CN108015763A - A kind of redundancy mechanical arm paths planning method of anti-noise jamming - Google Patents

Abstract

The invention discloses a redundant manipulator path planning method and system for anti-noise interference. The method includes: 1) establishing a time-varying quadratic programming model according to the actual redundant manipulator parameter index, and introducing redundancy The performance index of the manipulator; 2) Use the Lagrange multiplier method to optimize the optimal value of the time-varying quadratic programming model; 3) Design a standard matrix equation according to the optimization formula; 4) According to the actual physical model system and Standard matrix equation, design the deviation function equation of the system; 5) design a kind of anti-noise interference redundant mechanical arm path planning method according to the deviation function equation and power type variable parameter recursive neural dynamics method, the method obtained The network state solution of is the optimal solution. Under the interference of the external noise environment, the actual movement path of the redundant mechanical arm can also coincide with the expected path, which greatly improves the calculation speed, and has the characteristics of high precision, fast convergence, strong real-time performance, and good robustness.

Description

A path planning method for redundant manipulators with anti-noise interference

technical field

The invention relates to a path planning method of a manipulator, in particular to a path planning method of a redundant manipulator with anti-noise interference.

Background technique

The so-called noise interference is the interference caused by the various changes caused by the machinery that is performing the operation task, such as the switch machine, generator, and radio communication of the surrounding load equipment when the mechanical equipment performs the operation task. Noise interference often causes malfunctions of precision instruments or computer equipment, and may also cause errors in the execution of programs and files. Therefore, it is necessary to take into account the influence of the noise term when considering the path planning and operation of a complex mechanical system.

The so-called redundancy refers to an extra amount considered from a safety point of view. This amount is to ensure that instruments, equipment, or certain tasks can operate normally under abnormal conditions. At present, the idea and theory of redundancy are applied in most modern products and engineering designs. The redundant manipulator means that the number of degrees of freedom of the manipulator is more than the number of degrees of freedom necessary to complete the task. Due to more degrees of freedom, the redundant manipulator can also complete various tasks of the end effector. Additional work such as obstacle avoidance, joint angle limit constraints, and robotic arm singularity can be done at the same time. The traditional method used to solve the inverse kinematics problem of redundant manipulators is based on the pseudo-inverse method. This method has a large amount of calculation, poor real-time performance, and single problem constraints, which are greatly restricted in the actual application and operation of manipulators. In recent years, a scheme based on the quadratic programming problem to solve the motion planning of redundant manipulators has been proposed and developed to a certain extent. These are divided into numerical method solvers and neural network solvers. Compared with traditional numerical method solvers, recently emerging neural network solvers are more and more popular due to their good real-time performance and high efficiency.

In the existing technology, the closest method to solve the quadratic programming problem is the discrete numerical method, but when faced with huge and complex data, such a method is obviously inefficient and unstable. Therefore, a neural network model based on gradient descent is proposed and used to solve quadratic programming problems. However, such a neural network based on gradient descent cannot solve the quadratic programming problem very well, because the actual situation is often related to events, which will inevitably lead to some unestimable residual errors in the experiment, and these errors cannot converge to zero. . This means that we need faster convergence speed and higher convergence accuracy when dealing with quadratic programming problems. In such a background, Zhang Neural Network was proposed and developed well. Zhang neural network is a traditional method for solving the path planning of manipulators. Such a neural network model can solve the quadratic programming problem under time-varying conditions. Through the derived time coefficients, the Zhang neural network can obtain the most effective solution to the quadratic programming problem. However, when the calculation data becomes huge, especially when complex noise interference is to be considered, we often need more time to calculate the results, which is not good for practical operation.

Due to the fixed parameter recursive neural network methods such as traditional gradient neural network and Zhang neural network, the convergence parameter (in the actual circuit system, the value of the inductance parameter or the reciprocal value of the capacitance parameter) needs to be set as large as possible to obtain faster convergence performance. Such a requirement is unrealistic and difficult to satisfy when neural networks are applied in practical systems. In addition, in the actual system, the reciprocal of the inductance parameter value and the capacitance parameter value is usually time-varying, especially in large-scale power electronic systems, AC motor control systems, power network systems, etc., the system parameters are set to fixed values is unreasonable.

Contents of the invention

The purpose of the present invention is to overcome the deficiencies of the prior art, and provide a redundant manipulator path planning method that is resistant to noise interference. The method can make the actual movement path of the redundant manipulator also It can coincide with the expected path, greatly improving the calculation speed, and has the characteristics of high precision, fast convergence, strong real-time performance, and good robustness.

Another object of the present invention is to provide a redundant robotic arm path planning system that is resistant to noise interference.

The purpose of the present invention can be achieved by taking the following technical solutions:

A method for path planning of redundant manipulators against noise interference, the method comprising:

1) Establish a time-varying quadratic programming model according to the actual redundant manipulator parameter index, and introduce the performance index coefficient vector of the redundant manipulator;

2) Use the Lagrange multiplier method to optimize the optimal value of the time-varying quadratic programming model;

3) Design a standard matrix equation according to the optimization formula;

4) According to the actual physical model system and the standard matrix equation, the deviation function equation of the system is designed;

5) According to the deviation function equation and the power-type variable parameter recursive neural dynamics method, a redundant manipulator path planning method with anti-noise interference is designed. The network state solution obtained by this method is the optimal solution.

