Manufacturing device and modeling method of a millimeter-scale stretchable soft robot

Abstract

The application discloses a manufacturing device and a modeling method of a millimeter-scale stretchable soft robot, and belongs to the technical field of soft robots. In the manufacturing process, a hot pressing process based on a positioning mold is adopted: first, a plurality of films are shaped through laser cutting and a pressing mold is designed, then the films are arranged in sequence in the lower mold and the driving wires are inserted, the upper mold is closed, hot pressing is performed for a certain time, air cooling is performed, and demolding is performed, and finally, the upper and lower end covers are glued to form the soft body. In the modeling process, a displacement dominant sub-model and an elastic deformation dominant sub-model are established, and a conversion principle between the sub-models is proposed, so that accurate motion description of the wire / fluid driven soft robot is realized. Based on the above manufacturing process and combined with the analytical modeling method, the millimeter-level wire / fluid driven soft robot can be manufactured, and the structure miniaturization and the flexible deformation capability are realized.

Description

Technical Field

[0001] This invention belongs to the field of soft robot technology, and particularly relates to a manufacturing apparatus and modeling method for a millimeter-scale extendable soft robot. Background Technology

[0002] With the rapid development of interventional medicine, micro-industrial pipeline detection and other fields, higher requirements have been placed on the dexterity of millimeter-scale soft robots. An ideal micro soft robot not only needs to have multi-directional bending ability, but also needs to have axial extension function to achieve follow-up motion and real-time path planning in narrow apertures to achieve accurate access to the target position. However, achieving dexterous deformation with both "extension" and "multi-directional bending" at the millimeter scale faces huge challenges. In terms of manufacturing process and structural integration: (1) Structural contradiction between extension and bending. Traditional micro soft robots usually use isotropic silicone potting, and their structural stiffness is uniformly distributed. When this structure achieves axial extension, it often requires extremely high fluid pressure and is prone to radial over-expansion (balloon effect), which causes it to lose dexterity due to the increase in friction in narrow channels; (2) Difficulty in packaging multiple driving sources: Line / fluid drive can achieve dexterous motion of extension and bending at large scales, but when applied to a body with a diameter of several millimeters, the original manufacturing method is no longer applicable due to the high manufacturing precision. On the one hand, traditional bonding methods are difficult to form sub-millimeter level bonds, and 3D printed structures are prone to stress fatigue under frequent stretching-bending coupling motions, leading to interface peeling or cavity cracking; on the other hand, existing processes are difficult to perform robot assembly work (such as threading) at the millimeter scale. In terms of modeling and real-time control: (1) Multi-field coupling leads to computational redundancy. The coupling behavior of line drive and fluid drive is highly nonlinear. Although the existing finite element analysis method can accurately simulate the stretching and bending process, its nonlinear iterative calculation is time-consuming and cannot meet the requirements of real-time feedback control for micro robots in dynamic tasks; (2) There is a lack of accurate and efficient analytical models. Most existing constant curvature models assume that the robot length is constant and cannot describe soft robots with extension functions. Existing variable length models often ignore the constraint effect of line drive tension on the extension process. The industry urgently needs a model that can capture the stretching and bending coupling characteristics and maintain the analytical form to reduce the computational burden of the control system.

[0003] Therefore, it is necessary to provide a new technical solution to solve the above problems. Summary of the Invention

[0004] Purpose of the invention: The purpose of this invention is to overcome the problems of insufficient dexterity and complex multi-drive coupling modeling in the prior art of millimeter-scale soft robots, and to provide a manufacturing device for millimeter-scale extendable soft robots, for manufacturing soft robots with extendable functions.

[0005] The present invention also provides a modeling method for millimeter-scale stretchable soft robots, which can provide a soft robot model that can capture stretching and bending coupling features while maintaining an analytical form to reduce the computational burden on the control system.

[0006] Technical Solution: To solve the above problems, the manufacturing apparatus for a millimeter-scale stretchable soft robot provided by this invention adopts the following technical solution:

[0007] A manufacturing apparatus for a millimeter-scale stretchable soft robot includes an upper template, an upper pad mounted on the bottom surface of the upper template, a lower template located below the upper template, a lower pad mounted on the top surface of the lower template, a film stack located between the upper and lower pads, a central positioning pin located on the upper pad and passing through the film stack, and a drive line. An outer positioning pin is provided on one of the lower and upper templates, while the other has a positioning hole that mates with the outer positioning pin. The film stack and the central positioning pin form a hole-axis clearance fit. The lower template has a through-hole for threading, the lower pad has a through-hole for threading, the upper pad has a through-hole for threading, and the upper template has a through-hole for threading. The drive line sequentially passes through the through-holes in the lower template, the lower pad, the film stack, the upper pad, and the upper template. The film stack is pressed together in the middle by the upper and lower templates.

