CN115319755A - Feedback correction-based flexible joint compensation control method for GRU neural network robot - Google Patents

Feedback correction-based flexible joint compensation control method for GRU neural network robot Download PDF

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CN115319755A
CN115319755A CN202211137827.8A CN202211137827A CN115319755A CN 115319755 A CN115319755 A CN 115319755A CN 202211137827 A CN202211137827 A CN 202211137827A CN 115319755 A CN115319755 A CN 115319755A
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neural network
gru neural
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flexible joint
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党选举
张一晨
原翰玫
李晓
伍锡如
张向文
张斌
季运佳
邹水中
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Guilin University of Electronic Technology
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Guilin University of Electronic Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop

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Abstract

The invention discloses a feedback correction-based GRU neural network robot flexible joint compensation control method, which is characterized in that under the condition of a load torque sensor, the hysteresis characteristic of a joint under different loads is described by reflecting the characteristic between motor driving current and joint torsion angle of load change, a feedback structure is introduced on the basis of a GRU neural network, and a compensation quantity is formed by utilizing the error between a model output value and an expected output value and is fed back to a GRU neural network model for correcting the output value of the GRU neural network model so as to improve the GRU neural network model precision of the joint. The flexible joint hysteresis model predicts a torsion angle changing along with the load, and is used as a compensation quantity to modify an angle set value of a joint, so that the effective compensation of errors caused by the joint hysteresis characteristic is indirectly realized from the joint input end. The invention is a low-cost compensation control method, which is beneficial to the mass popularization in the high-end intelligent manufacturing of low-cost high-precision light industrial robots.

Description

Feedback correction-based flexible joint compensation control method for GRU neural network robot
Technical Field
The invention relates to the technical field of robot control, in particular to a feedback correction-based GRU (Gated Recurrent Unit) neural network robot flexible joint compensation control method.
Background
The light industrial robot is applied more and more widely in the fields of 3C, welding, medical treatment, part assembly, unmanned retail and the like by virtue of the advantages of safety, easiness in use, flexibility and the like. The structural design of the joints and the arm rods of the light industrial robot generally enables the robot to obtain the load ratio as high as possible under the light weight, and the flexibility is brought while the requirements for miniaturization and refinement are met. The flexibility of the joints and the arm rods causes the stability of the robot to be reduced in the motion process, wherein the flexible joints play a decisive role in the dynamic performance, the positioning precision and the motion stability of the robot. However, due to the existence of elastic deformation, nonlinear friction, backlash, assembly error and other factors, the input and output of the flexible joint show complex hysteresis characteristics, and the dynamic performance and the control accuracy of the robot are seriously influenced.
With the development of artificial intelligence technology, modeling methods based on data driving are widely applied to various fields, wherein machine learning methods become mainstream data driving methods by virtue of strong nonlinear fitting capability and are applied to the field of hysteresis modeling. The multi-value corresponding relation expressed by the hysteresis characteristic makes the traditional feedforward neural network useless, and the common method is to map the input-output relation into a single-value corresponding problem by expanding an input space and then use the neural network for fitting. However, since the flexible joint of the light industrial robot presents a complex hysteresis characteristic with strong nonlinearity and asymmetry, the existing hysteresis model has difficulty in accurately describing the characteristic hysteresis characteristic. In addition, the low-cost joint actuator without a load torque sensor also brings difficulties in modeling and compensating the hysteresis characteristic.
Disclosure of Invention
The invention provides a feedback correction-based compensation control method for a flexible joint of a GRU neural network robot, aiming at the problem that the existing hysteresis modeling method cannot accurately describe the special complex hysteresis characteristic of the joint under the condition of no load torque sensor.
