A Fault-Tolerant Iterative Learning Control Method for a Manipulator System Based on the Balance Factor

Abstract

The present invention discloses a fault-tolerant iterative learning control method for a robotic arm system based on a balance factor. Based on the derivative relationship between the parameters of the robotic arm system, the system is reconstructed into a second-order system, a backstepping error and a virtual controller are constructed. At the same time, to avoid the imperfect reset of the system state at the beginning of each iteration, a parameter update law based on the balance factor is constructed, and an iterative learning controller is designed to control the robotic arm system and compensate for actuator faults, parameter uncertainties and disturbances. Compared with traditional control methods that require an accurate mathematical model, the control algorithm proposed in the present invention is more novel and has simple application conditions. When this method is used for repetitive task operations, it effectively improves the control accuracy and has good engineering application value.

Description

Technical Field

[0001] The present invention relates to a control method for a robotic arm system, and more particularly to a fault-tolerant iterative learning control method for a robotic arm system based on a balance factor. Background Art

[0002] A robotic arm is a mechanical device that can simulate the movements of a human arm. It is usually composed of a series of joints and actuators and can perform precise and flexible operations in fields such as industrial production, medical surgery, and logistics. The design of a robotic arm can be customized according to different requirements and application scenarios. Some robotic arms are also equipped with sensors and vision systems to more accurately perceive and execute tasks. In modern industry, robotic arms have become important automation equipment, which can improve production efficiency, reduce costs, and can also complete some tasks that are dangerous or heavy for humans.

[0003] The control of a robotic arm needs to ensure that the robotic arm can accurately reach the specified position or posture when performing tasks and maintain stability, especially under high-speed movement or in complex environments. For some tasks that require real-time response, such as operations on an industrial production line, the robotic arm control system needs to be able to execute instructions quickly and accurately to avoid production interruptions or equipment damage. When working with humans or other equipment, the robotic arm needs to have safety, being able to avoid accidental injuries or damage. The robotic arm needs to be able to adapt to different working environments and task requirements, including workpieces of different shapes and sizes, as well as possible external disturbances and obstacles. Solving these difficulties requires comprehensive consideration of many factors such as mechanical structure design, control algorithm optimization, and sensor technology application, and continuous research and improvement are needed. Summary of the Invention

[0004] The object of the present invention is to propose a fault-tolerant iterative learning control method for a robotic arm system based on a balance factor, which can effectively solve problems such as dynamics, motion planning, and disturbance effects existing in the robotic arm system and achieve good control effects.

[0005] The specific technical solution of the present invention is as follows: A fault-tolerant iterative learning control method for a robotic arm system based on a balance factor, comprising the following steps:

[0006] The robotic arm system model is as follows:

[0007]

[0008] wherein, x1, k x2, and k respectively represent the joint position and joint velocity of the robotic arm, D k represents the inertia matrix, C k represents the centripetal Coriolis matrix, G k represents the gravity vector, Fk denotes the perturbation, denotes the controller with faults and satisfies where ρ k denotes the multiplicative fault, σ k denotes the additive fault, u k denotes the controller without faults;

[0009] Construct the backstepping error and the virtual controller, and the specific steps are as follows:

[0010]

[0011] In the formula, z 1，k、 z 2，k denotes the backstepping error, α 1，k denotes the virtual controller, and its form is as follows:

[0012]

[0013] In the formula, Γ1 denotes the gain matrix;

[0014] Express the unknown terms of the system as parameter uncertainties:

[0015]

[0016] In the formula, ξ k denotes the known regression matrix, and θ denotes the unknown vector;

[0017] Construct the parameter update law based on the balance factor in the following form:

[0018]

[0019] In the formula, are the estimated values of ψ and respectively, where ε represents an arbitrarily small positive constant, γ1, γ2, γ3 are positive gains, or tanh(Hk) represents the balance factor, k represents the number of iterations, and H is an arbitrarily large positive constant;

[0020] Establish a fault-tolerant iterative learning control scheme for the trajectory tracking of the robotic arm system involved in the present invention, in the following form:

[0021]

[0022]

[0023] In the formula, Γ2 is a positive definite gain matrix, and this algorithm can guarantee the convergence of the backstepping error. The proof process is as follows:

[0024] C001: Define the Lyapunov function of subsystem 1:

[0025]

[0026] C002: Take the derivative of V 1，k with respect to:

[0027]

[0028] C003: Define the Lyapunov function of subsystem 2:

[0029]

[0030] C004: Take the derivative of V 2，k with respect to:

[0031]

[0032] C005: Where λ2 is the minimum eigenvalue of Γ2;

[0033] C006: Select a composite energy function of the following form:

[0034] E k (t) = W 1，k (t) + W 2,k (t) + W 3，k (t) + W 4，k (t)

[0035]

[0036]

[0037]

[0038]

[0039] C007: Where

[0040] C008: Consider the difference ΔE k (t) of E k (t) between the k-th and (k - 1)-th times, where:

[0041]

[0042]

[0043]

[0044]

[0045] C009: According to C008, the following formula can be obtained:

[0046] C010: In the formula,

[0047] C011: Further, construct a composite energy function of the contraction mapping type:

[0048]

[0049]

[0050] C012: Further, considering the boundedness of E1(t), The derivation of is as follows:

[0051]

[0052] C013: From the boundedness of E1(t), the boundedness of E k can be obtained, and then the convergence form of the backstepping error is as follows:

[0053]

[0054] BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 is a flowchart of the method according to an embodiment of the present invention;

[0056] Figure 2 is a schematic diagram of a robotic arm system according to an embodiment of the present invention;

[0057] Figure 3 is an output tracking diagram of the 5th iteration of the method proposed by the present invention in an embodiment;

[0058] Figure 4 is an output tracking diagram of the 10th iteration of the method proposed by the present invention in an embodiment;

[0059] Figure 5 is an output tracking diagram of the 30th iteration of the method proposed by the present invention in an embodiment; DETAILED DESCRIPTION OF THE INVENTION

[0060] The present invention will be further clarified below with reference to specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. After reading the present invention, various equivalent modifications of the present invention by those skilled in the art fall within the scope defined by the appended claims of this application.

