Adaptive robust control method for multi-axis manipulators against non-sinusoidal periodic noise

Abstract

The present invention relates to an adaptive robust control method for a multi-axis manipulator for non-sinusoidal periodic noise, comprising the following steps: establishing a unified kinematic equation for the multi-axis manipulator based on the Jacobian matrix of the multi-axis manipulator; introducing a pseudo-inverse scheme to solve the manipulator kinematic equation and obtain differential equations for joint acceleration; designing an auto-disturbance rejection zeroing neural network for non-sinusoidal periodic noise; constructing an adaptive robust control equation for the multi-axis manipulator for non-sinusoidal periodic noise and solving it to obtain a corresponding control result; and driving the multi-axis manipulator to complete a corresponding motion planning task based on the control result. Compared with the prior art, the present invention proposes an adaptive robust control scheme for non-sinusoidal periodic noise based on the Jacobian matrix, adaptive control, and PID methods, enabling the multi-axis manipulator to still accurately complete specific motion planning tasks under the interference of non-sinusoidal periodic noise, effectively improving the robustness and accuracy of the multi-axis manipulator's motion control.

Description

Technical Field

[0001] The present invention relates to the technical field of robot motion control, and in particular to an adaptive robust control method for a multi-axis robot arm against non-sinusoidal periodic noise. Background Art

[0002] Robotic arm motion control is a core topic in the field of robotics. Simply put, when we want the robot's end effector (such as the end gripper of the robot arm) to accurately follow a predetermined path, When moving, it is necessary to calculate the angle configuration that each joint of the robot should reach at time t Once these joint angles are determined, the robotic arm can be controlled by motors so that its end effector can move along the desired path, completing the path tracking task.

[0003] Given the widespread application of multi-axis robotic arms in industrial automation, medical surgery, space exploration, and other fields, their kinematic control has always attracted much attention. Among the many control strategies, two methods are particularly common: one is based on the inverse or pseudo-inverse of the Jacobian matrix for control, and the other is based on quadratic programming (QP) methods. Considering the widespread application of multi-axis robotic arms in various fields and their huge future development potential, when designing motion control methods, special consideration must be given to their noise immunity. This is because in practical applications, robots often face various complex and noisy environments, which may affect the effectiveness and accuracy of kinematic control. Therefore, noise immunity has become a key factor in developing reliable and robust kinematic control methods.

[0004] In engineering practice, especially in scenarios such as robotics and power line transmission, a special noise problem is often encountered: non-sinusoidal periodic noise. Suppressing this type of noise has always been a critical issue that needs to be addressed. This type of noise is not only complex and affects system performance, but may also pose a threat to the stable operation of the equipment. To address this issue, existing research uses Fourier series analysis to decompose non-sinusoidal periodic noise into a DC component and the superposition of multiple harmonic components, thereby providing a theoretical basis and solution for subsequent noise suppression. However, most existing methods only target certain specific types of noise, such as constant noise and ramp noise, and cannot effectively eliminate more general noise. For robotic arms, non-sinusoidal periodic noise is also a problem that cannot be ignored, but there is currently no control method that can effectively suppress non-sinusoidal periodic noise, resulting in poor anti-interference performance of robotic arm motion control, making it difficult to complete the corresponding movements efficiently and accurately. Summary of the Invention

[0005] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a multi-axis robot arm adaptive robust control method for non-sinusoidal periodic noise, which can improve the robustness and accuracy of multi-axis robot arm motion control under noise interference.

[0006] The object of the present invention can be achieved by the following technical solution: A multi-axis manipulator adaptive robust control method for non-sinusoidal periodic noise comprises the following steps:

[0007] S1. Based on the Jacobian matrix of the multi-axis manipulator, a unified kinematic equation of the multi-axis manipulator is established;

[0008] S2. Introduce a pseudo-inverse scheme to solve the kinematic equations of the manipulator and obtain the differential equations for the joint accelerations;

[0009] S3. Design an auto-disturbance rejection zeroing neural network for non-sinusoidal periodic noise;

[0010] S4. For non-sinusoidal periodic noise, construct the adaptive robust control equation of the multi-axis manipulator and solve it to obtain the corresponding control results;

[0011] S5. According to the control results, drive the multi-axis robotic arm to complete the corresponding motion planning task.

