An error compensation method and control system based on time delay estimation

Abstract

This invention relates to an error compensation method and control system based on time delay estimation. The time delay estimation error compensation method combines a gradient compensator and a disturbance observer. The gradient compensator compensates for the fast time-varying portion of the time delay estimation error, while the disturbance observer compensates for the slow time-varying portion. After time delay estimation error compensation, the controller exhibits significantly improved resistance to load and disturbance variations, as well as enhanced trajectory tracking performance. This embedded control system operates on a bare-metal microcontroller environment, providing robust performance for the deployment and execution of the control algorithm. It communicates with the host computer in real-time via LWIP TCP communication and controls the motor's real-time operation via a CAN bus architecture. The lightweight embedded system reduces algorithm deployment costs and provides a reliable development framework for robotic arm trajectory tracking methods.

Description

Technical Field

[0001] This invention relates to the field of robot system control technology, and in particular to a method and control system for tracking the trajectory of a robotic arm. Background Technology

[0002] Robotic arms are typical nonlinear systems, characterized by strong coupling and time-varying properties. During high-speed motion, the significant changes in inertia and substantial nonlinear effects can lead to large errors when using traditional servo closed-loop controllers. To achieve accurate tracking of high-precision trajectories, the robot's dynamic characteristics must be considered, and dynamic compensation methods must be employed to quickly achieve steady-state adjustments, thereby reducing output errors. Such a control strategy helps to more effectively handle the complex nonlinear behavior of the system, improving the robot's performance and accuracy during motion.

[0003] The higher the degrees of freedom of a robotic arm, the more complex its dynamic model becomes. Traditional robotic arm control algorithms based on dynamic models (such as torque calculation, sliding mode control, and fuzzy control) suffer from problems such as inaccurate nominal model estimation, high computational load, and poor real-time performance. To address these issues, a time-delay controller is proposed that eliminates the need for a priori dynamic model acquisition, offering advantages such as low computational load and low hardware requirements, making it widely popular among researchers both domestically and internationally. The core of the time-delay control algorithm lies in time-delay estimation technology, which uses the state variables from the previous moment to estimate the lumped dynamic quantities (inertia, centrifugal force, Coriolis force, gravity, friction, and the sum of external disturbances) at the current moment. While time-delay estimation simplifies the computation of the robotic arm's dynamic model, its inherent nature inevitably introduces the problem of time-delay estimation errors. Reducing these errors is a critical issue that time-delay controllers urgently need to address.

[0004] Common time delay estimation error compensation methods include robust control compensation strategies (sliding mode algorithm, H∞ algorithm, etc.), which utilize the robustness of the control algorithm to compensate for the time delay estimation error of the time delay controller. However, this method is only suitable for small-scale load and disturbance variations. For time-varying, large-scale load and disturbance variations, designing adaptive rates for the control gain is the mainstream approach. Adaptive control gains can adaptively compensate for rapidly changing time delay estimation errors. However, these adaptive rates either have overly complex parameters, making them unsuitable for practical deployment, or the controller's tracking accuracy is lower than that of a fixed-parameter control gain. To address these issues, there is an urgent need for a simple and reliable method that can improve both load and disturbance variation capabilities and controller trajectory tracking performance. Summary of the Invention

[0005] The purpose of this invention is to overcome the limitations of existing technologies, such as limited applicability to small load and disturbance variations and overly complex control parameters. It provides a time delay estimation error compensation method that helps the time delay controller adapt to a wide range of load and disturbance variations. Furthermore, it addresses the challenges of difficult and costly deployment of robotic arm control algorithms, providing a low-cost, lightweight embedded control system for deploying robotic arm control algorithms.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] As a first aspect of the present invention, an error compensation method based on time delay estimation is provided for trajectory tracking control of a multi-degree-of-freedom robotic arm, characterized in that the method includes the following steps:

[0008] The lumped unknown dynamic model of a multi-degree-of-freedom robotic arm is estimated using a time delay estimation method, and the time delay estimation error is obtained.

