Robot stable tracking control method in large turbulent flow environment based on learning

Abstract

The invention belongs to the technical field of robots, and relates to a learning-based stable tracking control method for a robot in a large turbulent flow environment. According to the method, a learning-based stable control strategy is provided for uncertainty in the turbulent flow environment, structural transformation of the strategy is achieved through tolerance errors, and the adaptability of the robot in the complex and changeable turbulent flow environment is improved. Compared with the prior art, the robustness of the trajectory tracking control strategy of the underwater robot can be improved, and the practical engineering application value can be improved due to the combination of the strategy and the sensing data.

Description

Technical Field

[0001] The invention belongs to the technical field of robots and relates to a stable tracking control method of a robot in a large disturbance environment based on learning. Background Art

[0002] Underwater robots have broad application prospects in the fields of marine resource exploration, underwater engineering applications, naval battlefield monitoring, and underwater precision guidance. Most underwater robots require the end effector to contact the underwater object or environment. Especially in the turbulent environment, the trajectory tracking control of underwater robots is still challenging in the presence of highly nonlinear dynamics and unknown hydrodynamic effects. However, facing the complex turbulent environment, remote control operation requires high operating skills and experience, and there are certain limitations. In comparison, stable tracking technology can not only enable the robot to move accurately along the predetermined trajectory, but also make autonomous adjustments according to environmental changes, which will greatly improve the robot's work efficiency in dynamic turbulent environments.

[0003] Nowadays, many research methods have made certain progress in the stable tracking control of underwater robots. On the one hand, for robots in simple environments or simple structures, the environment in which the robot is located can be accurately described based on traditional physical modeling methods, which can more accurately predict the robot's movement and environmental changes. In particular, physical modeling can be integrated with sensor data, such as underwater sonar, underwater cameras, etc., to further optimize the robot's control strategy. On the other hand, for complex underwater operating environments, data-driven modeling methods make up for the defects of physical modeling difficulties. By building models with a large amount of measured data, robots can adapt to various complex underwater environments more flexibly and handle nonlinear, irregular underwater motion and environmental changes. In addition, data-driven modeling methods can be trained offline on large-scale data sets and predict and reason when underwater robots are running. In order to improve the adaptability of robots in turbulent environments, the efficiency and accuracy of tracking control can be improved by imitating the morphology, movement mechanism and behavior of marine organisms. The improvements in these methods provide new ideas and methods for improving the precise control of underwater robots.

[0004] However, the robot control system in a turbulent environment is quite complex and has multiple strong constraints, including the complexity of the mathematical model, the difficulty of controlling the end effector, and the disturbance of the water flow. When designing a control scheme, a series of problems may be faced: the environment may be unknown, the system may be subject to unknown but bounded external disturbances, and sensor measurements are not always accurate. Some studies may also be limited by environmental conditions, task requirements, and target factors, and are only effective in specific scenarios. Especially in a dynamic turbulent environment, the convergence time of the control strategy is not ideal, and even the convergence of the system is difficult to guarantee. These problems may cause the system to exhibit unpredictable instability, and we must consider these constraints when designing the controller. Moreover, the external turbulence causes the rapid degradation of the controller performance, which exacerbates the complexity of the operation task. Therefore, the tracking control of underwater robots is still challenging in the presence of highly nonlinear dynamics and unknown hydrodynamic effects.

[0005] Patent CN112286227B proposes an underwater robot trajectory control method and system based on a differential tracker and a disturbance observer. By constructing an underwater robot dynamics model and a robot disturbance observer, an underwater robot trajectory tracking controller and an underwater robot position controller are obtained, thereby realizing underwater robot trajectory control.

[0006] Patent CN111240345A realizes underwater robot trajectory tracking based on a dual BP network reinforcement learning framework. The reinforcement learning method can be used to combine reinforcement learning with the dual BP network through continuous interaction with the environment to adjust the speed and heading of the underwater robot online.

[0007] Patent CN110209152B provides a deep reinforcement learning control method for vertical path following of an intelligent underwater robot. In view of the complex and changeable marine environment in which the intelligent underwater robot is located, the traditional control method cannot actively interact with the environment. A deterministic policy gradient is used to complete the path following control task of the intelligent underwater robot through a distributed method.

