Fuzzy adaptive sliding mode control calculation method for dual-arm collaborative robot

Abstract

The application discloses a fuzzy adaptive sliding mode control calculation method for a dual-arm collaborative robot, relates to the technical field of industrial control and intelligent robots, and comprises the following steps: acquiring real-time sensor data in an environment, determining geometric constraint conditions by analyzing the data, adopting population diversity coding to process initial parameter randomization to generate geometric initialization of a left-arm sliding mode surface, a right-arm sliding mode surface and a collaborative constraint sliding mode surface, obtaining an environment variable set under current task requirements, calculating and evaluating an initial design by using a fitness function according to the environment variable set, embedding and processing coding bit strings in combination with constraint conditions, determining preliminary adjustment parameters under a population size setting, and obtaining an optimized shape framework; the fuzzy adaptive sliding mode control calculation method for the dual-arm collaborative robot realizes effective adaptation to geometric constraints and improvement of collaborative control performance, reduces path interference and conflict occurrence, and enhances the adaptability and control efficiency of the system in a variable environment.

Description

Technical Field

[0001] This invention relates to the field of industrial control and intelligent robot technology, specifically to a fuzzy adaptive sliding mode control calculation method for dual-arm collaborative robots. Background Technology

[0002] In existing industrial robot control, although sliding mode control is widely used due to its strong robustness, in dual-arm cooperative operation scenarios, existing methods generally lack unified modeling of real-time data from multiple sources of sensors and online construction of environmental variable sets, making it difficult to determine geometric constraints and cooperative relative pose constraints in a timely and stable manner. Sliding surface design is often oriented towards a single arm or independent channel, making it difficult to simultaneously form the left arm sliding surface, the right arm sliding surface, and the cooperative constraint sliding surface and complete geometric initialization. Moreover, it often relies on empirical parameters and lacks objective evaluation based on fitness functions and parameterized shape frameworks for the left and right arms and cooperative surfaces, resulting in insufficient initialization accuracy and convergence efficiency, which in turn affects the trackability and stability domain under complex tasks.

[0003] Furthermore, existing technologies do not adequately utilize historical information on trajectory contour characteristics, lacking a mechanism to extract sample bias into adaptive correction coefficients and formulate dynamic contour update rules accordingly. Under external disturbances or path congestion, the control layer lacks the ability to intrinsically integrate robustness assessment with path interference sign detection, and it also fails to form a closed-loop linkage with equipment interaction data and conflict detection thresholds. The application of variable path generation and variable operation probabilities also lacks a unified process for mapping them into control conflict quantification indicators and driving path adjustment and contour sequence iteration. Regarding control law solutions, most methods still employ fixed gain or a single switching term, lacking explicit fuzzy adaptive sliding mode terms to participate in dual-arm torque / velocity calculations, making it difficult to balance chatter suppression and constraint satisfaction. Simultaneously, they lack online verification of task matching based on real-time feedback data and output of the final sliding surface configuration, making it difficult to stably generate left / right arm joint torque or velocity commands. Summary of the Invention

[0004] The purpose of this invention is to provide a fuzzy adaptive sliding mode control calculation method for dual-arm collaborative robots, thereby solving the problems existing in the prior art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a fuzzy adaptive sliding mode control calculation method for dual-arm collaborative robots, the method comprising the following steps:

[0006] S1. Acquire real-time sensor data in the environment, determine geometric constraints by analyzing the data, and use population diversity coding to process the initial parameters to randomize and generate the geometric initialization of the left arm sliding surface, the right arm sliding surface, and the cooperative constraint sliding surface, thereby obtaining the set of environmental variables under the current task requirements.

[0007] S2. Based on the set of environmental variables, the fitness function is used to evaluate the initial design. Combined with the constraint condition embedding processing of the encoded bit string representation, the preliminary adjustment parameters under the population size setting are determined to obtain the optimized shape framework.

[0008] S3. By optimizing the shape framework, obtain historical data samples of contour characteristics. If the matching degree between the sample and the task requirements is lower than the preset threshold, use the initial iteration number to generate processing samples and obtain the adaptive correction coefficient of contour characteristics. The correction coefficient is used as the initial value for gain and parameter tuning. The correction coefficient is used to initialize the fuzzy rule weight and fuzzy gain.

[0009] S4. Based on the adaptive correction coefficient, determine the dynamic contour update rule of the sliding surface, integrate the robustness assessment of the design to detect path interference signs, construct a fuzzy inference engine, take the sliding surface and the sliding surface change rate as input, and tune the switching gain and boundary layer thickness online to obtain the contour adjustment sequence for the variable environment.

[0010] S5. By adjusting the contour sequence, obtain the equipment interaction data in the collaborative operation. If the data shows signs of path interference, then fuse the mutated path generation to determine the conflict detection threshold and obtain the quantitative index calculation result for controlling the conflict.

[0011] Preferably, step S1 includes acquiring real-time sensor data in the environment, removing noise using a preset filtering algorithm to obtain a clean sensor dataset; analyzing the clean sensor dataset and using a clustering algorithm to determine geometric constraints to obtain an environmental geometric parameter set; randomizing initial parameters using a population diversity coding method to generate a parameter initialization set for the environmental geometric parameter set; constructing geometric models of the left and right arm sliding surfaces based on the parameter initialization set to obtain an independent sliding surface set; if the independent sliding surface set satisfies a preset collaborative constraint threshold, generating a collaborative constraint sliding surface using a geometric optimization algorithm to obtain a collaborative sliding surface model; adjusting the environmental variable set by analyzing the matching degree between the collaborative sliding surface model and the task requirement analysis to obtain an optimized environmental variable set; and updating the sliding surface generation parameters based on the optimized environmental variable set to obtain the final task-adapted sliding surface set.

[0012] Preferably, step S2 includes: acquiring a set of environmental variables; processing the data using a preset feature extraction algorithm to generate a set of feature vectors; calculating the fitness of individuals using a genetic algorithm based on the set of feature vectors to obtain a fitness evaluation result; generating a set of encoded bit strings using a constraint embedding method if the fitness evaluation result meets a preset threshold, otherwise adjusting the set of feature vectors; optimizing parameter configuration using a simulated annealing algorithm based on the set of encoded bit strings to obtain a preliminary parameter set; constructing a geometric representation of the shape framework using the preliminary parameter set to obtain an initial shape model; adjusting the geometric parameters using an iterative optimization method if the initial shape model meets the task constraint threshold to obtain an optimized shape framework; and generating an updated set of environmental variables for task adaptation based on the optimized shape framework.

[0013] Preferably, step S3 includes obtaining historical sample data of contour features from the optimized shape framework, removing outliers from the sample data using a data cleaning method to obtain a cleaned sample dataset; if the matching degree between the cleaned sample dataset and the task requirements is lower than a preset threshold, then grouping the sample dataset using a k-means clustering algorithm to obtain a feature group set; based on the feature group set, extracting the main feature vectors using a principal component analysis algorithm to obtain a dimensionality-reduced feature vector set; if the feature expressive power of the dimensionality-reduced feature vector set is lower than a preset threshold, then adjusting the feature vector weights using a gradient boosting method to obtain an optimized feature weight set; generating adaptive correction coefficients based on the optimized feature weight set, applying the correction coefficients to the fuzzy rule weights using a linear mapping method to obtain an updated fuzzy rule set; using the updated fuzzy rule set, adjusting the initial parameter configuration using a fuzzy gain algorithm to obtain an optimized parameter configuration set; and updating the geometric expression of the shape framework using the optimized parameter configuration set to obtain a final shape model adapted to the task requirements.

[0014] Preferably, step S4 includes extracting dynamic features from adaptive correction coefficients, decomposing the coefficient matrix using principal component analysis (PCA) to obtain a set of principal feature vectors; constructing sliding surface update rules based on the set of principal feature vectors, and generating an initial dynamic rule set using a weighted linear combination method; if the matching degree between the initial dynamic rule set and path interference signs is lower than a preset threshold, then using a support vector machine (SVM) algorithm to classify the rule set to obtain an optimized dynamic rule set; integrating robustness assessment detection with the optimized dynamic rule set, processing the interference sign data using a mean filtering method to obtain a smoothed interference feature set; constructing a fuzzy inference engine based on the smoothed interference feature set, using the sliding surface change rate as input, adjusting the switching gain through membership function mapping to obtain an updated gain parameter set; using the updated gain parameter set, combining it with boundary layer thickness adjustment rules, tuning the thickness parameters online using a linear interpolation method to obtain a parameter configuration set adapted to the environment; generating a contour adjustment sequence using the parameter configuration set, predicting the stability of the adjustment sequence using time series analysis to obtain the final contour adjustment sequence.

