Apparatus and methods for locomotion within constrained environments

Abstract

Exemplary embodiments of the present disclosure include an apparatus comprising a flexible annular member further comprising a central opening, and a plurality of flexible extensions extending radially from the flexible annular member. Exemplary embodiments further comprise a housing located within the central opening of the flexible annular member, and a locomotion mechanism configured to impart motion to the plurality of flexible extensions extending radially from the flexible annular member. In certain embodiments the locomotion mechanism may comprise a vibration mechanism, an inflation mechanism or a combination of a vibration mechanism and an inflation mechanism.

Description

DESCRIPTIONAPPARATUS AND METHODS FOR LOCOMOTION WITHIN CONSTRAINED ENVIRONMENTSCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Application Serial No. 63 / 716,011, titled “Apparatus and methods for locomotion within constrained environments,'’ on November 4, 2024.

[0002] This application incorporates the entire contents of the foregoing application herein by reference.TECHNICAL FIELD

[0003] Various embodiments generally relate to locomotion within constrained environments.BACKGROUND

[0004] A need exists for the adaptive locomotion of an apparatus in constrained cavities with variable geometries, including for example industrial applications (e.g. pipes, pipelines) and medical applications (e.g. endoscopic systems).

[0005] Such apparatus can be used to perform various functions including, for example, inspection. For industrial applications, pipeline systems are considered the most effective way of transporting gas and fluids in industrial factories, oil refineries, automobiles, machinery, spaces and aviation, etc.

[0006] This type of transportation is regularly used for safe and cost-effective reasons [1], [2], However, pipeline networks are usually placed in enclosed and confined spaces, such as hydraulic oil or fuel systems in aircraft, cargo vessels, or gas systems in households, etc., which limits the approach of humans for proceeding with periodic maintenance.

[0007] Therefore, the demand for having a tool or a method to inspect the conditions of pipeline systems draws attention from engineers and researchers. However, apart from the assembly condition, this type of transportation system typically includes non-uniform pipe dimensions and shapes (e.g., straight sections to sharp curves).

[0008] Such systems may, for example, cover significant distances, extending from a few centimeters to hundreds of meters. Regular inspections of both the exterior and interior of these pipelines are essential to ensure their reliable operation. To be deployed and used in such environments, various robots with different propulsion mechanisms have been4922-7473-8524, v. 1 1developed [3], including wheel-driven [4]—

[0010] , walking-based

[0011] —

[0013] , crawler-based robots

[0014] —

[0021] , vibration-based [3],

[0022] —

[0024] , and other locomotion mechanisms

[0025] ,

[0026] .

[0009] Recently, especially for use in smaller-sized (centimeter-scale) pipelines, scaling down robots with these types of navigation mechanisms has posed challenges. Various studies have been exploring different strategies to address the challenges of miniaturizing conventional mechanical structures [3].

[0010] Bioinspired soft robots that utilize smart materials such as piezoelectric actuators

[0027] —

[0030] , dielectric elastomer actuators (DEAs)

[0031]

[0034] , fluidic elastomer actuators

[0035] —

[0038] , hydrogels

[0039] —

[0041] , shape memory alloys (SMAs)

[0042] —

[0044] , and magnetic actuators

[0045] —

[0047] , for actuation have been explored in prior research. These methods, which occupy less space, exhibit higher power and energy density, and are more adaptable to small-scale dimensions, offer distinct advantages for pipeline locomotion.

[0011] Soft robots made from low-modulus materials, which mimic the elasticity of biological tissues, can passively adapt to varying dimensions and shapes of pipes due to their flexibility and high adaptability. In pipeline inspection, the tubular environment can present challenges depending on factors such as curvature, the presence of substances within the pipeline, or transitions between different diameters. As a result, achieving agile navigation, effective inspection, particularly in small-scale pipes, and adaptability across different pipe sizes during inspection missions remains a significant challenge [3].

[0012] Although the aforementioned methods demonstrate excellent locomotion performance in both curved and straight small-scale pipes, bioinspired soft robots designed for pipe inspection still face limitations, including a limited ability to handle varying pipe sizes or adapt to and navigate transition areas between different pipe diameters.

[0013] In addition, in certain scenarios the robot may need to contend with liquid or gas flow during the inspection, where a hollow body structure would be more advantageous for forward locomotion. However, the currently developed concepts are generally solid in the middle body resulting in impeding the flow rate. Furthermore, existing bioinspired soft robots require complicated control in which feedback is essential for realization of resulting locomotion.

[0014] Accordingly, a need exists to provide apparatus and methods for locomotion within constrained environments to address the shortcomings of existing systems.4922-7473-8524, v. 1 2SUMMARY

[0015] Exemplary embodiments of the present disclosure relate to apparatus and methods comprising a soft robot with adaptive morphology designed to enhance interaction between the robot’s body and the surrounding environment through predetermined vibrations, enabling traversal through cavities. Exemplary embodiments feature a soft, inflatable skin covered with an array of flexible limbs or extensions.:

[0016] Certain embodiments include an apparatus comprising a flexible annular member, where the flexible annular member comprises a first end and a second end; a central opening extending from the first end of the flexible annular member to the second end of the flexible annular member; a plurality of flexible extensions extending radially from the flexible annular member, where the flexible extensions are angled towards the second end of the flexible annular member; a housing located within the central opening of the flexible annular member, where: the housing comprises: a first end and a second end; a central opening extending from the first end of the housing to the second end of the housing; and a locomotion mechanism configured to impart motion to the plurality of flexible extensions extending radially from the flexible annular member.

[0017] In particular embodiments the locomotion mechanism is configured to vibrate the plurality of flexible extensions extending from the flexible annular member. In some embodiments the locomotion mechanism comprises an eccentric motor. In specific embodiments the locomotion mechanism comprises a piezoelectric element. In certain embodiments the locomotion mechanism comprises an inflation device configured to inflate and deflate the flexible annular member.

[0018] In particular embodiments a flexible extension of the plurality of flexible extensions comprises: a base portion and a distal portion; the base portion is located a first distance from the second end of the flexible annular member; the distal portion is located a second distance from the second end of the flexible annular member; and the first distance is greater than the second distance. In some embodiments each flexible extension of the plurality of flexible extensions comprises: a base portion and a distal portion; the base portion is located a first distance from the second end of the flexible annular member; the distal portion is located a second distance from the second end of the flexible annular member; and the first distance is greater than the second distance.

[0019] In specific embodiments a flexible extension of the plurality of flexible extensions comprises a curved profile. In certain embodiments each flexible extension of the plurality of flexible extensions comprises a curved profile. In particular embodiments a flexible4922-7473-8524, v. 1 3extension of the plurality of flexible extensions comprises a linear profile. In some embodiments each flexible extension of the plurality of flexible extensions comprises a linear profile. Specific embodiments further comprise a camera and / or a light.

[0020] Certain embodiments further comprise: a first seal configured to seal the first end of the flexible annular member to the first end of the housing; and a second seal configured to seal the second end of the flexible annular member to the second end of the housing. Particular embodiments further comprise an actuator configured to change the orientation of the plurality of flexible extensions such that the plurality of flexible extensions are angled toward the first end of the flexible annular member. Some embodiments further comprise an inertial measurement unit (IMU). Specific embodiments further comprise an integral source of pressurized fluid. In certain embodiments the flexible annular member comprises embedded sensors. In particular embodiments, the flexible annular member includes embedded flexible strain sensors configured to directly measure interaction forces.

[0021] In particular embodiments the embedded sensors are tactile sensors. In some embodiments the apparatus is tethered to a control system. In specific embodiments the apparatus communicates wirelessly with a control system. In certain embodiments the apparatus comprises an integrated battery. In particular embodiments the integrated battery is configured to be charged remotely. In some embodiments the flexible annular member is formed from of silicone, poly amide- 12, or a poly ether block amide.

[0022] Particular embodiments further comprise: a second flexible annular member, wherein the second flexible annular member comprises: a first end and a second end; a central opening extending from the first end of the second flexible annular member to the second end of the second flexible annular member; a plurality of flexible extensions extending from the second flexible annular member, wherein the flexible extensions are angled towards the second end of the second flexible annular member; a second housing located within the central opening of the flexible annular member, wherein the second housing comprises: a first end and a second end; a central opening extending from the first end of the second housing to the second end of the second housing; and a second locomotion mechanism configured to impart motion to the plurality of flexible extensions extending radially from the second flexible annular member.In some embodiments the apparatus is configured to be operated using a remote user via a robotic system. In specific embodiments the robotic system comprises a joystick. In certain embodiments the apparatus is configured to provide visual and / or haptic feedback to the user. In particular embodiments the apparatus is configured to move in an autonomous4922-7473-8524, v. 1 4mode. In some embodiments the autonomous mode is controlled by artificial intelligence (Al) algorithms. In some embodiments, the apparatus including the autonomous mode is controlled by artificial intelligence (Al) algorithms, the Al based control operations comprising: detecting visual or tactile sense data; generating an Al-based diagnosis with an artificial intelligence engine communicating with the control system; and, selecting an appropriate AI-Based control through vibration and pneumatic outputs to drive the locomotion mechanism.

[0023] In specific embodiments the autonomous mode is controlled by embedded sensors.

[0024] Certain embodiments included a method of moving an apparatus within a constrained environment, the method comprising: inserting the apparatus into the constrained environment, wherein the apparatus comprises a flexible annular member comprising a plurality of flexible extensions; inflating the flexible annular member so that the plurality of flexible extensions engage the constrained environment; and vibrating the apparatus so that the plurality of flexible extensions move the apparatus with respect to the constrained environment.

[0025] Particular embodiments include a method of moving an apparatus within a constrained environment, the method comprising: inserting the apparatus into the constrained environment, wherein the apparatus comprises a flexible annular member comprising a plurality of flexible extensions; inflating the flexible annular member so that the plurality of flexible extensions engage the constrained environment; and cyclically deflating and inflating the apparatus so that the plurality of flexible extensions move the apparatus with respect to the constrained environment.

[0026] Specific embodiments include a method of moving an apparatus within a constrained environment, the method comprising: inserting the apparatus into the constrained environment, wherein the apparatus comprises a flexible annular member comprising a plurality of flexible extensions; inflating the flexible annular member so that the plurality of flexible extensions engage the constrained environment; and vibrating the apparatus and cyclically deflating and inflating the apparatus so that the plurality of flexible extensions move the apparatus with respect to the constrained environment.

[0027] In the present disclosure, the term “coupled” is defined as connected, although not necessarily directly, and not necessarily mechanically.

[0028] The use of the word “a” or “an” when used in conjunction with the term “comprising” in the claims and / or the specification may mean “one,” but it is also consistent with the meaning of “one or more” or “at least one.” The terms “approximately, “about” or4922-7473-8524, v. 1 5“substantially” mean, in general, the stated value plus or minus 10%. The use of the term “or” in the claims is used to mean “and / or” unless explicitly indicated to refer to alternatives only or the alternative are mutually exclusive, although the disclosure supports a definition that refers to only alternatives and “and / or.”

[0029] The terms “comprise” (and any form of comprise, such as “comprises” and “comprising"), “have” (and any form of have, such as “has" and “having”), “include” (and any form of include, such as “includes” and “including”) and “contain” (and any form of contain, such as “contains” and “containing”) are open-ended linking verbs. As a result, a method or device that “comprises,” “has,” “includes” or “contains” one or more steps or elements, possesses those one or more steps or elements, but is not limited to possessing only those one or more elements. Likewise, a step of a method or an element of a device that “comprises,” “has,” “includes” or “contains” one or more features, possesses those one or more features, but is not limited to possessing only those one or more features. Furthermore, a device or structure that is configured in a certain way is configured in at least that way, but may also be configured in ways that are not listed.

[0030] The terms “inflate”, “inflatable”, “inflation” and similar terms relate to an expansion of a flexible member by a fluid, including a fluid in a gas or liquid state.

[0031] As used herein any reference to "we" as a pronoun herein refers generally to laboratory personnel or other contributors who assisted in the laboratory procedures and data collection and is not intended to represent an inventorship role by said laboratory personnel or other contributors in any subject matter disclosed herein.

[0032] Other objects, features and advantages of the present invention will become apparent from the following detailed description. It should be understood, however, that the detailed description and the specific examples, while indicating specific embodiments of the invention, are given by way of illustration only, since various changes and modifications within the spirit and scope of the invention will be apparent to those skilled in the art from this detailed description.4922-7473-8524, v. 1 6BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The following drawings form part of the present specification and are included to further demonstrate certain aspects of the present invention. The invention may be better understood by reference to one or more of these drawings in combination with the detailed description of specific embodiments presented herein.

[0034] FIG. 1 illustrates an exploded perspective view of an exemplary embodiment according to the present disclosure.

[0035] FIG. 2 illustrates a side view of the embodiment of FIG. 1.

[0036] FIG. 3 illustrates an end view of the embodiment of FIG. 1.

[0037] FIG. 4 illustrates a perspective view of the embodiment of FIG. 1 in a deflated state.

[0038] FIG. 5 illustrates a perspective view of the embodiment of FIG. 1 in an inflated state.

[0039] FIG. 6 illustrates a perspective view of the embodiment of FIG. 1 during operation.

[0040] FIG. 7 illustrates a schematic side view of a flexible annular member of an exemplary embodiment of the present disclosure.

[0041] FIG. 8 illustrates a graphical representation of the principle of operation and different modes of locomotion for the embodiment of FIG. 1.

[0042] FIG. 9 illustrates the relation between the applied pressures and the obtained expansion radii of soft skin for the embodiment of FIG. 1.

[0043] FIG. 10 illustrates the shapes of the soft skin when subjected to three pressure air values in three tube dimensions for the embodiment of FIG. 1.

[0044] FIG. 11 illustrates obtained propulsion forces conducted under different operating conditions for the embodiment of FIG. 1.

[0045] FIG. 12 illustrates obtained position date collected under different operating conditions for the embodiment of FIG. 1.

[0046] FIG. 13 illustrates software simulations under different operating conditions for the embodiment of FIG. 1.

[0047] FIG. 14 illustrates evaluation of the embodiment of FIG. 1 when coping with critical zone in pipeline systems.

[0048] FIG. 15 illustrates a fabrication process for the embodiment of FIG. 1.

[0049] FIG. 16 illustrates a graph of the relation between vibration frequency and average velocity on for the embodiment of FIG. 1 during a vibration mode of locomotion.

[0050] FIG. 17 illustrates a propulsion force measurement system used to measure the propulsion force of the embodiment of FIG. 1.4922-7473-8524, v. 1 7

[0051] FIG. 18 illustrates an experimental measurement system to collect position data of the embodiment of FIG. lin one direction with respect to the applying pressure input.

[0052] FIG. 19 illustrates a side view of an embodiment comprising first and second apparatus oriented in opposing directions to provide both forward and rearward movement.

[0053] FIG. 20 illustrates a schematic view of an embodiment comprising actuators configured to change the orientation of flexible extensions with the flexible extensions in a first position.

[0054] FIG. 21 illustrates a schematic view of the embodiment of FIG. 20 with the flexible extensions in a second position.

[0001] FIG. 22 A depicts exemplary graphs depicting displacement behaviors vary according to different average deflation rates, Dfra, and the lowest threshold pressure, P^- (A, B, C).

[0055] FIG. 22B depicts an exemplary table including the parameters applied to an embodiment of the present disclosure to examine the average locomotion speed at different pipe inclination angles.

[0056] FIG. 23 depicts a graph including the average locomotion speed of an embodiment of the present disclosure in different inclined angles of pipe configurations.

[0057] FIG. 24 depicts an exemplary table including parameter values of the soft spike embodiment.

[0058] FIG. 25 depicts an exemplary table including design parameter values of three patterns and their locomotion performance, (e.g., mode 1, mode 2, and mode 3).

[0059] FIG. 26 depicts an exemplary analysis of the morphological design of the robot’s limb and its physical property.

[0060] FIG. 27 depicts an exemplary transformation of normal force to the horizontal propulsion force in relationship to the morphological design of the soft spike (Dragon Skin™ 10 material).

[0061] FIG. 28 depicts an exemplary stick-slip mechanism.

[0062] FIG. 29 depicts exemplary embodiment dimensions including (A) the front view of PFR; ODS = 27mm, IDSB = ODF = 15mm, ODSB= 17 mm; (B) the side view of PFR; LB = 30 mm. (C) The cross-section of the 3D printing mold presents the dimensions of the soft spike.

[0063] FIG. 30 depicts an exemplary setup to measure vibration frequency (Hz) of the eccentric mass4922-7473-8524, v. 1 8

[0064] FIG. 31 depicts the exemplary relationship between the applied voltage (V) and the vibration frequency (Hz).

[0065] FIG. 32 depicts the exemplary set-up to indirectly evaluate the maximum traveling distance.

[0066] FIG. 33 depicts an exemplary demonstration of applying constraints and loads to the soft skin in the simulation model. (A) Fixed constraints are applied to the inner circle of the soft skin. (B) The pressure load type is applied to the inner surface of the soft skin.

[0067] FIG. 34 depicts an exemplary Abaqus (i.e., finite element computer code, software suit for finite element analysis and computer aided engineering, developer: Dassault Systems Similia Corp) simulation procedure.

[0068] FIG. 35 depicts an exemplary prepared sample to measure the stiffness behaviors of three patterns of soft spikes.

[0069] FIG. 36 depicts the stiffness behaviors of three patterns, i.e., 3x5, 5x5, and 7x5 soft spike patterns, of the exemplary prepared samples depicted in FIG. 35.

[0070] FIG. 37 depicts an exemplary table disclosing the vibration frequencies and the corresponding amplitudes of the sinusoidal signals of the centripetal force.

[0071] FIG. 38 depicts an exemplary robot in the flexible membrane having embedded flexible strain sensors to directly measure the interaction force.

[0072] FIG. 39 depicts an exemplary illustrative use-case system coupling two or more exemplary robots as depicted in FIG. 38 to enable forward and backward motion and carrying different sensors in each robot.

[0073] FIG. 40 depicts an exemplary illustrative use-case scenario including the illustrative use-case embodiment of FIG. 39 being controlled by manipulating the voltage polarity, such that the robot moves left or right in T-shape junctions.

[0074] FIG. 41 depicts an exemplary block diagram of autonomous control of the locomotion and sensing.

[0075] FIG. 42 depicts a conceptual illustration of the proposed pufferfish-inspired soft robot inspection.

[0076] FIG. 43 depicts the four PFR configurations considered in this study

[0077] FIG. 44 depicts a table including design parameters of PFR robots including geometry and material.

[0078] FIG. 45 depicts developed vibration model for PFR.

[0079] FIG. 46 depicts a beam and system parameters used in a exemplary model.4922-7473-8524, v. 1 9

[0080] FIG. 47 depicts a calculated angular frequencies of the developed model corresponding to the PFR1-PFR3 designs as a function of balloon stiffness (1-80 N / m). The horizontal green line indicates the nominal speed of the eccentric motor, while the vertical green line marks the balloon stiffness at which the natural frequency matches the motor speed.

[0081] FIG. 48 depicts the rigid housing is designed to hold the eccentric motor at its center, creating a balanced center of mass and enabling efficient vibration driven locomotion.

[0082] FIG. 49 depicts a fabrication procedure of soft skin with fins along with exploded view of PFR.

[0083] FIG. 50 depicts the experimental setup includes the following: [1] a horizontal tube; [2] a vertical tube with an inner diameter of 30 mm serving as the test environment, [3] a magnetic tracking system for measuring robot’s position, [4] a programmable air system for regulating the internal pressure of the robot, and, [5] a DC-DC adjustable step-down voltage regulator module providing 3 V to the eccentric motor. [6] The demonstration of four distinct fabricated PFR robots (PFR1-PFR4).

[0084] FIG. 51 depicts locomotion performance of PFR robots in horizontal and vertical pipes.

[0085] FIG. 52 depicts average speeds of PFR1-PFR3 at different internally modulated pressures, measured in a horizontal pipe with a 30 mm inner diameter and 400 mm length.

