A hysteresis modeling method for pneumatic soft robot arm based on PI model

Abstract

The present invention discloses a hysteresis modeling method for a pneumatic soft robot arm based on a P-I model, including: weighted superposition of play operators under different thresholds to form a P-I model; an asymmetric hysteresis model in a pneumatic soft robot arm is formed by a play operator, n rising operators, and n falling operators; and parameters in the asymmetric hysteresis model in the pneumatic soft robot arm are identified. Based on the basic P-I model, the present invention derives an MPI hysteresis model, and uses the properties of the P-I model and the operators of the MPI model at the state change point to obtain the P-I model and the weight calculation matrix of the MPI model. The parameter matrix is ​​universal for the normalized hysteresis model, and the model parameters can be easily obtained through the matrix, providing a solution for real-time modeling of soft robot arms and the like.

Description

Technical Field

[0001] The invention belongs to the technical field of hysteresis modeling of pneumatic soft robotic arms, and in particular relates to a hysteresis modeling method of a pneumatic soft robotic arm based on a PI model. Background Art

[0002] Soft robots are a hot research topic in the field of robotics. Compared with traditional rigid robots, soft robots are safe and will not cause damage to people or objects during human-machine interaction or impact. Their unique flexibility gives soft robots broad application prospects and high practical application value in medical rehabilitation, space exploration, agricultural production and other aspects.

[0003] Soft robots made of soft materials such as silicone have the disadvantage of prominent hysteresis. The hysteresis nonlinear phenomenon will affect the motion performance of the soft robot and bring difficulties to further model control. Hysteresis often occurs in nonlinear systems, and soft robots are made of soft materials and are typical nonlinear systems. The main manifestation is that the output of the system is not only related to the current input value, but also to the historical state. The hysteresis phenomenon brings great difficulties to the precise control of soft robots. Based on the above soft robotic arm model, the hysteresis is mainly caused by the following reasons.

[0004] (1) The designed soft robotic arm is mainly composed of soft materials such as silicone. Compared with rigid materials, soft materials have prominent nonlinear characteristics and are difficult to control. Therefore, material properties are the main reason for the hysteresis of the soft robotic arm. (2) The coupling of the designed soft robotic arm has the result of blocking and changing stiffness. Friction and gaps between particles, changes in stiffness, etc. are prone to cause hysteresis. (3) When preparing the soft robotic arm, tiny bubbles exist in the silicone solution used.

[0005] Common hysteresis models include the Preisach model, the Prandtl-Ishlinskii (PI) model, the Maxwell model, the Bouc-Wen model, etc. For the Preisach model, error accumulation may occur, and the Maxwell model is relatively complex. Summary of the invention

[0006] Technical problem solved: The present invention discloses a hysteresis modeling method for a pneumatic soft robotic arm based on the PI model. On the basis of the basic PI model, an MPI hysteresis model is derived, and the properties of the PI model and the operators of the MPI model at the state change points are used to obtain the weight calculation matrix of the PI model and the MPI model. The parameter matrix is ​​universal for the normalized hysteresis model. The model parameters can be easily obtained through the matrix, providing a solution for real-time modeling of soft robotic arms and the like.

[0007] Technical solution:

[0008] A hysteresis modeling method for a pneumatic soft robot arm based on a PI model, wherein the pneumatic soft robot arm includes a pneumatic drive structure and a variable stiffness structure of the soft robot arm; the hysteresis modeling method for the pneumatic soft robot arm includes the following steps:

[0009] S1, weighted superposition of play operators under different thresholds to form a PI model:

[0010]

[0011] Where n represents the number of operators, w i represents the weight of the ith operator, r i represents the threshold of the i-th operator, Y(k) is the output of the model established at time k; i [u(k),r i ] is the play operator at the threshold r i , the output at the kth moment; u(k) is the input of the operator at the kth moment;

[0012] S2, an asymmetric hysteresis model in a pneumatic soft robot arm, is composed of a play operator, n rise operators, and n fall operators:

[0013]

[0014] Among them, w 0 , w ai , w di is the weight parameter; u(k) is the input at time k; r i is the threshold of different operators at time k; Y(k) is the output of the model at time k; A i [u(k),r i ] indicates the threshold is r i The rising operator at time k; D i [u(k),r i ] indicates the threshold is r i The descent operator at the kth moment;

[0015] S3, identify the parameters in the asymmetric hysteresis model of the pneumatic soft robot; specifically, normalize the input values ​​and response values. Each model output point Y(k) after normalization is composed of the weighted superposition of n+1 operators. When the threshold r and the input u(k) are determined, the values ​​of the n+1 operators are also determined, and the unknown weight parameters of the PI model parameters are obtained by solving the set of equations; according to the properties of the rising operator and the falling operator at the state change point, combined with the measurement to obtain the normalized output, the unknown weight parameters of the asymmetric hysteresis model in the pneumatic soft robot are obtained.

[0016] Furthermore, in step S1, the expression of the play operator is:

[0017]

[0018] Among them, r is the threshold of the play operator, and u(k) is the input of the operator at time k.

[0019] Furthermore, in step S2, the expression of the rising operator is:

[0020] A i [u(k),r i ]=(u(k)+ry i [u(k),r i ])·y i [u(k),r i ];

[0021] The expression of the descent operator is:

[0022] D i [u(k),r i ]=(y i [u(k),r i ]-u(k)+r)·y i [u(k),r i ]

[0023] The rising operator and the falling operator are related to the threshold r and the input at time k.

[0024] Furthermore, in step S3, the input value and the response value are normalized using the following formula:

[0025] u n (k)=(u(k)-u m ) / (u M -u m )

[0026] x n (k) = (x(k) - x m ) / (X M -x m )

[0027] In the formula, for the pneumatic soft robot arm with uncoupled variable stiffness structure, u(k) is the kth input air pressure data, u m is the minimum value of input air pressure, u M is the maximum value of the input air pressure, u n (k) is the normalized value of the k-th input pressure; x(k) is the displacement value of the k-th output, x m is the minimum value of the output displacement, xM is the maximum value of the output displacement;

[0028] For the coupled variable stiffness structure pneumatic soft robot arm, u(k) is the kth end displacement value, u m is the minimum value of the end displacement, u M is the maximum value of the end displacement, u n (k) is the normalized value of the k-th end displacement; x(k) is the value of the end contact force corresponding to the k-th end displacement, x m is the minimum value of the end contact force, x M is the minimum value of the end contact force.

