Length self-sensing method of high polymer twisted and rolled artificial muscle based on coil structure

Abstract

The invention discloses a coil structure-based length self-sensing method for high polymer twisted artificial muscle, which comprises the following steps of: firstly, enabling the artificial muscle to be equivalent to N equidistant circular current loops, establishing an inductance calculation formula by combining a Biot-Savart law and a magnetic field superposition principle, and breaking through the limitation of a traditional solenoid model on a helical angle; then through MATLAB numerical simulation and iterative computation, fitting to obtain a power function describing the relation between inductance and length; and finally, proposing a parameter dynamic correction mode based on single-time initial inductance measurement according to complex factors such as actual magnetic flux leakage and skin effect, and realizing rapid adaptive calibration by adjusting a parameter b. In a word, the method creatively combines theoretical modeling with experimental correction, the sensing precision in a dynamic stretching scene is remarkably improved while the inductance-length macroscopic trend prediction capability is ensured, dependence on a large amount of experimental data is not needed, and the method has good engineering applicability and is worthy of popularization.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of flexible sensors, and particularly relates to a length self-sensing method of a high polymer twisted coil type artificial muscle based on a coil structure. BACKGROUND

[0002] Soft robots are widely concerned due to their wide application prospects in the fields of medical treatment and exoskeleton design. The key to the development of the soft robots lies in the sensing control of components, and traditional rigid sensors cannot meet the requirements, so flexible sensors emerge as the times require. The flexible sensors have good biocompatibility, can realize bending strain and touch sensing, improve the posture recognition sensitivity, and meet the requirements of human-computer interaction tasks.

[0003] In recent years, the field of flexible sensors has made significant progress, and the twisted coil artificial muscle (TCA) has become a research focus due to its sensing and driving integration characteristics. Compared with other driving modes, the electro-thermal driven artificial muscle (surface plated with silver) has the advantages of rapid response, simple and intuitive control, high driving efficiency and the like. The nylon spiral fiber artificial muscle also exhibits higher driving strain, energy density, power density and cycle life than other types of artificial muscles. In addition, the nylon spiral fiber artificial muscle also has excellent mechanical properties and good flexibility, and is closer to natural biological muscles in form. Compared with traditional rigid drivers such as motors, the artificial muscle can safely interact with humans and biological environments, and therefore has better symbiotic robot characteristics.

[0004] In order to realize accurate prediction of the length of the artificial muscle, the methods currently proposed include an external force-displacement model, a thermo-mechanical constitutive model and a multi-scale theoretical model. Most of these studies are based on displacement and resistance value modeling, or are based on displacement and temperature change modeling. However, these methods cannot isolate the single relationship of the length, which greatly reduces the reliability and adaptability of the model. The existing inductance and stroke modeling methods usually use the fitting empirical formula modeling method. However, there are still the following two points to be improved:

[0005] 1. Parameter dependence: There are two unknown parameters in the fitting empirical formula, and the parameters need to be obtained by fitting the experimental data, and multiple measurements need to be taken to improve the model accuracy, which brings many inconveniences to its application in practice.

[0006] 2. Dynamic parameter coupling: The creep effect caused by multiple stretching changes the geometric parameters (such as radius, initial length) of the artificial muscle, which brings errors to the measurement of inductance, and the change of the structure parameters of the artificial muscle caused by the stretching of the experiment makes it difficult for a single model to adapt to dynamic working conditions. SUMMARY

[0007] The application aims to overcome the defects and deficiencies of the prior art, and provides a length self-sensing method of a high polymer twisted type artificial muscle based on a coil structure, realizes simple and rapid sensing of the artificial muscle and is suitable for dynamic characteristics, and provides a new idea for high-precision and high-efficiency sensing of the artificial muscle.