In order to solve the problems, the invention is realized by the following technical scheme:
the GRU neural network robot flexible joint compensation control method based on feedback correction comprises the following steps:
step 1, inputting current i to a flexible joint of a robot at a time t <t> Kalman Filter Kalman (i) <t> ) Then the first input signal of the input layer of the improved GRU neural network at the time t is used; simultaneously outputs signals delta theta of the improved GRU neural network at t-1 <t-1> A second input signal at time t as an input layer of the modified GRU neural network;
step 2, firstly setting the angle of the flexible joint of the robot at the moment t-1
Figure BDA0003852119290000011
Angle measurement value of flexible joint of robot at t-1 moment
Figure BDA0003852119290000012
Making a difference to obtain a torsion angle delta theta of the flexible joint of the robot at the time t-1 d <t-1> Where Δ θ d <t-1> ＝θ d <t-1> -θ c <t-1> (ii) a Then the torsion angle delta theta of the flexible joint of the robot at the moment t-1 d <t-1> Output signal delta theta at time t-1 with improved GRU neural network <t-1> Taking difference to obtain a modeling error e of the torsion angle at the moment t-1 <t-1> Wherein e is <t-1> ＝Δθ d <t-1> -Δθ <t-1> (ii) a Modeling error e of torsion angle at time t-1 <t-1> As an output compensation signal of the improved GRU neural network at the time t;
and 3, based on the first input signal, the second input signal and the output compensation signal of the input layer of the improved GRU neural network at the time t, the hidden layer of the improved GRU neural network correlates the input current (the first input signal) with the historical information of the output torsion angle (the second input signal), and corrects the output of the improved GRU neural network through modeling error (the output compensation signal) to obtain the output signal delta theta of the output layer of the improved GRU neural network at the time t <t> To improve the joint modeling accuracy of the improved GRU neural network;
step 4, utilizing the output signal delta theta of the output layer of the improved GRU neural network at the time t <t> Setting the angle of the flexible joint of the robot at the moment t
Figure BDA0003852119290000021
Compensating to obtain the angle set value of the flexible joint of the robot after compensation at the moment t
Figure BDA0003852119290000022
Wherein
Figure BDA0003852119290000023
And the angle set value of the flexible joint of the robot after compensation at the moment t
Figure BDA0003852119290000024
The control end of the flexible joint of the robot is provided, and the purpose of improving the execution precision of the joint angle is achieved.
The mathematical model of the improved GRU neural network is as follows:
Figure BDA0003852119290000025
wherein, delta theta <t> Representing an improved GRU godOutput signal at time t, delta theta, via network y <t> Representing the intermediate output signal of the modified GRU neural network at time t, beta representing a compensation factor, e <t-1> Representing the output compensation signal at time t representing the modified GRU neural network,
Figure BDA0003852119290000026
indicating the updated gate state of the improved GRU neural network at time t,
Figure BDA0003852119290000027
indicating the reset gate state of the improved GRU neural network at time t,
Figure BDA0003852119290000028
represents the hidden state of the improved GRU neural network at the time t,
Figure BDA0003852119290000029
representing the first input signal of the modified GRU neural network at time t,
Figure BDA00038521192900000210
Figure BDA00038521192900000211
a second input signal representing the modified GRU neural network at time t,
Figure BDA00038521192900000212
Figure BDA00038521192900000213
representing the intermediate output signal, W, of the modified GRU neural network at time t-1 z1 、W r1 And W 1 Respectively representing the sum of the first input signals in the refresh gate, the reset gate and the hidden state
Figure BDA00038521192900000214
Corresponding weight, W z2 、W r2 And W 2 Respectively representing the AND of the refresh gate, reset gate and hidden stateSecond input signal
Figure BDA00038521192900000215
Corresponding weight, U z 、U r And U represents the output signals of the refresh gate, the reset gate and the hidden state and the middle output signal respectively
Figure BDA00038521192900000216
The corresponding weight value;
Figure BDA00038521192900000217
and b y Bias vectors representing an update gate, a reset gate, and a hidden state, respectively; σ (-) denotes a sigmoid activation function; tanh (·) represents a hyperbolic tangent activation function; an h indicates a Hadamard product.
Compared with the prior art, the invention describes the hysteresis characteristic of the joint under different loads by reflecting the characteristic between the motor driving current and the joint torsion angle of the load change under the condition of a load torque sensor, and provides a feedback correction-based GRU neural network flexible joint hysteresis model. The flexible joint hysteresis model predicts a torsion angle changing along with the load, and is used as a compensation quantity to modify an angle set value of a joint, so that the effective compensation of errors caused by the joint hysteresis characteristic is indirectly realized from the joint input end. The invention is a low-cost compensation control method, which is beneficial to the mass popularization in the high-end intelligent manufacturing of low-cost high-precision light industrial robots.
Drawings
Fig. 1 is a hysteresis curve between current and torsion angle.
Fig. 2 is a diagram of a GRU unit structure.
Fig. 3 is a diagram of a GRU neural network structure.
FIG. 4 is a block diagram of a GRU neural network hysteresis model based on feedback correction.
Fig. 5 is a schematic diagram of a feedback correction-based GRU neural network robot flexible joint compensation control method.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to specific examples.
