Hydraulic artificial muscle based on displacement control method of volume change

Abstract

A displacement control method for a load-varying hydraulic artificial muscle based on volume change belongs to the field of direct-drive hydraulic artificial muscle control. This invention addresses the problem that existing methods fail to consider the influence of load changes when determining the relationship between displacement and volume change of the artificial muscle, resulting in poor displacement control accuracy. The method includes determining the current change in artificial muscle volume V. ini The current artificial muscle output force F1 is determined based on the fitted curve of the experimental data. The desired artificial muscle length L is determined based on the fitted relationship between the artificial muscle length L and the output force F, and the current output force F1. cmd The corresponding initial true length L of the artificial muscle j02 Then, the actual stretching rate ε1 is calculated; subsequently, the expected length L of the artificial muscle is calculated. cmd The corresponding real volume change V cmd The volume change of the artificial muscle is controlled to be the same as the actual volume change V. cmd To achieve the desired length L of artificial muscle cmd Displacement control. This invention is used for displacement control of artificial muscles.

Description

Technical Field

[0001] This invention relates to a displacement control method for hydraulic artificial muscles based on volume changes under varying loads, belonging to the field of direct-drive hydraulic artificial muscle control. Background Technology

[0002] McKibben-type artificial muscles are cylindrical woven structures composed of an inner rubber layer and an outer fiber mesh. McKibben-type artificial muscles are generally fluid-driven, including pneumatic and hydraulic drives, and feature fast response, high efficiency, high force output, and light weight, making them promising for applications in fluid-driven robotics and other fields. Compared to pneumatic artificial muscles, hydraulic artificial muscles require a smaller flow volume to produce the same response, and offer higher reliability and lower cost.

[0003] Based on the control method, the control of hydraulic artificial muscles is mainly divided into valve-controlled and direct-drive volumetric control. Compared with the traditional valve-controlled method, direct-drive volumetric control avoids throttling losses and improves system reliability and service life. A direct-drive volumetric control system generally consists of a motor, a ball screw, and an injection pump (hydraulic cylinder). It uses the ball screw to convert the rotational motion of the motor into the linear motion of the injection pump piston, thereby adjusting the volume of the artificial muscle and changing the internal pressure, causing axial contraction and extension. Therefore, to achieve precise motion control of artificial muscles, it is necessary to know the precise correspondence between the change in artificial muscle volume and the rate of contraction, i.e., the displacement.

[0004] Foreign scholar Camp AS established a fixed-end cylindrical model of a direct-drive artificial muscle from a purely geometric perspective, assuming that the muscle's elongation (displacement) is only related to volume changes. However, this model completely ignores the influence of load, resulting in poor accuracy in displacement prediction when the load varies widely. Therefore, for direct-drive hydraulic artificial muscles, it is necessary to propose a method for controlling displacement based on volume changes, taking into account load variations. Summary of the Invention

[0005] To address the problem that existing methods fail to consider the influence of load changes when determining the relationship between displacement and volume change of artificial muscles, resulting in poor accuracy of displacement control, this invention provides a displacement control method for hydraulic artificial muscles based on volume change under varying load.

[0006] The present invention provides a displacement control method for a load-varying hydraulic artificial muscle based on volume variation, comprising:

[0007] Step 1: Determine the current change in artificial muscle volume V ini The current artificial muscle output force F1 is determined using one of the following methods:

[0008] Method 1: Under no-load conditions, the volume of the artificial muscle is varied according to volume increments to obtain the corresponding reference length L of the artificial muscle. j0 The change in artificial muscle volume V was obtained by fitting the data, and the artificial muscle reference length L was obtained. j0 Relationship;

[0009] Based on the change in artificial muscle volume V and the baseline length of artificial muscle L j0 The relational calculation yields the current artificial muscle reference length L. j01 Meanwhile, based on the current change in artificial muscle volume V ini The current bulk modulus E is calculated. j Then measure the initial pressure p of the artificial muscle's current fluid filling. ini Combined with the current standard length L of artificial muscle j01 and the current bulk modulus E j The current output force F1 is calculated.

[0010] Method 2: Perform polynomial data fitting based on experimental data to obtain the fitting relationship between the artificial muscle volume change V, the fluid filling pressure p, and the artificial muscle output force F; based on the fitting relationship, and based on the current artificial muscle volume change V... ini The measured initial filling pressure p ini Calculate the current output force F1;

[0011] Step 2: Based on the fitted relationship between the artificial muscle length L and the output force F, determine the expected length L of the artificial muscle according to the current output force F1. cmd The corresponding initial true length L of the artificial muscle j02 ;

[0012] Step 3: Based on the initial true length L of the artificial muscle j02 The true stretching ratio ε1 is calculated.