[0008] Patent CN107102644B proposes an underwater robot trajectory control method and control system based on deep reinforcement learning, which obtains the current state of the underwater robot and the target state of the next moment, and then inputs them into the decision neural network finally learned in the learning stage. The decision neural network calculates the propulsion force required by the underwater robot at the current moment.

[0009] In the prior art, methods based on physical modeling usually require complex modeling and solving of the environment, which may require a lot of computing resources and time. Even physical modeling may not be able to fully capture the complexity and uncertainty of the turbulent environment. The trajectory tracking control of the underwater robot is realized based on the combination of offline learning (such as neural networks, etc.) and compensation controllers. The size of the compensation effect is difficult to calculate accurately, and even the real-time performance is difficult to guarantee. At the same time, due to the large error of the robot's state information in the turbulent environment, the training process may face the problem of falling into local optimality or insufficient learning ability. Summary of the invention

[0010] The present invention aims to propose a learning-based stable tracking control strategy to improve the robustness of tracking control of underwater robots in turbulent environments. With the assistance of visual monitoring, the present invention directly designs strategies based on state errors (including tracking errors and turbulent errors) and handles uncertainties in turbulent environments in a learning-based manner. The design of tracking control strategies is achieved by analyzing the state errors in turbulent environments. It should be noted that the present invention directly models the tracking system with state errors, which enables the model to quickly adapt to new data and situations in a changing environment without retraining the overall model. This flexibility enables the model to capture changes in the environment in a timely manner, thereby improving the convergence and stability of the control strategy.

[0011] The technical solution of the present invention:

[0012] The stable tracking control method of the robot in a large disturbance environment based on learning, the specific steps are as follows:

[0013] Step 1: Collect demonstration data; collect the running trajectory of the robot end effector in the Cartesian coordinate system by manually dragging, including the actual trajectory and the expected trajectory;

[0014] Step 1.1 Expected trajectory

[0015] The robot's expected trajectory state in three-dimensional spaceΞ r (t) is given by the expected position ξ r (t) and the desired angle θ r (t) composition, i.e. Ξ r (t) = [ξ r (t),θ r (t)] T ,at this time

[0016] ξ r (t) = [ξ xr (t),ξ yr (t),ξ zr (t)] T (1)

[0017] θr (t) = [θ xr (t),θ yr (t),θ zr (t)] T (2)

[0018] Where t represents the running time index, the subscripts x, y and z are the symbols of the X-axis, Y-axis and Z-axis respectively, and the subscript r represents the desired state of the robot, that is, ξ xr (t),ξ yr (t) and ξ zr (t) represents the desired position of the robot’s end effector on the X-axis, Y-axis, and Z-axis, respectively, and θ xr (t),θ yr (t) and θ zr (t) represents the desired angles of the robot's end effector on the X-axis, Y-axis, and Z-axis, respectively. The superscript T represents the matrix transpose. The velocity state of the robot's desired trajectory state in three-dimensional space is expressed as represents the expected speed of the robot at time t, represents the expected angular velocity of the robot at time t;

[0019] Step 1.2 Actual trajectory

[0020] The actual trajectory state Ξ(t) of the robot in three-dimensional space consists of the actual position state ξ(t) and the actual angle state θ(t), that is, Ξ(t) = [ξ(t), θ(t)] T ,at this time

[0021] ξ(t)=[ξ x (t),ξ y (t),ξ z (t)] T (3)

[0022] θ(t)=[θ x (t),θ y (t),θ z (t)] T (4)

[0023] In the formula, ξ x (t),ξ y (t) and ξ z (t) represents the actual position of the robot’s end effector on the X-axis, Y-axis, and Z-axis, respectively, and θ x (t),θ y (t) and θ z (t) represents the actual angle of the robot's end effector on the X-axis, Y-axis and Z-axis respectively; at this time, the actual speed state of the robot in three-dimensional space is expressed as represents the velocity state corresponding to ξ(t) at time t, represents the angular velocity state corresponding to θ(t) at time t;

[0024] Step 1.3 Error between actual trajectory and expected trajectory

[0025] The tracking error and the disturbance error are unified as the state error e(t), satisfying the relationship

[0026] e(t)=Ξ r (t)-Ξ(t) (5)

