Kinematic modeling methods, equipment and products for pre-bending self-growing robots

Abstract

This application discloses a kinematic modeling method, device, and product for a pre-bending self-growing robot, relating to the field of self-growing robots. The method includes: when the bending angle is less than 53°, using a piecewise constant curvature model to describe the relationship between the length and bending angle of the annular fold structure, wherein the piecewise constant curvature model defines the cavity shape in the cross-section of the annular fold structure as a portion of a circle; when the bending angle is greater than 53° and less than 127°, using a target model to describe the relationship between the length and bending angle of the annular fold structure, wherein the target model defines the cavity shape in the cross-section of the annular fold structure as a semi-ellipse. Using different models at different stages can more accurately describe the relationship between the length and bending angle of the annular fold structure, solving the problem in the prior art where using a single model to describe the relationship between the length and bending angle of the annular fold structure in all cases leads to inaccurate descriptions.

Description

Technical Field

[0001] This application relates to the field of self-growing robots, and in particular to a kinematic modeling method, device and product for a pre-bending self-growing robot. Background Technology

[0002] Self-growing robots are a new type of soft robot that mimics vines. They can extend their length indefinitely by outwardly extending their material. Thanks to their strong compliance, self-growing robots can navigate by interacting with their environment, making them highly suitable for confined spaces. To realize the application of self-growing robots in restricted environments, they need appropriate steering control capabilities. Current research shows that steering in self-growing robots mainly includes active steering and passive steering. Active steering primarily uses pneumatic artificial muscles. Although it can actively achieve directional control, the compressibility of gas leads to low steering accuracy, and it is difficult to control the overall shape of the robot to achieve effective obstacle avoidance. Passive steering mainly relies on the pre-bending structure of the self-growing robot. By pre-fabricating specific structures on a thin film and combining them with environmental interaction navigation, the growth direction of the self-growing robot can be guided. This structure can fully utilize the compliance of the self-growing robot. However, current motion modeling of this structure mostly uses a piecewise constant curvature model, which describes the local shape of the robot as a curve with constant curvature. Although it has high accuracy at small turning angles, it introduces significant deviations when considering external loads or large deformations. Furthermore, current kinematic modeling methods are still relatively idealistic and fail to fully consider the constraints brought about by end effectors or sensors. Summary of the Invention

[0003] The purpose of this application is to provide a kinematic modeling method for pre-bent self-growing robots that can solve the problem that the existing technology uses a single model to describe the relationship between the length and bending angle of the annular fold structure in all cases, resulting in inaccurate description.

[0004] To achieve the above objectives, this application provides the following solution: In a first aspect, this application provides a kinematic modeling method for a pre-bent self-growing robot, the pre-bent self-growing robot comprising a cylindrical film, the cylindrical film having at least one annular fold structure, the annular fold structure being used to form a bending angle after the cylindrical film is inflated, the cylindrical film being divided into multiple segments by the annular fold structure. The kinematic modeling method is characterized by comprising: When the bending angle is less than 53°, a piecewise constant curvature model is used to describe the relationship between the length of the annular fold structure and the bending angle. The piecewise constant curvature model defines the cavity shape in the cross-section of the annular fold structure as a part of a circle. When the bending angle is greater than 53° and less than 127°, a target model is used to describe the relationship between the length of the annular fold structure and the bending angle. The target model defines the hollow shape of the cross-section of the annular fold structure as a semi-ellipse. The target model is as follows: in, l This indicates the length of the annular pleated structure. Indicates the bending angle, r This represents the radius of the cylindrical film. a Denotes the major axis of the semi-ellipse. b The minor axis of the semi-ellipse is represented.

[0005] In a second aspect, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the kinematic modeling method for the pre-bending self-growing robot described in any one of the above-mentioned methods.

[0006] Thirdly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the kinematic modeling method for the pre-bending self-growing robot described in any of the above-mentioned methods.

[0007] Fourthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the kinematic modeling method for the pre-bending self-growing robot described in any of the above-mentioned applications.

