A mechanical arm system distributed iterative learning control method based on loose alignment conditions

Abstract

The application discloses a mechanical arm system fault-tolerant distributed learning control method based on a loose alignment condition. The method designs an auxiliary system of loose alignment condition and compensation input saturation, constructs inverse step error, a virtual controller and compensation error. An iterative learning controller is designed to control the mechanical arm system and compensate for unknown inertia matrix, parameter uncertainty and disturbance, and convergence of the error system is analyzed by constructing a composite energy function. Compared with traditional control methods requiring accurate mathematical models, the control algorithm is more novel and the application condition is simple. When the method is used for repetitive task operation, the control precision is effectively improved, and the method has good engineering application value.

Description

Technical Field

[0001] This invention relates to a control method for a robotic arm system, specifically a distributed iterative learning control method for a robotic arm system based on relaxed alignment conditions. Background Technology

[0002] A robotic arm is a mechanical device that can mimic the movements of a human arm. It typically consists of a series of joints and actuators, enabling precise and flexible operations in fields such as industrial production, medical surgery, and logistics. Robotic arms can be customized to meet different needs and application scenarios. Some robotic arms are also equipped with sensors and vision systems for more accurate task perception and execution. In modern industry, robotic arms have become important automation equipment, improving production efficiency, reducing costs, and performing tasks that are dangerous or strenuous for humans.

[0003] Robotic arm control needs to ensure that the robotic arm can accurately reach the designated position or posture and maintain stability during task execution, especially in high-speed motion or complex environments. For tasks requiring real-time response, such as operations on industrial production lines, the robotic arm control system needs to execute instructions quickly and accurately to avoid production interruptions or equipment damage. When working alongside humans or other equipment, the robotic arm needs to be safe to prevent accidental injury or damage. The robotic arm needs to adapt to different working environments and task requirements, including workpieces of different shapes and sizes, as well as potential external interference and obstacles. Solving these challenges requires comprehensive consideration of factors such as mechanical structure design, control algorithm optimization, and sensor technology application, and necessitates continuous research and improvement. Summary of the Invention

[0004] The purpose of this invention is to propose a distributed iterative learning control method for robotic arm systems based on relaxed alignment conditions, which can effectively solve problems such as dynamics, motion planning, and disturbance effects in robotic arm systems and achieve good control results.

[0005] The specific technical solution of this invention is as follows: A distributed iterative learning control method for a robotic arm system based on relaxed alignment conditions, comprising the following steps:

[0006] The robotic arm system model is shown below:

[0007]

[0008] In the formula, x 1，j,k x 2,j,k Let D represent the joint position and joint velocity of the j-th robotic arm, respectively. j，k Let C represent the inertia matrix. j，k G represents the centripetal Coriolis matrix. j，kF represents the gravity vector. j，k Indicates a disturbance. This indicates a controller with input saturation, where k represents the number of system iterations;

[0009] Traditional alignment conditions require a closed loop in the reference orbit space, thus making them unsuitable for iteratively changing reference orbits. Therefore, a more relaxed alignment condition is designed to handle such reference orbits.

[0010] x 1,d,k =x 1,r，k -ω1(x 1，r，k (0)-x 1，r，k-1 (T))-ω2(x 2，r，k (0)-x 2，r,k-1 (T))

[0011] In the formula, x 1，d,k x 1,r,k Let ω1 and ω2 represent the modified reference orbit and the reference orbit, respectively, and let ω1 and ω2 represent the modification functions, which satisfy the following requirements:

[0012] ·ω1(0)=1,ω1(T a )=0, ω1(t)=0, t∈[T a [T]

[0013] ·

[0014] ·ω2(0)=0,ω2(T a )=0, ω2(t)=0, t∈[T a [T]

[0015] ·

[0016] In the formula T a Indicates the length of the modifier, and satisfies 0. <T a ≤T, where T is the time length of each iteration;

[0017] The design of an auxiliary system to compensate for input saturation is shown below:

[0018]

[0019] In the formula, δ 1，j,k δ 2,j，k Γ represents the state given by the known auxiliary system. 1，j ,Γ 2，J This indicates the feedback gain that needs to be designed, ε. j =1 / 0 indicates whether the j-th robotic arm can obtain information from the reference track, d j Let Δu represent the relative degree of the j-th robotic arm. j，k This represents the difference between the saturated input and the actual input.

[0020] The backstep error is constructed as follows:

[0021]

[0022] In the formula, a jl =1 / 0 indicates whether the j-th robotic arm can obtain information from the l-th robotic arm, α 1,j,k The virtual controller is represented as follows:

[0023]

[0024] The error compensation is constructed in the following form:

[0025] s i，j，k =z i，j，k -δ i,j，k i = 1, 2

[0026] An iterative learning controller is established to control the robotic arm system and compensate for unknown inertia matrices, parameter uncertainties, and disturbances, as shown below:

[0027]

[0028] In the formula, proj represents the upper and lower bounds of the parameter update, and γ 1，j γ 2,j This indicates the learning gain that needs to be designed. Xi represents a convergent series sequence, where q>0 and l>2. The convergence of the error system is analyzed by constructing a composite energy function. The specific steps are as follows:

[0029] C001: Define the Lyapunov function for subsystem 1:

[0030]

[0031] C002: For V 1，k Differentiate:

[0032]

[0033] C003: Define the Lyapunov function for subsystem 2:

[0034]

[0035] C004: For V 2，k Differentiate:

[0036]

[0037] C006: Select the following form of composite energy function:

[0038]

[0039] E j，k (t)=E 1，j，k +E 2，j，k +E 3，j，k

[0040] E 1,j,k (t)=V 1,j,k +V 2，j，k

[0041] ,

[0042] ,

[0043] C007: In the formula,

[0044] C008: Consider the E between the k-th and (k-1)-th times. j，k The difference ΔE (t) j，k (t), where:

[0045]

[0046]

[0047] C009: Based on C008, the following formula can be obtained:

[0048]

[0049] C010: Further, E is given. j，1 Proof of the boundedness of W1:

[0050] C011: Based on C009 and C010, the following formula can be obtained:

[0051]

[0052] C012: Based on C011, the convergence form of the compensation error can be obtained as follows:

[0053] Attached Figure Description

[0054] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0055] Figure 2 This is a schematic diagram of the robotic arm system according to an embodiment of the present invention;

[0056] Figure 3The image shows the position error convergence diagram after 35 iterations using the method proposed in this invention, as an example.