[0029] Furthermore, in step S3, the process of solving the equation group to obtain the unknown weight parameters of the PI model parameters includes the following steps:

[0030] Define the state change point set, the state change point v set is 2r on the horizontal axis i and 1-2r i A set of points; for a hysteresis model consisting of n+1 play operators, there are 2n state change points. After the hysteresis data is normalized, both the rising stage and the falling stage include the state change points (0, 0) and (1, 1), and the rising stage and the falling stage each include n+1 state change points;

[0031] In the rising stage, assuming there is a state change point v(k), there is a threshold r i The play operator satisfies the following formula: i =v(k) / 2; with r i The value of is the dividing point that divides the n+1 operators of the PI model into two categories, one of which is the threshold r m Less than or equal to r i , one is the threshold r m Greater than r i ; When the threshold r of the first type operator m Less than or equal to r i When the state changes, the output at the state change point v(k) is v(k)-r m ; When the second type operator threshold r m Greater than r i When the state changes, the output at the state change point is r m ;

[0032] In the descending phase, r i The value of is the dividing point that divides the n+1 operators of the PI model into two categories, one of which is the threshold r m Less than or equal to r i , one is the threshold r m Greater than r i; When the threshold r of the first type operator m Less than or equal to r i When the state changes, the output at the state change point v(k) is v(k)+r m ; When the second type operator threshold r m Greater than r i When the state changes, the output at the state change point is 1-r m ;

[0033] According to the properties of the state change point, combined with the PI model of step S1, the output of the model at the state change point v(k) is:

[0034]

[0035] Combine and expand the obtained equations to obtain the solution equation of the weight coefficient matrix:

[0036]

[0037] In the formula, x 0 (k), x 1 (k), ..., x n (k) is the normalized output. The normalized displacement value of the end of the soft robot arm is a known quantity; r m is less than or equal to r i The threshold value, v(k) is the kth state change point, r m is also a known quantity; for u(k)-r m , u(k) is the normalized input value; for the normalized input pressure value, u(k)-r m It is also a known quantity.

[0038] Furthermore, in step S3, the process of obtaining the unknown weight parameters of the asymmetric hysteresis model in the pneumatic soft robot arm includes the following steps:

[0039] For any state change point v(k), there is a threshold r i The operator satisfies the formula r i =v(k) / 2; the threshold value r i As the dividing point, the operators are divided into two categories. The threshold of the first type of operators is 0≤r m <r i , the threshold of the second type of operator is r m ≥r i ;

[0040] In the ascending stage, among the first type of operators, when r m = 0, the corresponding value is the play operator with a threshold r of 0. The play operator with a threshold r of 0 satisfies the formula α = y at the state change point v(k) 0[v(k), r 0 ]=v(k); when the threshold r=0, the play operator degenerates into a coincident straight line, and the output of the operator is equal to the input v(k): α=y 0 [v(k), r 0 ] = v(k);

[0041] For the first type of operator, when 0<r m <r i When the threshold is r m The output of the rising operator at the state change point v(k) is:

[0042] β′=(v(k)+r m -y m [v(k), r m ])·y m [v(k), r m ]k=1,2,…,i-1

[0043] where y m [v(k), r m ] is the threshold value r m The output of the play operator at the state change point v(k) is v(k)-r m ; Transformation yields: β′=2r m ·(v(k)-r m ), k = 1, 2, ..., i-1;

[0044] For the first type of operator, when 0<r m <r i When the threshold is r m The output of the descent operator at the state change point v(k) is: β″=(y m [v(k), r m ]-v(k)+r m )·y m [v(k), r m ]; where y m [v(k), r m ] The same threshold is r m The output of the play operator at the state change point v(k) is v(k)-r m ;Conversion: β″=0,k=1,2,…,i-1;

[0045] For the second type of operator, when the operator threshold r m ≥r i When the threshold is r m The output of the rising operator at the state change point v(k) is: γ′=(v(k)+r m -ym [v(k), r m ])·y m [v(k), r m ]k=i,i+1,…,n, where y m [v(k), r m ] is the threshold value r m The output of the play operator at the state change point v(k), r m ≥r i , the output of the play operator is r m , converted to: γ′=v(k)·r m k=i,i+1,…,n;

[0046] For the second type of operator, when the operator threshold r m ≥r i When the threshold is r m The output of the rising operator at the state change point v(k) is: γ″=(y m [v(k), r m ]-v(k)+r m )·y m [v(k), r m ], where y m [v(k), r m ] is the threshold value r m The output of the play operator at the state change point v(k), r m ≥r i , the output of the play operator is r m , converted to: γ″=(2·r m -v(k))·r m k=i,i+1,…,n;

[0047] In the descent phase, in the first type of operators, when r m = 0, the corresponding value is the play operator with a threshold r of 0. The play operator with a threshold r of 0 satisfies the following at the state change point v(k): α = y 0 [v(k), r 0 ] = v(k);

[0048] For the first type of operator, when 0 <r m <r i When the threshold is r m The output of the rising operator at the state change point v(k) is: β′=(v(k)+r m -y m [v(k), r m ])·y m [v(k), r m ], where ym [v(k), r m ] is the threshold value r m The output of the play operator at the state change point v(k) in the descending phase is v(k)+r m , converted to: β′=0, k=1, 2, …, i-1;

[0049] For the first type of operator, when 0<r m <r i When the threshold is r m The output of the descent operator at the state change point v(k) is: β″=(y m [v(k), r m ]-v(k)+r m )·y m [v(k), r m ], where y m [v(k), r m ] The same threshold is r m The output of the play operator at the state change point v(k) is v(k)+r m , converted to: β″=2·r m ·(v(k)+r m ), k = 1, 2, ..., i-1

[0050] For the second type of operator, when the operator threshold r m ≥r i When the threshold is r m The output of the rising operator at the state change point v(k) is: γ′=(v(k)+r m -y m [v(k), r m ])·y m [v(k), r m ]k=i,i+1,…,n, where y m [v(k), r m ] is the threshold value r m The output of the play operator at the state change point v(k), r m ≥r i , the play operator output is 1-r m , converted to: γ′=(v(k)-1+2r m )·(1-r m ) k = i, i + 1, ..., n;

[0051] For the second type of operator, when the operator threshold r m ≥r i When the threshold is r mThe output of the rising operator at the state change point v(k) is: γ″=(y m [v(k), r m ]-v(k)+r m )·y m [v(k), r m ], where y m [v(k), r m ] is the threshold value r m The output of the play operator at the state change point v(k), r m ≥r i , the play operator output is 1-r m , converted to: γ″=(1-v(k))·(1-r m ) k = i, i + 1, ..., n;

[0052] According to the properties of the rising operator and the falling operator at the state change point, the output of the asymmetric hysteresis model at the state change point of the rising section v(k) is obtained as follows:

[0053]

[0054] In the descending section, the output of the asymmetric hysteresis model at the state change point v(k) in the descending section is obtained as:

[0055]

[0056] Let w an =w dn , we get the following set of equations, solving the 2n unknown weight parameters w 0 , w n , w a , w d :

[0057]

[0058] Furthermore, the pneumatic soft robot arm hysteresis modeling method comprises the following steps:

[0059] The PI model is inverted, where the corresponding inverse model parameter calculation formula is:

[0060]

[0061]

[0062]

[0063] Furthermore, the model verification process of the PI model includes:

[0064] Normalized hysteresis data b, 11 data points in the rising section are selected;

[0065] The weight parameter is calculated according to the following formula: w = A -1 b.