Further, the time-varying quadratic programming model is established according to the actual redundant manipulator parameter index, and the performance index coefficient vector of the redundant manipulator is introduced, specifically including:

By formulating and modeling the parameter index of the actual redundant manipulator, the following kinematic equation expression of the redundant manipulator can be obtained:

f(θ(t))=r(t) (1)

Where θ(t) is the mechanical joint angle of the redundant manipulator; r(t) is the expected end trajectory of the redundant manipulator; f( ) is a nonlinear equation representing the joint angle of the redundant manipulator; Simultaneously deriving both ends of the equation can obtain the following expression of the inverse kinematics equation on the velocity layer of the redundant manipulator:

in is the Jacobian matrix of the redundant manipulator, n represents the number of degrees of freedom of the manipulator, and m represents the spatial dimension of the end trajectory of the manipulator; are the joint angles of the redundant manipulator and the derivatives of the terminal trajectory with respect to time; according to the above physical model, the following time-varying quadratic programming model can be established:

subject to J(θ(t))x(t)=B(t) (4)

in Q(t)=I(t) is the identity matrix; J(θ(t)) is the Jacobian matrix of the redundant mechanical arm; P(t) is the performance index coefficient vector;

The performance index coefficient vector P(t) of the redundant manipulator is introduced, and its specific design formula is: in Represents the joint offset response coefficient, θ(t), θ(0) represent the joint state and initial joint state during the movement of the redundant manipulator, respectively.

Further, the Lagrange multiplier method is used to optimize the optimal value of the time-varying quadratic programming model, which specifically includes:

In order to obtain the partial derivative information about the optimal solution and the Lagrange multiplier for the time-varying quadratic programming problem, the Lagrange multiplier method can be used for the time-varying quadratic programming problem (3)(4) to get the following Mode:

in is the Lagrangian multiplier; from the Lagrangian theorem, if and exists and is continuous, then the following two formulas are established, that is

The time-varying parameter matrix and vectors Q(t), P(t), J(t), and B(t) are composed of the actual physical model system sensor acquisition signal and the system's expected operating status signal; the time-varying parameter matrix and vector Q(t), P(t), J(t), B(t), and their time derivatives is known or can be estimated within a certain range of accuracy requirements; there is a time-varying quadratic programming problem (3) (4) about the optimal solution and about the partial derivative information of the Lagrange multiplier, and can be used The Lagrangian multiplier method expresses the above information as optimization formulas (6)(7).

Further, the described design of a standard matrix equation according to the optimization formula specifically includes:

According to the optimization formula (6) (7), the following standard matrix equations for the time-varying quadratic programming problem (3) (4) can be designed:

W(t)Y(t)=G(t) (8)

in

The time-varying coefficient matrix and vectors W(t), Y(t), G(t) are continuous and smooth in the real number domain.

Further, according to the actual physical model system and the standard matrix equation, the deviation function equation of the system is designed, which specifically includes:

According to the matrix equation (8) of the smooth time-varying quadratic programming problem of the obtained actual physical model system or numerical solution system, the deviation function equation of the available system is designed; in order to obtain the time-varying quadratic programming problem (3) (4) The optimal solution of , define a matrix-form deviation function equation as follows:

When the deviation function equation ε(t) converges to zero, the optimal solution x ^* (t) of the time-varying quadratic programming problem (3)(4) can be obtained.

Further, a noise-containing power-type variable-parameter recursive neural network model is established according to the deviation function equation and the power-type variable-parameter recursive neural dynamics method. The network state solution output by the model is the optimal solution, including:

The data in the time-varying parameter matrix can be input into the processing unit; through the obtained time-varying parameter matrix and its derivative information, combined with the power-type variable parameter recursive neural dynamics method in the real number field and using the monotonically increasing odd activation function, a Power-type variable parameter recursive neural network model with noise; according to the power-type variable parameter recursive neural dynamics method, the time derivative of the deviation function equation ε(t) needs to be negative definite; different from the fixed parameter recursive neural dynamics method, the power-type The design parameters that determine the convergence performance in the variable parameter recursive neural dynamics method are time-varying, and the time-varying parameters are defined as follows:

Among them, γ>0 is an artificially designed constant coefficient parameter, and Φ(·) is a monotonically increasing odd activation array.

Substituting the deviation function equation and its derivative information into the design formula (8), the power-type variable parameter recursive neural network model in the real number field can be expressed by the following implicit dynamic equation

in is partial derivative information.

If there are noise interference and hardware operation errors, the following noise-containing power variable parameter recurrent neural network model can be obtained:

Among them, ΔD(t) is the noise term of the coefficient matrix; ΔK(t) is the error term when the hardware is running.

