Method and device for shape control of a soft arm under gravity and external load in an aqueous environment

Abstract

The application provides a shape control method and device of a soft arm under gravity and external load in a water environment, which is mathematical modeling analysis on the shape of the soft arm under gravity or other external force conditions, first establishes a geometric model of the soft arm based on fiber binding, then calculates the posture or curvature of the soft arm in the force-free state through the maximum volume method and the virtual work principle, and takes the curvature as the boundary condition for solving the Euler-Bernoulli beam second-order ordinary differential equation, and further analyzes the posture of the soft arm under gravity or external force when driven by a specific internal cavity pressure in the water environment, and further calculates the internal cavity pressure required for the specified posture through the shooting method, so as to realize the accurate control of the fiber woven soft arm in the water environment.

Description

Technical Field

[0001] The present invention relates to the technical field of soft arm control, and in particular to a method and device for controlling the shape of a soft arm under gravity and external load in an aquatic environment. Background Art

[0002] The bionic soft arm primarily uses wrapping to achieve damage-free deployment and retrieval of underwater communication nodes, greatly facilitating node deployment. Compared to rigid robotic arms, soft arms are made of inexpensive soft materials, resulting in high energy density, high flexibility, and unlimited degrees of freedom. Therefore, they have great potential for exploration in complex terrain, medical surgery, safe human-machine interaction, and non-destructive grasping of objects, while also making human-machine interaction safer.

[0003] Currently, the main driving methods for soft arms include fluid drive, wire drive, shape memory alloy drive, electroactive polymer drive, and hybrid drive. Among them, fluid drive includes pneumatic drive. Depending on the structure, pneumatic drive soft arms also include fiber braided, spiral, grid, origami, and special types.

[0004] Fiber-braided arms primarily involve wrapping fibers around or embedding them in an elastic cavity. When the cavity is inflated, it expands both longitudinally and transversely, causing deformation. When using fiber-braided soft arms for specific tasks, existing control methods are computationally complex and prone to non-convergence issues. For precise control, an accurate and streamlined control method for fiber-braided soft arms is required. Summary of the Invention

[0005] In view of this, an embodiment of the present invention provides a method and device for controlling the shape of a soft arm under gravity and external loads in an aqueous environment, so as to eliminate or improve one or more defects existing in the prior art and solve the problem that the prior art lacks a streamlined control method for fiber-woven soft arms.

[0006] The technical solutions of the present invention are as follows:

[0007] In one aspect, the present invention provides a method for controlling the shape of a soft arm under gravity and external load in an aquatic environment, comprising:

[0008] A morphological analysis model of the soft arm under fiber constraint in a water environment is obtained, wherein the morphological analysis model establishes an elongation model under a preset fiber line winding angle, and uses a preset material property model to constrain the axial expansion ratio and the radial expansion ratio; based on the maximum volume method and virtual work theory, the axial expansion ratio and the radial expansion ratio are solved according to the shape parameters of the soft arm and the inner cavity pressure, and the curvature of the end of the soft arm is calculated to obtain the boundary conditions; under a set force state, the position and posture of the soft arm are calculated according to the boundary conditions using the Euler-Bernoulli beam equation;

[0009] Obtaining the morphological parameters, target force state parameters, and target posture parameters of the soft arm in a specified application scenario, and calculating the target intracavity pressure required to be input for the soft arm under the target force state parameters and target posture parameters using a shooting method based on the morphological analysis model; the morphological parameters include the initial length and cross-sectional area of ​​the soft arm; the target force state parameters include the position of the force point, the force direction, and the force magnitude;

[0010] The target inner cavity pressure is input to the soft arm.

[0011] In some embodiments, the preset fiber winding angle is greater than 54.73 degrees, and the elongation model is:

[0012] λ1 2 (cosψ) 2 +λ2 2 (sinψ) 2 =1;

[0013] Wherein, λ1 represents the axial expansion ratio, λ2 represents the radial expansion ratio, and ψ represents the preset fiber winding angle.

[0014] In some embodiments, the preset material property model adopts an incompressible material property model, which is expressed as:

[0015] W=C 10 (I-3);

[0016]

[0017] Where W represents the strain energy density, C 10 The constant parameters related to the material of the soft arm, I is the first invariant of the Cauchy-Green strain tensor, and λ3 represents the circumferential shear amount.