[0008] To achieve the above-mentioned purpose, the technical scheme provided by the application is as follows: a length self-sensing method of a high polymer twisted type artificial muscle based on a coil structure, comprising the following steps:

[0009] S1, according to the structural characteristics of the artificial muscle being a spiral spring, the artificial muscle is equivalent to a coil structure, that is, N equidistant circular current rings, the magnetic field of a single circular current ring is calculated through the Biot-Savart law, the magnetic fields of the N circular current rings are superposed, and finally the total magnetic field of the whole artificial muscle is obtained, and finally the inductance formula is obtained through the Faraday's law of electromagnetic induction;

[0010] S2, based on the inductance formula obtained in step S1, the solver in the MATLAB mathematical software is used for iterative solution, the inductance values of the artificial muscle under different lengths are solved, and data fitting is performed to obtain a related power function as an inductance-length model of the artificial muscle;

[0011] S3, the inductance of the artificial muscle is actually measured by using a digital bridge instrument, the actually measured inductance value is taken as a constraint quantity, the power function obtained in step S2 is constrained and corrected, and the new power function is taken as a self-sensing model of the artificial muscle; when the artificial muscle is driven, a constant high-frequency alternating current signal is input to the artificial muscle through the digital bridge instrument or a signal generator, and then the inductance value of the artificial muscle is measured, which is substituted into the self-sensing model to obtain the length of the artificial muscle.

[0012] Further, in step S1, the artificial muscle is equivalent to N equidistant circular current rings, and the formula is:

[0013]

[0014] In the formula, x0' is the total axial length of the artificial muscle under no stretching, V is the ring distance, and m is the thickness of a single ring;

[0015] The total magnetic field of the artificial muscle is the superposition of the magnetic fields of the N equidistant circular current rings; a space rectangular coordinate system is established, having three coordinate axes X, Y and Z, according to the Biot-Savart law, the magnetic field intensity B of a single circular current ring at the Z-axis distance point P is:

[0016]

[0017] In the formula, is the distance vector of the current element to point P, is the direction vector of the magnetic field intensity, μ is the vacuum permeability, and I is the current, is the direction vector of the current element, and U is the distance from the current element to point P;

[0018] After the direction vectors in the above formula (2) are unified into the direction vectors in the form of spatial rectangular coordinates, the total magnetic field at the top end, i.e., z = 0, is:

[0019]

[0020] In the formula, B' is the total magnetic field, V is the ring distance, i is the number of bits of each circular current ring, x and y represent the coordinate variables of the current point, X', Y', and Z' represent the coordinates of the reference point;

[0021] According to the structural relationship in the coil space, formula (4) is obtained:

[0022] V = 2D tan β (4)

[0023] In the formula, β is the actual spiral angle, and D is the diameter of the circular current ring;

[0024] By Faraday's law of electromagnetic induction, i.e., using the continuity of magnetic flux, the top end magnetic flux is calculated and integrated, and the following inductance formula applicable to the axial magnetic field dominant is finally obtained, and the inductance L is obtained:

[0025]

[0026] In the formula, r is the cross-sectional radius.

[0027] Further, in step S2, the specific introduction of solving by using the solver in the MATLAB mathematical software is as follows:

[0028] First, set the initialization: create an n-order empty matrix as a data container for the magnetic field intensity distribution, set the initial iteration number and radius parameters; then in the spatial region x 2 +y 2 ≤r 2 , based on the geometric parameters of the circular current ring, the local magnetic field intensity is calculated by Biot-Savart law, and the result is stored in the corresponding position of the matrix;

[0029] After storing the result in the corresponding position, iterative calculation is performed, the number of circular current rings N-1 is set as the upper limit, and the number of bits i of the circular current ring is set as the condition; if the condition i≤N-1 is met, the next round of iteration is continued, and the current parameters are maintained; if the condition i≤N-1 is not met, the global analysis stage is entered, the matrix elements are summed to evaluate the overall magnetic field distribution, and the inductance value and the pitch of the whole artificial muscle are calculated synchronously;

[0030] According to the analysis result, the distance between the two circular current rings is dynamically adjusted, and through the differential form of V=V+dv, dv represents a micro-increment, and the loop calculation is continuously carried out, so that the inductance value under different pitches is obtained, that is, the inductance value under different lengths of the artificial muscle;

[0031] Since different pitches correspond to different stretching lengths of the artificial muscle, after the inductance value under different lengths of the artificial muscle is solved, data fitting is performed, and finally the power function relationship between inductance and length can be calculated as the inductance-length model of the artificial muscle, as follows:

[0032] L=ax1 b +c (6)

[0033] In the formula, a, b and c are characteristic parameters fitted by a theoretical model, and x1 is the length of the artificial muscle.