[0008] Furthermore, the film stack includes a PI main film, a titanium alloy intermediate plate, a PI inner film, a PTFE inner film, a titanium alloy outer plate, and a PTFE outer film; the titanium alloy intermediate plate has a circular receiving opening in the middle position, the PTFE inner film is received in the circular receiving opening and is clearance-fitted with the circular receiving opening, one titanium alloy intermediate plate and one PTFE inner film together form a first film group; the PTFE outer film has a circular receiving opening in the middle position, the PI inner film is received in the circular receiving opening and is clearance-fitted with the circular receiving opening of the PTFE outer film, one PI inner film (63) and one PTFE outer film together form a second film group; the PI main film has a central hole in the middle position, the PI inner film has a central hole in the middle position, the PTFE inner film has a central hole in the middle position, the titanium alloy outer plate has a central hole in the middle position, each central hole forms a hole-axis clearance fit with the central positioning pin; the outer hole of the titanium alloy intermediate plate and the outer hole of the titanium alloy outer plate pass through the drive line.

[0009] Furthermore, the thin film stack comprises three parts: a first part consisting of a titanium alloy outer plate, a PI main film, and a second film group stacked coaxially from top to bottom; a second part consisting of several third film groups stacked coaxially from top to bottom, each third film group comprising a PI main film, a first film group, another PI main film, and a second film group stacked coaxially from top to bottom; and a third part consisting of a PI main film and a titanium alloy outer plate stacked coaxially from top to bottom; the first, second, and third parts are stacked coaxially from top to bottom.

[0010] Furthermore, the lower template forms a hole-axis clearance fit with the lower optical axis of the outer positioning pin through the lower template positioning hole, and forms a hole-axis clearance fit with the center positioning pin through the lower template center hole; the upper shim has the same shape as the lower shim, wherein the lower shim forms a hole-axis clearance fit with the lower optical axis of the outer positioning pin and the center positioning pin through the lower shim positioning hole and the lower shim center hole, respectively.

[0011] Furthermore, the PI main film, PI inner film, PTFE inner film, and PTFE outer film in the film stack are all processed using femtosecond green laser.

[0012] Furthermore, the titanium alloy intermediate plate and the titanium alloy outer plate are cleaned with an ultrasonic cleaner in a 5% NaOH solution at 60°C for 30 minutes, and then cleaned in deionized water at 60°C for 30 minutes.

[0013] Furthermore, the film stack is hot-pressed at 10 N pressure and 200°C for 120 minutes. After hot pressing, the film stack needs to be glued with matching upper and lower end caps. The upper end cap is used to seal the distal end, while the lower end cap is used to integrate the flow channel and provide tendon channels for external wiring drive devices and fluid drive devices to drive.

[0014] The modeling method for millimeter-scale stretchable soft robots provided by this invention adopts the following technical solution:

[0015] A modeling method for millimeter-scale stretchable soft robots involves setting up displacement-dominant sub-models and elastic deformation-dominant sub-models along the length of the fluid-driven soft robot, while also defining the transformation principles between the sub-models. The displacement-dominant sub-model represents the total volume V of the internal cavity. c The volume generated by rotating a planar region about the z-axis is given by the fact that the final structure of the thin film stack after the injected fluid expands into a bellows structure. Therefore, the planar region is decomposed into two parts: one part corresponds to twice the area of ​​the internal trapezoid AMNB to generate a double-truncated cone, and the other part corresponds to twice the area of ​​the arc MN formed by the trapezoidal side and the bellows structure, as shown below:

[0016] (1),

[0017] Where V is the total injection volume and n is the number of bellows. and These are the volumes generated by the rotation of the trapezoid and the segment, respectively; due to The volume of the truncated cone can be further expressed as:

[0018] (2),

[0019] Where h c It is the half height of a single bellows, r i It is the inner diameter of the bellows, r o It is the outer diameter of the bellows; let the radius of the arc MN be r. c Based on the Pappus-Guldinus theorem, it is derived that... :