[0008] According to the specific embodiments provided in this application, the following technical effects are disclosed: This application provides a kinematic modeling method, device, and product for a pre-bending self-growing robot. Different models are used to describe the relationship between the length and bending angle of the annular pleated structure under different conditions. The critical point is whether the shape of the cavity in the cross-section of the annular pleated structure changes. When the bending angle is less than 53°, the cavity shape is part of a circle, and a piecewise constant curvature model is used for description. When the bending angle is greater than 53°, the cavity shape is a semi-ellipse, and a target model is used for description. Using different models at different stages can more accurately describe the relationship between the length and bending angle of the annular pleated structure, solving the problem of inaccurate descriptions caused by using a single model to describe the relationship between the length and bending angle of the annular pleated structure in all cases in existing technologies. Attached Figure Description

[0009] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 This is an architectural diagram of a pre-bending self-growing robot according to one embodiment of this application; Figure 2 This is a structural diagram of a pre-bending self-growing robot according to one embodiment of this application; Figure 3 This is a schematic diagram of an annular pleated structure in one embodiment of this application; Figure 4 This is a schematic diagram illustrating the relationship between the length and bending angle of the annular pleated structure in one embodiment of this application. Figure 1 ; Figure 5 This is a schematic diagram illustrating the relationship between the length and bending angle of the annular pleated structure in one embodiment of this application. Figure 2 ; Figure 6 This is a schematic diagram illustrating the relationship between the length and bending angle of the annular pleated structure in one embodiment of this application. Figure 3 ; Figure 7 This is a schematic diagram illustrating the relationship between the length and bending angle of the annular pleated structure in one embodiment of this application. Figure 4 ; Figure 8 This is a schematic diagram of the end structure of the tubular film in one embodiment of this application; Figure 9 This is a schematic diagram of the diameter constraint of the inner mechanism in one embodiment of this application; Figure 10This is a schematic diagram of the length constraint of the inner mechanism in one embodiment of this application; Figure 11 This is a schematic diagram of the continuous rotational constraint of the inner mechanism in one embodiment of this application; Figure 12 This is a schematic diagram of the constraints on the outer mechanism in one embodiment of this application; Figure 13 This is a schematic diagram showing the length of the tubular film in one embodiment of this application. Detailed Implementation

[0011] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0012] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0013] The kinematic modeling method for a pre-bending self-growing robot provided in this application embodiment can be applied to a terminal or server.

[0014] The terminal can be, but is not limited to, various desktop computers, laptops, smartphones, and tablets. The server can be a standalone server, a server cluster consisting of multiple servers, or a cloud server.

[0015] In one exemplary embodiment, such as Figure 1 As shown, a kinematic modeling method for a pre-bending self-growing robot is provided. The pre-bending self-growing robot includes a cylindrical film with at least one annular fold structure. The annular fold structure is used to form a bending angle after the cylindrical film is inflated. The cylindrical film is divided into multiple segments by the annular fold structure. This kinematic modeling method is executed by a computer device, specifically by a computer device such as a terminal or server alone, or by both a terminal and a server. In this embodiment, the method is described using a server as an example, including the following steps 110 to 120.

[0016] Step 110: When the bending angle is less than the first angle, the relationship between the length and bending angle of the annular fold structure is described by the piecewise constant curvature model. The first angle is the critical angle at which the shape of the cavity in the cross section of the annular fold structure changes. The piecewise constant curvature model defines the shape of the cavity in the cross section of the annular fold structure as a part of a circle.

[0017] Step 120: When the bending angle is greater than the first angle and less than the second angle, the target model is used to describe the relationship between the length and bending angle of the annular fold structure. The second angle is the limit bending angle of the annular fold structure. The target model defines the hollow cavity shape in the cross-section of the annular fold structure as a semi-ellipse. The target model is as follows: in, l Indicates the length of the annular fold structure. Indicates the bending angle. r represents the radius of the cylindrical film, a This represents the major axis of the ellipse. b The minor axis of the ellipse is represented.

[0018] In the above technical solution, the relationship between the length and bending angle of the annular fold structure is modeled using a piecewise modeling strategy. At small angles, the cross-section of the annular fold structure is circular, which can be approximated using an isocurvature model; however, at large angles, considering the Brazier effect, the cross-section will buckle into an ellipse under stress. In this case, the extreme case of bending angle is considered, and a linear interpolation method is used to determine the mapping relationship between the length and bending angle of the annular fold structure. It should be noted that in this embodiment, the shape of the cross-section is the shape of the cavity enclosed by the cylindrical film in the cross-section of the annular fold structure.

[0019] Before introducing the modeling process in detail, we will first introduce the structure of the pre-bent self-growing robot by way of example, so as to illustrate the modeling process more clearly.

