A method for optimizing the trajectory deviation of the multi-section boom end of a concrete pump truck

Abstract

The present invention provides a method for optimizing the trajectory deviation of the end of a multi-section arm of a concrete pump truck, comprising: S1: using a Jacobian matrix to establish a nonlinear three-dimensional space dynamic equation of a rule tracking system of a multi-section arm concrete pump truck; S2: using a fuzzy logic expression method to transform the obtained three-dimensional space dynamic equation into a fuzzy model of the nonlinear three-dimensional space dynamic equation; S3: introducing an integral sliding film function, using a BP neural network to approximate the influence of unknown position deviation, and reconstructing the solution of the learning algorithm in a robust control framework of the discrete system; S4: designing a BP neural network optimization learning algorithm based on state feedback control; the method for optimizing the trajectory deviation of the end of a multi-section arm of a concrete pump truck provided by the present invention can reduce the deviation of the motion trajectory of the end of the segment arm of the concrete pump truck, make the pouring process safer and more reliable, and is suitable for further promotion and application.

Description

Technical Field

[0001] The present invention relates to the technical field of pump truck segmented boom control, and in particular to a method for optimizing trajectory deviation of a terminal end of a multi-segmented boom of a concrete pump truck. Background Art

[0002] With the rapid development of prefabricated building construction technology, concrete pump trucks, used for both transportation and pouring, have become indispensable construction equipment. To meet the demands of high-altitude, real-time pouring operations, concrete pump trucks typically utilize a multi-section boom with coordinated control. However, controlling the trajectory of the concrete pump truck's multi-section boom can impact pouring safety and construction quality.

[0003] To this end, the present invention proposes a method for optimizing the trajectory deviation of the end of a multi-section boom of a concrete pump truck. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a method for optimizing the trajectory deviation of the end of a multi-section boom of a concrete pump truck.

[0005] In order to solve the above problems, the present invention adopts the following technical solutions:

[0006] A method for optimizing the trajectory deviation of a multi-section boom end of a concrete pump truck comprises the following steps:

[0007] S1: The nonlinear three-dimensional dynamic equations of the multi-section boom concrete pump truck tracking system are established using the Jacobian matrix;

[0008] S2: The obtained three-dimensional space dynamic equation is transformed into a fuzzy model of nonlinear three-dimensional space dynamic equation using fuzzy logic expression method;

[0009] S3: Introducing the integral sliding film function, using BP neural network to approximate the unknown position deviation effect, and reconstructing the learning algorithm solution in the robust control framework of discrete systems;

[0010] S4: Design a BP neural network optimization learning algorithm based on state feedback control.

[0011] Furthermore, the multi-section arm concrete pump truck is a four-section arm concrete pump truck.

[0012] Furthermore, S1 specifically includes the following steps:

[0013] S1.1: Based on the spatial coordinate relationship, the following spatial coordinate equations of the four-section boom concrete pump truck system are obtained:

[0014] x=l1cosθ1+l2cosθ2+l3cosθ3+l4cosθ4 (1)

[0015] y=l1sinθ1+l2sinθ2+l3sinθ3+l4sinθ4 (2)

[0016] z=xtanθ z (3)

[0017] Among them, x, y, z represent the spatial coordinates X, Y, Z positions of the end of the four-section boom concrete pump truck, θ1, θ2, θ3, θ4 are the angles from the first section boom to the fourth section boom in the projection of the coordinate plane X, Y, respectively. z It is the angle between the pump truck arm and the X axis in the projection of the coordinate X, Z plane. l1, l2, l3, and l4 are the lengths from the first to the fourth arm respectively.

[0018] S1.2: Define x d ,y d ,z d are the reference coordinates of the concrete pump truck end, then after subtracting the reference coordinates from both sides of equations (1) to (3), we get:

[0019] ε x =xx d =l1cosθ1+l2cosθ2+l3cosθ3+l4cosθ4-x d , (4)

[0020] ε y =yy d =l1sinθ1+l2sinθ2+l3sinθ3+l4sinθ4-y d , (5)

[0021] ε z =zz d =xtanθ z -z d , (6)

[0022] S1.3: Taking the derivatives of both sides of equations (4) to (6), we obtain:

[0023]

[0024]

[0025]