[0009] An estimation error compensator is used to compensate for the time delay estimation error of the time delay controller. The estimation error compensator includes:

[0010] Gradient compensator is used to compensate for the fast time-varying part of the time delay estimation error;

[0011] A perturbation observer is used to compensate for the slow time-varying part of the time delay estimation error.

[0012] As a preferred technical solution, the lumped unknown dynamic model estimated using the time delay estimation method is specifically represented as follows:

[0013]

[0014] in, τ is a positive definite diagonal matrix representing the control gain of the time-delay controller; t This represents the joint torque vector at the current time t; This indicates the time delay estimation error; Represents the lumped unknown dynamic model vector of the system; This represents the time delay estimation vector.

[0015] As a preferred technical solution, the lumped unknown dynamic model vector Specifically, it is expressed as follows:

[0016]

[0017] Where M(q) represents the inertia matrix, G(q) represents the centrifugal force and Coriolis force matrices, and G(q) represents the gravity vector. τ represents the frictional force vector. d This represents the lumped external disturbance vector.

[0018] As a preferred technical solution, the time delay estimation vector The specific calculations are as follows:

[0019]

[0020] Among them, vector q, These represent the position, velocity, and angular velocity of the joint, respectively; τ t-L and These are the torque and angular acceleration at the previous moment, respectively; The lumped unknown dynamics at time tL; when the time delay L is sufficiently small, Approaching time t This is a vector of time delay estimates.

[0021] As a preferred technical solution, the time delay controller including the estimation error compensator is specifically represented as follows:

[0022]

[0023] in, The desired acceleration vector; Represents the velocity error; μ1 = diag(μ 11 ,μ 12 ,...,μ 1n K is a diagonal matrix with constants; K = diag(K) 11 ,K 22 ,...,K nn ) is the diagonal robust gain matrix, and sgn(·) is the sign function; t The sliding mode vector; This is the estimated time delay value after compensation by the estimation error compensator. These are the gradient compensator and the perturbation observer, respectively.

[0024] As a preferred technical solution, the gradient compensator is represented as follows:

[0025]

[0026] Where η is the proportionality coefficient, 0 ≤ η < 1; This represents the estimated time delay after compensation by the gradient error compensator.

[0027] As a preferred technical solution, the disturbance observer for the time delay control is represented as follows:

[0028]

[0029] in, It is an estimate of the time delay estimation error; l > 0 is a positive constant; z is an auxiliary state variable, which has the following form:

[0030]

[0031] Where, τ t This represents the joint torque vector at the current time t; This represents a gradient compensator; This represents the estimated value of the time delay estimation error.

[0032] As a preferred technical solution, the remaining time delay estimation error after compensation by the estimation error compensator utilizes the approach rate of the controller. offset.

[0033] As a second aspect of the present invention, an embedded control system is provided for deploying a robotic arm control algorithm, the embedded control system comprising:

[0034] A calculation control unit is used to calculate and execute the error compensation method described above, wherein the calculation control unit includes a microcontroller;

[0035] The microcontroller communicates with the host computer in real time and controls the motor of the robotic arm in real time through CAN bus communication.

[0036] As a preferred technical solution, the system operation process includes the following steps:

[0037] Establish communication connections between the various components of the system and complete the initialization;

[0038] The microcontroller receives instructions from the host computer and executes the robotic arm control algorithm;

[0039] The microcontroller obtains and calculates the current parameters of the robotic arm motor from the robotic arm driver via bus communication;

[0040] The microcontroller sequentially calculates the system's time delay estimate, gradient compensator value, disturbance observer value, sliding mode surface value, and controller torque value, and obtains the controller output:

[0041] The microcontroller calculates the auxiliary state variables of the disturbance observer and updates the controller state;

[0042] The microcontroller sends torque values ​​to the motor driver of the robotic arm via CAN bus communication.

