A method for solving positioning accuracy reliability of a filling robot based on joint simulation

Abstract

The application discloses a kind of based on joint simulation filling manipulator positioning precision reliability solution method, comprising: determining and initializing random variable, respectively manipulator mass and rotational inertia, the mass and rotational inertia of rotary chassis, manipulator initial position, contact stiffness, contact damping and friction coefficient;Using Latin hypercube sampling method obtains random variable sample value;Establish the manipulator dynamics model of manipulator;For the drive module of manipulator, a double-loop control strategy of PID is used to establish a joint simulation model;The collected random variable sample is imported into adams_sub module, and the rotary angle value corresponding to each group of samples is obtained by batch simulation, to establish the neural network proxy model of rotary error;The rotary positioning precision reliability of manipulator is obtained by using truncated importance sampling method.The application greatly improves the reliability solving efficiency.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of complex mechanical structure reliability solving, in particular to a reliability solving method based on joint simulation. BACKGROUND

[0002] With the increasing demand for the firing speed of artillery in military battlefield, the artillery loading system has developed from manual loading to semi-automatic loading and gradually to the current mainstream of full-automatic loading. As one of the key components of the automatic loading system, the manipulator is mainly responsible for the tasks of accessing and transferring the projectile, and is an important mechanism connecting the cartridge case and the projectile coordination arm. The positioning accuracy of the manipulator plays an important role in the reliability of the whole loading system, so it is of great significance to solve the positioning accuracy reliability of the manipulator.

[0003] As a complex electromechanical coupling model, it is difficult to directly obtain the explicit function function of the positioning accuracy reliability of the manipulator, and the conventional solving method not only does not consider the control module of the model, but also uses the Monte Carlo method for solving, which needs to obtain a large amount of simulation data, and the solving efficiency is very low. SUMMARY

[0004] The purpose of the present application is to provide a loading manipulator positioning accuracy reliability solving method based on joint simulation, which considers the influencing factors affecting the positioning accuracy of the manipulator, and constructs a neural network proxy model to greatly improve the reliability solving efficiency.

[0005] The technical solution for achieving the purpose of the present application is:

[0006] A loading manipulator positioning accuracy reliability solving method based on joint simulation, comprising the following steps:

[0007] Step 1, determine and initialize random variables, which are the mass and rotational inertia of the manipulator, the mass and rotational inertia of the rotary chassis, the initial position of the manipulator, the contact stiffness, the contact damping and the friction coefficient;

[0008] Step 2, use the Latin hypercube sampling method to obtain random variable sample values;

[0009] Step 3, establish a manipulator dynamics model of the manipulator;

[0010] Step 4, for the driving module of the manipulator, a PID double-loop control strategy is adopted to establish a joint simulation model;

[0011] Step 5, import the collected random variable samples into the adams_sub module, and batch simulation is performed to obtain the corresponding manipulator rotation angle value of each group of samples, so as to establish a neural network proxy model of the rotation error;

[0012] Step 6, the rotary positioning accuracy reliability of the manipulator is solved by using the truncated importance sampling method.

[0013] Compared with the prior art, the present application has the following advantages:

[0014] (1) By considering the control module of the rotary motion of the manipulator, more accurate output response values can be obtained in the form of joint simulation;

[0015] (2) The solution efficiency of the reliability of the complex model can be greatly improved by constructing an accurate neural network proxy model and using the truncated importance sampling method. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 The flowchart of the method designed by the present application is shown.

[0017] Figure 2 The three-dimensional structure diagram of the manipulator is shown.

[0018] Figure 3 The joint simulation interface diagram is shown.

[0019] Figure 4 The comparison diagram of the rotary angle test results and simulation results of the manipulator is shown.

[0020] Figure 5 The comparison diagram of the rotary angle test results and simulation results of the manipulator is shown.

[0021] Figure 6 The performance diagram of the positioning error proxy model of the projectile rotary angle based on the neural network is shown. DETAILED DESCRIPTION

[0022] The present application will be further described below in combination with the drawings and specific embodiments.

