For $λ_{2} > 1.6,$ the inflation is under the nonlinear stage and the required pressures remain constant, making it difficult to adjust the inflation ratio $r^{*}$ and to tune the interaction between DBAA and lumen.

FIG. 4.

Analytical modeling and experimental results of the inflation of DBAA in free space with various wall thicknesses of the chamber (h = 1/1.5/2/2.5 mm).

Validation of lumen’s outward deformation under the actuation of DBAA

In this section, DBAA is inserted into a tubular environment (Fig. 3B), as opposed to the standalone DBAA used in the validation of inflation in free space. The lumen samples have the following parameters: lumen’s wall thickness H = 1/1.5/2/2.5 mm and initial inner radius $R_{i n}$ =15/17.5/20/22.5 mm ( $R_{i n}$ ≠R). Detailed experimental description can be found in Supplementary Data S1.

Both analytical and experimental results are shown in Figure 5. The analytical and experimental results are well cross-validated across all 16 samples. Required pressure for lumen’s deformation $P_{i n - b t}$ initially increases with $R^{*}$ and then stabilizes even as the radius continues to grow. This shares a similar trend with that in chamber’s inflation in free space. The starting pressure to activate the contact between chambers and lumen is positively correlated to $R_{i n}$ and $P_{i n - b t}$ is positively related to h. The high consistency between the analytical and experimental results indicates that the analytical modeling accurately predicts contact pressure $P_{contact - I}$ and $P_{i n - b t}$ to achieve specific inflation ratios of lumen.

FIG. 5.

Analytical modeling and experimental results of outward deformation of lumen under the actuation of DBAA with various wall thicknesses (H = 1/1.5/2/2.5 mm) and initial inner radii ( $R_{i n}$ =15/17.5/20/22.5 mm) of the lumen.

Validation of inward deformation of the lumen supported by inflated DBAA

As illustrated in Figure 1B, there are two steps to realize lumen’s inward deformation (as shown in Fig. 3C-I and C-II). Detailed description of geometric parameters and experiments can be found in Supplementary Data S1. Two parameters are investigated: $R_{i n}$ =15/17.5/20/22.5 mm and lumen’s outward deformation ration in first step $Λ_{2} =$ 105%/110%/120%.

The experimental results are plotted in Figure 6, together with analytical results. Lumen’s radius $R^{* *}$ decreases with an increase in the negative pressure value, and the required pressure $P_{d e}$ experiences a dramatic increase when lumen’s radius approaches MUS’s radius of DBAA, indicating that the cavity is fully compressed. The required pressure is larger when $R_{i n}$ and $Λ_{2}$ are larger, with weights of the effect derived from $Λ_{2}$ being much lower than that from lumen’s $R_{i n}$ . The consistency between the analytical and experimental value diminishes in samples with higher $R_{i n}$ and higher $Λ_{2}$ . One potential reason is that lumen develops some folds instead of just an elastic inward deformation when deformation is significant, and the folds cannot be accurately modeled by analytical simulation. The existence of folds rather than lumen’s excessive elastic strain can effectively avoid stretching and invasiveness to colon tissue.

FIG. 6.

Analytical modeling and experimental results of inward deformation of lumen under suction with various and initial inner radii ( $R_{i n}$ =15/17.5/20/22.5 mm) of the lumen and various outward deformation ratios of the lumen ( $Λ_{2} =$ 105%/110%120%).

Validation of the anchoring force without suction of the lumen

This section focuses on validating analytical modeling of the anchoring force resulting from the inflation of chambers of DBAA. The experimental setup is shown in Figure 3D, with detailed description in Supplementary Data S1 and Supplementary Video S3.

The relationship between the anchoring force $F_{anchor - I}$ and lumen’s inflated radius $R^{*}$ is illustrated in Figure 7. The analytical results are shown within a region of anchoring force, considering the variation in the friction coefficient during the test ( $μ$ is 0.123 and 0.136 before and after pulling DBAA inside the lumen, respectively). The experimental results align well with the predicted anchoring force region. $F_{anchor - I}$ increases with the increase of $R^{*}$ , providing a larger contact area and contact pressure. Key $Λ_{2}$ corresponding $R^{*}$ is also labeled in the figures. Notably, $F_{anchor - I}$ is bigger inside the lumen with a larger $R_{i n}$ when $Λ_{2}$ is identical. For example, when $Λ_{2}$ is 120%, the anchoring forces are 2.15 N and 4.19 N when $R_{i n}$ are 15 and 22.5 mm, respectively.

FIG. 7.

Analytical modeling and experimental results of anchoring force without the suction applied to the cavity between the inflated DBAA and external lumen with various initial inner radii ( $R_{i n}$ =15/17.5/20/22.5 mm). The key strains of lumen in latitudinal direction ( $Λ_{2} =$ 105%/110%120%) are labeled to demonstrate the lumen’s deformation.

Validation of the anchoring force with suction of the lumen

This section explores the validation of anchoring force modeling with lumen’s suction in addition to the inflation of the chambers of DBAA. The experimental setup is shown in Figure 3E, with detailed description in Supplementary Data S1and Supplementary Video S4. Two groups of samples were tested: $R_{i n}$ =15mm, while $Λ_{2}$ = 105%/110%/120%; $Λ_{2}$ = 105% while the $R_{i n}$ = 15/17.5/20/22.5 mm.

