Fault-tolerant tracking control method for robot manipulator based on hybrid observer

Abstract

The application discloses a kind of mechanical arm fault-tolerant tracking control methods based on hybrid observer, steps are as follows:1, the mechanical arm system considering system dynamics uncertainty and actuator failure is established;2, the fixed time sliding surface of mechanical arm system is established;3, according to the fixed time sliding surface of the established mechanical arm system, the neural network enhanced estimation function of mechanical arm system is established;4, according to the established mechanical arm system considering system dynamics uncertainty and actuator failure, the fixed time sliding surface of mechanical arm system and the neural network enhanced estimation function of mechanical arm system, the hybrid observer of mechanical arm system is established;5, the mechanical arm fault-tolerant tracking controller based on hybrid observer is established;6, the established mechanical arm fault-tolerant tracking controller based on hybrid observer is input into the mechanical arm system considering system dynamics uncertainty and actuator failure, i.e. the trajectory tracking control of each joint of mechanical arm system is realized quickly and accurately, the interference of system dynamics uncertainty and actuator failure factor is faced by the method of the application, with good robustness.

Description

Technical Field

[0001] This invention belongs to the field of robotic arm control technology, and in particular relates to a fault-tolerant tracking control method for robotic arms based on a hybrid observer. Background Technology

[0002] Robotic arms, as crucial tools for modern industrial automation and high-precision task execution, are widely used in manufacturing, medical surgery, space exploration, and other fields. The accuracy and robustness of their trajectory tracking control directly impact the system's efficiency and safety. Therefore, achieving high-precision and robust trajectory tracking control under various environmental conditions has become a significant research direction.

[0003] However, due to the high coupling and nonlinearity of the robotic arm system itself, and the frequent influence of actuator failures and system dynamic uncertainties in real-world environments, the robotic arm system cannot accurately feedback system state information, affecting the accuracy and reliability of trajectory tracking. Sliding mode control is a robust control method that can handle external disturbances based on the signed gain term. Model predictive control predicts and optimizes based on the system model, but its computational complexity is high and its real-time performance is poor. In active fault-tolerant control, the fault estimation observer can acquire fault information and return it to the controller for reconfiguration, but both model predictive control and fault estimation observers are highly dependent on the model during the design process, and their expressions are relatively complex. Summary of the Invention

[0004] To address the problems existing in the prior art, the present invention aims to provide a fault-tolerant tracking control method for robotic arms based on a hybrid observer. This method accurately estimates the joint angular velocity state of the robotic arm system, overcomes the impact of dynamic uncertainties and actuator failures on the tracking performance of the robotic arm system, ensures that the robotic arm system quickly reaches the preset trajectory, and provides a higher level of robustness and tracking performance.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A fault-tolerant tracking control method for a robotic arm based on a hybrid observer includes the following steps:

[0007] Step 1: Establish a robotic arm system considering system dynamics uncertainties and actuator failures, represented as follows:

[0008]

[0009] Where x and v are the joint angle vector and joint angular velocity vector of the robotic arm system, respectively. and Let f(x,v) be the derivatives of x and v, respectively; f(x,v) be the system dynamics uncertainty of the robotic arm system; g(x) be the control gain matrix of the robotic arm system; and u be the fault-tolerant tracking controller of the robotic arm based on a hybrid observer. Let ρ be the total actuator failure of the robotic arm system, and let χ be the multiplicative failure coefficient and additive failure coefficient of the actuator of the robotic arm system, respectively, satisfying 0≤|ρ|≤1, where χ is any real number;

[0010] Step 2: Based on the established robotic arm system considering system dynamics uncertainties and actuator failures, establish the fixed-time sliding surface of the robotic arm system, represented as:

[0011]

[0012] Where s is the fixed-time sliding surface of the robotic arm system, and the joint angle vector observation error of the robotic arm system is... These are the joint angle vector observations of the robotic arm system. Let β1 be the differential of e1 after passing through a first-order differentiator, and β2 be the gain coefficient matrices of the fixed-time sliding mode surface. Both β1 and β2 are diagonal positive definite matrices. sig 2 (e1) and For a sliding mode component of a fixed-time terminal sliding surface, for any dimension vector θ, θ1,…,θ n For each component of vector θ, κ>0, the sig function satisfies

