Intelligent spraying robot multi-task collaborative operation method and system

Abstract

The invention provides an intelligent spraying robot multi-task collaborative operation method and system. The method comprises the steps that a discrete sliding mode controller considering a sampling period is constructed based on a discrete state equation; introducing an auxiliary state variable to design an adaptive barrier function; establishing a T product dynamic system control model to realize online parameter identification; and a hierarchical control architecture is adopted to realize multi-robot cooperative control. According to the scheme, the problems that in the prior art, discrete implementation precision is reduced, controller parameters are difficult to adjust in a self-adaptive mode, and an effective data driving control strategy is lacked are solved, and efficient collaborative operation of the multiple spraying robots is achieved.

Description

Technical Field

[0001] This application relates to the field of industrial automation technology, and particularly to a method and system for multi-task collaborative operation of an intelligent spraying robot. Background Art

[0002] Intelligent spraying robots are an important research direction in the field of industrial automation, mainly applied to scenarios such as automobile manufacturing and furniture processing that require large-area and high-precision spraying. Multi-robot collaborative operation has become a key technology to improve production efficiency.

[0003] Currently, common spraying robot systems mainly adopt single-machine operation or simple multi-machine collaborative modes. For example, multi-robot fixed-point spraying is achieved through preset trajectory planning, or simple collaborative motion control is achieved by using basic obstacle avoidance algorithms. These systems often have problems such as low collaborative efficiency and inaccurate trajectory planning when dealing with complex workpieces or high-efficiency spraying tasks.

[0004] A more advanced technology adopts a robot trajectory tracking method based on sliding mode control, and constructs a Lyapunov function to ensure system stability. This method introduces a non-linear term in the controller design to compensate for system uncertainties and external disturbances, and can improve the robustness and control accuracy of the system to a certain extent.

[0005] However, the existing technologies still have the following problems: traditional sliding mode controllers often ignore the influence of the sampling period during discrete implementation, resulting in a decrease in control accuracy; it is difficult to adaptively adjust the controller parameters according to the actual working conditions, and the system has poor adaptability; there is a lack of effective data-driven control strategies for complex dynamic systems, and it is difficult to accurately describe the dynamic characteristics of the system; the multi-robot collaborative control strategy is imperfect, and it is difficult to achieve efficient collaborative operation. Summary of the Invention

[0006] In view of this, this application provides a method and system for multi-task collaborative operation of an intelligent spraying robot, which solves the problems in the existing technologies that traditional sliding mode controllers ignore the influence of the sampling period during discrete implementation, resulting in a decrease in control accuracy, it is difficult to adaptively adjust the controller parameters according to the actual working conditions, and there is a lack of effective data-driven control strategies for complex dynamic systems.

[0007] An embodiment of this application provides a method for multi-task collaborative operation of an intelligent spraying robot, including:

[0008] Collect the joint angle, angular velocity, torque data and control parameters of the spraying robot as state data, establish a discrete state equation including the sampling period T based on the state data, introduce a sampling period compensation term to design a sliding mode switching surface, construct a discrete Lyapunov function, and generate a first control quantity;

[0009] Based on the first control quantity, combined with the robot joint angle limit, speed limit, acceleration limit, and workspace boundary constraint, construct an adaptive barrier function, optimize the barrier function parameters using the gradient descent method, and generate a second control quantity;

[0010] Based on the second control quantity, collect the input and output data of the spraying robot during on-line operation, construct a T-product dynamic system control model, realize on-line identification and update of the model parameters, and generate a third control quantity;

[0011] Based on the third control quantity, establish a multi-robot kinematics and dynamics model, adopt a hierarchical control strategy to achieve multi-robot cooperative control, output control instructions that meet the requirements of workload balance and spraying quality, and control multiple spraying robots to complete cooperative operations.

[0012] Based on the state data, establish a discrete state equation including the sampling period T, including:

[0013] Perform Taylor expansion on the robot dynamics equation at the sampling moment, retain the second-order term, and establish a discrete state equation including the sampling period T;

[0014] Based on the discrete state equation, design an improved sliding mode switching surface and construct a quadratic discrete Lyapunov function;

[0015] Analyze the forward difference of the discrete Lyapunov function to obtain the stability condition;

[0016] According to the stability condition, design a discrete sliding mode controller including an equivalent control term and a switching control term, and generate the first control quantity.

[0017] Design a discrete sliding mode controller including an equivalent control term and a switching control term, including:

[0018] Based on the stability condition, design an equivalent control term to compensate for the known dynamics of the system and design a switching control term to cancel external disturbances;

[0019] Adopt a continuous reaching law in the discrete sliding mode controller, and set the boundary layer thickness to a value within the range of 0.01 - 0.1;

[0020] Use a saturation function to replace the sign function in the switching control term to generate the first control quantity.

[0021] Construct an adaptive barrier function, including:

[0022] Set the robot joint angle limit to ±170 degrees, the speed limit to ±180 degrees per second, and the acceleration limit to ±900 degrees per square second;

[0023] Introduce an auxiliary state variable ξ with a value range of 0.1 - 10, and construct a logarithmic barrier function B(x, ξ) = -ln((g(x) + ξ) / ξ), where g(x) represents the constraint function;

[0024] By adjusting the value of the auxiliary state variable ξ, dynamically change the steepness of the barrier function to generate an adaptive barrier function.

[0025] Use the gradient descent method to optimize the barrier function parameters, including:

[0026] Construct a composite Lyapunov function V(x, ξ), and design an adaptive law ξ' = -γ(B(x, ξ) - α), where γ is the adaptive gain with a value range of 1 - 10, and α is the expected barrier function value;

[0027] Use the stochastic gradient descent method to update the parameters, and set the parameter update step size to 0.01 - 0.1;

[0028] Introduce a momentum coefficient of 0.9 and an adaptive learning rate strategy to generate the second control quantity.

[0029] Construct a T-product dynamic system control model, including:

[0030] Collect the joint angle data, angular velocity data, motor torque data, and end - pose data of the spraying robot within the sampling period T as input data;

[0031] Divide the system state space into N sub - spaces, where the value range of N is 4 - 8, and each sub - space corresponds to a local linear model;

[0032] Select the cubic B - spline basis function as the basis function, construct the tensor representation of the state transition matrix, and generate the T - product dynamic system model structure.

[0033] Implement online identification and update of model parameters, including:

[0034] Based on the T - product dynamic system model structure, use the Tucker decomposition method to decompose the high - dimensional parameter identification problem into sub - problems in three dimensions;

[0035] Construct a weighted least - squares optimization problem, set the weight coefficient to 0.1 - 1.0, and use the L2 regularization method to solve each local model parameter;

[0036] Use the recursive least - squares algorithm to update the model parameters, and set the exponential forgetting factor to 0.95 - 0.99;

[0037] Adjust the model structure based on a sliding time window of 100 - 500 sampling points, limit the parameter change rate within 20%, and generate the third control quantity.

[0038] Multi-robot cooperative control is achieved by adopting a hierarchical control strategy, including:

[0039] Based on the third control quantity, an improved Hungarian algorithm is adopted for task allocation, and the optimization objectives include:

[0040] Minimize the overall energy consumption, make the workload difference of each robot less than 15%, and control the spraying overlap rate within 5%-10%;

[0041] In the global layer, an improved RRT* algorithm is used to generate a collision-free path, and the sampling point spacing is set to 50-100 millimeters;

[0042] In the local layer, a quintic polynomial function is used to optimize the trajectory, with the position error limited to ±0.1 millimeter and the attitude error limited to ±0.1 degree.

[0043] Achieve multi-robot cooperative control, including:

[0044] Adopt a hierarchical control architecture, and the control period is: 100 milliseconds for the upper-layer cooperative controller and 1 millisecond for the lower-layer independent controller;

[0045] Establish the coupling relationship between robots through the virtual structure method, and the coupling stiffness coefficient is set to 10-100;

[0046] Design an event-triggered distributed control strategy, and the trigger threshold is set to a position error of 0.5 millimeter or an attitude error of 0.5 degree;

[0047] Introduce a prediction compensation mechanism of 100-200 milliseconds to ensure the stability of the system when the communication delay and data loss rate do not exceed 5%.