[0012] Furthermore, the unified kinematic equation of the multi-axis manipulator in step S1 is an acceleration layer motion control equation based on a differential equation, specifically:

[0013]

[0014] Where θ(t) is the joint angle, is the joint acceleration vector, is the derivative of the Jacobian matrix J(t) with respect to time t, and They are q d The first and second time derivatives of (t), represents the feedback gain, and ψ(t) represents a differentiable nonlinear mapping.

[0015] Furthermore, the step S2 uses pseudo-inverse to obtain the solution of the multi-axis manipulator joint acceleration:

[0016]

[0017] Among them, J T (t) is the transpose of J(t).

[0018] Furthermore, the step S3 specifically includes the following steps:

[0019] S31. Establish a mathematical model of non-sinusoidal periodic noise and obtain a mathematical expression for each noise component;

[0020] S32. Based on the mathematical model of non-sinusoidal periodic noise, a unified model of a return-to-zero neural network contaminated by noise is established;

[0021] S33. Based on the unified model of zeroing neural network, an auto-disturbance rejection zeroing neural network model is established by introducing adaptive terms.

[0022] Furthermore, the mathematical model of the non-sinusoidal periodic noise in step S31 is specifically:

[0023]

[0024] Among them, A k 、f k and Represent the amplitude, frequency and phase of periodic noise respectively, ω k represents the angular frequency, assuming A k and is an unknown parameter, f k are known parameters, assuming is non-sinusoidal periodic noise, n ij (t) is an element of N(t), which is decomposed into a Fourier series, including the DC component, the fundamental component and the kth harmonic component;

[0025] When k = 1, it indicates that the non-sinusoidal periodic noise contains only DC components and fundamental components. The corresponding mathematical model is:

[0026]

[0027] Among them, A0 is the DC component and A1 is the fundamental component.

[0028] Furthermore, the zeroing neural network unified model in step S32 is specifically:

[0029]

[0030] Among them, E(t) is a compact matrix,

[0031] Furthermore, in step S33, if the non-sinusoidal periodic noise only contains a DC component and a fundamental component, the corresponding ADRC-Zero neural network model is specifically:

[0032]

[0033] Among them, Θ(t) and Ψ(t) are adaptive terms.

[0034] Furthermore, in step S33, if the non-sinusoidal periodic noise includes a DC component and multiple harmonic components, the corresponding ADRC-Zero neural network model is obtained according to the superposition principle as follows:

[0035]

[0036] Among them, Θ(t) and Ψ(t) are adaptive terms.

[0037] Furthermore, in step S4, if the non-sinusoidal periodic noise only contains a DC component and a fundamental wave component, the corresponding multi-axis robotic arm adaptive robust control equation is:

[0038]

[0039] Where I is the identity matrix.

[0040] Furthermore, in step S4, if the non-sinusoidal periodic noise contains a DC component and multiple harmonic components, the corresponding multi-axis robotic arm adaptive robust control equation is:

[0041]

[0042] Where I is the identity matrix.

[0043] Compared with the prior art, the present invention has the following advantages:

[0044] This paper establishes the kinematic equations of the acceleration layer of a multi-axis manipulator based on its Jacobian matrix, and introduces a pseudo-inverse scheme to solve the manipulator's motion equations. Furthermore, considering the possible presence of non-sinusoidal periodic noise interference, an anti-disturbance zeroing neural network is constructed. Furthermore, an adaptive robust control equation for the multi-axis manipulator is constructed, and the corresponding control results are solved to drive the multi-axis manipulator to complete the corresponding motion planning task. This method ensures that the multi-axis manipulator can accurately execute specific planning tasks even in the presence of noise interference, effectively improving the manipulator's motion planning accuracy in practical applications.

[0045] The present invention incorporates an adaptive law into a traditional zeroing neural network, enabling simultaneous calculation of relevant control parameters while eliminating errors. This differs from conventional methods, which eliminate errors first and then perform calculations. The method provided by the present invention enables simultaneous adaptive error elimination and calculations using a parallel approach, saving time. This significantly improves computational efficiency when dealing with large amounts of data.