According to definition, we know

Y(t):=[x ^T (t),λ ^T (t)] ^T

=[x ₁ (t), x ₂ (t), . . . , x _n (t), λ ₁ (t), λ ₂ (t), . . . , λ _m (t)] ^T (13)

where Y(t) has initial value

According to the implicit dynamic equation (12), the redundant manipulator path planning method and network implementation for anti-noise interference in the real number domain can be obtained; the output of the network is the time-varying quadratic programming problem in the real number domain (3)(4) the optimal solution of .

The network state solution obtained by the redundant manipulator path planning method based on anti-noise interference is the optimal solution of the time-varying quadratic programming problem (3) (4) of the actual physical system or numerical solution system; The output of the optimal solution of the solver is obtained, and the optimal solution of the actual physical system or numerical solution system in the form of a smooth time-varying quadratic programming problem in the real number field is completed, and the obtained network state solution is the obtained noise interference The optimal solution for redundant manipulator motion planning.

Another object of the present invention can take following technical scheme to reach:

The external environment input module is used for acquiring and analyzing data input from the external environment, and the above data constitute the basis of the content of the time-varying parameter matrix.

The input interface circuit module is used for external setting data and as an interface channel between processors, and can be realized by circuits and protocols of different interfaces according to different sensors.

The processor module is used to process external input data, and obtain the optimal solution of the redundant manipulator motion path planning method designed based on the power-type variable parameter recursive neural dynamics method for noise interference.

The output interface module is used for the interface between the data solved by the redundant manipulator motion path planning method for anti-noise interference and the system optimal theoretical solution request end, where the interface can be a circuit interface or a return value of a program, according to the design It varies from system to system.

The output environment module is used to realize the purpose of the redundant manipulator motion path planning method disturbed by noise based on the power type variable parameter recursive neural dynamics method.

Further, the external environment input module specifically includes:

The external sensor data acquisition sub-unit collects the dynamic parameters of the system through sensors, such as displacement, velocity, acceleration, angular velocity and other physical quantities;

The data analysis sub-unit of the expected goal realization state conducts systematic theoretical analysis by analyzing known or collected physical quantities.

Further, the processor module specifically includes:

The time-varying parameter matrix subunit is used to complete the matrix or vectorization of external input data;

Anti-noise interference redundant manipulator path planning method sub-unit, anti-noise interference redundant manipulator movement path planning method is the core part of the system, through modeling, formulation, analysis and design of the system data in advance Type, including the system model obtained by mathematical modeling, so as to design the deviation function equation, and use the power-type variable parameter recursive neural dynamics method to design a redundant manipulator motion path planning method for noise interference.

Further, the described output environment module specifically includes:

The optimal solution request terminal unit is used to obtain the optimal solution of the real number field smooth time-varying quadratic programming problem of the actual physical system or numerical solution system. This port sends an instruction request to the solution system when the solution parameters need to be obtained. , and accept the solution result;

The redundant manipulator path planning terminal unit is used to convert the parameters output by the optimal solution request end into relevant data, and finally input it into the manipulator control program for path planning and control of the manipulator.

The present invention has following beneficial effect to prior art:

The present invention is based on a power-type variable parameter recursive neural dynamics model method, which is different from the traditional fixed parameter recursive neural dynamics method. The motion path planning method for redundant mechanical arms disturbed by noise has global convergence characteristics, and the deviation can converge to zero at a super-exponential speed, which greatly improves the calculation speed, and has the characteristics of high precision, fast convergence, strong real-time performance, and good robustness. The method is described by the ubiquitous implicit dynamic model, which can make full use of the derivative information of each time-varying parameter from the two levels of method and system, and can approach the optimal solution of the problem quickly, accurately and in real time; It solves a series of related problems such as motion planning of redundant manipulators.

Description of drawings

FIG. 1 is a flow chart of a redundant robotic arm movement path planning method for anti-noise interference according to Embodiment 1 of the present invention.

FIG. 2 is a frame diagram of the implementation of the noise-resistant redundant robotic arm motion path planning system of the present invention.

Fig. 3 is a trajectory diagram when the redundant mechanical arm disturbed by noise of the present invention performs a motion path planning task.

FIG. 4 is a graph of the actual path and the expected path when the noise-disturbed redundant manipulator of the present invention performs a motion path planning task.

Fig. 5 is an error graph in the X-axis, Y-axis, and Z-axis directions when the noise-disturbed redundant robotic arm of the present invention performs a motion path planning task.

FIG. 6 is a curve diagram of norm error when the noise-disturbed redundant manipulator of the present invention performs a motion path planning task.

Detailed ways

The present invention will be further described in detail below in conjunction with the embodiments and the accompanying drawings, but the embodiments of the present invention are not limited thereto.