[0048] The embodiment of the present application also provides an intelligent spraying robot multi-task cooperative operation system, including:

[0049] A data acquisition module for collecting the joint angle, angular velocity, torque data and control parameters of the spraying robot;

[0050] A discrete sliding mode control module for receiving the data of the data acquisition module and generating a first control quantity, and the discrete sliding mode control module is connected to the adaptive barrier function module through a data bus;

[0051] An adaptive barrier function module for receiving the first control quantity and generating a second control quantity in combination with the robot system constraints, and the adaptive barrier function module is connected to the dynamic model module through a real-time data interface;

[0052] A dynamic model module for receiving the second control quantity, performing online parameter identification, and generating a third control quantity, and the dynamic model module is connected to the cooperative control module through Ethernet;

[0053] A collaborative control module, configured to receive the third control quantity, plan a multi-robot collaborative trajectory, and output a control instruction. The collaborative control module is connected to each robot controller through a CAN bus to complete the multi-task collaborative operation of the spraying robot.

[0054] An embodiment of the present application further provides a computer device, which includes:

[0055] At least one processor; and,

[0056] A memory communicatively connected to the at least one processor; wherein,

[0057] The memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the above-mentioned intelligent spraying robot multi-task collaborative operation method.

[0058] An embodiment of the present application further provides a computer-readable storage medium, which stores computer instructions for causing a computer to execute the above-mentioned intelligent spraying robot multi-task collaborative operation method.

[0059] An embodiment of the present application further provides a computer program product, including computer instructions, which implement the steps of the above-mentioned intelligent spraying robot multi-task collaborative operation method when executed by a processor.

[0060] The present application has the following technical effects:

[0061] 1. By designing a discrete sliding mode controller considering the influence of the sampling period, the problem of reduced accuracy in traditional discrete implementation is solved, and the control accuracy is improved;

[0062] 2. An auxiliary state variable is introduced to adaptively adjust the barrier function parameters, improving the system's adaptability to environmental changes and enhancing the system's robustness;

[0063] 3. The T-product dynamic system modeling method is adopted to achieve high-precision modeling of complex nonlinear systems, providing accurate system model support;

[0064] 4. The multi-robot collaborative control system implemented based on the above technologies can efficiently complete complex spraying tasks, improving production efficiency and spraying quality. Description of the Drawings

[0065] To more clearly illustrate the technical solutions of the embodiments of the present disclosure, the accompanying drawings required for the embodiments will be briefly introduced below. The accompanying drawings here are incorporated into the specification and constitute a part of this specification. These accompanying drawings show the embodiments that conform to the present disclosure and, together with the specification, are used to illustrate the technical solutions of the present disclosure. It should be understood that the following accompanying drawings only show some embodiments of the present disclosure and should not be regarded as limiting the scope. For those of ordinary skill in the art, other related accompanying drawings can be obtained based on these accompanying drawings without creative efforts.

[0066] Figure 1 It is a flowchart of the multi-task collaborative operation method of the intelligent spraying robot provided by the embodiment of the present application;

[0067] Figure 2 It is an architecture diagram of the multi-robot collaborative control system provided by the embodiment of the present application. Specific embodiments

[0068] To make the objectives, technical solutions, and advantages of the embodiments of the present disclosure clearer, the technical solutions in the embodiments of the present disclosure will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present disclosure. Obviously, the described embodiments are only some of the embodiments of the present disclosure, rather than all of them. The components of the embodiments of the present disclosure usually described and illustrated in the accompanying drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present disclosure provided in the accompanying drawings is not intended to limit the scope of the claimed present disclosure, but merely represents the selected embodiments of the present disclosure. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present disclosure without creative efforts fall within the scope of protection of the present disclosure.

[0069] As Figure 1 shown, the embodiment of the present application provides a multi-task collaborative operation method for an intelligent spraying robot, including:

[0070] S1: Collect the joint angles, angular velocities, torque data, and control parameters of the spraying robot as state data, establish a discrete state equation including the sampling period T based on the state data, introduce a sampling period compensation term to design a sliding mode switching surface, construct a discrete Lyapunov function, and generate a first control quantity;

[0071] S1 includes:

[0072] S1.1: Perform Taylor expansion on the robot dynamics equation at the sampling moment, retain the second-order term, and establish a discrete state equation including the sampling period T;

[0073] When constructing the discrete state equation, it is first necessary to consider the continuous dynamics model of the spraying robot, which usually includes the inertia matrix, the Coriolis force matrix, and the gravity term. Traditional methods often directly use the Euler method for discretization, ignoring the influence of higher-order terms. This method innovatively uses Taylor series expansion and retains the second-order term, enabling the discrete model to more accurately describe the dynamic characteristics of the system. Specifically, at each sampling moment, the derivative of the state variable is expanded by Taylor series, and then truncated to the second-order term to obtain a discrete state equation containing the sampling period T. This processing method can effectively compensate for the model error caused by sampling discretization and provide a more accurate system model for subsequent controller design.

[0074] S1.2: Based on the discrete state equation, design an improved sliding mode switching surface and construct a quadratic discrete Lyapunov function;

[0075] After obtaining the discrete state equation, it is necessary to design an appropriate sliding mode switching surface to guide the system state to converge to the desired trajectory. Traditional sliding mode switching surface design usually does not consider the influence of discrete sampling, resulting in a decline in actual control performance. To address this issue, this method designs an improved sliding mode switching surface, which explicitly introduces a sampling period compensation term. This compensation term can predict the change in the system state at the next sampling moment and adjust the current control strategy accordingly, effectively reducing the tracking error caused by discrete implementation. After designing the sliding mode switching surface, construct a quadratic discrete Lyapunov function based on the switching surface to provide a theoretical tool for subsequent stability analysis. This form of Lyapunov function has good mathematical properties and is convenient for deriving stability conditions.

[0076] S1.3: Analyze the forward difference of the discrete Lyapunov function to obtain the stability conditions;

[0077] To ensure the stability of the system, it is necessary to analyze the change of the constructed discrete Lyapunov function at adjacent sampling moments. By calculating the forward difference of the Lyapunov function, that is, the difference between the function values at the current moment and the next moment, sufficient conditions for ensuring the stability of the system can be derived. In the discrete domain, the stability conditions usually require the forward difference of the function to be negative or satisfy a certain decreasing relationship. Based on the obtained discrete state equation and the improved sliding mode switching surface, the forward difference expression is derived in detail, and the stability conditions that the controller design needs to satisfy are obtained through mathematical transformation. These conditions are directly related to the selection of controller parameters and are crucial for ensuring the stable operation of the system.

[0078] S1.4: According to the stability conditions, design a discrete sliding mode controller containing an equivalent control term and a switching control term to generate the first control quantity;

[0079] Based on the stability conditions derived above, design the complete discrete sliding mode controller structure. This controller consists of two parts: an equivalent control term and a switching control term. The equivalent control term is mainly responsible for compensating the deterministic dynamic part of the system, enabling the system state to stably reach the sliding mode switching surface without disturbances; the switching control term is mainly used to counteract the uncertainties and external disturbances in the system, enhancing the robustness of the system. The combined effect of the two control quantities can ensure that the system has good tracking performance and anti-interference ability under various working conditions. By reasonably designing the controller structure and parameters, ensure that the stability conditions derived above are satisfied, and finally generate the first control quantity as the preliminary control input of the system.