[0027] At this time, the first-order derivative of the state error is the speed error Expressed as

[0028]

[0029] Design an appropriate strategy to calculate the velocity correction value; calculate the velocity error from the state error e(t) Get the corrected state of the robot at the next moment; the speed error e.(t) is designed to be

[0030]

[0031] Among them, F(·) is an unknown relationship, which represents the control strategy. At this time, the state after control at time t+1 is called the modified state Ξ(t+1), which is calculated as

[0032]

[0033] Where Ξ(t) represents the actual state of the robot's end effector at time t, Δt represents the time difference between two times t and t+1, Indicates the actual speed state of the robot's end effector at time t;

[0034] Step 2: Control strategy design; design of trajectory tracking control strategy based on incremental extreme learning machine IELM, that is, the design of unknown relation F(·); use Lyapunov function to derive the constraint conditions of strategy training, in order to ensure the stability of robot control system;

[0035] Step 2.1: Strategy structure; Assuming that an IELM model with L-1 hidden nodes is constructed, the unknown relationship F(·) between the state error and the speed error is calculated as

[0036]

[0037] Among them, the speed error represents the output of the control strategy, which has L-1 hidden nodes. The superscript T is the transpose, l=1,2,...,L-1 represents the number of hidden nodes. is the output weight of hidden layer node l, and denote the input weights and biases of the randomly configured hidden layer nodes l, respectively, φ is a continuous and differentiable activation function with

[0038]

[0039] in, is the first-order derivative of the activation function;

[0040] The activation function is as follows

[0041]

[0042] Suppose the output of the newly added hidden layer node L is for

[0043]

[0044] In the formula, the input weight of the newly added hidden layer node is and deviation All are randomly generated in [0,1];

[0045] At this time, the learning error of the control strategy Expressed as

[0046]

[0047] In the formula, Represents the expected output value of the control strategy;

[0048] In the process of dynamic increment of hidden layer nodes, in order to improve the speed of model training, it is only necessary to calculate the output weight of the newly added hidden layer node L without updating all the parameters of the network; that is, the output weight Calculated as

[0049]

[0050] Step 2.2: Constraints for parameter training; constructing the Lyapunov function

[0051]

[0052] at this time, The derivative of is written as

[0053]

[0054] in,

[0055]

[0056] here

[0057]

[0058] in but

[0059]

[0060] According to the mean value theorem, if or have

[0061]

[0062] at this time

[0063]

[0064] Since φ(0)=0 in formula (10), we have

[0065]

[0066] Given b l =0, if Established, required

[0067]

[0068] Here φ′(s l )>0, but

[0069]

[0070] Combined with steps 2.1 and 2.2, the state error between the actual trajectory and the desired trajectory obtained in step 1.3 is used as the input of the control strategy, and the speed error is used as the output of the strategy; the constraint condition for the global asymptotic stability of the system is

[0071]

[0072] in, Indicates the state error of the collected demonstration data, represents the speed error corresponding to the state error, N represents the number of data points for demonstration, and < represents semi-negative definite;

[0073] At this time, the robot's corrected state at time t+1 Satisfaction relationship

[0074] Ξ(t+1)=Ψ(F(e(t))) (26)

[0075] In the formula, m represents the state dimension of the robot’s end effector, Ψ(·) represents formulas (1)-(9), which is called the state transition process;

[0076] Step 3: Visual inspection;

[0077] Step 3.1: Complete the visual calibration of the depth camera and the robot, obtain the internal and external parameter matrix of the camera, and then obtain the camera space and robot space transformation matrix G;

[0078] Step 3.2: Fix the ARUCO code to the end of the robot's mechanical arm and use OpenCV to implement visual detection; the detected position is used as the robot's real-time position Ξ(t);

[0079] Step 4: Collect the discrete points of the desired trajectory through human-machine teaching, and generate the desired trajectory Ξ using spline interpolation r (t), combine step 3.2 and formula (5) to calculate the state error e(t);

[0080] Step 5: Transplant the control strategy trained in step 2 into the robot to realize the tracking control of the robot to the new desired trajectory.