[0015] Preferably, step S5 includes extracting device interaction data through a contour adjustment sequence, dividing the data into multiple time segments using a time series segmentation method to obtain a segmented interaction dataset; if path interference is present in the segmented interaction dataset, analyzing the interference signal strength using a Fourier transform method to obtain an interference frequency feature set; constructing multiple candidate paths using a mutation path generation method based on the interference frequency feature set to obtain a candidate path set; performing conflict detection using a support vector machine algorithm on the candidate path set to determine whether the candidate paths exceed a preset conflict detection threshold, thus obtaining a conflict path subset; if the conflict path subset is not empty, integrating the control conflict index and the collaborative operation mode using a weighted average method to generate an adjusted path parameter set; optimizing the dynamic change trend of the device interaction data using a linear interpolation method based on the adjusted path parameter set to obtain a smoothed path sequence; and updating the contour adjustment sequence using the smoothed path sequence to generate the final collaborative operation path configuration set.

[0016] Preferably, the method further includes S6: based on the calculation results of the quantification indicators, using path adjustment fusion iterative contour adjustment sequence, combined with interference sign identification to determine the mitigation mapping under the probability of mutation operation, calculating the dual-arm control law, and obtaining an optimized collaborative control instruction set. Specifically, this includes extracting key features through the quantification indicator set using principal component analysis to generate a feature vector set; dividing the data into groups using clustering analysis based on the feature vector set to obtain a dynamic interactive data subset; if there are abnormal fluctuations in the dynamic interactive data subset, extracting signal frequency features through Fourier transform to generate a frequency feature set.

[0017] Preferably, step S6 further includes calculating the probability distribution of mutation operations using a Bayesian inference method based on the frequency feature set to obtain a probability distribution set; generating a path adjustment strategy and constructing a mitigation mapping set using the probability distribution set; optimizing the dual-arm control law parameters using a linear interpolation method based on the mitigation mapping set to generate a control parameter set; and updating the contour sequence adjustment and generating an optimized cooperative instruction set using the control parameter set.

[0018] Preferably, the method further includes S7: acquiring real-time feedback data through an optimized collaborative control instruction set; if the data meets the task requirements, outputting the final sliding surface configuration and generating joint torque commands or joint velocity commands for the left and right arms to obtain a control strategy adapted to geometric constraints. Specifically, this includes acquiring real-time feedback data, extracting dynamic change features from the data using time series analysis to obtain a dynamic feature set; using the dynamic feature set, classifying whether the data meets the task requirements using a support vector machine method to determine the classification result; if the classification result meets the task requirements, generating an initial sliding surface configuration based on the dynamic feature set to obtain the sliding surface parameters.

[0019] Preferably, step S7 further includes calculating the joint torque commands of the left and right arms using the sliding surface parameters to generate a torque command set; optimizing the commands using a linear programming method based on the torque command set and geometric constraints to obtain an optimized command set; generating a control strategy adapted to geometric constraints by optimizing the command set and determining the final control output; and adjusting the dynamic feature set and regenerating the sliding surface configuration by real-time feedback data if the classification result does not meet the task requirements.

[0020] As can be seen from the above technical solution, the present invention has the following beneficial effects:

[0021] This invention acquires real-time sensor data from variable environments and determines geometric constraints and cooperative relative pose constraints. It employs population diversity coding to randomize initialization parameters, generating geometric initializations for the left arm sliding surface, right arm sliding surface, and cooperative constraint sliding surface. Based on a set of environmental variables and combined with a fitness function, an optimized shape framework for parameterizing the left and right arms and cooperative sliding surfaces is formed, thereby improving the accuracy and convergence efficiency of sliding surface initialization. Furthermore, adaptive correction coefficients obtained from historical samples are used as initial values ​​for the rule weights / gains of the fuzzy adaptive module. Based on dynamic contour update rules, combined with robustness evaluation and path interference detection, a contour adjustment sequence for variable environments is generated, achieving online optimization of the sliding surface and its parameters. Based on the interaction data of equipment in collaborative operations and the judgment of conflict detection thresholds, combined with variable path generation and variable operation probability, the quantitative index calculation results of control conflict are obtained. Based on this, path adjustment and contour sequence iteration are performed, and the dual-arm control law is calculated by generating fuzzy adaptive sliding mode terms, outputting an optimized collaborative control instruction set. The task requirement matching degree is checked by real-time feedback data, and finally the sliding mode surface configuration is output and the left / right arm joint torque or speed commands are generated. This achieves effective adaptation to geometric constraints and improves collaborative control performance, reduces path interference and conflict occurrence, and enhances the system's adaptability and control efficiency in variable environments. Attached Figure Description

[0022] Figure 1 This is a flowchart of the fuzzy adaptive sliding mode control calculation method for dual-arm collaborative robots according to the present invention. Detailed Implementation

[0023] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] like Figure 1 As shown, this invention provides a technical solution: a fuzzy adaptive sliding mode control calculation method for dual-arm collaborative robots, the method comprising the following steps:

[0025] S1. Acquire real-time sensor data in the environment, determine geometric constraints by analyzing the data, and use population diversity coding to process the initial parameters to randomize and generate the geometric initialization of the left arm sliding surface, the right arm sliding surface, and the cooperative constraint sliding surface, thereby obtaining the set of environmental variables under the current task requirements.

[0026] S2. Based on the set of environmental variables, the fitness function is used to evaluate the initial design. Combined with the constraint condition embedding processing of the encoded bit string representation, the preliminary adjustment parameters under the population size setting are determined to obtain the optimized shape framework.

[0027] S3. By optimizing the shape framework, obtain historical data samples of contour characteristics. If the matching degree between the sample and the task requirements is lower than the preset threshold, use the initial iteration number to generate processing samples and obtain the adaptive correction coefficient of contour characteristics. The correction coefficient is used as the initial value for gain and parameter tuning. The correction coefficient is used to initialize the fuzzy rule weight and fuzzy gain.

[0028] S4. Based on the adaptive correction coefficient, determine the dynamic contour update rule of the sliding surface, integrate the robustness assessment of the design to detect path interference signs, construct a fuzzy inference engine, take the sliding surface and the sliding surface change rate as input, and tune the switching gain and boundary layer thickness online to obtain the contour adjustment sequence for the variable environment.

[0029] S5. By adjusting the contour sequence, obtain the equipment interaction data in the collaborative operation. If the data shows signs of path interference, then fuse the mutated path generation to determine the conflict detection threshold and obtain the quantitative index calculation result for controlling the conflict.

[0030] S6. Based on the quantitative index calculation results, the path adjustment fusion iterative contour adjustment sequence is adopted, and the mitigation mapping under the probability of mutation operation is determined by combining the interference sign identification. The dual-arm control law is calculated to obtain the optimized cooperative control instruction set.

[0031] S7. By optimizing the collaborative control instruction set, real-time feedback data is obtained. If the data meets the task requirements, the final sliding surface configuration is output, and joint torque or speed commands for the left and right arms are generated to obtain a control strategy that adapts to geometric constraints.

[0032] This implementation method is based on fuzzy control theory and sliding mode variable structure control principle. By combining evolutionary computation methods and adaptive parameter adjustment mechanisms, it constructs a computational method for stable, robust, and high-precision control of a dual-arm collaborative robot in complex environments. The overall workflow can be divided into seven stages: task environment modeling, sliding mode surface construction and initialization, adaptive adjustment of control parameters, dynamic updating of the fuzzy controller, disturbance detection and path adjustment, control law optimization output, and feedback closed-loop control. Specifically, in the task initialization stage, real-time environmental information is collected by various types of sensors deployed in the collaborative environment (such as laser rangefinders, depth cameras, and vision trackers), forming a raw dataset containing spatial location, obstacle boundaries, and collaborative object states. Through data preprocessing and feature extraction, geometric constraints for task execution are constructed, including dual-arm reachability constraints, obstacle dynamic boundaries, and interactive object dimensions. Subsequently, population diversity encoding (such as real number serial encoding and multi-target individual perturbation strategies) is used to initialize the sliding mode surface shape parameters, where the sliding mode surface includes the left arm sliding mode surface, the right arm sliding mode surface, and a collaborative constraint sliding mode surface for coordinating the collaborative motion of the two arms. The sliding surface defines the mapping relationship between control state variables (such as error state) and switching functions, and its construction is directly constrained by the current set of environmental variables. An initial population generation algorithm is used for shape encoding to ensure the sliding controller has a diverse initial policy set. After the initial policies are formed, each sliding surface is evaluated multiple times based on a preset fitness function (comprehensively considering control stability, response time, error convergence rate, etc.), and combined with an embedded bit string encoding structure for environmental geometric constraints, the sliding surface parameters are progressively adjusted, ultimately forming a sliding surface shape framework with locally optimal contour features. To further improve the control's adaptability to unstructured environments, a task contour characteristic matching mechanism is introduced. This mechanism analyzes the current sliding surface's fit based on historical task data samples (including path trajectories, disturbance responses, execution results, etc.) and triggers a correction mechanism when the matching degree falls below a threshold. New samples are generated iteratively, and contour fitting deviation analysis is performed with existing samples to generate adaptive correction coefficients. These correction coefficients are used to dynamically adjust the rule weights and initial gain values ​​of the fuzzy controller, ensuring that the controller can quickly adjust its control response strategy under nonlinear dynamic conditions. The fuzzy inference engine, as the core decision-making module, takes the current state and rate of change of the sliding surface as input. It generates output control variables in real time through fuzzy membership function mapping and a rule base, while simultaneously tuning the sliding mode gain and boundary layer thickness online to achieve adaptive switching between different operating modes. This process incorporates a robustness evaluation mechanism to detect potential path disturbances, such as collision approach, sudden load changes, or joint jitter, providing early warnings and adjusting the control response amplitude and strategy strength. Based on this, a contour adjustment sequence drives the path reconstruction operation during dual-arm task execution.The system collects equipment interaction data during the collaboration process and uses a mutation path generation model to determine conflicts. An interference intensity scoring model is constructed using quantitative indicators (such as minimum safe distance, conflict area overlap rate, and trajectory interference) to provide a basis for subsequent path adjustment. Finally, based on the conflict quantification results, a fusion-based path adjustment mechanism is executed. While maintaining the continuity of the task trajectory, the joint control commands (including torque control or speed control commands) for the left and right arms are regenerated by adjusting the sliding mode profile sequence, the mapping relationship between mutation operation probabilities and control laws. The entire control process forms a highly adaptive control chain consisting of "data perception—rule correction—dynamic adjustment—feedback closed loop," achieving the dynamic optimal control objective under task conditions.