[0020] (3),

[0021] The effective centroid distance D and cross-sectional area A are derived using the following formula:

[0022] (4),

[0023] Where c is the chord length of the arc MN, and d is the perpendicular distance from the center O to MN. r is the central angle corresponding to the chord of the arc MN. seg It is the distance from the centroid of the arc MN to the center O of the circle; r c Further derivation is as follows:

[0024] (5),

[0025] Substitute equations (2)-(5) into equation (1) and note The derivation of a single parameter Controlled motion-dominant behavior, i.e., mapping V trans It is the feature volume value of the sub-model transformation flag.

[0026] Furthermore, the elastic deformation-dominated sub-model study shows that when the volume of the internal cavity reaches its maximum value, the deformation-dominated model begins to dominate the kinematics, at which point the elongation is determined by elastic deformation; considering the initial length, the mapping... The derivation is as follows:

[0027] (6),

[0028] Where t is the film thickness and E is the Young's modulus of the film material; It is a constant related to the Poisson's ratio of the material. The pressure-volume proportionality constant, V, is characterized experimentally. trans It is the feature volume value of the sub-model transformation flag.

[0029] Furthermore, the transformation principle between sub-models depends on V. trans The value of is expressed as follows:

[0030] (7),

[0031] Where l is the length of the bellows busbar. , yes The root in [0, 1];

[0032] Therefore, the piecewise model describing the length variation of this soft robot is as follows:

[0033] (8).

[0034] Beneficial effects: Compared with the prior art, the significant advantages of this invention are (1) achieving high integration and manufacturing consistency of the stretchable soft robot structure at the millimeter scale. This invention adopts a thin film hot pressing process based on positioning mold, avoiding the defects of traditional mold casting method at the millimeter scale such as easy generation of bubbles and uneven wall thickness, as well as the problem of limited mechanical properties of 3D printing materials. Through sub-millimeter bonding, the compact integration of drive channels and fluid cavities is achieved, ensuring the structural integrity of millimeter-level actuators under complex loads, and the process repeatability is high, greatly improving the yield and mass production feasibility of micro soft robots; (2) taking into account both the high precision of motion description and the real-time performance of control. The segmented analytical model proposed in this invention cleverly avoids the high-complexity finite element nonlinear iterative calculation, significantly reducing the computational overhead of the system, and is expected to realize high-frequency real-time closed-loop control on low-computing-power embedded platforms. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of the soft robot manufacturing system of the present invention;

[0036] Figure 2 This is a schematic diagram of the template for manufacturing the soft robot of the present invention;

[0037] Figure 3 This is a schematic diagram of the upper pad used in the manufacturing of the soft robot of the present invention;

[0038] Figure 4 This is a schematic diagram of the template for manufacturing the soft robot of the present invention;

[0039] Figure 5This is a schematic diagram of the lower pad manufactured by the soft robot of the present invention;

[0040] Figure 6 This is a schematic diagram of the film shape of the present invention;

[0041] Figure 7 This is a schematic diagram of the thin film arrangement of the present invention;

[0042] Figure 8 This is a schematic diagram of the soft robot structure of the present invention;

[0043] Figure 9 This is a schematic diagram of the soft robot length modeling method of the present invention;

[0044] Figure 10 This is a schematic diagram of the shape and modeling parameters of the soft robot of the present invention. Detailed Implementation

[0045] like Figures 1 to 7 As shown, a manufacturing apparatus for a millimeter-scale stretchable soft robot in this embodiment includes an upper template 1, an upper pad 2, a lower template 3, a lower pad 4, an outer positioning pin 5, a film stack 6, a central positioning pin 7, and a drive line 8.

[0046] The lower template 3 forms a hole-axis clearance fit with the lower optical axis of the outer positioning pin 5 through the lower template positioning hole 31, and forms a hole-axis clearance fit with the center positioning pin 7 through the lower template center hole 32. The upper shim 2 and the lower shim 4 have the same shape, wherein the lower shim 4 forms a hole-axis clearance fit with the lower optical axis of the outer positioning pin 5 and the center positioning pin 7 through the lower shim positioning hole 41 and the lower shim center hole 42, respectively.