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

[0044] 1) The time delay estimation error compensation method proposed in this invention does not affect the structure of the time delay controller. The designed time delay error compensator uses a gradient compensator to compensate for the fast time-varying part of the time delay estimation error, improving the controller's load and disturbance variation range; the disturbance observer compensates for the slow time-varying part of the time delay estimation error, improving the controller's robustness. This can significantly reduce the estimation error generated by time delay estimation, allowing the time delay controller to adapt to a wide range of load and disturbance variations under a fixed control gain. Furthermore, this method can be applied to various forms of advanced time delay controllers, has a simple structure, and only requires setting the proportional coefficient and positive constant in the gradient compensator and disturbance observer to significantly improve the tracking accuracy and robustness of the original time delay controller.

[0045] 2) This invention provides a lightweight embedded control system that leverages the advantages of LWIP TCP communication—small memory footprint, high data processing efficiency, and strong real-time performance—to improve the real-time communication capability between the embedded control system and the host computer. By controlling the motor through a CAN bus architecture, the real-time control performance between the control system and the motor is enhanced. Its bare-metal environment operation provides greater performance requirements and better timing for the control algorithm. This system framework has strong versatility; in addition to the control algorithm proposed in this invention, it can also deploy various advanced dynamic control algorithms, reducing algorithm deployment costs and providing a reliable development framework for robotic arm trajectory tracking control algorithms. Attached Figure Description

[0046] Figure 1 This is a flowchart of the control algorithm for error compensation based on time delay estimation in this invention.

[0047] Figure 2 This is a schematic diagram of a motion platform system in one embodiment of the present invention;

[0048] Figure 3 This is a flowchart of the motion platform in one embodiment of the present invention;

[0049] Figure 4 This is a trajectory tracking effect diagram in one embodiment of the present invention;

[0050] Figure 5 This is a comparison diagram of trajectory tracking errors in one embodiment of the present invention;

[0051] Figure 6 This is a comparison chart of time delay estimation errors in one embodiment of the present invention. Detailed Implementation

[0052] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0053] Example 1

[0054] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0055] Example 1

[0056] This invention proposes an error compensation method based on time delay estimation to improve the trajectory tracking performance of a multi-degree-of-freedom robotic arm, comprising the following steps:

[0057]

[0058] Where, vector These represent the joint's position, velocity, and angular velocity, respectively. Represents the inertia matrix. Represents the matrices of centrifugal force and Coriolis force. Represents the gravity vector. Represents the friction force vector. Represents the lumped external disturbance vector. This represents the joint torque vector at the current time t.

[0059] Step 2: By introducing a positive definite diagonal matrix Equation (1) becomes:

[0060]

[0061] in, This represents the control gain of the delay controller. The vector representing the lumped unknown dynamic model of the system (sum of inertia, centrifugal force, Coriolis force, gravity, friction, and external disturbances):

[0062]

[0063] Step 3: Estimate the lumped unknown dynamic model using the time delay estimation method:

[0064]

[0065] Using the torque τ from the previous moment t-L and angular acceleration Calculate the lumped unknown dynamics at time tL When the time delay L is small enough Approaching time t This is a vector of time delay estimates.

[0066] Let the time delay estimation error be:

[0067]

[0068] Step 4: Substitute equation (5) into equation (2) to get:

[0069]

[0070] Step 5: The gradient compensator is designed as follows:

[0071]

[0072] Where η is the proportionality constant, 0 ≤ η < 1. This represents the estimated time delay after compensation by the gradient error compensator.

[0073] The system model after compensation by the gradient compensator is as follows:

[0074]

[0075] in, This represents the time delay estimation error after compensation by the gradient compensator.