[0046] The present invention takes into account different situations of non-sinusoidal periodic noise. For the situation containing only DC components and fundamental components, and for the situation containing DC components and multiple harmonic components, the robot arm motion control method in a noisy environment is designed respectively. It can effectively suppress non-sinusoidal periodic noise, so that the multi-axis robot arm can still accurately complete specific motion planning tasks under the interference of non-sinusoidal periodic noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 Schematic diagram of the method flow of the present invention;

[0048] Figure 2 Schematic diagram of the application process of the embodiment;

[0049] Figure 3 4 is a block diagram of an auto-disturbance rejection zeroing neural network in an embodiment;

[0050] Figure 4 This is a diagram of the adaptive robust control framework of a multi-axis robotic arm in an embodiment;

[0051] Figure 5 Schematic diagram of the motion trajectory of the self-disturbance rejection four-link robotic arm in the embodiment;

[0052] Figure 6 Schematic diagram of the end motion trajectory of the self-disturbance rejection four-link robotic arm in the embodiment;

[0053] Figure 7 Schematic diagram of the end position error of the self-disturbance rejection four-link robotic arm in the embodiment. DETAILED DESCRIPTION

[0054] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0055] Example

[0056] like Figure 1 As shown, a multi-axis manipulator adaptive robust control method for non-sinusoidal periodic noise includes the following steps:

[0057] S1. Based on the Jacobian matrix of the multi-axis manipulator, a unified kinematic equation of the multi-axis manipulator is established;

[0058] S2. Introduce a pseudo-inverse scheme to solve the kinematic equations of the manipulator and obtain the differential equations for the joint accelerations;

[0059] S3. Design an auto-disturbance rejection zeroing neural network for non-sinusoidal periodic noise;

[0060] S4. For non-sinusoidal periodic noise, construct the adaptive robust control equation of the multi-axis manipulator and solve it to obtain the corresponding control results;

[0061] S5. According to the control results, drive the multi-axis robotic arm to complete the corresponding motion planning task.

[0062] This embodiment applies the above technical solution, such as Figure 2 As shown, the main process includes:

[0063] In step S1, the kinematic equation of the multi-axis manipulator is established based on the Jacobian matrix of the multi-axis manipulator. This embodiment takes a four-link manipulator as an example. In practical applications, the scope of application of this solution is not limited to a specific number of manipulator axes.

[0064] For the four-link robotic arm, the Jacobian matrix is ​​constructed as follows:

[0065]

[0066] According to the Jacobian matrix, the robotic arm motion control model of the acceleration layer is as follows:

[0067]

[0068] Where θ(t) is the joint angle, is the joint acceleration vector, is the derivative of the Jacobian matrix J(t) with respect to time t. and They are q d The first and second time derivatives of (t). Represents the feedback gain. ψ(t) represents a differentiable nonlinear mapping.

[0069] In step S2, the pseudo-inverse method is used to solve the equation of motion of the manipulator, and the following differential equation for the joint angle is obtained:

[0070]

[0071] Among them J T (t) represents the transpose of J(t).

[0072] In step S3, Figure 3 As shown in Figure 1, an auto-disturbance rejection and zeroing neural network is designed for non-sinusoidal periodic noise.

[0073] First, mathematical models of non-sinusoidal periodic noise, including DC components and fundamental components, as well as DC components and multi-harmonic components, are established to obtain the mathematical expression of each noise component.

[0074]

[0075] Among them, i∈1,…,m, j∈1,…,n, A k , fk and (k∈1,…,l) represent the amplitude, frequency and phase of periodic noise respectively, ω k represents the angular frequency, assuming A k and is an unknown parameter, f k are known parameters. Assume It is non-sinusoidal periodic noise. ij (t) is an element of the noise vector N(t), which can be decomposed into a Fourier series, which includes a DC component and harmonic components. Among these harmonic components, there are fundamental components and k-th harmonic components.

