CN113759713B - Harmonic reducer error compensation control method by mixing memristor model with neural network - Google Patents

Abstract

The invention discloses a harmonic reducer error compensation control method with a memristor model and a neural network mixed, which is used for improving the memristor model into a memristor hysteresis model and describing the basic change rule of hysteresis output of the harmonic reducer; and compensating the difference between the harmonic reducer hysteresis model and the memristive hysteresis model by means of an RBF neural network with nonlinear fitting capability. The RBF neural network is overlapped with memristor hysteresis model output to form a harmonic reducer hybrid hysteresis model, torsion angle output under different torques is predicted through harmonic reducer hysteresis characteristic modeling, and transmission error compensation is carried out from a harmonic reducer driving end. Completely different from a method for solving the transmission error of the harmonic speed reducer from the manufacturing perspective, the complex structure of the harmonic speed reducer and a complex operation mechanism of forward and reverse rotation transmission of periodic engagement, disengagement and re-engagement between the flexible gear and the rigid gear are avoided, and the conversion precision of the harmonic speed reducer is improved from the aspects of information modeling and compensation.

Description

Error compensation control method of harmonic reducer by mixing memristive model and neural network

Technical field

The invention relates to the field of robot precision control technology, and specifically relates to a harmonic reducer error compensation control method that mixes a memristor model and a neural network.

Background technique

The harmonic reducer, which has the advantages of large transmission ratio, compact structure, and high transmission accuracy, is one of the core components of the industrial robot transmission system. However, during the transmission process of the harmonic reducer, various frictions, backlash, transmission errors and other reasons caused by the elliptical deformation of the flexspline cause the harmonic reducer to exhibit hysteresis characteristics, which is an inherent property of the harmonic reducer and severely restricts it. Improves the transmission accuracy of the harmonic reducer. In view of the nonlinear characteristics of domestic harmonic reducers, in addition to solving them from the perspective of structure and processing, compensating the hysteresis characteristics of the harmonic reducer through modeling is another effective way to improve the transmission accuracy of the harmonic transmission system.

In view of the hysteresis characteristics displayed by the reducer, the existing method is to discuss many interference factors and build a related hysteresis model. However, the formation of hysteresis in harmonic reducers is affected by many factors, such as assembly errors in static state, transmission hysteresis during movement, and various forms of internal friction and interference. Existing methods only deal with one or several interferences in the reducer. factors are discussed, and the influence of other nonlinear factors on the hysteresis characteristics of the reducer is ignored, resulting in the accuracy of the built hysteresis model of the reducer being not high.

Contents of the invention

The present invention aims at the problem that the harmonic reducer exhibits hysteretic characteristics of load torque and torsion angle as the load changes, resulting in a decrease in the conversion accuracy of the harmonic reducer, and provides a harmonic reducer error that mixes a memristive model and a neural network. Compensation control method.

In order to solve the above problems, the present invention is implemented through the following technical solutions:

The harmonic reducer error compensation control method mixed with memristive model and neural network includes the following steps:

Step 1. Collect the output shaft torque u(k) and output torsion angle θ _d (k) of the harmonic reducer at the M historical moments closest to the current time to be compensated k′;

Step 2. Construct a hybrid hysteresis model in which the memristive hysteresis model is connected in parallel with the neural network, and use the output shaft torque u(k) of the harmonic reducer of the M historical moments closest to the current time to be compensated k′ collected in step 1. and the output torsion angle θ _d (k) to train the hybrid hysteresis model to obtain the hybrid hysteresis model at the current time to be compensated k′; during the training process of the hybrid hysteresis model:

Step 2.1. Send the output shaft torque u(k) of the harmonic reducer at M historical moments into the memristive hysteresis model, and obtain the output torsion angle θ ₀ (k) of the memristive hysteresis model at M historical moments. ;

Step 2.2. Combine the output shaft torque u(k) of the harmonic reducer at M historical moments, the output torsion angle θ ₀ (k) of the memristive hysteresis model, and the output torsion angle θ(k-1) of the RBF dynamic neural network. ) as the input of the RBF dynamic neural network, and the deviation value θ _e (k) of the output torsion angle θ _d (k) of the harmonic reducer at M historical moments and the output torsion angle θ ₀ (k) of the memristive hysteresis model ) as the error of the RBF dynamic neural network, the output torsion angle θ(k) of the RBF dynamic neural network at M historical moments is obtained;

Step 2.3. Add the output torsion angle θ ₀ (k) of the memristive hysteresis model at M historical moments and the output torsion angle θ (k) of the RBF dynamic neural network to obtain the unit torsion angle compensation amount at M historical moments.