[0018] In some embodiments, the axial expansion ratio and the radial expansion ratio are solved based on the shape parameters of the soft arm and the inner cavity pressure based on the maximum volume method and the virtual work theory, and the curvature of the end of the soft arm is calculated to obtain the boundary conditions, including:

[0019] Establish the basic model of maximizing volume, the expression is:

[0020]

[0021] Wherein, V represents the volume of the soft arm, A represents the cross-sectional area, and L * represents the length of the soft arm after deformation, r0 represents the initial inner diameter of the soft arm, λ1 represents the axial expansion ratio, and λ2 represents the radial expansion ratio;

[0022] According to the virtual work theory, a virtual work theoretical model is established, and the expression is:

[0023]

[0024]

[0025] Wherein, V represents the volume of the soft arm, W represents the strain energy density, P represents the inner cavity pressure of the soft arm, λ1 represents the axial expansion ratio, λ2 represents the radial expansion ratio, Indicates partial derivative;

[0026] The axial expansion ratio and the radial expansion ratio are solved according to the elongation model and the virtual work theory model, and the end curvature of the soft arm is calculated. The expression is:

[0027]

[0028] Wherein, R represents the curvature radius of the end of the soft arm, λ1 represents the axial expansion ratio, λ2 represents the radial expansion ratio, and r t represents the wall thickness of the soft arm, r represents the inner diameter of the soft arm after deformation, and r0 represents the initial inner diameter of the soft arm.

[0029] In some embodiments, under a set force state, the position and posture of the soft arm are calculated using the Euler-Bernoulli beam equation according to the boundary conditions, wherein the static model expression of the soft arm under the action of gravity alone is:

[0030]

[0031] The static model expression under the force condition at the end of the soft arm is:

[0032]

[0033] G=(ρ g -ρ w )Vg;

[0034]

[0035]

[0036]

[0037] Where EI is the stiffness parameter of the soft arm, θ(s) represents the angle between the tangent and the horizontal direction at a distance s from the end of the soft arm, θ′(s) represents the first derivative of θ(s), G represents the force state of the soft arm in the water environment, and ρ w represents the density of water, ρ g represents the material density of the soft arm, and q represents the load per unit length.

[0038] In some embodiments, after inputting the target intracavity pressure to the soft arm, the method further includes:

[0039] The actual posture parameters of the software arm after inputting the target inner cavity pressure are obtained, and the actual posture parameters are compared with the target posture parameters. When the deviation is higher than the set value, an alarm prompt message is issued.

[0040] In some embodiments, the method further includes: obtaining the actual posture parameters and the target posture parameters, and adding them to a control log.

[0041] In some embodiments, the method further comprises:

[0042] Calculating a control error rate based on the multiple target posture parameters recorded in the control log and their corresponding actual posture parameters;

[0043] When the control error rate is higher than a set value, a correction amount is added to the morphological analysis model according to the control error rate.

[0044] On the other hand, the present invention also includes an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the program.

[0045] On the other hand, the present invention also includes a computer-readable storage medium having a computer program stored thereon, which implements the steps of the above method when executed by a processor.

[0046] The beneficial effects of the present invention are at least:

[0047] In the method and device for morphological control of a soft arm under gravity and external loads in an aqueous environment described in the present invention, mathematical modeling and analysis are performed on the shape of the soft arm under gravity or other external force conditions. First, a geometric model of the soft arm based on fiber constraint is established, and then the posture or curvature of the soft arm in a non-stressed state is calculated by maximizing the volume method and the principle of virtual work. The curvature is used as the boundary condition for solving the second-order ordinary differential equation of the Euler Bernoulli beam, and then the posture of the soft arm itself under the action of gravity or external force when driven by a specific inner cavity pressure in the aqueous environment is analyzed. The inner cavity pressure required for the specified posture is further calculated by the shooting method, thereby achieving precise control of the fiber-braided soft arm in the aqueous environment.

[0048] Additional advantages, objects, and features of the present invention will be set forth in part in the following description and will in part become apparent to those skilled in the art upon examination of the following or may be learned by practice of the present invention. The objects and other advantages of the present invention may be realized and attained by the structure particularly pointed out in the written description and claims thereof as well as in the accompanying drawings.

