Filling manipulator positioning precision reliability solving method based on joint simulation

Abstract

The invention discloses a joint simulation-based filling manipulator positioning precision reliability solving method, which comprises the following steps of: determining and initializing random variables, namely the mass and rotational inertia of a manipulator, the mass and rotational inertia of a rotary chassis, the initial position of the manipulator, the contact rigidity, the contact damping and the friction coefficient; using a Latin hypercube sampling method to obtain a random variable sample value; establishing a mechanical arm dynamic model of the mechanical arm; a PID double-loop control strategy is adopted for a driving module of the manipulator to establish a joint simulation model; importing the collected random variable samples into an adamssub module, performing batch simulation to obtain manipulator rotation angle values corresponding to each group of samples, and establishing a neural network agent model of rotation errors; and solving by using a truncation important sampling method to obtain the rotation positioning precision reliability of the manipulator. According to the method, the reliability solving efficiency is greatly improved.

Description

Technical Field

[0001] This invention belongs to the field of reliability solving for complex mechanical structures, and in particular, it is a reliability solving method based on co-simulation. Background Technology

[0002] As the demands for artillery firing speed on the military battlefield increase, artillery loading systems have evolved from manual loading to semi-automatic loading and have gradually developed into the current mainstream fully automatic loading system. The robotic arm, as a key component of the automatic loading system, is primarily responsible for the storage, retrieval, and transfer of projectiles. It is a crucial mechanism connecting the magazine and the projectile coordination arm, and its positioning accuracy plays a vital role in the reliability of the entire loading system. Therefore, solving the problem of the robotic arm's positioning accuracy and reliability is of great significance.

[0003] As a complex electromechanical coupling model, it is difficult to directly obtain the display function of its positioning accuracy and reliability. Conventional solution methods not only fail to take the control module of the model into account, but also require a large amount of simulation data to solve the problem using the Monte Carlo method, resulting in very low solution efficiency. Summary of the Invention

[0004] The purpose of this invention is to provide a method for solving the reliability of the positioning accuracy of a loading robot based on co-simulation. By taking into account the factors affecting the rotational positioning accuracy of the robot, a neural network surrogate model is constructed, which greatly improves the efficiency of reliability solution.

[0005] The technical solution to achieve the purpose of this invention is as follows:

[0006] A method for solving the reliability of positioning accuracy of a loading robot based on co-simulation includes the following steps:

[0007] Step 1: Determine and initialize random variables, namely the mass and moment of inertia of the robot arm, the mass and moment of inertia of the rotating chassis, the initial position of the robot arm, contact stiffness, contact damping, and coefficient of friction.

[0008] Step 2: Use the Latin hypercube sampling method to obtain sample values ​​for random variables;

[0009] Step 3: Establish the dynamic model of the robotic arm;

[0010] Step 4: Establish a joint simulation model for the drive module of the robotic arm using a PID dual-loop control strategy;

[0011] Step 5: Import the collected random variable samples into the adams_sub module, and perform batch simulations to obtain the robot arm rotation angle value corresponding to each group of samples, thereby establishing a neural network surrogate model for rotation error;

[0012] Step 6: Use the truncated importance sampling method to solve for the reliability of the robot's rotational positioning accuracy.

[0013] The significant advantages of this invention compared to existing technologies are:

[0014] (1) By taking into account the control module of the robot's rotary motion, a more accurate output response value can be obtained through co-simulation.

[0015] (2) By constructing an accurate neural network surrogate model and using the truncated importance sampling method, the solution efficiency of complex models can be greatly improved. Attached Figure Description

[0016] Figure 1 This is a flowchart of the design method of the present invention.

[0017] Figure 2 This is a 3D structural diagram of the robotic arm.

[0018] Figure 3 This is a diagram of the co-simulation interface.

[0019] Figure 4 This is a comparison chart of the experimental results and simulation results of the robot's rotation angle.