[0013] Step 3: Based on the established fixed-time sliding surface of the robotic arm system, establish the neural network enhancement estimation function for the robotic arm system, expressed as:

[0014]

[0015] in, For the neural network weights of the robotic arm system, Here, K1 and K2 are the transpose of the neural network weights of the robotic arm system, respectively, and K1 and K2 are the gain matrices of the neural network enhancement estimation function. The neural network input is... φ(z w Let be the neural network basis functions of the robotic arm system, expressed as:

[0016]

[0017] Where m is the number of layers in the neural network, σ j Let c be the width of the j-th neural network basis function. j For the j-th neural network basis function network center, S1(z) w ),…,S m(z w Let be the basis functions of the neural network of the robotic arm system, which are the components of each layer of the neural network. To update the neural network weights of the robotic arm system, the adaptive rate of the neural network is expressed as:

[0018]

[0019] in, Let Γ be the norm of the neural network weights of the robotic arm system, and let Γ be the learning rate of the biased neural network.

[0020] Step four: Based on the established robotic arm system considering system dynamics uncertainties and actuator failures, the fixed-time sliding surface of the robotic arm system, and the neural network-enhanced estimation function of the robotic arm system, a hybrid observer for the robotic arm system is established, expressed as:

[0021]

[0022] in, and These are the observations of the joint angle vector x and joint angular velocity vector v of the robotic arm system by the hybrid observer, respectively. and They are respectively and The derivative of For the extended state variables of the hybrid observer, for The derivatives of β3, β4, and β5 are the gain matrices of the hybrid observer. and These are components of the hybrid observer;

[0023] Step 5: Based on the established neural network augmentation estimation function and the established hybrid observer of the robotic arm system, establish a fault-tolerant tracking controller for the robotic arm based on the hybrid observer, expressed as:

[0024]

[0025] Where, x d and These are the predetermined trajectories for the joint angles and joint angular velocities of the robotic arm system, respectively. for The derivatives, μ1, μ2, and μ3, are the gain coefficients of the fault-tolerant tracking controller for the hybrid observer-based robotic arm, sig 2 (r) and Here, r is a component of the fault-tolerant tracking controller for a robotic arm based on a hybrid observer, and r is the tracking error of the robotic arm system, expressed as:

[0026]

[0027] Step six involves inputting the established fault-tolerant tracking controller for the robotic arm based on a hybrid observer into the robotic arm system that considers system dynamics uncertainties and actuator failures. This enables fast and accurate trajectory tracking control of each joint of the robotic arm system, and demonstrates excellent robustness in the face of interference from system dynamics uncertainties and actuator failures.

[0028] Compared with the prior art, the present invention has the following advantages:

[0029] 1. This invention designs a hybrid observer that integrates neural networks and a fixed-time sliding surface, enabling the observer to estimate the dynamic uncertainties and actuator failures of the robotic arm system and feed them back to the controller, thereby improving the robustness of the robotic arm system.

[0030] 2. By establishing a fixed-time sliding surface for the robotic arm system, this invention enables the observation error of the hybrid observer to converge at a faster rate throughout the entire process;

[0031] 3. This invention designs a hybrid observer to observe the angular velocity of the robotic arm system, enabling good tracking performance even when the angular velocity of the robotic arm system is difficult to measure. Attached Figure Description

[0032] Figure 1 A flowchart illustrating a fault-tolerant tracking control method for a robotic arm based on a hybrid observer, provided in an embodiment of the present invention;

[0033] Figure 2 This is a schematic diagram of the angle tracking change curve of joint 1 in a two-joint robotic arm system provided in an embodiment of the present invention;

[0034] Figure 3 This is a schematic diagram of the joint 2 angle tracking change curve of the two-joint robotic arm system provided in an embodiment of the present invention;