Step 3. Send the output shaft torque u(k′) and output torsion angle θ _d (k′) of the harmonic reducer at the current time k′ to be compensated to the current time k′ to be compensated obtained in step 2. In the mixed hysteresis model, the unit torsion angle compensation amount at the current time to be compensated k′ is obtained.

Step 4. Calculate the unit torsion angle compensation amount of the current time k′ obtained in step 3 to After multiplied by the reduction ratio N of the harmonic reducer, the input end torsion angle compensation amount of the harmonic reducer at the current time k' to be compensated is obtained/> Then the input end torsion angle compensation amount of the harmonic reducer at the current time k′ to be compensated/> Add it to the torsion angle set at the input end of the harmonic reducer at the current time k' to be compensated, to realize the transmission error compensation control of the harmonic reducer;

Among them, k=1,2,…,M, k′=M+1,M+2,…, M is the number of set historical moments.

In the above step 2.1, the output twist angle θ ₀ (k) of the memristive hysteresis model at the kth historical moment is:

In the formula, u(k) is the output shaft torque of the harmonic reducer at the kth historical moment, M(z) is the resistance value of the memristor, k=1,2,…,M, M is the setting the number of historical moments.

In the above step 2.2, the deviation value θ _e (k) at the kth historical moment is:

θ _e (k) = θ _d (k) - θ ₀ (k)

In the formula, θ _d (k) is the output torsion angle of the harmonic reducer at the kth historical moment, θ ₀ (k) is the output torsion angle of the memristive hysteresis model at the kth historical moment, k = 1,2 ,...,M, M is the number of set historical moments.

In step 2.3 above, the unit torsion angle compensation amount at the kth historical moment for:

In the formula, θ ₀ (k) is the output torsion angle of the memristive hysteresis model at the kth historical moment, θ (k) is the output torsion angle of the RBF dynamic neural network at the kth historical moment, k = 1,2, ...,M,M is the number of set historical moments.

Compared with the existing technology, the present invention has the following characteristics:

1. Considering that directly using the memristive hysteresis model harmonic reducer to model, there are model errors and the parameters are difficult to identify online, so the RBF (radial Basis Function) neural network is used to effectively compensate the output error of the memristive hysteresis model, and the memristive hysteresis model will be used. The hybrid hysteresis model of the harmonic reducer composed of a hysteresis model and an RBF neural network in parallel is used to describe the complex hysteresis characteristics of the reducer, effectively improving the accuracy of the hysteresis model.

2. With the help of the memory characteristics of the memristor model, after improving it, a memristive hysteresis model is constructed to describe the nonlinear hysteresis characteristics of the harmonic reducer.

3. Completely different from the manufacturing perspective, it avoids the complex structure of the harmonic reducer and the complex operating mechanism of the forward and reverse transmission of periodic engagement, disengagement, and re-engagement between the flexspline and the rigid spline. Through the hysteresis model of the harmonic reducer, the torsion angle of the harmonic reducer is predicted under different loads, and the transmission error compensation control is carried out from the drive input end of the harmonic reducer. From the perspective of information modeling and feedforward compensation, the harmonics are improved. Reducer conversion accuracy.

Description of the drawings

Figure 1 shows the structure of the mixed hysteresis model.

Figure 2 shows the hysteresis characteristic curve of the memristor model.

Figure 3 shows the memristive hysteresis model characteristic curve.

Figure 4 is a comparison diagram between the output of the memristive hysteresis model and the output of the harmonic reducer.

Figure 5 shows the RBF dynamic neural network structure.