[0020] Figure 5 This is a comparison chart of the experimental results and simulation results of the robot's rotational angular velocity.

[0021] Figure 6 The image shows the performance of a neural network-based surrogate model for positioning error of projectile rotation angle. Detailed Implementation

[0022] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0023] This invention establishes an electromechanical coupling model of the manipulator through co-simulation, and constructs a neural network surrogate model of the manipulator's positioning accuracy error using a small number of sample values, thereby improving the efficiency of reliability solution; combined with Figure 1 The specific process includes the following steps:

[0024] Step 1: Determine and initialize random variables:

[0025] As a key component of the automated loading system, the robotic arm is primarily responsible for the storage, retrieval, and transfer of projectiles. It is a crucial mechanism connecting the magazine and the projectile coordination arm. Its three-dimensional structure is as follows: Figure 2As shown. Through analysis, it was found that the factors affecting the positioning accuracy of the robot mainly include three aspects: (1) the processing and assembly errors of the parts: the size error, quality error and assembly error generated during the manufacturing and assembly process affect the positioning accuracy of the robot; (2) the gear contact parameters: the rotation process of the robot is the gear rotation to send the projectile to the contact position of the projectile arm, and the change of the contact parameters will affect its positioning accuracy; (3) the friction coefficient: the firing environment of the cannon is relatively harsh, and the change of the friction coefficient during its gear transmission will also affect the positioning accuracy of the mechanism. Therefore, the following random variables are selected as the solution for the positioning accuracy of the robot: the mass m1 and moment of inertia I1 of the robot, the mass m2 and moment of inertia I2 of the chassis, the initial position l of the robot, the contact stiffness k, the contact damping c and the friction coefficient μ:

[0026] By reasonably selecting the influencing factors on the rotation and positioning of the robotic arm, a reasonable distribution is given, and the corresponding reliability is solved.

[0027] Step 2: Based on previous measurement data and rules of thumb, the distribution type of the eight random variables selected above is normal distribution. The random variable sample values ​​obtained by using the Latin hypercube sampling method can ensure both the randomness and relative uniformity of the sample, avoiding the problem of excessive sample aggregation that exists in simple random sampling. When training the neural network, 70% of the sampled samples are randomly selected as the training set, and 15% are selected as the test set and validation set.

[0028] Step 3: By establishing a geometric dynamic model consistent with the physical prototype, the above random variables are added as design variables to ensure that the sample values ​​of the input variables can be passed into the dynamic model during the next co-simulation.

[0029] Step 4: Establish a joint simulation model for the robot's drive module using a PID dual-loop control strategy, see [link / details]. Figure 3 The adams_sub module is a robot dynamics model exported from the ADAMS software, while the other modules are control simulation modules built in Simulink. The PID control formula is as follows:

[0030]

[0031] Where t is time, K p For proportional gain; K I K is the integration constant; D U is the differential constant; u(t) is the motor rotation torque output by the PID controller; e(t) is the real-time error between the planned value and the measured value of the robot's rotation angle.

[0032] Step 5: Import the random variable samples collected in Step 2. Figure 3 In the adams_sub module shown, batch simulations are used to obtain the robot's rotation angle value corresponding to each group of samples, thereby establishing a neural network surrogate model for the rotation error:

[0033] A backpropagation (BP) neural network typically consists of an input layer, intermediate layers, and an output layer. In this embodiment, the sigmoid function is chosen as the activation function between all layers, and the predicted rotation angle of the robotic arm is used as the input layer. Simulation sample value y of the robot arm's rotation angle i The mean squared error between the two sides is used 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 robotic arm neural network surrogate model, ||W|| represents the Euclidean norm; N is the number of training samples of the robotic arm random variables extracted through the Latin hypercube; W and B represent the weight matrix and bias matrix of each random variable affecting the robotic arm's rotation and positioning error, respectively. The entire training process corresponds to finding the optimal W and B to obtain the minimum loss function P(W,B).