[0049] Those skilled in the art will understand that the purposes and advantages that can be achieved by the present invention are not limited to the above specific descriptions, and the above and other purposes that can be achieved by the present invention will be more clearly understood based on the following detailed description. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] The drawings described herein are used to provide a further understanding of the present invention, constitute a part of this application, and do not constitute a limitation of the present invention. In the drawings:

[0051] Figure 1 Schematic diagram of a flow chart of a method for controlling the shape of a soft arm under gravity and external loads in an aqueous environment according to an embodiment of the present invention.

[0052] Figure 2 This is a logical diagram of a morphological analysis model in a morphological control method of a soft arm under gravity and external loads in an aqueous environment according to an embodiment of the present invention.

[0053] Figure 3 (a) and Figure 3 (b) Schematic diagram of the force analysis of the soft arm in a water environment under the action of gravity alone.

[0054] Figure 3 (c) and Figure 3 (d) Schematic diagram of force analysis of the soft arm in a water environment under the action of gravity and external forces F1 and F2.

[0055] Figure 4 Comparison between model predictions and experimental results when changing the input pressure to maintain the end load weight.

[0056] Figure 5 Comparison between model predictions and experimental results when the end load is varied to maintain the input pressure constant.

[0057] Figure 6 A comparison between the model prediction and experimental results when the load is applied to the middle part of the soft arm and the input pressure is changed. DETAILED DESCRIPTION

[0058] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments and the accompanying drawings. Here, the exemplary embodiments of the present invention and their descriptions are used to explain the present invention, but are not intended to limit the present invention.

[0059] It should also be noted that, in order to avoid obscuring the present invention due to unnecessary details, the accompanying drawings only show structures and / or processing steps closely related to the solutions according to the present invention, while other details that are not closely related to the present invention are omitted.

[0060] It should be emphasized that the term "include / comprises" when used herein refers to the existence of features, elements, steps or components, but does not exclude the existence or addition of one or more other features, elements, steps or components.

[0061] It should also be noted that, unless otherwise specified, the term "connection" herein may refer not only to a direct connection but also to an indirect connection involving an intermediate.

[0062] Existing technologies present significant difficulties and challenges in accurately modeling soft arms, as they are made of hyperelastic materials (such as silicone), which exhibit significant deformation and nonlinear properties. Current modeling methods for soft arms can be broadly categorized into two main categories: those that ignore external forces and those that consider them. Modeling methods that ignore external forces primarily include constant curvature or piecewise constant curvature models; these methods are fast but lack accuracy. Modeling methods that consider external forces primarily include Cosserat rods theory, Kane's method, and absolute coordinate system modeling. However, these methods are complex to implement and prone to non-convergence. Due to the low accuracy and complexity of soft arm modeling, a simple, highly accurate, and easily implemented modeling algorithm is needed to effectively predict the deformation of soft arms under their own gravity and other external forces.

[0063] The present invention provides a method for controlling the shape of a fiber-woven soft arm driven by air pressure under gravity and external load in a water environment, such as Figure 1 As shown, it includes steps S101 to S103:

[0064] Step S101: Refer to Figure 2 , obtain the morphological analysis model of the soft arm under fiber constraint in the water environment, the morphological analysis model establishes an elongation model under the preset fiber line winding angle, and uses the preset material property model to constrain the axial expansion ratio and radial expansion ratio; based on the maximum volume method and virtual work theory, the axial expansion ratio and radial expansion ratio are solved according to the shape parameters of the soft arm and the inner cavity pressure, and the curvature of the end of the soft arm is calculated to obtain the boundary conditions; under the set force state, the Euler Bernoulli beam equation is used to calculate the position and posture of the soft arm according to the boundary conditions.

[0065] Step S102: Obtain the morphological parameters, target force state parameters, and target posture parameters of the soft arm in a specified application scenario. Using the target shooting method based on the morphological analysis model, the target intracavity pressure required for the soft arm under these target force state parameters and target posture parameters is calculated. The morphological parameters include the soft arm's initial length and cross-sectional area; the target force state parameters include the position, direction, and magnitude of the force applied to the soft arm.

[0066] Step S103: inputting the target inner cavity pressure to the soft arm.