Figure 6 shows the mixed hysteresis model.

Figure 7 shows the compensation control system for transmission error of harmonic reducer in industrial robot joints.

Detailed ways

In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be further described in detail below with reference to specific examples.

From a system perspective, the output torsion angle is the difference between the theoretical output and the actual output of the harmonic reducer, which changes with the load. The present invention constructs a hybrid hysteresis model that can describe the hysteresis relationship between the reducer output shaft torque and the output torsion angle. The hybrid hysteresis model is a parallel structure: on the one hand, the hysteresis characteristics of the memristor model are improved to make the hysteresis curve consistent with the hysteresis characteristic curve of the harmonic reducer; on the other hand, the memristor hysteresis model characteristic curve is consistent with the hysteresis characteristic curve of the harmonic reducer. The difference between the hysteresis characteristic curves of the harmonic reducer is compensated by using the nonlinear fitting ability of the neural network. The memristive hysteresis model is superimposed on the neural network, and the structure of the constructed hybrid hysteresis model is shown in Figure 1.

1) Memristive hysteresis model

A memristor hysteresis model is constructed based on the dynamic characteristics of the memristor model, so that its output can show the basic changing law of the hysteresis output of the harmonic reducer.

The difference between the memristor model hysteresis curve and the harmonic reducer hysteresis characteristic curve in Figure 2 is that the two hysteresis characteristic curves have different directions and the memristor hysteresis characteristic curve has an intersection at the abscissa of 0, so the memristor model needs to be improved. Make its output consistent with the change pattern of the hysteresis curve of the harmonic reducer. Transform the direction of the memristor output curve into a "bowtie"shape; then approximately regard the curve as symmetric about the torsion angle θ ₀ =-u when the input torque u < 0, and use equation (1) to solve the output curve's abscissa: The intersection point at 0, the improved memristive hysteresis model is shown in formula (1), and the corresponding curve is shown in Figure 3.

Where M(z) is the resistance value of the memristor:

M(z)＝R _ON z+R _OFF (1-z) (2)

In the formula, D is the total thickness of the memristor, ω is the width of the doped region, R _ON and R _OFF are extreme resistances, μ _v ≈10 ^-14 m ² s ^-1 V ^-1 is the average ion drift rate, is the proportional factor between the moving speed of the boundary and the torsion angle, F _n (z) is the window function, F _n (z) = 1, and z is the internal state variable. Take R _ON =100Ω, R _OFF =1.6kΩ, D=10nm, z=0.6.

Collect the output shaft torque u and the actual output torsion angle θ _d of the harmonic reducer; use the collected experimental data torque u(k) as the input of the memristive hysteresis model, and obtain the output θ of the memristive hysteresis model from Equation (1) ₀ (k), adjust the parameters of the memristive hysteresis model. Under the same input, the harmonic reducer u(k) and θ _d (k) characteristic curves match the memristive hysteresis model u(k) and θ ₀ (k) characteristic curves. For example, as shown in Figure 4.

The memristive hysteresis model characteristic curve is similar to the hysteresis characteristic curve of the harmonic reducer, but there are errors, and it is difficult to identify the parameters of the memristive hysteresis model online. The invention uses an RBF dynamic neural network with parameter self-learning capability to compensate for the difference between the memristive hysteresis model characteristic curve and the hysteresis characteristic curve of the harmonic reducer.

2)RBF dynamic neural network

The neural network structure is shown in Figure 5. In the RBF neural network, assume the harmonic reducer output shaft torque u(k), the memristive hysteresis model output θ ₀ (k) and the value of the RBF neural network at the previous moment θ ( k-1) as neural network input.

The difference θ _e (k) is the difference between the torsion angle output θ _d (k) of the harmonic reducer at time k and the output θ ₀ (k) of the memristive hysteresis model. Its expression is:

θ _e (k)＝θ _d (k)-θ ₀ (k) (5)

θ _e (k) is used for RBF parameter learning. In the RBF network, w=[w ₁ , _wi ,…,w _n ] ^T is the output weight vector, φ=[φ ₁ ,φ _i ,…,φ _n ] ^T is the radial basis vector, φ _i is the Gaussian function, the input of the neural network X=[u(k),θ ₀ (k),θ(k-1)] ^T , i=1,2,…n The resulting neural network model is:

Among them, C _i = [c _i1 , c _ij ...c _nm ] ^T and b _i are the center point vector and width of the i-th neuron respectively, j = 1, 2, ... mb _i > 0.