[0076] When k = 1, the non-sinusoidal periodic noise contains only DC components and fundamental components, which is converted into the following form:

[0077]

[0078] When k>1, the non-sinusoidal periodic noise contains a DC component and a kth harmonic component, in the following form:

[0079]

[0080] Then, a unified model of the noise-contaminated zeroing neural network is established under different noise models. The traditional zeroing neural network structure is as follows:

[0081]

[0082] in, N(t) represents the aforementioned non-sinusoidal periodic noise. To adaptively suppress noise, a new return-to-zero neural network model with active interference suppression is introduced. In the newly proposed ADNR return-to-zero neural network, an adaptive term Θ(t) is added to the evolution equation of E(t). The ADNR return-to-zero neural network model can be expressed as follows:

[0083]

[0084] Where E(t) is a compact matrix, which can be decomposed into the following form:

[0085]

[0086] Then we design an auto-disturbance rejection zeroing neural network that can solve the equation and suppress noise at the same time. When k = 1, the expression corresponding to non-sinusoidal periodic noise can be obtained:

[0087]

[0088] Continuing to derive both sides of the above equation, we can get:

[0089]

[0090] make but Writing it as a matrix expression yields:

[0091]

[0092] in Similar to N(t) and n ij (t), h ij (t) represents the matrix In the absence of A1 and In the case of values ​​of f1, the noise can be eliminated by applying the adaptive law of f1.

[0093] For the case where the noise contains DC components and fundamental components, the auto-disturbance rejection zeroing neural network is designed as follows:

[0094]

[0095] Theoretical proof and practical application can illustrate the convergence of this self-disturbance rejection zeroing neural network.

[0096] When k>1, the non-sinusoidal periodic noise contains a DC component and a kth harmonic component, in the following form:

[0097]

[0098] Taking the derivative of the noise with respect to t, we get:

[0099]

[0100] On this basis, we can continue to derive t and obtain:

[0101]

[0102] The error dynamics are written in matrix form as follows:

[0103]

[0104] According to the superposition principle, the auto-disturbance rejection neural network model in multi-harmonic scenarios can be obtained:

[0105]

[0106] Theoretical proof and practical application can illustrate the convergence of this zero-based neural network.

[0107] It can be seen that for the case where non-sinusoidal periodic noise contains DC component and fundamental component, the ADNR neural network is composed of the proportional term of error -γE(t), non-sinusoidal periodic noise N(t), adaptive law Θ(t) and integral term The integral term is used to eliminate the DC component in non-sinusoidal periodic noise;

[0108] For the case where non-sinusoidal periodic noise contains DC components and multi-harmonic components, the anti-disturbance zeroing neural network is used Adaptively eliminate the kth harmonic component in non-sinusoidal periodic noise.

[0109] In step S4, based on the multi-axis manipulator motion model solution obtained by pseudo-inversion, a multi-axis manipulator motion control method is designed using an auto-disturbance rejection zeroing neural network for non-sinusoidal periodic waves.

[0110] like Figure 4 As shown, by expressing the desired end-effector path as It is necessary to determine θ(t) in real time. By defining The auto-disturbance rejection and zeroing neural network constructed in step S3 can be used to obtain A(t), thereby designing a kinematic control scheme that is robust to non-sinusoidal periodic noise.

[0111] The multi-axis robotic arm motion control method obtained using the traditional integral enhanced zeroing neural network is as follows:

[0112]

[0113] When dealing with certain non-sinusoidal periodic disturbances, the state does not fully converge, but instead converges to an upper bound on the error. When the noise amplitude is large, traditional methods cannot effectively eliminate it. The adaptive robust control method proposed in this solution solves this problem.

[0114] When the noise only contains DC components and fundamental components, the following adaptive robust control method is designed using the auto-disturbance rejection zeroing neural network:

[0115]

[0116] When there is non-sinusoidal periodic noise consisting of a DC component and a kth harmonic component during motion, the noise has a known DC component A0 and a frequency f k , unknown amplitude A k and phase Based on the established multi-axis robotic arm motion model, the following adaptive robust control method is designed using the auto-disturbance rejection zeroing neural network:

[0117]

[0118] Finally, the multi-axis robotic arm controller drives the robotic arm to complete specific motion planning tasks accurately and efficiently based on the calculation results of the adaptive robust control method.