Example 1:

As shown in FIG. 1, the present embodiment provides a method for path planning of a redundant manipulator with anti-noise interference, and the method includes the following steps:

S1. Establish a time-varying quadratic programming model according to the actual redundant manipulator parameter index, and introduce the performance index coefficient vector of the redundant manipulator;

S11. Establish a time-varying quadratic programming model:

By formulating and modeling the parameter index of the actual redundant manipulator, the following kinematic equation expression of the redundant manipulator can be obtained:

f(θ(t))=r(t) (1)

Where θ(t) is the mechanical joint angle of the redundant manipulator; r(t) is the expected end trajectory of the redundant manipulator; f( ) is a nonlinear equation representing the joint angle of the redundant manipulator; Simultaneously deriving both ends of the equation can obtain the following expression of the inverse kinematics equation on the velocity layer of the redundant manipulator:

in is the Jacobian matrix of the redundant manipulator, n represents the number of degrees of freedom of the manipulator, and m represents the spatial dimension of the end trajectory of the manipulator; are the joint angles of the redundant manipulator and the derivatives of the terminal trajectory with respect to time; according to the above physical model, the following time-varying quadratic programming model can be established:

subject to J(θ(t))x(t)=B(t) (4)

in Q(t)=I(t) is the identity matrix; J(θ(t)) is the Jacobian matrix of the redundant mechanical arm; P(t) is the performance index coefficient vector;

S12. The performance index coefficient vector P(t) of the redundant mechanical arm is introduced, and its specific design formula is: in Represents the joint offset response coefficient, θ(t), θ(0) represent the joint state and initial joint state during the movement of the redundant manipulator, respectively.

S2. Using the Lagrange multiplier method to optimize the optimal value of the time-varying quadratic programming model;

In order to obtain the partial derivative information about the optimal solution and the Lagrange multiplier for the time-varying quadratic programming problem, the Lagrange multiplier method can be used for the time-varying quadratic programming problem (3)(4) to get the following Mode:

in is the Lagrangian multiplier; from the Lagrangian theorem, if and exists and is continuous, then the following two formulas are established, that is

The time-varying parameter matrix and vectors Q(t), P(t), J(t), and B(t) are composed of the actual physical model system sensor acquisition signal and the system's expected operating status signal; the time-varying parameter matrix and vector Q(t), P(t), A(t), B(t), and their time derivatives is known or can be estimated within a certain range of accuracy requirements; there is a time-varying quadratic programming problem (3) (4) about the optimal solution and about the partial derivative information of the Lagrange multiplier, and can be used The Lagrangian multiplier method expresses the above information as optimization formulas (6)(7).

S3, designing a standard matrix equation according to the optimization formula;

According to the optimization formula (6) (7), the following standard matrix equations for the time-varying quadratic programming problem (3) (4) can be designed:

W(t)Y(t)=G(t) (8)

in

The time-varying coefficient matrix and vectors W(t), Y(t), G(t) are continuous and smooth in the real number domain.

S4. According to the actual physical model system and the standard matrix equation, the deviation function equation of the system is designed;

According to the matrix equation (8) of the smooth time-varying quadratic programming problem of the obtained actual physical model system or numerical solution system, the deviation function equation of the available system is designed; in order to obtain the time-varying quadratic programming problem (3)(4) The optimal solution of , define a matrix-form deviation function equation as follows:

When the deviation function equation ε(t) converges to zero, the optimal solution x ^* (t) of the time-varying quadratic programming problem (3)(4) can be obtained.

S5. According to the deviation function equation and the power-type variable parameter recursive neural dynamics method, a redundant manipulator path planning method for anti-noise interference is designed, and the network state solution obtained by this method is the optimal solution;

The data in the time-varying parameter matrix can be input into the processing unit; through the obtained time-varying parameter matrix and its derivative information, combined with the power-type variable parameter recursive neural dynamics method in the real number field and using the monotonically increasing odd activation function, a Power-type variable parameter recursive neural network model with noise; according to the power-type variable parameter recursive neural dynamics method, the time derivative of the deviation function equation ε(t) needs to be negative definite; different from the fixed parameter recursive neural dynamics method, the power-type The design parameters that determine the convergence performance in the variable parameter recursive neural dynamics method are time-varying, and the time-varying parameters are defined as follows:

Among them, γ>0 is an artificially designed constant coefficient parameter, and Φ(·) is a monotonically increasing odd activation array.

Substituting the deviation function equation and its derivative information into the design formula (8), the power-type variable parameter recursive neural network model in the real number field can be expressed by the following implicit dynamic equation

in is partial derivative information.

If there are noise interference and hardware operation errors, the following noise-containing power variable parameter recurrent neural network model can be obtained:

Among them, ΔD(t) is the noise term of the coefficient matrix; ΔK(t) is the error term when the hardware is running.

According to definition, we know

Y(t):=[x ^T (t),λ ^T (t)] ^T

=[x ₁ (t), x ₂ (t), . . . , x _n (t), λ ₁ (t), λ ₂ (t), . . . , λ _m (t)] ^T (13)

where Y(t) has initial value

According to the implicit dynamic equation (12), the redundant manipulator path planning method and network implementation for anti-noise interference in the real number domain can be obtained; the output of the network is the time-varying quadratic programming problem in the real number domain (3)(4) optimal solution of .

The network state solution obtained by the redundant manipulator path planning method based on anti-noise interference is the optimal solution of the time-varying quadratic programming problem (3) (4) of the actual physical system or numerical solution system; The output of the optimal solution of the solver is obtained, and the optimal solution of the actual physical system or numerical solution system in the form of a smooth time-varying quadratic programming problem in the real number field is completed, and the obtained network state solution is the obtained noise interference The optimal solution for redundant manipulator motion planning.