[0013] Step 4: Calculate the expected length L of the artificial muscle based on the actual stretch rate ε1. cmd The corresponding real volume change V cmd ;

[0014] Step 5: Control the volume change of the artificial muscle to match the actual volume change V. cmd To achieve the desired length L of artificial muscle cmd Displacement control.

[0015] According to the displacement control method for hydraulic artificial muscles based on volume change under varying load of the present invention, in step one, the change in artificial muscle volume V and the reference length of artificial muscle L are obtained. j0 The relational approach is as follows:

[0016] The artificial muscle is filled with liquid water using a syringe pump with a cross-sectional area of ​​S, so that the relative pressure inside the artificial muscle is 0. This is the initial state of the artificial muscle. At this time, it is a no-load condition, with output force F = 0 N, filling pressure p = 0 bar, and initial displacement of the syringe pump x = 0.

[0017] As the volume changes sequentially from j to j+1, the piston of the syringe pump is displaced by j*Δx, where Δx is the piston displacement change corresponding to each volume change stage. The corresponding change in artificial muscle volume is V = j*Δx*S. The corresponding baseline length L of the artificial muscle is recorded. j0 Until the volume series j reaches the target series;

[0018] Based on the change in volume fraction j, the change in artificial muscle volume V and the baseline length of artificial muscle L are... j0 Polynomial data fitting was performed on the correspondence to obtain the change in artificial muscle volume V and the artificial muscle reference length L under no-load conditions. j0 The relational expression.

[0019] According to the displacement control method for hydraulic artificial muscles based on volume change in load variation of the present invention, in the first method of step one, the change in artificial muscle volume V is related to the artificial muscle reference length L. j0 The relation is:

[0020]

[0021] In the formula H n-k Here, n represents the coefficients of the fitting polynomial relating volume change to length, and H represents the polynomial coefficients. n-k The highest power, k = 0, 1, 2, ..., n;

[0022] When V = V ini L was calculated j0 =L j01 .

[0023] According to the displacement control method of the hydraulic artificial muscle based on volume change for load variation of the present invention, in the first method of step one, the current bulk elastic modulus E is calculated. j The method is as follows:

[0024] Assuming the artificial muscle is a nonlinear viscoelastic body, the bulk elastic modulus E has a nonlinear relationship with the change in volume V of the artificial muscle; based on the statics equation of the artificial muscle, the current bulk elastic modulus E is calculated. j :

[0025]

[0026] In the formula C m-qHere, m represents the coefficients of the fitting polynomial between the volume change and the bulk modulus, and C represents the polynomial coefficients. m-q The highest degree, q = 0, 1, 2, ..., m.

[0027] According to the displacement control method of the hydraulic artificial muscle based on volume change for load variation of the present invention, in step one, the method for calculating the current output force F1 is as follows:

[0028]

[0029] In the formula The equivalent area of ​​action of artificial muscle:

[0030]

[0031] In the formula, D0 is the original diameter of the artificial muscle, θ0 is the original weaving angle of the artificial muscle, and ε0 is the reference stretch rate.

[0032] Artificial muscles consist of an inner rubber cylinder and an outer woven fiber mesh. s F represents the elastic force of the rubber sleeve inside the artificial muscle. r The frictional force between the woven fiber mesh and the rubber cylinder:

[0033]

[0034]

[0035] In the formula t k Let θ be the thickness of the rubber sleeve, θ be the current weaving angle of the artificial muscle, and μ be the coefficient of friction between the fiber mesh and the rubber sleeve. j0 The artificial muscle weaving angle is related to the volume change series j.

