Real-time control method of robotic arm based on adaptive error coefficient recursive neural network

Abstract

The invention discloses a real-time control method for a robotic arm based on an adaptive error coefficient recursive neural network, which relates to the technical field of robotic arm control and comprises the following steps: S1, determining the real-time control problem of the robotic arm; S2, constructing a recursive neural network; S3, optimizing the recursive neural network to obtain an adaptive error coefficient recursive neural network; S4, using the adaptive error coefficient recursive neural network to iteratively solve the real-time control problem of the robotic arm to complete the control of the robotic arm.

Description

Technical Field

[0001] The present invention relates to the technical field of robot arm control, and in particular to a real-time control method for a robot arm based on an adaptive error coefficient recursive neural network. Background Art

[0002] When solving the real-time control problem of the robot arm, it is difficult to take into account the lag error of the time-varying problem and the huge and time-consuming process of matrix inversion. Although the traditional recursive neural network based on the gradient algorithm does not use the process of matrix inversion, it has lag errors for time-varying problems and cannot complete the task well. Although the annihilation neural network can complete the task well for time-varying problems, it cannot avoid the huge and time-consuming process of matrix inversion. Summary of the invention

[0003] In order to solve the above problems, the present invention proposes a real-time control method for a robotic arm based on an adaptive error coefficient recursive neural network.

[0004] The technical solution of the present invention is: a real-time control method of a mechanical arm based on an adaptive error coefficient recursive neural network comprises the following steps:

[0005] S1. Determine the real-time control problem of the robotic arm;

[0006] S2, build a recursive neural network;

[0007] S3, optimizing the recursive neural network to obtain an adaptive error coefficient recursive neural network;

[0008] S4. Use the adaptive error coefficient recursive neural network to iteratively solve the real-time control problem of the robotic arm to complete the control of the robotic arm.

[0009] Furthermore, in S1, the expression of the real-time control problem of the robot arm is:

[0010] ;

[0011] In the formula, represents the speed of the end effector of the robot arm, represents the Jacobian matrix, represents the joint velocity of the robot arm, Indicates time.

[0012] Furthermore, S2 includes the following sub-steps:

[0013] S21, constructing a scalar-based energy function;

[0014] S22. Determine a recursive neural network according to a scalar-based energy function.

[0015] Furthermore, in S21, the scalar-based energy function The expression is:

[0016] ;

[0017] ;

[0018] In the formula, represents the Frobenius norm, represents the error function, Indicates time, represents the speed of the end effector of the robot arm, represents the Jacobian matrix, Indicates the joint velocity of the robot arm.

[0019] Furthermore, in S22, the model expression of the recursive neural network is for:

[0020] ;

[0021] In the formula, represents the parameter that controls the convergence speed of the recurrent neural network, represents the speed of the end effector of the robot arm, represents the Jacobian matrix, represents the joint velocity of the robot arm, Indicates time, Represents matrix transpose.

[0022] Furthermore, in S3, the model expression of the adaptive error coefficient recursive neural network is for:

[0023] ;

[0024] In the formula, represents the parameter that controls the convergence speed of the adaptive error coefficient recurrent neural network, represents the adaptive residual coefficient, represents the activation function, represents the speed of the end effector of the robot arm, represents the Jacobian matrix, represents the joint velocity of the robot arm, Indicates time, Represents matrix transpose.

[0025] Furthermore, the adaptive residual coefficient The calculation formula is:

[0026] ;

[0027] In the formula, represents the matrix transpose, represents the speed of the end effector of the robot arm, represents the Jacobian matrix, represents the joint velocity of the robot arm, Indicates time, represents the derivative of the Jacobian matrix.

[0028] The beneficial effects of the present invention are:

[0029] (1) The present invention brings forward-looking prediction capabilities to the robot control system by utilizing the derivative information of the relevant equations, significantly reduces the lag error of the robot when performing complex actions, ensures the stability and accuracy of the robot movement, and thus improves the operating efficiency and work quality of the robot;

[0030] (2) The present invention is based on the design of the gradient algorithm, which effectively avoids the cumbersome matrix inversion problem involved in the robot arm control algorithm. It not only simplifies the calculation process and reduces the complexity of the algorithm, but also significantly improves the real-time performance of the robot arm control system, allowing the robot arm to respond to instructions more quickly.