[0080] S1.4 includes:

[0081] S1.4.1: Based on the stability conditions, design an equivalent control term to compensate for the known dynamics of the system, and design a switching control term to counteract external disturbances;

[0082] The design of the equivalent control term is based on the deterministic dynamic model of the system. By solving the conditions for keeping the system state on the sliding mode switching surface, the control input for compensating the known dynamics of the system is obtained. Specifically, substitute the discrete state equation of the system into the expression of the sliding mode switching surface, and through mathematical derivation, the calculation formula for the equivalent control term is obtained. This control term can effectively compensate for the nonlinear dynamics of the system, including the effects of inertia, Coriolis force, and gravity. The switching control term mainly targets the uncertainties and external disturbances in the system. Its design principle is to ensure that under the maximum disturbance amplitude, the system state can still be attracted near the sliding mode switching surface. By reasonably setting the control gain, ensure that the switching control term has sufficient control strength to counteract various disturbance factors. S1.4.2: In the discrete sliding mode controller, adopt a continuous reaching law, and set the boundary layer thickness to a value within the range of 0.01 - 0.1;

[0083] The commonly used sign function in traditional sliding mode control will cause high-frequency jitter of the control input, which has an adverse effect on the system actuator. To solve this problem, this method adopts a continuous reaching law to replace the traditional discontinuous switching strategy. The continuous reaching law forms a smooth transition region near the sliding mode switching surface by introducing the concept of a boundary layer, making the change of the control input smoother. According to a large amount of experimental data and theoretical analysis, setting the boundary layer thickness within the range of 0.01 - 0.1 can effectively reduce system jitter while ensuring control performance. The specific value of the boundary layer thickness can be fine-tuned according to the actual application scenario. A smaller value is beneficial to improving control accuracy, while a larger value helps to reduce the jitter phenomenon.

[0084] S1.4.3: Use a saturation function to replace the sign function in the switching control term to generate the first control quantity;

[0085] To further reduce control jitter, a saturation function is used to replace the traditional sign function in the switching control term. The saturation function changes linearly near the sliding mode switching surface and remains at a fixed value outside the boundary layer. This characteristic makes the control input change more smoothly when the system state approaches the target trajectory. In specific implementation, a saturation function with the ratio of the switching surface value to the boundary layer thickness as the independent variable is defined. When the absolute value of this ratio is less than 1, the function output is proportional to the input; when the absolute value is greater than or equal to 1, the function output is ±1. This design not only retains the robustness characteristics of sliding mode control but also effectively solves the chattering problem. By reasonably combining the equivalent control term and the switching control term with the saturation function, a smooth and effective first control quantity is finally generated, providing the basic input for the subsequent control link.

[0086] S2: Based on the first control quantity, combined with the robot joint angle limit, speed limit, acceleration limit, and workspace boundary constraint, construct an adaptive barrier function, and use the gradient descent method to optimize the barrier function parameters to generate a second control quantity;

[0087] S2 includes:

[0088] S2.1: Set the robot joint angle limit to ±170 degrees, the speed limit to ±180 degrees per second, and the acceleration limit to ±900 degrees per square second;

[0089] Before constructing the adaptive barrier function, it is first necessary to clearly define the system constraints. For the spray painting robot system, the most basic physical constraints include joint angle limit, speed limit, and acceleration limit. According to the mechanical structure and actuator characteristics of the robot, the joint angle limit is set to ±170 degrees. This setting not only considers the physical movement range of the robotic arm but also reserves a 10-degree safety margin to prevent possible unstable states when the robotic arm approaches the limit position. The speed limit is set to ±180 degrees per second, which is determined based on the maximum rotational speed of the motor and the reduction ratio to ensure precise control of the system during high-speed movement. The acceleration limit is set to ±900 degrees per square second, which takes into account the dynamic response characteristics of the mechanical structure and the requirements of the spray painting process for smoothness, avoiding excessive acceleration that may cause mechanical vibration or uneven spraying. These constraint conditions together form the basis for the subsequent barrier function design.

[0090] S2.2: Introduce an auxiliary state variable ξ with a value range of 0.1 - 10, and construct a logarithmic barrier function B(x, ξ) = -ln((g(x) + ξ) / ξ), where g(x) represents the constraint function;

[0091] Traditional barrier functions usually have a fixed shape and are difficult to adjust dynamically according to the system state. To solve this problem, this method innovatively introduces an auxiliary state variable ξ, whose value range is set to 0.1 - 10, and is used to dynamically adjust the characteristics of the barrier function. Based on this auxiliary variable, a logarithmic barrier function B(x, ξ) = -ln((g(x) + ξ) / ξ) is constructed, where g(x) represents the constraint function, reflecting the distance between the system state and the constraint boundary. This structure of the barrier function has special properties: when the system state approaches the constraint boundary, g(x) approaches zero, and the value of the barrier function increases rapidly, generating a strong repulsive force; when the system state is far from the constraint boundary, the value of the barrier function is small, and the impact on the system is limited. By introducing the auxiliary variable ξ, the steepness and range of action of the barrier function can be dynamically adjusted, enabling the system to not only meet the constraint requirements but also maintain good performance.

[0092] S2.3: By adjusting the value of the auxiliary state variable ξ, dynamically change the steepness of the barrier function to generate an adaptive barrier function;

[0093] The adjustment of the auxiliary state variable ξ is the key to realizing the adaptive characteristics of the barrier function. When the system state is far from the constraint boundary, the value of ξ can be set larger. At this time, the gradient of the barrier function is smaller, and the system can move more freely, which is beneficial to improving the control performance; when the system state approaches the constraint boundary, the value of ξ is decreased, making the barrier function steeper near the constraint boundary, generating a stronger repulsive force to ensure that the constraint conditions are not violated. This dynamic adjustment strategy enables the barrier function to automatically adjust its characteristics according to the changes in the system state, ensuring both the satisfaction of the constraints and minimizing the impact on the system performance. By reasonably designing the adjustment mechanism of ξ, the barrier function is equipped with adaptive capabilities, can adapt to different working conditions and task requirements, and form a truly adaptive barrier function.

[0094] S2.4: Construct a composite Lyapunov function V(x, ξ), and design an adaptive law ξ' = -γγ(B(xξ) - α), where γ is the adaptive gain, and its value range is 1 - 10, and α is the expected value of the barrier function;

[0095] To design the adaptive adjustment rule for the auxiliary state variable ξ, it is necessary to construct a composite Lyapunov function V(x, ξ) that includes the system state and the auxiliary variable. This function comprehensively considers the stability of the system state and the satisfaction of constraints, providing a theoretical basis for adaptive adjustment. Based on this composite Lyapunov function, the adaptive law for the auxiliary variable is designed as ξ' = -γγ(B(xξ) - α), where γ is the adaptive gain, and its value range is set to 1 - 10, and α is the expected value of the barrier function. This design idea follows the gradient descent principle. When the current barrier function value is higher than the expected value, the value of ξ increases to weaken the influence of the barrier function; when the barrier function value is lower than the expected value, the value of ξ decreases to enhance the effect of the barrier function. The adaptive gain γ controls the adjustment speed. A larger γ value makes the system respond faster but may lead to over-adjustment; a smaller γ value makes the adjustment process smoother but the response is slower. In practical applications, the γ value can be adjusted according to the system characteristics and task requirements to obtain the best performance.

[0096] S2.5: Update the parameters using the stochastic gradient descent method, and set the parameter update step size to 0.01 - 0.1;

[0097] To optimize the performance of the barrier function, in addition to the adaptive adjustment of the auxiliary variable, it is also necessary to optimize the parameters of the barrier function itself. This method uses the stochastic gradient descent method for parameter update. This method has the characteristics of high computational efficiency and easy implementation, and is suitable for online application scenarios. During the optimization process, first define an appropriate performance index function, which usually includes the measurement of control accuracy and constraint satisfaction. Then, calculate the gradient of the performance index function with respect to each parameter and update the parameters in the gradient direction. To ensure the stability of the optimization process, the parameter update step size is set in the range of 0.01 - 0.1. A smaller step size makes the optimization process smoother but the convergence speed is slower; a larger step size can accelerate convergence but may lead to parameter oscillation. In practical applications, the step size can be dynamically adjusted according to the response characteristics of the system and the urgency of the task to balance the requirements of convergence speed and stability.