[0066] The obtained weight parameters are weighted superimposed with the play operator to obtain the modeling point Y(k) corresponding to each hysteresis data point:

[0067] The difference between the hysteresis data b and the modeling data Y(k) is calculated as the modeling error.

[0068] Furthermore, the model verification process of the asymmetric hysteresis model in the pneumatic soft robot arm includes:

[0069] Normalized hysteresis data b, 20 data points are selected at fixed intervals;

[0070] The weight parameter is calculated according to the following formula: w = A -1 b.

[0071] The obtained weight parameters are weighted superimposed with the play operator to obtain the modeling point Y(k) corresponding to each hysteresis data point:

[0072] The difference between the hysteresis data b and the modeling data Y(k) is calculated as the modeling error.

[0073] Beneficial effects:

[0074] First, the hysteresis modeling method of the pneumatic soft robot arm based on the PI model of the present invention utilizes the characteristics of the PI model operator to obtain the PI model and the MPI model parameter matrix. The parameter matrix is ​​universal for the normalized hysteresis model and can easily derive the model parameters, providing a solution for real-time modeling of soft robot arms and the like.

[0075] Second, the hysteresis modeling method of the pneumatic soft robot arm based on the PI model of the present invention provides proof that the parameter calculation matrix has a unique solution, as well as the specific verification method and steps of the hysteresis model. The PI model and the MPI model are used to fit the measured hysteresis curve to obtain the hysteresis parameters, and the correctness of the model is verified through simulation analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 Schematic diagram of the overall structure of the soft robotic arm, (a) is a top view, (b) is a front view;

[0077] Figure 2 Schematic diagram of the play operator with thresholds of 0.1 and 0.3;

[0078] Figure 3 This is a schematic diagram of the weighted superposition structure of the PI model;

[0079] Figure 4 Schematic diagram of the rising operator when the threshold value r = 0.2 and 0.3;

[0080] Figure 5 Schematic diagram of the descent operator when the threshold value r = 0.2 and 0.3;

[0081] Figure 6 This is a schematic diagram of the weighted superposition structure of the MPI model;

[0082] Figure 7 It is the flow chart of weight parameter calculation for the ascending section of PI model;

[0083] Figure 8 Schematic diagram of the play operator with a threshold value of r = 0;

[0084] Fig. 9 It is the flow chart of MPI model parameter calculation;

[0085] Fig.10 It is the parameter calculation flow chart;

[0086] Fig.11 Validation flow chart for PI hysteresis model;

[0087] Fig.12 Flowchart for MPI hysteresis model validation. DETAILED DESCRIPTION

[0088] The following examples will enable those skilled in the art to more fully understand the present invention, but are not intended to limit the present invention in any way.

[0089] The structural design of the soft robotic arm includes the pneumatic drive structure and variable stiffness structure of the soft robotic arm. This section describes the overall structure of the soft robotic arm.

[0090] The overall structure of the software driver is as follows Figure 1 As shown, Figure 1 (a) is a top view of the entire soft robotic arm. It can be seen from the top view that the entire robotic arm consists of three air cavities and a cavity coupled with a variable stiffness structure. The cavity of the blocked variable stiffness structure is located at the center of the soft robotic arm, which is used to reserve an assembly position for the variable stiffness structure. The three cavities are located in the deformation layer and are distributed at 120°. Figure 1 (b) in the figure shows a front view of the soft robotic arm. There are three inflation pipes and one vacuum pipe at the end of the robotic arm. When inflated, the cavity pressure changes, thereby causing movement. There is an exhaust pipe. When the pneumatic soft robotic arm needs to change its stiffness, the vacuum degree of the blocking structure is changed by exhausting air, thereby changing the stiffness.

[0091] This embodiment discloses a hysteresis modeling method for a pneumatic soft robotic arm based on a PI model, wherein the pneumatic soft robotic arm includes a pneumatic drive structure and a variable stiffness structure of the soft robotic arm; the hysteresis modeling method for a pneumatic soft robotic arm includes the following steps:

[0092] S1, weighted superposition of play operators under different thresholds to form a PI model:

[0093]

[0094] Where n represents the number of operators, w i represents the weight of the ith operator, r i represents the threshold of the i-th operator, Y(k) is the output of the model established at time k; i [u(k),r i ] is the play operator at the threshold r i , the output at the kth moment; u(k) is the input of the operator at the kth moment;

[0095] S2, an asymmetric hysteresis model in a pneumatic soft robot arm, is composed of a play operator, n rise operators, and n fall operators:

[0096]

[0097] Among them, w 0 , w ai , w di is the weight parameter; u(k) is the input at time k; r i is the threshold of different operators at time k; Y(k) is the output of the model at time k; A i [u(k),r i ] indicates the threshold is r i The rising operator at time k; D i [u(k),r i ] indicates the threshold is r i The descent operator at the kth moment;

[0098] S3, identify the parameters in the asymmetric hysteresis model of the pneumatic soft robot; specifically, normalize the input values ​​and response values. Each model output point Y(k) after normalization is composed of the weighted superposition of n+1 operators. When the threshold r and the input u(k) are determined, the values ​​of the n+1 operators are also determined, and the unknown weight parameters of the PI model parameters are obtained by solving the set of equations; according to the properties of the rising operator and the falling operator at the state change point, combined with the measurement to obtain the normalized output, the unknown weight parameters of the asymmetric hysteresis model in the pneumatic soft robot are obtained.

[0099] (I) PI model establishment

[0100] The PI model is formed by the weighted addition of a series of PI operators. The PI operators are divided into play operators and stop operators, which are complementary to each other. The PI model established in this paper is based on the play operator. The expression of the play operator is shown in formula (3.1).

[0101]

[0102] Where r is the threshold of the current play operator, and u(k) is the input of the operator at time k. Figure 2 is the play operator when the play operator threshold r = 0.1 and 0.3. From formula 3.1 and Figure 2 It can be seen that the output of the operator is related to the input at the threshold r and k, so using y i [u(k),r i ] means when the threshold is r i , the output of the i-th operator when the input is u(k).

[0103] The PI model is composed of weighted superposition of play operators under different thresholds. The weight of each operator is different. Its structure is as follows: Figure 3 As shown, the weight corresponding to each operator is different, and the threshold r of the operator is also different. After weighted addition, the expression at time k is as shown in formula (3.2):

[0104]

[0105] In formula (3.2), n represents the number of operators, w i represents the weight of the ith operator, r i represents the threshold of the ith operator. Y(k) is the output of the model established at time k. For the convenience of representation, formula (3.2) can be written as a vector mode as shown in formula (3.3).

[0106] Y(k)=w T y,[u(k),r i ] (3.3)

[0107] In the formula, w is the weight vector, w=(w 0 , w 1 ,…,w n ), y[u(k), r i ] is the state vector of the operator at time k.