[0067] In this embodiment, in order to simplify the calculation complexity while ensuring the control accuracy, two assumptions are put forward. The first is that the material of the soft arm is isotropic and incompressible. The second is that the stiffness of the fiber line used to wrap the soft arm is much greater than the stiffness of the silicone material. It is assumed that the fiber line wrapped around the soft arm is incompressible.

[0068] Based on these two assumptions, we can predict the effect of the fiber winding angle on the morphology of the soft arm. Specifically, when the fiber winding angle is greater than 54.73 degrees, the soft arm is in an elongation model under excitation, extending axially and shortening radially. When the fiber winding angle is less than 54.73 degrees, the soft arm is in a contraction model, shortening in length and expanding radially under excitation. When the fiber winding angle is equal to 54.73 degrees, the soft arm's morphology does not change under excitation, neither axially nor radially, a state known as self-locking.

[0069] In step S101 of this embodiment, an elongation model of the soft arm is established under a preset fiber winding angle, wherein the preset fiber winding angle can be 85 degrees. Under this condition, the soft arm is an elongation model, and when excited, it will elongate axially and shorten radially. Because the material is incompressible, this embodiment uses the Neo-Hookean Model as the material property model. This model is applicable to soft arms with deformations less than 50%, which meets the applicable conditions of this patent.

[0070] Specifically, since the preset fiber winding angle is greater than 54.73 degrees, the elongation model is:

[0071] λ1 2 (cosψ) 2 +λ2 2 (sinψ) 2 =1; (1)

[0072] Wherein, λ1 represents the axial expansion ratio, λ2 represents the radial expansion ratio, and ψ represents the preset fiber winding angle.

[0073] In some embodiments, the preset material property model adopts an incompressible material property model, which is expressed as:

[0074] W=C 10 (I-3); (2)

[0075]

[0076] Where W represents the strain energy density, C 10 The constant parameters related to the soft arm material, I is the first invariant of the Cauchy-Green strain tensor, and λ3 represents the circumferential shear.

[0077] In some embodiments, the axial expansion ratio and radial expansion ratio are solved based on the shape parameters of the soft arm and the inner cavity pressure based on the maximum volume method and virtual work theory, and the curvature of the soft arm end is calculated to obtain the boundary conditions, including:

[0078] Establish the basic model of maximizing volume, the expression is:

[0079]

[0080] Among them, V represents the volume of the soft arm, A represents the cross-sectional area, and L * represents the length of the soft arm after deformation, r0 represents the initial inner diameter of the soft arm, λ1 represents the axial expansion ratio, and λ2 represents the radial expansion ratio.

[0081] According to the virtual work theory, a virtual work theoretical model is established, and the expression is:

[0082]

[0083]

[0084] Where V represents the volume of the soft arm, W represents the strain energy density, P represents the inner cavity pressure of the soft arm, λ1 represents the axial expansion ratio, and λ2 represents the radial expansion ratio. It means partial derivative.

[0085] The axial expansion ratio and the radial expansion ratio are solved according to the elongation model and the virtual work theory model, and the end curvature of the soft arm is calculated. Specifically, according to equations 1 to 6, the expression for the end curvature of the soft arm can be calculated as follows:

[0086]

[0087] Among them, R represents the curvature radius of the soft arm end, λ1 represents the axial expansion ratio, λ2 represents the radial expansion ratio, and r t Represents the wall thickness of the soft arm, r represents the inner diameter of the soft arm after deformation, and r0 represents the initial inner diameter of the soft arm.

[0088] The Euler–Bernoulli beam theory is a key equation in engineering mechanics and classical beam mechanics. It is a simplified linear elastic theory used to calculate the forces and deformation characteristics of beams. This example uses the radius of curvature of the soft arm's end calculated in Equation 7 to calculate boundary conditions. Substituting this into the Euler–Bernoulli beam theory allows the calculation of the soft arm's position and state.

[0089] In some embodiments, under a set force state, the position of the soft arm is calculated using the Euler-Bernoulli beam equation according to the boundary conditions, wherein the static model expression of the soft arm under the action of gravity alone is:

[0090]

[0091] The static model expression under the force condition at the end of the soft arm is:

[0092]

[0093] G=(ρ g -ρ w )Vg; (10)

[0094]

[0095]

[0096]

[0097] Where EI is the stiffness parameter of the soft arm, θ(s) represents the angle between the tangent and the horizontal direction at a distance s from the end of the soft arm, θ′(s) represents the first-order derivative of θ(s), G represents the force state of the soft arm in the water environment, and ρ w represents the density of water, ρ g represents the material density of the soft arm, and q represents the load per unit length.