[0020] For example, refer to Figure 1 and Figure 2 The pre-bending self-growing robot mainly comprises a driving air source, a material storage mechanism, a self-growing robot body, a pre-bending structure, and an end effector / sensor. The self-growing robot body is a cylindrical film, and the pre-bending structure is an annular pleated structure on the cylindrical film. The cylindrical film can be made of polyethylene plastic film or nylon cloth. One end of the cylindrical film is fixedly mounted on the material storage mechanism; in the non-working state, the other end of the cylindrical film is inside and wound around the reel of the material storage mechanism. The driving air source is typically composed of an air pump or an airbag storing compressed air. The driving air source is connected to the material storage mechanism through an air tube and provides the pressure required for the growth of the cylindrical film, causing it to continuously extend outwards. When the cylindrical film is filled with gas, its end extends to a specific position.

[0021] The shape of the annular fold structure is referenced. Figure 3 Normally, without wrinkles, a tubular membrane can fully expand after inflation, forming a flat outer surface, and the membrane is in a straight line. To induce bending in the tubular membrane, a bending angle is created. A ring-shaped pleated structure can be formed on a cylindrical film. One side of the pleated structure is then fixed, preventing it from unfolding after inflation (essentially shortening the length of that side of the cylindrical film). The other side of the pleated structure is left unfixed, allowing it to unfold upon inflation. This creates a length difference between the two sides after inflation, causing the cylindrical film to bend at the pleated structure and towards the fixed side. The pleated structure can be fixed using methods such as tape, heat sealing, or latches. For example, with tape, both ends are attached to the ends of the pleated structure. Because the tape lacks elasticity, it restricts the distance between the two ends of the pleated structure, preventing it from unfolding. The length of the pleated structure is... l , through a length of l The pleated structure allows the length of the tubular film to be shortened by 2. l This causes the tubular film to be inflated and form a bending angle at the annular fold structure. Understandably, the length of the folded structure... l and bending angle A mapping relationship exists.

[0022] By implementing steps 110 and 120 above, the relationship between the length and bending angle of the annular fold structure can be established more accurately.

[0023] Reference Figure 4 It can be seen that when the bending angle is small, the cross-section at the annular fold structure is circular (radius is...). r The cross-section consists of two parts: a solid portion of thin-film-on-thin-film (below the wavy line) and a cavity portion enclosed by the thin films (above the wavy line). These two parts together form a circle, with the wavy line representing the boundary of the solid portion. A piecewise constant curvature model can be used to describe the relationship between the length and bending angle of the annular folded structure. The piecewise constant curvature model is as follows: .

[0024] Establish a coordinate system with the center of the cross-section as the origin, and satisfy the following relationship based on geometric relations. h 1= h 2 . h 1 is half the length difference between the inner and outer membranes. h 2 This represents the thickness of the solid portion within the cross-section. Where: in, α for Figure 4 The angle of ∠AOB. Figure 4 In the diagram, D and B are the intersection points of the cross section with the x-axis, C is the intersection point of the cross section with the y-axis, and E and A are the two endpoints of the boundary (wavy line) of the solid part.

[0025] Reference Figure 5 As the bending angle increases, the boundary of the solid part gradually moves closer to the x-axis. When α When the angle is 0°, that is, when the boundary of the solid part develops to the x-axis, it can be known that... h 1= r Then through h 2 The formula can be used to calculate the bending angle at this time. It is 53°.

[0026] Reference Figure 6 When the bending angle increases again, according to the Brazier effect, the boundary of the solid portion will not continue to extend upwards. Instead, as the bending angle increases, the cavity portion will become a semi-ellipse with gradually increasing eccentricity, while the total width of the cavity and solid portions remains at 2. r Therefore, in this example, the first angle is 53°.

[0027] Reference Figure 7 When bent to its limit angle, the cavity completely closes, and the semi-ellipse becomes a straight line. At this point, the cross-section consists entirely of a solid portion of thin film over thin film, and the length of line segment GH is equal to the width FH of the solid portion, i.e., GH = FH = 2. r The intersection point I of the extension of line segment FH and line segment JG is the midpoint of line segment JG, i.e., IG = r .according to Figure 7 According to geometric relations: The bending angle at this point is found to be 127°. Therefore, the second angle in this example is 127°.