[0086] Like reference symbols in the various drawings indicate like elements.DETAILED DESCRIPTION

[0087] Apparatus, systems, and related methods relate to a vibration-propelled robot with adaptive morphology that can navigate confined cavities using predetermined control strategies. Robots with adaptive morphology may facilitate the interaction between the body and the surrounding environment to generate adaptive functions without complicated control strategies. Some embodiments, may, for example, include a vibration-propelled soft robot with inflatable structure that can explore cavities with predetermined locomotive strategies because of the adaptive morphology of the robot.

[0088] In complex systems like oil refineries and aircraft engines, pipelines of varying diameters and shapes may, for example, be essential for transporting fluids. Inspecting pipelines poses significant challenges, especially for centimeter-scale pipelines. Challenges remain in handling different pipe sizes, navigating transitions, and managing fluid flow during inspections.

[0089] Some embodiments of the vibration-propelled robot with adaptive morphology may, for example, include a robot including an inflatable soft skin covered with flexible spikes4922-7473-8524, v. 1 10that contact the surrounding environment. Under vibration, the asymmetrical friction distribution at the tips of the spikes induces the robot's forward motion. Especially with specific inflation, the robot can traverse pipes under various conditions without requiring feedback control. The robot's hollow structure facilitates fluid flow, and its specialized front-mounted camera enhances inspection capabilities.

[0090] Some embodiments of the vibration-propelled robot with adaptive morphology may, for example, include an embodiment termed a PufferFace robot (PFR) embodiment, that aims to improve adaptability, navigation, and functionality in diverse pipeline environments. PFR is capable of traversing cavities varying from 1 to 1.5 times the outer diameter of PFR and critical zones in pipeline systems, such as the 90-deg elbow, T-shape connectors, and high curvature sections with predetermined control strategies. Some locomotion modes of PFR (e.g., mode 2, explained further below) may, for example, generate a propelled force of up to 20-fold to 35-fold the weight of PFR.

[0091] Adaptive morphology can be regarded as an aspect of intelligence. Traditional robots with fixed morphologies, such as industrial robots, require centralized controllers to perform complex computations for tasks like position control or force control, especially when encountering sudden environmental changes.

[0092] In contrast, a robot with adaptive morphology may, for example, adjust to environmental variations with minimal computational effort, as its adaptive structure inherently accommodates these changes locally. Consequently, adaptive morphology allows the robot to reduce computational demands for specific tasks, suggesting that intelligence is integrated into the physical body itself, known as embodied intelligence. Therefore, considering the robot's morphology, the working environment, and the way interaction occurs are the keys to developing smarter robot bodies with high adaptivity with low computational burden.

[0093] Some embodiments, may, for example, incorporate adaptive locomotion of a robot in constrained cavities with variable geometries, such as pipes. Pipeline systems are considered the most effective way of transporting gas and fluids in industrial factories, oil refineries, automobiles, machinery, spaces and aviation, etc. This type of transportation is regularly used for safe and cost-effective reasons (1), (2). However, pipeline networks are usually placed in enclosed and confined spaces, such as hydraulic oil or fuel systems in aircraft, cargo vessels, or gas systems in households, etc., which limits the approach of humans for proceeding with periodic maintenance. Therefore, the demand for having a tool or a method to inspect the conditions of pipeline systems draws attention from engineers4922-7473-8524, v. 1 11and researchers. However, apart from the assembly condition, this type of transportation system is composed of not only a single-size pipe but a wide range of sizes, ranging from a few millimeters to several centimeters, and can have various shapes, from straight sections to sharp curves.

[0094] For context, pipelines may, for example, cover significant distances, extending from a few centimeters to hundreds of meters. Regular inspections of both the exterior and interior of these pipelines are essential to ensure their reliable operation. To be deployed and used in such environments, various robots with different propulsion mechanisms have been developed (3) including wheel-driven (4 10), walking-based (11-13), crawler-based robots (14-21), vibration-based (22-24), and other locomotion mechanisms (25), (26).

[0095] However, adapting robots with these types of navigation mechanisms for use in smaller (centimeter-scale) pipelines has posed difficulties. Various studies have been exploring different strategies to address the challenges of miniaturizing conventional mechanical structures (3). Bioinspired soft robots that utilize smart materials such as piezoelectric actuators (27-30), dielectric elastomer actuators (DEAs) (31-34), fluidic elastomer actuators (35-38), hydrogels (39-41) shape memory alloys (SMAs) (42-44), and magnetic actuators (45-47), for actuation have also been explored in prior research. These methods, which occupy less space, exhibit higher power and energy density, and are more adaptable to small-scale dimensions, offer distinct advantages for pipeline locomotion. Soft robots made from low-modulus materials, which mimic the elasticity of biological tissues, can passively adapt to varying dimensions and shapes of pipes due to their flexibility and high adaptability.

[0096] For context in pipeline inspection, the tubular environment may, for example, present challenges depending on factors such as curvature, the presence of substances within the pipeline, or transitions between different diameters. As a result, achieving agile navigation, effective inspection, particularly in small-scale pipes, and adaptability across different pipe sizes during inspection missions remains a significant challenge (3).

[0097] Although the aforementioned methods demonstrate excellent locomotion performance in both curved and straight small-scale pipes, bioinspired soft robots designed for pipe inspection still face the following limitations:

[0098] 1) Limited ability to handle varying pipe sizes or adapt to and navigate transition areas between different pipe diameters.

[0099] 2) In certain scenarios, the robot may need to contend with liquid or gas flow during the inspection, where a hollow body structure would be more advantageous for forward4922-7473-8524, v. 1 12locomotion. However, the currently developed concepts are generally solid in the middle body, resulting in impeding the flow rate.

[0100] 3) Complicated control in which feedback is essential for the realization of resulting locomotion.

[0101] Soft robot embodiments with adaptive morphology may, for example, be designed to enhance interaction between the robot's body and the surrounding environment through vibrations, enabling traversal through cavities.

[0102] In certain embodiments, the PFR features soft, inflatable skin and flexible limbs. This design reflects the inflation / deflation mechanism that allows for shape adaptability in cavities with variable geometries. The morphology of exemplary embodiments of the present disclosure improve adaptability to surrounding cavities and facilitates vibration- induced locomotion.

[0103] PFR embodiments may, for example, advantageously provide adaptability to varying cavity environments. PFR embodiments may, for example, include a hollow structure that facilitates the flow of gases and fluids during inspection operations. PFR embodiments may, for example, include an adaptive morphology and a vibration-inflation locomotion mechanism that enables the PFR to navigate complex, constrained tubular conditions with a predetermined control strategy.

[0104] The proposed PFR needs to be capable of propelling itself in confined and / or constrained environments of various sizes. Considering the characteristics of the environments in which it will be applied, the proposed robot should be miniaturizable, capable of a wide range of size adjustments, self-propelled, and easy to fabricate to ensure fulfillment of the above-mentioned requirements.

[0105] Referring initially to FIGS. 1-3, an apparatus 100 configured for locomotion within constrained environments is shown. In exemplary embodiments, apparatus 100 can be sized and configured for a broad spectrum of applications, including, for example industrial applications (e.g. oil, natural gas or petrochemical processing and transportation piping and equipment) or biological applications (e.g. gastrointestinal or vascular systems).

[0106] In the exemplary embodiment shown, apparatus 100 comprises an flexible annular member 110 comprising a first end 111, a second end 1 12 and a central opening 113 extending from first end 111 to second 112 end of flexible annular member 110. In the illustrated embodiment, flexible annular member 110 further comprises a plurality of flexible extensions 115 extending radially from flexible annular member 110, where flexible extensions 115 are angled towards second end 112 of flexible annular member 110.4922-7473-8524, v. 1 13In the specific embodiment shown, flexible extensions 115 are arranged in a pattern of fourteen rows parallel to a central axis 101 of apparatus 100 and five rings extending radially around central axis 101. It is understood that other embodiments according to the present disclosure may comprise significantly different arrangements of flexible extensions 115. Furthermore, the use of the terns “rows” and “rings” is for discussion purposes when referencing the embodiments shown in the figures and is not intended to limit the arrangement of flexible extensions 1 15 in other embodiments.

[0107] Apparatus 100 also comprises a housing 120 located within central opening 113 of flexible annular member 110. Apparatus 100 further comprises a first seal 141 and a second seal 142 configured to seal first end 111 and second 112 of flexible annular member 110 to housing 120. In specific embodiments, first seal 141 and second seal 142 may be configured as threaded seals. In the illustrated embodiment, housing 120 comprises a first end 121 and a second end 122 as well as a central opening 123 extending from first end 121 of housing 120 to second end 122 of housing 120. In the embodiment shown, housing 120 also comprises a camera 124 and a light 125. Central opening 123 in housing 120 can allow fluid encountered within a constrained environment to pass through apparatus 100, thereby reducing fluid forces exerted on apparatus 100 and minimizing the effects of apparatus 100 on the operational aspects of a constrained environment into which apparatus 100 is deployed. For example, in certain embodiments apparatus 100 can be deployed into piping systems while the piping system continues to transport fluid.

[0108] Exemplary embodiments of the present disclosure also comprise an inflation device 132 coupled to a conduit 134 and a port 136. In particular embodiments, inflation device 132 can be coupled to a source of higher-pressure fluid (not shown in the figures) to direct the higher-pressure fluid into central opening 113 of flexible annular member 110 via conduit 134 and port 136. In certain embodiments inflation device 132 can be configured as a control valve that can be coupled to source of higher-pressure fluid 139 and a control system 145 via a conduit 138, which can also serve as a tether to retrieve apparatus 100. In particular embodiments, the higher-pressure fluid can be an inert gas or a liquid (e.g. water, saline or other suitable fluid) at pressure that is above ambient pressure.

[0109] As this higher-pressure fluid is directed into central opening 113 of flexible annular member 110, first seal 141 and second seal 142 restrict the higher-pressure fluid from exiting central opening 113 via first end 111 or second end 112 of flexible annular member 110. In exemplary embodiments, flexible annular member 1 10 is formed from a flexible material that allows for inflation e.g. radial expansion of flexible annular member 1 10 with4922-7473-8524, v. 1 14respect to central axis 101 and housing 120). In particular embodiments, flexible annular member may be formed from silicone, polyamide-12, or a polyether block amide (e.g. Pebax®) or similar stretchable material that can resist harsh environments, including elevated temperatures and corrosive liquids.

[0110] Some embodiments, as shown in FIGS. 1-3, include a PFR including a hollow-shaped rigid frame and an inflatable torus-shaped soft balloon, similar in structure to the surface of a pufferfish, attached to the frame. The inflatable mechanism of a pufferfish, which inflates by drawing water into its stomach, motivated us to develop a rigid frame with a built-in air channel to inflate and deflate the soft skin. The spikes on the skin of a pufferfish inspired the incorporation of a vibration mechanism to generate locomotion. This mechanism is compact and integrated into the PFR’s body structure, leveraging the asymmetric friction distribution at the tips of the spikes.

[0111] FIG. 4 illustrates apparatus 100 in a normal or deflated state before flexible annular member 110 is expanded via a higher-pressure fluid. FIG. 5 illustrates apparatus 100 in an expanded or inflated state after flexible annular member 110 is expanded via a higher- pressure fluid such that the outer diameter of flexible annular member 110 and flexible extensions 115 is increased. In particular embodiments, the higher-pressure fluid used to expand flexible annular member 110 can be the same fluid contained in the constrained environment in which apparatus 100 is deployed. For example, if apparatus 100 is inserted into a piping system comprising a hydraulic fluid, the same hydraulic fluid can be used to expand / inflate flexible annular member 110. While leaks of higher-pressure fluid from apparatus 100 are not anticipated, utilizing the same fluid within flexible annular member 110 that is contained within the constrained environment can prevent any contamination of the constrained environment should a leak occur.

[0112] In some embodiments, include a PFR including an air pressure hose connected to the rigid frame (see FIG. 4) that enables the inflation and deflation of the balloon, allowing the conformable body of PFR to adapt easily to various tubular diameters (illustrated in FIG 6). Additionally, a DC vibration motor, a miniature camera, and an LED are installed within the rigid frame, supporting both the self-propulsion and inspection capabilities of the proposed robot in constrained environments. Note that the hollow-shaped frame and torusshaped balloon mechanism is designed to adapt to inspection environments with liquid or gas flows.

[0113] The proposed design for the PFR presents advantages capable of concurrently fulfilling all the aforementioned design requirements: 1) As shown in FIG. 4, the overall size of the4922-7473-8524, v. 1 15robot is miniaturized and compact before the soft skin inflates, making it suitable for applications in tight and confined spaces. The thin thickness and high elasticity of the soft skin allow for significant diameter changes with small variations in air pressure and effectively conform to asymmetric internal geometries of pipes when PFR experiences the inflation state (FIG. 5 and FIG. 4)

[0114] Considering the viable flow of fluids or gases in the environment where the proposed PFR is utilized, the overall structure of the robot, responsible for rigidity, is designed in a hollow-shaped. FIG. 1 illustrates the complete mechanical configuration of the proposed PFR embodiment. This robot comprises three primary components, i.e., the hollow-shaped rigid frame, the soft skin with spikes pattern, and the vibration-driven source, as shown below.

[0115] By combining the vibration generated by the miniature vibrator and the inflation / deflation activated by the pressurized air, PFR can perform adaptive locomotion to overcome critical constrained conditions that are regularly found in pipeline networks thanks to the hyperelastic feature of the soft skin and spikes without involving complex control algorithms.

[0116] The PFR in some embodiments includes a hollow-shaped rigid frame configured to minimize the overall size of the robot. The frame incorporates multiple essential components: The camera and LED for inspection are attached to the front section of the rigid frame, while the eccentric DC motor for self-propulsion is installed inside the rigid frame to ensure operational stability. The rigid frame incorporates two peripheral notches to securely fix the soft skin in place and prevent any air leakage. The soft skin is fixed on the rigid frame through a knot of thread. The dimensions of the rigid frame are established according to the inner diameter of the inspection environment. In other words, the diameter of the robot, including the soft skin before inflation, should be smaller than the minimum inner diameter of the inspection environment. Given these design specifications and to ensure broad applicability without loss of generality, the following dimensions and specific components were chosen for this study: inner diameter IDF = 12 mm, an outer diameter ODF = 15 mm, and a total length LB = 30 mm.

[0117] The PFR in some embodiments includes a soft skin with spike pattern. The 1-mm thickness of soft skin with a spike pattern (see FIG. 1 and FIG. 3) plays an important role in generating propulsion force and adapting to the variety of working cavities. During locomotion, the behavior of spikes can be compared to spring-damper systems. They are compressed and then rapidly and consistently released under high-frequency excitations4922-7473-8524, v. 1 16from the eccentric DC motor, propelling the PFR forward. These spikes are integrated into a monolithic structure with the soft skin, which is required to inflate and deflate in a proper sequence, allowing the robot's skin to match the inner diameter of the tubular environment without impeding its forward movement. The selection of the skin's material is paramount due to the characteristics of the locomotion strategy of the PFR. The spikes might produce insufficient propulsion force if their stiffness is low; however, applying a material with high shore hardness could hinder the inflation process of the skin. Therefore, the mechanical properties of the soft skin material should be thoroughly considered. After working on several prototypes ranging from 00-10 to 30A Shore Hardness, the present disclosure found that a suitable stiffness for exemplary applications is 10A Shore Hardness. In the illustrated embodiment, the silicone rubber utilized for the 1-mm soft skin is the Dragon Skin™ 10 MEDIUM (DS-10M), a product from Smooth-On Inc.

[0118] Some embodiments incorporate a vibration-driven source. The vibration-driven source may, for example, include a DC motor attached with an eccentric mass on the main shaft. When the eccentric mass rotates, it is subjected to a centripetal force, causing a vibration phenomenon to the secured hollow rigid frame. The vibration frequencies induced by the centripetal force rely on the applied voltage to the DC motor. The elucidated relationship between the applied voltage and the vibration frequency is depicted in FIG. 37.

[0119] As shown in the partial section view FIG. 6, the ability of flexible annular member 110 to expand or inflate can allow apparatus 100 to increase in diameter such that flexible extensions 115 remain engaged with a constrained environment 190 e.g. a piping system) of varying diameters. Exemplary embodiments of the present disclosure also comprise a locomotion mechanism 130 configured to impart motion to flexible extensions 115 extending radially from flexible annular member 110. The ability of apparatus 100 to conform to the constrained environment and adapt to various sized and configurations of cavities, in addition to locomotion mechanism 130, can allow apparatus 100 to move through tortuous paths, including tight radius bends and vertical sections as shown in FIG. 6.

[0120] In certain embodiments, locomotion mechanism 130 is comprised of only inflation device 132. As discussed further below, in such embodiments cycling pressure of the higher-pressure fluid to inflation device 132 can inflate and deflate flexible annular member 110 and provide the source of locomotion in such embodiments. In other embodiments, inflation device 132 is used only to inflate flexible annular member 110 and is not used to cyclically inflate and deflate flexible annular member 1 10 to provide locomotion. In such4922-7473-8524, v. 1 17embodiments, locomotion mechanism 130 can comprise a vibration device 131 as the source of locomotion for apparatus 100. In particular embodiments, vibration device 131 may be configured as a rotating eccentric mass. For example, specific embodiments may comprise an electric motor 133 with a rotating shaft 135 eccentrically coupled to a mass 137, such that rotation of shaft 135 causes mass 137 to rotate eccentrically around shaft 135. With mass 137 eccentrically positioned on shaft 135, rotation of shaft 135 creates a centripetal force that can impart vibration to housing 120 and flexible annular member 110. As explained in further detail below, this vibration can compress and release flexible members 115 to provide locomotion of apparatus 100 within a constrained environment (e.g., movement of apparatus 100 within a lumen or other constrained environment). In certain embodiments vibration device 131 may comprise one or more piezoelectric actuators in lieu of or in addition to a rotating eccentric mass.

[0121] In still other embodiments, vibration device 131 can be used in conjunction with inflation device 132 to provide locomotion. In such embodiments, vibration device 131 can vibrate flexible extensions 115, and inflation device 132 can inflate and deflate flexible annular member 110 to provide a combined locomotion force.

[0122] Referring specifically now to FIG. 7, in the embodiment shown, each flexible extension 115 comprises a base portion 116 and a distal portion 117, wherein base portion 116 is located closer to central opening 113 as compared to distal portion 117. As shown in FIG. 7, distal portion 117 is located a distance LI from second end 1 12, while base portion 116 is located a distance L2 from second end 112 (where LI and L2 are measured parallel to central axis 101). Accordingly, flexible extension 115 is angled towards second end 112 of flexible annular member 110. While only one base portion 116 and distal portion 117 is labeled in FIG. 7 for a single flexible extension 115 in FIG. 7 for purposes of clarity, it is understood that additional flexible extensions 115 are similarly configured. In addition, while flexible extensions 115 in FIG. 7 are illustrated with a curved profile, other embodiments may comprise flexible extensions with different profiles, including for example, a linear profile that includes a straight line between base portion 116 and distal portion 117. As further explained below, having flexible extensions 115 angled towards an end (in the embodiment shown, second end 112) of flexible annular member 110 provides significant advantages during operation of apparatus 100. In the embodiment shown, flexible annular member 110 further comprise one or more skin can have embedded sensors 107, including for example sensors configured to provide embodied intelligence in soft robotics. In certain embodiments, apparatus 100 may be tele -operated by control4922-7473-8524, v. 1 18system 145 (shown in FIG. 1) using a remote user via a joystick or another robotic system. This system can provide visual and haptic feedback through the monitor and joystick or robotic system to the user to inform the user about the textural and force or haptic information of the inspection area. The user can then command apparatus 100 to proceed or stay at a specified location. Particular embodiments of apparatus 100 may also operate in an autonomous mode which use embedded sensors 107 and / or Artificial Intelligence (Al) algorithms, such that apparatus 100 can autonomously navigate through the environment and send the visual and force information to a user. In such embodied intelligence, using embedded sensors 107 and Al, apparatus 100 can determine what to do autonomously and navigate through the inspection environment (e.g. pipe) and perform the inspection.