[0034] Further, in step S3, a correction method taking parameter b as the core is proposed, and a new power function is obtained as the self-perception model of the artificial muscle: first, the inductance value of the artificial muscle in the initial state is directly measured using a digital bridge instrument, then the parameter b value is recalculated according to the inductance value, and the following new power function is obtained as the self-perception model of the artificial muscle, and the mathematical expression is:

[0035]

[0036] In the formula, L0 is the measured initial inductance, and x0 is the initial length of the artificial muscle; by correcting the parameter b through single measurement data, the dependence of the empirical formula on a large amount of experimental data is avoided, and the rapid self-adaptive ability of the model is realized;

[0037] At the same time, the correction method has wide applicability for dynamic stretching prediction of the artificial muscle, and has no requirement on the selection of experimental data points in model correction; when the inductance value in the initial state is not used to correct the parameters, the inductance value of the artificial muscle after stretching is used to correct and calculate the parameters, and the prediction accuracy of the corrected self-perception model still meets the accuracy requirement of engineering application.

[0038] Compared with the prior art, the present application has the following advantages and beneficial effects:

[0039] The existing research provides various implementation methods for length self-sensing of the high polymer twisted type artificial muscle, wherein the temperature self-sensing method and the resistance self-sensing method are used more. The temperature self-sensing method detects the artificial surface temperature by detecting the resistance value change of the thermistor generated with the temperature, and then performs data fitting between the temperature and the length to realize the length self-sensing of the muscle. The resistance self-sensing method directly monitors the resistance value (input voltage / current) of the silver plating layer on the muscle surface. Since the silver plating layer has metal characteristics, the resistivity thereof changes with the temperature, and the temperature change causes the length change. Therefore, the length change of the muscle can be reflected by the resistance value, and the length self-sensing of the artificial muscle is realized.

[0040] Although the existing method realizes the length sensing by associating the muscle length with other parameters, the above method has certain limitations. Both methods establish the length model of the artificial muscle by the data fitting method, but the length of the artificial muscle is related to the driving temperature and the applied load. When the load changes, the displacement generated by the same driving voltage (temperature) is different, which causes poor adaptability of the model.

[0041] The present application fully considers the influence of the driving temperature and the load on the length, and therefore adopts the inductance model to directly establish the relationship between the measured value and the length, avoids the above problems, realizes the higher precision and more accurate self-sensing of the artificial muscle, simultaneously provides a new method for the length self-sensing of the artificial muscle, and promotes the application of the high polymer twisted type artificial muscle in the field of soft robots. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 It is an isometric circular current loop schematic diagram.

[0043] Figure 2 It is a Biot-Savart law schematic diagram.

[0044] Figure 3 It is a MATLAB iterative algorithm flowchart. DETAILED DESCRIPTION

[0045] The present application will be further described in detail below in combination with the embodiments and the drawings, but the embodiments of the present application are not limited thereto.

[0046] The present embodiment discloses a length self-sensing method of a high polymer twisted type artificial muscle based on a coil structure, and the specific conditions are as follows:

[0047] S1, according to the structural characteristics of the artificial muscle being a helical spring, the artificial muscle is equivalent to a coil structure, i.e. N equidistant circular current loops, the magnetic field of a single circular current loop is calculated by Biot-Savart law, then the magnetic fields of the N circular current loops are superimposed, and finally the total magnetic field of the whole artificial muscle is obtained, and the inductance formula is obtained by Faraday's law of electromagnetic induction (the existing inductance calculation formula of long straight solenoid requires that the rise angle of the solenoid coil should not exceed 5°, so it is not applicable to the high polymer twisted type artificial muscle with a larger rise angle), which is specifically introduced as follows:

[0048] As shown in Figure 1 , the artificial muscle is equivalent to N equidistant circular current loops, and the formula is:

[0049]

[0050] In the formula, x'0 is the total axial length of the artificial muscle when it is not stretched, V is the ring distance, and m is the thickness of a single ring.