[0023] The present application establishes an electromechanical coupling model of the manipulator in the form of joint simulation, constructs a neural network proxy model of the positioning accuracy error of the manipulator by using a small amount of sample values, and achieves the purpose of improving the reliability solution efficiency. Figure 1 The specific process includes the following steps:

[0024] Step 1, determine and initialize random variables:

[0025] The manipulator is one of the key components of the automatic loading system, mainly responsible for the storage and transmission of the projectile, and is an important mechanism connecting the cartridge and the coordination arm, and its three-dimensional structure is shown in Figure 2The factors affecting the positioning accuracy of the manipulator are mainly composed of three aspects: (1) the machining and assembly errors of parts: the dimensional errors, mass errors and errors generated during the assembly process affect the positioning accuracy of the manipulator; (2) gear contact parameters: the rotation of the gear sends the projectile to the handover position of the coordination arm, and the change of the contact parameters will affect the positioning accuracy; (3) friction coefficient: the firing environment of the gun is relatively harsh, and the change of the friction coefficient during the gear transmission will also affect the positioning accuracy of the mechanism. Therefore, the following random variables are selected as the solution of the positioning accuracy of the manipulator, respectively, the mass m1 and the rotational inertia I1 of the manipulator, the mass m2 and the rotational inertia I2 of the chassis, the initial position l of the manipulator, the contact stiffness k, the contact damping c and the friction coefficient μ:

[0026] By reasonably selecting the factors affecting the positioning of the manipulator, the corresponding reliability is solved.

[0027] Step 2, according to the previous measurement data and experience rule, the distribution type of the above selected 8 random variables is normal distribution, the random variable sample value obtained by using Latin hypercube sampling method can ensure the randomness and relative uniformity of the sample, and avoid the problem of excessive aggregation of simple random sampling. When training the neural network, randomly select 70% of the extracted samples as the training set, and the test set and the validation set are both 15%;

[0028] Step 3, by establishing the geometric dynamics model consistent with the physical prototype, and then adding the above random variables as design variables, so as to ensure that the input variable sample value can be transmitted into the dynamics model in the next step of co-simulation;

[0029] Step 4, the PID double-loop control strategy is adopted for the drive module of the manipulator to establish the co-simulation model, as shown in Figure 3 , where the adams_sub module is the dynamics model of the manipulator derived from ADAMS software, and the remaining modules are the control simulation modules built in simulink. The PID control formula is as follows:

[0030]

[0031] Where, t is time, K p is proportional gain; K I is integral constant; K D is differential constant; u(t) is the motor rotation torque output by the PID controller; e(t) is the real-time error between the rotation angle planning value and the measured value of the manipulator.

[0032] Step 5, by importing the random variable samples collected in step 2 intoFigure 3 In the adams_sub module shown, batch simulation obtains the mechanical hand rotation angle value corresponding to each group of samples, so as to establish a neural network proxy model of rotation error:

[0033] The BP neural network is generally composed of an input layer, an intermediate layer and an output layer. In this embodiment, the sigmoid function is selected as the activation function between all layers, and the mechanical hand rotation angle prediction value and the mechanical hand rotation angle simulation sample value y i The mean square error between them is taken as the loss function of the neural network, and its expression is:

[0034]

[0035] In the formula, P(W, B) is the loss function of the established mechanical hand neural network proxy model, || represents the Euclidean norm; N is the number of training samples of the mechanical hand random variables extracted by Latin hypercube; W, B represent the weight matrix and bias matrix of each random variable affecting the rotation positioning error of the mechanical hand respectively. The whole training process corresponds to finding the best W, B to obtain the minimum loss function P(W, B).

[0036] The proxy model of the positioning error is obtained as follows:

[0037] Y=F(X,W,B)

[0038] In the formula, Y represents the error between the mechanical hand rotation angle obtained by neural network training and the planned angle; X represents the random variable of the mechanical hand structure input of the network, X=[m1, I1, m2, I2, l, k, c, μ].