[0123] Referring back now to FIG. 2, the outer diameter ODs of flexible annular member 110 (including flexible members 115) is shown with flexible members 115 in an uncompressed state. During operation flexible members 115 can become compressed such that the ODs of flexible annular member 110 is reduced, as explained further below. The ability to cyclically compress and release flexible members 115, in combination with the configuration flexible members 115 angled toward second end 112, provides for effective locomotion of apparatus 100 through lumens of varying sizes, configurations and applications.

[0124] Referring now to FIG. 8, a graphical representation of the principle of operation and different modes of locomotion for apparatus 100 is shown for an embodiment in which the locomotion mechanism comprises both vibration device 131 and inflation device 132 as described in the discussion of previous figures. For purposes of clarity, individual elements of apparatus 100 are not labeled in FIG. 8. In Panel A in the upper left portion of FIG. 8, apparatus 100 is in a lumen 150 that has an inner diameter (ID) that exceeds the outer diameter ODs of apparatus 100. While lumen 150 is shown for illustrative purposes in FIG. 8, it is understood that apparatus 100 may be operated in other constrained environments, including for example, in narrow spaces between planar walls or other irregular small spaces, including those within industrial or biological applications.

[0125] The left portion of Panel A illustrates a side view of apparatus 100 in a section view of lumen 150, while the right portion of Panel A illustrates an end view of apparatus 100 in lumen 150. As shown in the end view of Panel A, flexible annular member 110 is in a normal or non-inflated state and there are only three rows of flexible members 115 contacting lumen 150. In Panel B in the upper right portion of FIG. 8, flexible annular4922-7473-8524, v. 1 19member 110 has been inflated via inflation device 132 (shown in FIG. 1) such that flexible annular member 110 engages lumen 150.

[0126] In certain embodiments, a vector of centripetal force, FC, is generated by vibration device 131 with electric motor 133 rotating eccentric mass 137 (shown in FIG. 1) and relies on its rotation angle, <p. In certain embodiments, this is the primary driven source in mode 1 of locomotion. In Panel B in the upper right portion of FIG. 8, apparatus 100 is transformed from the normal state into the inflation state via inflation device 132 (shown in FIG. 1), facilitating the adaptation of the flexible annular member 110 to a bigger- diameter condition of the cavity environment. In addition to the adaptive function, the apparatus 100 can also perform slow locomotion by inflating and deflating flexible annular member 110 with a specific activation cycle, thanks to the stick-slip phenomenon. This form of locomotion is categorized as Mode 2. In Panel C of FIG. 8, the modes of locomotion graphically illustrated. Mode 3 of locomotion is a combination of the vibration (Mode 1) and inflation / deflation process (Mode 2).

[0127] FIG. 1 exhibits two actuation components for the locomotion mechanism, including electric motor 133 rotating eccentric mass 137 and inflation device 132, which may comprise a pressurized air inlet in some embodiments. The combination of these two actuators is able to deliver three locomotion modes with three distinguishable postures. The first and second modes are activated by the vibration motor and the air inlet, respectively. The third one is generated via simultaneous activation of the vibration excitation and the air input.

[0128] Vibration-based locomotion models have been developed to target applications for pipeline systems. Such proposed locomotion postures rely on the excitation frequencies of vibration sources, which are derived from a rotation of an eccentric mass

[0022] ,

[0048] ,

[0049] or stimulation of a piezoelectric actuator supplied with high voltages [3],

[0027] —

[0030] . Within the present disclosure, this locomotion strategy is referred to as Mode 1. The operational fundamental involves the stick and slip phenomenon, alternatively known as the asymmetric friction force. When the eccentric mass rotates, it generates a centripetal force vector periodically in the plane perpendicular to the motion direction. Thus, the entire robot body is subjected to a sinusoidal centripetal force. As a consequence, the elastic limbs run into the compression and the release period cyclically. The stick phase corresponds to compression, while the slip phase corresponds to release. The working principle of Mode 1 of the locomotion is presented in Panel C of FIG. 8. One potential limitation of Mode 14922-7473-8524, v. 1 20is that it may not be able to provide locomotion against gravity in tubular conditions where the inner diameter exceeds the outer diameter (ODs) of apparatus 100.

[0129] Other embodiments may only use a variation of pressurization for the higher-pressure fluid used to inflate flexible annular member 110 for locomotion. In the present disclosure, this is referred to as Mode 2. In this mode, the propulsion motion of apparatus 100 (also referred to herein as an inflatable locomotive robot, or FLR) solely happens due to the sequential inflation and deflation of the robot. In contrast to Mode 1 and Mode 3, the delivered velocity of this mode is slower due to the activation method (sequentially inflating and deflating the soft skin), which is able to yield only a small amount of net displacement, Df=r)pM2, after a complete cycle of inflation to deflation process (see FIG. 8 Panel C, Mode 2) for the demonstration of the locomotion of Mode 2. During the inflation, the flexible annular member 110 and flexible extensions 115 are compressed (the stick phase occurs). When FLR rapidly deflates, the slip mechanism happens, generating a net displacement in one cycle of applying pressure. The deflation rate is characterized by an average pressure decline in one second and represented it by the Dfrparameter. In Mode 2, to obtain a net displacement, we determined that Dfrshould vary from 10 to 15 kPa / s. The average velocity in this mode is approximately 0.5 mm / s. However, the most significant advantage of Mode 2 is the ability to create substantial propelled forces (see Fig. 5) that outperform the rest of the locomotion modes. The maximum generated propulsion forces are even 20 to 35 times higher than the total weight of FLR (see the Propulsion force examination for more information). This propelled force is produced as a result of the soaring up of the inlet pressure in the inflation process. The pressurized air compresses the soft skin and spike pattern against the pipe wall, increasing the normal force on the spikes and causing deformation. The spikes’ morphology transforms this normal force into a forward-propelling horizontal force (See the Supplementary Section and the stick phase in Mode 2. Consequently, Mode 2 of motion creates a solid pulling force when every limb is subjected to being highly deformed. Hence, we capitalized on this feature in particular contexts, such as approaching target points for inspection tasks with a built-in camera, overcoming complex regions, or regions with highly resistant force.

[0130] For example, in a vibration and pressurization change mode, Mode 3 may, for example, be considered the combination of Mode 1 and Mode 2. Mode 3 is primarily utilized to manipulate FLR in cavity environments. Because we aim to develop an adaptable soft robot, FLR has to transform its outer soft skin flexibly and rapidly to adapt to varying working environments. Therefore, when encountering pipes that are bigger than FLR’s4922-7473-8524, v. 1 21outer diameter, FLR activates the air channel to expand the soft skin and anchor its soft spikes to the pipe wall. At the same time, the vibration from the eccentric mass is initiated and maintained consistently, leading to the appearance of the centripetal force (see Fig. 2C, Mode 3). FLR obtains the forward motion in the deflation phase (the light green area) (see Mode 3 of Locomotion in Fig. 6C). During deflating, the pressurized air reaches a specific pressure point P*MS- At this point, FLR behaves roughly similar to Mode 1 and Mode 2, where the built-in vibrator yields sinusoidal centripetal force Fc, acting on the entire soft body and the soft spikes. The stick-slip phenomenon is induced periodically, yielding a displacement , DfpM3, over one cycle of activated input pressure. Note that DfpM3 is significantly bigger than D!='‘PM2 although they both obtain a displacement after a single cycle of activated input pressure. Nevertheless, in Mode 2 FLR only undergoes one cycle of stick and slip, whereas in Mode 3 the number of times the stick and slip occurs corresponds to the vibration frequency. Therefore, the average velocity of Mode 3 far outweighs Mode 2. The reduction slope of the pressurized air is regulated via a flow control valve of SMC, model AS2052F. The pressure drop might behave non-linearly depending on the pipe size. We determined the threshold of Dfrshould be 7 kPa / s. If the pressure falls faster than 7 kPa / s, the displacement will be significantly reduced, or even the FLR will stand still in the worst scenario.

[0131] Regarding the centripetal force from the vibration source, the frequency and the amplitude of FC rely on the rotation speed of the eccentric mass. As depicted in Fig. 8A and 8B, a frame of reference, XTr YTr Z fr , is attached to the hollow frame on which the vibrator is mounted. The FC rotates in the plane containing Y'fr axis and Z" fr axis. The following function determines the vector of the centripetal force: )yfr - sin u.'.4)zft.b ( I )

[0133] In the given context, me, re, and OJV stand for the eccentric mass, the radius from the eccentric mass to the center of rotation, and the angular velocity of the rotation, respectively, y'fr and Yfr denote unit vectors along the YTr and Z" fr axis. To experimentally investigate the influence of the sole vibration frequency on the FLR’s locomotion, as presented in Mode 1 in Fig. 8C, the entire body of FLR is subjected to the excitation of the centripetal force, FC, resulting in a displacement Df after every cycle of FC.

[0134] Thus, it’s imperative to elucidate the correlation between motion velocity and frequency originating from the vibration source. To achieve this, we employed a high-speed4922-7473-8524, v. 1 22camera to determine the rotation per minute (RPM) of the eccentric mass mounted on the DC motor. The obtained results of RPM are equivalent to the induced vibration frequencies.

[0135] FIG. 16 depicts the relationship between vibration frequency and average velocity in Mode 1 of locomotion. Mode 1 strategy is merely activated when FLR horizontally traverses in tubular conditions where the inner diameters are equal to the outer diameter of FLR, ODS.

[0136] FIG. 8 Panel B and FIG. 8 Panel C present the adapting and conformable mechanism of FLR’s body when dealing with variable cavities. The determination of necessary pressure values to inflate FLR to reasonable radii fitting with the tubular sizes cannot be neglected. The soft skin is fabricated by the Dragon Skin™ 10 silicone rubber. This specification allows FLR to expand up to two and a half fold the outer diameter of FLR at the normal state. The FLR’s soft skin can efficiently perform large deformations thanks to the hyperelastic characteristic of the fabricated material.

[0137] Some embodiments, may, for example, include locomotion mode. The working principle of the PFR is straightforward and intuitive. FIG. 1 exhibits two actuation components, including the eccentric DC motor and the pressurized air inlet. The combination of these two actuators is able to deliver three locomotion modes with three distinguishable postures. The first and second modes are activated by the vibration motor and the air inlet, respectively. The third one is generated via simultaneous activation of the vibration excitation and the air input.

[0138] For example, in a Vibration only Mode (Mode 1): Vibration-based locomotion models have been developed to target applications for pipeline systems. Such proposed locomotion postures completely rely on the excitation frequencies of vibration sources, which are derived from a rotation of an eccentric mass (22), (49), (50) or stimulation of a piezoelectric actuator supplied with high voltages (3), (27-30). Within this paper, we consider this locomotion strategy as Mode 1. The working principle of Mode 1 of the locomotion is presented in FIG. 8, section C (Mode 3 of locomotion).

[0139] The locomotion speed in Mode 1 may, for example, be determined by the excitation frequency of the vibration-driven source. The average velocities corresponding to various vibration frequencies are shown in FIG. 16. The maximum velocity was reported at approximately 0.7 Body Length / second (BL / s) at 64 Hz.

[0140] Some embodiments may, for example, include a variation of pressurization only Mode (e.g., Mode 2). FIG.8 depicts Mode 2. Mode 2 may, for example, be used to obtain a net4922-7473-8524, v. 1 23displacement. For example, the average deflation rate Df" may, for example, vary from 10 to 15 kPa / s. The average velocity in this mode may, for example, approximately be 0.5 mm / s. However, the most significant advantage of Mode 2 is the ability to create substantial propelled forces (see FIG. 11) that outperform the rest of the locomotion modes. The maximum generated propulsion forces may, for example, be 20 to 35 times higher than the total weight of PFR (see the Propulsion force examination for more information). This propelled force is produced as a result of the soaring up of the inlet pressure in the inflation process. The pressurized air compresses the soft skin and spike pattern against the pipe wall, increasing the normal force on the spikes and causing deformation. The spikes' morphology transforms this normal force into a forward-propelling horizontal force (See the stick phase in Mode 2 and FIG. 27). Consequently, Mode 2 of motion creates a solid pulling force when every limb is subjected to being highly deformed. Hence, we capitalized on this feature in particular contexts, such as approaching target points for inspection tasks with a built-in camera, overcoming complex regions, or regions with highly resistant force.

[0141] FIG. 8 depicts an operation principle and locomotion modes of PFR. The PFR is in the tubular condition whose inner diameter exceeds the PFR’s outer diameter. The PFR is in a normal state. Thus, there are only three rows of elastic limbs contacting the environment. A vector of centripetal force, FC, is generated by the DC vibrator and relies on its rotation angle, cp. This is the primary driven source in mode 1 of locomotion.

[0142] The PFR is transformed from the normal state into the inflation state via the supplying air channel, facilitating the adaptation of the PFR’ s soft body to a bigger-diameter condition of the cavity environment. In addition to the adaptive function, the PFR can also perform slow locomotion by inflating and deflating the soft skin with a specific activation cycle, thanks to the stick-slip phenomenon. This form of locomotion is categorized as Mode 2.

[0143] Mode 3 is a combination of vibration and inflation / deflation process. In the subset figure of Mode 3, the dash-dot line and the solid line, which are out of phase by JI / 2, stand for the centripetal force vector components in the plane containing Yfraxis and Zfraxis, respectively.

[0144] Mode 3 is the combination of Mode 1 and Mode 2. It is primarily utilized to manipulate PFR in cavity environments. Because some embodiments may, for example, aim to develop an adaptable soft robot, PFR has to transform its outer soft skin flexibly and rapidly to adapt to varying working environments. Therefore, when encountering pipes that are bigger than PFR's outer diameter, PFR activates the air channel to expand the soft skin and4922-7473-8524, v. 1 24anchor its soft spikes to the pipe wall. At the same time, the vibration from the eccentric mass is initiated and maintained consistently, leading to the appearance of the centripetal force (see FIG. 8, Mode 3).

[0145] Some embodiments of the PFR may, for example, obtain the forward motion in the deflation phase (the light green area) (see Mode 3 of Locomotion in FIG. 11). Mode 3 functions similar to Mode 1 , with forward motion driven by the stick-slip mechanism. The asymmetric friction distributed at the tips of the soft spikes, causing the stick-slip mechanism, is described in the Design section of the Supplementary Material. We observed that in Mode 3, PFR achieves an average speed of approximately 0.6 BL / s in the 30 mm pipe and 0.2 BL / s in the 41 mm pipe during horizontal movement. We empirically determined that the threshold £> / " should be approximately 6 kPa / s. If the pressure falls faster than 6 kPa / s, the displacement will be significantly reduced, or even PFR will stand still in the worst case scenario.

[0146] Some embodiments may, for example, be used to examine the vibration frequency. Regarding the centripetal force from the vibration source, the frequency and the amplitude of Fc rely on the rotation speed of the eccentric mass. As depicted in Fig. 2A and Fig. 2B, a frame of reference, X^.Y^rZ^r, is attached to the hollow frame on which the vibrator is mounted. When the eccentric mass rotates, the hollow-shape frame is subjected to the centripetal force, Fc, which rotates in the plane containing Y fraxis and Zfraxis. Note that the centripetal force vector direction should point toward the rotation center; however, we offset the vector’s tail to the rotation center to demonstrate its influence on the rigid frame (i.e., a reaction force vector of the centripetal force). The following function determines the vector of the centripetal force:

[0148] In the given context, me, re, a)v, g stand for the eccentric mass, the radius from the eccentric mass to the center of rotation, the angular velocity of the rotation, and the gravitational vector, respectively. The unit vectors along the Y frand Zfraxes are denoted by yfrand zfr.

[0149] To experimentally investigate the influence of the sole vibration frequency on PFR’s locomotion, as presented in Mode 1 in FIG. 8, the entire body of PFR is subjected to the excitation of the centripetal force, Fc, resulting in a displacement, Dp^ after every cycle of Fc. Thus, it's imperative to elucidate the correlation between motion velocity and frequency originating from the vibration source. To achieve this, we employed a high-speed4922-7473-8524, v. 1 25camera to capture the marker’s rotation attached to the eccentric mass (see FIG. 30). The data collected was then processed to determine the dominant frequencies, which represented the vibration frequencies. The relationship between applied voltage and vibration frequency is shown in FIG. 31. Also, FIG. 33 illustrates the connection between vibration frequency and average velocity in Mode 1 of locomotion. Mode 1 strategy is merely activated when PFR horizontally traverses in tubular conditions where the inner diameters are equal to the outer diameter of PFR, ODs.

[0150] To determine the correlation between the input pressure and the expansion shape of the soft skin, we adopted the hyperelastic simulation function from ABAQUS software to handle this task, and the Yeoh model was of interest because, based on the working conditions aiming to, the maximum strain might reach up to 200 %, where the Yeoh model provides the best-fit

[0050] . We then justified the simulation results with the experiment by capturing FLR states corresponding to the applied pressures. Then, we processed them with image processing software. After the empirical verification, the outcomes of the simulation will be employed to determine the needed pressure values for FLR when it encounters arbitrary boundary conditions.

[0151] The expansion curves of FLR (experiment and simulation) when it is subjected to the inlet pressure are demonstrated in FIG. 9. Panel A of FIG. 9 illustrates employing a hyperelastic simulation module of ABAQUS to identify the radius behavior corresponding to the applied pressure. The simulation can be utilized to determine arbitrary radii corresponding to desired tubular working conditions. FIG. 9 Panel B illustrates identifying the expansion radius by capturing the inflation state. FIG. 9 Panel C illustrates the outcomes of the empirical and simulated methods were obtained.

[0152] We did not include the soft spikes (z.e. also referred to herein as flexible extensions) in the simulation model to reduce the calculating time. Yet, the simulation still illustrates reliable outcomes in five cases of applied pressure. These expansion performances suggest that FLR can cope with cavities that are two times bigger than FLR’ s body; however, it was reported that at 30 kPa, there were small shaded white regions appearing on the stretched skin surface; consequently, within this design concept, we merely aim to test FLR at the 1.5xODs state.

[0153] Exemplary embodiments of the present disclosure provide an inflatable version of FLR so that it can adapt and locomote in tubular conditions, which have diameter dimensions vary from 1 xOD.s to L5xODx (OD i.e., the outer diameter of the robot). Based on these boundary conditions, we examined the locomotion performances in straight and plain pipes4922-7473-8524, v. 1 26of three inner diameter dimensions, i.e., ID1=30 mm, ID2=36 mm, ID3=41 mm. The purpose of these experiments was to measure the propulsion force of the proposed novel concept robot within pipes of various sizes. An overview of the experimental scheme is shown in FIG. 17. In this scenario, we measured the propelled force generated from the soft spike pattern by activating Mode 3 of the locomotion of FLR. The examination was conducted in three different pipes with varying inner diameters ( ID1? = 30 mm, ID2p = 36 mm, 1D3P = 41 mm). The motor’s vibration frequencies are set to 64 Hz, 137 Hz, 160 Hz, and 192 Hz, while the air pressure inside the soft robot is set to 20 kPa, 23 kPa, and 26 kPa. The selection of pressure values is based on the assessment of the inflation radius and the supplying pressure so that FLR can expand to have enough contact with the pipe wall. The experiment was performed for a total of 36 cases, considering the combination of the four different motor vibration frequencies, three air pressure levels, and three pipe inner diameters. The states of FLR, when it is supplied with air from the pump, are presented in FIG. 10.

[0154] FIG. 9 depicts the relationship between the applied pressures and the obtained expansion radii of soft skin. For example, by employing the hyperelastic simulation module of ABAQUS to identify the radius behavior corresponding to the applied pressure. The simulation can be utilized to determine arbitrary radii corresponding to desired tubular working conditions. For example, by identifying the expansion radius by capturing the inflation state. For example, the relationship may, for example, then be derived by a Comparison of the obtained empirical and simulation results.