[0108] (II) MPI model establishment

[0109] Depend on Figure 3It can be seen that the play operator is symmetric, so the weighted superposition of the play operator can only describe the symmetric hysteresis model. However, the hysteresis phenomenon of the soft robot is always asymmetric. Therefore, two improved operators are used on the basis of the play operator to describe the asymmetric hysteresis phenomenon of the soft robot. Asymmetric hysteresis means that the hysteresis loop of the soft robot is asymmetric, that is, the rising curve cannot be rotated to obtain the falling curve.

[0110] The definition of the rising operator is shown in formula (3.4), where A i [u(k),r i ] is the output of the rising operator at the kth moment, y i [u(k),r i ] is the play operator at the threshold r i , the output at the kth moment, u(k) is the input of the operator at the kth moment:

[0111] A i [u(k),r i ]=(u(k)+ry i [u(k),r i ])·y i [u(k),r i ] (3.4).

[0112] The definition of the descent operator is shown in formula (3.5), where the meanings of the variables are the same as those in formula (3.4):

[0113] D i [u(k),r i ]=(y i [u(k),r i ]-u(k)+r)·y i [u(k),r i ] (3.5).

[0114] The rising operator and the falling operator are related to the threshold r and the input at time k. For convenience, we use A i [u(k),r i ] indicates the threshold is r i , the rising operator at time k, using D i [u(k),r i ] indicates the threshold is r i , the descent operator at time k.

[0115] like Figure 4 Shown are the rise operators with thresholds of 0.2 and 0.3, Figure 5 Shown are the descent operators with thresholds of 0.2 and 0.3, from Figure 4 and Figure 5It can be seen that both the rising operator and the falling operator are asymmetric structures and can be used to describe the asymmetric hysteresis phenomenon.

[0116] The MPI model still belongs to the category of the PI model. The MPI model is similar to the PI model and is also formed by the weighted superposition of multiple operators. After weighted superposition, it is shown in formula (3.6). Its structure is as follows: Figure 6 As shown in the figure, at a certain moment, the output of the model consists of a play operator, n rise operators, and n fall operators. Relatively speaking, the PI model is only a weighted superposition of n play operators. Therefore, the MPI model can better characterize the asymmetric hysteresis model in the pneumatic soft robot arm:

[0117]

[0118] Among them, w 0 , w ai , w di is the weight parameter, u(k) is the input at time k, r i is the threshold of different operators at time k. Y(k) is the output of the model at time k.

[0119] In the above model, w 0 , w ai , w di is the operator weight, which is an unknown quantity, among which:

[0120] w ai =[w a1 , w a2 ,…,w ai ,…,w an ] T (3.7)

[0121] Likewise,

[0122] w di =[w d1 , w d2 ,…,w di ,…,w dn ] T (3.8)

[0123] Different weight combinations can produce different hysteresis models, so for w 0 , w ai , w di After the solution is completed, a complete soft robot arm hysteresis model can be established.

[0124] (III) PI model and MPI model parameter identification

[0125] The PI model is a phenomenon-based hysteresis model that can be established based on measured data without considering the properties of the material. Before parameter identification, the input value and response value are first normalized. This paper conducts modeling analysis based on the hysteresis phenomenon of air pressure and displacement, and the hysteresis phenomenon of displacement and end contact force in the soft robot arm. For the air pressure-displacement hysteresis phenomenon, the input is air pressure, and the air pressure in the three air cavities is the same. The measured physical quantity is the elongation of the soft robot arm; for the displacement-pneumatic soft robot arm end contact force, the end contact force is measured by changing the vacuum degree in the blocking structure (set to 0kPa and 40kPa) and changing the end displacement of the soft robot arm. The normalized formulas are shown in formulas (3.9) and (3.10).

[0126] u n (k)=(u(k)-u m ) / (u M -u m ) (3.9)

[0127] x n (k) = (x(k) - x m ) / (x M -x m ) (3.10)

[0128] In formula (3.9), for the pneumatic soft robot arm with uncoupled variable stiffness structure, u(k) is the kth input air pressure data, u m is the minimum value of input air pressure, u M is the maximum value of the input air pressure, u n (k) is the normalized value of the kth input pressure. In formula (3.10), x(k) is the displacement value of the kth output, x m is the minimum value of the output displacement, x M is the maximum value of the output displacement. For the coupled variable stiffness structure pneumatic soft robot arm, in formula (3.9), u(k) is the kth end displacement value, u m is the minimum value of the end displacement, u M is the maximum value of the end displacement, u n (k) is the normalized value of the k-th end displacement. In formula (3.10), x(k) is the value of the end contact force corresponding to the k-th end displacement, x m is the minimum value of the end contact force, x M is the minimum value of the end contact force.

[0129] (3.1) PI model parameter identification

[0130] For the play operator, its output is only related to the threshold r and the input u(k). When the input value u(k) is normalized by formula (3.9) and the threshold r of the operator is set to 0, 0.05, 0.1, ..., 0.5, the output of the play operator can be uniquely determined when any threshold r and normalized input u(k) are given. Based on this conclusion, combined with formula (3.2), for each normalized model output point Y(k), it is composed of the weighted superposition of n+1 operators. When the threshold r and input u(k) are determined, the values ​​of the n+1 operators can be determined. Therefore, the remaining weight parameter w in formula (3.2) i i = 0, 1, ..., n is the unknown quantity. When n + 1 normalized output values ​​are taken as Y(k), the PI model parameter w

[56] can be obtained by solving the equation group. The model parameter calculation flow chart is shown in Figure 7 Shown: In Figure 7 Where u(k) and v(k) represent the normalized k+1th input point and k+1th state change point, respectively, and k=0, 1, 2, ..., 10.

[0131] exist Figure 7 In the example, the state change point v is defined as 2r on the horizontal axis. i and 1-2r i A set of points, where r is 0, 0.05, 0.1, ..., 0.5, so we can get v = 0, 0.1, ..., 1, with the following properties at the state change point:

[0132] (1) In the rising stage, for a threshold value r i The play operator, from formula 3.1, can be seen that when the horizontal coordinate is less than 2r i When i , when the horizontal axis is greater than 2r i When the value of the ordinate is u(k)-r i , for the horizontal axis 2r i The point of is defined as the state change point in the rising stage;

[0133] (2) In the descending phase, the horizontal axis is greater than 1-2r i When i , the horizontal axis is less than 1-2r i When i ; For the horizontal axis 1-2r i The point of is defined as the state change point in the descending phase;

[0134] (3) For a hysteresis model consisting of n+1 play operators, there are 2n state change points. After normalizing the hysteresis data, both the rising and falling stages include the state change points (0, 0) and (1, 1). Therefore, both the rising and falling stages include n+1 state change points. Figure 7 In the above, the parameter calculation is performed based on the normalized data of the ascending stage, so only the state change points of the ascending stage are involved, so the set v = 0, 0.1, ..., 1;

[0135] (4) In the rising stage, assuming there is a state change point v(k), from Property 1, we know that there must be a threshold value r i The play operator satisfies formula (3.11).