[0098] In step S102, based on the morphological analysis model established in step S101, the target intracavity pressure that needs to be input is calculated using the shooting method. For a specific operation task, the final force condition and posture state of the soft arm are known. For example, when the end of the soft arm is used to hoist a specified communication node, the size, direction and position of the acceptance are all determined. Based on the known material, initial shape and fiber winding method of the soft arm, the final form that the soft arm needs to achieve in order to complete the task under a specified task can be predicted. Therefore, the shooting method can be used to calculate the target intracavity pressure that needs to be input for a known soft arm to reach a specified posture under a specified acceptance state.

[0099] In step S103, the soft arm is inflated according to the target inner cavity pressure obtained in step S102 so that it can accurately complete the control task.

[0100] In some embodiments, after step S103, that is, after the target intracavity pressure is input to the software arm, it also includes: obtaining the actual posture parameters of the software arm after the target intracavity pressure is input, comparing the actual posture parameters with the target posture parameters, and issuing an alarm prompt message when the deviation is higher than the set value.

[0101] In some embodiments, the method further includes: obtaining actual posture parameters and target posture parameters, and adding them to a control log.

[0102] In some embodiments, the method further includes: calculating a control error rate based on multiple target posture parameters recorded in the control log and their corresponding actual posture parameters; when the control error rate is higher than a set value, adding a correction to the morphological analysis model based on the control error rate.

[0103] On the other hand, the present invention also includes an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the program.

[0104] On the other hand, the present invention also includes a computer-readable storage medium having a computer program stored thereon, which implements the steps of the above method when executed by a processor.

[0105] The morphological analysis model of the present invention is described below with reference to a specific embodiment:

[0106] This example provides a morphological analysis model for a fiber-constrained soft arm in a water environment. This model predicts the shape of the soft arm based on the maximum volume method, the principle of virtual work, and the Euler-Bernoulli beam theory. The specific process includes steps 1 to 4:

[0107] Step 1: Establish a geometric model based on the fiber binding layer and select the material property model.

[0108] Step 2: Derivation of the shape change of the soft arm under zero-gravity conditions, using the maximum volume method and the principle of virtual work to solve the curvature and other parameters of the soft arm.

[0109] Step 3: Establish the second-order ordinary differential equation of the Euler-Bernoulli beam of the water-driven soft arm under external forces in different directions.

[0110] Step 4: Substitute the curvature parameter obtained in step 2 into the second-order ordinary differential equation in step 3 as a boundary condition to analyze the influence of external force on the soft arm and obtain the posture state of the soft arm; integrate and solve the obtained posture state, and finally obtain the shape of the soft arm under the influence of external force.

[0111] Specifically, in step 1, a geometric model based on the fiber-bound layer is established, and a material property model is selected. The geometric model of the morphological changes of the soft arm under fiber-bound conditions can be found in Equation 1. This equation requires the following assumptions: 1) The soft arm material is isotropic and the main body material is incompressible. 2) The fiber strands are much stiffer than the silicone material, assuming they are inextensible.

[0112] These two assumptions can be used to predict the effect of the fiber winding angle on the morphology of the soft arm. For example, if the fiber winding angle is greater than 54.73 degrees, the soft arm will be in an elongation model under excitation, extending axially and shortening radially. If it is less than 54.73 degrees, the soft arm will be in a contraction model, shortening in length and expanding radially under excitation. If it is equal to 54.73 degrees, the soft arm's morphology will not change under excitation, neither axially nor radially, resulting in a self-locking state.

[0113] In this example, the fiber winding angle is set at 85 degrees, meaning the soft arm's morphology changes to an elongation model. Because the material is incompressible, the Neo-Hookean model is used as the material property model. Referring to Equations 2 and 3 above, this model is applicable when the soft arm's deformation is less than 50%, meeting the requirements of this example.

[0114] In step 2, the shape change of the soft arm under zero-gravity conditions is derived, and the parameters such as the curvature of the end of the soft arm are solved using the maximum volume method and the principle of virtual work.

[0115] The maximum volume method and the principle of virtual work are used to solve the process of the soft arm shape changing with the pressure of the inner cavity. Referring to the above formula 4, it is the basic model of maximum volume.