[0047] The thin film stack 6 and the central positioning pin 7 form a hole-shaft clearance fit;

[0048] The drive line 8 passes through the lower template wire hole 33, the lower gasket wire hole 43, the film stack 6, the upper gasket wire hole 23, and the upper template wire hole 13 in sequence.

[0049] The upper gasket 2 and the upper template 1 are respectively connected to the upper optical axis of the outer positioning pin 5 and the center positioning pin 7 through the upper gasket positioning hole 21 and the upper gasket center hole 22, the upper template positioning hole 11 and the upper template center hole 12 to form a hole-axis clearance fit. Finally, the film stack 6 is pressed in the middle through the upper template 1 and the lower template 3.

[0050] The thin film stack 6 includes a PI main film 61, a titanium alloy intermediate plate 62, a PI inner film 63, a PTFE inner film 64, a titanium alloy outer plate 65, and a PTFE outer film 66.

[0051] In the aforementioned films, the inner edge 611 of the PI main film, the inner edge 632 of the PI inner film, the inner edge 641 of the PTFE inner film, and the inner edge 651 of the titanium alloy outer plate form a hole-shaft clearance fit with the central positioning pin 7; the outer holes 622 and 652 of the titanium alloy intermediate plate pass through the drive line 8; the inner edge 621 of the titanium alloy intermediate plate and the outer edge 642 of the PTFE inner film are in clearance fit; the outer edge 631 of the PI inner film and the inner edge 661 of the PTFE outer film are in clearance fit.

[0052] The arrangement order of the thin film stack 6 from top to bottom is: titanium alloy outer plate 65, PI main film 61, PI inner film 63 and PTFE outer film 66, and then repeats n times: PI main film 61, titanium alloy intermediate plate 62 and PTFE inner film 64, PI main film 61, PI inner film 63 and PTFE outer film 66, and finally add PI main film 61 and titanium alloy outer plate 65, resulting in n actuator drive units.

[0053] All the films in the thin film stack 6 were processed using a femtosecond green laser.

[0054] The titanium alloy intermediate plate 62 and the titanium alloy outer plate 65 were first cleaned with an ultrasonic cleaner in a 5% NaOH solution at 60°C for 30 minutes, and then cleaned in deionized water at 60°C for 30 minutes.

[0055] The manufacturing system requires hot pressing at 10 N pressure and 200°C for 120 minutes.

[0056] After hot pressing, the film stacking needs to be glued with matching upper and lower end caps. After the lower end cap seals the integrated flow channel, external wiring drive equipment and injection pump can be used for driving.

[0057] like Figure 8 As shown in this embodiment, a manufacturing apparatus for a millimeter-scale extendable soft robot produces a fluid-driven soft robot consisting of an upper end cap 71, a lower end cap 73, and a corrugated structure 75 in the middle. The corrugated structure 75 forms an internal cavity 72, which is driven by a flow channel 74 integrated in the lower end cap 73. Furthermore, the corrugated structure 75 integrates a drive line 8. The soft robot as a whole can be driven by external drive devices and fluid drive devices.

[0058] like Figure 9 and Figure 10 As shown, the modeling method for the fluid-driven soft robot of the present invention specifically includes the following model: its length direction modeling is divided into two sub-models, the first sub-model is the displacement-dominant sub-model, the second sub-model is the elastic deformation-dominant sub-model, and a conversion principle between sub-models.

[0059] Furthermore, the displacement-dominant sub-model considers the total volume V of the internal cavity... cConsidered as the volume generated by rotating a planar region around the z-axis, since the final structure of the thin film stack after expansion by the injected fluid is a corrugated structure, the rotating region can be decomposed into two parts: one part corresponds to twice the area of ​​the internal trapezoidal AMNB (generating a double-truncated cone), and the other part corresponds to twice the area of ​​the arc-shaped MN formed by the trapezoidal side and the corrugated envelope, as shown below:

[0060] (1)

[0061] Where V is the total injection volume. and These represent the volumes generated by the rotation of the trapezoid and the arc, respectively, and n is the number of bellows. Because... The volume of the truncated cone can be further expressed as:

[0062] (2)

[0063] Where h c It is the half-height of a single ripple, r i It is the inner diameter of the corrugations, r o It is the outer diameter of the corrugation. Assume the radius of the arc is r. c According to the Pappus-Guldinus theorem, it can be derived that... :

[0064] (3)

[0065] The effective centroid distance D and the cross-sectional area A can be derived through a series of geometric relationships:

[0066] (4)

[0067] Where c is the length of chord MN, and d is the perpendicular distance from the center O to MN. It is the central angle corresponding to chord MN, r seg It is the distance from the centroid of the arc to the center O of the circle. c The following can be further deduced:

[0068] (5)

[0069] Substitute equations (2)-(5) into equation (1) and note It can be deduced that a single parameter Controlled motion-dominant behavior, i.e., mapping .