[0155] FIG. 8 (e.g., Mode 2 and Mode 3, B and C) present the adapting and conformable mechanism of PFR's body when dealing with variable cavities. The determination of necessary pressure values to inflate PFR to reasonable radii fitting with the tubular sizes cannot be neglected. The soft skin is fabricated in this embodiment by the Dragon Skin™ 10 silicone rubber. The use of Dragon Skin™ 10 silicone rubber may, for example, allow the PFR to expand up to two and a half fold the outer diameter of PFR at the normal state. The PFR's soft skin can efficiently perform large deformations thanks to the hyperelastic characteristic of the fabricated material.

[0156] For context, to determine the correlation between the input pressure and the expansion shape of the soft skin, users of the PFR may, for example, adopt the hyperelastic simulation function from ABAQUS software to handle this task. For example, a Yeoh model was of interest because, based on the working conditions aiming to, the maximum strain might reach up to 200%, where the Yeoh model provides the best-fit (51 ).4922-7473-8524, v. 1 27

[0157] Users of the PFR may, for example, then justify the simulation results with the experiment by capturing PFR states corresponding to the applied pressures.

[0158] Then, users may, for example, process the taken images with image processing software. After the empirical verification, the outcomes of the simulation will be employed to determine the needed pressure values for PFR when it encounters arbitrary boundary conditions. The expansion curves of PFR (experiment and simulation) when it is subjected to the inlet pressure are demonstrated in FIG. 9.

[0159] Some embodiments may, for example, be used for propulsion force examination. For example, some embodiments may, for example, be configured to include an inflatable version of PFR so that it can adapt and locomote in tubular conditions, which have diameter dimensions vary from IxODs to 1.5xODs (ODs i.e., the outer diameter of the robot).

[0160] Based on these boundary conditions, the locomotion performances in straight and plain pipes of three inner diameter dimensions, i.e., IDp =30 mm, IDp =36 mm, IDp =41 mm were examined. The purpose of these experiments was to measure the propulsion force of the proposed novel concept robot within pipes of various sizes.

[0161] An overview of the experimental scheme is shown in FIG. 17. In this scenario, the propelled force generated from the soft spike pattern by activating Mode 3 of the locomotion of PFR was measured. The examination was conducted in three different pipe sizes as mentioned above. The motor's vibration frequencies are set to 64 Hz, 137 Hz, 160 Hz, and 192 Hz, while the air pressure inside the soft robot is set to 20 kPa, 23 kPa, and 26 kPa. The selection of pressure values is based on the assessment of the inflation radius and the supplying pressure so that PFR can expand to have enough contact with the pipe wall.

[0162] In FIG. 10 Panels (A, B, C), Panels (D, E, F), and Panels (G, H, I) are cases in which FLR is tested in 30-mm, 36-mm, and 41 -mm tubes, respectively. The inset figure in (C) illustrates the traces of the contacting soft limbs with the wall. The white infill squares stand for the contacting spikes, whereas the sole-solid-line squares represent the non-contacting spikes. Each row of soft spikes in the radial direction is numbered from one to five from right to left. Each white square stands for 14 radially distributed soft spikes.

[0163] FIG. 11 exhibits 36 cases of the generated thrust force along with the inflation / deflation states of FLR. Generally, the force graph at any given vibration frequency and applied pressure always illustrates two patterns. The smooth curves are at the inflation phase, and the noisy curves are at the end of the deflation phase of the input pressure. As presented in FIG. 8, at the inflation phase, the soft body expands and contacts the cavity wall, yielding4922-7473-8524, v. 1 28deformations on the morphological limb pattern of FLR and leading to boosting the force. The elastic deformations from the spikes primarily account for the soaring up of the force at this step. The maximum acquiring values are from 20 to 35 times the total weight of FLR (10 grams). Looking at FIG. 10 and FIG. 11, it is observed that the value of the peaks of the obtained force corresponds to the number of the contacting limbs. In the 30-mm tube, four rows of FLR legs are compressed under all testing values of pressure, whereas there are only two to three rows of limbs that are deformed in the 36-mm and 41 -mm experiments, causing a slight drop of the highest induced force. However, with this capability of generating force, it suggests that FLR can easily interlock its body in vertical working conditions by inflating the soft skin to serve particular inspection purposes. When FLR experiences the deflation phase, its soft body begins shrinking gradually, corresponding to the release rate of the pressure, leading to decreases in the forces; accordingly, the force curves become noisy due to the influences of the vibration excitation frequencies. The noisy patterns vary according to frequencies. In the 30-mm pipe, the noises appear nearly at the end of the deflation phase, and they are formed by the stick-slip mechanism, which is explained in FIG. 8. The locomotion was also reported to occur at this deflation area. When the pressure drops to a specific value, P*M3, the forward locomotion is generated (see Mode 3 of locomotion explanation in Fig. 2). When the pipe diameters are larger than ODs, the 36 mm and 41 mm ones, it was observed the more the DC motor vibrates, the earlier and the noisier the force curves behave. This indicates that in these contexts, FLR might obtain higher displacements. In addition, it is noticed in FIG. 11 that in the 30 mm pipe, there are no significant differences between the response at 23 kPa and 26 kPa. Analogous observations can be figured out in the 36-mm and the 41 -mm cases. The interaction states of FLR can explain this behavior (see FIG. 10), as the number of soft spikes deformed during inflation remains consistent between 23 kPa and 26 kPa. From these force curves and the deformed conditions of FLR’s limbs in pipes at 23 kPa and 26 kPa, it can be advocated that the generated displacement could be similar between 23 kPa and 26 kPa.

[0164] In the above sections, we present the explanations for the locomotion modes. In certain embodiments, Mode 3 is the primary mode that delivers the forward motion of FLR in cavities. Hence, we focused on investigating the motion performance of FLR when Mode 3 was being activated. The experimental parameters were applied analogously to the propulsion force test, including testing in three boundary conditions, i.e. ID 30 mm, ID 36 mm, and ID 41 mm; four vibration frequencies, i.e. 64 Hz, 137 Hz, 160 Hz, and 192 Hz;4922-7473-8524, v. 1 29three levels of input pressure, i.e. 20 kPa, 23 kPa, and 26 kPa. The measurement scheme is shown in FIG. 18. To observe the X position of FLR corresponding to the applying pressure, we connected the programmable air pump and a 5 Degree of Freedom (DOF) electromagnetic tracking (EM) sensor (Aurora 5 DOF Sensor Northern Digital Inc., Canada) to Robot Operating System (ROS) environment installed on an external computer. The utilized EM sensor is small, compact, and lightweight (the size of the sensor tip - 0.3x2.5 mm). The sensor tether was small, tiny in diameter and had highly bendable and flexible properties. Such features allowed to eliminate the influence of the sensor mass on displacement outcome and diminish the induced friction force acting on the sensor tether. ROS enabled us to collect the sensing data together with the pressure data in real-time.

[0165] FIG. 11 depicts the obtained propulsion forces conducted in the IPp = 30 mm, IPp = 36 mm and IPp = 41 mm pipes in the aforementioned pre-setting conditions. (A, D, G), (B, E, H), and (C, F, I) demonstrate the results in the cases of applying pressures 20kpa, 23kpa, and 26kpa, respectively.

[0166] FIG. 12 depicts the collected results of the horizontal displacement of FLR. In order to plot a position line with a shaded area, we repeated each experiment three times on each pair of pressures and vibration frequencies. In general, FIG. 12 demonstrated that the higher the vibration frequency is applied, the higher the displacement is generated in Mode 3. At the lowest tested frequency (i.e., 64Hz), FLR barely moves even though this frequency brings the highest velocity in Mode 1 of locomotion. In contrast, the average velocity at 192 Hz appears in the lower-than 5 mm / s zone in Mode 1 but gains the highest displacement values in Mode 3. Movements in Mode 3 have the same behaviors that always occur during the deflation phase. When the pressure air drops to a particular point P*M3, FLR begins moving forward. The displacements in the 36 mm and 41 mm circumstances demonstrate better results than 30 mm cases in terms of achieving displacement over one applied pressure cycle. This response comes from the deflation rate, Dfr. As demonstrated in FIG. 10. in spaces whose cross sections are as approximately small as FLR size. FLR faces difficulty in retaining the curvy shape due to the restriction of the boundary; consequently, more soft spikes come into contact with the pipe wall, yielding more compression force on the soft skin. Thereby, the soft skin more rapidly shrinks in the deflation phase, leading to the reduction of the deflation spans. In the 36 mm and 41 mm pipes, there is more space for FLR to acquire the curved shape, so there are fewer soft limbs contacting the boundary wall (see FIG. 10). Hence, the deflation phase lasts4922-7473-8524, v. 1 30longer in those contexts in exchange for more induced displacement. In addition, it can be noticed in the pressure curves of FIG. 12, especially the regions in the red dash ovals, that the appearances of the pressure curves differ from pipe sizes. When the diameter increases, the growth of the pressure in the inflation phase exhibits the same transformations that the slopes of the pressure curves suddenly decrease at the tip regions of the curves. The bigger the pipe, the more the slope declines. From these characteristics of pressure behaviors, FLR can actively detect the change in the dimension of the interacting cavity environment, i.e., in complicated pipeline networks, where operators cannot determine the variation of the tubular dimension. Besides, these displacement performances reveal the best pair of values, applied pressure: PMS = 23 kpa and vibration frequency f= 160 Hz so that they allow FLR to travel through all testing cavity conditions. Although these performances do not dominate the locomotion speed compared to most other developed terrestrial soft designs [3], the locomotion mechanism of FLR demonstrates an effective way of controlling. The induced displacement outcomes reveal a template that FLR is able to traverse through any pipeline systems with diameter sizes varying from 1 to 1.5 times the outer diameter of FLR by a predetermined form of controlling method.

[0167] Because of the complicated locomotion behavior of FLR during Mode 3, we decided to adopt the Finite Element Method (FEM) to simulate the locomotion of FLR. To address this problem, we proceeded with the dynamics analysis in a similar way to the characterization of the inflation radius. The Dynamic Explicit module of ABAQUS was utilized for this task. In the FEM-based simulation, the soft skin with spikes was characterized by the Yeoh model, known for accurately modeling hyperelastic material deformation

[0050] . Instead of using a full 3D model of FLR, we simplified it into a 2D model to reduce computational costs. Thanks to the cylindrical structure of FLR, as well as the pipeline, they allowed we to replace the symmetric 3D frame with a 2D cross-section of both FLR and the flow channel of the working environment. Hence, the simplification still represents the nature of the simulation of FLR in actual working conditions. The simplified procedure of the simulation is presented in the supplementary section.

[0168] FIG. 12 depicts the PFR’s position data in X direction was collected when testing in IDj = 30 mm, IDp = 36 mm and IDp = 41 mm pipes in the pre-setting conditions. (A, D, G), (B, E, H), (C, F, I) illustrate the results in the cases of applying pressures 20kpa, 23kpa, and 26kpa, respectively.4922-7473-8524, v. 1 31

[0169] Fig. 12 depicts the collected results of the horizontal displacement of PFR. To plot a position line with a shaded area (one standard deviation), the experiment was repeated three times on each pair of pressures and vibration frequencies.

[0170] In general, FIG. 12 demonstrated that the higher the vibration frequency is applied, the higher the displacement is generated in Mode 3. At the lowest tested frequency (z. e. , 64Hz), PFR barely moves even though this frequency brings the highest velocity in Mode 1 of locomotion. In contrast, the average velocity at 192 Hz appears in the lower-than 5 mm / s zone in Mode 1 but gains the highest displacement values in Mode 3. Movements in Mode 3 have the same behaviors that always occur during the deflation phase. The locomotion of PFR can only be achieved within a specific pressure range, from P„3to P^3, of the deflation phase. The displacements in the 36 mm and 41 mm circumstances demonstrate better results than the 30 mm cases in terms of achieving displacement over one applied pressure cycle. This response comes from the average deflation rate, Df“ .

[0171] As demonstrated in FIG. 10, in spaces whose cross sections are as approximately small as PFR size, PFR faces difficulty in retaining the curvy shape due to the restriction of the boundary; consequently, more soft spikes encounter the pipe wall, yielding more compression force on the soft skin. Thereby, the soft skin more rapidly shrinks in the deflation phase, leading to the reduction of the deflation spans. In the 36 mm and 41 mm pipes, there is more space for PFR to acquire the curved shape, so there are fewer soft limbs contacting the boundary wall (see FIG. 10).

[0172] Hence, the deflation phase lasts longer in those contexts in exchange for more induced displacement. In addition, it can be noticed in the pressure curves of FIG. 6, especially the regions in the red dash ovals, that the appearances of the pressure curves differ from pipe sizes. When the diameter increases, the growth of the pressure in the inflation phase exhibits the same transformations that the slopes of the pressure curves suddenly decrease at the tip regions of the curves.

[0173] The bigger the pipe, the more the slope declines. From these characteristics of the pressure behaviors, PFR can actively detect the change in the dimension of the interacting cavity environment, i.e., in complicated pipeline networks, where operators cannot determine the variation of the tubular dimension. Besides, these displacement performances reveal the best pair of values, applied pressure: PM3=23 kPa and vibration frequency f = 192 Hz so that they allow PFR to travel through all testing cavity conditions. Although these performances do not dominate the locomotion speed compared to most other4922-7473-8524, v. 1 32developed terrestrial soft designs (3), the locomotion mechanism of PFR demonstrates an effective way of controlling. The induced displacement outcomes reveal a template that PFR is able to traverse through any pipeline systems with diameter sizes varying from 1 to 1.5 times the outer diameter of PFR by a simple form of controlling method.

[0174] The simulation results of FLR in ABAQUS are shown in FIG. 13. FIG 13A shows one of the simulations of FLR to examine the displacement performances. The testing parameters in FIG. 13 A include the 30-mm pipe, applied pressure: 23kpa, vibration frequency: 192Hz. FIG. 13 B, C, D, E illustrate the use of ABAQUS simulation to review the traverse capability of FLR when dealing with environments. These conditions are critical cases that are regularly assembled in pipeline systems [4],

[0175] FIG. 13A presents one of the simulations to investigate the displacements of FLR. Additionally, we also utilize this simulation model to examine the FLR’s capability of traversing critical zones in pipeline systems. This FEM- based approach can assess the FLR’s ability beforehand to overcome predetermined tubular constraints before actual deployment. The examinations in the simulation environment are illustrated in FIG. 13 B, C, D, E. The simulated positions of FLR in horizontal condition are plotted in FIG. 13, the red dash lines. Based on the obtained position dataset, we decided only to take the best- determined input parameters, i.e., 23 kPa, and 160 Hz, for the simulation model. Firstly, the response of the simulation well reflects the basis of Mode3 locomotion in two points, including the standstill phase that occurs when input pressure is higher than PMS* values, and the generated displacements over one cycle of applying pressure well matches with the experimental values.

[0176] Apart from studying the locomotion and constructing the FEM-based dynamics simulation in ABAQUS to evaluate and predict the behaviors of FLR in a regular condition, a plain pipe installed horizontally, we challenged FLR’s capability of traversing through critical zones of any pipeline system, including the elbow turning sections, branches, traveling horizontally to vertically [4], transition areas from small to big cavity and vice versa in both horizontal and vertical conditions, and the steering ability when dealing with T-shaped pipe. All these zones could be assessed by simulations, and in every test, FLR exhibits the feasibility of surmounting all these challenging zones in a pipeline network.

[0177] FIG. 14 presents the performance of FLR in those conditions. From FIG. 14A to FIG. 141, FLR could completely traverse all these designed set-ups of the experiment. FIG. 14 A to FIG. 14F are the adaptability experiments. FLR was deployed in variable cavities with the inner diameter varying from 1 to 1.5 times the outer diameter of FLR. In general, the4922-7473-8524, v. 1 33speed of FLR drops when it has to deal with larger pipes because the FLR needs to inflate to bigger radii, leading to the extension of the deflation spans. For the cases of traveling through transition areas, FIG. 14 D, E, C, F, it is easier and faster to move horizontally than vertically. Moreover, FLR finds it less complicated to go through the small-to-big transition areas due to the inclined angle of the design of the soft spikes. We wanted to test the FLR’s capability of overcoming extreme curvature conditions in a network of pipes, such as a 90- degree elbow configuration (see FIG. 14G, H). FLR overcame a 90-degree turning section with the influence of gravity in both simulation and experiment. FLR is a vibration-based soft design, and the source of vibration is a DC motor equipped with an eccentric mass. Therefore, we figured out that FLR can navigate to the left or right at branch locations by changing the rotation direction of the eccentric mass. FIG. 141 illustrates the navigation ability of FLR at the T branch section. In the last step, we proceed with trials with the complete version of FLR, including a high-lumen LED and a tiny camera, a NanEye™ camera, for inspection missions in dark conditions. FIGS. 14 J, K show the recorded images from the NanEye™ camera with the aid of the light from the LED. In all these experiments, we only activate Mode 3 of strategy locomotion with the 23-kPa pressure and 160-Hz vibration frequency. Thanks to the high adaptability of soft skin, FLR can deliver locomotion through variable working environments with a predetermined control method, Mode 3.

[0178] As disclosed herein we have proposed a unique design of a bio-inspired soft robot that features a novel, hybrid propulsion mechanism, sometimes referred to herein as an flexible locomotion robot (FLR), and possesses a high adaptability to cavities with variable geometries. In one specific embodiment, a 10-shore-hardness material, Dragon Skin™ 10, fabricates the outer skin of FLR. This silicone rubber allows the soft skin of FLR to withstand a strain of up to 150% (in one specific case), providing the ability for FLR to deal with a wide range of cavity sizes, from 1 to 1.5 times the outer diameter of FLR. FLR is built with two sources of actuation represented by two input parameters, including pressure input and vibration frequency input. FLR can obtain three modes of locomotion based on these parameters. Mode 3 primarily delivers propulsive motion, whereas Mode 2 is suitable for the approach to inspecting targets at close ranges due to the slow speed. In particular, Mode 2 is ideal for inspection tasks in vertical conditions, thanks to the capability of generating high friction force against the backward motion caused by gravity. Based on our experiments, this force is 20-fold to 35-fold more than the weight of FLR. Besides the high adaptability, the soft skin of FLR also brings another advantage when it4922-7473-8524, v. 1 34can indirectly determine the transformation in the diameter of the interacting cavity environment based on the change of the pressure curve at the inflation phase. We assessed the traverse ability of FLR in critical conditions of a pipeline network, including the high curvature pipes, the 90-degree elbow tubes, the small-pipe-to-big-pipe transition areas and vice versa, even with the influence of gravity, and the steering at the T branch. FLR is equipped with a miniature camera and light source to assist the inspection task in dark conditions. In addition, we have presented a FEM-based method to simulate the locomotion of FLR in the testing scenarios. The purpose is to evaluate the capability of overcoming predefined constrained environments before deploying the FLR to actual conditions. The outcomes of the simulation are consistent with the experimental results. Although FLR demonstrates promising capabilities in coping with critical configurations of pipeline systems, the average locomotion speed of FLR is not dominant in the field of pipe inspection robots due to the movement mechanism of Mode 3 of FLR. In a specific condition, the inner diameter of the cavity is nearly the same as the size of FLR, the average velocity of FLR is reported at 0.6 BL / s (Body Length / second). Yet, when moving in larger tubes, i.e., 1.5 times the size of FLR, the obtained average velocity is only 0.1 BL / s (3 mm / s).

[0179] In FIGS. 14A, B, G, H, FLR overcomes elbow turning sections. In FIGS.14D, E, C, F, FLR surpasses transition areas, whose diameters vary from small to big ones, especially in C, F, gravity against the forward motion of FLR. In FIG. 141, FLR performs the steering ability by changing the rotation direction of the vibration. In FIGS. 14J and K, FLR proceeds with inspection missions in dark conditions. The high-lumen LED is activated to support the record from the NanEye™ camera. In FIGS. 14 C, G, F, the red dash circles demonstrate positions where FLR hangs its body to prepare for the upward motion against gravity. Note that the diameter dimensions in this figure stand for the inner diameters of the pipe.