[0036] According to the displacement control method for hydraulic artificial muscles based on volume change according to the load variation of the present invention, the calculation method for the reference elongation ratio ε0 is as follows:

[0037] ε0=(L0-L j01 ) / L0,(7)

[0038] In the formula, L0 is the original length of the artificial muscle;

[0039] The method for calculating the current weaving angle θ of the artificial muscle is as follows:

[0040]

[0041] According to the displacement control method of the hydraulic artificial muscle based on volume change for load variation of the present invention, in the second method of step one, the method for calculating the current output force F1 is as follows:

[0042] Based on the linear relationship between pressure and load force under the condition that the change in artificial muscle volume V remains constant, the output force F of the artificial muscle is applied stepwise within the maximum output force range of the artificial muscle to obtain the corresponding change in artificial muscle volume V and filling pressure p. Polynomial fitting is then performed to obtain the fitting relationship:

[0043]

[0044] In the formula a M-e Here, M represents the coefficients of the first fitted polynomial for the filling pressure, and a represents the polynomial coefficients. M-e The highest order, e = 0, 1, 2, ..., M; b N-f Here, b represents the coefficients of the second fitted polynomial for the filling pressure, and N represents the polynomial coefficients. N-f The highest power, f = 0, 1, 2, ..., N;

[0045] When V = V ini p = p ini The result is F = F1.

[0046] According to the displacement control method of the hydraulic artificial muscle based on volume change for load variation of the present invention, in step two, the initial true length L of the artificial muscle... j02 The calculation method is as follows:

[0047] L cmd =L j02 +k f F1, (10)

[0048] In the formula k f This is the coefficient for the load term.

[0049] According to the displacement control method for hydraulic artificial muscles based on volume change under varying load according to the present invention, the calculation method for the true elongation rate ε1 in step three is as follows:

[0050] ε1=(L0-L j02 ) / L0. (11)

[0051] According to the displacement control method for hydraulic artificial muscles based on volume change under varying loads of the present invention, step four involves calculating the actual volume change V. cmd The method is as follows:

[0052]

[0053] The beneficial effects of this invention are as follows: The method of this invention is applicable to determining the volume-displacement relationship of direct-drive hydraulic artificial muscles under a wide range of load variations. Based on the traditional volume-displacement relationship model based on pure geometry, it considers the influence of load on the elongation rate during the artificial muscle's operation, thus determining the relationship between volume, displacement, and load in direct-drive artificial muscles. Using the method of this invention for displacement control of artificial muscles can improve the accuracy of displacement control when the load varies widely.

[0054] The method of this invention can be used to determine the relationship between volume-displacement and volume-extensibility of artificial muscles. Attached Figure Description

[0055] Figure 1 This is a schematic flowchart of the displacement control method for a hydraulic artificial muscle based on volume change with load variation as described in this invention.

[0056] Figure 2 This is a flowchart of the experimental procedure for the static characteristics of artificial muscle in the method of this invention;

[0057] Figure 3 This is a simulation curve of the θ0-F of the artificial muscle in the method of this invention;

[0058] Figure 4 This is a schematic diagram of the direct-drive artificial muscle experimental system in the method of this invention. Detailed Implementation

[0059] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0060] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0061] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0062] Specific Implementation Method 1: Combination Figure 1 , Figure 2 and Figure 4 As shown, this invention provides a displacement control method for a hydraulic artificial muscle based on volume change under varying load, comprising:

[0063] Step 1: Determine the current change in artificial muscle volume V ini The current artificial muscle output force F1 is determined using one of the following methods:

[0064] Method 1: Under no-load conditions, the volume of the artificial muscle is varied according to volume increments to obtain the corresponding reference length L of the artificial muscle. j0 The change in artificial muscle volume V was obtained by fitting the data, and the artificial muscle reference length L was obtained. j0 Relationship;

[0065] Based on the change in artificial muscle volume V and the baseline length of artificial muscle L j0 The relational calculation yields the current artificial muscle reference length L. j01 Meanwhile, based on the current change in artificial muscle volume V ini The current bulk modulus E is calculated. j Then measure the initial pressure p of the artificial muscle's current fluid filling. ini Combined with the current standard length L of artificial muscle j01 and the current bulk modulus E j The current output force F1 is calculated.

[0066] Method 2: Perform polynomial data fitting based on experimental data to obtain the fitting relationship between the artificial muscle volume change V, the fluid filling pressure p, and the artificial muscle output force F; based on the fitting relationship, and based on the current artificial muscle volume change V... ini The measured initial filling pressure p ini Calculate the current output force F1;

[0067] Step 2: Based on the fitted relationship between the artificial muscle length L and the output force F, determine the expected length L of the artificial muscle according to the current output force F1. cmd The corresponding initial true length L of the artificial muscle j02 ;

[0068] Step 3: Based on the initial true length L of the artificial muscle j02 The true stretching ratio ε1 is calculated.