[0033] This method exhibits strong adaptability and robustness, effectively improving the control accuracy and execution efficiency of a dual-arm collaborative robot. Under varying geometric environments and path disturbances, the introduction of a sliding surface dynamic adjustment mechanism and fuzzy inference structure significantly enhances the detection and response capabilities to path interference, ensuring the coordination of the left and right arms during collaborative operations. The optimized control instruction set and parameter adjustment mechanism reduce errors and conflicts during task execution, improving control stability and efficiency. Furthermore, the introduction of a sample matching mechanism and gain self-adjustment function enables agile response of control parameters to task changes, demonstrating promising prospects for industrial applications.

[0034] S1 includes acquiring real-time sensor data in the environment, removing noise through a preset filtering algorithm to obtain a clean sensor dataset; analyzing the clean sensor dataset and using a clustering algorithm to determine geometric constraints to obtain an environmental geometric parameter set; randomizing initial parameters for the environmental geometric parameter set using a population diversity coding method to generate a parameter initialization set; constructing geometric models of the left and right arm sliding surfaces based on the parameter initialization set to obtain an independent sliding surface set; if the independent sliding surface set meets a preset collaborative constraint threshold, generating a collaborative constraint sliding surface through a geometric optimization algorithm to obtain a collaborative sliding surface model; adjusting the environmental variable set by analyzing the matching degree between the collaborative sliding surface model and the task requirement analysis to obtain an optimized environmental variable set; and updating the sliding surface generation parameters based on the optimized environmental variable set to obtain the final task-adapted sliding surface set.

[0035] In this embodiment, the complete working principle of step S1 includes seven consecutive processing steps, namely data acquisition, noise removal, geometric constraint identification, parameter initialization, sliding surface construction, collaborative threshold judgment, and sliding surface optimization. First, the robot control acquires raw data from multiple real-time sensors deployed in the working environment. Sensor types may include 3D depth sensors, structured light cameras, and inertial measurement units. These devices acquire approximately thirty frames of raw images and point cloud data per second, with a total data volume of approximately two million data points per second. The raw dataset contains a large number of high-frequency noise points affected by background light, motion vibration, etc. The built-in data cleaning module uses a median filtering algorithm with a fixed window length to denoise the raw data. The processing method is as follows: every ten frames of data is considered a cycle, and the position of each point in adjacent frames is sorted according to the coordinate axis direction. The median position value is taken as the representative position of the point within that cycle, ultimately forming a clean sensor dataset without abnormal drift.

[0036] After the dataset is constructed, the geometric constraint analysis process begins. The analysis method employs a density-based spatial clustering algorithm. The clustering trigger condition is set as follows: within a cubic space, each cubic block has a volume of one cubic decimeter. If there are more than twenty consecutive point cloud data points within a block, and the average distance between these points in three-dimensional Euclidean space is less than 0.1 meters, then the spatial block is identified as having a physical obstacle or structural boundary. After analysis, structural labels are generated for these spatial blocks, and their geometric attributes, such as center point coordinates, boundary length, normal direction, and orientation angle, are recorded. All data is processed using a unified unit to generate an environmental geometric parameter set.

[0037] After acquiring the environmental geometric parameter set, a parameter initialization process is performed. The initialization parameters include six dimensions: three spatial control point positions, two sliding surface direction vectors, and one initial sliding surface weight value. Each control point position is represented by a three-dimensional coordinate, with its range set to no more than ±1 meter within the maximum working radius of the current task area. The direction vector is randomly selected from a set of directions whose angle with the target operating direction is less than 45 degrees. The weight value is used to adjust the slope of the sliding surface in the switching function, and its value range is set to a real value between 0.1 and 1. All parameters are encoded using real numbers, forming a complete set of initial sliding surface parameters. Parameter initialization employs a population random generation mechanism, generating fifty different parameter sets at a time, which are recorded using an index matrix.

[0038] The parameter codes are read one group at a time from the parameter initialization set. Each code contains six numerical parameters: the first three values ​​are the three-dimensional spatial coordinates of three control points, representing the X, Y, and Z coordinates of points A, B, and C respectively, for a total of nine coordinate values ​​in meters. The fourth and fifth values ​​are two spatial orientation angles, representing the pitch and yaw angles of the sliding surface, in degrees, used to determine the orientation of the surface in three-dimensional space. The sixth value is the initial weight value of the sliding surface, a dimensionless real number, typically set between 0.1 and 1.0, used to adjust the sensitivity and tilt of the switching function in the sliding mode controller. After decoding, the geometric mapping stage begins. A three-dimensional plane is defined using the coordinates of three control points. Specifically, point A serves as the starting control point for the sliding surface; point B is used to establish the direction vector; and point C provides the spatial offset. These three points together define a non-collinear surface. Based on the spatial relationship between these three points, the normal vector and the offset from the origin of the plane are calculated, and the geometric foundation surface of the sliding surface is established accordingly. Next, the plane is rotated to a set direction based on the pitch and yaw angles. The pitch angle represents the rotation angle of the plane around the X-axis, and the yaw angle represents the rotation angle around the Z-axis. A three-dimensional rotation transformation is performed based on these two angles to ensure that the sliding surface orientation is consistent with the collaborative task direction. Subsequently, this geometric model is bound to the initial weight parameters to construct a complete sliding surface model object. This model includes: the spatial position of the surface (composed of three points); the orientation of the surface (given by the direction angle); control weights (determining the adjustment role of the surface in the control law); and additional attributes (such as surface dimensions, control domain boundaries, etc., extended according to the default algorithm). After constructing a sliding surface model, it is categorized as either a left-arm or right-arm sliding surface. This categorization is determined by the identifier field of the corresponding code in the initialization set (e.g., the first 25 sets for the left arm and the last 25 sets for the right arm, or a separate flag indicates this). This process is repeated for all initialization parameter sets, ultimately forming a left-arm sliding surface set and a right-arm sliding surface set, which are then merged to form an independent sliding surface set. Each sliding surface possesses a complete spatial geometric definition, directional attributes, and control weights, and can be directly used for subsequent collaborative evaluation and fuzzy controller construction.

[0039] After constructing the independent sliding surfaces, it is determined whether the left and right sliding surfaces satisfy the cooperative constraint conditions. The evaluation basis for the cooperative constraint is the coupling error value between the sliding surfaces, which is defined as the maximum deviation of the control variables in the overlapping area of ​​the sliding surfaces. Specifically, fifty equidistant sampling points are extracted in the overlapping area of ​​the two sliding surfaces, and the difference in normal distance between the points on the two sliding surfaces is calculated. The maximum value is taken as the coupling error value. The preset cooperative constraint threshold is 0.05 meters. That is, if the coupling error value of all sliding surfaces is less than or equal to 0.05 meters, it is determined that the cooperative control requirements are met. Once the judgment is passed, the cooperative sliding surface construction process is executed. The method is as follows: linear interpolation is performed on the control points in the left and right sliding surfaces, and the two sets of control points are connected in corresponding order to form a new intermediate control point group. The direction vectors are also superimposed proportionally and normalized. The initial weight value is the average value of the left and right sides, and finally a cooperative sliding surface model is formed.

[0040] Subsequently, a matching degree analysis was performed on the current task requirements based on the collaborative sliding surface model. The analysis indicators included four aspects: sliding surface profile shape, control direction consistency, coverage trajectory integrity, and error tolerance satisfaction. Task requirement parameters were provided by the task scheduler, including the desired motion trajectory direction, maximum allowable control error, expected load state, and operation time window. Each of the four indicators was scored out of 100%, and the average of the four indicators was the matching degree score. If the score was below 80%, the current sliding surface was considered not to fully meet the task requirements, and the environmental variable set needed adjustment. The adjustment method was to linearly correct the position and direction terms in the environmental geometric parameter set according to the error direction, delete obstacle data with excessive deviations, and regenerate the environmental geometric parameter set. Based on the optimized geometric parameter set, the parameter initialization, sliding surface generation, and collaborative surface construction processes were run again, ultimately obtaining a set of sliding surfaces that met the constraints and fully matched the task. This set was used for the subsequent design of the fuzzy adaptive sliding controller and the generation of control laws.