[0180] In one specific embodiment the 1-mm soft skin is fabricated by Dragon Skin™ 10 of Smooth-On. The rigid hollow frame is 3D printed by an SLA 3D printer (Form3, Formlabs Inc). The utilized resin is Clear V4 supplied by Formlabs. The source of vibration is an eccentric mass attached to a DC motor. This type of vibrator can be easily found and bought on online-selling platforms. The vibrator, the LED, and the air pressure hose are adhered to the frame by an adhesive (LOCTITE 416 of Henkel Adhesives). The NanEye™ camera (ams-OSRAM AG) is firmly fixed to the frame with a sealant tape. To firmly hold the soft4922-7473-8524, v. 1 35skin on the frame, we used threads to tie the skin to the peripheral notches of the hollowshaped frame.

[0181] FIG. 14 depicts the evaluation of PFR performance when coping with critical zones in pipeline systems by the empiricism and simulation approaches. (A, B, I, J) PFR overcomes elbow turning sections in real condition and in simulation environment in (C, K). (D, E, F, H) PFR surpasses transition areas in real condition, whose diameters vary from small to big ones, especially in (D, H), gravity against the forward motion of PFR. (G) PFR traverse a small-to-big transition area in simulation environment. (L) PFR performs the steering ability by changing the rotation direction of the vibration. (M, N) PFR proceeds with inspection missions in dark conditions. The high-lumen LED is activated to support the record from the NanEye camera. In (D, H, I), the red dash circles demonstrate positions where PFR hangs its body to prepare for the upward motion against gravity. Note that the diameter dimensions in this figure stand for the inner diameters of the pipe.

[0182] FIG 14. depicts the dynamic explicit simulation model in ABAQUS. For example, because of the complicated locomotion behavior of PFR during Mode 3, we decided to adopt the Finite Element Method (FEM) to simulate the locomotion of PFR. To address this problem, we proceeded with the dynamics analysis in a similar way to the characterization of the inflation radius. The Dynamic Explicit module of ABAQUS was utilized for this task. In the FEM-based simulation, soft skin with spikes was characterized by the Yeoh model, known for accurately modeling hyperelastic material deformation (51). Instead of using a full 3D model of PFR, we simplified it to a 2D model to reduce computational costs. Thanks to the cylindrical structure of PFR, as well as the pipeline, they allowed us to replace the symmetric 3D frame with a 2D cross-section of both PFR and the flow channel of the working environment. Hence, the simplification still represents the nature of the simulation of PFR in actual working conditions. The simplified procedure of the simulation is presented in the supplementary section. The simulation results of PFR in ABAQUS are shown in Fig. 6 and Fig. 7C, G, K. The simulated positions of PFR in the horizontal condition are plotted in Fig. 6 via the black solid lines. Firstly, the response of the simulations well reflects the basis of Mode 3 locomotion in two points: the standstill phase occurs when input pressure is higher than P^3value, and motion begins when the pressure drop below P j3value then stops when the pressure falls below P^3. Secondly, the generated displacements over one cycle of applying pressure perfectly matches with the experimental values. Although there are discrepancies between the simulation and the4922-7473-8524, v. 1 36experiment outcomes, these differences can be attributed to the friction between the tethers and the tube wall and the tethers’ vibration, which regularly caused the entanglement between the wires and the tube edge. However, these barriers can be handled by applying cable deployment mechanism. Other reasons are presented in the Discussion section. Additionally, we also utilize this simulation model to examine PFR’s capability of traversing critical zones in pipeline systems. This FEM-based approach can assess the PFR's ability beforehand to overcome predetermined tubular constraints before actual deployment. The examinations in the simulation environment are illustrated in FIGS. 9C, G, and K. These simulation outcomes were then justified by empirical method and presented in the next section.

[0183] FIG. 14 depicts the locomotion performance in critical zones of pipeline systems. Apart from studying the locomotion and constructing the FEM-based dynamics simulation in ABAQUS to evaluate and predict the behaviors of PFR in a regular condition, a plain pipe installed horizontally, we challenged PFR's capability of traversing through critical zones of any pipeline system, including the elbow turning sections - high curvature sections, branches, traveling horizontally to vertically (4), transition areas from small to big cavity and vice versa in both horizontal and vertical conditions, and the steering ability when dealing with T-shaped pipe. All these zones could be assessed by simulations, and in every test, PFR exhibits the feasibility of surmounting all these challenging zones in a pipeline network.

[0184] FIG. 14 presents the performance of PFR in those conditions. From FIG.14 A-N depicted in FIG. 14, the PFR could completely traverse all these designed set-ups of the experiment. FIGS. A-H are adaptability experiments. PFR was deployed in variable cavities with the inner diameter varying from 1 to 1.5 times the outer diameter of PFR.

[0185] In general, the speed of PFR drops when it must deal with larger pipes because the PFR needs to inflate to bigger radii, leading to the extension of the deflation spans. For the cases of traveling through transition areas, in FIGS. 14D, E, F, H, it is easier and faster to move horizontally than vertically.

[0186] Moreover, PFR finds it less complicated to go through the small-to-big transition areas due to the inclined angle of the design of the soft spikes. Notably, the simulation tool also exhibited the same result as the tests for traversing transition areas (see FIG14G).

[0187] For example, the PFR's capability of overcoming extreme curvature conditions in a network of pipes may, for example, be examined, such as a 90-degree elbow configuration. The PFR demonstrated its ability to navigate zones with shaip curvatures, successfully4922-7473-8524, v. 1 37handling C-shaped and 90-degree turns even under the influence of gravity (see FIG. 14A, B, I, J).

[0188] The simulation model showed successful traversal on these challenging curves before being tested in actual conditions (see FIG. 14 C , K). PFR is a vibration-based soft design, and the source of vibration is a DC motor equipped with an eccentric mass.

[0189] Therefore, it may be detennined that PFR can navigate to the left or right at branch locations by changing the rotation direction of the eccentric mass. FIG. 14L illustrates the navigation ability of PFR at the T branch section. In the last step, we proceed with trials with the complete version of PFR, including a high-lumen LED and a tiny camera, a NanEye camera, for inspection missions in dark conditions.

[0190] FIG 14N shows the recorded images from the NanEye camera with the aid of the light from the LED. In all these experiments, we only activate Mode 3 of strategy locomotion with the 23-kPa pressure and 192-Hz vibration frequency. Thanks to the high adaptability of soft skin, PFR can deliver locomotion through variable working environments with a simple control method, Mode 3. Finally, from these evaluations, it is suggested that the proposed simulation framework can be utilized to pre-assess the success rate of PFR when dealing with an arbitrary pipeline condition before deploying the robot to the actual site.

[0191] In some embodiments, the unique design of a bio-inspired soft robot includes a hybrid propulsion mechanism, called PufferFace Robot - PFR, and possesses a high adaptability to cavities with variable geometries. A 10-sho re-hardness material. Dragon Skin™ 10, may, for example, be used in fabricating the outer skin of PFR.

[0192] This silicone rubber allows the soft skin of PFR to withstand a strain of up to 150% (in exemplary embodiments), providing the ability for PFR to deal with a wide range of cavity sizes, from 1 to 1.5 times the outer diameter of PFR. It is worth highlighting that the current design is the result of experiments performed under various conditions, where we used different types of miniature vibrators and three types of silicone materials (Dragon Skin™ 10, Dragon Skin™ 30, and Ecoflex™ 00-30).

[0193] Locomotion may, for example, be improved by using a harder material (Dragon Skin™ 30) for the spike structure while keeping the skin as Dragon Skin™ 10 for easier inflation, though this makes the fabrication process more complicated. In this study, the same spike patern was used across various environments, but it is expected that locomotion performance could be further improved if spike patterns are optimized for the specific environments intended for future applications.4922-7473-8524, v. 1 38

[0194] Research may, for example, be conducted to determine mathematical equations to model the number and size of spikes and the resulting propulsion force of spikes that determine their patterns on the limited surface area of the soft skin.

[0015] Users may, for example, use models to optimal propulsion force for various applied environments. In addition, the system controlling the deflation rate of PFR needs to be improved to fully characterize the non-linear behavior of the pressure curve during deflating instead of using the average deflation rate parameter, Df

[0196] Some embodiments of the PFR may, for example, be built with two sources of actuation represented by two input parameters, including pressure input and vibration frequency input. PFR can obtain three modes of locomotion based on these parameters. Mode 3 primarily delivers propulsive motion, whereas Mode 2 is suitable for the approach to inspecting targets at close ranges due to the slow speed. Additionally, since Mode 2 can securely anchor the body to the pipe wall, it is well-suited for inspection tasks in vertical conditions, where the robot needs to suspend its body against gravity for extended periods. Based on the experimental data, PFR in Mode 2 can generate a static propelled force that is 20-fold to 35-fold more than the weight of PFR. However, Mode 2 locomotion is limited to forward motion in horizontal pipes.

[0197] Besides the high adaptability, the soft skin of PFR also brings another advantage when it can indirectly determine the transformation in the diameter of the interacting cavity environment based on the change of the pressure curve at the inflation phase.

[0198] It was determined the traverse ability of PFR in critical conditions of a pipeline network, may, for example, include the high curvature pipes, the 90-degree elbow tubes, the small- pipe-to-big-pipe transition areas and vice versa, even with the influence of gravity, and the steering at the T branch. PFR is equipped with a miniature camera and light source to assist the inspection task in dark conditions.

[0199] Additional experiments were performed to quantitatively analyze the effect of air pressure inside the soft skin on the robot’s moving speed. The robot achieves the highest speed when the air pressure sufficiently decreases during deflation, allowing the spikes on the soft skin to create appropriate friction with the inner surface of the pipe. However, the relationship between the air pressure inside the soft skin, the friction between the spikes and the inner surface of the pipe during the inflation / deflation process, and the moving speed have not been mathematically defined, which limits the ability to determine the optimal air pressure for achieving the highest moving speed.4922-7473-8524, v. 1 39

[0200] Some embodiments may, for example, use mathematical models with high accuracy for these relationships to determine the optimal air pressure for achieving a high moving speed of the robot.

[0201] As depicted, FEM-based simulation model may, for example, be used to transform complex 3D model into a 2D model, significantly lowering computational costs while still accurately capturing the essential physical behaviors of the real system.

[0202] Testing was conducted to assess the PFR’s ability to navigate predefined constrained environments before deploying it in real-world conditions and to analyze the impact of parameters such as vibration frequency and average deflation rate on its motion performance. Overall, the proposed simplified simulation approach is acceptable for the following reasons: the 2-D simulation model accurately captures the key features of Mode 3, including the standstill during the inflation phase and locomotion during the deflation phase. Although the model was tested under twelve different conditions - comprising three pipe sizes and four vibration frequencies with one pressure threshold - the simulation data consistently showed that displacement increases corresponding to the rising vibration frequency across all scenarios.

[0203] The model also demonstrated the adaptability of the soft skin to various pipe sizes, using a single equivalent activated pressure value to the applied pressure set at 23 kPa. Nevertheless, there are discrepancies between the simulation outcomes and the experimental results in terms of displacement values and the out-of-phase time-position data between the simulated and the experiment approach. These errors might come from factors that are challenging to consider in the simulation procedure, including the effects of the tether vibration, the friction between wires and the inner wall of the pipes, and the defects of the soft skin and spikes during the fabrication process.

[0204] The simplified process from the 3D to the 2D space cannot fully represent all physical features of the actual model. The non-linear properties of the hyperelastic material also made it difficult to capture precise displacement data. Therefore, this study did not attempt to develop a simulation model with high accuracy of displacement data. Instead, the focus is on exploring the underlying physical behaviors, such as the effects of the inflation / deflation mechanism and the vibration frequency on the locomotion and evaluating the traversal capability to critical constraints that can be used for intuitive design of the proposed robot.

[0205] In this study, a bio-inspired robot, named the PufferFace Robot (PFR) , which utilizes a hybrid propulsion system was used. The proposed robot has the following contributions:4922-7473-8524, v. 1 40adaptability to diverse cavity environments, a hollow structure that allows efficient gas and fluid flow during inspections, and an adaptive design that enables PFR to navigate complex tubular systems with simple control.

[0206] Some embodiments may, for example, incorporate mathematically modeling to determine the required number and size of spikes, along with the resulting propulsion force, to determine their patterns on the limited surface area of the soft skin. A method for optimizing propulsion force for various applied environments may, for example, be derived. A mathematical model of the relationship between the air pressure inside the soft skin and the robot’s moving speed, as well as a closed-loop control strategy based on this mathematical model to achieve the optimal moving speed of the robot may, for example, be derived.

[0207] During the testing, the PFR embodiment included a 1-mm soft skin fabricated by Dragon Skin™ 10 MEDIUM of Smooth-On. A small amount of red pigment (PMS 186C, Silc Pig, Smooth-On) also was used to make the robot easier to detect and capture during the physical experiments conducted inside the pipe. The rigid hollow frame is 3D printed by an SLA 3D printer (Form3, Formlabs Inc). The utilized resin is Clear V4 supplied by Formlabs. The source of vibration is an eccentric mass attached to a DC motor. This type of vibrator can be easily found and bought on online-selling platforms. The vibrator, the LED, and the air pressure hose are adhered to the frame by an adhesive (LOCTITE 416 of Henkel Adhesives). The NanEye camera (ams-OSRAM AG) is firmly fixed to the frame by sealant tape. To firmly hold the soft skin on the frame, we used threads to tie the skin to the peripheral notches of the hollow-shaped frame. Based on the dimensions of the hollowshaped rigid frame, a polyurethane tube (TU0212C-20, SMC) was used as the inflation line for soft skin.

[0208] Some embodiments of the PFR may, for example, include soft skin. To fabricate soft skin with small soft limbs, a molding technique was employed. The mold was prepared by printing from a 3D printer. Because the limb size is quite small, the forming process in a 3D printing mold with Dragon Skin™ 10 needs some additional remarks to avoid the defects existing in the final product. The details of the steps to make soft skin with soft limbs are presented in FIG. 15

[0209] Some embodiments, of the PFR may, for example, be used in inflation radius simulation. For example, the Yeoh model for hyperelastic simulation may, for example, be used. To work with the Yeoh model, three coefficients are required for the simulation model. These three material constants are adapted from (57), i.e., Ci = 36 kPa, C2 = 0.254922-7473-8524, v. 1 41kPa, and C3 = 0.023 kPa. The applied density for the silicon rubber, Dragon Skin™ 10, material is 1.07 x 109metric ton / mm3. Subsequently, we applied the fixed constraints to both ends of the soft skin, which are firmly tied by threads in the real condition (see FIG. 1). Then, the pressure values, i.e., 10, 15, 20, 25, 30 kPa, were applied to the inner surface of the soft skin.

[0210] The deformation data of the skin in the middle cross-section of the robot in the axial direction may, for example, be collected. The applied mesh type and size are quad- dominated mesh and 0.25mm, respectively. FIG. 33 illustrates the constraints applied to the soft skin and how the pressure load is applied to it.

[0211] Some embodiments, may, for example, incorporate locomotion modes principle. For example, in Mode 1 the operational fundamental involves the asymmetric friction force, resulting in the occurrence of the stick and slip phenomenon. When the eccentric mass rotates, it generates a centripetal force vector periodically in the plane perpendicular to the motion direction. Thus, the entire robot body is subjected to a sinusoidal centripetal force. As a consequence, the elastic limbs run into the compression and the release period cyclically. The stick phase corresponds to compression, while the slip phase corresponds to release. The limitation of Mode 1 is that it cannot provide locomotion against gravity in tubular conditions where the inner diameter exceeds the outer diameter (ODS) of the PFR, see FIG. 8.

[0212] In Mode 2, the propulsion motion of PFR solely happens due to the sequential inflation and deflation of the robot. In contrast to Mode 1 and Mode 3, the delivered velocity of this mode is very slow due to the activation method (sequentially inflating and deflating the soft skin), which is able to yield only a small amount of net displacement, D2, after a complete cycle of inflation to deflation process (see Fig. 2C, Mode 2).

[0213] During the inflation, the soft skin and the spikes are compressed (the stick phase occurs). When PFR rapidly deflates, the slip mechanism happens, generating a net displacement, D2, in one cycle of applying pressure. This phenomenon can be explained from the energy perspective: when the limbs are rapidly restored, potential energy is transformed into kinetic energy, leading to a net displacement D2. Moreover, in a conservative system, the sum of kinetic energy and potential energy is constant. Therefore, the faster or the slower potential energy is transformed into kinetic energy, the faster or the slower the velocity can be obtained. If the deflation rate in Mode 2 is slow, a net displacement cannot be obtained because the soft spikes are released back to the initial4922-7473-8524, v. 1 42position. We characterized the average deflation rate by an average pressure decline in one second and represented it by theparameter.

[0214] In Mode 3: Considering the deflation phase, which primarily generates forward locomotion for PFR, when the pressurized air reaches a specific pressure point, PM3, PFR behaves roughly similar to Mode 1 and Mode 2, where the built-in vibrator yields sinusoidal centripetal force, FC, acting on the entire soft body and the soft spikes. The stick-slip phenomenon is induced periodically, yielding a displacement, D3, over one cycle of activated input pressure. The forward motion continues until the pressure drops below a certain threshold, PSM3. where it can no longer sustain the inflation radius required for the soft spikes to maintain contact with the tubular wall. As a result, the stick-slip mechanism ceases, and no further motion occurs until the next deflation cycle begins. Note that D3 is significantly bigger than D2, although they both obtain a displacement after a single cycle of activated input pressure. Nevertheless, in Mode 2, PFR only undergoes one cycle of stick and slip, whereas, in Mode 3, the number of times the stick and slip occur corresponds to the vibration frequency. Therefore, the average velocity of Mode 3 far outweighs Mode 2. The reduction slope of the pressurized air is regulated via a flow control valve of SMC, model AS2052F. Similarly to Mode 2, the pressure curve during deflating is characterized by the average deflation speed, kPa / s, and defined by the Df " parameter. The pressure drop might behave non-linearly depending on the pipe size.

[0215] Some embodiments of the PFR may, for example, be used in dynamic explicit simulation in ABAQUS method. Due to the symmetric structure of the cavity environments, the cylindrical shape of the pipe was transformed into the 2D form. The analogous procedure is proceeded with PFR in order to reduce the computational cost of the simulation. The detailed guideline for the simulation is presented in supplementary material, “ABAQUS simulation procedure” and FIG. 34. The frictional coefficient between PFR and the testing pipes, acrylic pipes, is approximately 0.7.

[0216] To fabricate the soft skin with small soft limbs, we employed a molding technique. The mold was prepared by printing from a 3D printer. Because the limb size is quite small, the forming process in a 3D printing mold with Dragon Skin™ 10 needs some additional remarks to avoid the defects existing in the final product. The details of the steps to make one embodiment of a flexible annular member with flexible extensions are presented in FIG. 15. The illustrated procedure comprises three main stages, including the fabrication of the soft skin, the fabrication of the hollow rigid frame, the assembly of the skin, frame,4922-7473-8524, v. 1 43with other parts, i.e., NanEye™ camera, LED, DC vibration motor, and supplying air pressure hose.

[0217] A dynamic explicit simulation was performed using ABAQUS software. Due to the symmetric structure of the cavity environments, we can simplify the cylindrical shape of the pipe into the 2D form. The analogous procedure is proceeded with FLR in order to reduce the computational cost of the simulation. The detailed guideline for the simulation is presented in herein. The frictional coefficient between FLR and the testing pipes, acrylic pipes, is approximately 0.7.

[0218] In certain embodiments apparatus 100 can move in one direction via locomotion provided by Mode 1, Mode 2 and / or Mode 3. For example, Modes 1, 2 and / or 3 can be used to move apparatus 100 in a toward direction (e.g. in which first end 111 is the leading end). When it is desired to move apparatus 100 in a rearward direction (e.g. in which second end 112 is the leading end), flexible annular member 110 can be returned to a normal or deflated state and force can be applied to conduit 138 (shown in FIG. 1) or another physical tether coupled to apparatus 100. The application of a pulling force to a physical tether can be used to remove apparatus 100 from the constrained environment.