[0098] S2.6: Introduce a momentum coefficient of 0.9 and an adaptive learning rate strategy to generate the second control quantity;

[0099] To further improve the efficiency and stability of parameter optimization, a momentum term and an adaptive learning rate strategy are introduced based on the stochastic gradient descent method. The momentum coefficient is set to 0.9. This setting enables parameter updates to consider not only the current gradient but also the historical update direction, which helps to overcome local optima and accelerate the convergence process. The adaptive learning rate strategy dynamically adjusts the learning rate according to the changes in the gradient during the optimization process. When the gradient directions are consistent for several consecutive times, the learning rate is appropriately increased to accelerate convergence; when the gradient directions change frequently, the learning rate is decreased to improve stability. Through these improved strategies, the parameter optimization process becomes more efficient and robust, and can quickly adapt to system state and environmental changes. Based on the optimized barrier function parameters and the adaptively adjusted auxiliary variables, combined with the first control quantity in the previous step, a second control quantity that comprehensively considers the constraint conditions is generated, providing an input for the subsequent control link.

[0100] S3: Based on the second control quantity, collect the input and output data during the on-line operation of the spraying robot, construct a T-product dynamic system control model, realize on-line identification and update of model parameters, and generate a third control quantity;

[0101] S3 includes:

[0102] S3.1: Collect the joint angle data, angular velocity data, motor torque data, and end-effector pose data of the spraying robot within the sampling period T as input data;

[0103] Before constructing a data-driven T-product dynamic system control model, comprehensive data collection work needs to be carried out first. This method designs a multi-dimensional and high-precision data collection strategy to systematically collect various key data of the spraying robot during operation. Specifically, through the encoders built into the robot control system, collect the angle data of each joint, which directly reflects the pose information of the robot; through angular velocity sensors, obtain the angular velocity data of each joint, which reflects the dynamic characteristics of the robot; through the current detection circuit of the motor driver, indirectly obtain the motor torque data, which reflects the dynamic characteristics during the robot's movement; through forward kinematics calculation or an external vision system, collect the pose data of the robot's end effector, which reflects the actual position and pose of the robot in the workspace. Special attention is paid to the consistency of the sampling period during the data collection process to ensure that all data can accurately correspond to the same time point, providing high-quality basic data for subsequent model construction.

[0104] S3.2: Divide the system state space into N subspaces, where the value range of N is 4 - 8, and each subspace corresponds to a local linear model;

[0105] Traditional global non - linear models often have difficulty accurately describing the dynamic characteristics of complex systems, while simple linear models lack expressive power. To solve this contradiction, this method adopts the idea of piece - wise linearization and divides the entire state space of the system into multiple sub - spaces. According to the complexity and non - linear degree of the spraying robot system, the state space is selected to be divided into 4 to 8 sub - spaces, and this range is determined based on a large number of experiments and theoretical analyses. If the number of sub - spaces is too small, the coverage range of each sub - space will be too large, resulting in insufficient accuracy of the local linear model; if the number of sub - spaces is too large, the model will be too complex, increasing the computational burden and possibly causing over - fitting problems. In the actual division process, uniform division or non - uniform division methods based on data density can be used to ensure that the system behavior within each sub - space can be well approximated by a linear model. A local linear model is constructed for each sub - space, and these local models together form the complete system model.

[0106] S3.3: Select the cubic B - spline basis function as the basis function, construct the tensor representation of the state - transition matrix, and generate the T - product dynamic system model structure;

[0107] To achieve smooth transitions between sub - spaces and the continuity of the overall model, this method selects the cubic B - spline basis function as the basic building block. The cubic B - spline basis function has good smoothness and local support properties, which can reduce the abrupt changes at the boundaries of sub - spaces while ensuring the continuity of the model. Based on these basis functions, the tensor representation form of the state - transition matrix is constructed. Specifically, the state - transition relationship of the system is expressed as a weighted combination of multiple basis functions, and these weight parameters form a high - dimensional tensor. Each dimension of the tensor corresponds to an aspect of the system state, such as joint angle, angular velocity, etc. This representation method not only maintains the structural simplicity of the model but also has the ability to express complex non - linear relationships. By reasonably designing the tensor structure and dimension division, a complete T - product dynamic system model framework is formed, which can uniformly describe the dynamic behavior of the system under different working conditions and provides a structural basis for subsequent parameter identification.

[0108] S3.4: Based on the T - product dynamic system model structure, use the Tucker decomposition method to decompose the high - dimensional parameter identification problem into sub - problems of three dimensions;

[0109] The parameters in the T-product dynamic system model exhibit a high-dimensional tensor structure. Directly identifying the parameters for the entire tensor involves a huge computational cost and low efficiency. To address this issue, this method adopts the Tucker decomposition technique, which decomposes the high-dimensional parameter identification problem into multiple low-dimensional sub-problems. Tucker decomposition is a generalized tensor decomposition method that can decompose a high-dimensional tensor into the product form of a core tensor and several factor matrices. In this application, the parameter tensor is decomposed into sub-problems of three main dimensions, which respectively correspond to the configuration space, velocity space, and control input space of the robot. Through this decomposition, a large number of parameters that originally needed to be identified simultaneously are divided into several relatively independent parameter sets, greatly reducing the computational complexity. During the decomposition process, an approximate model is first constructed based on the initial data, and then the factor matrices are iteratively optimized by the alternating least squares method to finally obtain the complete decomposition result. This method not only improves the computational efficiency but also enhances the stability and noise resistance of parameter identification.

[0110] S3.5: Construct a weighted least squares optimization problem with the weight coefficient set to 0.1 - 1.0, and use the L2 regularization method to solve each local model parameter;

[0111] After obtaining the sub-problems of each dimension of the Tucker decomposition, it is necessary to accurately identify the parameters of each local linear model. This method constructs a weighted least squares optimization problem and determines the optimal parameter values by minimizing the prediction error. To handle the differences in the importance of different data points, a weight coefficient mechanism is introduced, and the weight range is set from 0.1 to 1.0. Data points closer to the current working point are given higher weights to ensure higher accuracy of the local model within the working area; while data points farther away are given lower weights to reduce their influence. At the same time, to prevent overfitting and improve the generalization ability of the model, the L2 regularization method is adopted, and a penalty term of the parameter norm is added to the optimization objective function. The introduction of L2 regularization makes the model parameters tend to take smaller values, enhancing the smoothness and stability of the model. The optimization problem is solved by numerical methods such as the conjugate gradient method or the quasi-Newton method, and finally the optimal parameter estimates of each local model are obtained. In this way, both the fitting accuracy of the local model is guaranteed and the risk of overfitting is avoided.

[0112] S3.6: Use the recursive least squares algorithm to update the model parameters, with the exponential forgetting factor set to 0.95 - 0.99;

[0113] The dynamic characteristics of the spraying robot system may change over time. Factors such as mechanical wear and environmental temperature changes can affect the system behavior. To enable the model to adapt to these changes, this method uses the recursive least squares algorithm to implement online updating of model parameters. The core idea of this algorithm is that when new data arrives, instead of reprocessing all historical data, it directly calculates the updated parameter estimates based on the previous parameter estimates and the information increment of the new data. To balance the influence of historical data and new data, an exponential forgetting factor is introduced, and the value range of this factor is set from 0.95 to 0.99. The smaller the forgetting factor, the faster the algorithm responds to new data, but it may lead to an increase in the volatility of parameter estimates; the larger the forgetting factor, the more stable the algorithm, but the response to system changes is slower. In practical applications, the value of the forgetting factor can be dynamically adjusted according to the system characteristics and the speed of environmental changes. Through the online updating mechanism of the recursive least squares algorithm, the model can continuously track the dynamic changes of the system and maintain good prediction accuracy.