In order to model the hysteresis characteristic between the motor driving current reflecting the load change and the joint torsion angle under the condition of no load torque sensor and describe the complex hysteresis characteristic presented by the joint along with the load change, the invention provides a feedback correction based flexible joint hysteresis modeling method of a GRU (Gated Current Unit) neural network.
The driving current of the motor reflects the change of the load, the output torque of the motor is indirectly determined, and the hysteresis characteristic between the driving current of the motor and the output torsion angle is described by establishing a model under the condition of no load torque sensor, so that the hysteresis modeling and compensation with low cost can be realized. The current is obtained by a joint internal current sensor, and the definition of the torsion angle is as follows:
Δθ＝θ d -θ c (1)
wherein, theta d To theoretically output the angle (i.e., the angle set value), θ c For the actual output angle (i.e., the angle measurement), Δ θ is a twist angle that is a deviation of the theoretical output angle from the actual output angle.
Fig. 1 is a hysteresis characteristic curve between joint motor driving current and joint torsion angle obtained through experiments, and reveals that the curve shows severe non-linearity and multi-valued correspondence due to fluctuation of input current, so that the modeling difficulty of the joint is increased. As can be seen from FIG. 1, the hysteresis characteristic is comprehensively expressed in the joint actuator that the output at the current moment is not only related to the input data at the current moment, but also related to the historical input data of the system, which accords with the description of the time series problem, so the invention constructs the hysteresis model on the basis of the GRU neural network with long-term memory capability.
The gated cyclic unit (GRU) as a variant of the conventional RNN (recurrent neural network) solves the problem of weak RNN long-term memory, and compared with the long-term memory network (LSTM), both can effectively learn the internal association in the long-term sequence, but the GRU has fewer gate structures, fewer parameters to learn and relatively faster learning speed. Research has shown that GRUs perform better than LSTM in some cases with small amounts of data. The structure of the GRU unit is shown in FIG. 2, and the mathematical model is as follows:
Figure BDA0003852119290000041
wherein the content of the first and second substances,
Figure BDA0003852119290000042
indicating the updated gate state of the jth GRU cell at time t,
Figure BDA0003852119290000043
indicating the reset gate state of the jth GRU cell at time t,
Figure BDA0003852119290000044
indicating the hidden state of the jth GRU unit at time t,
Figure BDA0003852119290000045
and
Figure BDA0003852119290000046
respectively representing the output signal of the jth GRU unit at time t and a time t-1 before time t, x <t> An input signal representing time t; w z 、W r W represents AND x in the update gate, reset gate and hidden state, respectively <t> The corresponding weight value; u shape z 、U r U represents the AND of the refresh gate, reset gate and hidden state, respectively
Figure BDA0003852119290000047
The corresponding weight value;
Figure BDA0003852119290000048
b j bias vectors representing an update gate, a reset gate, and a hidden state, respectively; σ (-) denotes a sigmoid activation function; tanh (·) represents a hyperbolic tangent activation function; as indicates Hadamard product, which means multiplication of elements of corresponding positions.
Updating door
Figure BDA0003852119290000049
Determining the output quantity of GRU unit at the current time t
Figure BDA00038521192900000410
Resetting the gate to the extent that history information needs to be forgotten and new information needs to be added
Figure BDA00038521192900000411
Determining hidden states
Figure BDA00038521192900000412
Degree of forgetting the history information. The two gate structures have the functions of selecting and storing historical information, and the two gate structures jointly determine the processing capacity of the GRU unit for time series data.
The output of the hysteresis characteristic is not only related to the input signal at the current time, but is also affected by the historical input signal. Aiming at the problem of dependence of lag modeling on historical data, the GRU neural network can effectively learn the potential relevance of the input time sequence. A single GRU unit can capture relevant information of different time scales in a self-adaptive mode, and a plurality of GRU units are connected in parallel to be used as a part of a hidden layer of the neural network, so that the learning capacity of the neural network under strong interference can be further enhanced. The GRU neural network uses a plurality of GRU units connected in parallel as a hidden layer of the GRU neural network, as shown in fig. 3. X for input layer of GRU neural network <t> Representing the input time series. Each circulation unit in the hidden layer of the GRU neural network represents a GRU unit, and the gate represents the number of the GRU unitsAfter many experiments, the network can obtain good results when n is 20. GRU neural network output layer y <t> ＝W y h <t> ，W y In order to output the weight vector of the layer,
Figure BDA0003852119290000051
where T is the transpose operation. the loss function at time t is as follows:
Figure BDA0003852119290000052
wherein, y <t> The output value of the GRU neural network at the time t;
Figure BDA0003852119290000053
is the target value at time t; the total loss function is
Figure BDA0003852119290000054
The GRU neural network trains the weights of each layer using a time-backpropagation method (BPTT).