[0081] Beneficial effects of the invention: The invention proposes a learning-based stable control strategy for the uncertainty in the disturbance environment, realizes the structural transformation of the strategy by tolerating errors, and improves the adaptability of the robot in the complex and changeable disturbance environment. Compared with the prior art, the invention can not only improve the robustness of the underwater robot trajectory tracking control strategy, but also improve the actual engineering application value due to the combination of the strategy and sensor data. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 It is a framework diagram of the method of the present invention.

[0083] Figure 2 It is the expected trajectory and teaching trajectory collected through the human-machine teaching method.

[0084] Figure 3 is the visual inspection result.

[0085] Figure 4 It is the newly generated teaching trajectory.

[0086] Figure 5 is an experimental result diagram of the embodiment, i.e., the running trajectory of the Magician robot. DETAILED DESCRIPTION

[0087] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0088] The robot stable tracking control method in a large disturbance environment based on learning of the present invention comprises:

[0089] Step 1: Collect the expected trajectory and the teaching trajectory;

[0090] Step 2: Train the control strategy and obtain the strategy parameters.

[0091] Step 3: Perform visual calibration to obtain the real-time position of the robot.

[0092] Step 4: Given a new desired trajectory.

[0093] Step 5: Physical testing.

[0094] The specific steps are as follows:

[0095] Step 1: Collect demonstration data. Collect the running trajectory of the robot end effector in the Cartesian coordinate system by manually dragging, including the actual trajectory and the expected trajectory.

[0096] Step 1.1 Expected trajectory

[0097] The expected trajectory state of the robot in three-dimensional spaceΞ r (t) is given by the expected position ξ r (t) and the desired angle θ r (t) composition, i.e. Ξ r (t) = [ξ r (t),θ r (t)] T ,at this time

[0098] ξ r (t) = [ξ xr (t),ξ yr (t),ξ zr (t)] T (27)

[0099] θ r (t) = [θ xr (t),θ yr (t),θ zr (t)] T (28)

[0100] Where t represents the running time index, the subscripts x, y and z are the symbols of the X-axis, Y-axis and Z-axis respectively, and the subscript r represents the desired state of the robot, that is, ξ xr (t),ξ yr (t) and ξ zr (t) represents the desired position of the robot’s end effector on the X-axis, Y-axis, and Z-axis, respectively, and θ xr (t),θ yr(t) and θ zr (t) represents the desired angles of the robot's end effector on the X-axis, Y-axis, and Z-axis, respectively, and the superscript T represents the matrix transpose. It should be noted that the robot's operating state (position and velocity, angle and angular velocity) is continuous and differentiable because the problem comes from the actual physical system. At this time, the rate of change of the robot's desired trajectory state in three-dimensional space (velocity state) is expressed as represents the expected speed of the robot at time t, represents the expected angular velocity of the robot at time t.

[0101] Step 1.2 Actual trajectory

[0102] The actual trajectory state Ξ(t) of the robot in three-dimensional space consists of the actual position state ξ(t) and the actual angle state θ(t), that is, Ξ(t) = [ξ(t), θ(t)] T ,at this time

[0103] ξ(t)=[ξ x (t),ξ y (t),ξ z (t)] T (29)

[0104] θ(t)=[θ x (t),θ y (t),θ z (t)] T (30)

[0105] In the formula, ξ x (t),ξ y (t) and ξ z (t) represents the actual position of the robot’s end effector on the X-axis, Y-axis, and Z-axis, respectively, and θ x (t),θ y (t) and θ z (t) represents the actual angle of the robot's end effector on the X-axis, Y-axis, and Z-axis respectively. At this time, the actual velocity state of the robot in three-dimensional space is expressed as represents the velocity state corresponding to ξ(t) at time t, represents the angular velocity state of θ(t) at time t.