[0026] S1.4: Define N x ,N y ,N z The deviation of the spatial coordinates X, Y, and Z is respectively affected, and equations (7) to (9) are rewritten as the following system state space expressions:

[0027]

[0028] Where ε is the position deviation, B(t) is the input matrix of the system, u(t) is the control input, and N is the unknown deviation disturbance;

[0029]

[0030]

[0031]

[0032]

[0033] Furthermore, S2 specifically includes the following steps:

[0034] S2.1: The obtained three-dimensional dynamic nonlinear equation, where the variables θ1, θ2, θ3, θ4, θ z respectively Perform piecewise linearization, and the variable x is piecewise linearized at [16m, 17m, 18m], so 729 fuzzy rules are obtained, as follows:

[0035] Fuzzy rule R l : If θ1 is θ2 is θ3 is θ4 is θ5 is θ6 is

[0036] So

[0037] Among them, R l is the lth fuzzy rule, is a fuzzy set, B l is the input parameter matrix under the lth fuzzy rule;

[0038] S2.2: Define fuzzy sets for reasoning and the normalized membership function μ l ,get:

[0039]

[0040] S2.3: By combining the membership functions, the following fuzzy system model is obtained:

[0041]

[0042] Furthermore, S3 specifically includes the following steps:

[0043] S3.1: Introduce the following integral synovial function:

[0044]

[0045] Where S represents the integral synovial function; F represents the synovial function mapping; It refers to the position deviation of the end;

[0046] S3.2: Derivative equation (15) and substitute it into equation (14) to obtain:

[0047]

[0048] Therefore, u(t) can be designed as follows:

[0049]

[0050] available:

[0051] S3.3: Introduce BP neural network to approximate the unknown position deviation effect N, define is an approximation of N, then the input-output characteristic relationship of the BP neural network is obtained:

[0052]

[0053] Among them, f is the function mapping of BP neural network, W and V are the learned weight values, σ is a bounded function, is the input of the neural network;

[0054] S3.4: Perform Taylor expansion on formula (19) to obtain:

[0055]

[0056] Among them, ΔW, ΔV, They are W, V, The step increase value of

[0057] S3.5: Due to Subtract N(t+1) from both sides of formula (20) to obtain:

[0058]

[0059] in,

[0060]

[0061] S3.6: Known Therefore, the learning rate U(t) can be designed as follows:

[0062] U(t)=G∈ (22)

[0063] Where G is the controller mapping iteration matrix to be determined;

[0064] S3.7: Substitute the learning rate U(t) in (22) into the BP neural network system in (21), and we get:

[0065]

[0066] Where I is the identity matrix.

[0067] Furthermore, S4 specifically includes the following steps:

[0068] S4.1: Establish the Lyapunov function as follows:

[0069] V(t)=∈ T (t)P∈(t), (24)

[0070] Where P is a positive definite symmetric matrix;

[0071] S4.2: Calculate the difference function ΔV(t) of the Lyapunov function and obtain:

[0072] V(t)=V(t+1)-V(t)=∈ T (t+1)P∈(t+1)-∈ T (t)P∈(t) (25)

[0073] S4.3: Define the matrix H, which is obtained from formula (23):

[0074]

[0075] S4.4: Given the following performance indicator function J(t):

[0076]

[0077] Among them, γ is the performance index;

[0078] S4.5: Combining equations (25)-(27), we obtain the following nonlinear matrix inequality:

[0079]

[0080] When formula (28) holds true, we can get Indicates that the system is stable, that is, the learning algorithm (22) makes the BP neural network output used The influence of position deviation N can be accurately approximated, where Sym{H} is H+H T ;

[0081] In addition, when formula (28) holds, J(t) < 0, which means that the system is stable with performance index γ;

[0082] S4.6: Define G:

[0083]

[0084] Among them, g is the linear matrix parameter;

[0085] S4.7: Substituting equation (29) into equation (28), we obtain:

[0086]

[0087] Then the learning rate parameter g can be obtained by the following formula:

[0088]

[0089] S4.8: Substituting formula (29) into formula (22), the learning rate obtained is as follows:

[0090]

[0091] S4.9: Substituting into formula (32), the final learning rate is as follows:

[0092]

[0093]

[0094] Substituting ΔW and ΔV obtained from (33) and (34) into formula (20) can make the error at time t+1 smaller, reduce the position deviation of the end of the boom, and improve the accuracy of the trajectory control of the concrete pump truck arm.