[0070] Furthermore, the elastic deformation-dominated sub-model study shows that when the volume within the corrugated cavity reaches its maximum, the deformation-dominated model begins to dominate the kinematics, at which point the elongation is determined by elastic deformation. Considering the initial length, the mapping... The following analysis and derivation can be performed:

[0071] (6)

[0072] Where t is the film thickness and E is the Young's modulus of the film material. It is a constant related to the Poisson's ratio of the material. The pressure-volume proportionality constant, V, is characterized experimentally. trans It is the feature volume value of the sub-model transformation flag.

[0073] Furthermore, the transformation principle between sub-models depends on V. trans The value of is expressed as follows:

[0074] (7)

[0075] Where l is the length of the bellows busbar. , yes The root in [0, 1].

[0076] Therefore, the piecewise model describing the length of this actuator is as follows:

[0077] (8).

Claims

1. A manufacturing apparatus for a millimeter-scale stretchable soft robot, characterized in that, Includes an upper template (1), an upper gasket (2) installed on the bottom surface of the upper template (1), a lower template (3) located below the upper template (1), a lower gasket (4) installed on the top surface of the lower template (3), a film stack (6) located between the upper gasket (2) and the lower gasket (4), a central positioning pin (7) located on the upper gasket (2) and passing through the film stack (6), and a drive line (8); an outer positioning pin (5) is provided in one of the lower template (3) and the upper template (1), and a positioning hole (31) that cooperates with the outer positioning pin (5) is provided in the other; the film stack (6) and the central positioning pin (7) form a hole-shaft clearance fit; The lower template is provided with a through lower template wire hole (33), the lower pad is provided with a through lower pad wire hole (43), the upper pad is provided with a through upper pad wire hole (23), and the upper template is provided with a through upper template wire hole (13). The driving line (8) passes through the lower template wire hole (33), the lower pad wire hole (43), the film stack (6), the upper pad wire hole (23), and the upper template wire hole (13) in sequence. The film stack (6) is pressed together in the middle by the upper template (1) and the lower template (2).

2. The manufacturing apparatus for a millimeter-scale stretchable soft robot as described in claim 1, characterized in that, The film stack (6) includes a PI main film (61), a titanium alloy intermediate plate (62), a PI inner film (63), a PTFE inner film (64), a titanium alloy outer plate (65), and a PTFE outer film (66). The titanium alloy intermediate plate (62) has a circular receiving port (621) in the middle position. The PTFE inner film (64) is received in the circular receiving port (621) and is in a clearance fit with the circular receiving port (621). One titanium alloy intermediate plate (62) and one PTFE inner film (64) together form a first film group. The PTFE outer film (66) has a circular receiving port (661) in the middle position. The PI inner film (63) is received in the circular receiving port (661) and is in a clearance fit with the circular receiving port (661). One PI inner film (63) and one PTFE outer film (66) together form a second film group. The PI main film has a central hole (611) in the middle, the PI inner film has a central hole (632) in the middle, the PTFE inner film has a central hole (641) in the middle, and the titanium alloy outer plate has a central hole (651) in the middle. Each central hole forms a hole-shaft clearance fit with the central positioning pin (7). The outer holes (622) of the titanium alloy middle plate and the outer holes (652) of the titanium alloy outer plate pass through the drive line (8).

3. The manufacturing apparatus for a millimeter-scale stretchable soft robot as described in claim 2, characterized in that, The thin film stack (6) consists of three parts. Part 1: A titanium alloy outer plate (65), a PI main film (61) and a second film assembly are coaxially stacked from top to bottom; Part 2: Several third film groups coaxially stacked from top to bottom, each third film group including a PI main film (61), a first film group, another PI main film (61) and a second film group coaxially stacked from top to bottom; Part 3: A PI master film (61) and a titanium alloy outer plate (65) are coaxially stacked from top to bottom. The first part, the second part, and the third part are stacked coaxially from top to bottom.