[0106] Step 1.3 Error between actual trajectory and expected trajectory

[0107] The tracking error and the disturbance error are unified as the state error e(t), satisfying the relationship

[0108] e(t)=Ξ r(t)-Ξ(t) (31)

[0109] At this time, the first-order derivative of the state error is the speed error Expressed as

[0110]

[0111] In the control process, in order to achieve real-time and stable trajectory tracking, when the position error converges to 0, the speed error should also converge to 0. In other words, the goal of the trajectory tracking problem is to design an appropriate control law to minimize the error at each moment. In order to achieve the running speed consistent with the expected speed, the speed error e.(t) can be said to be a control strategy. That is, the present invention needs to design an appropriate strategy to calculate the speed correction value. The speed error is calculated by the state error e(t). Get the corrected state of the robot at the next moment. Speed ​​Error Can be designed as

[0112]

[0113] Among them, F(·) is an unknown relationship, which represents the control strategy. At this time, the state after control (at time t+1) is called the modified state Ξ(t+1), which is calculated as

[0114]

[0115] Where Ξ(t) represents the actual state of the robot's end effector at time t, Δt represents the time difference between two times (t and t+1), Represents the actual velocity state (including angular velocity) of the robot's end effector at time t.

[0116] Step 2: Control strategy design. The trajectory tracking control strategy is designed based on the incremental extreme learning machine (IELM), that is, the unknown relationship F(·) is designed; the constraints of the strategy training are derived using the Lyapunov function to ensure the stability of the robot control system.

[0117] Step 2.1: Strategy structure. Assuming that an IELM model with L-1 hidden nodes is constructed, the unknown relationship F(·) between the state error and the speed error can be calculated as

[0118]

[0119] Among them, the speed error represents the output of the control strategy (with L-1 hidden nodes), with the superscript Tis the transpose, l=1,2,...,L-1 represents the number of hidden layer nodes, is the output weight of hidden layer node l, and denote the input weights and biases of the randomly configured hidden layer nodes l, respectively, φ is a continuous and differentiable activation function with

[0120]

[0121] in, is the first-order derivative of the activation function.

[0122] The selection of activation function is diverse, and different activation functions have different fitting effects. The present invention selects the activation function as follows

[0123]

[0124] Suppose the output of the newly added hidden layer node L is for

[0125]

[0126] In the formula, the input weight of the newly added hidden layer node is and deviation They are all randomly generated in [0,1].

[0127] At this time, the learning error of the control strategy Expressed as

[0128]

[0129] In the formula, Represents the expected output value of the control strategy.

[0130] In the process of dynamic increment of hidden layer nodes, in order to improve the speed of model training, the present invention only needs to calculate the output weight of the newly added hidden layer node L, without updating all the parameters of the network. Calculated as

[0131]

[0132] Step 2.2: Constraints for parameter training. Constructing the Lyapunov function

[0133]

[0134] at this time, The derivative of is written as

[0135]

[0136] in,

[0137]

[0138] here

[0139]

[0140] in but

[0141]

[0142] According to the mean value theorem, if or have

[0143]

[0144] at this time

[0145]

[0146] Since φ(0)=0 in formula (10), we have

[0147]

[0148] Given b l =0, if Established, required

[0149]

[0150] Here φ′(s l )>0, but

[0151]

[0152] Combined with steps 2.1 and 2.2, the state error between the actual trajectory and the desired trajectory obtained in step 1.3 is used as the input of the control strategy, and the velocity error is used as the output of the strategy. The constraint condition for the global asymptotic stability of the system is

[0153]

[0154] in, Indicates the state error of the collected demonstration data, It represents the speed error corresponding to the state error, N represents the number of data points for demonstration, and < represents semi-negative definite.

[0155] For the above optimization problems, optimization toolboxes of different software can be used to solve them.

[0156] At this time, the robot's corrected state at time t+1 Satisfaction relationship

[0157] Ξ(t+1)=Ψ(F(e(t))) (52)

[0158] Where m represents the state dimension of the robot’s end effector, and Ψ(·) represents formulas (1)-(9), which is called the state transition process.

[0159] Step 3: Visual inspection.

[0160] Step 3.1: Complete the visual calibration of the depth camera and the robot, obtain the camera's internal and external parameter matrices, and then obtain the camera space and robot space transformation matrix G.

[0161] Step 3.2: Fix the ARUCO code to the end of the robot’s mechanical arm and use OpenCV to implement visual detection; the detected position is used as the robot’s real-time position Ξ(t).

[0162] Step 4: Collect the discrete points of the desired trajectory through human-machine teaching, and generate the desired trajectory Ξ using spline interpolation r (t), combine step 3.2 and formula (5) to calculate the state error e(t).