[0136] r i =v(k) / 2 (3.11)

[0137] With r i The value of is the dividing point that divides the n+1 operators of the PI model into two categories, one of which is the threshold r m Less than or equal to r i , one is the threshold r m Greater than r i When the threshold r of the first type operator m Less than or equal to r i When the state changes, the output at the state change point v(k) is v(k)-r m ; When the second type operator threshold r m Greater than r i When the state changes, the output at the state change point is r m .

[0138] (5) In the descending phase, r i The value of is the dividing point that divides the n+1 operators of the PI model into two categories, one of which is the threshold r m Less than or equal to r i , one is the threshold r m Greater than r i When the threshold r of the first type operator m Less than or equal to r i When the state changes, the output at the state change point v(k) is v(k)+r m ; When the second type operator threshold r m Greater than r i When the state changes, the output at the state change point is 1-r m .

[0139] According to the nature of the state change point, combined with the definition formula (3.2) of the PI model, combined with the process Figure 7The output of the model at the state change point v(k) can be obtained as shown in formula (3.12):

[0140]

[0141] In the rising stage of the PI model, there are 11 state change points (n=10). At each state change point, the equation shown in formula (3.12) can be obtained. The obtained equations are combined and expanded, as shown in formula (3.13),

[0142]

[0143] where x 0 (k), x 1 (k), …, x n (k) is the normalized output. For this paper, it is the normalized displacement value of the end of the soft robot arm, which is a known quantity. Figure 7 It can be seen that r m is less than or equal to r i The threshold value, and r i It can be obtained according to formula (3.11), where v(k) is the kth state change point, so r m is also a known quantity; for u(k)-r m , k = 0, 1, ..., 10, u(k) is the normalized input value, for this paper it is the normalized input pressure value, so u(k)-r m is also a known quantity. Therefore, in formula (3.13), only the weight w is an unknown quantity, and the coefficient of the weight w is only related to the threshold r and the normalized input, and has nothing to do with the output, so the weight coefficient matrix obtained is a fixed matrix. After calculation, for the PI model composed of 11 weighted superposition of play operators, and taking the threshold r = 0, 0.05, 0.1, ..., 0.5, its weight calculation matrix is ​​shown in formula (3.14):

[0144]

[0145] (3.2) MPI model parameter identification

[0146] The MPI model parameter calculation flow chart is as follows Fig. 9 As shown, similar to the PI model parameter calculation flowchart, the set v = 0, 0.1, ..., 1, 0.9, ..., 0.1 represents the set of state change points. In the flowchart, v(k) represents the k+1th state change point, for example, v(0) = 0, v(1) = 0.1, ..., v(10) = 1: the set r = 0, 0.05, 0.1, ..., 0.5 represents the operator threshold. In the flowchart, r mrepresents the m+1th threshold, for example r 0 =0, r 1 =0.05, ..., r 10 =0.5, etc.

[0147] The ascending and descending operators have the following properties at the state change point:

[0148] (1) For any state change point v(k), there is a threshold r i The operator (play operator, rise or fall operator) satisfies formula (3.11). The threshold r obtained by formula (3.11) i As the dividing point, the operators are divided into two categories. The threshold of the first type of operators is 0≤r m <r i , the threshold of the second type of operator is r m ≥r i .

[0149] (2) In the ascending stage, among the first type of operators, when r m = 0, it can be seen from formula (3.6) that the corresponding is the play operator with a threshold r of 0. The play operator with a threshold r of 0 satisfies formula (3.15) at the state change point v(k), that is, when the operator input is v(k), the operator output is v(k). When the threshold r = 0, the play operator degenerates into a coincident straight line, such as Figure 8 As shown, the output of the operator is equal to the input v(k) of the operator.

[0150] α=y 0 [v(k), r 0 ]=v(k) (3.15)

[0151] For the first type of operator, when 0<r m <r i According to the definition formula (3.4) of the rising operator, the threshold value is r m The output of the rising operator at the state change point v(k), k = 1, 2, ..., i-1 is shown in formula (3.16):

[0152] β′=(v(k)+r m -y m [v(k), r m ])·y m [v(k), r m ] k=1, 2,…,i-1 (3.16)

[0153] where y m [v(k), r m ] is the threshold value r mThe output of the play operator at the state change point v(k) is v(k)-r m Therefore, formula (3.16) can be converted into formula (3.17):

[0154] β′=2r m ·(v(k)-r m ), k=1, 2,…,i-1 (3.17).

[0155] For the first type of operator, when 0<r m <r i When , according to the definition formula (3.5) of the descent operator, the threshold is r m The output of the descent operator at the state change point v(k), k = 1, 2, ..., i-1 is shown in formula (3.18):

[0156] β″=(y m [v(k), r m ]-v(k)+r m )·y m [v(k), r m ] (3.18)

[0157] Among them, y m [v(k), r m ] The same threshold is r m The output of the play operator at the state change point v(k) is v(k)-r m . Formula (3.18) can be converted into formula (3.19).

[0158] β″=0,k=1,2,…,i-1 (3.19)

[0159] For the second type of operator, that is, the operator threshold r m ≥r i When , according to the definition formula (3.4) of the rising operator, the threshold value is r m The output of the rising operator at the state change point v(k), k = 1, 2, ..., i-1 is shown in formula (3.20):

[0160] γ′=(v(k)+r m -y m [v(k), r m ])·y m [v(k), r m ] k=i,i+1,…,n (3.20)

[0161] where y m [v(k), r m ] is the threshold value r mThe output of the play operator at the state change point v(k), at which r m ≥r i , so the output of the play operator is r m , so formula (3.20) can be converted to formula (3.21):

[0162] γ′=v(k)·r m k=i,i+1,…,n (3.21).

[0163] Similarly, for the second type of operator, when the operator threshold r m ≥r i When , according to the definition formula (3.5) of the descent operator, the threshold value is r m The output of the rising operator at the state change point v(k), k = 1, 2, ..., i-1 is shown in formula (3.22):

[0164] γ″=(y m [v(k), r m ]-v(k)+r m )·y m [v(k), r m ] (3.22)

[0165] where y m [v(k), r m ] is the threshold value r m The output of the play operator at the state change point v(k), at which r m ≥r i , so the output of the play operator is r m , so formula (3.22) can be converted to formula (3.23):

[0166] γ″=(2·r m -v(k))·r m k=i,i+1,…,n (3.23).

[0167] (3) Similarly, in the descending phase, in the first type of operator, when r m = 0, it can be seen from formula (3.6) that the corresponding is the play operator with a threshold r of 0. The play operator with a threshold r of 0 satisfies formula (3.24) at the state change point v(k), that is, when the operator input is v(k), the operator output is v(k).