[0041] The cooperative constraint threshold is set to 0.05 meters, based on the comprehensive requirements for control accuracy, stability, and tolerance range when a dual-arm collaborative robot performs synchronous control tasks. This threshold is used to determine whether the coupling error between the left and right sliding surfaces within the overlapping control area is within an acceptable range. The coupling error is specifically defined as the difference in the maximum normal distance between the two sliding surfaces at corresponding positions. By sampling 50 equally spaced points within the overlapping area, the normal difference between the corresponding points on the two sliding surfaces is calculated, and the maximum value is taken as the coupling error value, which is then compared with the threshold. When the maximum coupling error is less than or equal to 0.05 meters, the cooperative control conditions are considered met. The selection of this value mainly considers the following three factors: First, based on the actual operational precision requirements of industrial robots, the allowable control error in fine operation scenarios is usually no more than 5 cm; second, considering the stability of the switching function of sliding mode control, simulation and experimental results show that when the sliding surface coupling error is controlled within 5 cm, the controller response is stable, with no obvious high-frequency jitter or drift; third, combining the current sensor accuracy and controller closed-loop response performance, the threshold is set to 0.05 m under the influence of comprehensive error sources. This avoids coordination failure due to excessively small errors and ensures the continuity and stability of subsequent fuzzy control strategies. Therefore, setting the coordination constraint threshold to 0.05 m has sufficient engineering basis and conforms to control logic, ensuring that the control strategy has good robustness and task adaptability in dynamic environments.

[0042] S2 includes: acquiring a set of environmental variables; processing the data using a pre-defined feature extraction algorithm to generate a set of feature vectors; calculating the fitness of individuals using a genetic algorithm based on the set of feature vectors to obtain fitness evaluation results; if the fitness evaluation results meet a pre-defined threshold, generating a set of encoded bit strings using a constraint embedding method; otherwise, adjusting the set of feature vectors; optimizing parameter configuration using a simulated annealing algorithm based on the set of encoded bit strings to obtain a preliminary parameter set; constructing a geometric representation of the shape framework using the preliminary parameter set to obtain an initial shape model; if the initial shape model meets the task constraint threshold, adjusting the geometric parameters using an iterative optimization method to obtain an optimized shape framework; and generating an updated set of environmental variables for task adaptation based on the optimized shape framework.

[0043] In this embodiment, the specific working principle of step S2 revolves around the task adaptability optimization of sliding mode control parameters. Relying on a continuous operation process including feature extraction, evolutionary optimization, geometric modeling, and threshold constraint judgment, the algorithm controls the dynamic calculation of sliding surface generation parameters and the orderly updating of environmental variables. First, the set of environmental variables input from the previous process is obtained. Each data item in this set includes the three-dimensional coordinates of the control points, the length of the boundary structure, the curvature of the obstacle edge, the path direction vector, and the reachable area information. All data units are standardized in the International System of Units (SI), with coordinates in meters, angles in degrees, and changes in boundary and curvature measured per meter. The built-in feature extraction algorithm is applied to this set to extract four key features: the structure density value, the average boundary curvature, the average control point spacing, and the path direction deviation angle. These features constitute each individual feature vector in the feature vector set. The specific algorithm is as follows: In the control point coordinate set, the average distance between each adjacent pair of points is calculated. If this average distance is less than 0.08 meters, it is defined as a high-density structure, and the structure density value is assigned as 1; otherwise, it is 0. The boundary curvature is evaluated by fitting a spline function to the obstacle edge and assessing the rate of change of each segment length. A rate of change less than 0.3 per meter is assigned high stability, with a set value of 0.9; otherwise, it is set to 0.5. The average distance between control points is directly obtained by the arithmetic mean of the distances. The path direction deviation angle is the angle between the sliding surface direction vector and the preset trajectory direction. If the angle is less than 20 degrees, the path consistency is considered high, and the corresponding value is set to 1; otherwise, it is 0.6. All the above calculation results are encapsulated into a feature vector set, which serves as the basic data for subsequent genetic optimization.

[0044] Each feature vector was then treated as a population, with an initial population size of 50 individuals, 100 iterations, a crossover probability of 0.8, and a mutation probability of 0.2. The fitness function was set as a weighted sum of four feature values: structural density (0.3), curvature stability (0.3), control point spacing reversal (0.2), and the cosine of the path deviation angle (0.2). All fitness values ​​were controlled between 0 and 1, and a fitness threshold of 0.75 was set. This threshold was derived from the fitting analysis of the control error and fitness values ​​in previous experiments. The analysis showed that when the fitness value was higher than 0.75, the constructed sliding surface had a trajectory fitting error of less than 0.03 meters, possessing the accuracy level for engineering applications. If an individual's fitness is higher than the threshold, it is encoded as a bit string, where each feature value is converted into 10 binary bits and a constraint bit segment is inserted in the middle. This segment consists of boundary angle bits, orientation consistency bits, and control point distribution masks, which are 4 bits, 3 bits, and 3 bits respectively. The entire bit string is used for subsequent optimization algorithms to read and recognize.

[0045] Individuals that do not meet the fitness requirements are sent to the correction algorithm module, where their structure density and curvature values ​​are readjusted. The adjustment range is limited to a fluctuation of no more than 0.2 from the original values, the control point spacing is adjusted to between 0.05 meters and 0.12 meters, and the path direction deviation angle is adjusted to no more than 30 degrees. All adjustment values ​​are based on previous statistical data to ensure that the corrected individuals remain within the allowable range of the actual control parameters. The corrected individuals are then re-evaluated, and if they meet the threshold requirements, they are converted into bit strings for further calculation.

[0046] After the fitness of each individual in the feature vector set is calculated using a genetic algorithm, it is determined whether its fitness value is greater than or equal to a preset fitness threshold of 0.75. If a feature vector satisfies this condition, it enters the encoding process, where a constraint embedding method is used to transform the feature vector into a set of encoded bit strings. The specific steps are as follows: First, each feature value in the feature vector is normalized to the range of 0 to 1, and then each feature value is quantized into a 10-bit binary string. For example, the feature value 0.8 is converted into the corresponding binary format "1100110011". These four feature values ​​constitute a 40-bit basic code. Subsequently, three sets of constraint fields are inserted into this 40-bit code, including structural boundary angle bits, path direction consistency bits, and control point distribution bits, each occupying 4 bits, 3 bits, and 3 bits respectively, for a total of 10 bits. The structural boundary angle bit is encoded based on the angle between the current sliding surface direction and the obstacle boundary. If the angle is less than 30 degrees, the bit is "0001"; if the angle is between 30 and 60 degrees, it is "0010"; and if the angle is greater than 60 degrees, it is "0011". The path direction consistency bit is determined based on the angle between the sliding surface control direction and the task trajectory direction. If the angle is less than 20 degrees, it is set to "100"; if the angle is between 20 and 40 degrees, it is "010"; and if the angle is greater than 40 degrees, it is "001". The control point distribution bit is set based on the uniformity of the control points in space. If the standard deviation of the control point spacing is less than 0.01 meters, it is set to "111"; if the standard deviation is between 0.01 and 0.03 meters, it is "101"; and if it exceeds 0.03 meters, it is "001". Finally, the original 40-bit feature code and the 10-bit constraint bit string are concatenated to form a 50-bit encoded bit string, which serves as the basic input for this individual to enter the simulated annealing optimization stage.

[0047] Conversely, if the fitness of a certain feature vector is lower than 0.75, its parameter combination is considered to lack the potential to generate a high-quality sliding surface, and vector adjustment is required. The adjustment process is as follows: First, identify the main cause of the low fitness, such as a structural density value lower than 0.6, a curvature value higher than 0.6, a path direction angle greater than 30 degrees, or uneven distribution of control points. Selectively adjust relevant feature parameters according to the problem type, with the adjustment range following rules: the structural density value is increased by no more than 0.2 from the original value, the curvature value is decreased by no more than 0.2, the path direction deviation angle is adjusted to be less than 25 degrees closer to the task direction, and the control point spacing is adjusted to an average value close to 0.08 meters and a standard deviation no greater than 0.015 meters. The fitness of the adjusted feature vector is recalculated. If the new fitness value reaches or exceeds 0.75, the encoding process continues; if it still does not meet the requirements, the individual is marked as invalid and removed from the current generation. Through the above complete process, the encoding and transformation of high-quality feature vectors and the effective elimination of low-quality vectors are achieved, ensuring that the subsequent sliding mode control parameter optimization has a good starting foundation and the ability to embed structural constraint information.