[0039] Therefore, the limit state equation can be expressed as:

[0040] g=ε lim -|F(X,W,B)|

[0041] In the formula, g is the limit state equation of the rotation positioning accuracy of the mechanical hand; ε lim is a given rotation angle error threshold.

[0042] Step 6, the neural network proxy model established above is used to replace the complex mechanical hand dynamics model to predict the corresponding rotation angle value under each group of random variables, and the rotation positioning accuracy reliability of the mechanical hand is summarized by solving the above steps:

[0043] The limit state function of the positioning accuracy of the mechanical hand can be defined as:

[0044] g=ε lim -|ζ e- ζ(m1, I1, m2, I2, l, k, c, μ)

[0045] where ζ e is the planning value of the rotation angle of the manipulator, and ζ(·) is the actual simulation value of the rotation angle. ζ e - ζ(m1, I1, m2, I2, l, k, c, μ) is directly obtained by the surrogate model of the positioning error in step 5.

[0046] In an n-dimensional independent standard normal space, the reliability index β refers to the shortest distance from the coordinate origin to the limit state surface, and thus the failure domain is located outside the hypersphere with the origin as the center and β as the radius. The indicator function in the region outside the β hypersphere is defined as:

[0047]

[0048] where I β (x) is the indicator function, that is, 0 if the sample point falls within the β hypersphere, and 1 otherwise; and x is the sample point extracted in the reliability solving process.

[0049] The truncated importance sampling density function of the positioning accuracy of the manipulator rotation can be expressed as:

[0050]

[0051] where h X (x) is the importance sampling density function of the positioning accuracy of the manipulator rotation. According to the truncated importance sampling density function, the corresponding function value does not need to be calculated for the sample points falling within the β sphere, thereby improving the calculation efficiency.

[0052] The calculation formula of the failure probability of the positioning accuracy of the manipulator is:

[0053]

[0054] where I F (x) is the indicator function of the importance sampling method of the positioning accuracy of the manipulator rotation; and f X (x) is the probability density function of the positioning accuracy of the manipulator rotation.

[0055] According to the importance sampling density function, M sample points {x1, x2, …, x M} T of the input variable x are extracted, and the failure probability estimate value obtained by the truncated importance sampling method is:

[0056]

[0057] where M represents the number of samples of the manipulator variable extracted by the importance sampling method; and IF (x i ) represents the indicator function of the importance sampling method of the rotation positioning accuracy of the i th manipulator; I β (x i ) represents the indicator function of the truncated importance sampling method of the rotation positioning accuracy of the i th manipulator; f X (x i ) represents the probability density function value of the rotation positioning accuracy of the i th manipulator; h X (x i ) represents the importance sampling probability density function value of the rotation positioning accuracy of the i th manipulator; when the failure probability is calculated by the truncated importance sampling method, for the sample points x i , since the corresponding indicator function is 0, it is not necessary to calculate the function function value of these sample points, and therefore the calculation efficiency is higher than that of the traditional importance sampling method.

[0058] The obtained failure probability can be used to judge whether the structure meets the use requirements, and provide a reference basis for later reliability-based design optimization. The positioning accuracy reliability requirement of the manipulator in the automatic loading system of the gun is very high, and when it is lower than 0.98, the control strategy needs to be adjusted or the parts need to be replaced to meet the use requirements. The sum of the failure probability and the reliability is 1, and therefore the obtained failure probability is lower than 0.02.

[0059] By considering the control module of the model, more accurate reliability results can be obtained, and the accuracy of the established proxy model can replace the complex dynamic model to improve the solving efficiency.

[0060] Embodiment 1

[0061] Although the above description process of the reliability solving method takes the manipulator as the solving object, the method is also applicable to other complex electromechanical coupling models. In order to explain the operation process and solving effect of the application of the method in detail, the application of the present application is described in detail below with a specific engineering example.