[0028] When the bending angle is between 53° and 127°, assuming the major axis of the semi-ellipse is 'a' and the minor axis is 'b', the bending angle can be approximated using linear interpolation. The values ​​of a and b that are between 53° and 127°.

[0029] Then it can be based on a and bDetermine the relationship between the length and bending angle of the annular fold structure.

[0030] From the above derivation, we can see that: when the bending angle is small, the cross-section of the annular fold structure (consisting of the cavity portion enclosed by the thin film and the solid portion of the thin film-on-thin film) is circular. In this case, a piecewise constant curvature model can be used to describe the relationship between the length and bending angle of the annular fold structure. When the bending angle is large, due to the Brazier effect, the cavity portion of the cross-section of the annular fold structure changes to a semi-ellipse. In this case, a target model is used to describe the relationship between the length and bending angle of the annular fold structure. The target model is: in, l Indicates the length of the annular fold structure. Indicates the bending angle. r represents the radius of the cylindrical film, a Denotes the major axis of the semi-ellipse. b The minor axis of the semi-ellipse is represented.

[0031] In summary, this embodiment employs different models to describe the relationship between the length and bending angle of the annular folded structure under different conditions. The critical point is whether the shape of the cavity in the cross-section of the annular folded structure changes. When the bending angle is less than a first angle, the cavity shape is a portion of a circle, and a piecewise constant curvature model is used for description. When the bending angle is greater than the first angle, the cavity shape is a semi-ellipse, and a target model is used for description. Using different models at different stages allows for a more accurate description of the relationship between the length and bending angle of the annular folded structure, solving the problem of inaccurate descriptions caused by using a single model to describe the relationship in all cases in existing technologies.

[0032] In one example, one side of the annular pleated structure is bound by tape to restrict its extension, while the other side is free to extend, thus creating a bending angle. Considering that the tape has a certain width and is not an ideal line shape without width, the annular pleated structure is not simply a line whose length is fixed. l Instead, they are all fixed under a narrow surface. l That is, the length of the annular pleated structure on both sides of the tape (perpendicular to the width of the tape) is also limited. l After the equivalent transformation, the equivalent length of the annular pleated structure at the centerline of the tape (the centerline distributed along the length of the tape) is greater than... lThis equivalent length is the maximum length of the annular pleated structure after the tubular film is bent. More precisely, in this embodiment, the relationship established is between the maximum length of the annular pleated structure after the tubular film is bent and the bending angle. Under ideal conditions where the adhesive strip has no width, the length of the annular pleated structure before bending the tubular film is the maximum length of the annular pleated structure after bending. However, in practical situations, it is necessary to correct the length of the annular pleated structure before bending based on the width of the adhesive strip. Therefore, preferably, the length of the annular pleated structure... l The length of the corrected annular fold structure: in, l n This indicates the measured length of the annular folded structure (before the tubular film is bent). c This indicates the width of the adhesive surface of the tape.

[0033] It should be noted that when the width of the adhesive strip is small, the measured length of the annular pleated structure does not need to be corrected, and the measured length of the annular pleated structure is determined as the length of the annular pleated structure. l This will introduce a slight calculation error.

[0034] In this embodiment, in addition to establishing the relationship between the bending angle of the cylindrical film at the annular fold structure and the length of the annular fold structure, it is also possible to suggest the placement positions of each annular fold structure on the cylindrical film and the relationship between the bending angle at each position and the end position of the cylindrical film. Therefore, in this embodiment, the kinematic modeling method for the pre-bent self-growing robot further includes: Step 130: Under the premise of introducing passage constraints, establish a target relationship model between the end position of the cylindrical film and the number, position and bending angle of the annular fold structure; wherein, the passage constraints are used to ensure that the end mechanism of the cylindrical film can pass through the cylindrical film.

[0035] Specifically, the target relationship model is as follows: in, P x and P y These represent the x-coordinate and y-coordinate of the end position, respectively. n Indicates the number of annular folds. This represents the bending angle of the i-th annular pleated structure after inflation. L i This represents the length of the i-th segment of the tubular film after inflation.

[0036] Specifically, the passage constraints are primarily considered based on the shape of the end mechanism of the cylindrical film. For example, the end mechanism of the cylindrical film is an end-sensing / actuating mechanism, typically having two configurations.