Let the error loss function be:

According to the gradient descent method, the neural network weights are updated as follows:

w _i (k ₎ = _wi (k-1)+Δw _i (k)+α(wi (k-1) _-wi (k-2)) (9)

b _i (k)=b _i (k-1)+Δb _i (k)+α(b _i (k-1)-b _i (k-2)) (11)

c _ij (k)＝c _ij (k-1)+Δc _ij (k)+α(c _ij (k-1)-c _ij (k-2)) (13)

Among them, eta∈[0,1] is the learning rate; α∈[0,1] is the momentum factor, i=1,...6, j=1,...3. k is the current time to be compensated, k-1 is the time before the current time, and k-2 is the time before k-1. w _i (k), w _i (k-1), w _i (k-2), respectively represent the i-th implicit node weight corresponding to the current moment to be compensated for k, the moment before k, and the moment before k-1. Coefficient w _i value. Δw _i (k) The incremental value of the weighting coefficient w _i of the i-th implicit node k at the current time to be compensated. The meanings of other parameters b _i and c _ij are similar to w _i .

The RBF neural network is connected in parallel with the memristive hysteresis model, the neural network parameters are adjusted, and a hybrid hysteresis model of the harmonic reducer is constructed, which is used to describe the mutation and non-smooth hysteresis characteristics of the harmonic reducer.

3) Hybrid hysteresis model of harmonic reducer using memristive hysteresis model and neural network in parallel

Adjust the parameters of the memristive hysteresis model so that it can show the basic changing law of the reducer characteristic curve; for the difference between the output of the memristive hysteresis model and the hysteresis characteristics of the harmonic reducer, learn it through the parallel RBF neural network and Compensation; the hybrid hysteresis model constructed by superimposing the memristive hysteresis model and the neural network is shown in Figure 6. The dotted line in the figure represents the hybrid hysteresis model constructed by the parallel structure.

The input torque u(k) of the harmonic reducer hysteresis model and the corresponding model output torsion angle are:

Based on the above analysis, the harmonic reducer error compensation control method based on the hybrid memristor model and neural network implemented by the present invention includes the following steps:

Step 1. Collect the output shaft torque u(k) and output torsion angle θ _d (k) of the harmonic reducer at the M historical moments closest to the current time to be compensated k′.

Among them, k=1, 2,...,M, k'=M+1, M+2,..., M is the number of set historical moments. In this embodiment, M=100.

Step 2. Construct a hybrid hysteresis model in which the memristive hysteresis model is connected in parallel with the neural network, and use the output shaft torque u(k) of the harmonic reducer of the M historical moments closest to the current time to be compensated k′ collected in step 1. and the output torsion angle θ _d (k) to train the hybrid hysteresis model to obtain the hybrid hysteresis model at the current time to be compensated k′; during the training process of the hybrid hysteresis model:

Step 2.1. Send the output shaft torque u(k) of the harmonic reducer at M historical moments into the memristive hysteresis model, and obtain the output torsion angle θ ₀ (k) of the memristive hysteresis model at M historical moments. ;

Among them, the output twist angle θ ₀ (k) of the memristive hysteresis model at the kth historical moment is:

In the formula, u(k) is the output shaft torque of the harmonic reducer at the kth historical moment, and M(z) is the resistance value of the memristor.