In order to further improve the modeling precision of the GRU neural network on the complex hysteresis curve, the invention introduces a feedback structure into the hysteresis model by means of the thought of feedback error elimination, and adds a compensation quantity consisting of the prediction error of the model on the basis of the general GRU neural network. Because the neural network has certain deviation between the predicted value of the torsion angle and the actual output torsion angle of the joint, the error of the model is obtained by comparing the measured value of the torsion angle of the joint with the output value of the model, and the predicted value of the model at the next moment is corrected by using the error of the model. By the error compensation quantity, the error of the model is reduced or even eliminated, and the aim of improving the modeling precision is fulfilled. A GRU neural network hysteresis model based on feedback correction is shown in fig. 4.
Since the prediction error at the initial stage of the neural network training is large, and the amplitude of the compensation amount is limited by using the tanh hyperbolic tangent function, the GRU neural network output layer formula (4) based on the feedback correction is as follows:
Δθ <t> ＝Δθ y <t> +βtanh(e <t-1> ) (4)
Δθ y <t> ＝W y h (5)
e <t-1> ＝Δθ d <t-1 >-Δθ <t-1> (6)
Δθ d <t-1> ＝θ d <t-1> -θ c <t-1> (7)
wherein, delta theta y <t> Represents the intermediate output signal of the improved GRU neural network at the time t, as shown in formula (5); e.g. of the type <t-1> For the modeling error of the torsion angle at the previous moment, as in equation (6), from the measured value Δ θ of the torsion angle at the previous moment d <t-1> Torsion angle delta theta with neural network output <t-1> Subtracting to obtain; delta theta d <t-1> The measured value of the joint torsion angle at the previous moment is represented by a formula (7), and the angle theta is output by the joint theory d <t-1> Angle theta with actual output c <t-1> And subtracting to obtain the result. Modeling error e of torsion angle at previous moment <t-1> After amplitude limiting of the tanh function and multiplication of the tanh function by a compensation coefficient beta, compensation quantity of feedback correction of an output layer of the GRU neural network is formed, and the beta is obtained by self-learning of the neural network and self-adaptive adjustment is carried out on the compensation quantity.
The modeling process of the joint hysteresis characteristic is as follows:
(1) Equation (8) input current data i suppression using Kalman filtering <t> White gaussian noise;
(2) Using the filtered current signal as an input signal of a GRU neural network
Figure BDA0003852119290000055
The signal input by the neural network also has the output delta theta of the previous time model <t-1> I.e. by
Figure BDA0003852119290000056
(3) Through calculation of a GRU neural network, a feedback structure is added behind an output layer, and a model error e of the previous moment is calculated <t-1> Feeding the feedback into an output layer to be used as compensation, and obtaining the output delta theta of the neural network <t> ；
(4) Will delta theta <t> And introducing a neural network input layer to perform circulation at the next moment. The output value delta theta of the neural network at the t-1 moment <t- 1 > As the input of the neural network at the time t, the dimensionality of input information is increased, the input current signal is correlated with the historical information of the output torsion angle, and the model prediction precision is improved.
x <t> ＝Kalman(i <t> ) (8)
Δθ <t> ＝GRU_g(x <t> ，Δθ <t-1> ，c <t-1> ) (9)
Wherein Kalman (·) denotes a linear Kalman filter, and GRU _ g (·) denotes equations (2) and (4).
The design principle of the low-cost joint actuator enables the actuator to be free of a load torque sensor, an encoder is only arranged at the motor end, and the encoder is not arranged at the output end of the speed reducer. The motor driving current can effectively reflect the change of the load, and becomes important data of low-cost hysteresis compensation under the condition of no-load torque sensor. Aiming at the problem that the torsion angle cannot be obtained due to the fact that no encoder is arranged at the output end of the speed reducer, a joint model with a feedback structure is established from the angle of integral joint modeling in an experiment. Wherein the content of the first and second substances,
Figure BDA0003852119290000061
is a joint output angle theoretical value (angle set value);
Figure BDA0003852119290000062
is the actual value of the joint output angle (i.e., the angle measurement). The torsion angle being obtained by subtracting the angle measurement from the joint angle setting, i.e.