[0037] Configuration as Figure 8 As shown in Figure a, it is located on the outer side of the thin film at the end of the self-growing robot. It mainly consists of an end cap and sensors, with the sensors mounted on the outer surface of the end cap. Optionally, it can be equipped with sensors such as cameras, force sensors, and inertial devices to provide the self-growing robot with visual, force, or attitude information. Furthermore, a gripper can be installed as the end effector of the self-growing robot. During the growth process of the self-growing robot, the thin film material flips outward, causing the end cap to grow along with it and ensuring it remains at the end of the self-growing robot.

[0038] Configuration Two Figure 8 As shown in Figure b, it is located inside the film. It mainly consists of a support, passive rollers, and sensors. There are two passive rollers, their outer surfaces coated with a high-friction material, and they are connected to the support via bearings. Simultaneously, the passive rollers are in direct contact with the tail material of the self-growing robot's film. Furthermore, the sensors are fixed to the support; electromagnetic induction or inertial devices can be selected as the sensor components. During the outward growth of the self-growing robot material, due to the high friction at the rollers, the advancing tail material drives the end effector sensing / actuator to grow along with it, ensuring it remains at the end of the self-growing robot.

[0039] In Configuration 1, the end mechanism is fitted onto the end of the cylindrical film via an end cap, moving as the end of the cylindrical film extends. When the end of the cylindrical film bends during extension, the limitation of the bending angle by the annular portion in the end cap needs to be considered. For example, if the inner diameter of the annular portion is only slightly larger than the diameter of the cylindrical film, then when the end of the cylindrical film extends at a large angle, the cylindrical film may come into contact with the inner wall of the annular portion, thus affecting the extension of the end of the cylindrical film. Therefore, the end mechanism of Configuration 1 can be considered equivalent to the outer annular mechanism.

[0040] In configuration two, the end mechanism is located inside the end of the cylindrical film. When the end of the cylindrical film extends to a large angle, the end mechanism of configuration two will abut against the inner wall of the end of the cylindrical film, thus affecting the extension of the end of the cylindrical film. Therefore, the end mechanism of configuration two can be equivalent to the inner mechanism of a rectangle.

[0041] Accordingly, the passage constraints include a first constraint to ensure the passage of the inner mechanism inside the tubular membrane and a second constraint to ensure the passage of the outer mechanism outside the tubular membrane. The first constraint includes a diameter constraint, a length constraint, and a continuous corner constraint.

[0042] Regarding diameter constraints, refer to... Figure 9 In the extreme case, the width limitation occurs just as the inner mechanism enters the cylindrical channel. At this point, it is necessary to ensure that the contact point C between the inner mechanism and the cylindrical film is above line segment BA. Under this condition, the following relationship can be obtained: Length constraints mean that the length of the inner mechanism cannot be infinitely long, such as... Figure 10 As shown, when it is in the extreme position, i.e., the rotation angle When the value is 2, it is necessary to ensure that the inner mechanism is located above line segment EF to avoid interference. At this time, the following geometric relationship exists: Continuous rotation constraint, refer to Figure 11 When a large bending angle is required for a tubular film, using a single large bending angle will prevent the inner mechanism from passing smoothly. Therefore, multiple consecutive small-angle bends are employed. However, if the spacing between consecutive bending angles is too small, the inner mechanism may still encounter obstruction. To simplify the calculation, it is assumed that adjacent bending angles have the same magnitude and direction, and that the spacing between adjacent annular fold structures is... l m for: in, d Indicates the width of the inner mechanism. D represents the diameter of the cylindrical film, Indicates the bending angle. l 0 indicates the length of the inner mechanism. l m This indicates the distance between two adjacent annular fold structures.

[0043] Reference Figure 12 The second constraint is: in, D 0 represents the inner diameter of the outer mechanism. l 1 indicates the length of the outer mechanism.

[0044] Once the dimensions of the inner or outer mechanism are determined, the design of the number, position, and bending angle of the annular fold structure can be constrained by the first or second constraint.