[0051] The total magnetic field of the artificial muscle is the superposition of the magnetic fields of the N equidistant circular current loops; a space rectangular coordinate system is established, having X, Y and Z three coordinate axes, as shown in Figure 2 According to Biot-Savart law, the magnetic field intensity B of a single circular current loop at the Z-axis distance point P is:

[0052]

[0053] In the formula, is the distance vector of the current element to point P, is the direction vector of the magnetic field intensity, μ is the vacuum permeability, I is the current, is the direction vector of the current element, and U is the distance of the current element to point P;

[0054] After the direction vectors in the above formula (2) are unified into the direction vectors in the form of space rectangular coordinates, the total magnetic field at the top end (i.e. z=0) is:

[0055]

[0056] In the formula, B' is the total magnetic field, V is the ring distance, i is the number of each circular current loop, x and y represent the coordinate variables of the current point, and X', Y' and Z' represent the coordinates of the reference point.

[0057] According to the structural relationship in the coil space, formula (4) is obtained:

[0058] V=2D tanβ (4)

[0059] In the formula, β is the actual helix angle, and D is the diameter of the circular current loop.

[0060] By Faraday's law of electromagnetic induction, i.e. using the magnetic flux continuity, the top magnetic flux is calculated and integrated, and finally the following inductance formula is obtained to obtain the inductance L:

[0061]

[0062] In the formula, r is the cross-sectional radius; the above inductance formula is applicable to inductance calculation dominated by axial magnetic field.

[0063] S2, based on the inductance formula obtained in step S1, the solver in MATLAB mathematical software is used for iterative solution, as shown in Figure 3 The specific introduction is as follows:

[0064] First, set the initialization: create an empty matrix of n order as a data container for the magnetic field intensity distribution, set the initial iteration number and radius parameter; then in the space region x 2 +y 2 ≤r 2 , based on the geometric parameters of the circular current ring, the local magnetic field intensity is calculated by Biot-Savart law, and the result is stored in the corresponding position of the matrix;

[0065] After storing the result in the corresponding position, iterative calculation is performed, setting the number of circular current rings N-1 as the upper limit and the number of circular current rings i as the condition; if the condition is met i≤N-1, the next round of iteration is continued, and the current parameters are maintained; if the condition is not met i≤N-1, the global analysis stage is entered, the sum of the matrix elements is calculated to evaluate the overall magnetic field distribution, and the inductance value and pitch of the whole artificial muscle are calculated at the same time;

[0066] According to the analysis result, the distance between the two circular current rings is dynamically adjusted, and through the differential form V=V+dv, dv represents a small increment, and the loop calculation is continuously carried out, and the inductance value under different pitch is obtained, that is, the inductance value of the artificial muscle under different length;

[0067] Since different pitches correspond to different stretching lengths of the artificial muscle, after solving the inductance value of the artificial muscle under different lengths, data fitting is performed, and finally the power function of the relationship between inductance and length can be calculated as the inductance-length model of the artificial muscle, as shown below:

[0068] L=ax1 b +c(6)

[0069] In the formula, a, b, and c are characteristic parameters fitted by the theoretical model, and x1 is the length of the artificial muscle.