[0069] Step 4: Calculate the expected length L of the artificial muscle based on the actual stretch rate ε1. cmd The corresponding real volume change V cmd ;

[0070] Step 5: Control the volume change of the artificial muscle to match the actual volume change V. cmd To achieve the desired length L of artificial muscle cmd Displacement control.

[0071] In this embodiment, the artificial muscle can be implemented using McKibben-type artificial muscles.

[0072] Furthermore, combined with Figure 1 and Figure 2 As shown, in a specific implementation of method one of step one, the change in artificial muscle volume V and the reference length of artificial muscle L are obtained. j0 The relational approach is as follows:

[0073] Setting the initial state: The artificial muscle is filled with liquid water using a syringe pump with a cross-sectional area of ​​S, so that the relative pressure inside the artificial muscle is 0. This is the initial state of the artificial muscle. At this time, it is a no-load condition, the output force F = 0N, the filling pressure p = 0bar, and the initial displacement of the syringe pump x = 0. At this time, the force loading stage i = 0.

[0074] Loading and recording data: Sequentially adjust the volume levels j = j + 1, causing the syringe pump piston to displace j * Δx, where Δx is the piston displacement change corresponding to each volume change level. Keeping the piston displacement constant, record the corresponding artificial muscle volume change V = j * Δx * S, and record the corresponding artificial muscle baseline length L. j0 Until the volume series j reaches the target series;

[0075] Based on the change in volume fraction j, the change in artificial muscle volume V and the baseline length of artificial muscle L are... j0 Polynomial data fitting was performed on the correspondence to obtain the change in artificial muscle volume V and the artificial muscle reference length L under no-load conditions. j0 The relational expression.

[0076] In Method 1 of Step 1, the change in artificial muscle volume V is related to the baseline length of the artificial muscle L. j0 The relation is:

[0077]

[0078] In the formula H n-k Here, n represents the coefficients of the fitting polynomial relating volume change to length, and H represents the polynomial coefficients. n-k The highest number of iterations, k = 0, 1, 2, ..., n; n can be reasonably selected according to the fitting accuracy and calculation requirements;

[0079] When V = V ini L was calculated j0 =L j01 .

[0080] In step one, method one, the current bulk modulus E is calculated. j The method is as follows:

[0081] Assuming the artificial muscle is a nonlinear viscoelastic body, the bulk elastic modulus E has a nonlinear relationship with the change in volume V of the artificial muscle, but it is unaffected by the output force F and the filling pressure p. Based on the statics equation for artificial muscles, the current bulk elastic modulus E is calculated.j :

[0082]

[0083] In the formula C m-q Here, m represents the coefficients of the fitting polynomial between the volume change and the bulk modulus, and C represents the polynomial coefficients. m-q The highest number of iterations, q = 0, 1, 2, ..., m, where m can be reasonably selected based on the fitting accuracy and calculation requirements.

[0084] In step one, method one, the method for calculating the current output force F1 is as follows:

[0085] Output force F and the internal fluid pressure p and elastic force F of the artificial muscle s Friction force F r There is a corresponding relationship. Elastic force F s and frictional force F r It includes the elastic modulus; therefore, the volume change V of the artificial muscle and the bulk elastic modulus E can be determined. j The relationship between the frictional force F and the frictional force F. r The direction of friction is related to the form of loading. In the experiment, the load continuously increases, and the artificial muscle continuously stretches. Here, it is assumed that the direction of friction is opposite to that of the external load force.

[0086]

[0087] In the formula The equivalent area of ​​action of artificial muscle:

[0088]

[0089] In the formula, D0 is the original diameter of the artificial muscle, θ0 is the original weaving angle of the artificial muscle, and ε0 is the reference stretch rate.

[0090] Artificial muscles consist of an inner rubber cylinder and an outer woven fiber mesh. s F represents the elastic force of the rubber sleeve inside the artificial muscle. r The frictional force between the woven fiber mesh and the rubber cylinder:

[0091]

[0092]

[0093] In the formula t k Let θ be the thickness of the rubber sleeve, θ be the current weaving angle of the artificial muscle, and μ be the coefficient of friction between the fiber mesh and the rubber sleeve. j0 The artificial muscle weaving angle is related to the volume change series j.

[0094] In this embodiment, the initial weaving angle θ0 of the artificial muscle is determined based on the mathematical model of an ideal cylinder of the woven artificial muscle. Since the output force is only related to the diameter and pressure, the contraction rate can be assumed to be 0 during simulation, and the influence of elastic force can be ignored.