Example 2:

As shown in Figure 2, this embodiment provides a redundant robotic arm path planning system that is resistant to noise interference, and the specific purposes of each module are as follows:

The external environment input module is used for acquiring and analyzing data input from the external environment.

The input interface circuit module is used for external setting data and as an interface channel between processors, and can be realized by circuits and protocols of different interfaces according to different sensors.

The processor module is used to process the external input data, that is, to obtain the optimal solution of the noise-resistant redundant manipulator motion path planning method designed based on the power-type variable parameter recursive neural dynamics method.

The output interface module is used for the interface between the data solved by the redundant manipulator motion path planning method for anti-noise interference and the system optimal theoretical solution request end, where the interface can be a circuit interface or a return value of a program, according to the design It varies from system to system.

The output environment module is used to realize the redundant manipulator motion path planning method based on the power-type variable parameter recursive neural dynamics method for anti-noise interference.

External environment input module, specifically including:

The external sensor data acquisition sub-unit collects the dynamic parameters of the system through sensors, such as displacement, velocity, acceleration, angular velocity and other physical quantities;

The data analysis sub-unit of the expected goal realization state conducts systematic theoretical analysis by analyzing known or collected physical quantities.

Processor modules, specifically:

The time-varying parameter matrix subunit is used to complete the matrix or vectorization of external input data;

Anti-noise interference redundant manipulator path planning method sub-unit, anti-noise interference redundant manipulator movement path planning method is the core part of the system, through modeling, formulation, analysis and design of the system data in advance Type, including the system model obtained by mathematical modeling, so as to design the deviation function equation, and use the power-type variable parameter recursive neural dynamics method to design a redundant manipulator motion path planning method for noise interference.

Output environment modules, specifically including:

The optimal solution request terminal unit is used to obtain the optimal solution of the real number field smooth time-varying quadratic programming problem of the actual physical system or numerical solution system. This port sends an instruction request to the solution system when the solution parameters need to be obtained. , and accept the solution result;

The path planning terminal unit of the redundant manipulator is used to convert the parameters output by the optimal solution request end into relevant verses, and finally input them into the manipulator control program to plan and control the manipulator path.

Example 3:

The MATLAB simulation experiment of this embodiment is based on the Kinova-JACO ² lightweight bionic manipulator. The total weight of this type of robotic arm is 4.4kg, and the maximum control distance is 77cm.

This type of redundant robotic arm contains a total of 6 degrees of freedom, that is, θ(t) contains 6 elements; the spatial dimension at the end of the robotic arm is 3, including three directions: X axis, Y axis, and Z axis; Its Jacobian matrix is The initial joint angle of the redundant manipulator is set as θ(0)=[1.675,2.843,-3.216,4.187,-1.710,-2.650]; the task execution cycle t is set to 8s; the parameter γ is set to Set at 80. In this example, in order to demonstrate the superiority of the variable parameter neural solver proposed by the present invention for the motion planning of the redundant manipulator, the expected trajectory of the Kinova-JACO ² lightweight bionic redundant manipulator is set It is a complex butterfly shape, and the parameter diameter of the butterfly shape track is 45cm. According to the Kinova-JACO ² redundant manipulator physical model set above, the following time-varying quadratic programming model can be established by solving it on the velocity layer:

Among them, I(t) is the identity matrix; and They are:

According to the steps and methods mentioned above, the following matrix equation can be designed, namely

W(t)Y(t)=G(t) (16)

in

In order to obtain the optimal solution of the above-mentioned time-varying quadratic programming model for solving the motion path of redundant manipulators, a matrix-form deviation function equation is defined as follows

ε(t)=W(t)Y(t)-G(t) (17)

According to the power-type variable parameter recursive neural dynamics method, a power-type time-varying parameter is designed and used in the present invention, and its design formula is as follows

Among them, the parameter γ is set to 80.

According to the deviation function equation and its derivative information, the power-type variable parameter recurrent neural network model in the real number field can be expressed by the following implicit dynamic equation

in is the partial derivative information; ΔD(t) is the noise term of the coefficient matrix; ΔK(t) is the error term when the hardware is running. In order to better simulate the noise interference encountered by the redundant manipulator during actual operation, in this example, the noise term ΔD(t) and the error term ΔK(t) are composed of a series of complex sine and cosine functions. The expression looks like this:

According to the definition of Y(t), we know that

Y(t):=[x ^T (t),λ ^T (t)] ^T

=[x ₁ (t), x ₂ (t), ..., x _n (t), λ ₁ (t), λ ₂ (t), ..., λ _m (t)] ^T (20)

where Y(t) has an initial value Y(0)=Y ₀ .

According to the implicit dynamic equation shown above, the redundant manipulator path planning method and network implementation for anti-noise interference in the real number domain can be obtained; the output result of the network is the optimal solution of the time-varying quadratic programming problem in the real number domain. Output the optimal solution of the solver obtained by the processor, and complete the optimal solution of the actual physical system or numerical solution system in the form of a smooth time-varying quadratic programming problem in the real number field. The obtained network state solution is the optimal solution for the motion planning of the redundant manipulator system disturbed by noise in this simulation example.