[0116] Refer to the above formulas 2 and 3 for the incompressible material property model (Neo-Hookean Model), W is the strain energy density, C 10is a constant that can be fitted through experiments. In the above formula (3), I is the first invariant of the Cauchy-Green strain tensor.

[0117] The axial extension and radial contraction of the soft arm can be calculated using the principle of virtual work (Formula 5), ​​where P represents the pressure inside the soft arm. Then, the curvature k of the end of the soft arm can be calculated using Formula 7, R is the radius of curvature, and r is the radius of curvature. t Represents the wall thickness of the soft body arm. Note that this solution does not take gravity and external forces into account.

[0118] In step 3, the second-order ordinary differential equation of the Euler-Bernoulli beam of the water-driven soft arm under the conditions of external forces in different directions is established; Figure 3 According to the different force forms and force directions, the corresponding Euler-Bernoulli beam second-order ordinary differential equations were established. Figure 3 (a) and Figure 3 (b) is a schematic diagram of the force analysis of the soft arm in water environment under the action of gravity only. Figure 3 (c) and Figure 3 (d) Schematic diagram of force analysis of the soft arm in a water environment under the action of gravity and external forces F1 and F2.

[0119] Refer to formulas 10 and 11 above, Figure 3 (a) and Figure 3 (b) shows the static model of the soft arm under its own gravity. EI is the stiffness parameter of the soft arm, which can be obtained by fitting the value through experiments. θ(s) represents the angle between the horizontal plane and the tangent of the soft arm, and θ0(s) represents the angle between the tangent of the soft arm end and the horizontal direction. q represents the load per unit length, and s represents the arc length. The density of water ρ w Equal to 997kg / m3, through actual measurement of the density ρ of the silica gel model used g 1108kg / m3. Figure 3 (c) and Figure 3 (d) When the force is in the middle part, the soft arm is divided into two parts. θ1(s) represents the angle between the tangent and the horizontal direction at a distance s from the end of the soft arm in the first part. θ2(s) represents the angle between the tangent and the horizontal direction at a distance s from the end of the soft arm in the second part. F1 and F2 are external forces in different directions on the soft arm. The static model under the conditions that the soft arm is subjected to its own gravity and external forces in other directions can refer to the above equations 8 and 9.

[0120] Step 4: Substitute the curvature parameter obtained in step 2 into the second-order ordinary differential equation in step 3 as a boundary condition to analyze the influence of external force on the soft arm and obtain the posture state of the soft arm;

[0121] Equations 12 and 13 above are the boundary conditions for the second-order ordinary differential equation for the Euler-Bernoulli beam. Substituting these into equations 8 and 9 above, the position of the soft arm can be obtained through integration.

[0122] Furthermore, model verification experiments were carried out by changing the input pressure value under the conditions of gravity and fixed external force.

[0123] The algorithm in this embodiment requires the following devices: a soft arm, a water-displacement device, and its water tank. The auxiliary verification equipment consists of a high-definition camera, a calibrated chessboard, and additional load weights. The soft arm is the object being measured, while the water-displacement device injects water into the arm to precisely control the pressure. The high-definition camera records how the arm's shape changes with input pressure, and the chessboard measures the scale of the camera's pixels.

[0124] The model algorithm of this embodiment was verified through experiments under the conditions that the soft arm was subjected to its own gravity and a fixed external force.

[0125] Before conducting the experiment, it is necessary to fit the value of the stiffness parameter EI of the soft arm through multiple sets of experiments. The fitting method is to hang a weight of known mass at the end of the soft arm, set the pressure in the input soft arm cavity to be constant, change the weights of different masses, and use a high-definition camera to record and process the shape of the soft arm. Finally, use formula 8 or 9 to make a prediction and compare it with the actual soft arm shape until a set of parameters is found to make the model data and the actual data fit accurately. The acceptable error rate can be set to 0.5%. In this embodiment, the measured stiffness value is 0.011Pa.m at a fixed input pressure of 66kpa. 4 .

[0126] pass Figure 4 It can be seen that the error rate of the model proposed in this embodiment is between 3.96% and 9.75%. The time taken to solve the ordinary differential equation is 0.013 seconds.