[0114] S3.7: Adjust the model structure based on a sliding time window of 100 - 500 sampling points, limit the parameter change rate within 20%, and generate the third control quantity;

[0115] In addition to the online updating of parameters, the model structure itself also needs to be adaptively adjusted according to the changes in system behavior. This method designs a model structure adjustment mechanism based on a sliding time window, and the window size is set from 100 to 500 sampling points. A smaller window size enables the model to quickly respond to changes in system behavior, but it may be more sensitive to noise and interference; a larger window size provides a more stable estimate, but the response to system changes is slower. Based on the data within the sliding window, periodically evaluate the applicability of the current model structure, including aspects such as subspace division and basis function selection. When the evaluation index is lower than the preset threshold, trigger the re - optimization of the model structure. To ensure the smoothness of system control, limit the change rate of parameters in each adjustment to no more than 20%, avoiding drastic fluctuations in control output caused by model mutations. Finally, based on the updated model parameters and the optimized model structure, combined with the second control quantity in the previous step, generate a more accurate third control quantity, providing a reliable basis for multi - robot cooperative control. This control model with adaptive learning ability can effectively cope with various working condition changes and uncertainties, and maintain the high - performance operation of the system.

[0116] S4: Based on the third control quantity, establish the kinematics and dynamics models of multiple robots, adopt a hierarchical control strategy to achieve multi - robot cooperative control, output control instructions that meet the requirements of workload balance and spraying quality, and control multiple spraying robots to complete cooperative operations;

[0117] S4 includes:

[0118] S4.1: The improved Hungarian algorithm is used for task allocation. The optimization objectives include: minimizing the overall energy consumption, ensuring that the workload difference among robots is less than 15%, and controlling the spraying overlap rate within 5%-10%.

[0119] The efficiency of the multi-robot collaborative spraying system depends to a large extent on the rationality of task allocation. This method uses the improved Hungarian algorithm for task allocation. This algorithm is a classic combinatorial optimization method that can solve the optimal solution of the assignment problem. Based on the traditional Hungarian algorithm, a multi-objective optimization mechanism is introduced, considering three key factors: minimizing energy consumption, load balancing, and spraying quality. Minimizing energy consumption is mainly achieved by optimizing the robot's motion trajectory and work area, minimizing unnecessary large-scale movements and acceleration / deceleration processes; load balancing ensures that the workload difference among robots is controlled within 15%, avoiding the situation where some robots are overloaded while others are idle, and improving the overall system efficiency; the spraying overlap rate is controlled within the range of 5%-10%. This setting not only ensures that there are no blank areas on the workpiece surface but also avoids material waste and uneven surface quality caused by excessive overlap. During the algorithm implementation process, the entire spraying task is first divided into multiple subtasks, then a cost matrix for task allocation is constructed, and finally the optimal allocation scheme is solved through iterative optimization. This multi-objective optimization task allocation strategy lays a solid foundation for subsequent collaborative control.

[0120] S4.2: The improved RRT* algorithm is used to generate collision-free paths at the global level, and the sampling point spacing is set to 50-100 mm.

[0121] After task allocation, it is necessary to plan safe and efficient motion paths for each robot. This method uses a hierarchical planning strategy. First, at the global level, the improved RRT* (Rapidly-exploring Random Tree Star) algorithm is used to generate a collision-free basic path. The RRT* algorithm is a random sampling path planning method with the ability to efficiently explore complex environments. Based on the traditional RRT* algorithm, this method introduces a heuristic sampling strategy and a dynamic search radius adjustment mechanism to improve the algorithm's performance in the spraying environment. The heuristic sampling strategy adjusts the distribution of sampling points according to the workpiece surface characteristics and spraying requirements, making the algorithm more inclined to conduct detailed exploration in key areas; the dynamic search radius is automatically adjusted according to the environmental complexity, using a larger radius in open areas to accelerate convergence and a smaller radius in narrow areas to improve accuracy. The sampling point spacing is set to 50-100 mm, and this range is determined comprehensively according to the spraying process requirements and computational efficiency. Too small a spacing will lead to a sharp increase in the computational amount with limited accuracy improvement, while too large a spacing may miss important path options. Through this improved RRT* algorithm, a global path that meets the collision-free requirements can be efficiently generated, providing a basis for subsequent trajectory optimization.

[0122] S4.3: Optimize the trajectory using a fifth - degree polynomial function in the local layer, with the position error limited to ±0.1 mm and the attitude error limited to ±0.1 degrees.

[0123] Global path planning mainly focuses on generating collision - free paths, while local trajectory optimization emphasizes improving the smoothness and dynamic feasibility of the path to meet the high requirements of spraying quality. In this method, a fifth - degree polynomial function is used for trajectory optimization at the local level. The fifth - degree polynomial is chosen because it can ensure the continuity of velocity and acceleration while providing enough degrees of freedom to meet the boundary conditions. During the optimization process, taking the key points of the global path as constraints, combined with the dynamic characteristics of the robot and the requirements of the spraying process, an optimization objective function is constructed. This function usually includes multiple performance indicators such as trajectory length, energy consumption, spraying uniformity, etc. By using numerical optimization methods to solve for the optimal parameters, a smooth trajectory that meets various constraints is generated. In terms of precision control, the position error is limited to ±0.1 mm and the attitude error is limited to ±0.1 degrees. This precision requirement is determined based on the needs of high - quality spraying processes. To achieve this precision goal, the kinematic errors of the robot, dynamic non - linearities, and the response characteristics of the spraying system are specifically considered during the trajectory optimization process. Through the combination of feed - forward compensation and feedback correction, high - precision trajectory tracking is ensured.

[0124] S4.4: Adopt a hierarchical control architecture with a control period of: 100 ms for the upper - layer cooperative controller and 1 ms for the lower - layer independent controller.

[0125] The complexity of the multi - robot cooperative control system requires a hierarchical control architecture to divide the system functions according to time scales and abstraction levels. This method designs a two - layer control architecture: the upper layer is the cooperative controller, which is mainly responsible for the coordination and synchronization between multiple robots to ensure the coordinated execution of the overall task; the lower layer is the independent controller for each robot, which is responsible for the precise trajectory tracking and action execution of a single robot. There are obvious differences in the control period settings of the two levels: the control period of the upper - layer cooperative controller is 100 ms. This setting takes into account the computational complexity and communication delay of multi - robot coordination decisions while meeting the time response requirements of cooperative tasks; the control period of the lower - layer independent controller is 1 ms. This high - frequency control ensures the precise execution of single - robot actions and can respond in a timely manner to dynamic changes and external disturbances. The two - level controllers exchange information through a two - way communication mechanism: the upper - layer controller sends task instructions and coordination signals to the lower layer, and the lower - layer controller feeds back the execution status and environmental information to the upper layer. This hierarchical control architecture not only ensures the overall coordination of the system but also maintains the high precision and real - time performance of single - robot control.

[0126] S4.5: Establish the coupling relationship between robots through the virtual structure method, and set the coupling stiffness coefficient to 10 - 100;

[0127] To achieve the coordinated movement of multiple robots, it is necessary to establish a coupling relationship between them so that they can work together as a whole. This method uses the virtual structure method to construct this coupling relationship. The core idea of this method is to regard multiple robots as nodes connected to a virtual rigid body structure, and achieve the coordinated control of each robot by controlling the overall movement of the virtual structure. In the specific implementation process, first define the topological relationship of the virtual structure, and determine the relative positions of each robot in the virtual structure according to the task requirements and workpiece characteristics; then design a virtual spring-damper system to connect each robot to the virtual structure to form an elastic coupling network. The coupling stiffness coefficient is the key parameter to control the coupling strength, and the setting range is 10 - 100. A lower stiffness coefficient makes the system more flexible, and each robot has a larger independent adaptation space, which is suitable for processing workpieces with complex shapes or requiring local adjustment; a higher stiffness coefficient makes the system more rigid, and the movements of each robot are more synchronized, which is suitable for precision spraying tasks that require strict coordination. In practical applications, the coupling stiffness can be dynamically adjusted according to the characteristics of different workpieces and spraying requirements to achieve the best collaborative effect.