Both the analytical modeling and experimental results are plotted in Figure 8. As elucidated in the geometric test, the cavity undergoes complete compression under a small pressure. Subsequently, the anchoring force is exclusively influenced by the applied pressure. Therefore, the pressure serves as the independent variable in this figure. The experimental anchoring force aligns well with analytical modeling anchoring force region. It is evident that the anchoring force is positively proportional to the applied pressure $P_{d e}$ when $R_{i n}$ and $Λ_{2}$ are fixed. The anchoring force increases with the increase of $R_{i n}$ when $Λ_{2}$ and $P_{d e}$ are identical due to the increasing contact area. When $R_{i n}$ and $P_{d e}$ are the same, $Λ_{2}$ does not significantly affect the anchoring force. One possible reason can be the area under suction is mainly attributed to MUS of DBAA ( $S_{contact - S C}$ ) rather than the dome part formed by inflated chamber of DBAA ( $S_{contact - S A}$ ) regardless of the value of $Λ_{2}$ .

FIG. 8.

Analytical modeling and experimental results of anchoring force with the suction applied to the cavity between the inflated DBAA and lumen with various initial inner radii ( $R_{i n}$ =15/17.5/20/22.5 mm) of the lumen and various outward deformation ratios of the lumen ( $Λ_{2} =$ 105%/110%120%).

The effectiveness of suction can be validated by Figure 9A. It shows intuitive comparison of the exerted anchoring force without and with 35 kPa suction when lumen undergoes low expansion and low invasiveness ( $Λ_{2}$ =105%). It is evident that the application of suction can dramatically increase anchoring force in all lumen samples with various radii. For example, for a sample with $R_{i n}$ =22.5 mm, $Λ_{2}$ =105%, the anchoring force $F_{anchor - I S}$ is 15.16 N when 35 kPa negative pressure is applied, which is more than 12.5 times of the force $F_{anchor - I}$ (1.21 N) without the application of negative pressure.

FIG. 9.

The comparison of the anchoring result: (A) the anchoring force when the deformation ratio is fixed and (B) the required deformation ratio when targeted anchoring force is fixed.

Enhancement in safety can be indicated by Figure 9B, where the required deformation ratio ( $Λ_{2}$ ) is illustrated to target a 5 N anchoring force, selected to oppose a representative resistance force on the colonoscope tether when pulled forward inside a colonic lumen.²⁹ When no suction is applied, a large deformation ratio (e.g., $Λ_{2} =$ 144% when $R_{i n} = 15 m m$ ) is required to reach this value, leading us to suppose that a higher invasiveness on patients can occur due to colon stretching in order to obtain a larger anchoring force. In contrast, the selected 5 N anchoring force can be obtained with a very low deformation of the lumen when combined with suction. Furthermore, the anchoring force provided by suction of the cavity can effectively cover the entire resistance force range (target: 0–8.5 N),²⁹ which cannot be achieved by a pure inflation of chambers regardless of the deformation ratio. With this anchoring force, the DBAA can provide a firm base for earthworm-like locomotion and avoid potential backward slipping.

Conclusions

This article introduces an innovative DBAA designed to enhance the safety and locomotion efficiency of earthworm-like soft robots within soft tubular environments, such as colonic lumen. Simultaneously, a corresponding anchoring mechanism is proposed to provide substantial anchoring force while minimizing lumen’s elastic deformation and potential trauma. Analytical modeling of DBAA and lumens are investigated, encompassing geometric deformation analysis and anchoring force analysis under various conditions. The geometric modeling includes DBAA’s inflation in free space and lumen’s outward deformation induced by DBAA’s inflation. Both aspects contribute to estimating the necessary pressure to establish a sealed cavity between lumen and inflated DBAA. Furthermore, geometric modeling also encompasses analysis of lumen’s inward deformation under suction, enabling prediction of the required pressure to achieve complete compression of the cavity and subsequent contact pressure between DBAA and lumen. The force analysis focuses on the anchoring force modeling in the absence and presence of negative pressure within the cavity for demonstrating the effectiveness of the proposed mechanism. Correspondingly, a series of experiments are conducted to examine the accuracy of the analysis. Both the analytical and experimental results show notable consistency in various scenarios, indicating that the analytical modeling can provide guidelines for designing and controlling DBAA. Importantly, the result about anchoring force with and without suction indicates that the proposed DBAA and corresponding mechanism can significantly increase the anchoring force (>10 times) while maintaining low expansion of lumen (105%). DBAA efficiently contributes to the locomotion of the robot inside colonic lumen, increasing anchoring force and minimizing patients’ discomfort and invasiveness.

In the future, the control of DBAA will be further investigated based on ISM modeling. In addition, pressure and displacement sensors can be integrated into balloon to provide real-time feedback, thus facilitating development of a fully automated inspection system based on this feedback for colonoscopy. Moreover, ex vivo and in vivo tests inside the animal body will be conducted to thoroughly evaluate the effectiveness of the proposed actuator and anchoring method in more realistic environments.

Footnotes

Acknowledgments

The authors wish to thank Dr. Yu Huan and Ms. Vanessa Mainardi for the silicone curing of the preliminary version of prototype.

Authors’ Contributions

X.R.: Conceptualization (lead), investigation (lead), methodology (equal), visualization (equal), writing—original draft (lead), and writing—review and editing (supporting). T.P.: Conceptualization, investigation (supporting), methodology (equal), visualization (equal), and writing—review and editing (supporting). P.D.: Conceptualization (supporting), writing—review and editing (supporting). S.W.: Visualization (supporting), writing—review and editing (supporting). P.C.: Conceptualization (supporting), supervision (supporting), G.C.: Conceptualization (supporting), supervision (supporting), writing—review and editing (supporting). Z.L.: Conceptualization (supporting), funding acquisition (lead), resources (lead), supervision (lead), visualization (supporting), and writing—review and editing (supporting).

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This work was supported in part by the Research Grant Council General Research Fund under Projects 14214322, 14200623, and Collaborative Research Fund C4042-23GF, and in part by the CUHK strategic seed funding for collaborative research scheme 22/21 (SSFCRS).

Supplementary Material

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