[0127] Furthermore, a model verification experiment was conducted by varying the external force value and fixing the input pressure. In this model verification, the pressure value in the cavity was fixed at 90 kPa, and the validity of the model proposed in this embodiment was verified by varying the mass of the end weight from 5 grams to 30 grams.

[0128] pass Figure 5 It can be seen that the error rate of the model proposed in this embodiment is between 3.09% and 4.98%. The time taken to solve the ordinary differential equation is the same as that of the first experiment.

[0129] Furthermore, an external force was applied to the middle part of the soft arm, and model verification experiments were carried out by changing the input pressure.

[0130] In this model verification, a 40-gram load was applied to the middle part of the soft arm instead of the end, and the input pressure was changed between 50 and 100 kPa to verify the effectiveness of the model proposed in this patent.

[0131] pass Figure 6 It can be seen that the error rate of the model proposed in this embodiment is between 3.05% and 8.72%. The time taken by the model to solve the ordinary differential equation is 0.035s.

[0132] Based on the morphological analysis model constructed in this embodiment, a target shooting method is used to reversely solve the target intracavity pressure input based on the soft arm's morphological parameters, target force state parameters, and target posture parameters. The morphological parameters include the soft arm's initial length and cross-sectional area; the target force state parameters include the position, direction, and magnitude of the force applied to the soft arm. The target posture parameters represent the desired target shape.

[0133] In summary, the method and device for morphological control of a soft arm under gravity and external loads in an aqueous environment described in the present invention perform mathematical modeling and analysis on the shape of the soft arm under gravity or other external force conditions. First, a geometric model of the soft arm based on fiber constraint is established, and then the posture or curvature of the soft arm in a non-stressed state is calculated by maximizing the volume method and the principle of virtual work, and the curvature is used as the boundary condition for solving the second-order ordinary differential equation of the Euler Bernoulli beam. Then, when driven by a specific inner cavity pressure in an aqueous environment, the posture of the soft arm itself under the action of gravity or external force is analyzed, and the inner cavity pressure required for the specified posture is further calculated by the shooting method, thereby realizing precise control of the fiber-braided soft arm in an aqueous environment.

[0134] Those skilled in the art will appreciate that the various exemplary components, systems, and methods described in conjunction with the embodiments disclosed herein can be implemented in hardware, software, or a combination of both. Whether hardware or software is used depends on the specific application and design constraints of the technical solution. Professionals and technicians may use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of the present invention. When implemented in hardware, it may be, for example, an electronic circuit, an application-specific integrated circuit (ASIC), appropriate firmware, a plug-in, a function card, etc. When implemented in software, the elements of the present invention are programs or code segments used to perform the required tasks. The program or code segment may be stored in a machine-readable medium or transmitted over a transmission medium or communication link via a data signal carried in a carrier wave. "Machine-readable medium" may include any medium capable of storing or transmitting information. Examples of machine-readable media include electronic circuits, semiconductor memory devices, ROM, flash memory, erasable ROM (EROM), floppy disks, CD-ROMs, optical disks, hard disks, fiber optic media, radio frequency (RF) links, etc. The code segments may be downloaded via a computer network such as the Internet or an intranet.

[0135] It should also be noted that the exemplary embodiments described herein describe methods or systems based on a series of steps or devices. However, the present invention is not limited to the order of the steps described above. In other words, the steps may be performed in the order described in the embodiments, or in a different order, or several steps may be performed simultaneously.

[0136] In the present invention, features described and / or illustrated for one embodiment may be used in the same or similar manner in one or more other embodiments, and / or combined with or replace features of other embodiments.

[0137] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A method for controlling the shape of a soft arm under gravity and external load in an aqueous environment, characterized in that: include: A morphological analysis model of the soft arm under fiber constraint in a water environment is obtained, wherein the morphological analysis model establishes an elongation model under a preset fiber line winding angle, and uses a preset material property model to constrain the axial expansion ratio and the radial expansion ratio; based on the maximum volume method and virtual work theory, the axial expansion ratio and the radial expansion ratio are solved according to the shape parameters of the soft arm and the inner cavity pressure, and the curvature of the end of the soft arm is calculated to obtain the boundary conditions; under a set force state, the position and posture of the soft arm are calculated according to the boundary conditions using the Euler-Bernoulli beam equation; Obtaining the morphological parameters, target force state parameters, and target posture parameters of the soft arm in a specified application scenario, and calculating the target intracavity pressure required to be input by the soft arm under the target force state parameters and target posture parameters using a shooting method according to the morphological analysis model; The morphological parameters include the initial length and cross-sectional area of ​​the soft arm; the target force state parameters include the force point position, force direction and force magnitude of the soft arm; The target inner cavity pressure is input to the soft arm.