[0219] In certain embodiments, however, apparatus 100 can be wirelessly controlled via a control system such that retrieval of apparatus 100 can be accomplished without a physical tether coupled to apparatus 100. In one example of an untethered embodiment, a dual apparatus 200 shown in FIG. 19 comprises a first and second apparatus 100 oriented in opposing directions to provide both forward and rearward movement. The principles of operation for each apparatus 100 are equivalent to the single apparatus embodiments described herein. When movement is desired in one direction, the appropriate apparatus 100 can provide locomotion as desired while the secondary apparatus 100 remains in a normal or deflated state. If it is desired to lock apparatus 200 into a stationary position, both apparatus 100 can be inflated to resist movement in either direction with respect to the constrained environment.

[0220] In still other embodiments that do not rely on a physical tether for retrieval, apparatus 100 may comprise actuators that are configured to change the orientation of flexible extensions 115. Referring now to FIGS. 20-21 an embodiment is shown comprising actuators 160 configured to change the orientation of flexible extensions 115 from an orientation in which flexible extensions 115 are originally angled toward second end 112 as shown in FIG. 20. Actuators 160 can then be actuated (e.g. by linearly translation towards second end 112) such that a force exerted on flexible extensions 115 causes flexible4922-7473-8524, v. 1 44extensions 115 to become angled toward first end 111, as shown in FIG. 21. Such an embodiment can allow for the use of a single flexible annular member 110 to provide locomotion in both a forward direction (e.g. in which first end 11 1 is the leading end) and a rearward direction (e.g. in which second 112 is the leading end). In certain embodiments (including for example, embodiments without a physical tether), apparatus 100 can be wirelessly controlled. In the embodiment shown in FIGS. 20-21, apparatus 100 comprises an integrated source of higher-pressure fluid 139 (e.g. air, water, or saline, etc.) to provide for expansion of flexible annular member 110 as well as an inertial measurement unit (IMU) sensor 147 to provide location and motion data for apparatus 100. In addition, while a generally cylindrical configuration for apparatus 100 is shown in the figures, other exemplary embodiments of the present disclosure may comprise a tapered configuration, for example, to reduce drag forces from fluid encountered within a constrained environment.

[0221] FIG. 22A depicts exemplary graphs 2200 depicting displacement behaviors vary according to different average deflation rates, Df ", and the lowest threshold pressure, P„3. (A, B, C) the displacement behavior varies according to the average deflation rate, Df", in the 30mm, 36mm, and 41mm cases, respectively. (D, E, F) the displacement behavior varies according to the lowest threshold pressure, P^3, in the 30 mm, 36 mm, and 41 mm cases, respectively. (G, H, I) The variations of displacement in the 30 mm, 36 mm, and 41 mm vertical pipes correspond to the thresholds of PSM3, e., 9 kPa, 12 kPa, 13 kPa, respectively.

[0222] The outcomes show how PFR locomotion performs in different scenarios of pressure values, vibration frequencies, and pipe sizes. The results also indicate the best pair of oscillation frequency and maximum pressure values, i.e., 23 kPa and 192 Hz. This experimental data is still concerned with how displacement would vaiy if the average deflation rate, Df", were kept consistent.

[0223] The pressure curves in FIG. 11 were generated by allowing the compressed air inside the soft skin to deflate naturally, resulting in differing behavior of the curves. Thus, to address this question, additional experiments were conducted additional experiments to assess displacement behaviors under the same average deflation rate.

[0224] Based on the results in FIG. 11, the maximum applied pressure and the vibration frequency at 23 kPa and 192 Hz for the following experiment were selected.4922-7473-8524, v. 1 45

[0225] FIG. 12 exhibits the behaviors of PFR displacement according to two pressure variables, including the average deflation rate, Z> / “, and the minimum threshold pressure, PSM3. The dotted line represents the air pressure inside the soft skin, while the solid line represents the distance the robot moved inside the pipe. The slope of the solid line indicates the robot' s moving speed.

[0226] The experimental outcomes in FIG. 12 (A, B, C) suggest that at Df “ approximately 1.3 kPa, PFR can obtain the farthest distance in one pressure cycle. In contrast to the performance in Fig. 6, where the deflation mechanism is not specified, the PFR displacement in the 30 mm pipe is greater than in the 36 mm and 41 mm pipes. This is because the lower deflation speed allows the soft spikes to maintain contact with the pipe for a longer duration. The distance traveled in a single pressure cycle decreases as the deflation speed increases, and if the pressure drops faster than roughly 6 kPa / s, the forward motion may come to a complete halt. Besides, note that in FIG. 12 (A, B, C), the PSM3values represent the minimum pressure, at which the spikes partem barely touch the tubular wall.”

[0227] As described, the pressure curve is characterized by three variables, i.e., the maximum pressure value, the average deflation rate, Df “, and the minimum threshold pressure, P^3. FIG. 12 may, for example, be used to clarity the influences of the highest pressure and the Df “ to the motion capability.

[0228] The results from FIG. 12 may, for example, be used to determine the effects of the lowest pressure, PSM3, in which the forward motion is achievable. This value is specified beforehand in the closed-loop pressure control device. Fig. 12 (D, E, F) indicate the displacement results at various preset values of PSM3(note that these experiments were proceeded with the best deflation speed Dfra» 1.3 kPa / s).

[0229] These graphs highlight the significance of the pressure curve. Ifis set too high, causing the soft spikes to remain heavily compressed. Therefore, there is less opportunity for the stick-slip mechanism to occur, limiting the generation of locomotion. In contrast, in vertical cases, the robot will fall off, if it cannot retain sufficient pressure to anchor itself securely to the wall.

[0230] Therefore, the role of Pfj3is significant in vertical conditions. Further, additional experiments conducted to identify the proper thresholds, ensuring upward motion while preventing the robot from losing height when the pressure drops below certain limits. Fig.4922-7473-8524, v. 1 4612 (G, H, I) displays the minimum values of P^3at which upward motion is sustained without the robot falling”

[0002] FIG. 22B depicts an exemplary table including the parameters applied to PFR to examine the average locomotion speed at different pipe inclination angles. The average locomotion speed of the PFR at different pipe inclination angles was accessed using the most effective parameters characterizing the pressure curve (i.e., maximum pressure, average deflation rate, Dfra, and the minimum threshold pressures,The motion speed, which can be later used to assess robot’s performance in terms of its relative speed versus its body length (Body Length / second - BL / s) compared with other similar robots. FIG. 22B presents the obtained average locomotion speed at different pipe inclination angles.

[0231] FIG. 23 depicts a graph 2300 including the average locomotion speed of PFR in different inclined angles of pipe configurations. FIG. 23 illustrates the average speed performance of PFR in three cavity environments, i.e., the 30 mm 2305, 36 mm 2310, and 41 mm pipes 2315. Considering practical applications, the maximum traveling distance capability of the PFR was indirectly analyzed through separate experiments. The experiments estimated that the PFR can travel a maximum distance of approximately 6.5 m in a vertical pipe and between 8.45 m and 13 m in a horizontal pipe. If the mass of the camera and electrical wires connected to the robot can be further reduced in the future, the maximum traveling distance is expected to improve. However, the maximum traveling distance may vary depending on changes in the environment in which the robot operates (See FIG. 32).

[0232] FIG. 24 depicts an exemplary table including parameter values of the soft spike embodiment. Exemplary embodiments of a PufferFace Robot (PFR) includes three main components: the soft skin incorporated with a soft “spikes” pattern, the hollow-shape rigid frame, and the vibration source. Note that since the soft spikes play a vital role in contributing to the motion of PFR, we might use three words, i.e., “limb”, “spike”, and “barb” interchangeably hereafter.

[0233] The PFR along with other embodiments may, for example, include a robot that can traverse and adapt to variable cross-section sizes of pipeline systems at a centimeter scale. Therefore, the general geometry property of the design is vital as pipeline networks might be constructed with critical sections, such as the elbow turning and T-connector sections,4922-7473-8524, v. 1 47which restrain the robot motion. To overcome these constraints, the study of H.R. Choi et al., (2001) (4) suggested that the total length and diameter of the robot should be determined according to the smallest radius of the pipeline curvature, or the motion robot will be impeded at the elbow turning sections. Consequently, we determined that the ratio between the length and diameter should be approximately one in certain embodiments of the present disclosure.[0234J As previously discussed, the background and motivation to select the vibration mechanism as the primary driven method for this design concept was due to its simple and compact design of the vibration motor, which might be suitable for small-scale applications. Based on the dimensions of the selected DC vibration motor and the ratio requirements for the robot in a constrained pipeline network, we initially determined the preliminary values of the total length, LB = 30 mm, and the outer diameter, OD ~ 26 mm - 32 mm, for the robot configuration.

[0235] Subsequently, it is important to analyze and select the shape of the robot limb so that the robot can obtain locomotion when it is subjected to the oscillation frequencies from the vibration source. The robot limb’s design parameters were referred to and selected from we’ prior vibration-based soft robot model (48). The curved shape of the soft spike was inspired by C-shaped prosthetic metallic legs (52), (53). This structure has been shown to convert the potential energy stored in the deformed limbs into kinetic energy, aiding in forward movement. This capability is crucial for generating locomotion in the vibrationbased robot.

[0236] The design parameters and physical properties of the spike are presented in FIG. 26. FIG. 26A exhibits the characterization of one barb design by Ri, R2, and Ws parameters. This curved shape can be equivalently simplified by an inclined straight beam. The inclination property is essential for inducing the asymmetric friction phenomenon (see FIG. 26B) and generating the forward motion of a vibration-driven model (54, 55, 56). Hence, limb designs for a vibration-based robot must have the inclined feature.

[0237] The inclined functionality may, for example, be shown via an experiment (see FIG. 27). FIG. 28 is supplementary information for explaining the behavior of the collected force data in Fig. 28B. This examination demonstrates that when the soft spikes are vertically compressed by a force, Fz(t), causing a deformation, Dz, they simultaneously generate a propulsion force horizontally because of the resistance of the friction force, Ffr+, between the limb and the substrate attached to the sensor. The potential energy is stored in the deformed soft spikes. When the restoration of the compressed soft limbs occurs rapidly, the4922-7473-8524, v. 1 48potential energy can be transformed into kinetic energy, leading to the limbs and the soft body obtaining a net displacement, ND. A forward motion will occur if the limbs are continuously subjected to deformation and restoration. These two opposite phases can be considered as the stick and slip phases. Besides, due to the non-symmetric morphology of the spike design, friction resistance to the forward motion, Ffr_, is significantly lower than the backward motion, F&+ (see FIG. 26B); consequently, the soft spikes and the soft body tend to move onwards instead of backward. With this curved design, the locomotion of the vibration-based robot can be achieved. Therefore, we decided to adopt this morphological limb design to the soft spikes of PFR. The design parameters of the spike are presented in FIG. 22B.

[0238] FIG. 25 depicts an exemplary table including design parameter values of three patterns and their locomotion performance, (e.g., mode 1, mode 2, and mode 3). After determining the necessary design parameters for the robot’s limbs, three prototypes were developed to evaluate the locomotion performance between different patterns. FIG. 29 exhibits the dimensions of the PFR’s design. FIG. 29A and FIG. 29B demonstrate the pattern of PFR, which is characterized by the number of i and j.

[0239] FIG. 25 shows the design parameters of three patterns and their locomotion performance. The first model cannot advance, while the third exhibited extremely low locomotion speed. Only the second model achieved the best locomotion speed and adapted to a cavity 1.5 times larger than its outer diameter. In the first model, the limited number of spikes failed to generate sufficient thrust, causing it to remain stationary. In contrast, the third design added more spikes, which increased its size and mass, leading to a significantly slower movement speed. As a result, we chose the second design (see FIG. 34), as it met the initial objective of being capable of navigating through a pipeline system with varying cavity conditions.

[0003] FIG. 26 depicts an exemplary analysis 2600 of the morphological design of the robot’s limb and its physical property. Fig. 26 depicts the morphological design of the robot’s limb and its physical property. (A) the curved shape of the limb is characterized by Ri, R2, and Ws parameters. (B) This curved shape can be equivalently simplified by an inclined straight beam. The inclination property is essential for inducing the asymmetric friction phenomenon and generating the forward motion of a vibration-driven design.4922-7473-8524, v. 1 49

[0240] FIG. 27 depicts an exemplary transformation 2700 of normal force to the horizontal propulsion force in relationship to the morphological design of the soft spike (Dragon Skin™ 10 material). Exemplary transformation 2700 employs a 3-axis force sensor 2705 of Tecgihan, Model USL06-H5 - resolution 0.001 N, to measure the correlation between the normal force and the generated horizontal force of a soft spike pattern sample 2715 along a linear guide 2710. The obtained relation between the normal force and the transformed horizontal propulsion force. Exemplary transformation 2700 depicts a Force (N) by Z displacement (mm) graph, including Fz spikes 2720, and Fx spikes 2725.

[0241] FIG. 28 depicts an exemplary stick-slip mechanism and FIG. 29 depicts an exemplary PFR dimensions 2900 including (A) the front view of PFR; ODS = 27mm, IDSB = ODF = 15mm, ODSB= 17 mm; (B) the side view of PFR; LB = 30 mm. (C) The cross-section of the 3D printing mold presents the dimensions of the soft spike.

[0242] The fabrication process of the soft skin with a spike pattern is shown in FIG. 15. In Step 1, we initially utilized an FDM 3D printer (Raise 3D Pro2 Series, RAISE3D Inc.) to create a mold, which includes spike shapes. In Steps 2 and 3, the silicone (DS-10M) was poured into the mold and thoroughly degassed. To get the air bubbles removed from the compound of Dragon Skin™ 10A and 10B efficiently, we recommend putting the pre-mixed part A and part B of Dragon Skin 10™ into the fridge for one hour before mixing them and keeping the mixture in the vacuum chamber for at least 10 minutes. By this method, we achieved soft-skin samples without any air bubbles inside the skin. This step is paramount because the existing air bubbles might cause the leakage of the compressed air, affecting the inflation and deflation phase of PFR. After allowing it to cure sufficiently at room temperature for 8 hours, the soft skin was extracted from the mold (Steps 4 and 5).

[0243] An SLA 3D printer (Form3, Formlabs Inc) and clear resin was used to make a hollowshaped rigid frame (Step 6). After wrapping the extracted soft skin around the printed hollow-shaped rigid frame and fixing it in place with cable ties, we use a stick to thoroughly add more silicone to the gap so that the skin can be closed (Step 7). The DC vibration motor, air pressure hose, and LED are attached to the rigid frame via adhesive (LOCTITE 416, Henkel Adhesives), while the camera is fixed with sealant tape (Step 8). In Step 9, the soft skin was attached to the peripheral notches of the hollow-shaped frame using threads.

[0244] FIG. 30 depicts an exemplary setup to measure vibration frequency (Hz) of the eccentric mass. The experimental set up may, for example, be used to characterize the vibration frequency. The locomotion of PFR can be activated by two input parameters, including the vibration frequency and the pressurized air. The three modes of locomotion may, for4922-7473-8524, v. 1 50example, be categorized based on these two inputs. The vibration frequency determines the influence of the centripetal force on the entire body of PFR. The centripetal force is characterized by the angular speed of the eccentric mass on the motor and can be calculated as follows:

[0245] Fc= mea> [recos a>vt)y^r+ resin(a>vt)zr+ meg (1).

[0246] In the given context, me, re, a>v, and g stand for the eccentric mass, the radius from the eccentric mass to the center of rotation, the angular frequency of the rotation (rad / s), and the gravitational vector, respectively. yfrand zfrdenote unit vectors along the Yfrand Zfraxis (these notations are based on Fig. 8A, B).

[0247] A high-precision electronic scale (resolution: 0.001 gram) was utilized and an optical microscope to determine me, re. The values of me, reare 0.572 gram and 1.72mm. To determine the angular frequency a>vof the centripetal force, we employed a high-speed camera, SONY DSCRX10M4 model featuring 960 frames per second (fps) of high-speed motion capture, to record the rotation of the eccentric mass mounted on the DC motor. The experimental setup to collect time-position data of the eccentric mass for the centripetal force is presented in FIG. 30. The motion capture video was processed by the OpenCV package, and then the time -position data was extracted in the CSV format. Subsequently, this data was analyzed by the Fast Fourier Transform (FFT) to determine the dominant frequency (Hz) in the frequency domain. These dominant frequencies represent the vibration frequency (Hz) of the centripetal force corresponding to the applied voltage (V). Consequently, we can determine the relation between the vibration frequency (Hz) induced by the centripetal force and the applied voltage (V) to the DC motor. The angular frequency (rad / s) is equal to 2TI times the vibration frequency (Hz).

[0248] In addition, the selection of the high-speed camera, featuring a 960-Hz sampling frequency, to determine the vibration frequencies, was justified. We measured the maximum vibration frequency of the vibrator at 3V by using a piezoelectric disc (CUI Devices CEB-35D26) connected to a KEYSIGHT InfiniiVision DSOX2002A oscilloscope to determine the highest vibration frequency corresponding to the maximum applied voltage, 3V (see FIG. 30).

[0249] The frequency of the voltage signal collected from the piezoelectric disc was approximately 235Hz. Based on the Shannon theorem, which requires that the sampling rate must be at least twice the highest frequency of the experimental vibration frequency to4922-7473-8524, v. 1 51capture its frequency bandwidth accurately (57), the selection of the high-speed camera in this experiment was validated.

[0250] The motor’s angular frequency is proportional to the applied voltage. We utilized the 8-bit PWM output of Arduino UNO together with the LN298 driver to regulate the voltage supplied to the DC vibrator (see FIG. 17). Besides, the LN298 driver allows us to change the rotation direction of the DC motor. The relationship between the supplied voltage (V) and the vibration frequency (Hz) is exhibited in FIG. 31.

[0251] FIG. 31 depicts the exemplary relationship between the applied voltage (V) and the vibration frequency (Hz). In the following steps, we investigated the average locomotion speed of PFR when it was merely subjected to the excitation from the vibrator, Mode 1 of locomotion. The obtained average locomotion speed with respect to vibration frequency in Mode 1 is depicted in FIG. 16.

[0252] Experiments to measure Propulsion force were conducted. The experimental scheme to determine the propulsion force is presented in FIG. 30. Power was supplied to the vibrator motor through the DC power supply, and the vibration frequency of the motor was controlled via a microcontroller (Arduino Uno, Arduino) and a motor driver (L298N Motor Drive Controller). The inflation and deflation of the soft robot are controlled through the pneumatic actuation system (Programmable Air, Crowd Supply).

[0253] The system consists of two air pumps, three solenoid valves, and an air pressure sensor. With this setup, the air pressure inside the soft robot is actively controlled using the pressure sensor. The propulsion force was measured by connecting the robot and the force gauge (DFG55, OMEGA) with a tendon.

[0254] Experiments may, for example, be used to measure displacement. The experimental setup for measuring displacement in relation to applied pressure is shown in FIG. 18. The parameters used in the experiment were applied similarly to the propulsion force tests, including three boundary conditions (ID 30 mm, ID 36 mm, and ID 41 mm), four vibration frequencies (64 Hz, 137 Hz, 160 Hz, and 192 Hz), and three input pressure levels (20 kPa, 23 kPa, and 26 kPa).

[0255] To observe the X position of PFR corresponding to the applying pressure, we connected the programmable air pump and a 5 Degree Of Freedom (DOF) electromagnetic tracking (EM) sensor (Aurora 5 DOF Sensor Northern Digital Inc., Canada) to Robot Operating System (ROS) environment installed on an external computer. The utilized EM sensor is small, compact, and lightweight (the size of the sensor tip - 0.3x2.5 mm). The sensor tether was small, tiny in diameter, and had highly bendable and flexible properties. Such features4922-7473-8524, v. 1 52allowed us to eliminate the influence of the sensor mass on displacement outcome and diminish the induced friction force acting on the sensor tether. ROS enabled us to collect the sensing data together with the pressure data in real time.