[0076] Step 7: The disturbance observer based on time delay control is designed as follows:

[0077]

[0078] in, This is an estimate of the time delay estimation error. l > 0 is a positive constant. It is an auxiliary state variable, and its form is as follows:

[0079]

[0080] The estimated time delay after compensation by the perturbation observer is:

[0081]

[0082] Substituting equation (11) into equation (8), we get:

[0083]

[0084] in, To estimate the time delay error after compensation by the error compensator:

[0085]

[0086] The time delay estimation error compensator proposed in this invention is applicable in principle to various forms of time delay controllers. Here, a classic time delay controller is used to represent the time delay control part in the control framework.

[0087] Step 8: The sliding surface is:

[0088]

[0089] in, Let be the sliding mode vector. It is a diagonal matrix with positive constants. The position tracking error is defined as... speed error For e t The derivative with respect to time t. Let be the desired position vector. Let be the desired acceleration vector.

[0090] Step 9: Design a time delay controller that includes a compensator:

[0091]

[0092] in, It is the diagonal robust gain matrix, and sgn(·) is the sign function.

[0093] Substituting equation (15) into equation (12) yields:

[0094]

[0095] The remaining time delay estimation error is utilized using the controller's approximation rate. offset.

[0096] Stability analysis is performed on the compensator and the time delay controller with the compensator applied.

[0097] Differentiating equation (13) with respect to time t and substituting it into equations (8), (9), and (10), we get:

[0098]

[0099] For any chosen positive definite matrix Q O There always exists a positive definite matrix of the form P O Satisfy the following formula:

[0100] l T P O +P O l = -Q O (18)

[0101] The Lyapunov equation is defined as follows:

[0102]

[0103] Differentiating the Lyapunov function with respect to time t:

[0104]

[0105] Substituting equation (18) into equation (20), we get:

[0106]

[0107] Assume that the time delay estimation error and its reciprocal have bounded edges.

[0108]

[0109] Where ||·|| is the 2-norm. Let λ min (Q O ) for Q O The smallest eigenvalue, λ min (Q O ) > 0.

[0110]

[0111] When the compensated time delay estimation error satisfies hour, The compensator is bounded and stable. A stability analysis is performed on the time-delay controller with the compensator applied.

[0112] The Lyapunov equation is defined as follows:

[0113]

[0114] Differentiating the Lyapunov equation with respect to time t yields:

[0115]

[0116] in,

[0117] Time delay estimation error after compensation by the compensator Bounded, assumption For a positive definite matrix, when the robust gain hour, The system asymptotically converges to the equilibrium point.

[0118] The time delay estimation error compensation method proposed in this invention does not affect the structure of the time delay controller and can be applied to various forms of advanced time delay controllers. Furthermore, its structure is simple, requiring only the setting of two parameters, which can significantly improve the tracking accuracy and robustness of the original time delay controller.

[0119] Example 2

[0120] To address the challenges of deploying dynamic control algorithms and the high testing costs, this invention also provides a lightweight embedded control system for deploying robotic arm control algorithms, as well as an error compensation method based on time delay estimation as described in the above embodiments.

[0121] An embedded control system deployed in a bare-metal environment based on the STM32H7 microcontroller utilizes Lightweight Web Interface (LWIP) TCP communication for real-time communication with the host computer, controls motor operation in real-time via CAN bus communication, and leverages the floating-point processing unit (FPU) of the STM32H7 chip to accelerate the calculation of the control algorithm. Its operation includes the following steps:

[0122] Step 1: Initialize the embedded system peripheral drivers (clock, serial port, GPIO, CAN, FMC, ETH, timer, FPU, etc.);

[0123] Step 2: The embedded TCP client establishes a communication connection with the host computer server;

[0124] Step 3: Initialize the parameters of the control algorithm;

[0125] Step 4: When the timer reaches the control step size, the main loop is entered once;

[0126] Step 5: Send the following commands to the motor driver sequentially via CAN communication: search for motor, enable motor, and return motor to zero.

[0127] Step 6: When the microcontroller receives the instruction from the host computer via serial port interrupt, the motor is set to torque working mode and the control algorithm is executed.