2. The method for controlling the shape of a soft arm under gravity and external load in an underwater environment according to claim 1, characterized in that: The preset fiber winding angle is greater than 54.73 degrees, and the elongation model is: λ1 2 (cosψ) 2 +λ2 2 (sinψ) 2 =1; Wherein, λ1 represents the axial expansion ratio, λ2 represents the radial expansion ratio, and ψ represents the preset fiber winding angle.

3. The method for controlling the shape of a soft arm under gravity and external load in an underwater environment according to claim 2, characterized in that: The preset material property model adopts an incompressible material property model, and the expression is: W=C 10 (I-3); Where W represents the strain energy density, C 10 The constant parameters related to the material of the soft arm, I is the first invariant of the Cauchy-Green strain tensor, and λ3 represents the circumferential shear amount.

4. The method for controlling the shape of a soft arm under gravity and external load in an underwater environment according to claim 3, characterized in that: Based on the maximum volume method and the virtual work theory, the axial expansion ratio and the radial expansion ratio are solved according to the shape parameters of the soft arm and the inner cavity pressure, and the curvature of the end of the soft arm is calculated to obtain the boundary conditions, including: Establish the basic model of maximizing volume, the expression is: Wherein, V represents the volume of the soft arm, A represents the cross-sectional area, and L * represents the length of the soft arm after deformation, r0 represents the initial inner diameter of the soft arm, λ1 represents the axial expansion ratio, and λ2 represents the radial expansion ratio; According to the virtual work theory, a virtual work theoretical model is established, and the expression is: Wherein, V represents the volume of the soft arm, W represents the strain energy density, P represents the inner cavity pressure of the soft arm, λ1 represents the axial expansion ratio, λ2 represents the radial expansion ratio, Indicates partial derivative; The axial expansion ratio and the radial expansion ratio are solved according to the elongation model and the virtual work theory model, and the end curvature of the soft arm is calculated. The expression is: Wherein, R represents the curvature radius of the end of the soft arm, λ1 represents the axial expansion ratio, λ2 represents the radial expansion ratio, and r t represents the wall thickness of the soft arm, r represents the inner diameter of the soft arm after deformation, and r0 represents the initial inner diameter of the soft arm.

5. The method for controlling the shape of a soft arm under gravity and external load in an underwater environment according to claim 4, characterized in that: Under the set force state, the position and posture of the soft arm are calculated using the Euler-Bernoulli beam equation according to the boundary conditions, wherein the static model expression of the soft arm under the action of gravity alone is: The static model expression under the force condition at the end of the soft arm is: G=(ρ g -r w )Vg; Where EI is the stiffness parameter of the soft arm, θ(s) represents the angle between the tangent and the horizontal direction at a distance s from the end of the soft arm, θ′(s) represents the first derivative of θ(s), G represents the force state of the soft arm in the water environment, and ρ w represents the density of water, ρ g represents the material density of the soft arm, and q represents the load per unit length.

6. The method for controlling the shape of a soft arm under gravity and external load in an underwater environment according to claim 5, characterized in that: After inputting the target inner cavity pressure to the soft arm, the method further includes: The actual posture parameters of the software arm after inputting the target inner cavity pressure are obtained, and the actual posture parameters are compared with the target posture parameters. When the deviation is higher than the set value, an alarm prompt message is issued.

7. The method for controlling the shape of a soft arm under gravity and external load in an underwater environment according to claim 6, characterized in that: The method further comprises: Obtain the actual pose parameters and the target pose parameters, and add them to the control log.

8. The method for controlling the shape of a soft arm under gravity and external load in an underwater environment according to claim 7, characterized in that: The method further comprises: Calculating a control error rate based on the multiple target posture parameters recorded in the control log and their corresponding actual posture parameters; When the control error rate is higher than a set value, a correction amount is added to the morphological analysis model according to the control error rate.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the method according to any one of claims 1 to 8 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

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