4. The manufacturing apparatus for a millimeter-scale stretchable soft robot as described in claim 1, characterized in that, The lower template (3) forms a hole-axis clearance fit with the lower optical axis of the outer positioning pin (5) through the lower template positioning hole (31), and forms a hole-axis clearance fit with the center positioning pin (7) through the lower template center hole (32); the upper gasket (2) and the lower gasket (4) have the same shape, wherein the lower gasket (4) forms a hole-axis clearance fit with the lower optical axis of the outer positioning pin (5) and the center positioning pin (7) through the lower gasket positioning hole (41) and the lower gasket center hole (42) respectively.

5. The manufacturing apparatus for a millimeter-scale stretchable soft robot as described in claim 1, characterized in that, The PI main film (61), PI inner film (63), PTFE inner film (64), and PTFE outer film (66) in the film stack (6) are all processed by femtosecond green laser.

6. The manufacturing apparatus for a millimeter-scale stretchable soft robot as described in claim 1, characterized in that, The titanium alloy intermediate plate (62) and the titanium alloy outer plate (65) were cleaned for 30 minutes in a 5% NaOH solution at 60°C using an ultrasonic cleaner, and then cleaned for 30 minutes in deionized water at 60°C.

7. The manufacturing apparatus for a millimeter-scale stretchable soft robot as described in claim 1, characterized in that, The film stack (6) was hot-pressed at 10 N pressure and 200 °C for 120 minutes; After hot pressing, the film stack requires adhesive-fitted upper and lower end caps, wherein the upper end cap (71) is used to seal the distal end, while the lower end cap (73) is used to integrate the flow channel (74) and provide tendon channels for external wiring drive devices and fluid drive devices to be driven.

8. A modeling method for a millimeter-scale stretchable soft robot, characterized in that, A displacement-dominant sub-model and an elastic deformation-dominant sub-model will be set along the length direction of the fluid-driven soft robot, and the conversion principle between the sub-models will be set. The displacement-dominant sub-model considers the total volume V of the internal cavity (72) c The volume generated by rotating a planar region (81) about the z-axis is such that, since the final structure of the thin film stack (6) after the fluid injection expansion is a bellows structure (75), the planar region (81) is decomposed into two parts: one part corresponds to twice the area of ​​the inner trapezoid AMNB (82) to generate a double-truncated cone, and the other part corresponds to twice the area of ​​the arc MN (83) formed by the trapezoidal side and the bellows structure (75), as shown below: （1）， Where V is the total injection volume and n is the number of bellows. and These are the volumes generated by the rotation of the trapezoid and the segment, respectively; due to The volume of the truncated cone can be further expressed as: （2）， Where h c It is the half height of a single bellows, r i It is the inner diameter of the bellows, r o It is the outer diameter of the bellows; let the radius of the arc MN (83) be r. c Based on the Pappus-Guldinus theorem, it is derived that... : （3）， The effective centroid distance D and cross-sectional area A are derived using the following formula: （4）， Where c is the chord length of the arc MN (83), and d is the perpendicular distance from the center O to MN. It is the central angle corresponding to the chord of the arc MN (83), r seg It is the distance from the centroid of the arc MN (83) to the center O of the circle; r c Further derivation is as follows: （5）， Substitute equations (2)-(5) into equation (1) and note The derivation of a single parameter Controlled motion-dominant behavior, i.e., mapping V trans It is the feature volume value of the sub-model transformation flag.

9. The modeling method for a millimeter-scale stretchable soft robot as described in claim 8, characterized in that, The elastic deformation-dominant sub-model study shows that when the volume of the internal cavity (72) reaches its maximum value, the deformation-dominant model begins to dominate the kinematics, and the elongation at this time is determined by elastic deformation; considering the initial length, the mapping... The derivation is as follows: （6）， Where t is the film thickness and E is the Young's modulus of the film material; It is a constant related to the Poisson's ratio of the material. The pressure-volume proportionality constant, V, is characterized experimentally. trans It is the feature volume value of the sub-model transformation flag.

10. The modeling method for a millimeter-scale stretchable soft robot as described in claim 9, characterized in that, The transformation principle between sub-models depends on V trans The value of is expressed as follows: （7）， Where l is the length of the bellows busbar. , yes The root in [0,1]; Therefore, the piecewise model describing the length variation of this soft robot is as follows: （8）。

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