[0035] Figure 4 This is a schematic diagram of the angular velocity tracking curve of joint 1 of the two-joint robotic arm system provided in an embodiment of the present invention;

[0036] Figure 5 This is a schematic diagram of the angular velocity tracking curve of joint 1 of the two-joint robotic arm system provided in an embodiment of the present invention; Detailed Implementation

[0037] To enable those skilled in the art of robotic arm control to better understand the method of this invention, the invention will be described in more detail below through embodiments and accompanying drawings. It should be emphasized that the embodiments of this invention are based on the technical solutions of this invention and are only used to illustrate the invention, not to limit its scope. The implementation of this invention is not limited thereto.

[0038] Figure 1 This is a flowchart illustrating a fault-tolerant tracking control method for a robotic arm based on a hybrid observer, provided in an embodiment of the present invention. The embodiment uses a two-joint robotic arm for trajectory tracking control. It should be noted that although this embodiment uses a two-joint robotic arm as an example, the trajectory tracking control method proposed in this invention is applicable to trajectory control technology for robotic arms with any number of joints, and these applications fall within the scope of protection of this invention.

[0039] A fault-tolerant tracking control method for a robotic arm based on a hybrid observer includes the following steps:

[0040] Step 1: Establish a robotic arm system considering system dynamics uncertainties and actuator failures, represented as follows:

[0041]

[0042] Where x and v are the joint angle vector and joint angular velocity vector of the robotic arm system, respectively. and The derivatives of x and v are respectively, f(x,v)=-M -1 (x)(C(x,v)v+G(x)) represents the system dynamics uncertainty of the robotic arm system. Let be the control gain matrix of the robotic arm system, and u be the fault-tolerant tracking controller of the robotic arm based on a hybrid observer. The total actuator failure of the robotic arm system is represented by ρ and χ, which are the multiplicative and additive failure coefficients of the actuators in the robotic arm system, respectively. The various matrices and failure coefficients are expressed as follows:

[0043]

[0044]

[0045] ρ = 0.7 + 0.1sin(2t)

[0046] χ = 1.5 + 0.5cos(2t)

[0047] In this system, the joint angle vector and joint angular velocity vector of the two-joint robotic arm are x = [q1, q2]. The acceleration due to gravity is g = 9.8 m / s². 2p1, p2, p3, p4, and p5 are all functions of the link lengths l1 and l2, link masses m1 and m2, and link moments of inertia J1 and J2 of the two-joint robotic arm system. Let p1 = 2, p2 = 0.448, p3 = 0.56, p4 = 2.56, and p5 = 0.56. The length of the first link in the two-joint robotic arm system is l1 = 1m, the length of the second link is l2 = 0.8m, the mass of the first link is m1 = 2kg, the mass of the second link is m2 = 1.5kg, and the moment of inertia of the first link is J1 = 0.25kg·m. 2 The moment of inertia of the second connecting rod is J2 = 0.112 kg·m. 2 ;

[0048] Step 2: Based on the established robotic arm system considering system dynamics uncertainties and actuator failures, establish the fixed-time sliding surface of the robotic arm system, represented as:

[0049]

[0050] Where s is the fixed-time sliding surface of the robotic arm system, and the joint angle vector observation error of the robotic arm system is... These are the joint angle vector observations of the robotic arm system. Let β1 be the differential of e1 after passing through a first-order differentiator, and β2 be the gain coefficient matrices of the fixed-time sliding surface. Both β1 and β2 are diagonal positive definite matrices with diagonal elements of 5. 2 (e1) and For a sliding mode component of a fixed-time terminal sliding surface, for any dimension vector θ, θ1,…,θ n For each component of vector θ, κ>0, the sig function satisfies

[0051] Step 3: Based on the established fixed-time sliding surface of the robotic arm system, establish the neural network enhancement estimation function for the robotic arm system, expressed as:

[0052]