[0128] Step 7: Calculate the current reference trajectory, reference velocity, and reference acceleration;

[0129] Step 8: Obtain and calculate the current position, speed, acceleration, and current data of the motor from the driver via CAN communication;

[0130] Step 9: Calculate the controller output:

[0131] a) Calculate the estimated time delay using formula (4);

[0132] b) Calculate the gradient compensator value, using formula (7);

[0133] c) Calculate the disturbance observer value, using formula (9);

[0134] d) Calculate the sliding surface value, using formula (14);

[0135] e) Calculate the controller torque value, using formula (15);

[0136] Step 10: Calculate controller state update:

[0137] a) Calculate the auxiliary state variables of the disturbance observer, formula (10);

[0138] Step 11: Send the torque value to the motor driver via CAN communication;

[0139] Step 12: Put the data required by the host computer into the data buffer;

[0140] Step 13: If the ETH peripheral FIFO is empty and the data buffer contains data to be sent, then send the data to the host computer via TCP communication; otherwise, skip this step.

[0141] Step 14: Repeat Step 4, Step 7, Step 8, Step 9, Step 10, Step 11, Step 12, and Step 13 in sequence;

[0142] Step 15: When the motion platform reaches its maximum working time, or the host computer sends a stop command, stop executing the control algorithm and shut down the motor.

[0143] The lightweight embedded control system provided in this embodiment leverages the advantages of LWIP TCP communication—small memory footprint, high data processing efficiency, and strong real-time performance—to improve the real-time communication capability between the embedded control system and the host computer. The motor is controlled via a CAN bus architecture, enhancing the real-time control performance between the control system and the motor. Its bare-metal environment operation provides greater performance requirements and better timing for the control algorithm. This system framework is highly versatile; in addition to the control algorithm proposed in this invention, it can deploy various advanced dynamic control algorithms, reducing deployment costs and providing a reliable development framework for robotic arm trajectory tracking control algorithms.

[0144] Example 3

[0145] To verify the performance of the control algorithm, the proposed control algorithm is deployed on a lightweight embedded motion platform control system in this embodiment.

[0146] motion platform structure such as Figure 2As shown, the platform uses INNFOS SCA QDD PR60-36 (joint 1) and QDD NE30-36 (joint 2) integrated drive-electric joint modules. Their rated speeds are 83.3 rpm and 111.1 rpm, respectively. Their rated torques are 22.9 Nm and 6.5 Nm, respectively. The encoder is a 14-bit absolute encoder with an accuracy of 0.022°. The reducer is a planetary reducer with a reduction ratio of 1:36. The main controller chip is an STM32H743IIT6 microcontroller with a main frequency of 480 MHz. The host computer is an x86 architecture general-purpose computer responsible for issuing commands and receiving motor and controller data in real time.

[0147] Figure 2 The two-degree-of-freedom motion platform is a simplified structure for robotic arms, used to simulate the working effect of dynamic control algorithms for multi-degree-of-freedom serial robotic arms. In practical applications, the working degrees of freedom can be increased according to requirements.

[0148] The entire motion platform system runs on a bare-metal STM32H7 microcontroller, with a control step size set to 1ms. Data transmission and command issuance between the microcontroller and the motor are handled via CAN communication. Communication between the microcontroller and the host computer utilizes a combination of LWIP TCP communication and UART serial communication. LWIP TCP communication handles real-time data exchange, while UART serial communication is used for command transmission and debugging.

[0149] The control input is set to q when time t < 10 units (s). d =[sin(0.2π(t)),-sin(0.2π(t))] T Units (rad). When time t >= 10 units (s), q d =[sin(0.6π(t)),-sin(0.6π(t))] T The unit is rad. Simultaneously, with parameters unchanged, the controller's control performance was tested under terminal loads of 0 kg and 1 kg. Both sets of experiments used the same time-delay controller; one set used a controller with a time-delay estimation error compensator, and the other used the original time-delay controller without the compensator. For comparison.