[0128] S4.6: Design a distributed control strategy based on event triggering, and set the triggering threshold to a position error of 0.5 mm or an attitude error of 0.5 degrees;

[0129] Traditional time-triggered control strategies need to communicate and calculate at fixed time intervals, which easily causes waste of network resources and excessive computational burden. To improve system efficiency, this method designs a distributed control strategy based on event triggering, and only performs control calculations and information interactions when there are significant changes in the system state. The triggering condition is set to a position error reaching 0.5 mm or an attitude error reaching 0.5 degrees. This threshold is determined comprehensively according to the spraying quality requirements and system dynamic characteristics. Setting the threshold too small will lead to frequent triggering and lose the resource-saving advantage of event triggering; setting the threshold too large may affect control performance. During actual operation, each robot independently monitors its own state. When the error exceeds the triggering threshold, it sends a status update request to the cooperative controller and receives the updated control instruction. At the same time, a maximum non-trigger time limit is introduced to ensure that even if the system is in a stable state for a long time, information can be updated regularly to prevent collaborative failure caused by communication interruption. This distributed control strategy based on event triggering greatly reduces the communication burden and computational resource consumption of the system while maintaining good control performance.

[0130] S4.7: Introduce a prediction compensation mechanism of 100 - 200 milliseconds to ensure the stability of the system when the communication delay and data loss rate do not exceed 5%.

[0131] In an actual multi-robot cooperation system, communication delay and data loss are inevitable problems, and these factors may seriously affect the stability and control performance of the system. To address these challenges, this method introduces a prediction compensation mechanism. By predicting the system state in the next 100 - 200 milliseconds, control instructions are generated in advance to effectively compensate for the impact of communication delay. The setting of the prediction time range takes into account the typical communication delay and controller response time of the system. If the prediction time is too short, it is difficult to effectively compensate for the delay; if the prediction time is too long, inaccurate prediction may be caused by cumulative errors. The prediction model is based on the T-product dynamic system model constructed previously and combines a Kalman filter to achieve state estimation and prediction. At the same time, a packet loss handling mechanism is designed. When data loss is detected, the system will generate an estimated value based on historical data and the prediction model to maintain the continuity of control. Through theoretical analysis and experimental verification, this prediction compensation mechanism can ensure that the system still operates stably under the condition that the communication delay and data loss rate do not exceed 5%. This feature is particularly important for multi-robot cooperation systems in actual industrial environments, greatly improving the robustness and reliability of the system and providing guarantee for the completion of high-quality spraying tasks.

[0132] In another embodiment, the steps of the intelligent spraying robot multi-task cooperation operation method include:

[0133] First, in the process of constructing a discretized sliding mode control framework, it is necessary to establish the discrete state equation of the system. Considering the influence of the sampling period T in the actual control system, the continuous system model is discretized. Specifically, the dynamic equation of the robot is Taylor-expanded at the sampling time tk and the high-order terms are retained to obtain a more accurate discrete state equation. This processing method is different from the traditional direct truncation method and can better retain the dynamic characteristics of the system.

[0134] For the spraying robot system, its dynamic equation can be expressed as:

[0135]

[0136] Among them, M(q) is the inertia matrix, is the Coriolis force and centrifugal force matrix, G(q) is the gravity matrix, and τ is the control input.

[0137] Define the system state as Then the state space representation of the system is:

[0138]

[0139] Among them, f(x) and g(x) are nonlinear functions, and u is the control input.

[0140] By performing Taylor expansion and retaining the second-order terms, the discrete state equation is obtained:

[0141] x(k + 1) = x(k) + Tf(x(k), u(k))+(T 2 / 2)f'(x(k), u(k))f(x(k), u(k))+O(T 3 )

[0142] where T is the sampling period, and f' represents the derivative of the function f with respect to x.

[0143] After obtaining the discrete state equation, an improved sliding mode switching surface is designed. Traditional switching surface design often ignores the influence of discrete sampling, resulting in possible chattering in the actual operation of the system. To solve this problem, a sampling period compensation term σ(k) is introduced in the switching surface design. The core idea of this compensation term is to predict the change trend of the system state within each sampling period and adjust the switching surface parameters accordingly. The sliding mode switching surface is defined as:

[0144] σ(k)=s(k)+αTs(k + 1|k)

[0145] where s(k) is the conventional sliding mode switching surface, s(k + 1|k) is the predicted value of the switching surface at the next moment, and α is the weight coefficient.

[0146] To ensure that the designed controller can make the system state converge to the sliding mode surface and maintain stable motion, an appropriate discrete Lyapunov function is constructed. The quadratic function V(k)=1 / 2σ(k)^2 based on the switching surface is selected as the candidate Lyapunov function. By analyzing the forward difference of the function in the discrete domain ΔV(k)=V(k + 1)-V(k), the controller design condition for ensuring system stability is derived:

[0147] ΔV(k)=V(k + 1)-V(k)≤-ηV(k)

[0148] where η is a positive constant representing the convergence rate.

[0149] Based on the above analysis, a complete discrete sliding mode controller is designed. The design of the controller includes both an equivalent control term ueq(k) for compensating the known dynamics of the system and a switching control term us(k) for canceling system uncertainties and external disturbances. To reduce the chattering phenomenon in discrete implementation, a continuous reaching law is adopted instead of the traditional sign function, and a boundary layer design is introduced. Specifically, the control law is expressed as:

[0150] u(k)=ueq(k)+us(k)

[0151] where ueq(k)=-(g(x(k))^T g(x(k))) -1g(x(k))^T [f(x(k)) + (σ(k) - s(k)) / T]

[0152] u_s(k) = -K·sat(σ(k) / Φ)

[0153] Where K is the control gain matrix, sat(·) is the saturation function, and Φ is the boundary layer thickness, which is set in the range of 0.01 - 0.1.

[0154] Through the above design, a discrete sliding mode controller considering the influence of the sampling period is realized, effectively solving the problem of accuracy degradation in traditional discrete implementation.

[0155] Secondly, before designing the auxiliary variable adaptive barrier function, the constraint conditions and performance indexes of the system are first clearly defined. For the spraying robot system, the main constraints include physical constraints such as the robot joint angle limit (±170 degrees), speed limit (±180 degrees / second), acceleration limit (±900 degrees per second squared), and the workspace boundary. These constraints can be mathematically expressed in the form of inequality constraints g(x) ≤ 0.

[0156] To achieve the softening treatment and adaptive adjustment of the constraints, an auxiliary state variable ξ is innovatively introduced to construct the adaptive barrier function structure. Specifically, for each constraint condition, a logarithmic barrier function of the form B(x, ξ) = -ln((g(x) + ξ) / ξ) is constructed, where ξ is an auxiliary variable with a value range between 0.1 and 10. The special feature of this structure is that by adjusting the value of ξ, the steepness of the barrier function can be dynamically changed, thereby achieving the adaptive control of the constraint boundary.

[0157] Next, designing the parameter adaptive law is the key to realizing the dynamic adjustment of the barrier function. Using the method based on Lyapunov stability theory, the adaptive update law of the auxiliary variable ξ is designed. Specifically, a composite Lyapunov function V(x, ξ) containing the system state and the auxiliary variable is constructed, and by solving the condition dV / dt ≤ 0, the adaptive law of ξ is derived:

[0158] ξ' = -γ(B(x, ξ) - α)

[0159] Where γ is the adaptive gain, with a value range of 1 - 10, and α is the desired value of the barrier function.