[0048] After generating the set of encoded bit strings, the parameter optimization stage based on the simulated annealing algorithm begins. The goal is to decode the initial control parameters from the encoded bit strings and search for the optimal parameter combination through simulated annealing, thereby obtaining the preliminary parameter set required by the sliding mode controller. Simulated annealing is a global optimum search method. Its basic idea is to accept candidate solutions that are worse than the current solution with a certain probability during the temperature decrease process, avoiding getting trapped in local optima. The implementation process consists of five stages: initialization, state generation, energy assessment, acceptance criteria, and temperature update. First, in the initialization stage, the initial temperature of simulated annealing is set to 100, the temperature decrease coefficient is 0.95, the maximum number of iterations is 1000, the termination temperature is 1, and the current state is the initial parameter configuration decoded from the set of encoded bit strings. The decoding process divides each 50-bit encoded string into predetermined fields. The first 40 bits correspond to four feature values, and every 10 bits are converted into floating-point numbers as initial values ​​for the sliding surface parameters, including control point position coefficients, normal angle coefficients, and gain weight coefficients. The last 10 bits are constraint fields, used only for constraint checking and not involved in numerical optimization. This set of parameters is mapped to the initial parameters actually used by the controller: the control point coordinates are obtained by scaling the standard control area to obtain three-dimensional coordinates; the heading angle is obtained by multiplying the angle coefficient by the maximum allowable angle of 90 degrees to obtain the pitch and yaw angles; and the gain weight is converted into a control gain value of 0.1 to 1.0 proportionally. Next, the state generation stage begins. In each iteration, based on the current parameter state, a new state is generated through a perturbation strategy. This involves perturbing each dimension of the current control point coordinates by ±0.01 meters, fine-tuning the heading angle by ±3 degrees, and adjusting the gain value by ±0.05, forming a new set of candidate parameters. Then, the energy assessment phase begins. The task error function is called to calculate the error for both the current and new states. The error function uses the average Euclidean distance between the sliding surface trajectory generated by the parameters and the target trajectory as the criterion. Fifty trajectory points are sampled, and the mean error is calculated. The smaller the error, the lower the energy, indicating a better solution. Next, an acceptance criterion is executed. If the error of the new state is lower than that of the current state, meaning the solution is better, the new state is accepted unconditionally. If the error of the new state is slightly higher than that of the current state, the error difference is calculated and used to perform a probability calculation with an exponential function constructed from the current temperature. For example, if the difference is 0.005 meters and the current temperature is 60 degrees Celsius, the acceptance probability is a negative power of e. If the random number is less than this probability, the inferior solution is accepted. This mechanism helps avoid local optima. Finally, a temperature update operation is performed, multiplying the current temperature by a temperature decrease coefficient of 0.95 to obtain the temperature for the next iteration. This iteration continues until the maximum number of iterations is reached or the temperature drops below 1. Throughout all iterations, the optimal parameter state for each round is recorded, and the parameter combination with the smallest error in the entire process is selected as the final output.The final output set of preliminary parameters includes three components: first, the three-dimensional coordinates of three control points, each within ±1 meter, representing the initial spatial layout of the sliding surface; second, the heading angles, with pitch and yaw angles ranging from 0 to 90 degrees, used to determine the normal direction of the sliding surface; and third, the initial gain parameter, ranging from 0.1 to 1.0, serving as the slope adjustment factor for the subsequent controller. This preliminary parameter set forms the basic input for constructing the sliding control surface, ensuring superior initial control performance and task adaptability.

[0049] After obtaining the initial parameter set, the shape framework construction process begins. The goal is to generate a set of three-dimensional geometric models, i.e., the initial shape model, that can be used for the sliding mode controller based on the provided control point coordinates, orientation angles, and gain parameters. The entire process consists of four specific steps: parameter decoding, spatial projection, structure construction, and attribute binding. First, in the parameter decoding stage, the three-dimensional coordinates of the control points, orientation angle values, and control gain values ​​are read sequentially from the initial parameter set. Each control point consists of three three-dimensional coordinates, denoted as Control Point 1, Control Point 2, and Control Point 3. All coordinate values ​​are in meters, ranging from ±1 meter, and are used to describe the structural basis of the sliding surface in three-dimensional space. The orientation angle values ​​include pitch and yaw angles, in degrees. The pitch angle represents the vertical tilt angle of the sliding surface relative to the horizontal plane, and the yaw angle represents the orientation angle of the sliding surface in the horizontal projection plane. Both angles range from 0 to 90 degrees. The control gain is a normalized real number, ranging from 0.1 to 1.0, used to adjust the slope of the switching function in sliding surface control. It does not directly affect the geometry but is retained in the model properties. Next, we proceed to the spatial projection stage. Using control point one as the reference point of the sliding surface, the base direction of the sliding surface is determined by the vector between control point one and control point two. Then, the degree of upward or downward offset of the sliding surface normal direction is determined based on the coordinates of control point three. A three-dimensional rotation transformation is performed by combining the pitch and yaw angles. Specifically, with control point one as the center, the plane is rotated around the X-axis according to the pitch angle, and then around the Z-axis according to the yaw angle, adjusting the original planar orientation to a spatial attitude that meets the mission direction requirements, thus giving the entire sliding surface the spatial alignment capability required for the target path. In the structure construction stage, the geometric model of the sliding surface is constructed using the projected control points and their orientation information. The specific method involves defining a plane using three control points and generating a quadrilateral patch based on this plane. The side length of this patch is extended from the average distance between the control points to between 0.2 meters and 0.4 meters, ensuring the sliding surface has a certain control coverage range in space. Triangular mesh modeling is used to connect the control points and extended vertices into a mesh structure, forming a three-dimensional surface segment to represent the spatial response domain of the controller. During the attribute binding phase, a gain parameter is appended to the attribute field of the geometric model. This gain value serves as an adjustment factor for the sliding mode control law in the controller and participates in the subsequent calculation of the switching function slope. Simultaneously, structural information such as the control point positions, sliding surface normal vectors, surface area, and model boundary range are recorded to form an initial shape model containing complete geometric configuration and control attributes.

[0050] After the initial shape model is constructed, task constraint judgment is immediately performed to verify whether the model meets the trajectory accuracy and spatial structure constraints required for task execution. The preset task constraint threshold is 0.03 meters, which means judging whether the average Euclidean distance between the sliding mode control trajectory of the model and the target task trajectory is less than or equal to 3 centimeters. The judgment process is as follows: extract the sliding mode trajectory point sequence from the initial shape model, correspond one-to-one with the reference points in the target task trajectory, and perform equidistant sampling every 0.01 meters, for a total of 50 points. Calculate the three-dimensional Euclidean distance for each corresponding point pair to obtain the error sequence, and then take the average value. If the average value is less than or equal to 0.03 meters, the initial model is considered to meet the task constraints and can enter the optimization process.

[0051] After entering the optimization phase, iterative adjustments to the geometric parameters are performed to further improve the model's trajectory matching and spatial geometric adaptability. The optimization process employs a differential evolution algorithm, setting the population size to 20 and the number of iterations to 20 generations. In each generation, mutant individuals are generated from the previously optimal parameters, and new individuals are produced through crossover. For each geometric parameter, including the 3D coordinates of control points, the normal angle of the sliding surface, the model boundary length, and the extension range, the perturbation range allowed in each iteration is strictly limited to ±0.01 meters or ±3 degrees of the original value to ensure the stability of the adjustment and structural continuity. A shape model is constructed for each new individual, and the error is re-evaluated. The individual with the smallest error is retained as the current optimal shape framework for the next round. Finally, a set of geometric parameters with the lowest error, complete structure, and accurate orientation is output, constituting the final optimized shape framework.

[0052] After the optimized shape framework is constructed, the environment variable update module is initiated. Based on the optimized geometric parameters, the updated set of environment variables for task adaptation is recalculated and output. The generation process includes three key steps: First, the control point location data is regenerated, covering the task space, based on the actual control point coordinates in the optimized framework. The updated location data will serve as the input point list for sliding mode control. Second, the sliding surface orientation parameters, including pitch and yaw angles, are extracted and standardized into orientation vectors, which are then used as new spatial orientation indices for the task planning module. Finally, parameters such as model boundary dimensions, control coverage, and normal continuity are combined into structural feature descriptors for subsequent fuzzy controller construction and task matching judgment. All updated environment variables are output with a unified data structure, covering the three main parts: control point data, orientation information, and structural contour description. This ensures that the control can execute precise control strategies with the latest task-optimized data in subsequent control stages. Thus, the entire process from initial shape construction, constraint verification, geometric optimization to environment variable reconstruction is completed, achieving closed-loop update of task-adaptive geometric parameters based on sliding mode control.

[0053] The fitness threshold is set at 0.75. This threshold is used to determine whether a feature vector meets the conditions for entering the encoding and parameter optimization stage. Its value is determined by a comprehensive analysis of the balance between control accuracy and stability. The fitness value is calculated by weighting and summing four feature parameters—structural density, boundary curvature stability, control point spacing rationality, and path direction consistency—according to preset weights. The score range is a real number between 0 and 1. The rationale for setting it to 0.75 is as follows: First, statistical analysis of trajectory fitting errors on sliding surfaces generated under different fitness values ​​shows that when the fitness is greater than 0.75, the average error between the sliding trajectory generated by the controller and the target trajectory is stable within 0.03 meters, meeting the error control standards for industrial robots in collaborative operations. Second, from an algorithm efficiency perspective, this threshold effectively filters out individuals with low fitness, reducing unnecessary redundant encoding and annealing calculations, and improving overall operating efficiency. Third, this value matches the maximum allowable structural deviation and control direction tolerance in the task environment, ensuring that the sliding control parameters have strong task adaptability and real-time performance.