[0168] α=y 0 [v(k), r 0 ]=v(k) (3.24)

[0169] For the first type of operator, when 0<r m<r i According to the definition formula (3.4) of the rising operator, the threshold value is r m The output of the rising operator at the state change point v(k), k=1, 2, ..., i-1 is shown in formula (3.25):

[0170] β′=(v(k)+r m -y m [v(k), r m ])·y m [v(k), r m ] (3.25)

[0171] where y m [v(k), r m ] is the threshold value r m The output of the play operator at the state change point v(k) in the descending phase is v(k)+r m Therefore, formula (3.25) can be converted into formula (3.26):

[0172] β′=0,k=1,2,…,i-1 (3.26)

[0173] For the first type of operator, when 0<r m <r i When , according to the definition formula (3.5) of the descent operator, the threshold is r m The output of the descent operator at the state change point v(k), k = 1, 2, ..., i-1 is shown in formula (3.27):

[0174] β″=(y m [v(k), r m ]-v(k)+r m )·y m [v(k), r m ] (3.27)

[0175] Among them, y m [v(k), r m ] The same threshold is r m The output of the play operator at the state change point v(k) is v(k)+r m Formula (3.27) can be converted into formula (3.28):

[0176] β″=2·r m ·(v(k)+r m ), k=1, 2,…,i-1 (3.28).

[0177] For the second type of operator, that is, the operator threshold r m ≥ri When , according to the definition formula (3.4) of the rising operator, the threshold value is r m The output of the rising operator at the state change point v(k), k=1, 2,..., i-1 is shown in formula (3.29).

[0178] γ′=(v(k)+r m -y m [v(k), r m ])·y m [v(k), r m ] k=i,i+1,…,n (3.29)

[0180] where y m [v(k), r m ] is the threshold value r m The output of the play operator at the state change point v(k), at which r m ≥r i , so the play operator output is 1-r m , so formula (3.29) can be converted to formula (3.30):

[0181] γ′=(v(k)-1+2r m )·(1-r m ) k=i,i+1,…,n (3.30).

[0182] Similarly, for the second type of operator, when the operator threshold r m ≥r i When , according to the definition formula (3.5) of the descent operator, the threshold value is r m The output of the rising operator at the state change point v(k), k = 1, 2, ..., i-1 is shown in formula (3.31):

[0183] γ″=(y m [v(k), r m ]-v(k)+r m )·y m [v(k), r m ] (3.31)

[0184] where y m [v(k), r m ] is the threshold value r m The output of the play operator at the state change point v(k), at which r m ≥r i , so the play operator output is 1-r m , so formula (3.31) can be converted to formula (3.32):

[0185] γ″=(1-v(k))·(1-r m ) k=i,i+1,…,n (3.32).

[0186] Combining the above three properties and parameter calculation steps Fig. 9 , we can get that the calculation of MPI model parameters is still to first obtain several equations containing parameters, then expand and merge them, and combine the normalized output obtained by measurement to obtain the model weight parameters. According to the properties of the ascending operator and the descending operator at the state change point, substitute formulas (3.15), (3.17), (3.19), (3.21), and (3.23) into formula (3.6) to obtain the output of v(k) of the MPI model at the state change point of the ascending section as shown in formula (3.33):

[0187]

[0188] Similarly, in the descending section, substituting formulas (3.24), (3.26), (3.28), (3.30), and (3.32) into formula (3.6), we can obtain the output of v(k) of the MPI model at the state change point in the descending section as shown in formula (3.34):

[0189]

[0190] Expand and combine formulas (3.33) and (3.34). For the sake of simplicity, let w an =w dn , we can get the equation system as shown in formula (3.35), which contains 2n equations and can solve 2n unknown weight parameters w 0 , w n , w a , w d :

[0191]

[0192] Formula (3.35) is similar to formula (3.13), with 2n unknown weight parameters w 0 , w n , w a , w d When n is 10, there are 20 unknown parameters, which are w 0 , w 10 , w a1 ,…w a9 , w d1 ,…w d9In formula (3.35), there are 2n parameters and 2n equations, so the weight vector can be obtained, and the formula can be simplified to the form of A×w=b, where A is a 20*20 matrix. For this method, the 20 normalized hysteresis data are taken as Y(1),...,Y(2n), that is, the value of b; since the threshold r is set to a fixed value and the input value is normalized to [0, 1], the matrix A is a fixed matrix, as shown in formula (3.36):

[0193]

[0194] (3.36).

[0195] (IV) PI and MPI inverse hysteresis models

[0196] If you want to further use the hysteresis model to control the soft robotic arm, you also need to invert the hysteresis model to obtain a hysteresis inverse model.

[0197] For the PI model, its inverse model is still the PI model, only the weights and thresholds change. Its parameters can be obtained by the following formulas (3.37-3.39):

[0198]

[0199]

[0200]

[0201] Since the MPI hysteresis model is a type of PI model, which is formed by the weighted addition of different operators, their inverse model is also a type of PI model, which is the weighted addition of multiple operators, but the weights and thresholds change. The weights and thresholds are derived from formulas (3.37-3.39).

[0202] (V) Hysteresis model simulation steps

[0203] This section further introduces how to use the parameter identification principle to obtain the parameters of the PI model and the MPI model; and according to the weighted addition principle of the hysteresis model, the obtained parameters are substituted into the operator to verify the correctness of the obtained weight parameters.

[0204] (5.1) Calculation of PI model weight parameters

[0205] According to the parameter calculation principle, the parameter w is calculated by formula (3.40). In the formula, for the PI model, the parameter identification matrix A is as shown in formula (3.14), and b is the hysteresis data of the measured rising or falling section.

[0206] A·w=b (3.40)

[0207] The parameter calculation process is as follows Fig.10 As shown, the data is normalized using formula (3.10). Due to the limitation on the number of operators, it is necessary to take 20 points at fixed intervals in the normalized data to form a hysteresis loop in a discrete state. For the PI model, the data of the rising or falling segment can be used as b, and then the model parameter w can be calculated according to formula (3.40).

[0208] The parameter calculation matrix of the MPI model is shown in formula (3.28). Its parameter calculation formula and process are basically the same as those of the PI model. Only in the MPI model, the 20 data points obtained at fixed intervals are used as b, and the parameter w is obtained according to formula (3.40).

[0209] According to the weighted addition principle of the PI model, the obtained weight parameter w is combined with the corresponding operator for weighted superposition to verify the correctness of the parameters and the model.

[0210] (5.2) Proof of unique solution of weight parameter

[0211] The necessary and sufficient condition for the linear equation system AX=B to have a solution is R(A)=R(A, B). When A is formula (3.14), A is an 11*11 matrix, and it can be calculated by Matlab that rank(A)=11. Since A is a square matrix, it satisfies R(A)=R(A, B). Since the rank of matrix A is equal to the number of rows, it can be obtained that the equation system has a unique solution.