[0163] Step 5: Transplant the control strategy trained in step 2 into the robot to realize the tracking control of the robot to the new desired trajectory.

[0164] The present invention focuses on analyzing the robustness of robot trajectory tracking, that is, the focus on the real-time trajectory deviation and recovery of the robot. The actual situation is that there are many types of robots, and different types of robots have different characteristics. In order to evaluate the performance of the proposed control strategy, the present invention must select a robot that is susceptible to external environmental disturbances. Relatively speaking, the Magician robot has the characteristics of miniaturization, limited load capacity, low rigidity and poor precision, and is easily affected by the external environment during movement. Therefore, this embodiment uses a small Magician robot to verify the anti-interference ability of the proposed control strategy.

[0165] In the experimental setup, different forms of real disturbances are used to test the robustness of the robot during trajectory tracking. Figure 2As shown in the figure, three forms of external disturbances are designed during the robot's trajectory tracking process. Disturbance 1 is to drag the robot in a direction away from the desired trajectory. Disturbance 2 is to give the robot forward resistance, making it difficult to move forward. Disturbance 3 is to drag the robot in the opposite direction, making it away from the end point. In this way, the three disturbance methods can vividly simulate the water flow disturbance of the robot in different directions or at different angles. In other words, in reality, different forms of interference are applied to the trajectory tracking performed by the Magician robot as a means to test the robustness of the proposed control strategy. The original intention of this design is also to allow the robot to withstand complex and changeable external influences, so as to more comprehensively test the stability of the proposed control strategy.

[0166] Obviously, different forms of external disturbances will have different degrees of impact on the robot. The present invention uses a visual monitoring method to obtain the real-time trajectory of the robot. In this way, it can not only test the theoretical advancement of the control strategy, but more importantly, it provides a testing platform in actual application scenarios. This can also evaluate the practical value of the present invention in a real environment.

[0167] The experimental results are as follows Figure 2 As shown in the figure, the dotted line represents the expected trajectory and the solid line represents the real-time trajectory. The figure shows the real-time running status of the Magician robot. It can be seen that when the robot is subjected to external disturbances, it is in a state of continuous shaking. Facts show that once the tracking trajectory deviates, the robot will correct in the direction of the expected trajectory due to the existence of the control strategy. In other words, the proposed control strategy has a certain resistance to actual external disturbances.

[0168] In summary, the small Magician robot is subjected to external disturbances by actual interference, which causes deviations in the robot. The robot can correct its state under external disturbances and eliminate actual deviations according to the control strategy proposed by the present invention. The effectiveness of the control strategy is proved through the design and verification of the control strategy.