[0160] To optimize the barrier function parameters and improve the system performance, a parameter optimization algorithm based on gradient descent is established. By defining a suitable performance index function J(θ) (θ represents the set of parameters to be optimized), the random gradient descent method is used for parameter update:

[0161]

[0162] Among them, η is the learning rate, and its value range is 0.01 - 0.1. To improve the optimization efficiency, a momentum term and an adaptive learning rate strategy are introduced:

[0163]

[0164] Through the above design, the adaptive barrier function control based on auxiliary variables is realized, ensuring the satisfaction of constraints. At the same time, the control strategy can be dynamically adjusted according to the system state, significantly improving the adaptability and performance of the system.

[0165] Again, when establishing the data-driven T-product dynamic system control model, the acquisition of system input and output data is carried out first. A multi-dimensional data acquisition strategy is adopted, and state variables such as the joint angles, angular velocities, motor torques, and end poses of the robot, as well as control input signals and environmental parameters, are recorded simultaneously. Special attention is paid to the selection of the sampling frequency during the data acquisition process to ensure that the dynamic characteristics of the system can be fully captured. To improve the data quality, a filtering algorithm is used to preprocess the original data to remove noise and outliers.

[0166] After obtaining a high-quality data set, the structure of the T-product dynamic model is constructed. The core idea of the T-product model is to decompose the nonlinear dynamic system into the tensor product form of multiple local linear models. Specifically, first, the system state space is divided into N subspaces (N takes values from 4 to 8), and each subspace corresponds to a local linear model. Then, by defining appropriate basis functions (selecting cubic B-spline basis functions), the tensor representation of the state transition matrix is constructed. The advantage of this structural design is that it not only maintains the nonlinear expression ability of the model but also facilitates subsequent parameter identification and controller design.

[0167] The design of the model parameter identification algorithm is a key step to ensure the accuracy of the T-product model. A parameter identification method based on tensor decomposition is adopted to transform the high-dimensional parameter identification problem into several low-dimensional sub-problems. Specifically, when implementing, first, the high-dimensional parameter identification problem is decomposed into sub-problems of three dimensions based on the Tucker decomposition method to obtain the basic factors of each dimension. Then, by constructing a weighted least squares optimization problem with the weight coefficient set to 0.1 - 1.0 and combining the L2 regularization technique, the parameters of each local model are solved. To improve the identification efficiency and accuracy, an adaptive step size strategy and an early stopping criterion are introduced to effectively avoid the overfitting problem.

[0168] Finally, to enable the model to adapt to changes in system parameters and working environments, an online update mechanism for the model was implemented. This mechanism consists of two main parts: one is the fast parameter update based on the recursive least squares (RLS) algorithm, and the other is the adaptive adjustment of the model structure based on a sliding time window. During the online update process, an exponential forgetting factor is used to balance the influence of historical data and new data, and the exponential forgetting factor is set to 0.95 - 0.99. At the same time, the parameter change rate is set to be within 20% to ensure the smoothness of model updates. In addition, a sliding time window based on 100 - 500 sampling points is established for the adaptive adjustment of the model structure. When the model accuracy drops to a preset threshold, the re-optimization of the model structure is triggered.

[0169] Through the above design, a T-product dynamic system model with adaptive capabilities was realized. This design can not only accurately describe the nonlinear dynamic characteristics of the system, but also maintain the timeliness of the model through the online update mechanism, providing a reliable system model support for subsequent controller design.

[0170] Finally, when implementing the multi-robot cooperative control algorithm, it is first necessary to establish accurate multi-robot kinematic and dynamic models. For each spraying robot, an improved D-H parameter method is used to establish the kinematic model, including forward kinematic and inverse kinematic equations. At the same time, the Lagrangian method is used to derive the dynamic equation of the robot, considering the influence of factors such as joint inertia, Coriolis force, and gravity. In particular, special factors such as the nozzle reaction force during the spraying process and the added mass generated by the paint flow are also considered in the dynamic modeling. To improve the model accuracy, a friction compensation model based on experimental data is introduced, including the influence of Coulomb friction, viscous friction, and static friction.

[0171] After completing the basic modeling, efficient task allocation and trajectory planning strategies are designed. The task allocation uses an improved Hungarian algorithm, considering multiple optimization objectives, including workload balance, energy consumption minimization, and spraying quality optimization. The specific objectives include: minimizing the overall energy consumption, making the workload difference between each robot less than 15%, and controlling the spraying overlap rate within 5% - 10%. The trajectory planning is divided into two levels: global planning and local planning. At the global level, an improved RRT* algorithm is used to generate a collision-free rough path, and the sampling point spacing is set to 50 - 100 mm. At the local level, a trajectory optimization method based on a fifth-order polynomial is used to ensure the smoothness and dynamic feasibility of the trajectory, with the position error limited to ±0.1 mm and the attitude error limited to ±0.1 degrees. To improve the planning efficiency, a parallel planning strategy based on workspace division is designed, and a dynamic priority mechanism is introduced to handle potential conflicts between multiple robots.

[0172] Based on the discrete sliding mode controller, adaptive barrier function, and T-product dynamic model developed above, a multi-robot cooperative control system is implemented. The control system adopts a hierarchical architecture: the upper layer is the cooperative controller, which is responsible for the synchronization and coordination of multiple robots, with a control period of 100 milliseconds; the lower layer is the independent controller of each robot, which realizes precise trajectory tracking, with a control period of 1 millisecond. The cooperative controller establishes the coupling relationship between robots through the virtual structure method, sets the coupling stiffness coefficient to 10 - 100, and uses a synchronization control algorithm based on consensus theory to ensure the coordinated movement of multiple robots. To handle practical problems such as communication delays and data loss, a distributed control strategy based on event triggering is designed, with the triggering threshold set to a position error of 0.5 millimeters or an attitude error of 0.5 degrees, and a prediction compensation mechanism of 100 - 200 milliseconds is introduced to ensure the stability of the system when the communication delay and data loss rate do not exceed 5%.

[0173] Finally, to ensure the safe operation of the multi-robot system, a complete collision avoidance and safety protection mechanism is constructed. Collision avoidance adopts a multi-level approach: static obstacles are handled by an improved artificial potential field method, and dynamic obstacles (including other robots) use the velocity obstacle method for real-time obstacle avoidance. The safety protection mechanism includes multiple levels: at the hardware level, emergency stop and limit protection are set; at the software level, real-time monitoring and fault diagnosis are implemented; at the system level, a safety state machine is established to define multiple safety levels and corresponding processing strategies. In particular, an anomaly detection algorithm based on deep learning is also developed, which can early warn of potential safety hazards.

[0174] Through the above implementation manners, the present application realizes an intelligent spraying robot multi-task cooperative operation method and system. This method combines the discrete sliding mode controller design considering the influence of the sampling period, the auxiliary variable adaptive barrier function, the data-driven T-product dynamic system control model, and the multi-robot cooperative control strategy, solves problems such as the decline of discrete implementation accuracy, the difficulty of self-adaptive adjustment of controller parameters, and the lack of effective data-driven control strategies in the prior art, and realizes the efficient cooperative operation of multiple spraying robots.

[0175] In addition, the present application also provides an intelligent spraying robot multi-task cooperative operation system, including a data acquisition module, a discretized sliding mode control module, an adaptive barrier function module, a dynamic model module, and a cooperative control module. Data interaction and control signal transmission are realized between the modules through connection methods such as data buses, real-time data interfaces, Ethernet, and CAN buses, and together they complete the multi-task cooperative operation of the spraying robot.