[0095]

[0096] The simulation curve of θ0-F is plotted based on the above formula, as follows: Figure 3 As shown, by comparing with the experimental curve ε0-F, the size of the initial weaving angle of the artificial muscle can be obtained.

[0097] The calculation method for the baseline scaling factor ε0 is as follows:

[0098] ε0=(L0-L j01 ) / L0,(7)

[0099] In the formula, L0 is the original length of the artificial muscle;

[0100] The method for calculating the current weaving angle θ of the artificial muscle is as follows:

[0101]

[0102] According to formula (3), LF curves for different volumes can be plotted. The value of the elastic modulus can be adjusted to make the curve fit the experimental data as closely as possible. The elastic modulus value with the best fit is recorded.

[0103] At the same time, combined Figure 1 and Figure 2 As shown, in the specific implementation of method two in step one, the method for calculating and obtaining the current output force F1 is as follows:

[0104] Based on the linear relationship between pressure and load force under the condition that the change in artificial muscle volume V remains constant, the output force F of the artificial muscle is applied stepwise within the maximum output force range of the artificial muscle to obtain the corresponding change in artificial muscle volume V and filling pressure p. Polynomial fitting is then performed to obtain the fitting relationship:

[0105]

[0106] In the formula a M-e Here, M represents the coefficients of the first fitted polynomial for the filling pressure, and a represents the polynomial coefficients. M-e The highest order, e = 0, 1, 2, ..., M; b N-f Here, b represents the coefficients of the second fitted polynomial for the filling pressure, and N represents the polynomial coefficients. N-f The highest power, f = 0, 1, 2, ..., N;

[0107] When V = V ini p = p iniThe result is F = F1.

[0108] In this embodiment, the experimental data for the change in artificial muscle volume V and the filling pressure p are obtained as follows:

[0109] The maximum load force of the artificial muscle is set to F. max Rated pressure is p max Within the rated load range, the artificial muscle is applied in stages, and the output force F is set as follows:

[0110] F = i * ΔF,

[0111] In the formula, i represents the force loading level, ΔF represents the change in force at each loading stage, and ΔF = F max / I,i=1,2,3,...,I;

[0112] Record the output force F, the artificial muscle length L, and the pressure gauge reading p.

[0113] If the current filling pressure p is less than the rated pressure p max That is, p <p max Continue testing with i = i + 1 until the change in artificial muscle volume V exceeds the maximum change in volume V. max The experiment was then concluded. The data were then statistically analyzed.

[0114] Furthermore, in step two, the initial actual length L of the artificial muscle... j02 The calculation method is as follows:

[0115] L cmd =L j02 +k f F1, (10)

[0116] In the formula k f This is the coefficient for the load term.

[0117] Formula (10) is obtained through data fitting: given a certain volume of artificial muscle, the elongation of artificial muscle is linearly related to the output force, and its slope is independent of the change in artificial muscle volume. Based on the measured data, including artificial muscle length L and output force F, data fitting is performed to obtain the above relationship between artificial muscle length L and output force F.

[0118] L here cmd The calculation takes into account the effect of load, L j02 The length corresponding to volume j when the load force is 0 is the load term coefficient k. f The value of is the slope of the linear fit between the actual length and the load force in the experimental data.

[0119] The method for calculating the true stretching ratio ε1 in step three is as follows:

[0120] ε1=(L0-L j02 ) / L0. (11)

[0121] Step four involves calculating the actual volume change V. cmd The method is as follows:

[0122]

[0123] The stretching rate of hydraulic artificial muscles is related to the volume change. When the volume change of hydraulic artificial muscles is known, the stretching rate of the corresponding artificial muscles can also be predicted according to formula (12).

[0124] In the method of this invention, data is obtained through experiments to acquire experimental curves showing the characteristic relationship between volume change, pressure, and output force of the hydraulic artificial muscle. Therefore, given a desired elongation, the volume change of the artificial muscle can be calculated even under unknown load conditions. In this embodiment, the initial volume change V of the hydraulic artificial muscle is known. ini Given L cmd Then, the initial pressure p of the artificial muscle was measured. ini The actual volume change V that satisfies the desired length can be obtained. cmd Since the actual elongation of the artificial muscle is related not only to the volume of the hydraulic artificial muscle but also to the load change, the volume change of the artificial muscle must be corrected according to the load change based on the expected elongation. The output force can be calculated from the theoretical relationship between load and output force in formula (3) or the empirical relationship between output force, pressure and volume in formula (9). Then, according to formulas (10) and (12), the volume change of the artificial muscle corresponding to the pure geometric relationship of volume-length can be calculated.