Claims

1. A learning-based robot stable tracking control method in a large disturbance environment, characterized in that: The specific steps are as follows: Step 1: Collect demonstration data; collect the running trajectory of the robot end effector in the Cartesian coordinate system by manually dragging, including the actual trajectory and the expected trajectory; Step 1.1 Expected trajectory The expected trajectory state of the robot in three-dimensional spaceΞ r (t) is given by the expected position ξ r (t) and the desired angle θ r (t) composition, i.e. Ξ r (t) = [ξ r (t),θ r (t)] T ,at this time x r (t)=[ξ xr (t),ξ yr (t),ξ zr (t)] T (1) i r (t)=[θ xr (t),θ yr (t),θ zr (t)] T (2) Where t represents the running time index, the subscripts x, y and z are the symbols of the X-axis, Y-axis and Z-axis respectively, and the subscript r represents the desired state of the robot, that is, ξ xr (t),ξ yr (t) and ξ zr (t) represents the desired position of the robot’s end effector on the X-axis, Y-axis, and Z-axis, respectively, and θ xr (t),θ yr (t) and θ zr (t) represents the desired angles of the robot's end effector on the X-axis, Y-axis, and Z-axis, respectively. The superscript T represents the matrix transpose. The velocity state of the robot's desired trajectory state in three-dimensional space is expressed as represents the expected speed of the robot at time t, represents the expected angular velocity of the robot at time t; Step 1.2 Actual trajectory The actual trajectory state Ξ(t) of the robot in three-dimensional space consists of the actual position state ξ(t) and the actual angle state θ(t), that is, Ξ(t) = [ξ(t), θ(t)] T ,at this time ξ(t)=[ξ x (t),ξ y (t),ξ z (t)] T (3) θ(t)=[θ x (t),θ y (t),θ z (t)] T (4) In the formula, ξ x (t),ξ y (t) and ξ z (t) represents the actual position of the robot’s end effector on the X-axis, Y-axis, and Z-axis, respectively, and θ x (t),θ y (t) and θ z (t) represents the actual angle of the robot's end effector on the X-axis, Y-axis and Z-axis respectively; at this time, the actual speed state of the robot in three-dimensional space is expressed as represents the velocity state corresponding to ξ(t) at time t, represents the angular velocity state corresponding to θ(t) at time t; Step 1.3 Error between actual trajectory and expected trajectory The tracking error and the disturbance error are unified as the state error e(t), satisfying the relationship e(t)=Ξ r (t)-Ξ(t) (5) At this time, the first-order derivative of the state error is the speed error Expressed as Design an appropriate strategy to calculate the velocity correction value; calculate the velocity error from the state error e(t) Get the robot's corrected state at the next moment; speed error Designed for Among them, F(·) is an unknown relationship, which represents the control strategy. At this time, the state after control at time t+1 is called the modified state Ξ(t+1), which is calculated as Where Ξ(t) represents the actual state of the robot's end effector at time t, Δt represents the time difference between two times t and t+1, Indicates the actual speed state of the robot's end effector at time t; Step 2: Control strategy design; design of trajectory tracking control strategy based on incremental extreme learning machine IELM, that is, the design of unknown relation F(·); use Lyapunov function to derive the constraint conditions of strategy training, in order to ensure the stability of robot control system; Step 2.1: Strategy structure; Assuming that an IELM model with L-1 hidden nodes is constructed, the unknown relationship F(·) between the state error and the speed error is calculated as Among them, the speed error represents the output of the control strategy, which has L-1 hidden nodes. The superscript T is the transpose, l=1,2,...,L-1 represents the number of hidden nodes. is the output weight of hidden layer node l, and denote the input weights and biases of the randomly configured hidden layer nodes l, respectively, φ is a continuous and differentiable activation function with in, is the first-order derivative of the activation function; The activation function is as follows Suppose the output of the newly added hidden layer node L is for In the formula, the input weight of the newly added hidden layer node is and deviation All are randomly generated in [0,1]; At this time, the learning error of the control strategy Expressed as In the formula, Represents the expected output value of the control strategy; In the process of dynamic increment of hidden layer nodes, in order to improve the speed of model training, it is only necessary to calculate the output weight of the newly added hidden layer node L without updating all the parameters of the network; that is, the output weight Calculated as Step 2.2: Constraints for parameter training; constructing the Lyapunov function at this time, The derivative of is written as in, here in but According to the mean value theorem, if or have at this time Since φ(0)=0 in formula (10), we have Given b l =0, if Established, required Here φ′(s l )>0, but Combined with steps 2.1 and 2.2, the state error between the actual trajectory and the desired trajectory obtained in step 1.3 is used as the input of the control strategy, and the speed error is used as the output of the strategy; the constraint condition for the global asymptotic stability of the system is in, Indicates the state error of the collected demonstration data, represents the speed error corresponding to the state error, N represents the number of data points for demonstration, and < represents semi-negative definite; At this time, the robot's corrected state at time t+1 Satisfaction relationship Ξ(t+1)=Ψ(F(e(t))) (26) In the formula, m represents the state dimension of the robot’s end effector, Ψ(·) represents formulas (1)-(9), which is called the state transition process; Step 3: Visual inspection; Step 3.1: Complete the visual calibration of the depth camera and the robot, obtain the camera's internal and external parameter matrices, and then obtain the camera space and robot space transformation matrix G; Step 3.2: Fix the ARUCO code to the end of the robot's mechanical arm and use OpenCV to implement visual detection; the detected position is used as the robot's real-time position Ξ(t); Step 4: Collect the discrete points of the desired trajectory through human-machine teaching, and generate the desired trajectory Ξ using spline interpolation r (t), combine step 3.2 and formula (5) to calculate the state error e(t); Step 5: Transplant the control strategy trained in step 2 into the robot to realize the tracking control of the robot to the new desired trajectory.

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