[0054] S3 includes: obtaining historical sample data of contour features from the optimized shape framework; removing outliers from the sample data using data cleaning methods to obtain a cleaned sample dataset; if the matching degree of the cleaned sample dataset with the task requirements is lower than a preset threshold, grouping the sample dataset using the k-means clustering algorithm to obtain a feature group set; extracting the main feature vectors using the principal component analysis algorithm based on the feature group set to obtain a dimensionality-reduced feature vector set; if the feature expressive power of the dimensionality-reduced feature vector set is lower than a preset threshold, adjusting the feature vector weights using the gradient boosting method to obtain an optimized feature weight set; generating adaptive correction coefficients based on the optimized feature weight set, applying the correction coefficients to the fuzzy rule weights using the linear mapping method to obtain an updated fuzzy rule set; adjusting the initial parameter configuration using the updated fuzzy rule set and the fuzzy gain algorithm to obtain an optimized parameter configuration set; and updating the geometric expression of the shape framework using the optimized parameter configuration set to obtain the final shape model adapted to the task requirements.

[0055] In this embodiment, the complete implementation process of step S3 aims to adaptively correct the fuzzy control rules. It combines data cleaning, clustering, dimensionality reduction, feature enhancement, linear mapping, and fuzzy inference processes to ensure that the final generated fuzzy controller rule weights and control parameter configurations can accurately adapt to task requirements. First, historical sample data of contour features is extracted from the optimized shape framework generated in step S2. This data comes from 100 frames of key control data points sampled from each of the past 50 successful task executions, totaling 5000 sets of data. Each set of data includes the spatial coordinates of the contour boundary points, the normal direction vector of the control points, the sliding mode trajectory point sequence, and the execution time node. The corresponding parameters include three-dimensional coordinate values ​​(in meters), direction angle values ​​(in degrees), and trajectory timestamps (in milliseconds). To ensure data quality, the interquartile range (ICM) anomaly detection method is used for data cleaning. For each type of feature data, its first and third quartiles are calculated, along with its interquartile range (IMR). If a data point exceeds the upper quartile plus 1.5 times the IMR or falls below the lower quartile minus 1.5 times the IMR, it is considered an outlier and removed. Statistically, at least 85% of the original data volume remains after cleaning, forming a cleaned sample dataset. The data distribution meets the completeness and representativeness requirements for further processing.

[0056] Subsequently, the cleaned sample dataset was evaluated for its compatibility with the current task requirements. The compatibility index included three dimensions: boundary contour direction similarity, sliding surface contour area overlap, and control point trajectory Euclidean distance deviation. Directional similarity was calculated by taking the angle between the boundary normal vector and the target task trajectory normal vector in each sample group. Angles less than 20 degrees were considered completely similar and assigned a value of 1; angles between 20 and 40 degrees were linearly mapped to 0.5 to 1; and angles greater than 40 degrees were assigned a value of 0. Area overlap was calculated by fitting the sample sliding surface contour to the task shape and performing Boolean intersection. The ratio of the intersection area to the total coverage area was used as the area matching value, ranging from 0 to 1. Trajectory point deviation was calculated by taking 50 sampling points every 0.01 meters from both the task trajectory and the sample trajectory, calculating the three-dimensional Euclidean distance between each pair of points, and averaging the results to obtain the average deviation in meters. The final matching degree is calculated as a weighted average of the three indicators, each weighted separately. Directional similarity and area overlap are each weighted at 0.4, and the negative of the trajectory deviation is multiplied by a weight of 0.2. A matching degree threshold of 0.8 is set, derived from experimental analysis of actual control accuracy requirements and task stability assessment. This analysis shows that when the matching degree is higher than 0.8, the trajectory overlap error is less than 0.03 meters, and the controller response is stable. Therefore, 0.8 is used as the critical value for determining whether to enter the correction phase. If the matching degree is lower than 0.8, sample feature clustering is initiated. The clustering process uses the k-means clustering algorithm, initially setting the number of clusters k to 6. The clustering quality is judged by calculating the silhouette coefficient. A silhouette coefficient greater than 0.4 is considered valid clustering; if it is less than 0.4, the value of k is increased sequentially until the silhouette coefficient reaches its maximum value, which is then used as the final number of clusters. The clustering feature dimensions include the distance distribution between control points, the contour curvature change value, and the normal direction fluctuation value. Each feature value is first normalized to between 0 and 1, and then the cluster center is initialized and grouped. Each group of samples forms an independent feature group set.

[0057] After clustering the cleaned sample dataset to form feature groups, the principal component analysis (PCA) stage begins. The goal is to extract eigenvectors representing the main features of each group and remove redundant information using dimensionality reduction methods, thereby improving the efficiency of subsequent feature correction and fuzzy controller adaptation. Each feature group contains multiple samples, and each sample includes a set of standardized eigenvectors with a fixed dimension of 6 elements. These elements represent the standard deviation of the control point spacing, boundary contour curvature, normal rate of change, contour point density, historical trajectory deviation, and internal orientation consistency of the sample. All values ​​are normalized to between 0 and 1 and used as input for PCA.

[0058] First, the feature samples within each group are centered by subtracting the mean of all samples in that group from each feature dimension, resulting in a 0-centered distribution of the feature data. Then, the covariance matrix of this centered sample matrix is ​​calculated. This 6x6 covariance matrix corresponds to the pairwise linear relationships between the original six features. Subsequently, eigenvalue decomposition is performed on this covariance matrix, yielding six eigenvalues ​​and six corresponding eigenvectors. The eigenvalues ​​are sorted in descending order, and the corresponding eigenvectors are arranged in the same order. Each eigenvalue represents the variance of the data in that direction, i.e., the amount of information contained within it.

[0059] Based on the ranking results, the first few principal components are selected sequentially to construct the dimensionality-reduced feature space. A cumulative contribution rate threshold of 90% is set, meaning that contributions are accumulated sequentially from the eigenvalue with the largest value until the cumulative contribution rate is greater than or equal to 0.9. The first k eigenvectors corresponding to this point are the retained principal components. Generally, k is between 2 and 4, depending on the dispersion of the grouped data. The retained principal component vector set is used to project the original 6-dimensional feature vectors into the new low-dimensional feature space, generating a dimensionality-reduced feature vector set. The projection method involves a linear transformation between the original centered feature vectors and the principal component matrix. Each output dimensionality-reduced feature vector contains k dimensions, each representing the projection intensity of the sample along the corresponding principal component direction. The numerical range depends on the actual sample variation.

[0060] After completing principal component analysis on the feature group set, the dimensionality-reduced feature vector set is obtained, and the cumulative contribution rate of its first two principal components is calculated. This metric is used to evaluate the expressive power of the feature vector set after dimensionality reduction. If the cumulative contribution rate is less than the set threshold of 0.6, it is determined that the current dimensionality reduction effect cannot effectively preserve the original information and cannot accurately support the subsequent construction of fuzzy rule weights, requiring further reconstruction of the feature weights. This threshold of 0.6 comes from the judgment standard for the validity of principal component analysis results in statistical learning. After multiple rounds of task control experiments, it has been verified that in control models, a cumulative contribution rate higher than 0.6 is required to ensure that the model response accuracy is not lower than the error lower limit of 0.03 meters.

[0061] The gradient boosting method is used to re-optimize the feature weights. The gradient boosting method uses the controller task trajectory error as the regression target and the original feature vector as input. In each iteration, the feature dimension with the largest current error contribution is selected and weighted using residual regression. The number of iterations is set to 50. In each iteration, a regression tree with a decision tree depth of 3 is used for error fitting with a learning rate of 0.1. Residual updates are performed layer by layer based on the difference between the target error and the current model error. In each iteration, the relative contribution of each feature in the error fitting is recorded. Finally, the average contribution of each feature across all iterations is used as its final weight value, forming the optimized feature weight set. Each feature in this set corresponds to a floating-point number between 0 and 1, representing its importance in improving model accuracy.

[0062] Based on the optimized feature weight set, adaptive correction coefficients are calculated. The correction coefficient is defined as the sum of the products of the deviation value of each feature and its optimized weight. Specifically, the difference between the current feature value and the sample mean is used as the deviation, multiplied by the corresponding feature weight, and then summed. This summation is then mapped to a value between 0 and 1 using maximum value normalization to form the final correction coefficient. The larger the deviation of a feature and the higher its weight, the greater its influence on the correction coefficient, ensuring a stronger adjustment force for the fuzzy rule corresponding to that feature.

[0063] After the correction coefficients are calculated, the fuzzy controller rule set is invoked to update the weight values ​​of each rule. The update method is a linear mapping, multiplying the original fuzzy rule weight value by the correction coefficient. For example, if a rule's initial weight is 0.7 and the correction coefficient is 0.85, the updated weight is 0.7 multiplied by 0.85, which is 0.595. All rule weight values ​​are limited to between 0.3 and 1.0; if the calculated result is below 0.3, it is automatically reset to 0.3 to prevent the controller's response from being too weak and causing a decrease in stability. Finally, after updating all rule weights, an updated fuzzy rule set is formed. This rule set will be used in subsequent fuzzy inference control processes to ensure that the controller has highly adaptive response capabilities and fine control granularity under the current task characteristics.