[0125] In this embodiment, step one presents two methods for calculating the output force. Method one uses one theoretical formula plus two empirical formulas for calculation; method two uses one empirical formula for calculation, which is simpler and more efficient.

[0126] The following experiment will verify this:

[0127] Specific Implementation Example 1: The experiment used an artificial muscle from FESTO, model DMSP-5-432, with a rated pressure of 6 bar and a maximum output force of 140 N.

[0128] 1.1) Set the initial state. Fill the artificial muscle with liquid water and measure that the internal pressure is 0. This is considered the initial state of the artificial muscle.

[0129] 1.2) Load and record data. After advancing the injection pump piston by 5mm, keep the piston displacement constant. Record the change in artificial muscle volume and the corresponding artificial muscle length L at this point. j0 .

[0130] 1.3) Apply progressively increasing load to the artificial muscle within the rated load range, with the loading force set as follows:

[0131] F = i * 9.8N

[0132] Record the load force F, the length L of the artificial muscle, and the pressure gauge reading p.

[0133] If the pressure p is less than the rated pressure of 6 bar, i = i + 1 and repeat step 1.3; otherwise, proceed to the next step.

[0134] 1.4) If V <V max If j = j + 1, repeat step 1.2; otherwise, the experiment ends.

[0135] 1.5) After the experiment, perform statistical analysis on the data.

[0136] 1.5.1) Determine the initial weaving angle

[0137] The data points where the expansion rate is 0 in the experiment are selected, and their output force values ​​correspond one-to-one with the output forces in the simulation curves. From the simulation curves... Figure 3 As can be seen, due to errors, the initial knitting angle varies within a range, with a maximum value not exceeding 20.17° (0.352 rad) and a minimum value greater than 19.48° (0.34 rad). Due to the influence of friction, the actual initial knitting angle should be smaller than the corresponding angle in the simulation curve. The range of the initial knitting angle should be between 18° and 19°. In this embodiment, taking 18.5° is more reasonable.

[0138] 1.5.2) Based on the measurement data, the change in artificial muscle volume V and its corresponding initial length L j0 Polynomial data fitting was performed to obtain the change in artificial muscle volume V and its corresponding initial length L. j0 The relationship between them:

[0139] Table 1 Experimental data on volume and its corresponding initial length

[0140]

[0141] The fitting yielded:

[0142] L j0 =H1V 6 -H2V 5 +H3V 4 -H4V 3 +H5V2 -H6V+H7,

[0143] Goodness of fit R 2 =0.9994.

[0144] The closer the goodness of fit is to 1, the better the fit. This proves that this implementation method has achieved an excellent fit.

[0145] Table 2 Polynomial Coefficients

[0146]

[0147] 1.5.3) Calculate the change in volume V of the artificial muscle and the bulk modulus of elasticity E. j The relationship between them.

[0148] Plot the LF curves for different volumes according to formula (3), and adjust the magnitude of the elastic modulus to make the curve fit the experimental data as closely as possible. Record the elastic modulus value with the best fit.

[0149] Table 3. Record of volumetric and elastic modulus data

[0150]

[0151] E j =-C1V 6 +C2V 5 -C3V 4 -C4V 3 +C5V 2 -C6V+C7R 2 =0.9979.

[0152] Table 4 Polynomial Coefficients

[0153]

[0154] 1.5.4) Based on the measured data of the artificial muscle volume change V, its corresponding gauge pressure p, and output force F, a polynomial data fitting was performed to obtain the relationship between the artificial muscle volume change V, its corresponding gauge pressure p, and output force F, and the goodness of fit R. 2 =0.9971.

[0155] p = (-0.0001V) 2 +0.0023V +0.0221)F + (0.0059V) 3 -0.122V 2 +0.9643V -0.1627);

[0156] 1.5.5) Based on the measured data of artificial muscle length L and output force F, data fitting is performed to obtain the relationship between artificial muscle length L and output force F. f The mean of the fitted slopes for each volume is taken, and its value is 0.057.

[0157] L = L j0 +0.057F.