[0070] S3, the inductance of the artificial muscle is actually measured by using a digital bridge instrument, the actually measured inductance value is taken as a constraint quantity, the power function obtained in step S2 is corrected, and a new power function is taken as a self-perception model of the artificial muscle, and the new power function is specifically introduced as follows:

[0071] A correction mode taking the parameter b as the core is proposed, a new power function is obtained as the self-perception model of the artificial muscle: the inductance value in the initial state of the artificial muscle is directly measured by using a digital bridge instrument, then the parameter b value is recalculated according to the inductance value, and the following new power function is taken as the self-perception model of the artificial muscle, and the mathematical expression is as follows:

[0072]

[0073] In the formula, L0 is the measured initial inductance, and x0 is the initial length of the artificial muscle; the parameter b is corrected through single actual measurement data, the dependence of a large amount of experimental data on the empirical formula is avoided, and the rapid self-adaptive ability of the model is realized;

[0074] Meanwhile, the correction mode has wide applicability for dynamic stretching prediction of the artificial muscle, and has no requirement on the selection of experimental data points in model correction. When the inductance value in the initial state is not used for correction of the parameter, instead, the length and inductance value of the artificial muscle after stretching are used for correction and calculation of the parameter b, through comparative analysis, it is known that the prediction accuracy of the self-perception model will have a small decrease, but still meets the accuracy requirement in engineering application.

[0075] When the artificial muscle is driven, a constant high-frequency alternating current signal is input to the artificial muscle through a digital bridge instrument or a signal generator, then the inductance value of the artificial muscle is measured, and the length of the artificial muscle can be obtained by substituting the inductance value into the self-perception model.

[0076] In summary, the method of the application firstly equivalent the artificial muscle to N equidistant circular current loops, establishes an inductance calculation formula by combining the Biot-Savart law and the magnetic field superposition principle, breaks through the limitation of the traditional solenoid model on the spiral angle; then the power function describing the relationship between inductance and length is fitted through MATLAB numerical simulation and iterative calculation; finally, a parameter dynamic correction mode based on single initial inductance measurement is proposed for complex factors such as actual magnetic leakage and skin effect, and the rapid self-adaptive calibration is realized by adjusting the parameter b. In summary, the method of the application innovatively combines theoretical modeling and experimental correction, ensures the inductance-length macro trend prediction ability, significantly improves the perception accuracy in the dynamic stretching scene, does not need to rely on a large amount of experimental data, has good engineering applicability, and is worth promoting.

[0077] The above embodiments are the preferred embodiments of the present application, but the embodiments of the present application are not limited to the above embodiments, and any changes, modifications, substitutions, combinations, simplifications, etc. made without departing from the spirit and principles of the present application should be equivalent replacement manners and should be included in the protection scope of the present application.

Claims

1. A length-sensing method for polymer twisted artificial muscles based on coil structures, characterized in that, Includes the following steps: S1. Based on the structural characteristics of artificial muscles as spiral springs, they are equivalent to coil structures, namely N equidistant circular current loops. The magnetic field of a single circular current loop is calculated using the Biot-Savart law. The magnetic fields of the N circular current loops are then superimposed to obtain the total magnetic field of the entire artificial muscle. Finally, the inductance formula is obtained using Faraday's law of electromagnetic induction. S2. Based on the inductance formula obtained in step S1, the solver in MATLAB mathematical software is used to iteratively solve the inductance value of the artificial muscle at different lengths. After that, the data is fitted to obtain the relevant power function as the inductance-length model of the artificial muscle. S3. Use a digital bridge instrument to actually measure the inductance of the artificial muscle. Use the actual measured inductance value as a constraint to constrain the power function obtained in step S2. The resulting power function is used as the self-sensing model of the artificial muscle. When the artificial muscle is driven, after inputting a constant high-frequency AC signal to the artificial muscle through a digital bridge instrument or signal generator, measure the inductance value of the artificial muscle and substitute it into the self-sensing model to obtain the length of the artificial muscle.