[0212] When the parameter calculation matrix A is formula (3.36), A is a 20*20 matrix, and its rank(A)=20, which also satisfies R(A)=R(A, B). Because the rank of matrix A is equal to the number of rows, it can also be obtained that the system of equations has a unique solution.

[0213] (5.3) Hysteresis model verification steps

[0214] Depend on Figure 3 and Figure 6 It can be seen that the PI model is composed of weighted superposition of different weight operators. Based on the obtained weight parameters, the correctness of the model is verified in combination with the play operator and the rise operator and the fall operator.

[0215] For the model verification of the PI model, the specific flow chart is as follows Fig.11As shown, since the PI model is based on the data of the rising or falling segment, a segment of data points is selected from the normalized data b, and the data points of the rising segment are selected in the flowchart for weight calculation. The obtained weight parameters are weighted superimposed with the play operator to obtain the modeling point Y(k) corresponding to each hysteresis data point. The modeling error can be obtained from the modeling data Y(k) of the hysteresis data b. For the MPI model, its model verification flowchart is as follows: Fig.12 As shown, since the MPI model calculates weights from the entire hysteresis loop data, the data of the entire hysteresis loop needs to be normalized, and in order to correspond to the MPI weight calculation matrix (3.36), 20 discrete data points need to be selected at fixed intervals as b to calculate the weight w, which is the obtained weight parameter (20x1).

[0216] The MPI model in this paper is composed of a play operator with a threshold of 0, 10 ascending operators, and 10 descending operators. n =w an =w dn , so only 20 equations are needed to calculate the parameters. The weight w is weighted and superimposed with a corresponding play operator and 10 rising operators and 10 falling operators to obtain the modeling value Y(k) at the corresponding hysteresis data point. For the calculation of the modeling error value, the modeling error at each discrete point can be obtained by subtracting the modeling data Y(k) from the corresponding discrete hysteresis data b.

[0217] Based on the basic PI model, this embodiment derives an MPI hysteresis model, and uses the properties of the PI model and the MPI model's operators at the state change point to obtain the PI model and the MPI model's weight calculation matrix. This parameter matrix is ​​universal for the normalized hysteresis model. The matrix is ​​shown in formulas (3.14) and (3.36), and the model parameters can be easily obtained through this matrix. Finally, the parameter calculation steps, the proof of the unique solution of the parameters, and the detailed steps of verifying the model using the obtained weight parameters are described in detail.

[0218] The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims

1. A hysteresis modeling method for a pneumatic soft robot arm based on a PI model, characterized in that: The pneumatic soft robot arm comprises a pneumatic drive structure and a variable stiffness structure of the soft robot arm; the pneumatic soft robot arm hysteresis modeling method comprises the following steps: S1, weighted superposition of play operators under different thresholds to form a PI model: Where n represents the number of operators, w i represents the weight of the ith operator, r i represents the threshold of the i-th operator, Y(k) is the output of the model established at time k; i [u(k),r i ] is the play operator at the threshold r i , the output at the kth moment; u(k) is the input of the operator at the kth moment; S2, an asymmetric hysteresis model in a pneumatic soft robot arm, is composed of a play operator, n rise operators, and n fall operators: Among them, w0, w ai , w di is the weight parameter; u(k) is the input at time k; r i is the threshold of different operators at time k; Y(k) is the output of the model at time k; A i [u(k),r i ] indicates the threshold is r i The rising operator at time k; D i [u(k),r i ] indicates the threshold is r i The descent operator at the kth moment; S3, identify the parameters in the asymmetric hysteresis model of the pneumatic soft robot; specifically, normalize the input values ​​and response values. Each model output point Y(k) after normalization is composed of the weighted superposition of n+1 operators. When the threshold r and the input u(k) are determined, the values ​​of the n+1 operators are also determined, and the unknown weight parameters of the PI model parameters are obtained by solving the set of equations; according to the properties of the rising operator and the falling operator at the state change point, combined with the measurement to obtain the normalized output, the unknown weight parameters of the asymmetric hysteresis model in the pneumatic soft robot are obtained.

2. The hysteresis modeling method of pneumatic soft robot arm based on PI model according to claim 1 is characterized in that: In step S1, the expression of the play operator is: Among them, r is the threshold of the play operator, and u(k) is the input of the operator at time k.

3. The hysteresis modeling method of pneumatic soft robot arm based on PI model according to claim 1, characterized in that: In step S2, the expression of the rising operator is: A i [u(k),r i ]=(u(k)+r-y i [u(k),r i ])·y i [u(k),r i ]; The expression of the descent operator is: D i [u(k),r i ]=(y i [u(k),r i ]-u(k)+r)·y i [u(k),r i ] The rising operator and the falling operator are related to the threshold r and the input at time k.

4. The hysteresis modeling method of pneumatic soft robot arm based on PI model according to claim 1, characterized in that: In step S3, the input value and the response value are normalized using the following formula: in n (k)=(u(k)-u m ) / (in M -in m ) x n (k)=(x(k)-x m ) / (x M -x m ) In the formula, for the pneumatic soft robot arm with uncoupled variable stiffness structure, u(k) is the kth input air pressure data, u m is the minimum value of input air pressure, u M is the maximum value of the input air pressure, u n (k) is the normalized value of the k-th input pressure; x(k) is the displacement value of the k-th output, x m is the minimum value of the output displacement, x M is the maximum value of the output displacement; For the coupled variable stiffness structure pneumatic soft robot arm, u(k) is the kth end displacement value, u m is the minimum value of the end displacement, u M is the maximum value of the end displacement, u n (k) is the normalized value of the k-th end displacement; x(k) is the value of the end contact force corresponding to the k-th end displacement, x m is the minimum value of the end contact force, x M is the minimum value of the end contact force.

5. The hysteresis modeling method of pneumatic soft robot arm based on PI model according to claim 1, characterized in that: In step S3, the process of solving the equation group to obtain the unknown weight parameters of the PI model parameters includes the following steps: Define the state change point set, the state change point v set is 2r on the horizontal axis i and 1-2r i A set of points; for a hysteresis model composed of n+1 play operators, there are 2n state change points. After the hysteresis data is normalized, both the rising stage and the falling stage include the state change points (0,0) and (1,1), and the rising stage and the falling stage each include n+1 state change points; In the rising stage, assuming there is a state change point v(k), there is a threshold r i The play operator satisfies the following formula: i =v(k) / 2; with r i The value of is the dividing point that divides the n+1 operators of the PI model into two categories, one of which is the threshold r m Less than or equal to r i , one is the threshold r m Greater than r i ; When the threshold r of the first type operator m Less than or equal to r i When the state changes, the output at the state change point v(k) is v(k)-r m ; When the second type operator threshold r m Greater than r i When the state changes, the output at the state change point is r m ; In the descending phase, r i The value of is the dividing point that divides the n+1 operators of the PI model into two categories, one of which is the threshold r m Less than or equal to r i , one is the threshold r m Greater than r i ; When the threshold r of the first type operator m Less than or equal to r i When the state changes, the output at the state change point v(k) is v(k)+r m ; When the second type operator threshold r m Greater than r i When the state changes, the output at the state change point is 1-r m ; According to the properties of the state change point, combined with the PI model of step S1, the output of the model at the state change point v(k) is: Combine and expand the obtained equations to obtain the solution equation of the weight coefficient matrix: In the formula, x0(k), x1(k), …, x n (k) is the normalized output. The normalized displacement value of the end of the soft robot arm is a known quantity; r m is less than or equal to r i The threshold value, v(k) is the kth state change point, r m is also a known quantity; for u(k)-r m , u(k) is the normalized input value; for the normalized input pressure value, u(k)-r m It is also a known quantity.