[0036] The surrogate model for the positioning error is thus expressed as follows:

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

[0038] In the formula, Y represents the error between the rotation angle of the robot arm obtained from the neural network training and the planned angle; X represents the random variable of the robot arm mechanism input to 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 for the rotational positioning accuracy of the robot arm; ε lim The given rotation angle error threshold.

[0042] Step 6: The neural network surrogate model established above is used to replace the complex manipulator dynamics model to predict the corresponding rotation angle value under each set of random variables. The reliability of the manipulator's rotation positioning accuracy is summarized in the above steps.

[0043] The limit state function for the positioning accuracy of the robotic arm can be defined as:

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

[0045] In the formula, ζ e Let ζ(·) be the planned rotation angle value for the robot arm, and ζ(·) be the actual rotation angle value obtained from simulation. e -ζ(m1,I1,m2,I2,l,k,c,μ)| This part is obtained directly through 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 origin to the limit state surface. Therefore, the failure domain lies outside a hypersphere with radius β centered at the origin. The indicator function within the region outside the β hypersphere is defined as:

[0047]

[0048] In the formula, I β (x) is the indicator function, which is 0 if the sample point falls within the β hypersphere, and 1 otherwise; x is the sample point extracted during the reliability solution process.

[0049] The truncated importance sampling density function for the rotational positioning accuracy of a robotic arm can be expressed as:

[0050]

[0051] In the formula, h X (x) represents the key sampling density function for the robot's rotational positioning accuracy. By truncating the key sampling density function, it is unnecessary to calculate the corresponding function value for sample points falling within the β-sphere, thus improving computational efficiency.

[0052] The formula for calculating the failure probability of the robot's positioning accuracy is as follows:

[0053]

[0054] In the formula, I F (x) is the indicator function of an important sampling method for the rotational positioning accuracy of the robot arm; f X (x) is the probability density function of the robot's rotational positioning accuracy.

[0055] M samples {x1, x2, ..., x3} of the input variable x are drawn according to the importance sampling density function. M} T Failure probability estimate obtained by truncated importance sampling method for:

[0056]

[0057] In the formula, M represents the number of samples of the robot variable drawn using the importance sampling method; IF (x i ) represents the indicator function of the important sampling method for the rotational positioning accuracy of the i-th robot arm; I β (x i f represents the indicator function of the truncated significance sampling method for the rotational positioning accuracy of the i-th robot arm; X (x i ) represents the probability density function value of the rotational positioning accuracy of the i-th robot arm; h X (x i ) represents the importance sampling probability density function value of the i-th robot arm rotation positioning accuracy; when calculating the failure probability using the truncated importance sampling method, for the sample point x falling into the β sphere... i Since the corresponding indicator function is 0, there is no need to calculate the function value of these sample points, so the computational efficiency is higher than that of traditional importance sampling methods.

[0058] The failure probability obtained by solving the problem can determine whether the structure meets the usage requirements and provide a reference for subsequent reliability-based design optimization. The positioning accuracy and reliability requirements of the robotic arm in the automatic loading system of artillery are very high. When it is lower than 0.98, the control strategy needs to be adjusted or the parts need to be replaced to meet the usage requirements. The sum of the failure probability and the reliability is 1, so the obtained failure probability must be lower than 0.02.

[0059] By taking the control module of the model into account, more accurate and reliable results can be obtained. At the same time, the accuracy of the established surrogate model can replace the complex dynamic model to improve the solution efficiency.

[0060] Example 1

[0061] Although the above explanation of the reliability solution method uses a robotic arm as the solution object, it is equally applicable to other complex electromechanical coupling models. To illustrate the operational process and solution results of the method in detail, the application of this invention will be explained in detail below using a specific engineering scenario as an example.