[0031] (3) The present invention introduces the concept of activation function, which is similar to the approach of zeroing neural networks, which helps to accelerate the convergence speed of the robot arm control model. In this way, the learning and adaptability of the robot arm is enhanced, the performance of the model is improved, and the stability and reliability of the robot arm in practical applications are further ensured, providing strong support for the application of the robot arm in the fields of precision machining, automated assembly, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a flow chart of the real-time control method of the robot arm based on the adaptive error coefficient recursive neural network;

[0033] Figure 2 The schematic diagram of the trajectory of the adaptive error coefficient recursive neural network controlling the real-time motion of the robot arm in three-dimensional space;

[0034] Figure 3 The comparison diagram between the task trajectory and the calculation trajectory of the adaptive error coefficient recurrent neural network on the horizontal plane;

[0035] Figure 4 Schematic diagram of the error of the adaptive error coefficient recursive neural network in each dimension;

[0036] Figure 5 It is a schematic diagram of the trajectory of the traditional recursive neural network based on the gradient algorithm controlling the real-time motion of the robotic arm in three-dimensional space;

[0037] Figure 6 This is a comparison diagram between the task trajectory and the calculation trajectory of the traditional gradient-based recursive neural network on the horizontal plane;

[0038] Figure 7 Schematic diagram of the error of the traditional recursive neural network based on the gradient algorithm in various dimensions;

[0039] Figure 8 A simulation result diagram for solving the time-varying matrix square root problem;

[0040] Fig. 9 The figure is a comparison between the calculated solution and the theoretical solution of the adaptive error coefficient recursive neural network;

[0041] Fig.10 This is a simulation result diagram of the adaptive error coefficient recursive neural network activated by the activation function in solving the time-varying matrix square root problem;

[0042] Fig.11 Comparison diagram between the calculated solution and the theoretical solution of the adaptive error coefficient recursive neural network after activation with the activation function. DETAILED DESCRIPTION

[0043] The embodiments of the present invention will be further described below in conjunction with the accompanying drawings.

[0044] like Figure 1 As shown, the present invention provides a real-time control method for a mechanical arm based on an adaptive error coefficient recursive neural network, comprising the following steps:

[0045] S1. Determine the real-time control problem of the robotic arm;

[0046] S2, build a recursive neural network;

[0047] S3, optimizing the recursive neural network to obtain an adaptive error coefficient recursive neural network;

[0048] S4. Use the adaptive error coefficient recursive neural network to iteratively solve the real-time control problem of the robotic arm to complete the control of the robotic arm.

[0049] In the embodiment of the present invention, in S1, the expression of the real-time control problem of the robotic arm is:

[0050] ;

[0051] In the formula, represents the speed of the end effector of the robot arm, represents the Jacobian matrix, represents the joint velocity of the robot arm, Indicates time.

[0052] Solving the time-varying matrix square root problem is generally expressed as: ;in, represents the position of the end effector of the robot arm, represents the joint angle of the robot arm, represents a smooth nonlinear function with unknown mapping, describing the relationship between the end effector position and the joint angle of the robot. The inherent nonlinearity and complexity of the joint velocity and end effector speed The mapping relationship is expressed by introducing the Jacobian matrix. .

[0053] In this embodiment of the present invention, S2 includes the following sub-steps:

[0054] S21, constructing a scalar-based energy function;

[0055] S22. Determine a recursive neural network according to a scalar-based energy function.

[0056] In the embodiment of the present invention, in S21, the scalar-based energy function The expression is:

[0057] ;

[0058] ;

[0059] In the formula, represents the Frobenius norm, represents the error function, Indicates time, represents the speed of the end effector of the robot arm, represents the Jacobian matrix, Indicates the joint velocity of the robot arm.

[0060] In the embodiment of the present invention, in S22, the model expression of the recursive neural network is for:

[0061] ;

[0062] In the formula, represents the parameter that controls the convergence speed of the recurrent neural network, represents the speed of the end effector of the robot arm, represents the Jacobian matrix, represents the joint velocity of the robot arm, Indicates time, Represents matrix transpose.

[0063] In the embodiment of the present invention, in S3, the model expression of the adaptive error coefficient recursive neural network is for:

[0064] ;

[0065] In the formula, represents the parameter that controls the convergence speed of the adaptive error coefficient recurrent neural network, represents the adaptive residual coefficient, represents the activation function, represents the speed of the end effector of the robot arm, represents the Jacobian matrix, represents the joint velocity of the robot arm, Indicates time, Represents matrix transpose.

[0066] In the embodiment of the present invention, the adaptive residual coefficient The calculation formula is:

[0067] ;

[0068] In the formula, represents the matrix transpose, represents the speed of the end effector of the robot arm, represents the Jacobian matrix, represents the joint velocity of the robot arm, Indicates time, represents the derivative of the Jacobian matrix.