[0256] FIG. 32 depicts the vibrator as attached to the piezoelectric disc by double-sided tape and connected to an oscilloscope to measure the maximum generated vibration frequency at 3V. The maximum traveling distance may, for example, be determined via estimation experiments. Regarding the maximum distance the PufferFace Robot can travel, the robot’s maximum traveling distance capability was indirectly examined. The outcomes from the propulsion force experiment suggested that the robot can obtain a long travel distance relative to its body length. Thus, it is rather challenging to set up a long pipeline to verify the longest achievable traveling distance. We only focus on examining the traveling distance in the straight pipe placed horizontally and vertically. In the vertical condition, the traveling distance is merely influenced by the mass of the tethers, including the motor wires and the air supply tether, which are the required components to generate the locomotion.

[0257] FIG. 32 shows the experimental outcomes of the maximum extra mass, equivalent to the length of the tether, that the robot can carry in vertical conditions. These results indicate the maximum traveling distance of the robot traveling vertically. In horizontal conditions, the traveling distance is higher than or equal to the distance of the vertical case because it is only influenced by the tether’s friction. We also tested the static friction coefficient of one meter of the air supply tether (a polyurethane tube, TU0212C-20 SMC) with the acrylic pipe. The static friction coefficient result varies from 0.5 to 0.75. This outcome suggests that the robot might travel a distance of 1.3 to 2 times the distance of the vertical case.

[0258] FIG. 33 depicts the exemplary set-up to indirectly evaluate the maximum traveling distance. For example, an ABAQUS simulation procedure may, for example, be used to conduct an inflation radius simulation. In this simulation task, the fixed constraint type was applied to the inner circle of the soft skin at the positions at which the soft skin is firmly tied by the threads at both ends of the soft skin. These fixed constraints restrict all translational and rotational movements of all nodes located in these two circles. FIG. 33 shows the configuration of the inflation simulation model.

[0259] FIG. 34 depicts an exemplary demonstration of applying constraints and loads to the soft skin in the simulation model. (A) Fixed constraints are applied to the inner circle of the soft skin. (B) The pressure load type is applied to the inner surface of the soft skin.

[0260] The simplification procedure proceeded as follows. In the first step, the cavity environment was reconstructed by using the Wire Model to represent the 3D symmetric4922-7473-8524, v. 1 53structure of the tube by two solid lines. The distance between the two lines is similar to the diameter of the pipe. Subsequently, the PFR's design is likewise symmetric; thus, it could be equivalently converted from the 3D to 2D model. To obtain the most simplified model, the parts, including the DC vibrator, the hollow frame, the LED, the camera, the air inlet, and the motor tethers, are all omitted. These components are represented by one node with mass, which is placed at the center of the mass of the 2D model of PFR and influenced by gravity.

[0261] FIG. 34 depicts the demonstration of the simplified simulation model on Abaqus. FIG. 34A shows the removal of unnecessary parts for the simulation. The regions of the soft skin that are taken into account in the simulation are between two knots. FIG. 34B exhibits the simplified model of the cavity and the soft skin of PFR. Because inflation only occurs at the soft skin regions limited between two knots, we applied the constraints at both ends of the soft skin. Thus, the deformation would not happen at the front and the rear. The pink arrows stand for the pressurized air that causes the skin to inflate. Based on the mechanism of Mode 3, we likewise specified the input pressure graph in the simulation as the pressure behavior in the experiment.

[0262] FIG. 34C presents the pressure curves that we characterized in the Abaqus model. Keep in mind that because this is the 2D simplified model, the simulated pressure differs from the actual one. Therefore, it is essential to determine the proper values in the 2D model that correspond to the utilizing values of pressure in the experiment. In this case, since we were focusing on simulating the performance of PFR at 23kPa, the corresponding value in the 2D model is 5kPa. This equivalent pressure value in the 2D model was chosen because we observed that at 23 kPa in 3D environment all spikes from j2 to ja would contact the pipe wall. Therefore, a pressure of 5 kPa was selected in the 2D model to achieve the same spike contact behavior.

[0263] FIG. 34 depicts an exemplary prepared samples to measure the stiffness behaviors of three patterns of soft spikes. Regarding the centripetal force, Fc, it is required to input the frequency and the amplitude of the oscillation. For simplicity, Fc is placed at the center of the mass of the model because the vibration affects similarly to every point of the frame. In addition, we followed the procedure below to obtain the simplified values of centripetal force for the 2D simulation task

[0264] Firstly, the stiffness behaviors of the soft limb patterns may, for example, be determined in three cases with different ranges of z, i.e., the 1stcase: from to i7, the 2ndcase: from ijto i5, and the 3rdcase: from z to z3. Note that since PFR’s structure is4922-7473-8524, v. 1 54symmetric, we only considered one half of PFR body. Subsequently, we employed a 3-axis sensor with resolution of 0.001, to measure the stiffness of these soft spike patterns (Dragon Skin™ 10 material).

[0265] FIG. 35 depicts the stiffness behaviors of three patterns, i.e., 3x5 3505, 5x5 3510, and 7x5 3515 soft spike patterns, of the exemplary prepared samples depicted in FIG. 35. FIG. 35 presents the experimental samples. FIG. 38 depicts an exemplary table disclosing the vibration frequencies and the corresponding amplitudes of the sinusoidal signals of the centripetal force. Tests similar to those in Fig. 8A were conducted, with the results displayed in FIG. 36. These results indicate that stiffness can be linearly scaled with the number of spikes. Since the generated centripetal force at the maximum tested frequency of 192 Hz was minimal, the relationship between the normal force and deformation was also considered linear. Therefore, the scaled centripetal force in 2D environment was conducted based on this method. FIG. 37 exhibits the input data of Fc amplitude and frequency.

[0266] FIG. 38 depicts an exemplary robot 3800 in the flexible membrane having embedded flexible strain sensors to directly measure the interaction force. Exemplary robot 3800 includes a flexible C-Shape Shipes 3805. Exemplary robot 3800 includes a network of strain based tactile sensors 3810. The sensors may, for example, light sensors. The sensors may, for example, include cameras. The sensors may, for example, include sonar sensors. The sensors may, for example, include touch sensors. Exemplary robot 3800 includes a vision-based surface tactile sensor camera field of view 3815. Vision-based surface tactile sensor camera field of view may be based on camera views attached along the side of the body of exemplary robot 3800.

[0267] Exemplary robot 3800 includes a front camera system 3820 and a front camera LED system 825. Front camera system 3820 and Front camera LED system 825 include a front camera situated between two opposing front camera LED (as depicted). Front camera system 3820 and front camera LED system 3825 may, for example, include one or more cameras. In some embodiments, front camera system 3820 and front camera LED system 3825 may, for example, include multiple types of cameras (e.g., 2D imaging cameras, 3D depth cameras, 2.5D cameras, RGB-D cameras, RBG-R cameras, stereo vision cameras, ultrasonic (ultrasound) cameras; infrared (thermal cameras), high speed cameras).

[0268] Exemplary robot 3800 includes vision-based surface tactile sensor RBG LEDS 3825. RBG LEDS 3825 may, for example, be configured to enable color-based navigation, object identification, and environmental mapping by emitting red, green, and blue light to detect4922-7473-8524, v. 1 55surfaces while traveling. The RBG LEDS 3825 may, for example, be situated on an adjacent panel. Three side- vision panels may, for example, be situated on a robot. In some embodiments, our panels may, for example, be situated on the robot.

[0269] Exemplary robot 3800 includes vision-based tactile sensor camera 3830. Vision-based tactile sensor camera 3830 may, for example, be used with RBG LEDS 3825. The controlled lighting may, for example, normalize color data across shadows or varying ambient light, enabling accurate object detection, lane following, and obstacle avoidance during navigation.

[0270] Exemplary robot 3800 includes an air inlet 3835. Air inlet 3835 may, for example, be used to inflate robot (as depicted in FIG. 39). Air inlet 3835 may, for example, be used to partially deflate robot (as depicted in FIG. 39). A paired robot may, for example, inflate a first robot and deflate a second robot to move forward. The paired robot may, for example, then deflate first robot and then reinflate first robot to navigate forward. The paired robot may, for example, inflate second robot and deflate first robot to move backwards

[0271] . In some embodiments, air inlet 3835 may, for example, be used to admit cooling airflow to ventilate electronics, prevent overheating, and maintain sensor accuracy during navigations with filters locking dust in mobile environments.

[0272] Exemplary robot 3800 includes an eccentric motor 3840. Eccentric motor 3840 may, for example, travel by generating vibration via rotating an off-center mass, aiding haptic feedback, locomotion, and sensory augmentation. Eccentric motor 3840 may, for example, be compact and low power to provide tactile navigation.

[0273] Specifically, exemplary robot 3800 may, for example, work in unison with additional robots. Multiple robots may, for example, be situated in a flexible membrane. Each robot may, for example, have embedded flexible strain sensors to directly measure interaction force (see FIG.40).

[0274] FIG. 39 depicts an exemplary illustrative use-case system coupling two or more exemplary robots as depicted in FIG. 38 to enable forward and backward motion and carrying different sensors in each robot. FIG. 39 depicts an exemplary front view. FIG. 39 depicts an exemplary side view. The exemplary robot 3800 may, for example, be referred to as an IMSR. The ISMR embodiment may, for example, be enveloped in a polyps tube. The ISMR embodiment may, for example, inflate, deflate, partially inflate, or partially inflate to travel. The ISMR embodiment may, for example, shift between a deflated state, a mid-inflated state, and a fully inflated state. The ISMR embodiment has a surface tactile sensor view. The ISMR embodiment has a camera view. The ISMR embodiment has a4922-7473-8524, v. 1 56firing thread. The ISMR embodiment has an LED. The ISMR embodiment has a visionbased surface tactile sensor camera. The ISMR embodiment has a rigid frame. The ISMR embodiment has an eccentric motor. The ISMR embodiment has a network of strain-based tactile sensors. The ISMR embodiment has soft skin with spikes.

[0275] FIG. 40 depicts an exemplary illustrative use-case scenario including the illustrative use-case embodiment of FIG. 39 being controlled by manipulating the voltage polarity, such that the robot moves left or right in T-shape junctions. The paired robot may, for example, use a RBG view to navigate. The paired robot may, for example, use a texture view to navigate. The controller may, for example, use the RBG view and texture view to make decisions to navigate. The controller may, for example, use the RBG view and texture view to make decisions to provide alerts.

[0276] FIG. 40 depicts two exemplary robots coupled together. The two exemplary robots have a variable diameter connecter. The variable diameter connector may, for example, be elastic. The variable diameter connector may, for example, include a spring. The paired robots navigate a 90-degree elbow connector. The paired robot navigates a T-Junction connector. The paired robots may, for example, navigate additional piping connectors.

[0277] The paired exemplary robots may, for example, navigate by swapping between fully inflated states and mid-inflated states. Air flow may, for example, be directed in through the air port to inflate the device. Air flow may, for example, be directed out of the air port to partially deflate. The paired exemplary robots may, for example, be used to detect corrosion (as depicted). The paired exemplary robots may, for example, be used to detect cracks (as depicted).

[0278] The paired embodiments may, for example, include two or more of these device coupled together to enable forward and backward motion. Each robot may, for example, carry different sensors.

[0279] FIG. 41 depicts an exemplary block diagram of autonomous control of the locomotion and sensing. FIG. 41 depicts an exemplary AI-Based control. The AI-Based control may, for example, control the vibration output in the robotic system. The Al-based control may, for example, control the pneumatic output in the robotic system. The robotic system may, for example, be used for locomotion. The locomotion may, for example, result in additional visual and tactile sensing inputs. Such inputs may, for example, be received by an artificial engine. The artificial engine may, for example, optimize detection techniques. The artificial engine may, for example, communicate with the Al-based control inputs and iterative feedback. The artificial intelligence engine may, for example, engage in mapping and4922-7473-8524, v. 1 57provide mapping data to the AI-Based Control The artificial intelligence and AI-Based controls and detection may, for example, be evaluated in an Al-based diagnosis engine. The operations may, for example, include determining visual indicators. The operations may, for example, include determined tactile sensing indicators. The operation may, for example, include evaluating detection based on the quality of inputs. The operations may, for example, include generating proposed outputs to the AI-Based control The Al-based control may, for example, generate predetermined vibration and pneumatic controls based on inputs.

[0280] For discussion further consideration of design and characterization of a vibration-driven pufferfish-inspired inflatable soft robot. This study presents the analytical modeling, design, fabrication, and experimental evaluation of a puffer fish inspired soft robot for pipe inspection applications. This inflatable soft robot employs vibration as its sole locomotion mechanism, with internal pressure serving as a control variable to (i) tune the stiffness and natural frequency of the inflatable structure, (ii) optimize vibration transmission and locomotion performance, and (iii) enable locomotion in varying-size pipes. To investigate the influence of vibration on locomotion, we develop a vibration model and analyze the effects of internal pressure, material properties, excitation frequency, and geometric design. Locomotion performance of the proposed robot is validated experimentally using four different prototypes with varying material stiffness and geometry. Results show that the optimized design can achieve locomotion speeds exceeding 100 mm / s in both horizontal and vertical tubes with varying diameters.

[0281] Pipeline inspection plays a vital role in ensuring the safety and reliability of complex fluid transport systems. Over time, pipelines are prone to cracks, corrosion, and structural defects that can lead to leaks or catastrophic failures. Regular inspection and preventive maintenance are therefore essential; however, inspecting confined and enclosed environments (such as hydraulic circuits in aircraft, fuel transfer systems in cargo vessels, and residential gas networks) remains challenging due to limited accessibility, variable diameters, and complex internal geometries.

[0282] Over the past two decades, researchers have developed a broad range of in-pipe inspection robotic systems employing various locomotion strategies, including inchwormlike crawling, tracked or wheeled mechanisms, screw driven propulsion, snake-like articulated designs, and soft robots. These systems are often integrated with sensing modalities such as cameras, digital scanners, or sonar systems to enable autonomous inspection and data collection.4922-7473-8524, v. 1 58

[0283] Despite these advances, rigid inspection robots remain constrained by limited flexibility and safety concerns. Their hard structures can impose high contact stresses on pipe surfaces, potentially damaging internal coatings or walls. Also, rigid mechanisms often struggle to navigate through narrow pipelines with varying diameters or complex geometries.

[0284] As opposed to rigid inspection robots, soft robots offer compliance and adaptability, allowing safer interactions with surrounding structures and more effective locomotion in irregular and unstructured environments. Their inherent flexibility enables smooth traversal through pipeline features such as reducers, non-circular cross-sections, and connectors.

[0285] Furthermore, their deformable bodies, such as the mechanisms proposed in, can conform to complex geometries, absorb impacts, and traverse confined regions safely, making them ideal candidates for next-generation in-situ inspection and intervention platforms. Among these, vibration-driven soft robots, have recently emerged as a promising alternative for small-scale, energy -efficient, and adaptive navigation within confined pipelines. Their simple actuation mechanisms, minimal hardware requirements, and ability to exploit resonance phenomena make them particularly attractive for environments where conventional rigid robots face limitations. Nevertheless, current soft robots generally exhibit low locomotion speeds and are often tailored to specific pipeline sizes or configurations, thereby limiting their adaptability to pipelines with varying geometries.

[0286] FIG. 42 depicts a conceptual illustration of the proposed pufferfish-inspired soft robot inspection. The pufferfish (Tetraodontidae) demonstrates a remarkable biological mechanism for adaptive morphology and stiffness control (see FIG. 42). By rapidly inflating its body through water or air intake, it transforms from a streamlined swimmer into a spherical, spiked structure. This transformation not only deters predators but also alters its hydrodynamic and mechanical characteristics, effectively tuning its rigidity, volume, and surface morphology in response to environmental stimuli. Such capabilities provide valuable insight into how engineered systems could modulate internal pressure to achieve tunable stiffness and dynamic shape adaptation. Inspired by this biological mechanism and vibration-driven soft pipe robots, Nguyen et al. proposed a bioinspired soft robotic system capable of mimicking the inflation-driven stiffness modulation observed in pufferfish.

[0287] FIG. 43 depicts the four PFR configurations considered in this study. As illustrated in FIG. 42, this robot features a soft balloon-like body that inflates to conform to pipes of varying diameters and complex geometries. Its inflatable skin is equipped with flexible fins4922-7473-8524, v. 1 59that generate asymmetric friction against the pipe wall. Thanks to its eccentric DC motor and inflation line, this robot uses a hybrid vibration-propulsion mechanism in which the robot vibrates while inflated to create asymmetric friction with the pipe wall, followed by rapid deflation that generates a thrusting motion, enabling accelerated forward locomotion. This combined action enables traversal through pipes with bends, branches, and varying cross-sections. Despite proposing an interesting soft robot and hybrid locomotion mechanism, the study conducted in does not provide a quantitative or analytical characterization of how fin geometry, material stiffness, balloon properties, or the placement of the eccentric motor and system center of mass influence vibration transmission and locomotion performance.

[0288] To address these limitations and as our main contribution, this study presents a physicsbased analytical model and experimental characterization of a modified pufferfish-inspired soft robot (PFR) driven solely by vibration under a fixed internal pressure. To understand the influence of vibration on locomotion, we study the effects of internal pressure, material properties, vibration excitation, and geometric design within constrained tubular environments.

[0289] First, by modeling the housing, inflatable balloon structure, and each fin-excited at its base using an eccentric motor- we capture the coupled interactions among material properties, geometric dimensions, and actuation frequency. We then validate the model experimentally by fabricating and testing four different PFR prototypes (FIG. 42 and FIG.44) and analyzing their locomotion behavior within confined tubular environments.

[0290] For context, as shown in FIG. 42, the proposed PFR comprises four primary components: (i) an eccentric DC motor, (ii) an inflatable balloon, (iii) an array of fins (cilia) integrated with the balloon, and (iv) a rigid housing that accommodates one or two motors, pneumatic line, and on-board cameras and sensors while securing the balloon to the structure. Unlike the previously reported hybrid locomotion mechanism in where both vibration and periodic inflation-deflation cycles were used simultaneously, this study focuses exclusively on vibration as the primary and sole driving mechanism of the proposed PFR. In our design, the internal pressure is regulated at a fixed value to modulate the stiffness of the inflatable structure and optimize vibration performance according to the fin geometry and material properties.

[0291] For context, the goal of this study was to demonstrate that, through optimal design of these parameters, vibration-only locomotion can achieve enhanced efficiency and significantly improved forward speed compared to hybrid actuation. The following sections4922-7473-8524, v. 1 60detail the modeling framework and its relationship to key design parameters, enabling analysis of how these factors influence the robot’s vibration characteristics.

[0292] FIG. 45 depicts developed vibration model for PFR. To investigate how the motion generated by the eccentric motor is transmitted through the elastic body of the PFR and into the tips of its fins, we first develop a simplified vibration model of the soft robot. This model enables analysis of how the fins’ material properties, geometric parameters, and base excitation influence the overall vibration efficiency and locomotion performance.

[0293] As shown in FIG. 45, in our three degree-of-freedom (DOF) vibration model, the rigid housing and motor are represented as a single lumped mass (nih), the balloon is modeled as a mass-spring-damper system (nib ,kb , Cb) with variable damping and stiffness values, which are modulated by internal pressure, and each fin is represented as a simplified straight cantilever beam with its corresponding mass, stiffness, and damping (mf , kf , cf ).

[0294] Based on this model and the free-body diagram of the system the corresponding equations of motion can be derived as follows:

[0295] where Xh, Xb, and Xf and their derivatives represent the displacement, velocity, and acceleration of the housing, balloon, and fins, respectively. Also, the excitation force generated by the unbalanced rotating mass mu attached to the motor shaft is given by:

[0296] where ruand co are distance from the axis of rotation to the center of the unbalanced mass (arm length) and angular velocity of the motor shaft, respectively. The system of equations can be expressed compactly in matrix form as follows:4922-7473-8524, v. 1 61

[0297] where mf , kf , and Cf denote the effective mass, stiffness, and damping coefficient of the fin, respectively; nib, kb, and Cb represent those of the balloon; and ma corresponds to the combined mass of the housing and motor.