[0061] Such as Figure 1As shown in the figure, a fault-tolerant iterative learning control method for a robotic arm system based on a balance factor includes the following steps:

[0062] Step 1: Set the initial values of the parameters;

[0063] Step 2: Update the algorithm parameters;

[0064] Step 3: According to the updated algorithm parameters, generate the control input u k (t) in real time;

[0065] Step 4: According to the tracking error and backstepping error generated by the control input u k (t), synchronously update the algorithm parameters;

[0066] Step 5: Repeat Steps 3 and 4 until the end of the current iteration and enter the next iteration;

[0067] Step 6: Now, introduce an embodiment of the present invention:

[0068] Consider the fault-tolerant iterative learning control problem of a robotic arm system based on a balance factor, and its corresponding mathematical model is:

[0069]

[0070] Among them, the system parameters are:

[0071] x 1，k x 2，k respectively represent the joint position and joint velocity of the robotic arm, D k represents the inertia matrix, C k represents the centripetal Coriolis matrix, G k represents the gravity vector, F k represents the disturbance, represents the controller with faults and satisfies where ρ k represents the multiplicative fault, σ k represents the additive fault, u k represents the controller without faults;

[0072] The desired reference trajectory is: y d = [3cos(0.5t); 2sin(0.5t)]; The desired operating time T of the system is 12 s;

[0073] Figure 1 is the flowchart of the method of the embodiment of the present invention; Figure 2 is the schematic diagram of the robotic arm system of the embodiment of the present invention; Applying the proposed method, Figure 3 、 4, 5 respectively represent the output tracking of the 5th, 10th, and 30th iterations of the method proposed in the present invention. It can be seen from these three figures that the proposed method has a good application effect in the robotic arm system, and a satisfactory tracking performance can be obtained after the 30th iteration.

[0074] References

[0075] [1] F. Zhang, D. Meng, X. Li. Chattering-free adaptive iterative 1earning for attitude tracking control of uncertain spacecraft. Automatica, vol. 151, 110902, 2023.

[0076] [2] J. Wei, Y. Hu, M. Sun. Adaptive iterative learning control for a class of nonlinear time-varying systems with unknown delays and input dead-zone. IEEE / CAA Journal of Automatica Sinica, vol. 1, pp. 302 - 314, 2014.

Claims

1. A fault-tolerant iterative learning control method for a robotic arm system based on a balance factor, characterized in that It includes the following steps: Based on the derivative relationship among the parameters of the robotic arm system, the system is reconstructed into a second-order system. Construct the backstepping error and the virtual controller. To avoid the imperfect reset of the system state at the beginning of each iteration, a parameter update law based on the balance factor is constructed. Design an iterative learning controller to control the robotic arm system and compensate for actuator faults, parameter uncertainties, and disturbances. Among them, based on the derivative relationship among the parameters of the robotic arm system, the system is reconstructed into a second-order system: where x 1,k x 2,k represent the joint position and joint velocity of the robotic arm respectively, D k represents the inertia matrix, C k represents the centripetal Coriolis matrix, G k represents the gravity vector, F k represents the disturbance, represents the controller with faults and satisfies where ρ k represents the multiplicative fault, σ k represents the additive fault, u k represents the controller without faults; Construct the backstepping error and the virtual controller. The specific steps are as follows: where z 1,k and z 2,k represent the backstepping error, and α 1,k represents the virtual controller, whose form is as follows: In the formula, Γ1 represents the gain matrix. To avoid the imperfect reset of the system state at the beginning of each iteration, a parameter update law based on the balance factor is constructed. The specific steps are as follows: Express the unknown terms of the system as parameter uncertainties. where ξ k denotes a known regression matrix and θ denotes an unknown vector; Construct a parameter update law based on the balance factor. The specific steps are as follows: wherein, are the estimated values of ψ and respectively, where ε represents an arbitrarily small positive constant, γ1, γ2, and γ3 are positive gains, or tanh(Hk) represents the equilibrium factor, k represents the number of iterations, and H is an arbitrarily large positive constant; Design an iterative learning controller to control the robotic arm system and compensate for actuator faults, parameter uncertainties, and disturbances. The specific steps are as follows: A fault-tolerant iterative learning control scheme for the trajectory tracking of the robotic arm system is established as follows: In the formula, Γ2 is a positive definite gain matrix. The proof process of the convergence of the backstepping error is as follows: B001: Define the Lyapunov function of subsystem 1: B002: Differentiate V 1,k with respect to: In the formula, λ1 is the minimum eigenvalue of Γ1. B003: Define the Lyapunov function of subsystem 2: B004: Differentiate V 2,k with respect to: In the formula, λ2 is the minimum eigenvalue of Γ2. B005: Select the composite energy function in the following form: E k E(t) = W 1,k E(t) + W 2,k E(t) + W 3,k E(t) + W 4,k E(t) B006: In the formula, B007: Consider the difference ΔE k (t) between the k-th and the (k - 1)-th E k (t), where: B008: From B007, the following equation can be obtained: B009: In the formula, B010: Further, construct a composite energy function of the contraction mapping type. B011: Further, give the boundedness proof of E1. B012: Due to the boundedness of E1(t), the boundedness of E k can be obtained, and then the convergence form of the backstepping error is as follows: 。

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