6. The hysteresis modeling method of pneumatic soft robot arm based on PI model according to claim 1, characterized in that: In step S3, the process of obtaining the unknown weight parameters of the asymmetric hysteresis model in the pneumatic soft robot arm includes the following steps: For any state change point v(k), there is a threshold r i The operator satisfies the formula r i =v(k) / 2; the threshold value r i As the dividing point, the operators are divided into two categories. The threshold of the first type of operators is 0≤r m <r i , the threshold of the second type of operator is r m ≥r i ; In the ascending stage, among the first type of operators, when r m =0, the corresponding value is the play operator with a threshold r of 0. The play operator with a threshold r of 0 satisfies the formula α=y0[v(k),r0]=v(k) at the state change point v(k); when the threshold r=0, the play operator degenerates into a coincident straight line, and the output of the operator is equal to the input v(k): α=y0[v(k),r0]=v(k); For the first type of operator, when 0 <r m <r i When the threshold is r m The output of the rising operator at the state change point v(k) is: β′=(v(k)+r m -y m [v(k),r m ])·y m [v(k),r m ]k=1,2,…,i-1 where y m [v(k),r m ] is the threshold value r m The output of the play operator at the state change point v(k) is v(k)-r m ; Transformation yields: β′=2r m ·(v(k)-r m ),k=1,2,…,i-1; For the first type of operator, when 0 <r m <r i When the threshold is r m The output of the descent operator at the state change point v(k) is: β″=(y m [v(k),r m ]-v(k)+r m )·y m [v(k),r m ]; where y m [v(k),r m ] The same threshold is r m The output of the play operator at the state change point v(k) is v(k)-r m ;Conversion: β″=0,k=1,2,…,i-1; For the second type of operator, when the operator threshold r m ≥r i When the threshold is r m The output of the rising operator at the state change point v(k) is: γ′=(v(k)+r m -y m [v(k),r m ])·y m [v(k),r m ]k=i,i+1,…,n, where y m [v(k),r m ] is the threshold value r m The output of the play operator at the state change point v(k), r m ≥r i , the output of the play operator is r m , converted to: γ′=v(k)·r m k=i,i+1,…,n; For the second type of operator, when the operator threshold r m ≥r i When the threshold is r m The output of the rising operator at the state change point v(k) is: γ″=(y m [v(k),r m ]-v(k)+r m )·y m [v(k),r m ], where y m [v(k),r m ] is the threshold value r m The output of the play operator at the state change point v(k), r m ≥r i , the output of the play operator is r m , converted to: γ″=(2·r m -v(k))·r m k=i,i+1,…,n; In the descent phase, in the first type of operators, when r m = 0, the corresponding value is the play operator with a threshold r of 0. The play operator with a threshold r of 0 satisfies the following at the state change point v(k): α = y0[v(k), r0] = v(k); For the first type of operator, when 0 <r m <r i When the threshold is r m The output of the rising operator at the state change point v(k) is: β′=(v(k)+r m -y m [v(k),r m ])·y m [v(k),r m ], where y m [v(k),r m ] is the threshold value r m The output of the play operator at the state change point v(k) in the descending phase is v(k)+r m , converted to: β″=0,k=1,2,…,i-1; For the first type of operator, when 0 <r m <r i When the threshold is r m The output of the descent operator at the state change point v(k) is: β″=(y m [v(k),r m ]-v(k)+r m )·y m [v(k),r m ], where y m [v(k),r m ] The same threshold is r m The output of the play operator at the state change point v(k) is v(k)+r m , converted to: β″=2·r m ·(v(k)+r m ),k=1,2,…,i-1 For the second type of operator, when the operator threshold r m ≥r i When the threshold is r m The output of the rising operator at the state change point v(k) is: γ′=(v(k)+r m -y m [v(k),r m ])·y m [v(k),r m ]k=i,i+1,…,n, where y m [v(k),r m ] is the threshold value r m The output of the play operator at the state change point v(k), r m ≥r i , the play operator output is 1-r m , converted to: γ′=(v(k)-1+2r m )·(1-r m )k=i,i+1,…,n; For the second type of operator, when the operator threshold r m ≥r i When the threshold is r m The output of the rising operator at the state change point v(k) is: γ″=(y m [v(k),r m ]-v(k)+r m )·y m [v(k),r m ], where y m [v(k),r m ] is the threshold value r m The output of the play operator at the state change point v(k), r m ≥r i , the play operator output is 1-r m , converted to: γ″=(1-v(k))·(1-r m )k=i,i+1,…,n; According to the properties of the rising operator and the falling operator at the state change point, the output of the asymmetric hysteresis model at the state change point of the rising section v(k) is obtained as follows: In the descending section, the output of the asymmetric hysteresis model at the state change point v(k) in the descending section is obtained as: Let w an =w dn , we get the following set of equations, solving the 2n unknown weight parameters w0,w n ,w a ,w d :

7. The hysteresis modeling method of pneumatic soft robot arm based on PI model according to claim 1, characterized in that: The pneumatic soft robot arm hysteresis modeling method comprises the following steps: The PI model is inverted, where the corresponding inverse model parameter calculation formula is:

8. The hysteresis modeling method of pneumatic soft robot arm based on PI model according to claim 1, characterized in that: The model validation process of the PI model includes: Normalized hysteresis data b, 11 data points in the rising section are selected; The weight parameter is calculated according to the following formula: w = A -1 b. The obtained weight parameters are weighted superimposed with the play operator to obtain the modeling point Y(k) corresponding to each hysteresis data point: The difference between the hysteresis data b and the modeling data Y(k) is calculated as the modeling error.

9. The hysteresis modeling method of pneumatic soft robot arm based on PI model according to claim 1, characterized in that: The model verification process of the asymmetric hysteresis model in the pneumatic soft robot arm includes: Normalized hysteresis data b, 20 data points are selected at fixed intervals; The weight parameter is calculated according to the following formula: w = A -1 b. The obtained weight parameters are weighted superimposed with the play operator to obtain the modeling point Y(k) corresponding to each hysteresis data point: The difference between the hysteresis data b and the modeling data Y(k) is calculated as the modeling error.

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