[0095] Based on the above scheme, the present invention also provides a computer-readable storage medium, which stores at least one instruction, at least one program, code set or instruction set. The at least one instruction, at least one program, code set or instruction set is loaded and executed by a processor to implement the above-mentioned method for optimizing the trajectory deviation of the multi-section arm end of a concrete pump truck.

[0096] Beneficial effects:

[0097] The present invention provides a method for optimizing the trajectory deviation of the end of a multi-section arm of a concrete pump truck, which can reduce the deviation of the motion trajectory of the end of the section arm of the concrete pump truck, improve the control accuracy of the section arm, and make the pouring process safer and more reliable.

[0098] This paper uses a commonly used four-section boom concrete pump truck as the research object. First, the Jacobian matrix is ​​used to establish the nonlinear three-dimensional dynamic equations of the four-section boom concrete pump truck's trajectory tracking system. Next, the obtained three-dimensional dynamic equations are transformed into fuzzy models using fuzzy logic. Furthermore, an integral sliding surface is designed, and a BP neural network is used to approximate the effects of unknown position deviations. The learning algorithm is then reconstructed within a robust control framework for discrete systems. Finally, a BP neural network optimization learning algorithm based on state feedback control is designed. This four-section boom concrete pump truck arm trajectory deviation optimization method can improve the accuracy of concrete pump truck arm trajectory control and is suitable for further promotion and application. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0100] Figure 1 It is a brief schematic diagram of the process of the present invention;

[0101] Figure 2 Schematic diagram of establishing spatial coordinates using the four-section boom of a concrete pump truck. DETAILED DESCRIPTION

[0102] The present invention will be described in further detail below with reference to the accompanying drawings and examples. It is particularly noted that the following examples are intended only to illustrate the present invention and are not intended to limit the scope of the present invention. Similarly, the following examples are only some embodiments of the present invention and are not intended to be exhaustive. All other embodiments obtained by those of ordinary skill in the art without creative effort are intended to fall within the scope of protection of the present invention.

[0103] Refer to the attached Figure 1 As shown, this embodiment provides a method for optimizing the trajectory deviation of a multi-section boom end of a concrete pump truck, comprising the following steps:

[0104] S1: Use the Jacobian matrix to establish the nonlinear three-dimensional dynamic equations of the multi-section boom concrete pump truck tracking system; specifically including:

[0105] S1.1: Based on the spatial coordinate relationship, the following spatial coordinate equations of the four-section boom concrete pump truck system are obtained:

[0106] x=l1cosθ1+l2cosθ2+l3cosθ3+l4cosθ4 (1)

[0107] y=l1sinθ1+l2sinθ2+l3sinθ3+l4sinθ4 (2)

[0108] z=xtanθ z (3)

[0109] Refer to the attached Figure 2 As shown, x, y, z represent the spatial coordinates X, Y, Z of the end of the four-section boom concrete pump truck, θ1, θ2, θ3, θ4 are the angles from the first section boom to the fourth section boom in the projection of the coordinate plane X, Y, respectively. z It is the angle between the pump truck arm and the X-axis in the projection of the coordinate X and Z planes. l1, l2, l3, and l4 are the lengths from the first to the fourth arm sections respectively. sin, cos, and tan are the sine, cosine, and tangent functions respectively.

[0110] S1.2: Define x d ,y d ,z d are the reference coordinates of the concrete pump truck end, then after subtracting the reference coordinates from both sides of equations (1) to (3), we get:

[0111] ε x =xx d =l1cosθ1+l2cosθ2+l3cosθ3+l4cosθ4-x d , (4)

[0112] ε y =yy d =l1sinθ1+l2sinθ2+l3sinθ3+l4sinθ4-y d , (5)

[0113] ε z =zz d =xtanθ z -z d , (6)

[0114] S1.3: Consider further that the end reference coordinates are usually constant over a small range of time, i.e. Taking the derivatives of both sides of formulas (4) to (6), we get:

[0115]

[0116]

[0117]

[0118] S1.4: Considering that the four-section boom concrete pump truck has a deviation in the end position due to the deformation of its own boom, and this deviation is difficult to quantify and obtain, we define N x ,N y ,N z The deviation of the spatial coordinates X, Y, and Z is respectively affected, and equations (7) to (9) are rewritten as the following system state space expressions:

[0119]

[0120] Where ε is the position deviation, B(t) is the input matrix of the system, u(t) is the control input, and N is the unknown deviation disturbance;

[0121]

[0122]

[0123]

[0124]

[0125] In this step, the Jacobian matrix is ​​used to establish the nonlinear three-dimensional dynamic equation of the four-section boom concrete pump truck tracking system, as shown in formula (10).