[0176] Specifically, as Figure 2 shown, the embodiment of the present application provides an intelligent spraying robot multi-task cooperative operation system, including:

[0177] A data acquisition module for collecting joint angle, angular velocity, torque data and control parameters of a spraying robot;

[0178] A discrete sliding mode control module for receiving the data from the data acquisition module and generating a first control quantity. The discrete sliding mode control module is connected to an adaptive barrier function module through a data bus;

[0179] An adaptive barrier function module for receiving the first control quantity and generating a second control quantity in combination with the robot system constraints. The adaptive barrier function module is connected to a dynamic model module through a real-time data interface;

[0180] A dynamic model module for receiving the second control quantity, performing online parameter identification, and generating a third control quantity. The dynamic model module is connected to a cooperative control module through an Ethernet;

[0181] A cooperative control module for receiving the third control quantity, planning multi-robot cooperative trajectories, and outputting control instructions. The cooperative control module is connected to each robot controller through a CAN bus to complete the multi-task cooperative operation of the spraying robot.

[0182] It should be noted that the parameter settings of each step in the above embodiments (such as boundary layer thickness, auxiliary state variable value range, adaptive gain, learning rate, exponential forgetting factor, etc.) are optimized values obtained based on a large amount of experimental data and theoretical analysis, and can be appropriately adjusted according to specific working conditions in actual applications to obtain the best control effect.

[0183] In addition, those skilled in the art can understand that the method provided in the embodiments of the present application is not only applicable to the spraying robot system, but can also be extended and applied to other types of multi-robot cooperative operation scenarios, such as industrial fields such as welding, assembly, and handling, and has a wide range of application prospects.

[0184] Finally, it should be noted that the above embodiments are only specific implementation manners of the present disclosure, used to illustrate the technical solutions of the present disclosure, rather than limiting them. The protection scope of the present disclosure is not limited thereto. Although the present disclosure has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: any person skilled in the art within the technical scope disclosed by the present disclosure can still modify or easily think of changes to the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications, changes or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present disclosure, and should all be covered by the protection scope of the present disclosure. Therefore, the protection scope of the present disclosure should be subject to the protection scope of the claims.

Claims

1. An intelligent spray robot multi-task collaborative operation method, characterized in that: include: Collecting joint angles, angular velocities, torque data and control parameters of the spraying robot as state data, establishing a discrete state equation including a sampling period T based on the state data, introducing a sampling period compensation term to design a sliding mode switching surface, constructing a discrete Lyapunov function, and generating a first control quantity; Based on the first control quantity, combined with the robot joint angle limit, speed limit, acceleration limit and workspace boundary constraint, an adaptive barrier function is constructed, and the barrier function parameters are optimized by the gradient descent method to generate a second control quantity; Based on the second control quantity, the input and output data of the spraying robot during online operation are collected, a T-product dynamic system control model is constructed, the model parameters are identified and updated online, and a third control quantity is generated; Based on the third control quantity, a multi-robot kinematic and dynamic model is established, and a hierarchical control strategy is adopted to realize multi-robot collaborative control, output control instructions that meet the workload balance and spraying quality requirements, and control multiple spraying robots to complete collaborative operations.

2. The method according to claim 1, characterized in that A discrete state equation including a sampling period T is established based on the state data, including: Taylor expansion is performed on the robot dynamics equation at the sampling time, the second-order terms are retained, and a discrete state equation including a sampling period T is established; based on the discrete state equation, an improved sliding mode switching surface is designed, and a quadratic discrete Lyapunov function is constructed; Analyzing the forward difference of the discrete Lyapunov function to obtain a stability condition; According to the stability condition, a discrete sliding mode controller including an equivalent control term and a switching control term is designed to generate the first control variable.

3. The method according to claim 2, characterized in that Design a discrete sliding mode controller with equivalent and switching control terms, including: Based on the stability conditions, equivalent control items are designed to compensate for known system dynamics, and switching control items are designed to offset external disturbances; A continuous reaching law is adopted in the discrete sliding mode controller to set the boundary layer thickness to a value within the range of 0.01-0.1; A saturation function is used in the switching control item instead of a sign function to generate the first control amount.

4. The method according to claim 1, characterized in that: Build an adaptive barrier function, including: Set the robot joint angle limit to ±170 degrees, the speed limit to ±180 degrees / second, and the acceleration limit to ±900 degrees / second squared; An auxiliary state variable ξ with a value range of 0.1-10 is introduced to construct a logarithmic barrier function B(x,ξ)=-ln((g(x)+ξ) / ξ), where g(x) represents a constraint function; By adjusting the value of the auxiliary state variable ξ, the steepness of the barrier function is dynamically changed to generate an adaptive barrier function.

5. The method according to claim 4, characterized in that The barrier function parameters are optimized using the gradient descent method, including: Construct a composite Lyapunov function V(x,ξ) and design an adaptive law ξ'=-γ(B(x,ξ)-α), where γ is the adaptive gain, ranging from 1 to 10, and α is the expected barrier function value; The stochastic gradient descent method is used to update the parameters, and the parameter update step size is set to 0.01-0.1; A momentum coefficient of 0.9 and an adaptive learning rate strategy are introduced to generate the second control quantity.

6. The method according to claim 1, characterized in that Construct a T-product dynamic system control model, including: Collecting joint angle data, angular velocity data, motor torque data and terminal position data of the spraying robot within a sampling period T as input data; The system state space is divided into N subspaces, where the value of N ranges from 4 to 8, and each subspace corresponds to a local linear model; The cubic B-spline basis function is selected as the basis function, the tensor representation of the state transfer matrix is ​​constructed, and the T-product dynamic system model structure is generated.

7. The method according to claim 6, characterized in that Realize online identification and update of model parameters, including: Based on the T-product dynamic system model structure, the Tucker decomposition method is used to decompose the high-dimensional parameter identification problem into sub-problems of three dimensions; A weighted least squares optimization problem was constructed, with the weight coefficient set to 0.1-1.0, and the L2 regularization method was used to solve each local model parameter; the model parameters were updated using a recursive least squares algorithm, and the exponential forgetting factor was set to 0.95-0.99; The model structure is adjusted based on a sliding time window of 100-500 sampling points, and the parameter change rate is limited within 20% to generate the third control amount.

8. The method according to claim 1, characterized in that A hierarchical control strategy is used to realize multi-robot collaborative control, including: based on the third control quantity, an improved Hungarian algorithm is used to perform task allocation, and the optimization objectives include: Minimize overall energy consumption, make the workload difference of each robot less than 15%, and control the spraying overlap rate to 5%-10%; The improved RRT* algorithm was used to generate collision-free paths at the global layer, and the sampling point spacing was set to 50-100 mm; A quintic polynomial function is used to optimize the trajectory at the local layer, with the position error limited to ±0.1 mm and the attitude error limited to ±0.1 degrees.

9. The method according to claim 8, characterized in that Realize multi-robot collaborative control, including: A hierarchical control architecture is adopted, with a control cycle of 100 milliseconds for the upper-layer collaborative controller and 1 millisecond for the lower-layer independent controller; The coupling relationship between robots is established through the virtual structure method, and the coupling stiffness coefficient is set to 10-100; Design a distributed control strategy based on event triggering, with the trigger threshold set to a position error of 0.5 mm or an attitude error of 0.5 degrees; A 100-200 millisecond prediction compensation mechanism is introduced to ensure the stability of the system when the communication delay and data loss rate do not exceed 5%.

10. An intelligent spraying robot multi-task collaborative operation system, characterized in that: include: Data acquisition module, used to collect joint angle, angular velocity, torque data and control parameters of the spray robot; A discretized sliding mode control module, used for receiving data from the data acquisition module and generating a first control quantity, wherein the discretized sliding mode control module is connected to the adaptive barrier function module via a data bus; An adaptive barrier function module, used for receiving the first control quantity and generating a second control quantity in combination with the robot system constraint, wherein the adaptive barrier function module is connected to the dynamic model module via a real-time data interface; A dynamic model module, used for receiving the second control quantity, performing online parameter identification, and generating a third control quantity, wherein the dynamic model module is connected to the collaborative control module via Ethernet; The collaborative control module is used to receive the third control quantity, plan the multi-robot collaborative trajectory, and output control instructions. The collaborative control module is connected to each robot controller through a CAN bus to complete the multi-task collaborative operation of the spray robot.

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