[0158] Table 5. Fitting slope for each volume

[0159]

[0160] The displacement control scheme using the method of this invention is as follows:

[0161] Step 1: Determine the output force F1:

[0162] Method 1: Given the current volume of the artificial muscle as 2.894 ml, calculate the initial length of 424.6019 mm and the elastic modulus of 2.1931 MPa corresponding to the current volume change according to Method 1. Given a gauge pressure of 3.89 bar, calculate the output force as 80.0852 N (actual output force is 78.48 N).

[0163] Method 2: Given the current artificial muscle volume of 2.894 ml and the gauge pressure of 3.89 bar, according to Method 2, the output force is calculated to be 76.6795 N (the actual output force is 78.48 N).

[0164] Step 2: Given the desired length L cmd Determine the initial length L corresponding to the required volume change. j02 :

[0165] Given a desired length of 432.5 mm and an output force of 80.0852 N calculated using Method 1, the initial length L corresponding to the required volume change is calculated. j02 The value is 427.9351 mm; the corresponding output force calculated by method 2 is 76.6795 N, and the initial length L corresponding to the required volume change is calculated. j02 It is 428.1293mm.

[0166] Step 3: Determine the required volume V cmd :

[0167] According to L j02 The length is 428.1293 mm, and the corresponding expansion rate is calculated to be 0.896%. Substituting the expansion rate into formula (12), the required volume is calculated to be 1.3344 ml (76.6795 N). Similarly, when the output force is 80.0852 N, the volume is calculated to be 1.4001 ml. The actual required volume is 1.447 ml.

[0168] Step 4: End

[0169] Other examples:

[0170] Similarly, the remaining calculations were performed following the steps described above. Using FESTO's DMSP-5-432 artificial muscle, initial volumes of 2.894 ml and 10.129 ml were used to calculate the desired lengths for different schemes. The calculation results for the two schemes are shown in the table below.

[0171] Table 6 Example 1: V = 2.894 ml, p = 3.89 bar

[0172]

[0173] Table 7 Example 2: V = 10.129 ml, p = 4.9 bar

[0174]

[0175] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A displacement control method for a hydraulic artificial muscle based on volume change under varying load, characterized in that... include, Step one: determine the current artificial muscle volume change amount V ini The current artificial muscle output force F1 is determined in one of the following ways: Manner one: in the no-load working condition, the volume of artificial muscle changes by volume series, and the corresponding artificial muscle reference length L is obtained j0 The relationship between the volume change V of artificial muscle and the reference length L of artificial muscle is obtained by fitting j0 ​ Based on the change in artificial muscle volume V and the baseline length of artificial muscle L j0 The relational calculation yields the current artificial muscle reference length L. j01 Meanwhile, based on the current change in artificial muscle volume V ini The current bulk modulus E is calculated. j Then measure the initial pressure p of the artificial muscle's current fluid filling. ini Combined with the current standard length L of artificial muscle j01 and the current bulk modulus E j The current output force F1 is calculated. The second mode is: according to the experimental data, a polynomial data fitting is performed to obtain a fitting relationship formula of the volume change V of the artificial muscle, the liquid filling pressure p and the output force F of the artificial muscle; according to the fitting relationship formula, the current output force F1 is calculated according to the current volume change V of the artificial muscle ini , the current liquid filling initial pressure p ini obtained by measurement Step 2: Based on the fitted relationship between the artificial muscle length L and the output force F, determine the expected length L of the artificial muscle according to the current output force F1. cmd The corresponding initial true length L of the artificial muscle j02 ; Step 3: Based on the initial true length L of the artificial muscle j02 The true stretching ratio ε1 is calculated. Step 4: Calculate the expected length L of the artificial muscle based on the actual stretch rate ε1. cmd The corresponding real volume change V cmd ; Step 5: Control the volume change of the artificial muscle to match the actual volume change V. cmd To achieve the desired length L of artificial muscle cmd Displacement control.

2. The displacement control method for a load-varying hydraulic artificial muscle based on volume change according to claim 1, characterized in that, In step one, method one, the change in artificial muscle volume V and the baseline length of artificial muscle L are obtained. j0 The relational method is as follows: The artificial muscle is filled with liquid water using a syringe pump with a cross-sectional area of ​​S, so that the relative pressure inside the artificial muscle is 0. This is the initial state of the artificial muscle. At this time, it is a no-load condition, with output force F = 0 N, filling pressure p = 0 bar, and initial displacement of the syringe pump x = 0. As the volume changes sequentially from j to j+1, the piston of the syringe pump is displaced by j*Δx, where Δx is the piston displacement change corresponding to each volume change stage. The corresponding change in artificial muscle volume is V = j*Δx*S. The corresponding baseline length L of the artificial muscle is recorded. j0 Until the volume series j reaches the target series; Based on the change in volume fraction j, the change in artificial muscle volume V and the baseline length of artificial muscle L are... j0 Polynomial data fitting was performed on the correspondence to obtain the change in artificial muscle volume V and the artificial muscle reference length L under no-load conditions. j0 The relational expression.