The specific experimental results of this simulation embodiment are shown in FIG. 3(a)(b), FIG. 4(a)(b), FIG. 5(a)(b) and FIG. 6(a)(b). Fig. 3(a)(b) is the trajectory diagram when the redundant mechanical arm disturbed by noise performs the motion path planning task when the novel method and the traditional method described in the present invention are respectively applied. Fig. 4 (a) (b) is the curve diagram of the actual path and the expected path when the redundant mechanical arm disturbed by the noise performs the motion path planning task under the situation of respectively applying the novel method and the traditional method described in the present invention . Fig. 5(a)(b) shows the directions of X-axis, Y-axis and Z-axis when the redundant mechanical arm interfered with by the noise performs the task of motion path planning when the novel method and the traditional method according to the present invention are respectively applied. The error graph above. Fig. 6 (a) (b) is the normal error curve graph when the redundant mechanical arm disturbed by the noise performs the motion path planning task when the new method and the traditional method described in the present invention are respectively applied. The numerical error ||e(t)|| ₂ is defined as the 2-norm of the sum of the errors in the X-axis, Y-axis, and Z-axis directions when the redundant manipulator performs path planning tasks.

As can be seen from Figures 3 and 4, when the noise-resistant redundant manipulator motion path planning method of the present invention is used to plan the path of the manipulator, the actual motion path can coincide with the expected path, that is, the path deviation can be quickly reduced. Converge to zero; and when using the traditional method for manipulator path planning, there is always a large deviation between the actual motion path and the expected path, and it is difficult to meet the accuracy requirements in the actual redundant manipulator operation.

As can be seen from Fig. 5, when applying the anti-noise interference redundant mechanical arm motion path planning method of the present invention to plan the mechanical arm path, the errors in the three directions of the X axis, the Y axis, and the Z axis can all be reduced by The fast speed converges to zero, that is, it can well eliminate the deviation between the actual motion path of the manipulator and the expected path; and when the traditional method is used for the path planning of the manipulator, it is difficult to achieve the same speed in the X-axis, Y-axis, and Z-axis. There is always a large deviation between the actual motion path and the expected path in the three directions, and it is difficult to meet the accuracy requirements in the actual redundant manipulator operation.

As can be seen from Fig. 6, when applying the redundant manipulator motion path planning method for anti-noise interference of the present invention to plan the manipulator path, its norm error can converge to zero at a very fast speed; Methods When the path planning of the manipulator is performed, the norm error always exists, that is, there is always a certain error when the manipulator performs the path planning task, and it is difficult to meet the accuracy requirements.

The experimental results of the above-mentioned simulation embodiment well demonstrate the superiority of the noise-resistant redundant manipulator motion path planning method of the present invention.

The above is only a preferred embodiment of the patent of the present invention, but the scope of protection of the patent of the present invention is not limited thereto. Anyone familiar with the technical field within the scope disclosed by the patent of the present invention, according to the scope of the patent of the present invention Equivalent replacements or changes to the technical solutions and their inventive concepts all fall within the scope of protection of the invention patent.

Claims (10)