Figure BDA0003852119290000063
Under the condition of no load torque sensor and no reducer output end encoder, a hysteresis model of current and torsion angle is constructed through limited data acquired by a joint current sensor and a motor end encoder, the hysteresis phenomenon caused by the current change to the difference between the actual output angle and the target output angle of the joint can be effectively described under the condition of a low-cost joint actuator, and the cost of hysteresis modeling and compensation is reduced. The error compensation of the set value of the joint angle is as follows:
Figure BDA0003852119290000064
wherein the content of the first and second substances,
Figure BDA0003852119290000065
the compensated joint angle setting is equal to the sum of the joint angle setting and the torsion angle predicted by the model. As the load changes, to
Figure BDA0003852119290000066
Angle after dynamic compensation
Figure BDA0003852119290000067
As a joint angle setting value.
Based on the above analysis, the feedback correction-based GRU neural network robot flexible joint compensation control method provided by the present invention, as shown in fig. 5, includes the following steps:
step 1, inputting current i to a flexible joint of a robot at time t <t> Performing Kalman filtering to obtain a first input signal of an input layer of the improved GRU neural network at a time t; simultaneously outputs signals delta theta of the improved GRU neural network at t-1 moment <t-1> A second input signal at time t as an input layer of the modified GRU neural network;
step 2, firstly, setting the angle of the flexible joint of the robot at the t-1 moment
Figure BDA0003852119290000068
Angle measurement value of flexible joint of robot at t-1 moment
Figure BDA0003852119290000069
Making a difference to obtain a torsion angle delta theta of the flexible joint of the robot at the time t-1 d <t-1> Where Δ θ d <t-1> ＝θ d <t-1> -θ c <t-1> (ii) a Then the torsion angle delta theta of the flexible joint of the robot at the moment t-1 d <t-1> Output signal delta theta at time t-1 with improved GRU neural network <t-1> Taking difference to obtain a modeling error e of the torsion angle at the moment t-1 <t-1> In which e is <t-1> ＝Δθ d <t-1> -Δθ <t-1> (ii) a Modeling error e of torsion angle at the time t-1 <t-1> As an output compensation signal of the improved GRU neural network at the time t;
and 3, based on the first input signal, the second input signal and the output compensation signal of the input layer of the improved GRU neural network at the time t, establishing correlation between the input current and historical information of the output torsion angle by the hidden layer of the improved GRU neural network, and correcting the output of the improved GRU neural network through modeling errors to obtain an output signal delta theta of the output layer of the improved GRU neural network at the time t <t> ；
The mathematical model of the improved GRU neural network is as follows:
Figure BDA0003852119290000071
wherein, delta theta <t> Representing the output signal, Δ θ, of the modified GRU neural network at time t y <t> Represents the intermediate output signal of the improved GRU neural network at time t, beta represents the compensation coefficient, e <t-1> Representing the output compensation signal at time t representing the modified GRU neural network,
Figure BDA0003852119290000072
indicating the updated gate state of the improved GRU neural network at time t,
Figure BDA0003852119290000073
indicating the reset gate state of the improved GRU neural network at time t,
Figure BDA0003852119290000074
represents the hidden state of the improved GRU neural network at the time t,
Figure BDA0003852119290000075
representing the first input signal of the improved GRU neural network at time t,
Figure BDA0003852119290000076
a second input signal representing the modified GRU neural network at time t,
Figure BDA0003852119290000077
representing the intermediate output signal, W, of the modified GRU neural network at time t-1 z1 、W r1 And W 1 Respectively representing the sum of the first input signals in the refresh gate, the reset gate and the hidden state
Figure BDA0003852119290000078
Corresponding weight, W z2 、W r2 And W 2 Representing the second input signal in the refresh gate, reset gate and hidden state, respectively
Figure BDA0003852119290000079
Corresponding weight, U z 、U r And U represents the output signals of the refresh gate, the reset gate and the hidden state and the middle output signal respectively
Figure BDA00038521192900000710
The corresponding weight value;
Figure BDA00038521192900000711
and b y Representing refresh, reset and hidden states, respectivelyA bias vector; σ (-) denotes a sigmoid activation function; tanh (·) represents a hyperbolic tangent activation function; as indicates the Hadamard product.
Step 4, utilizing the output signal delta theta of the output layer of the improved GRU neural network at the time t <t> Angle set value of robot flexible joint at t moment
Figure BDA00038521192900000712
Compensating to obtain the angle set value of the flexible joint of the robot after compensation at the moment t
Figure BDA00038521192900000713
Wherein
Figure BDA00038521192900000714
And the angle set value of the flexible joint of the robot after compensation at the moment t
Figure BDA00038521192900000715
And a control end provided for the flexible joint of the robot.