2. The length self-sensing method for polymer twisted artificial muscles based on coil structures according to claim 1, characterized in that, In step S1, the artificial muscle is equivalent to N equidistant circular current loops, as shown in the formula: In the formula, x′0 is the total axial length of the artificial muscle when it is not stretched, V is the ring pitch, and m is the thickness of a single ring; The total magnetic field of the artificial muscle is the superposition of the magnetic fields of N equidistant circular current loops. Establish a spatial rectangular coordinate system with three axes: X, Y, and Z. According to the Biot-Savart law, the magnetic field strength B of a single circular current loop at a distance P along the Z-axis is: In the formula, Let be the distance vector from the current element to point P. Let μ be the direction vector of the magnetic field strength, μ be the free permeability, and I be the current. Let U be the direction vector of the current element, and U be the distance from the current element to point P. After unifying the direction vectors in equation (2) into spatial rectangular coordinates, the total magnetic field at the apex, i.e., z = 0, is: In the formula, B' is the total magnetic field, V is the ring spacing, i is the number of bits in each circular current ring, x and y represent the coordinate variables of the current point, and X', Y', and Z' represent the coordinates of the reference point; Based on the spatial structural relationship of the coil, we obtain equation (4): V=2Dtanβ(4) In the formula, β is the actual helix angle, and D is the diameter of the circular current loop; By applying Faraday's law of electromagnetic induction, specifically utilizing the continuity of magnetic flux, calculating and integrating the magnetic flux at the apex, we obtain the following inductance formula applicable to axial magnetic fields, thus calculating the inductance L: In the formula, r is the cross-sectional radius.

3. The length self-sensing method for polymer twisted artificial muscles based on coil structures according to claim 2, characterized in that, The specific details of the solution process using the solver in MATLAB mathematical software in step S2 are as follows: First, initialize the system: create an n-order empty matrix as a data container for the magnetic field strength distribution, and set the initial iteration count and radius parameter; then, in the spatial region x... 2 +y 2 ≤r 2 Inside, based on the geometric parameters of the circular current loop, the local magnetic field strength is calculated using the Biot-Savart law, and the results are stored in the corresponding positions of the matrix; After storing the results in the corresponding location, iterative calculations are performed. The number of circular current loops is set to N-1 as the upper limit, and the number of digits of the circular current loops is i as the condition. If the condition is met (i≤N-1), the next iteration continues while maintaining the current parameters. If the condition is not met (i≤N-1), the global analysis phase is entered, the matrix elements are summed to evaluate the overall magnetic field distribution, and the inductance and pitch of the entire artificial muscle are calculated simultaneously. Based on the analysis results, the distance between the two circular current loops is dynamically adjusted, and the inductance value under different pitches is obtained by continuously performing cyclic calculations using the differential form V = V + dv, where dv represents a small increment. This is equivalent to the inductance value of the artificial muscle under different lengths. Since different pitches correspond to different artificial muscle stretching lengths, after solving for the inductance values ​​at different artificial muscle lengths, data fitting is performed to finally calculate a power function relating inductance and length, which serves as the inductance-length model of the artificial muscle, as shown below: L = ax1 b In equation +c(6), a, b, and c are characteristic parameters obtained by fitting the theoretical model, and x1 is the length of the artificial muscle.

4. The length self-sensing method for polymer twisted artificial muscles based on coil structures according to claim 3, characterized in that, In step S3, a correction method centered on parameter b is proposed to obtain a new power function as the self-sensing model of the artificial muscle: First, the inductance value of the artificial muscle in its initial state is directly measured using a digital bridge instrument. Then, the value of parameter b is recalculated based on the inductance value to obtain the following new power function as the self-sensing model of the artificial muscle, the mathematical expression of which is: In the formula, L0 is the measured initial inductance, and x0 is the initial length of the artificial muscle; by correcting the parameter b with single-test data, the reliance on a large amount of experimental data required by empirical formulas is avoided, and the model's rapid adaptive capability is realized. Meanwhile, this correction method has broad applicability to the dynamic stretching prediction of artificial muscles. There are no requirements on the selection of experimental data points for model correction. Instead of using the inductance value in the initial state to correct parameter b, the length and inductance value of the stretched artificial muscle are used to correct and calculate parameter b. The prediction accuracy of the corrected self-sensing model still meets the accuracy requirements for engineering applications.

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