Step 2.2. Combine the output shaft torque u(k) of the harmonic reducer at M historical moments, the output torsion angle θ ₀ (k) of the memristive hysteresis model, and the output torsion angle θ(k-1) of the RBF dynamic neural network. ) as the input of the RBF dynamic neural network, and the deviation value θ _e (k) of the output torsion angle θ _d (k) of the harmonic reducer at M historical moments and the output torsion angle θ ₀ (k) of the memristive hysteresis model ) as the error of the RBF dynamic neural network, the output torsion angle θ(k) of the RBF dynamic neural network at M historical moments is obtained;

The deviation value θ _e (k) at the kth historical moment is:

θ _e (k) = θ _d (k) - θ ₀ (k)

In the formula, θ _d (k) is the output torsion angle of the harmonic reducer at the kth historical moment, and θ ₀ (k) is the output torsion angle of the memristive hysteresis model at the kth historical moment.

Step 2.3. Add the output torsion angle θ ₀ (k) of the memristive hysteresis model at M historical moments and the output torsion angle θ (k) of the RBF dynamic neural network to obtain the unit torsion angle compensation amount at M historical moments.

Among them, the unit torsion angle compensation amount at the kth historical moment for:

In the formula, θ ₀ (k) is the output torsion angle of the memristive hysteresis model at the kth historical moment, and θ(k) is the output torsion angle of the RBF dynamic neural network at the kth historical moment.

Step 3. Send the output shaft torque u(k′) and output torsion angle θ _d (k′) of the harmonic reducer at the current time k′ to be compensated to the current time k′ to be compensated obtained in step 2. In the mixed hysteresis model, the unit torsion angle compensation amount at the current time to be compensated k′ is obtained.

Step 4. Calculate the unit torsion angle compensation amount of the current time k′ obtained in step 3 to After multiplied by the reduction ratio N of the harmonic reducer, the input end torsion angle compensation amount of the harmonic reducer at the current time k' to be compensated is obtained/> Then the input end torsion angle compensation amount of the harmonic reducer at the current time k′ to be compensated/> This is added to the torsion angle set at the input end of the harmonic reducer at the current time k' to be compensated, to realize the transmission error compensation control of the harmonic reducer.

From a system perspective, this invention comprehensively considers various interference factors that cause hysteresis of the harmonic reducer, takes the torque and torsion angle at the output end of the reducer as the research object, builds a hybrid hysteresis model, and describes the behavior of the reducer due to the influence of many factors. The complex hysteresis characteristics of the harmonic reducer are used to realize the compensation control of the transmission error caused by the hysteresis characteristics of the harmonic reducer.

The harmonic reducer error control system that implements the memristor model and neural network hybrid of the above method is shown in Figure 7. It consists of a coding angle detector, a torque detector and an embedded control system. The embedded control system includes analog-to-digital converters, data registers, program registers and microcontrollers. The encoding angle detector and torque detector are set on the output end of the harmonic reducer. The encoding angle detector is used to collect the angle obtained by the harmonic reducer at each moment. According to the input rotation angle set by the harmonic reducer, calculate The actual torsion angle is obtained, and the torque detector is used to collect the actual torque of the harmonic reducer in the flexible joint at each moment. The outputs of the encoded angle detector and torque detector are fed into the microcontroller via analog-to-digital converters. Data registers and program registers are connected on the microcontroller.

The present invention improves the memristor model into a memristor hysteresis model, which is used to describe the basic changing law of the hysteresis output of the harmonic reducer; it uses the RBF neural network with nonlinear fitting capabilities to compare the harmonic reducer hysteresis model and memristor hysteresis. Differences between models are compensated. The output of the RBF neural network and the memristive hysteresis model are superimposed to form a hybrid hysteresis model of the harmonic reducer. By modeling the hysteresis characteristics of the harmonic reducer, the torsion angle output under different torques is predicted and transmitted from the driving end of the harmonic reducer. Error compensation. It is completely different from the method of solving the transmission error of harmonic reducer from a manufacturing perspective. It avoids the complex structure of harmonic reducer and the complexity of forward and reverse transmission of periodic engagement, disengagement and re-engagement between flexspline and rigid spline. The operating mechanism improves the conversion accuracy of the harmonic reducer from the perspective of information modeling and compensation.

It should be noted that although the above embodiments of the present invention are illustrative, they are not limitations of the present invention, and therefore the present invention is not limited to the above specific embodiments. Without departing from the principle of the present invention, any other implementations obtained by those skilled in the art under the inspiration of the present invention will be deemed to be within the protection of the present invention.