[0053] in, For the neural network weights of the robotic arm system, K1 and K2 are the transpose of the neural network weights of the robotic arm system, respectively. K1 is a diagonal matrix with diagonal elements of 1, 1, and K2 is a diagonal matrix with diagonal elements of 3, 3. The neural network input is... φ(z w Let be the neural network basis functions of the robotic arm system, expressed as:

[0054]

[0055] Where m is the number of layers in the neural network, m = 10, σ j Let σ be the width of the j-th neural network basis function. j =2,c j Let c be the network center of the j-th neural network basis function. j =[0,1]×[0,1]×[0,1]×[0,1], S1(z w ),…,S m (z w Let be the basis functions of the neural network of the robotic arm system, which are the components of each layer of the neural network. To update the neural network weights of the robotic arm system, the adaptive rate of the neural network is expressed as:

[0056]

[0057] in, Let Γ be the norm of the neural network weights of the robotic arm system, and let Γ be the learning rate of the biased neural network. Γ is a diagonal matrix with diagonal elements of 100.

[0058] Step four: Based on the established robotic arm system considering system dynamics uncertainties and actuator failures, the fixed-time sliding surface of the robotic arm system, and the neural network-enhanced estimation function of the robotic arm system, a hybrid observer for the robotic arm system is established, expressed as:

[0059]

[0060] in, and These are the observations of the joint angle vector x and joint angular velocity vector v of the robotic arm system by the hybrid observer, respectively. They are respectively and The derivative of For the extended state variables of the hybrid observer, The derivatives of β3, β4, and β5 are the gain matrices of the hybrid observer, where β3 is a diagonal matrix with diagonal elements of 10, 10, and β4 and β5 are both diagonal positive definite matrices with diagonal elements of 2, 2. and These are components of the hybrid observer;

[0061] Step 5: Based on the established neural network augmentation estimation function and the established hybrid observer of the robotic arm system, establish a fault-tolerant tracking controller for the robotic arm based on the hybrid observer, expressed as:

[0062]

[0063] Where, x d and These are the predetermined trajectories for the joint angles and joint angular velocities of the robotic arm system, respectively. d =[sin(t); sin(t)], for The derivatives, μ1, μ2, and μ3, are the gain coefficients of the fault-tolerant tracking controller for the hybrid observer-based robotic arm, μ1 = 2.5, μ2 = 1.5, μ3 = 1.5, and sig 2 (r) and Here, r is a component of the fault-tolerant tracking controller for a robotic arm based on a hybrid observer, and r is the tracking error of the robotic arm system, expressed as:

[0064]

[0065] Step 7: Input the established fault-tolerant tracking controller for the robotic arm based on the hybrid observer into the robotic arm system that considers system dynamics uncertainties and actuator failures. This enables fast and accurate trajectory tracking control of each joint of the robotic arm system, and it has good robustness in the face of interference from system dynamics uncertainties and actuator failures.

[0066] Figure 2 This is a schematic diagram of the angle tracking change curve of joint 1 in a two-joint robotic arm system provided in an embodiment of the present invention. Figure 3 The figure shows a schematic diagram of the angle tracking change curve of joint 2 of the two-joint robotic arm system provided in the embodiment of the present invention. As can be seen from the figure, the angle tracking of the two joints of the robotic arm system can completely keep up with the predetermined trajectory in about 2.8s, and does not deviate from the predetermined trajectory after that, with a relatively fast and stable speed.

[0067] Figure 4 This is a schematic diagram of the angular velocity tracking curve of joint 1 in a two-joint robotic arm system provided in an embodiment of the present invention. Figure 5 The figure shows a schematic diagram of the angular velocity tracking change curve of joint 2 of the two-joint robotic arm system provided in the embodiment of the present invention. As can be seen from the figure, the angular velocity tracking of both joints of the robotic arm system completely follows the predetermined trajectory in about 3.5s, indicating that the hybrid observer has a good estimation effect on the uncertainty of system dynamics and actuator failure.