[0119] In summary, the adaptive robust multi-axis manipulator control method proposed in this scheme satisfies the form of PID control, and the proportional, integral and differential components are respectively -γE(t), Can eliminate DC component A0, frequency f k It is known that the harmonic amplitude A k , Phase Unknown non-sinusoidal periodic noise.

[0120] This embodiment performs a trajectory tracking test on a four-link robotic arm. The test results are as follows: Figures 5 to 7 shown. Figure 5 The motion trajectory diagram of the self-disturbance rejection four-link robotic arm is depicted. Figure 6 Capturing its terminal motion trajectory, Figure 7 The position error of the end of the manipulator is shown. This embodiment can effectively and accurately track the preset trajectory under non-sinusoidal periodic noise interference, indicating that the adaptive robust control method proposed in this scheme has high robustness and accuracy.

Claims

1. A multi-axis manipulator adaptive robust control method for non-sinusoidal periodic noise, characterized in that: The following steps are involved: S1. Based on the Jacobian matrix of the multi-axis manipulator, a unified kinematic equation of the multi-axis manipulator is established; S2. Introduce a pseudo-inverse scheme to solve the kinematic equations of the manipulator and obtain the differential equations for the joint accelerations; S3. Design an auto-disturbance rejection zeroing neural network for non-sinusoidal periodic noise; S4. For non-sinusoidal periodic noise, construct the adaptive robust control equation of the multi-axis manipulator and solve it to obtain the corresponding control results; S5. According to the control results, drive the multi-axis robotic arm to complete the corresponding motion planning task; The unified kinematic equation of the multi-axis manipulator in step S1 is the acceleration layer motion control equation based on the differential equation, specifically: Where θ(t) is the joint angle, is the joint acceleration vector, is the derivative of the Jacobian matrix J(t) with respect to time t, and They are q d The first and second time derivatives of (t), represents the feedback gain, ψ(t) represents a differentiable nonlinear mapping; Step S2 uses pseudo-inverse to obtain the solution of the multi-axis manipulator joint acceleration: Among them, J T (t) is the transpose of J(t); Step S3 specifically includes the following steps: S31. Establish a mathematical model of non-sinusoidal periodic noise and obtain a mathematical expression for each noise component; S32. Based on the mathematical model of non-sinusoidal periodic noise, a unified model of a return-to-zero neural network contaminated by noise is established; S33, based on the unified model of zeroing neural network, by introducing adaptive terms, an auto-disturbance rejection zeroing neural network model is established; The mathematical model of the non-sinusoidal periodic noise in step S31 is specifically: k∈1,L,l i∈1,L,m j∈1,L,n Among them, A k 、f k and Represent the amplitude, frequency and phase of periodic noise respectively, ω k represents the angular frequency, assuming A k and is an unknown parameter, f k are known parameters, assuming is non-sinusoidal periodic noise, n ij (t) is an element of N(t), which is decomposed into a Fourier series, including the DC component, the fundamental component and the kth harmonic component; When k = 1, it indicates that the non-sinusoidal periodic noise contains only DC components and fundamental components. The corresponding mathematical model is: Among them, A0 is the DC component and A1 is the fundamental component; The zeroing neural network unified model in step S32 is specifically: Among them, E(t) is a compact matrix, In step S33, if the non-sinusoidal periodic noise only contains a DC component and a fundamental component, the corresponding ADRC-Zero neural network model is specifically: Among them, Θ(t) and Ψ(t) are adaptive terms; In step S33, if the non-sinusoidal periodic noise contains a DC component and multiple harmonic components, the corresponding ADRC-Zero neural network model is obtained according to the superposition principle as follows: Among them, Θ(t) and Ψ(t) are adaptive terms; In step S4, the non-sinusoidal periodic noise only contains DC components and fundamental components, and the corresponding multi-axis manipulator adaptive robust control equation is: Where I is the identity matrix; In step S4, the non-sinusoidal periodic noise contains DC components and multiple harmonic components, and the corresponding multi-axis manipulator adaptive robust control equation is: Where I is the identity matrix.

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