Claims (4)

1. The error compensation control method of harmonic reducer using a mixture of memristive model and neural network is characterized by including the following steps: Step 1. Collect the output shaft torque u(k) and output torsion angle θ _d (k) of the harmonic reducer at the M historical moments closest to the current time to be compensated k′; Step 2. Construct a hybrid hysteresis model in which the memristive hysteresis model is connected in parallel with the neural network, and use the output shaft torque u(k) of the harmonic reducer of the M historical moments closest to the current time to be compensated k′ collected in step 1. and the output torsion angle θ _d (k) to train the hybrid hysteresis model to obtain the hybrid hysteresis model at the current time to be compensated k′; during the training process of the hybrid hysteresis model: Step 2.1. Send the output shaft torque u(k) of the harmonic reducer at M historical moments into the memristive hysteresis model, and obtain the output torsion angle θ ₀ (k) of the memristive hysteresis model at M historical moments. ; Step 2.2. Combine the output shaft torque u(k) of the harmonic reducer at M historical moments, the output torsion angle θ ₀ (k) of the memristive hysteresis model, and the output torsion angle θ(k-1) of the RBF dynamic neural network. ) as the input of the RBF dynamic neural network, and the deviation value θ _e (k) of the output torsion angle θ _d (k) of the harmonic reducer at M historical moments and the output torsion angle θ ₀ (k) of the memristive hysteresis model ) as the error of the RBF dynamic neural network, the output torsion angle θ(k) of the RBF dynamic neural network at M historical moments is obtained; Step 2.3. Add the output torsion angle θ ₀ (k) of the memristive hysteresis model at M historical moments and the output torsion angle θ (k) of the RBF dynamic neural network to obtain the unit torsion angle compensation amount at M historical moments. Step 3. Send the output shaft torque u(k′) and output torsion angle θ _d (k′) of the harmonic reducer at the current time k′ to be compensated to the current time k′ to be compensated obtained in step 2. In the mixed hysteresis model, the unit torsion angle compensation amount at the current time to be compensated k′ is obtained. Step 4. Calculate the unit torsion angle compensation amount of the current time k′ obtained in step 3 to After multiplied by the reduction ratio N of the harmonic reducer, the input end torsion angle compensation amount of the harmonic reducer at the current time k' to be compensated is obtained/> Then the input end torsion angle compensation amount of the harmonic reducer at the current time k′ to be compensated/> Add it to the torsion angle set at the input end of the harmonic reducer at the current time k' to be compensated, to realize the transmission error compensation control of the harmonic reducer; Among them, k=1,2,…,M, k′=M+1,M+2,…, M is the number of set historical moments. 2. The harmonic reducer error compensation control method mixing a memristive model and a neural network according to claim 1, characterized in that in step 2.1, the output torsion angle θ ₀ of the memristive hysteresis model at the kth historical moment (k) is: In the formula, u(k) is the output shaft torque of the harmonic reducer at the kth historical moment, M(z) is the resistance value of the memristor, k=1,2,…,M, M is the setting the number of historical moments. 3. The harmonic reducer error compensation control method mixed with memristive model and neural network according to claim 1, characterized in that in step 2.2, the deviation value θ _e (k) of the kth historical moment is: θ _e (k) = θ _d (k) - θ ₀ (k) In the formula, θ _d (k) is the output torsion angle of the harmonic reducer at the kth historical moment, θ ₀ (k) is the output torsion angle of the memristive hysteresis model at the kth historical moment, k = 1,2 ,...,M, M is the number of set historical moments. 4. The harmonic reducer error compensation control method mixed with memristive model and neural network according to claim 1, characterized in that in step 2.3, the unit torsion angle compensation amount at the kth historical moment for: In the formula, θ ₀ (k) is the output torsion angle of the memristive hysteresis model at the kth historical moment, θ (k) is the output torsion angle of the RBF dynamic neural network at the kth historical moment, k = 1,2, ...,M,M is the number of set historical moments.