It should be noted that, although the above-mentioned embodiments of the present invention are illustrative, the present invention is not limited thereto, and thus the present invention is not limited to the above-mentioned embodiments. Other embodiments, which can be made by those skilled in the art in light of the teachings of the present invention, are considered to be within the scope of the present invention without departing from its principles.

Claims (2)

1. The GRU neural network robot flexible joint compensation control method based on feedback correction is characterized by comprising the following steps:
step 1, inputting current i to a flexible joint of a robot at a time t <t> Performing Kalman filtering to obtain a first input signal of an input layer of the improved GRU neural network at a time t; simultaneously outputs signals delta theta of the improved GRU neural network at t-1 <t-1> A second input signal at the time t as an input layer of the improved GRU neural network;
step 2, firstly, the machine is processedAngle set value of human flexible joint at t-1 moment
Figure FDA0003852119280000011
Angle measurement value of flexible joint of robot at t-1 moment
Figure FDA0003852119280000012
Making a difference to obtain a torsion angle delta theta of the flexible joint of the robot at the moment t-1 d <t-1> Wherein Δ θ d <t-1> ＝θ d <t-1> -θ c <t-1> (ii) a Then the torsion angle delta theta of the flexible joint of the robot at the moment t-1 d <t-1> Output signal delta theta at time t-1 with improved GRU neural network <t-1> Taking difference to obtain a modeling error e of the torsion angle at the moment t-1 <t-1> Wherein e is <t-1> ＝Δθ d <t-1> -Δθ <t-1> (ii) a Modeling error e of torsion angle at time t-1 <t-1> As the output compensation signal of the improved GRU neural network at the t moment;
and 3, based on the first input signal, the second input signal and the output compensation signal of the input layer of the improved GRU neural network at the time t, establishing correlation between the input current and historical information of the output torsion angle by the hidden layer of the improved GRU neural network, and correcting the output of the improved GRU neural network through modeling errors to obtain an output signal delta theta of the output layer of the improved GRU neural network at the time t <t> ；
Step 4, utilizing the output signal delta theta of the output layer of the improved GRU neural network at the time t <t> Angle set value of robot flexible joint at t moment
Figure FDA0003852119280000013
Compensating to obtain the angle set value of the flexible joint of the robot after compensation at the moment t
Figure FDA0003852119280000014
Wherein
Figure FDA0003852119280000015
And the angle set value of the flexible joint of the robot after compensation at the moment t
Figure FDA0003852119280000016
And a control end provided for the flexible joint of the robot.
2. The feedback correction-based GRU neural network robot flexible joint compensation control method of claim 1, characterized in that the mathematical model of the improved GRU neural network is as follows:
Figure FDA0003852119280000017
wherein, delta theta <t> Representing the output signal, Δ θ, of the modified GRU neural network at time t y <t> Represents the intermediate output signal of the improved GRU neural network at time t, beta represents the compensation coefficient, e <t-1> Representing the output compensation signal at time t representing the modified GRU neural network,
Figure FDA0003852119280000018
indicating the updated gate state of the improved GRU neural network at time t,
Figure FDA0003852119280000019
indicating the reset gate state of the improved GRU neural network at time t,
Figure FDA00038521192800000110
represents the hidden state of the improved GRU neural network at the time t,
Figure FDA00038521192800000111
first input signal at time t representing an improved GRU neural network，
Figure FDA0003852119280000021
A second input signal representing the modified GRU neural network at time t,
Figure FDA0003852119280000022
representing the intermediate output signal, W, of the modified GRU neural network at time t-1 z1 、W r1 And W 1 Respectively representing the sum of the first input signals in the refresh gate, the reset gate and the hidden state
Figure FDA0003852119280000023
Corresponding weight value, W z2 、W r2 And W 2 Representing the second input signal in the refresh gate, reset gate and hidden state, respectively
Figure FDA0003852119280000024
Corresponding weight, U z 、U r And U represents the output signals of the refresh gate, the reset gate and the hidden state and the middle output signal respectively
Figure FDA0003852119280000025
The corresponding weight value;
Figure FDA0003852119280000026
and b y Bias vectors representing an update gate, a reset gate, and a hidden state, respectively; σ (-) denotes a sigmoid activation function; tanh (·) represents a hyperbolic tangent activation function; as indicates the Hadamard product.
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