1. A redundant mechanical arm path planning method for anti-noise interference, characterized in that: the method comprises: 1) Establish a time-varying quadratic programming model according to the actual redundant manipulator parameter index, and introduce the performance index of the redundant manipulator into the time-varying quadratic programming model; 2) Using the Lagrange multiplier method, the optimal value of the time-varying quadratic programming model is optimized to obtain the optimization formula; 3) Design a standard matrix equation according to the optimization formula; 4) According to the actual physical model system and the standard matrix equation, the deviation function equation of the system is designed; 5) According to the deviation function equation and the power-type variable parameter recursive neural dynamics method, a noise-containing power-type variable parameter recurrent neural network model is established, and the network state solution output by the model is the optimal solution. 2. a kind of anti-noise interference redundancy manipulator path planning method according to claim 1 is characterized in that: described according to actual redundancy manipulator parameter index establishment time-varying quadratic programming model, and introduces The motion planning index of the redundant manipulator, including: Formulate and model the parameter index of the actual redundant manipulator, and obtain the following expression of the inverse kinematics equation of the redundant manipulator: f(θ(t))=r(t) (1) Where θ(t) is the mechanical joint angle of the redundant manipulator; r(t) is the expected end trajectory of the redundant manipulator; f( ) is a nonlinear equation representing the joint angle of the redundant manipulator; Simultaneously deriving both ends of the equation to obtain the following expression of the inverse kinematics equation on the velocity layer of the redundant manipulator: <mrow><mi>J</mi><mrow><mo>(</mo><mi>&amp;theta;</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>)</mo></mrow><mover><mrow><mi>&amp;theta;</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mo>&amp;CenterDot;</mo></mover><mo>=</mo><mover><mi>r</mi><mo>&amp;CenterDot;</mo></mover><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>2</mn><mo>)</mo>mo></mrow></mrow> in is the Jacobian matrix of the redundant manipulator, n represents the number of degrees of freedom of the manipulator, and m represents the spatial dimension of the end trajectory of the manipulator; are the joint angles of the redundant manipulator and the derivatives of the terminal trajectory with respect to time; according to the above physical model, the following time-varying quadratic programming model can be established: <mrow><mtable><mtr><mtd><mrow><mi>min</mi><mi>i</mi><mi>m</mi><mi>i</mi><mi>z</mi><mi>e</mi></mrow></mtd><mtd><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mi>x</mi><mi>T</mi></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>Q</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><msup><mi>P</mi><mi>T</mi></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mtd></mtr></mtable><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow> subject to J(θ(t))x(t)=B(t) (4) in Q(t)=I(t) is the identity matrix; J(θ(t)) is the Jacobian matrix of the redundant mechanical arm; P(t) is the performance index coefficient vector; The performance index coefficient vector P(t) of the redundant manipulator is introduced, and its specific design formula is: in Represents the joint offset response coefficient, θ(t), θ(0) represent the joint state and initial joint state during the movement of the redundant manipulator, respectively. 3. a kind of anti-noise interference redundancy manipulator path planning method according to claim 2, is characterized in that: described use Lagrangian algorithm, carries out optimum value optimization to time-varying quadratic programming model, Specifically include: Time-varying quadratic programming model: <mrow><mtable><mtr><mtd><mrow><mi>min</mi><mi>i</mi><mi>m</mi><mi>i</mi><mi>z</mi><mi>e</mi></mrow></mtd><mtd><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mi>x</mi><mi>T</mi></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>Q</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><msup><mi>P</mi><mi>T</mi></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mtd></mtr></mtable><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow> subject to J(θ(t))x(t)=B(t) (4) In order to obtain the partial derivative information about the optimal solution and the Lagrange multiplier for the time-varying quadratic programming problem, the Lagrange multiplier method can be used for the time-varying quadratic programming problem (3)(4) to get the following Mode: in is the Lagrangian multiplier; from the Lagrangian theorem, if and exists and is continuous, then the following two formulas are established, that is Among them, the time-varying parameter matrix and vector Q(t), P(t), J(t), B(t) are composed of the actual physical model system sensor acquisition signal and the system's expected operating state signal; the time-varying parameter matrix and vector Q (t), P(t), J(t), B(t), and their time derivatives is known or can be estimated within a certain range of accuracy requirements; there is a time-varying quadratic programming problem (3) (4) about the optimal solution and about the partial derivative information of the Lagrange multiplier, and can be used The Lagrangian multiplier method expresses the above information as optimization formulas (6)(7). 4. the redundant mechanical arm path planning method of a kind of anti-noise interference according to claim 3, is characterized in that: described design a standard matrix equation according to optimization formula, specifically comprises: Optimization formula: According to the optimization formula (6) (7), the following standard matrix equations for the time-varying quadratic programming problem (3) (4) can be designed: W(t)Y(t)=G(t) (8) in The time-varying coefficient matrix and vectors W(t), Y(t), G(t) are continuous and smooth in the real number domain. 5. the redundant degree mechanical arm path planning method of a kind of anti-noise interference according to claim 4, it is characterized in that: described according to actual physical model system and standard matrix equation, design the deviation function equation of system, its Specifically include: Standard matrix equation: W(t)Y(t)=G(t) (8) According to the standard matrix equation (8) of the smooth time-varying quadratic programming problem of the obtained actual physical model system or numerical solution system, the deviation function equation of the available system is designed; in order to obtain the time-varying quadratic programming problem (3)(4 ), define a matrix-form deviation function equation as follows: When the deviation function equation ε(t) converges to zero, the optimal solution x ^* (t) of the time-varying quadratic programming problem (3)(4) can be obtained. 