[0057] Figure 4 The following is a velocity error convergence diagram for 35 iterations of the method proposed in this invention, as shown in the example. Detailed Implementation

[0058] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading the present invention, any modifications of the present invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0059] like Figure 1 As shown, a distributed iterative learning control method for a robotic arm system based on relaxed alignment conditions includes the following steps:

[0060] Step 1: Set initial parameter values;

[0061] Step 2: Update algorithm parameters;

[0062] Step 3: Generate control input u in real time based on the updated algorithm parameters. j，k (t);

[0063] Step 4: Based on the control input u j，k The tracking error and compensation error generated by (t) are used to synchronously update the algorithm parameters;

[0064] Step 5: Repeat steps 3 and 4 until the current iteration ends and the next iteration begins;

[0065] Step Six: An embodiment of the present invention is described below:

[0066] Consider the fault-tolerant iterative learning control problem of a robotic arm system based on a balance factor. The corresponding mathematical model is as follows:

[0067]

[0068] The system parameters are as follows:

[0069] x 1,j,k x 2，j，k Let D represent the joint position and joint velocity of the j-th robotic arm, respectively. j，k Let C represent the inertia matrix. j，k G represents the centripetal Coriolis matrix. j，k F represents the gravity vector. j，k Indicates a disturbance. This indicates a controller with input saturation, where k represents the number of system iterations;

[0070] The desired reference orbit is: x1，r,k (t)=[2sin(t)+0.05cos(k); 3cos(t)+0.01cos(k)]; The expected running time T of the system is 2πs;

[0071] Figure 1 This is a flowchart of a method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of a robotic arm system according to an embodiment of the present invention; applying the proposed method, Figure 3 , 4 The figures show the position and velocity error convergence graphs after 35 iterations of the proposed method. These two figures demonstrate that the proposed method performs well in robotic arm systems, achieving satisfactory tracking performance after the 10th iteration.

[0072] References

[0073] [1]D.Shen, JX.Xu.Distributed learning consensus for heterogenoushigh-order nonlinear multi-agent systems with output constraints.Automatica, vol.97, pp.64-72, 2018.

[0074] [2]

Claims

1. A distributed iterative learning control method for a robotic arm system based on relaxed alignment conditions, characterized in that, Includes the following steps: Design an auxiliary system with relaxed alignment conditions and input saturation compensation, constructing backstepping error, a virtual controller, and error compensation, specifically as follows: ， In the formula, Indicates the number of system iterations. and These represent the modified reference track and the reference track, respectively. and Let each represent a modifying function that satisfies the following requirements: ， In the formula Indicates the length of the modifier and satisfies , The duration of each iteration; The design of an auxiliary system to compensate for input saturation is shown below: ， In the formula, and Indicates the known state of the auxiliary system. and This indicates the feedback gain that needs to be designed. Indicates the first Can a robotic arm obtain information from a reference track? Indicates the first The relative degrees of the robotic arms This represents the difference between the saturated input and the actual input. Design an iterative learning controller to control the robotic arm system and compensate for unknown inertia matrices, parameter uncertainties, and disturbances, specifically: ， ， ， In the formula, and Indicates the backstepping error. and Indicates compensation error. Indicates a virtual controller. This indicates saturation constraints on the upper and lower bounds of the parameter. and This indicates the learning gain that needs to be designed. Denotes a convergent series sequence, where , ; Construct a composite energy function to analyze the convergence of the error system.

2. The distributed iterative learning control method for a robotic arm system based on relaxed alignment conditions according to claim 1, characterized in that, The specific steps for constructing the backstepping error, compensation error, and virtual controller are as follows: Consider the following with A system with a robotic arm: ， In the formula, and They represent the first The joint positions and joint velocities of a robotic arm. Represents the inertia matrix. Represents a centripetal Coriolis matrix. Represents the gravity vector. Indicates a disturbance. This indicates a controller with input saturation; The backstep error is constructed as follows: ， In the formula, Indicates the first Can the robotic arm start from the first...? The robotic arm obtains information. The virtual controller is represented as follows: ， The error compensation is constructed in the following form: 。 3. The distributed iterative learning control method for a robotic arm system based on relaxed alignment conditions according to claim 1, characterized in that, The specific steps for constructing a composite energy function to analyze the convergence of the error system are as follows: B001: Define the Lyapunov function for subsystem 1: ， B002: Yes Differentiate: ， B003: Define the Lyapunov function for subsystem 2: ， B004: Yes Differentiate: ， B005: Select the following form of composite energy function: ， ， ， ， ， B006: In the formula, , ; B007: Considering the first Next and first Second room difference ,in: ， ， ， B008: Based on B007, the following formula can be obtained: ， ， B009: Further, give and Proof of boundedness: ， ， B010: Based on B008 and B009, the following formula can be obtained: ， B011: Based on B010, the convergence form of the compensation error can be obtained as follows: ， 。

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