[0069] In an embodiment of the present invention, Figure 2 , Figure 3 and Figure 4 Displays simulation results generated by the adaptive error coefficient recursive neural network, Figure 5 , Figure 6 and Figure 7 Displays simulation results produced by a traditional gradient-based recurrent neural network model. Figure 2 and Figure 5 These two models control the real-time motion trajectory of the robotic arm in three-dimensional space. It can be clearly seen that the adaptive error coefficient recursive neural network can well draw the expected four-leaf clover trajectory, while the traditional recursive neural network model based on the gradient algorithm cannot successfully track the task trajectory because of the lag error when facing time-varying problems. Figure 3 and Figure 6 This is a comparison between the task trajectory and the calculated trajectory of the two models on the horizontal plane. It is also a good example of how the adaptive error coefficient recurrent neural network tracks the task trajectory more accurately than the latter. Figure 4 and Figure 7It shows the error of the two models in each dimension. It is intuitive to find that the error level of the AECRNN model is 10 -5 This example shows that the adaptive error coefficient recursive neural network can effectively solve the real-time control problem of the robot arm, and its practical application in industrial environments further confirms its efficiency and superior performance.

[0070] In an embodiment of the present invention, solving the time-varying matrix square root problem is generally expressed as: , ;in, represents a smooth and positive definite time-varying matrix, Represents the solution to the equation that needs to be solved.

[0071] The application of adaptive error coefficient recursive neural network based on gradient algorithm to this problem can be expressed as: ,in, To control the model convergence speed.

[0072] The examples are as follows: , Given the model parameters , .

[0073] Secondly, according to the given instance data, the adaptive error coefficient recursive neural network is incorporated to solve: Finally, the iterative model is calculated using a differential equation solver to output the residual of the system.

[0074] Figure 8 The simulation results of solving the time-varying matrix square root problem using the adaptive error coefficient recursive neural network (blue dashed line) and the gradient algorithm-based recursive neural network model (red solid line) are shown. Through analysis, it can be seen that the system residual of the gradient algorithm-based recursive neural network model cannot converge to zero and always maintains a distance from the zero value. The adaptive error coefficient recursive neural network can converge to zero very well, which means that the model breaks the limitation that the traditional gradient algorithm cannot solve time-varying problems in real time. Fig. 9 The comparison between the calculated solution and the theoretical solution using the adaptive error coefficient recursive neural network is shown. It can be seen that the adaptive error coefficient recursive neural network can quickly converge to the theoretical solution in a short time under four different initial states. Fig.10 The simulation results of the adaptive error coefficient recursive neural network activated by the activation function in solving the time-varying matrix square root problem are shown. Figure 8 It is obvious that the adaptive error coefficient recursive neural network activated by the activation function converges faster than that without the activation function. Fig.11The comparison between the calculated solution and the theoretical solution of the adaptive error coefficient recursive neural network after activation by the activation function is shown. It can be seen that the adaptive error coefficient recursive neural network after activation by the activation function can converge to the theoretical solution quickly in a shorter time under four different initial states.

[0075] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A real-time control method for a robotic arm based on an adaptive error coefficient recursive neural network, characterized in that: The following steps are involved: S1. Determine the real-time control problem of the robotic arm; S2, build a recursive neural network; S3, optimizing the recursive neural network to obtain an adaptive error coefficient recursive neural network; S4, using the adaptive error coefficient recursive neural network to iteratively solve the real-time control problem of the robotic arm to complete the control of the robotic arm; The S2 comprises the following sub-steps: S21, constructing a scalar-based energy function; S22, determining a recursive neural network according to a scalar-based energy function; In S21, the scalar energy function The expression is: ； ； In the formula, represents the Frobenius norm, represents the error function, Indicates time, represents the speed of the end effector of the robot arm, represents the Jacobian matrix, Indicates the joint velocity of the robot arm; In S22, the model expression of the recursive neural network is for: ； In the formula, represents the parameter that controls the convergence speed of the recurrent neural network, represents the speed of the end effector of the robot arm, represents the Jacobian matrix, represents the joint velocity of the robot arm, Indicates time, Represents matrix transpose.

2. The method for real-time control of a manipulator based on an adaptive error coefficient recursive neural network according to claim 1, characterized in that: In S1, the expression of the real-time control problem of the robot arm is: ； In the formula, represents the speed of the end effector of the robot arm, represents the Jacobian matrix, represents the joint velocity of the robot arm, Indicates time.

3. The real-time control method of a mechanical arm based on an adaptive error coefficient recursive neural network according to claim 1 is characterized in that: In S3, the model expression of the adaptive error coefficient recursive neural network is for: ； In the formula, represents the parameter that controls the convergence speed of the adaptive error coefficient recurrent neural network, represents the adaptive residual coefficient, represents the activation function, represents the speed of the end effector of the robot arm, represents the Jacobian matrix, represents the joint velocity of the robot arm, Indicates time, Represents matrix transpose.

4. The method for real-time control of a manipulator based on an adaptive error coefficient recursive neural network according to claim 3 is characterized in that: The adaptive residual coefficient The calculation formula is: ； In the formula, represents the matrix transpose, represents the speed of the end effector of the robot arm, represents the Jacobian matrix, represents the joint velocity of the robot arm, Indicates time, represents the derivative of the Jacobian matrix.

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