[0298] FIG. 46 depicts a beam and system parameters used in an exemplary model. To simplify the modeling process, each fin (cilium) is approximated as a cantilever beam of length L“5 mm, fixed at one end to the balloon surface and free at the other. Since the fin's cross section varies along its length, an average cross-sectional area is used to compute an equivalent second moment of area lavg. Based on this approximation, the fin stiffness can be estimated using classical beam theory as kf =where E is the Young’s modulus of the fin material and lavgis the second moment of area corresponding to the average cross section.

[0299] Accurate prediction of the system’s natural frequency requires the use of effective mass rather than total physical mass, as only a portion of the distributed mass contributes to the dynamic response at the free end of the beam. For a uniform cantilever beam, the effective 33 mass at the tip is approximately meff= —mtotai, where mtotaiis the total mass of the fin. In this study, all mass terms appearing in equation (3) correspond to effective masses, which are calculated from the measured total masses of each component and appropriately scaled. Of note, since the damping ratio of the materials used is negligible within the frequency range of interest, the damping coefficients of both the fin and the balloon are assumed to be zero for analytical modeling. The calculated values of stiffness and effective mass parameters used in the model are summarized in FIG. 46.

[0300] FIG. 47 depicts a calculated angular frequency of the developed model corresponding to the PFR1-PFR3 designs as a function of balloon stiffness (1-80 N / m). The horizontal green line indicates the nominal speed of the eccentric motor, while the vertical green line4922-7473-8524, v. 1 62marks the balloon stiffness at which the natural frequency matches the motor speed. Based on the parameters listed in FIG. 46, the three primary natural frequency modes (mnaturai) of the system were computed by calculating eigenvalues (X) of M-1K.

[0301] FIG. 48 depicts the rigid housing is designed to hold the eccentric motor at its center, creating a balanced center of mass and enabling efficient vibration driven locomotion. The rigid housing frame was

[0302] 3D-printed using Formlabs 3B+ (Formlabs Inc.) to ensure precision and structural stability. The frame houses the eccentric DC motor(s) for making vibration. It also has peripheral notches to enable secure fixation of the soft balloon to the housing and avoiding air leakage by tightening a threaded knot ensuring. Without loss of generality and to compare our results with the other robots

[0063] , frame dimensions were chosen based on the inner diameter of the inspection environment: inner diameter ID “12 mm, outer diameter OD “15 mm, and total length S “30 mm. As shown in Fig.5, two different housing configurations were fabricated to investigate the effect of motor placement on vibration amplitude: (i) a single eccentric motor positioned at the center, and (ii) two motors installed side-by-side. The eccentric motor (DC Mini Vibration Motors with 3 Volt and 14000 rpm, BestTong) and air tube with 2 mm OD and 1 mm ID (Clear Masterkleer PVC Plastic, McMaster 5233K111) are secured to the housing using super glue, ensuring that the motor remains stable during vibration and that no air leakage occurs from the tubing.

[0303] Concerning the fabrication of Soft balloon with integrated Fins, the soft balloon of PFR serves as a deformable interface between the robot and the pipeline, providing both locomotion and adaptability to varying diameters. To study the effect of material stiffness, the balloon was fabricated using Dragon Skin silicone (smooth on Inc.) with Shore hardness 10, 20, and 30. A mold-based casting process was used to fabricate the skin with fins. As shown in Fig. 6a, two distinct molds were designed to produce variations in fin geometry, including varying length (i.e., longer versus smaller fins). Part A and B of Silicone were mixed with 1 : 1 ratio, degassed, and poured into the mold. To ensure a uniform thickness of 1mm, excess silicone was wiped off the mold surface. The small thickness provides a lightweight balloon that can be inflated with relatively low pressure, allowing the robot to adapt to a wide range of pipeline diameters. After curing for four hours, the silicone skin with integrated fins was carefully removed.4922-7473-8524, v. 1 63

[0304] FIG. 49 depicts a fabrication procedure of soft skin with fins along with exploded view of PFR. As shown in Fig. 49(b), to investigate the effect of material stiffness on locomotion speed, this procedure was repeated using different silicone formulations, including Dragon Skin 00-10 (DS 10), Dragon Skin 00-20 (DS 20), and Dragon Skin 00-30 (Smooth-On, Inc.). After demolding, the flat silicone sheet (FIG. 49 (b)) is folded and wrapped around a cylindrical (see FIG. 49(c)) form with a diameter of 15mm. A fast-curing silicone 00-35 mixture (Smooth-On, Inc.) is then poured into the gap to secure the shape, forming a stable cylindrical balloon structure (see FIG. 49(d)). Finally, as shown in Fig. 49 (d), the soft skin is secured to the rigid housing using a threaded knot before conducting experiments.

[0305] For context of the evaluation experiments, the experimental setup used for this study, including: (1) A rigid circular acrylic pipe with an inner diameter of 30 mm, an outer diameter of 32 mm, and a total length of 400 mm, connected to an acrylic adapter that transitions from 32 mm to 40 mm in diameter over a length of 80 mm as the test environment; (2) A DC-DC adjustable step-down voltage regulator module employed to convert the 5 V supply from a DC adapter to the nominal operating voltage range of the eccentric motor (0-3 V). The output voltage was finely tuned using the onboard potentiometer to control the vibration amplitude generated by the motor; (3) A programmable air control system (Programmable Air, Crowd Supply) was utilized to regulate the internal pressure of the inflatable balloon. This system includes (a) a miniature compressor for inflation, (b) a vacuum pump for deflation, (c) three electromagnetic (solenoid) valves that control airflow and prevent leakage, (d) an Arduino Nano microcontroller governs system automation, and (e) an onboard pressure sensor provides real-time feedback of the balloon’s internal pressure; and (4) An Aurora NDI magnetic tracking system to measure the robot’s position with sampling rate of 40 Hz.

[0306] FIG. 50 depicts the experimental setup includes the following: (1) a horizontal tube; (2) vertical tube with an inner diameter of 30 mm serving as the test environment, (3) a magnetic tracking system for measuring robot’s position, (4) a programmable air system for regulating the internal pressure of the robot, and, (5) a DC-DC adjustable step-down voltage regulator module providing 3 V to the eccentric motor. (6)The demonstration of four distinct fabricated PFR robots (PFR1-PFR4).

[0307] To achieve synchronized and systematic data acquisition, all subsystems were integrated within the Robot Operating System (ROS) framework. The onboard pressure sensor and magnetic tracker continuously measured the internal pressure and spatial position of the robot, respectively, with data logged in real time for post-processing. A4922-7473-8524, v. 1 64custom graphical user interface (GUI) was developed to define target pressures, which were transmitted to the Arduino controller for automatic pressure regulation.

[0308] In context of the experimental procedures, to evaluate the locomotion performance of the fabricated robots (PFR1-PFR4), experiments were conducted in both horizontal and vertical pipes, as shown in FIG. 50. In the horizontal tests, each robot was inserted at one end of a 400 mm pipe and inflated to the target internal pressure listed in FIG.51. Once the desired pressure was reached, a 3 V input was applied to the eccentric motor to generate vibration and initiate motion. The robot then traversed the pipe until it reached the opposite end, where the motor was turned off. Robot position was tracked in real time using a magnetic tracker mounted on the housing. Of note, each experiment was repeated three times for every pressure level to ensure consistency. Also, the minimum pressure at which the robot stalled inside the tube was first identified, and tests were then conducted at multiple pressures below this threshold to assess the effect of internal pressure on locomotion. For example, the shorter-fin robot stalled at approximately 20 kPa, and experiments were performed at 5, 10, and 15 kPa. The longer-fin robot stalled around 12 kPa, and tests were conducted at 4, 6, 8, and 10 kPa.

[0309] For vertical pipe experiments, each robot was first secured inside the pipe, and the minimum internal pressure required to prevent falling was identified. The robot was then inserted from the bottom of a 400 mm vertical tube and inflated to this pressure to maintain stability. Once released, a 3 V input was applied to the eccentric motor to initiate vibration and upward locomotion. After reaching the top end of the tube, the motor was turned off. Similar to the horizontal experiments, the robot’s position was tracked in real time using the mounted magnetic tracker sensor. During testing, the robot’s position and traversal time were recorded to quantify locomotion speed and evaluate the correlation between internal pressure and performance. Each experiment was repeated three times for every pressure level. The results of these tests are summarized in FIG. 51 and illustrated in FIG. 52. FIG. 52 depicts average speeds of PFR1-PFR3 at different internally modulated pressures, measured in a horizontal pipe with a 30 mm inner diameter and 400 mm length.

[0310] For purposes of discussion, analysis of FIG. 47 shows that, as expected, one of the natural frequencies of the PFR is zero, corresponding to the rigid-body motion of the housing and remaining independent of the balloon stiffness or overall geometry. Examination of the other two non-zero modes reveals that the angular natural frequency, oo natural, increases with balloon stiffness (kb) across all three simulated PFR cases (i.e., PFR 1-3).4922-7473-8524, v. 1 65

[0311] The second mode rapidly approaches an asymptotic constant value, indicating that its resonance condition occurs at relatively low rotational speeds. In contrast, the third natural frequency exhibits a markedly different trend (rising with increased balloon stiffness) since greater stiffness, modulated by internal pressure, enhances the overall rigidity of the system. Given that the maximum operating speed of the selected eccentric motor is approximately 14,000 rpm at 3 V (indicated by the green line in FIG. 47), the analysis suggests that optimal vibration transmission from the eccentric motor to the fin tips occurs when the balloon stiffness is around 48 N / m. At this stiffness, the excitation frequency closely matches the system’s natural frequency, resulting in maximum vibration amplitude at the fin tips in free space or within sufficiently large-diameter pipes. Overall, this analysis highlights how internal pressure modulation directly influences the effective stiffness and natural frequency of the PFR. Importantly, to maximize locomotion efficiency, the robot should be designed to operate near its natural frequency. Beyond these observations, the analysis also provides valuable design guidance for selecting suitable material properties, balloon stiffness, and motor speed to achieve optimal vibration-driven locomotion performance. It is worth noting that in this work, our analysis was limited to PFR1-3; nevertheless, the proposed model can be readily extended to configurations with different fin designs or multiple motors.

[0312] To evaluate the effect of fin material stiffness on locomotion performance, we compared PFR1-PFR3, which share identical geometries but differ in silicone hardness (Dragon Skin 10, 20, and 30). As shown in FIG. 52 and summarized in FIG. 51, the robot’s average speed increases with greater silicone shore hardness. In other words, stiffer fins enable more efficient vibration transmission, thereby enhancing propulsion. This trend is consistent with the results of our vibration model and simulation studies (FIG. 47). For example, PFR3, fabricated with Dragon Skin 30, achieves approximately 1.3" higher speed than PFR1 (Dragon Skin 10) under identical internal pressures. Furthermore, increasing internal pressure also improves locomotion speed across all materials. As the balloon stiffens under higher inflation pressure, vibration energy is transferred more effectively to the fin tips- consistent with the trend in FIG.47, where the excitation frequency approaches the system’s natural frequency- resulting in enhanced locomotion efficiency. For instance, PFR3 exhibits a 1.75" increase in speed inside the horizontal pipe when pressure is raised from 5 kPa to 15 kPa.

[0313] Additionally, higher pressure increases the number of fins in contact with the tube surface, further amplifying thrust. These findings highlight the importance of active4922-7473-8524, v. 1 66pressure regulation based on pipe diameter to maximize locomotion performance. Investigation of FIG. 51 also reveals that, across all configurations (PFR1 ~ PFR3), the robot moves slightly faster in the horizontal tube than in the vertical one (at identical 15 kPa pressure), as part of the propulsive force in the vertical orientation is expended counteracting gravity.

[0314] However, this difference is minimal due to the robot’s low mass (10 g, 0.1 N) and the additional drag from the air tubing and motor cable, which slightly increases resistance during horizontal motion.

[0315] Unlike other off-center motor configurations, our design positions the eccentric motor at the center of the housing to maintain structural symmetry and stability. This modification alone improves locomotion speed by approximately 3-6 times (47-80 mm / s at different constant internal pressures versus 14 mm / s), despite the prior work combining vibration with cyclic inflation / deflation-based thrust, whereas our robot relies solely on vibration. These results demonstrate that housing and motor placement are critical factors in controlling the PFR’s center of mass and achieving high-speed, vibration driven locomotion.

[0316] To investigate the effect of fin length on locomotion performance, we compared PFR3 (short fins) and PFR4 (long fins), which share identical material properties and housing design.

[0317] As summarized in FIG. 44, PFR4 has fins with a height of 8 mm compared to 4.85 mm for PFR3, resulting in an overall diameter approximately 6.3 mm larger. Consequently, PFR4 maintains contact with the tube surface even without inflation. Due to this pre-contact condition, increasing internal pressure reduces its speed, as balloon expansion increases normal force and friction, constraining the robot against the tube walls. In contrast, PFR3 exhibits higher speeds with increasing pressure, since ball stalls at approximately 15 kPa, whereas PFR3 continues to move at the same pressure. Moreover, the longer fins of PFR4 provide greater passive grip, allowing upward motion in vertical tubes with minimal pressure input, while PFR3 requires pressurization to generate sufficient traction loon inflation enhances fin-wall interaction without inducing jamming.

[0318] For instance, PFR4 stalls at approximately 15 kPa, whereas PFR3 continues to move at the same pressure. Moreover, the longer fins of PFR4 provide greater passive grip, allowing upward motion in vertical tubes with minimal pressure input, while PFR3 requires pressurization to generate sufficient traction.4922-7473-8524, v. 1 67

[0319] In this study, we presented the analytical modeling, design, fabrication, and experimental evaluation of a puffer fish inspired pipe inspection soft robot. The robot employs vibration as its sole locomotion mechanism, where internal pressure serves as a control variable to tune the stiffness and natural frequency of the inflatable structure, thereby optimizing vibration transmission and locomotion performance based on the fin geometry and material properties. Four different PFR prototypes were fabricated and systematically analyzed to determine how balloon stiffness, silicone hardness, fin geometry, and center of mass affect locomotion efficiency.

[0320] Our results demonstrate that optimizing these parameters can enhance vibration-driven locomotion by 3-5 times compared to other robots (e.g.,

[0063] as compared in FIG. 51), achieving speeds exceeding 100 mm / s in both horizontal and vertical tubes with an inner diameter of 30 mm.

[0321] All of the apparatus, systems and / or methods disclosed and claimed herein can be made and executed without undue experimentation in light of the present disclosure. While the devices, systems and methods of this invention have been described in terms of particular embodiments, it will be apparent to those of skill in the art that variations may be applied to the devices, systems and / or methods in the steps or in the sequence of steps of the method described herein without departing from the concept, spirit and scope of the invention. All such similar substitutes and modifications apparent to those skilled in the art are deemed to be within the spirit, scope and concept of the invention as defined by the appended claims.4922-7473-8524, v. 1 68REFERENCES:

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Claims

CLAIMS:

1. An apparatus comprising: a flexible annular member, wherein the flexible annular member comprises: a first end and a second end; a central opening extending from the first end of the flexible annular member to the second end of the flexible annular member; a plurality of flexible extensions extending radially from the flexible annular member, wherein the flexible extensions are angled towards the second end of the flexible annular member; a housing located within the central opening of the flexible annular member, wherein: the housing comprises: a first end and a second end; a central opening extending from the first end of the housing to the second end of the housing; and, a locomotion mechanism configured to impart motion to the plurality of flexible extensions extending radially from the flexible annular member.

2. The apparatus of claim 1, wherein the locomotion mechanism is configured to vibrate the plurality of flexible extensions extending from the flexible annular member.

3. The apparatus of claim 1 or 2 wherein the locomotion mechanism comprises an eccentric motor.

4. The apparatus of any one of claims 1-3 wherein the locomotion mechanism comprises a piezoelectric element.

5. The apparatus of any one of claims 1-4 wherein the locomotion mechanism comprises an inflation device configured to inflate and deflate the flexible annular member.

6. The apparatus of any one of claims 1-5 wherein: a flexible extension of the plurality of flexible extensions comprises: a base portion and a distal portion;4922-7473-8524, v. 1 76the base portion is located a first distance from the second end of the flexible annular member; the distal portion is located a second distance from the second end of the flexible annular member; and, the first distance is greater than the second distance.

7. The apparatus of any one of claims 1-6 wherein: each flexible extension of the plurality of flexible extensions comprises: a base portion and a distal portion; the base portion is located a first distance from the second end of the flexible annular member; the distal portion is located a second distance from the second end of the flexible annular member; and, the first distance is greater than the second distance.

8. The apparatus of any one of claims 1-7, further comprising: a first seal configured to seal the first end of the flexible annular member to the first end of the housing; and a second seal configured to seal the second end of the flexible annular member to the second end of the housing.

9. The apparatus of any one of claims 1-8, further comprising an actuator configured to change the orientation of the plurality of flexible extensions such that the plurality of flexible extensions are angled toward the first end of the flexible annular member.

10. The apparatus of any one of claims 1-9, wherein the flexible annular member comprises embedded flexible strain sensors configured to directly measure interaction forces.

11. The apparatus of any one of claims 1-10, wherein the apparatus communicates wirelessly with a control system.

12. The apparatus of any one of claims 1-11, further comprising: a second flexible annular member, wherein the second flexible annular member comprises:4922-7473-8524, v. 1 77a first end and a second end; a central opening extending from the first end of the second flexible annular member to the second end of the second flexible annular member; a plurality of flexible extensions extending from the second flexible annular member, wherein the flexible extensions are angled towards the second end of the second flexible annular member; a second housing located within the central opening of the flexible annular member, wherein the second housing comprises: a first end and a second end; a central opening extending from the first end of the second housing to the second end of the second housing; and, a second locomotion mechanism configured to impart motion to the plurality of flexible extensions extending radially from the second flexible annular member.

13. The apparatus of any one of claims 1-12, wherein the apparatus is configured to be operated using a remote user via a robotic system.

14. The apparatus of any one of claims 1-13, wherein the apparatus is configured to provide visual and / or haptic feedback to the user.

15. The apparatus of any one of claims 1-14, wherein the apparatus is configured to move in an autonomous mode.

16. The apparatus of claim 15 wherein, the autonomous mode is controlled by artificial intelligence (Al) algorithms, the Al based control operations comprising: detecting visual or tactile sense data; generating an Al-based diagnosis with an artificial intelligence engine communicating with the control system; and, selecting an appropriate AI-Based control through vibration and pneumatic outputs to drive the locomotion mechanism.

17. The apparatus of claim 15 or 16 wherein, the autonomous mode is controlled by embedded sensors.4922-7473-8524, v. 1 7818. A method of moving an apparatus within a constrained environment, the method comprising: inserting the apparatus into the constrained environment, wherein the apparatus comprises a flexible annular member comprising a plurality of flexible extensions; inflating the flexible annular member so that the plurality of flexible extensions engage the constrained environment; and, vibrating the apparatus so that the plurality of flexible extensions move the apparatus with respect to the constrained environment.

19. A method of moving an apparatus within a constrained environment, the method comprising: inserting the apparatus into the constrained environment, wherein the apparatus comprises a flexible annular member comprising a plurality of flexible extensions; inflating the flexible annular member so that the plurality of flexible extensions engage the constrained environment; and, cyclically deflating and inflating the apparatus so that the plurality of flexible extensions move the apparatus with respect to the constrained environment.

20. A method of moving an apparatus within a constrained environment, the method comprising: inserting the apparatus into the constrained environment, wherein the apparatus comprises a flexible annular member comprising a plurality of flexible extensions; inflating the flexible annular member so that the plurality of flexible extensions engage the constrained environment; and, vibrating the apparatus and cyclically deflating and inflating the apparatus so that the plurality of flexible extensions move the apparatus with respect to the constrained environment.4922-7473-8524, v. 1 79

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