[0062] As shown in the manipulator dynamic model shown in Figure 2 , the selection and distribution type of the random variable are shown in Table 1. The solving is performed according to the above steps:

[0063] For the manipulator structure, the joint simulation interface is as shown in Figure 3 , the simulation model of the process is compared with the test results of the test sample machine, as shown in Figures 4-5 , to ensure the correctness of the simulation model. By extracting 1000 groups of initial samples, the neural network proxy model of the 10-10-8-1 structure is finally constructed, and the simulation results are as shown in Figure 6It can be seen that the correlation coefficients of the training set, the test set and the validation set are all above 0.98, which indicates that the constructed surrogate model has high precision and can replace the complex dynamic model for reliability solution. Finally, the reliability of the manipulator rotation positioning accuracy is 0.9915 by solving with the truncated importance sampling method.

[0064] Table 1

[0065]

Claims

1. A method for solving the positioning accuracy reliability of a filling robot based on joint simulation, characterized in that, Comprising the following steps: Step 1, determine and initialize random variables, respectively, the mass and rotational inertia of the manipulator, the mass and rotational inertia of the rotary base, the initial position of the manipulator, the contact stiffness, the contact damping and the friction coefficient; Step 2, use Latin hypercube sampling method to obtain random variable sample values; Step 3, establish the manipulator dynamics model of the manipulator; Step 4, for the drive module of the manipulator, a double-loop control strategy of PID is adopted to establish a joint simulation model; Step 5, import the collected random variable sample into the adams_sub module, and batch simulation is performed to obtain the rotary angle value of the manipulator corresponding to each sample group, so as to establish a neural network proxy model of the rotary error; The sigmoid function is selected as the activation function between all layers of the BP neural network, and the predicted value of the robot rotation angle is taken as the loss function of the neural network, and its expression is as follows: between the simulation sample value of the robot rotation angle ； In the formula, is the loss function of the established mechanical hand neural network agent model, represents the Euclidean norm; N is the number of training samples of the mechanical hand random variable extracted by Latin hypercube; respectively represent the weight matrix and the bias matrix of each random variable affecting the rotation positioning error of the mechanical hand. The proxy model of the positioning error is expressed as follows: ； In the formula, represents the error between the rotation angle of the manipulator obtained by neural network training and the planned angle; represents a random variable of the manipulator mechanism of the input of the network, are the mass and the moment of inertia of the manipulator, respectively, are the mass and the moment of inertia of the chassis, respectively, are the initial position, the contact stiffness, the contact damping and the friction coefficient of the manipulator, respectively.​​​​​​ The limit state equation can be expressed as: ； In the formula, is the limit state equation of the positioning accuracy of the robot rotation; is a given rotation angle error threshold value, is the rotation angle planning value of the robot, is the actual rotation angle value obtained by simulation. Step 6, the rotary positioning accuracy reliability of the manipulator is solved by using the truncated importance sampling method.

2. The method of claim 1, wherein, The PID control formula is as follows: ； wherein t is time, is a proportional gain; is an integral constant; is a differential constant; is a motor rotation torque output of the PID controller; is a real-time error between the robot rotation angle planning value and the measured value.

3. The method of claim 1, wherein the method is characterized by: The failure probability estimate value obtained by the truncated importance sampling method is: ； In the formula, M represents the number of samples of the robot variable extracted by using the importance sampling method; an indicator function of the importance sampling method representing the rotational positioning accuracy of the robot No. an indicator function of the importance sampling method representing the rotational positioning accuracy of the robot No. an indicator function of the truncated importance sampling method representing the rotational positioning accuracy of the robot No. an indicator function of the truncated importance sampling method representing the rotational positioning accuracy of the robot No. a probability density function value representing the rotational positioning accuracy of the robot No. a probability density function value representing the rotational positioning accuracy of the robot No. an importance sampling probability density function value representing the rotational positioning accuracy of the robot No. an importance sampling probability density function value representing the rotational positioning accuracy of the robot No.

4. The joint simulation-based positioning accuracy reliability solving method of the filling manipulator according to claim 3, characterized in that, ； wherein refers to the shortest distance from the coordinate origin to the limit state surface, is the i-th sample in the set of samples of input variables drawn according to the importance sampling density function .

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