6. a kind of anti-noise interference redundancy manipulator path planning method according to claim 5 is characterized in that: according to deviation function equation and power type variable parameter recursive neural dynamics method, set up a noise-containing power type variable Parameter recurrent neural network model, the network state solution output by the model is the optimal solution, including: The data in the time-varying parameter matrix can be input into the processing unit; through the obtained time-varying parameter matrix and its derivative information, combined with the power-type variable parameter recursive neural dynamics method in the real number domain and using the monotonically increasing odd activation function, a Power-type variable parameter recursive neural network model with noise; according to the power-type variable parameter recursive neural dynamics method, the time derivative of the deviation function equation ε(t) needs to be negative definite; different from the fixed parameter recursive neural dynamics method, the power-type The design parameters that determine the convergence performance in the variable parameter recursive neural dynamics method are time-varying, and the time-varying parameters are defined as follows: <mrow><mover><mi>&amp;epsiv;</mi><mo>&amp;CenterDot;</mo></mover><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><mi>d</mi><mi>&amp;epsiv;</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mo>-</mo><mrow><mo>(</mo><mi>&amp;gamma;</mi><mo>+</mo><msup><mi>t</mi><mi>&amp;gamma;</mi></msup><mo>)</mo></mrow><mi>&amp;Phi;</mi><mrow><mo>(</mo><mi>&amp;epsiv;</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>)</mo></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>10</mn><mo>)</mo></mrow></mrow> Among them, γ>0 is an artificially designed constant coefficient parameter, and Φ( ) is a monotonically increasing odd activation array; Substituting the deviation function equation and its derivative information into formula (8), If there is noise interference and hardware operation error, the following noise-containing power type variable parameter recurrent neural network model can be obtained: <mrow><mtable><mtr><mtd><mrow><mi>W</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mover><mi>Y</mi><mo>&amp;CenterDot;</mo></mover><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mo>-</mo><mrow><mo>(</mo><mover><mi>W</mi><mo>&amp;CenterDot;</mo></mover><mo>(</mo><mi>t</mi><mo>)</mo><mo>+</mo><mi>&amp;Delta;</mi><mi>D</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>)</mo></mrow><mi>Y</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>-</mo><mrow><mo>(</mo><mi>&amp;gamma;</mi><mo>+</mo><msup><mi>t</mi><mi>&amp;gamma;</mi></msup><mo>)</mo></mrow><mi>&amp;Phi;</mi><mrow><mo>(</mo><mi>W</mi><mo>(</mo><mi>t</mi><mo>)</mo><mi>Y</mi><mo>(</mo><mi>t</mi><mo>)</mo>mo><mo>-</mo><mi>G</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>)</mo></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mo>+</mo><mover><mi>G</mi><mo>&amp;CenterDot;</mo></mover><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><mi>&amp;Delta;</mi><mi>K</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mtd></mtr></mtable><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>11</mn><mo>)</mo></mrow></mrow> Where ΔD(t) is the noise term of the coefficient matrix; ΔK(t) is the error term when the hardware is running; where is partial derivative information; According to definition, we know <mrow><mtable><mtr><mtd><mrow><mi>Y</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>:</mo><mo>=</mo><msup><mrow><mo>&amp;lsqb;</mo><msup><mi>x</mi><mi>T</mi></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><msup><mi>&amp;lambda;</mi><mi>T</mi></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>&amp;rsqb;</mo></mrow><mi>T</mi></msup></mrow></mtd></mtr><mtr><mtd><mrow><mo>=</mo><msup><mrow><mo>&amp;lsqb;</mo><msub><mi>x</mi><mn>1</mn></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><msub><mi>x</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mn>...</mn><mo>,</mo><msub><mi>x</mi><mi>n</mi></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><msub><mi>&amp;lambda;</mi><mn>1</mn></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><msub><mi>&amp;lambda;</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mn>...</mn><mo>,</mo><msub><mi>&amp;lambda;</mi><mi>m</mi></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>&amp;rsqb;</mo></mrow><mi>T</mi></msup></mrow></mtd></mtr></mtable><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>12</mn><mo>)</mo></mrow></mrow> where Y(t) has initial value According to the implicit dynamic equation (11), the redundant manipulator path planning method and network implementation for anti-noise interference in the real number domain can be obtained; the output of the network is the time-varying quadratic programming problem in the real number domain (3)(4) the optimal solution of . 7. A system for implementing the noise-resistant redundant manipulator path planning method according to any one of claims 1-6, characterized in that: the system comprises: The external environment input module is used to acquire and analyze the acquisition and analysis of data input from the external environment, and the above data constitute the basis of the content of the time-varying parameter matrix; The input interface circuit module is used for external setting data and as an interface channel between processors, which can be realized by different interface circuits and protocols according to different sensors; The processor module is used to process external input data and obtain the optimal solution of the redundant manipulator motion path planning method designed based on the power-type variable parameter recursive neural dynamics method for anti-noise interference; The output interface module is used for the interface between the data solved by the redundant manipulator motion path planning method for anti-noise interference and the system optimal theoretical solution request end. This interface can be a circuit interface or a return value of a program. According to the design system different from each other; The output environment module is used to send a solution request to the processor module, and after the optimal solution result is obtained, the parameters are converted into relevant data for path planning and control of the robotic arm. 8. The system according to claim 7, wherein the external environment input module comprises: The external sensor data acquisition sub-unit is used to collect the dynamic parameters of the system through sensors; The data analysis subunit of the expected goal realization state is used to conduct systematic theoretical analysis by analyzing known or collected physical quantities. 9. The system according to claim 7, wherein the processor module comprises: The time-varying parameter matrix subunit is used to complete the matrix or vectorization of external input data; The redundant manipulator path planning method subunit for anti-noise interference, through modeling, formulating, analyzing and designing the configuration of the system data in advance, including the system model obtained by mathematical modeling, so as to design the deviation function equation, and A motion path planning method for redundant manipulators disturbed by noise is designed using a power-type variable parameter recursive neural dynamics method. 10. The system according to claim 7, wherein said output environment module comprises: The optimal solution request terminal unit is the requesting end that needs to obtain the optimal solution of the real number field smooth time-varying quadratic programming problem of the actual physical system or numerical solution system. This port sends instructions to the processor module solution system when it needs to obtain the solution parameters request and receive the solution result; The redundant manipulator path planning terminal unit is used to convert the parameters output by the optimal solution request terminal unit into relevant data, and finally input it into the manipulator control program for path planning and control of the manipulator.