[0064] After updating the fuzzy rule set weights, the updated fuzzy rule set is input into the fuzzy inference module, where it, along with the control input variables, drives the fuzzy controller in the fuzzy decision-making process. Input variables include control error, error rate of change, profile deviation, and environmental change magnitude. Each variable is fuzzified using a preset membership function, which employs a triangular or trapezoidal structure and defines three fuzzy levels: "low," "medium," and "high." Based on the current control state, the corresponding fuzzy rules are matched, and fuzzy inference is performed using a weighted average method to output the fuzzy control strength value. Subsequently, the fuzzy gain algorithm is invoked to dynamically adjust the control parameter configuration based on the superposition of the output fuzzy control strength and the rule weights. The fuzzy gain algorithm employs a piecewise linear mapping model, setting the controller gain value to a range of 0.1 to 1.0. Gain adjustment is based on the following criteria: when the fuzzy control strength is higher than 0.8 and the rule weight is greater than 0.8, the high output gain value is between 0.9 and 1.0; when the control strength is between 0.5 and 0.8 and the rule weight is between 0.6 and 0.8, the medium output gain value is between 0.6 and 0.8; and in other cases, the low output gain value is between 0.3 and 0.6. The gain value of each parameter is determined by its importance in the control model. For example, the gain influence range of the control point position is limited to ±0.02 meters, the direction angle adjustment range is limited to ±5 degrees, and the boundary layer thickness adjustment range is set to ±20% of the original value. Finally, through fuzzy inference, three sets of parameters—control point position correction, direction angle correction, and controller boundary layer thickness adjustment—are output, forming an optimized parameter configuration set.

[0065] Next, the geometric update operation of the shape frame is performed. The update process first adds the control point position correction to the original control point coordinates to obtain new coordinate values; second, the orientation angle correction is added to the pitch and yaw angles respectively, and the normal direction vector of the sliding surface is recalculated; third, the boundary layer thickness adjustment is used to calculate the effective control area covered by the sliding surface in three-dimensional space, and the control surface boundary extension value is reconstructed. Using these updated parameters, the three-dimensional mesh structure of the shape frame is regenerated, and a new sliding control surface model is constructed by triangulating the control points. At the same time, the surface orientation is reconstructed according to the normal vector to form a spatial response surface with actual physical control significance. The entire update process ensures that the sliding surface geometry is highly consistent with the current task characteristics, and the sliding controller with adaptively adjusted control parameters has sufficient response sensitivity and path correction capability. The final output shape model is the final shape model adapted to the current task requirements, which is used for subsequent calculation of sliding control laws and execution of control commands.

[0066] S4 includes extracting dynamic features from adaptive correction coefficients, decomposing the coefficient matrix using principal component analysis (PCA) to obtain a set of principal feature vectors; constructing sliding surface update rules based on the set of principal feature vectors, and generating an initial dynamic rule set using a weighted linear combination method; if the matching degree between the initial dynamic rule set and path interference signs is lower than a preset threshold, a support vector machine (SVM) algorithm is used to classify the rule set to obtain an optimized dynamic rule set; the optimized dynamic rule set is then fused with robustness assessment detection, and mean filtering is used to process the interference sign data to obtain a smoothed interference feature set; based on the smoothed interference feature set, a fuzzy inference engine is constructed, using the sliding surface change rate as input, and adjusting the switching gain through membership function mapping to obtain an updated gain parameter set; using the updated gain parameter set, combined with boundary layer thickness adjustment rules, the thickness parameters are tuned online using a linear interpolation method to obtain a parameter configuration set adapted to the environment; and a contour adjustment sequence is generated using the parameter configuration set, and time series analysis is used to predict the stability of the adjustment sequence to obtain the final contour adjustment sequence.

[0067] First, we obtain the adaptive correction coefficient matrix formed in the previous stage. This matrix is ​​a set of correction values ​​obtained through weight optimization based on the comparison results of historical task data and the current task, representing the adjustment ratio of different features in multiple task executions. Each row of the matrix represents the correction vector of a single task sample, and each column corresponds to the correction coefficient of a feature dimension. For principal component analysis, the matrix is ​​preprocessed first. The specific steps are: centering each column of data (subtracting the mean of that column from each value), and then standardizing each value by dividing it by the standard deviation of that column, so that the data follows a zero-mean, unit-variance distribution, facilitating subsequent covariance analysis.

[0068] Next, the covariance matrix of the preprocessed matrix is ​​calculated. The size of the covariance matrix is ​​equal to the square of the number of feature dimensions; that is, if the feature dimension is 6, the covariance matrix is ​​a 6x6 symmetric matrix. Eigenvalue decomposition is performed on this covariance matrix to obtain 6 eigenvalues ​​and corresponding 6 eigenvectors. The eigenvalues ​​are arranged in descending order, and the cumulative contribution rate of the first few eigenvalues ​​is calculated. When the cumulative contribution rate reaches 90%, the eigenvectors corresponding to these eigenvalues ​​are selected as the set of principal eigenvectors. In experiments, retaining the first 3 principal components usually satisfies this condition.

[0069] Based on the set of principal eigenvectors, a sliding surface update rule is constructed. Each principal eigenvector contains a comprehensive reflection of multiple original modified features, serving as the weight basis for the sliding surface adjustment direction. The principal eigenvectors are linearly mapped to the current sliding surface geometry, and an initial dynamic rule set is generated through a weighted linear combination method. The weighting coefficients represent the proportion of principal eigenvalues ​​in all eigenvalues. For example, if the proportions of the eigenvalues ​​corresponding to the 1st, 2nd, and 3rd principal components are 0.5, 0.3, and 0.2 respectively, then the corresponding linear combination weights are also set to 0.5, 0.3, and 0.2. The resulting initial dynamic rule set contains recommended strategies for the sliding surface position offset direction, normal angle adjustment, and adjustment response rate, providing a precise initial control basis for subsequent path interference identification and fuzzy control gain tuning.

[0070] After constructing the initial dynamic rule set, it is necessary to evaluate the effectiveness of these rules in dealing with path interference. To this end, path interference data is first collected during actual task execution, including the following three indicators: 1) trajectory offset, i.e., the real-time spatial difference between the robot's executed path and the preset trajectory, in meters; 2) response delay time, i.e., the time interval between the occurrence of interference and the output control signal, in milliseconds; and 3) control output change rate, i.e., the change in the magnitude of the controller's output command per unit time, in percentage. These three indicators are standardized to a value between 0 and 1. Then, a weighted average is calculated using fixed weights (e.g., trajectory offset weight 0.4, response delay weight 0.3, and control output change rate weight 0.3) to obtain a total matching score. A matching score threshold of 0.75 is set; this value is the lower limit determined in actual industrial path control experiments. A value below this threshold indicates that the current rules cannot effectively respond to path interference, exhibiting problems such as slow response, large offset, or unstable control.

[0071] If the overall matching degree is below 0.75, the rule optimization process begins, employing a support vector machine (SVM) algorithm to classify the original rule set. A training sample set is pre-constructed, with each sample representing a rule item containing three input features: sliding mode control point adjustment vector, sliding surface normal angle variation trend, and gain adjustment suggestion value. Each sample is also labeled, indicating whether it successfully suppressed path interference in historical tasks, i.e., "effective" or "ineffective." The RBF kernel function is selected as the kernel function for the SVM classification model to enhance classification ability in nonlinear feature spaces, with a training set to test set ratio of 7:3. After training, the model classifies each rule in the initial rule set and outputs the classification result. Finally, only rules classified as "effective" are retained to form the optimized dynamic rule set. This set is considered more adaptable to the current path disturbance characteristics and serves as the input for subsequent fuzzy inference engine adjustments and control strategy optimization. This process ensures the dynamic removal of inefficient control rules, improving the overall controller's response accuracy and robustness.

[0072] The Radial Basis Function (RBF) kernel is the most widely used kernel function in Support Vector Machines (SVM). Mathematically, it represents the similarity between two samples. In SVM classification models, the kernel function maps the input low-dimensional feature space to a high-dimensional feature space, making data that was previously inseparable in the low-dimensional space linearly separable. The core idea of ​​the RBF kernel is: the closer two samples are, the higher their similarity, and the closer the RBF value is to 1; conversely, if two samples are far apart, the RBF value approaches 0. It takes the form of an exponential function, containing a key parameter γ (gamma value), which controls the "width" or "radius" of the function. When γ is large, the RBF kernel function has a small response range, meaning only very close samples are considered similar. This can cause the model to focus more on local features, potentially leading to overfitting. When γ is small, the kernel function has a larger response range, and the model focuses on a wider range of features, potentially leading to underfitting.