[0045] Reference Figure 13 In the target relationship model, a section of cylindrical film can be regarded as a connecting rod, and a ring-shaped folded structure can be regarded as a joint. L i This represents the length of the i-th segment of the tubular film, which is also the length of the i-th link. For accurate calculation,L i This should be the inner length of the i-th segment of the tubular film after inflation, but this distance is often impossible to measure beforehand. A more convenient and direct measurement is the length of the i-th segment of the tubular film before inflation, which is also the midpoint distance between the annular pleats at both ends of the i-th segment. However, as the annular pleats bend, both the inner and outer lengths of the i-th segment of the tubular film change; the inner side is compressed, and the outer side is stretched. This results in the inner length of the i-th segment of the tubular film before and after inflation not being the same as the length before inflation. Therefore, it is necessary to correct the length of the i-th segment of the tubular film before inflation to obtain the inner length of the i-th segment of the tubular film after inflation. Therefore, preferably, the length of the i-th segment of the tubular film after inflation is: in, a i This represents the length of the i-th segment of the tubular film before inflation.

[0046] In summary, this is an example illustrating the kinematic modeling method for the pre-bending self-growing robot in this embodiment.

[0047] In one exemplary embodiment, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0048] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0049] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0050] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0051] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0052] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0053] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0054] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A kinematic modeling method for a pre-bent self-growing robot, the pre-bent self-growing robot comprising a cylindrical film, the cylindrical film having at least one annular fold structure, the annular fold structure being used to form a bending angle after the cylindrical film is inflated, the cylindrical film being divided into multiple segments by the annular fold structure; Its features are, The kinematic modeling methods include: When the bending angle is less than 53°, a piecewise constant curvature model is used to describe the relationship between the length of the annular fold structure and the bending angle. The piecewise constant curvature model defines the cavity shape in the cross-section of the annular fold structure as a part of a circle. When the bending angle is greater than 53° and less than 127°, a target model is used to describe the relationship between the length of the annular fold structure and the bending angle. The target model defines the hollow shape of the cross-section of the annular fold structure as a semi-ellipse. The target model is as follows: in, l This indicates the length of the annular pleated structure. Indicates the bending angle, r This represents the radius of the cylindrical film. a Denotes the major axis of the semi-ellipse. b The minor axis of the semi-ellipse is represented.

2. The kinematic modeling method for a pre-bending self-growing robot according to claim 1, characterized in that, The piecewise constant curvature model is as follows: 。 3. The kinematic modeling method for a pre-bending self-growing robot according to claim 1 or 2, characterized in that, One side of the annular pleated structure is restricted from stretching by adhesive tape, while the other side can stretch freely, thereby forming the bending angle. The length of the annular pleated structure l The corrected length of the annular pleated structure: in, l n This indicates the measured length of the annular fold structure. c This indicates the width of the adhesive surface of the tape.

4. The kinematic modeling method for a pre-bending self-growing robot according to claim 1, characterized in that, Also includes: Under the premise of introducing passage constraints, a target relationship model is established between the end position of the tubular film and the number and position of the annular pleated structures and the bending angle; wherein, the passage constraints are used to ensure that the end mechanism of the tubular film can pass through the tubular film.

5. The kinematic modeling method for a pre-bending self-growing robot according to claim 4, characterized in that, The end mechanism includes a rectangular inner mechanism and a ring-shaped outer mechanism; The passage constraints include a first constraint to ensure the passage of the inner mechanism inside the tubular film and a second constraint to ensure the passage of the outer mechanism outside the tubular film. The first constraint includes diameter constraint, length constraint, and continuous rotation angle constraint; The diameter constraint is: The length constraint is: The continuous rotation angle constraint is: in, d This indicates the width of the inner mechanism. D This indicates the diameter of the tubular film. Indicates the bending angle, l 0 represents the length of the inner mechanism. l m This indicates the distance between two adjacent annular fold structures; The second constraint is: in, D 0 represents the inner diameter of the outer mechanism. l 1 represents the length of the outer mechanism.

6. The kinematic modeling method for a pre-bending self-growing robot according to claim 4, characterized in that, The target relationship model is as follows: in, P x and P y The x and y coordinates of the end position are respectively represented. n This indicates the number of the annular fold structures. This represents the bending angle of the i-th annular pleated structure after inflation. L i This indicates the length of the tubular film in the i-th segment after inflation.

7. The kinematic modeling method for a pre-bending self-growing robot according to claim 6, characterized in that, The length of the tubular film in the i-th segment after inflation is: in, a i This indicates the length of the tubular film in the i-th segment before inflation.

8. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the kinematic modeling method for a pre-bending self-growing robot according to any one of claims 1-7.

9. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the kinematic modeling method for the pre-bending self-growing robot as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the kinematic modeling method for the pre-bending self-growing robot as described in any one of claims 1-7.

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