[0126] S2: The obtained three-dimensional space dynamic equation is transformed into a fuzzy model of the nonlinear three-dimensional space dynamic equation using the fuzzy logic expression method; specifically including:

[0127] S2.1: The obtained three-dimensional dynamic nonlinear equation, where the variables θ1, θ2, θ3, θ4, θ z respectively Perform piecewise linearization (five variables θ, each with three angle options, totaling 3^5 = 243 combinations); variable x is piecewise linearized at [16 meters, 17 meters, 18 meters], thus obtaining 729 fuzzy rules (x also has three length options, so the total number of combinations is 243 * 3 = 729), as follows:

[0128] Fuzzy rule R l : If θ1 is θ2 is θ3 is θ4 is θ5 is θ6 is

[0129] So

[0130] Among them, R lis the lth fuzzy rule, is a fuzzy set, B l is the input parameter matrix under the lth fuzzy rule;

[0131] S2.2: Define fuzzy sets for reasoning and the normalized membership function μ l ,get:

[0132]

[0133] S2.3: By combining the membership functions, the following fuzzy system model is obtained:

[0134]

[0135] In this step, the obtained nonlinear three-dimensional space dynamic equation is transformed into a fuzzy system model using the fuzzy logic expression method, as shown in formula (14).

[0136] S3: Introducing the integral sliding film function, using the BP neural network to approximate the unknown position deviation effect, and reconstructing the learning algorithm solution in the robust control framework of the discrete system; specifically including:

[0137] S3.1: Introduce the following integral synovial function:

[0138]

[0139] Where S represents the integral synovial function; F represents the synovial function mapping; It refers to the position deviation of the end;

[0140] S3.2: Here, we take the derivative of formula (15) and substitute it into formula (14), and we get:

[0141]

[0142] Clearly, we can design u(t) as follows:

[0143]

[0144] K f is the gain of the regular fuzzy controller, which shares the same fuzzy set as the fuzzy system.

[0145] available:

[0146] S3.3: Introduce BP neural network to approximate the unknown position deviation effect N, define is an approximation of N, then the input-output characteristic relationship of the BP neural network is obtained:

[0147]

[0148] Among them, f is the function mapping of the BP neural network, W and V are the learned weight values, and σ (the expression of the entire neural network) is a bounded function. is the input of the neural network, where the input is the inverse of the synovial function;

[0149] S3.4: Next, perform Taylor expansion on Equation (19) to obtain:

[0150]

[0151] Among them, ΔW, ΔV, They are W, V, The step increase value of

[0152] S3.5: Now, due to Subtract N(t+1) from both sides of formula (20) to obtain:

[0153]

[0154] in,

[0155]

[0156] S3.6: Due to known Therefore, we can design the learning rate U(t) as follows:

[0157]

[0158] Where G is the controller mapping iteration matrix to be determined; g1 g2 are the parameters to be determined.

[0159] S3.7: Further substitute the learning rate U(t) in (22) into the BP neural network system in (21), and we get:

[0160]

[0161] Where I is the identity matrix.

[0162] In this step, the integral sliding film function is introduced, the BP neural network is used to approximate the unknown position deviation effect, and the solution of the learning algorithm is reconstructed in the robust control framework of the discrete system.

[0163] S4: Design a BP neural network optimization learning algorithm based on state feedback control. Specifically including:

[0164] S4.1: First, to solve for the controller gain G, the Lyapunov function is established as follows:

[0165] V(t)=∈ T (t)P∈(t), (24)

[0166] Where P is a positive definite symmetric matrix;

[0167] S4.2: Calculate the difference function ΔV(t) of the Lyapunov function and obtain:

[0168] V(t)=V(t+1)-V(t)=∈ T (t+1)P∈(t+1)-∈ T (t)P∈(t) (25)

[0169] S4.3: Further define the matrix H (H is a variable introduced into the system, otherwise the system information cannot be used. H is an arbitrary matrix of appropriate dimensions. Its function is to introduce slack variables. It does not involve iteration. It can be either a variable or a specified constant. It does not affect our proposed method). From formula (23), we get:

[0170]

[0171] S4.4: Next, the following performance indicator function J(t) is given:

[0172]

[0173] Among them, γ is the performance indicator.