3. The displacement control method for a load-varying hydraulic artificial muscle based on volume change according to claim 2, characterized in that, In Method 1 of Step 1, the change in artificial muscle volume V is related to the baseline length of the artificial muscle L. j0 The relation is: In the formula H n-k Here, n represents the coefficients of the fitting polynomial relating volume change to length, and H represents the polynomial coefficients. n-k The highest power, k = 0, 1, 2, ..., n; When V = V ini L was calculated j0 =L j01 .

4. The displacement control method for a load-varying hydraulic artificial muscle based on volume change according to claim 2, characterized in that, In step one, method one, the current bulk modulus E is calculated. j The method is as follows: Assuming the artificial muscle is a nonlinear viscoelastic body, the bulk elastic modulus E has a nonlinear relationship with the change in volume V of the artificial muscle; based on the statics equation of the artificial muscle, the current bulk elastic modulus E is calculated. j : In the formula C m-q Here, m represents the coefficients of the fitting polynomial between the volume change and the bulk modulus, and C represents the polynomial coefficients. m-q The highest degree, q = 0, 1, 2, ..., m.

5. The displacement control method for a load-varying hydraulic artificial muscle based on volume change according to claim 4, characterized in that, In step one, method one, the method for calculating the current output force F1 is as follows: In the formula The equivalent area of ​​action of artificial muscle: In the formula, D0 is the original diameter of the artificial muscle, θ0 is the original weaving angle of the artificial muscle, and ε0 is the reference stretch rate. Artificial muscles consist of an inner rubber cylinder and an outer woven fiber mesh. s F represents the elastic force of the rubber sleeve inside the artificial muscle. r The frictional force between the woven fiber mesh and the rubber cylinder: In the formula t k Let θ be the thickness of the rubber sleeve, θ be the current weaving angle of the artificial muscle, and μ be the coefficient of friction between the fiber mesh and the rubber sleeve. j0 The artificial muscle weaving angle is related to the volume change series j.

6. The displacement control method for a load-varying hydraulic artificial muscle based on volume change according to claim 5, characterized in that, The calculation method for the baseline elongation ε0 is as follows: ε0=(L0-L j01 ) / L0, (7) In the formula, L0 is the original length of the artificial muscle; The method for calculating the current weaving angle θ of the artificial muscle is as follows:

7. The displacement control method for a load-varying hydraulic artificial muscle based on volume change according to claim 1, characterized in that, In step one, method two, the method for calculating the current output force F1 is as follows: Based on the linear relationship between pressure and load force under the condition that the change in artificial muscle volume V remains constant, the output force F of the artificial muscle is applied stepwise within the maximum output force range of the artificial muscle to obtain the corresponding change in artificial muscle volume V and filling pressure p. Polynomial fitting is then performed to obtain the fitting relationship: In the formula a M-e Here, M represents the coefficients of the first fitted polynomial for the filling pressure, and a represents the polynomial coefficients. M-e The highest order, e = 0, 1, 2, ..., M; b N-f Here, b represents the coefficients of the second fitted polynomial for the filling pressure, and N represents the polynomial coefficients. N-f The highest power, f = 0, 1, 2, ..., N; When V = V ini p = p ini The result is F = F1.

8. The displacement control method for a load-varying hydraulic artificial muscle based on volume change according to claim 6 or 7, characterized in that, In step two, the initial true length L of the artificial muscle j02 The calculation method is as follows: L cmd =L j02 +k f F1, (10) In the formula k f This is the coefficient for the load term.

9. The displacement control method for a load-varying hydraulic artificial muscle based on volume change according to claim 8, characterized in that, The method for calculating the true stretching ratio ε1 in step three is as follows: ε1=(L0-L j02 ) / L0。 (11) 10. The displacement control method for a load-varying hydraulic artificial muscle based on volume change according to claim 9, characterized in that, Step four involves calculating the actual volume change V. cmd The method is as follows:

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