[0150] The controller parameters are set as follows, with the original delay controller parameters being: K = diag(0.05, 0.05), μ1 = diag(3, 2). The time delay controller parameters with the added time delay estimation error compensator are: K=diag(0.05,0.05), μ1=diag(3,2), eta=diag(0.5,0.1), l=20.

[0151] Combination Figure 1Control algorithm flow and Figure 3 The present invention provides a lightweight embedded motion platform control system, the operation of which includes the following steps:

[0152] Step 1: Initialize the embedded system peripheral drivers (clock, serial port, GPIO, CAN, FMC, ETH, timer, FPU, etc.);

[0153] Step 2: The embedded TCP client establishes a communication connection with the host computer server;

[0154] Step 3: Initialize the parameters of the control algorithm;

[0155] Step 4: When the timer reaches the control step length (1ms), the main loop is entered once;

[0156] Step 5: Send the following commands to the motor driver sequentially via CAN communication: search for motor, enable motor, and return motor to zero.

[0157] Step 6: When the microcontroller receives the cmd=4 instruction from the host computer via serial port interrupt, the motor is set to torque working mode and the control algorithm is executed.

[0158] Step 7: Calculate the current reference trajectory, reference velocity, and reference acceleration;

[0159] Step 8: Obtain and calculate the current position, speed, acceleration, and current data of the motor from the driver via CAN communication;

[0160] Step 9: Calculate the controller output:

[0161] a) Calculate the estimated time delay using formula (4);

[0162] b) Calculate the gradient compensator value, using formula (7);

[0163] c) Calculate the disturbance observer value, using formula (9);

[0164] d) Calculate the sliding surface value, using formula (14);

[0165] e) Calculate the controller torque value, using formula (15);

[0166] Step 10: Calculate controller state update:

[0167] a) Calculate the auxiliary state variables of the disturbance observer, formula (10);

[0168] Step 11: Send the torque value to the motor driver via CAN communication;

[0169] Step 12: Put the data required by the host computer into the data buffer;

[0170] Step 13: If the ETH peripheral FIFO is empty and the data buffer contains data to be sent, then send the data to the host computer via TCP communication; otherwise, skip this step.

[0171] Step 14: Repeat Step 4, Step 7, Step 8, Step 9, Step 10, Step 11, Step 12, and Step 13 in sequence;

[0172] Step 15: When the motion platform reaches its maximum working time, or when the host computer sends a stop command cmd=5, set the flag bit flag=0, stop executing the control algorithm, and shut down the motor.

[0173] Experimental results are as follows Figure 4-6 As shown in the figure, the solid line represents the time delay controller with the added time delay estimation error compensator, and the dashed line represents the original time delay controller. Figure 4 This is a diagram showing the trajectory tracking effect. Figure 5 This is a comparison chart of trajectory tracking errors. Figure 4-5 The results show that in the first 10 seconds of the trajectory tracking task, the proposed control scheme not only exhibits extremely high trajectory tracking accuracy but also demonstrates superior stability. After 10 seconds, the trajectory frequency changes, and under the action of the time delay error compensator, the proposed scheme exhibits error fluctuations far lower than the original time delay control, indicating that the proposed controller has strong robustness. Figure 6 The graph shows a comparison of time delay estimation errors. At 10 seconds, the time delay estimation error jumps significantly due to changes in the control input. The comparison results show that the time delay estimation error is greatly reduced after compensation by the compensator, which improves the controller's ability to withstand load and disturbance changes.

[0174] The data quantification results use the mean absolute error (MAE) as the technical evaluation index. Table 1 shows the MAE results for trajectory tracking error. Table 2 shows the MAE results for time delay estimation error. The last row of each table contains parameters for the controller performance improvement after adding the compensator. The results show that adding the time delay estimation compensator significantly improves the controller tracking accuracy, and reducing the time delay estimation error also enhances the system's resilience to load and disturbance changes. The time delay estimation error compensator proposed in this invention has a configuration-independent feature and can be applied to more advanced time delay controllers.