[0174] S4.5: Now combining equations (25) to (27), we obtain the following nonlinear matrix inequality:

[0175]

[0176] When formula (28) holds true, we get This means that the system is stable, that is, the learning algorithm (22) makes the BP neural network output The influence of position deviation N can be accurately approximated, where Sym{H} is H+H T , * is a random number. In addition, when formula (28) holds, J(t)<0, which means that the system is stable with performance index γ.

[0177] S4.6: Here we have built a feedforward neural network (19) to approximate the unknown position deviation. However, the learning algorithm parameter G cannot be obtained by solving the above nonlinear matrix inequality (28), so we define G as follows:

[0178]

[0179] Among them, g is the linear matrix parameter;

[0180] S4.7: Next, substitute equation (29) into equation (28) to obtain:

[0181]

[0182] Then the learning rate parameter g can be obtained by the following formula:

[0183]

[0184] S4.8: Now, after substituting Equation (29) into Equation (22), we obtain the following learning rate:

[0185]

[0186] S4.9: Further Substituting into formula (32), the final learning rate is as follows:

[0187]

[0188]

[0189] This step designs the learning rate parameter g and re-defines the learning rate, as shown in Equations (33) and (34). By updating the control algorithm, the control variable is precisely controlled to ΔW. Substituting ΔV into Equation (20) can make the error at time T+1 smaller, reduce the position deviation of the boom end, and improve the accuracy of the concrete pump truck arm trajectory control.

[0190] The superscript T in the above formula represents transposition.

[0191] In addition, the functional units in various embodiments of the present invention may be integrated into a single processing unit, each unit may exist physically separately, or two or more units may be integrated into a single unit. The aforementioned integrated units may be implemented in the form of hardware or software functional units.