[0062] like Figure 2 The dynamic model of the robotic arm shown is illustrated in Table 1, with the selection and distribution types of random variables as listed. Solve the problem following the steps outlined above:

[0063] For the robotic arm structure, its co-simulation interface is as follows: Figure 3 As shown, the simulation model of this process was compared with the test results of the prototype. Figures 4-5 As shown, to ensure the correctness of the simulation model, 1000 initial samples were extracted, and a neural network surrogate model with a 10-10-8-1 structure was finally constructed. Figure 6It can be seen that the correlation coefficients of the training set, test set, and validation set are all above 0.98, indicating that the constructed surrogate model has high accuracy and can replace the complex dynamic model for reliability calculation. Finally, the reliability of the robot's rotary positioning accuracy is 0.9915, obtained by truncating the importance sampling method.

[0064] Table 1

[0065]

Claims

1. A method for solving the reliability of positioning accuracy of a loading robot based on joint simulation, characterized in that: The following steps are involved: Step 1: Determine and initialize random variables, which are the mass and moment of inertia of the manipulator, the mass and moment of inertia of the rotary chassis, the initial position of the manipulator, contact stiffness, contact damping and friction coefficient; Step 2: Use Latin hypercube sampling method to obtain random variable sample values; Step 3, establishing a manipulator dynamics model of the manipulator; Step 4: A joint simulation model is established using a PID dual-loop control strategy for the manipulator's drive module; Step 5: Import the collected random variable samples into the adams_sub module, and perform batch simulation to obtain the manipulator rotation angle value corresponding to each group of samples, so as to establish a neural network proxy model of rotation error; Step 6: Use the truncated important sampling method to solve the reliability of the rotary positioning accuracy of the manipulator.

2. The method for solving the reliability of positioning accuracy of a loading robot based on joint simulation according to claim 1 is characterized in that: The PID control formula is as follows: Where t is time, K p is the proportional gain; K I is the integration constant; K D is the differential constant; u(t) is the motor rotation torque output by the PID controller; e(t) is the real-time error between the planned value and the measured value of the manipulator rotation angle.

3. The method for solving the reliability of positioning accuracy of a loading robot based on joint simulation according to claim 1 is characterized in that: The sigmoid function is selected as the activation function between all layers of the BP neural network, and the predicted value of the manipulator rotation angle is The simulation sample value y of the manipulator rotation angle i The mean square error between is used as the loss function of the neural network, and its expression is: Where P(W, B) is the loss function of the established manipulator neural network proxy model, |||| represents the Euclidean norm; N is the number of training samples of the manipulator random variables extracted by Latin hypercube; W, B represent the weight matrix and deviation matrix of each random variable that affects the manipulator rotation positioning error, respectively; The proxy model of positioning error is expressed as follows: Y=F(X,W,B) Where Y represents the error between the manipulator rotation angle obtained by neural network training and the planned angle; X represents the random variable of the manipulator mechanism input by the network, X = [m1, I1, m2, I2, l, k, c, μ]; The limit state equation can be expressed as: g=ε lim -|ζ e -ζ(m1,I1,m2,I2,l,k,c,μ)| Where g is the limit state equation of the manipulator's rotary positioning accuracy; ε lim is the given rotation angle error threshold, ζ e is the planned value of the manipulator rotation angle, and ζ(·) is the rotation angle value obtained by actual simulation.

4. The method for solving the reliability of positioning accuracy of a loading robot based on joint simulation according to claim 1 is characterized in that: Failure probability estimates obtained using truncated importance sampling for: Where M represents the number of samples of manipulator variables extracted using the importance sampling method; I F (x i ) represents the indicator function of the important sampling method of the i-th manipulator rotation positioning accuracy; I β (x i ) represents the indicator function of the truncated importance sampling method for 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 important sampling probability density function value of the rotation positioning accuracy of the i-th manipulator.

5. The method for solving the reliability of positioning accuracy of a loading robot based on joint simulation according to claim 4 is characterized in that: Where β refers to the shortest distance from the origin to the limit state surface, x i is the i-th sample of the sample of input variables extracted according to the important sampling density function.

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