[0068] Throughout the simulation, the control system remained stable without any sudden step jumps or crashes. This demonstrates that the control method of this invention enables the robotic arm system to perform trajectory tracking tasks efficiently and stably, significantly improving the speed and accuracy of angle and angular velocity tracking. Even when faced with uncertainties in system dynamics and actuator malfunctions, the robotic arm's trajectory tracking still exhibits excellent stability without any significant deviation.

[0069] The application of this invention is not limited to the previously disclosed technical means, but includes technical solutions constituted by various combinations of these technical features. Although the preferred embodiments of this invention have been described in detail above, it is worth emphasizing that those skilled in the art can still make various improvements and modifications without departing from the principles of this invention. These improvements and modifications are also considered to be part of the protection scope of this invention. Therefore, the protection scope of this patent should cover all equivalent embodiments that conform to the combination of technical features, and not be limited to the specifically disclosed embodiments.

Claims

1. A fault-tolerant tracking control method for a robotic arm based on a hybrid observer, characterized in that: Includes the following steps: Step 1: Establish a robotic arm system considering system dynamics uncertainties and actuator failures, represented as follows: in, These are the joint angle vector and joint angular velocity vector of the robotic arm system, respectively. The derivative, , For a fault-tolerant tracking controller for a robotic arm based on a hybrid observer, The problem is a general actuator failure in the robotic arm system. and These are the multiplicative and additive failure coefficients of the actuators in the robotic arm system, respectively. ; Step 2: Based on the established robotic arm system considering system dynamics uncertainties and actuator failures, establish the fixed-time sliding surface of the robotic arm system, represented as: in, For the fixed-time sliding surface of the robotic arm system, the observation error of the joint angle vector of the robotic arm system. = for Differentiation after a first-order differentiator and The gain coefficient matrix of the fixed-time sliding mode surface. and All are diagonal positive definite matrices. and For a sliding surface component with a fixed time terminal, for For vectors The various components, The function satisfies ; Step 3: Based on the established fixed-time sliding surface of the robotic arm system, establish the neural network enhancement estimation function for the robotic arm system, expressed as: in, For the neural network weights of the robotic arm system, This is the transpose of the neural network weights of the robotic arm system. and The gain matrix of the neural network enhancement estimation function, and the neural network input. , The neural network basis functions of the robotic arm system are expressed as: in, The number of layers in the neural network. For the first The width of each neural network basis function. For the first The center of a neural network basis function network. Let be the basis functions of the neural network in each layer of the robotic arm system. To update the weights of the neural network in the robotic arm system, the adaptive rate of the neural network is expressed as: in, Let be the norm of the neural network weights of the robotic arm system, a symmetric positive definite matrix. The learning rate is used to bias the neural network; Step four: Based on the established robotic arm system considering system dynamics uncertainties and actuator failures, the fixed-time sliding surface of the robotic arm system, and the neural network-enhanced estimation function of the robotic arm system, a hybrid observer for the robotic arm system is established, expressed as: in, and These are the joint angle vectors of the robotic arm system as viewed by the hybrid observer. and joint angular velocity vector The observed values, and and The derivative, For the extended state variables of the hybrid observer, , and The gain matrix of the hybrid observer. and These are components of the hybrid observer; Step 5: Based on the established neural network augmentation estimation function and the established hybrid observer of the robotic arm system, establish a fault-tolerant tracking controller for the robotic arm based on the hybrid observer, expressed as: in, and These are the predetermined trajectories for the joint angles and joint angular velocities of the robotic arm system, respectively. for The derivative, , and These are all gain coefficients of a fault-tolerant tracking controller for a robotic arm based on a hybrid observer. This is a component of a hybrid observer-based fault-tolerant tracking controller for robotic arms. The tracking error of the robotic arm system is expressed as: Step six involves inputting the established fault-tolerant tracking controller for the robotic arm based on a hybrid observer into the robotic arm system that considers system dynamics uncertainties and actuator failures. This enables trajectory tracking control of each joint in the robotic arm system and provides robustness in the face of interference from system dynamics uncertainties and actuator failures.

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