[0192] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) or a processor to execute all or part of the steps of the various embodiments of the present invention. The aforementioned storage medium includes various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0193] The above descriptions are only some embodiments of the present invention and do not limit the scope of protection of the present invention. Any equivalent device or equivalent process transformation made by using the contents of the description and drawings of the present invention, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A method for optimizing the trajectory deviation of a multi-section boom end of a concrete pump truck, characterized in that: The steps include: S1: Use the Jacobian matrix to establish the nonlinear three-dimensional dynamic equations of the multi-section boom concrete pump truck tracking system; specifically, the following steps are included: S1.1: Based on the spatial coordinate relationship, the following spatial coordinate equations of the four-section boom concrete pump truck system are obtained: x=l1cosθ1+l2cosθ2+l3cosθ3+l4cosθ4 (1) y=l1sinθ1+l2sinθ2+l3sinθ3+l4sinθ4 (2) z=xtanθ z (3) Among them, x, y, z represent the spatial coordinates X, Y, Z positions of the end of the four-section boom concrete pump truck, θ1, θ2, θ3, θ4 are the angles from the first section boom to the fourth section boom in the projection of the coordinate plane X, Y, respectively. z It is the angle between the pump truck arm and the X axis in the projection of the coordinate X, Z plane. l1, l2, l3, and l4 are the lengths from the first to the fourth arm respectively. S1.2: Define x d ,y d ,z d are the reference coordinates of the concrete pump truck end, then after subtracting the reference coordinates from both sides of equations (1)-(3), we get: e x =xx d =l1cosθ1+l2cosθ2+l3cosθ3+l4cosθ4-x d , (4) e y =yyy d =l1sinθ1+l2sinθ2+l3sinθ3+l4sinθ4-y d , (5) ε z =zz d =xtanθ z -With d , (6) S1.3: Taking the derivatives of equations (4)-(6), we obtain: S1.4: Define N x ,N y ,N z The deviation of spatial coordinates X, Y, and Z is respectively affected, and equations (7)-(9) are rewritten as the following system state space expressions: Where ε is the position deviation, B(t) is the input matrix of the system, u(t) is the control input, and N is the unknown deviation disturbance; S2: The obtained three-dimensional space dynamic equation is transformed into a fuzzy model of the nonlinear three-dimensional space dynamic equation using a fuzzy logic expression method; specifically, the steps include: S2.1: The obtained three-dimensional dynamic nonlinear equation, where the variables θ1, θ2, θ3, θ4, θ z respectively Perform piecewise linearization, and the variable x is piecewise linearized at [16m, 17m, 18m], so 729 fuzzy rules are obtained, as follows: Fuzzy rule R l : If θ1 is θ2 is θ3 is θ4 is θ5 is θ6 is So Among them, R l is the lth fuzzy rule, is a fuzzy set, B l is the input parameter matrix under the lth fuzzy rule; S2.2: Define fuzzy sets for reasoning and the normalized membership function μ l ,get: S2.3: By combining the membership functions, the following fuzzy system model is obtained: S3: Introducing the integral sliding film function, using the BP neural network to approximate the unknown position deviation effect, and reconstructing the learning algorithm solution in the robust control framework of the discrete system; S3 specifically includes the following steps: S3.1: Introduce the following integral synovial function: Where S represents the integral synovial function; F represents the synovial function mapping; It refers to the position deviation of the end; S3.2: Derivative Equation (15) and substitute it into Equation (14) to obtain: Therefore, u(t) can be designed as follows: available: S3.3: Introduce BP neural network to approximate the unknown position deviation effect N, define is an approximation of N, then the input-output characteristic relationship of the BP neural network is obtained: Among them, f is the function mapping of BP neural network, W and V are the learned weight values, σ is a bounded function, is the input of the neural network; S3.4: Perform Taylor expansion on equation (19) to obtain: Among them, ΔW, ΔV, They are W, V, The step increase value of S3.5: Due to Subtracting N(t+1) from both sides of equation (20) yields: in, S3.6: Known Therefore, the learning rate U(t) can be designed as follows: U(t)=G∈ (22) Where G is the controller mapping iteration matrix to be determined; S3.7: Substituting the learning rate U(t) equation (22) into the BP neural network system equation (21), we obtain: Where I is the identity matrix; S4: Design a BP neural network optimization learning algorithm based on state feedback control.

2. A method for optimizing the trajectory deviation of a multi-section boom end of a concrete pump truck according to claim 1, characterized in that: The multi-section arm concrete pump truck is a four-section arm concrete pump truck.

3. The method for optimizing the trajectory deviation of the multi-section boom end of a concrete pump truck according to claim 1, characterized in that: S4 specifically includes the following steps: S4.1: Establish the Lyapunov function as follows: V(t)=∈ T (t)P∈(t), (24)where P is a positive definite symmetric matrix; S4.2: Calculate the difference function ΔV(t) of the Lyapunov function and obtain: V(t)=V(t+1)-V(t)=∈ T (t+1)P∈(t+1)-∈ T (t)P∈(t) (25) S4.3: Define the matrix H, which is obtained from equation (23): S4.4: Given the following performance indicator function J(t): Among them, γ is the performance index; S4.5: Simultaneously solving equations (25)-(27), we obtain the following nonlinear matrix inequality: When equation (28) holds true, we can get Indicates that the system is stable, that is, the learning rate equation (22) makes the BP neural network output used The influence of position deviation N can be accurately approximated, where Sym{H} is H+H T ; In addition, when equation (28) holds, J(t) < 0, which means that the system is stable with performance index γ; S4.6: Define G: Among them, g is the linear matrix parameter; S4.7: Substituting equation (29) into equation (28) yields: Then the learning rate parameter g can be obtained by the following equation: S4.8: Substituting equation (29) into equation (22), the learning rate obtained is as follows: S4.9: Substituting into equation (32), the final learning rate is as follows: Substituting the obtained ΔW and ΔV into equation (20) can make the error at time t+1 smaller and reduce the position deviation of the end of the joint arm.

4. A computer-readable storage medium, characterized in that: The storage medium stores at least one instruction, at least one program, code set or instruction set, and the at least one instruction, at least one program, code set or instruction set is loaded and executed by the processor to implement the method for optimizing the trajectory deviation of the end of the multi-section arm of a concrete pump truck as described in any one of claims 1 to 3.

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