[0175] Table 1. Tracking Error (MAE) Results

[0176]

[0177] Table 2. Results of Delay Estimation Error (MAE)

[0178]

[0179] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. An error compensation method based on time delay estimation for trajectory tracking control of a multi-degree-of-freedom robotic arm, characterized in that, The method uses a time delay estimation method to estimate the lumped unknown dynamic model of a multi-degree-of-freedom manipulator and obtains the time delay estimation error; An estimation error compensator is used to compensate for the time delay estimation error of the time delay controller. The estimation error compensator includes: a gradient compensator for compensating the fast time-varying part of the time delay estimation error; and a disturbance observer for compensating the slow time-varying part of the time delay estimation error. Specific steps include: Step 1: Construct the dynamic model of the multi-degree-of-freedom robotic arm: Where, vector , , These represent the joint's position, velocity, and angular velocity, respectively. Represents the inertia matrix. Represents the matrices of centrifugal force and Coriolis force. Represents the gravity vector. Represents the friction force vector. Represents the lumped external disturbance vector. Indicates the current time t The joint torque vector; Step 2: Introduce a positive definite diagonal matrix This transforms the dynamic model of the multi-degree-of-freedom robotic arm into: in, This represents the control gain of the delay controller; Indicates the angular velocity of the joint; Indicates the current time t The joint torque vector; The vector representing the lumped unknown dynamic model of the system: Step 3: Estimate the lumped unknown dynamic model using the time delay estimation method: using the torque from the previous moment. and angular acceleration Calculate tL Moment-time lumped unknown dynamic model vector When time delay L Enough hours Approaching t time ; Here is a vector of time delay estimates: Let the time delay estimation error for: Step 4: Substituting the time delay estimation error equation into the dynamic model equation introducing the positive definite diagonal matrix, we get: Step 5: The gradient compensator is designed as follows: in, This represents the estimated time delay after compensation by the gradient error compensator; It is a proportionality coefficient. ; The dynamic model after gradient compensator compensation is as follows: in, This represents the time delay estimation error after compensation by the gradient compensator; Step 7: The disturbance observer based on time delay control is designed as follows: in, It is an estimate of the time delay estimation error; It is a positive constant. It is an auxiliary state variable, and its form is as follows: Time delay estimate after perturbation observer compensation for: Substituting the time delay estimate after perturbation observer compensation into the dynamic model after gradient compensator compensation, we get: in, To estimate the time delay error after compensation by the error compensator: Step 8: The sliding surface is: in, The sliding mode vector; For position tracking error, For speed error; Let be the desired position vector. The desired acceleration vector; It is a diagonal matrix of positive constants; Step 9: Design a time delay controller that includes a compensator: in, It is a diagonal robust gain matrix. It is a symbolic function; Substituting the time-delay controller, which includes the compensator, into the dynamic model after compensation by the perturbation observer and gradient compensator, we get: The remaining time delay estimation error is utilized using the controller's approximation rate. offset.

2. An embedded control system for deploying a robotic arm control algorithm, characterized in that, The embedded control system includes: A calculation control unit is used to calculate and execute the error compensation method as described in claim 1, wherein the calculation control unit includes a microcontroller; The microcontroller communicates with the host computer in real time via LWIP TCP communication and controls the motor of the robotic arm in real time via CAN bus communication.

3. An embedded control system according to claim 2, characterized in that, The system operation process includes the following steps: Establish communication connections between the various components of the system and complete the initialization; The microcontroller receives instructions from the host computer and executes the robotic arm control algorithm. The microcontroller obtains and calculates the current parameters of the robotic arm motor from the robotic arm driver via bus communication; The microcontroller sequentially calculates the system's time delay estimate, gradient compensator value, disturbance observer value, sliding mode surface value, and controller torque value to obtain the controller's output. The microcontroller calculates the auxiliary state variables of the disturbance observer and updates the controller state; The microcontroller sends torque values ​​to the motor driver of the robotic arm via CAN bus communication.

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