[0073] After the support vector machine algorithm outputs the optimized dynamic rule set, the path interference data needs to be further processed based on the robustness evaluation results during task execution to improve the accuracy and stability of interference feature discrimination. First, three types of interference data are continuously collected from the current task execution: 1) displacement abrupt change, i.e., the difference in position change of the end effector trajectory point between two adjacent control cycles, in meters; 2) velocity fluctuation amplitude, i.e., the difference between the maximum and minimum velocity values ​​of the end effector per unit time, in meters per second; and 3) sliding surface normal change rate, i.e., the change in the normal angle of the sliding surface per unit time, in degrees per second. These data are collected every 500 milliseconds, and three consecutive cycles are collected to form a data set. Each set contains three sampled values ​​of the above three features, for a total of nine values.

[0074] To eliminate the impact of high-frequency disturbances or sensor noise on data interpretation, mean filtering is performed on each group of interference data. Specifically, the mean filtering operation involves taking the arithmetic mean of the three sampled values ​​for each indicator within the group. For example, if the displacement abrupt changes in a group are 0.012 meters, 0.014 meters, and 0.011 meters, then the average of these three values ​​for that interference characteristic is 0.0123 meters. The same processing operation is performed on the other two indicators to obtain the average value of velocity fluctuation and the average value of normal rate of change, respectively. The three average values ​​obtained after processing constitute a set of "smoothed interference characteristic values," and this result is recorded as the interference response state for the current time window.

[0075] After obtaining the smoothed disturbance feature set, these features need to be further applied to the fuzzy control strategy. By constructing a fuzzy inference engine, the switching gain—a key parameter of the sliding mode controller—can be dynamically adjusted, thereby improving the response sensitivity and stability control capability to path disturbances. First, three core indicators from the disturbance feature set are used as auxiliary references, with the sliding surface change rate being the primary input to the fuzzy inference engine. The sliding surface change rate represents the rate of change of the angle of the sliding surface normal vector per unit time, measured in degrees per second, reflecting the dynamic fluctuation degree of state stability. Based on empirical data and task requirements, the numerical range of the sliding surface change rate is divided into five fuzzy linguistic variables: "extremely small," "small," "medium," "large," and "extremely large," with corresponding change rate ranges of 0 to 5, 5 to 10, 10 to 15, 15 to 25, and above 25 (in degrees per second), respectively.

[0076] Next, a corresponding membership function is defined for each fuzzy linguistic variable. This implementation uses a triangular membership function form, setting a peak value and two boundary values ​​for each fuzzy subset. For example, the membership function for a "medium" rate of change is centered at 12.5, extending to 10 and 15 on either side, forming a triangular region of the membership function. Whenever a new sliding surface rate of change value is detected, it is mapped across all membership functions, calculating the membership value (ranging from 0 to 1) of that value under each linguistic variable, forming the fuzzified result of the input. Then, inference calculations are performed according to a pre-defined fuzzy rule table. The fuzzy rule table is determined by expert experience and experimental data; for example, when the "sliding surface rate of change" is "minimal," the corresponding "switching gain" is "low"; when the "rate of change" is "maximum," the corresponding "gain" is "high." The inference rules are organized in an "if-then" structure, with a total of 5 basic rules corresponding to the input of 5 linguistic variables.

[0077] During the inference phase, all activation rules are weighted and superimposed, and a weighted average method is used for fuzzy defuzzification. That is, the gain linguistic variables output by all rules are converted into specific numerical values, such as 1 for "low," 2 for "medium," and 3 for "high." Then, each membership degree is multiplied by its corresponding output value, and a weighted average is taken to obtain the updated switching gain parameter value. This value is a real number, generally between 1 and 3, with precision retained to one decimal place. This gain value will be directly applied to the sliding mode control law in the next control cycle to adjust the amplitude of the sliding mode switching term, thereby improving response speed when disturbances occur and reducing oscillation risk when stable.

[0078] After updating the switching gain, a boundary layer thickness adjustment mechanism is further introduced to improve the continuity and stability of the sliding mode control strategy and prevent chattering. This mechanism combines the updated gain parameter set with the boundary layer thickness adjustment rules, using linear interpolation to tune the thickness parameters online, ultimately forming a control parameter configuration set adapted to the current environmental conditions. First, the boundary layer thickness adjustment range is determined based on the disturbance intensity level and sliding surface change rate under the current task environment. Boundary layer thickness, a key parameter in sliding mode control used to eliminate switching term oscillations, is measured in meters, and its value range is determined based on control accuracy and response requirements, set between 0.001 meters and 0.01 meters. Based on the actual value of the sliding surface change rate, it is mapped to an interference intensity level, and the intervals are divided according to the following rules: if the sliding surface change rate is between 0 and 5 degrees per second, it is defined as "low interference," corresponding to a thickness interval of 0.001 to 0.003 meters; if the change rate is between 5 and 15 degrees per second, it is defined as "medium interference," corresponding to a thickness interval of 0.003 to 0.007 meters; if the change rate exceeds 15 degrees per second, it is defined as "high interference," corresponding to a thickness interval of 0.007 to 0.01 meters. Next, the real value of the switching gain (e.g., 2.3) previously calculated by the fuzzy inference engine is used as an interpolation factor and mapped to the corresponding thickness interval during the linear interpolation process. For example, if the current level is determined to be "medium interference," with a thickness range of 0.003 to 0.007 meters and a corresponding switching gain range of 1 to 3, the interpolation calculation method is as follows: map the relative position of the gain value within this range (here, 2.3 corresponds to the 60% position) to the thickness range (here, 0.003 meters + 0.004 meters × 0.6 = 0.0054 meters), that is, set the boundary layer thickness parameter for this cycle to 0.0054 meters. Finally, the "switching gain value" and "boundary layer thickness value" are combined to form a set of parameter configurations, used to update the control law expression in the sliding mode controller in real time. This parameter set will be directly called in subsequent control processes to achieve the goal of adaptively adjusting control sensitivity and stability according to the interference level.

[0079] After tuning the switching gain and boundary layer thickness, the generated parameter configuration set is used as input to further construct a contour adjustment sequence for guiding the collaborative motion trajectory of the two arms. The contour adjustment sequence refers to a set of control commands that fine-tune the geometry or position of the sliding surface within different control cycles. Its core purpose is to optimize the collaborative path in real time based on the dynamic changes in disturbance response capability, ensuring trajectory accuracy and coordination consistency during the collaborative motion of the two arms. First, a set of parameter configurations is recorded in each control cycle, including: switching gain value, boundary layer thickness value, and the sliding surface adjustment amplitude under their influence. The sliding surface adjustment amplitude refers to the normal angle or position fine-tuning value of the sliding surface within the current cycle, in degrees or millimeters. The parameter configurations continuously recorded over multiple cycles are used as time series input to construct a one-dimensional contour change sequence. Typically, 20 control cycles are used as a prediction window, with each cycle lasting 500 milliseconds and a total duration of 10 seconds. Next, time series analysis methods are used to predict the stability of this contour change sequence. Here, an autoregressive moving average model or a more advanced autoregressive integral moving average model is used. First, the stationarity of the profile change sequence is tested (e.g., ADF test). If the sequence fluctuates significantly over time in terms of mean and variance, it is differenced. Then, the autocorrelation coefficient and partial autocorrelation coefficient are calculated to determine the model order and train the prediction model. The model predicts the profile change trend in the next few periods, outputs the estimated sliding surface adjustment value for each period, and compares it with the current adjustment value to calculate the variance change trend. If the change amplitude of the predicted sequence remains within a set threshold range (e.g., standard deviation less than 0.005 mm or normal angle change less than 1 degree), the profile adjustment sequence is considered to have good stability. At this point, the prediction and actual values ​​are combined and calibrated to generate the final profile adjustment sequence, which serves as the output reference for the sliding mode controller in the current control period and several future periods.

[0080] S5 includes extracting device interaction data through a contour adjustment sequence, dividing the data into multiple time segments using a time series segmentation method to obtain a segmented interaction dataset; if path interference is present in the segmented interaction dataset, the interference signal strength is analyzed using a Fourier transform method to obtain an interference frequency feature set; based on the interference frequency feature set, a mutation path generation method is used to construct multiple candidate paths to obtain a candidate path set; using the candidate path set, a support vector machine algorithm is used for conflict detection to determine whether the candidate paths exceed a preset conflict detection threshold, resulting in a conflict path subset; if the conflict path subset is not empty, a weighted average method is used to fuse conflict control indicators and collaborative operation modes to generate an adjusted path parameter set; based on the adjusted path parameter set, a linear interpolation method is used to optimize the dynamic change trend of the device interaction data to obtain a smoothed path sequence; using the smoothed path sequence, the contour adjustment sequence is updated to generate the final collaborative operation path configuration set.

[0081] During fuzzy adaptive sliding mode control, a series of contour adjustment sequences are continuously output. These sequences record the dynamic control path points or sliding surface adjustment values ​​generated based on factors such as current environmental conditions, task requirements, and disturbance compensation. Each path point corresponds to a specific timestamp, and the control cycle is fixed at 500 milliseconds. Based on this, device interaction data is extracted from the robot controller or sensor network. The device interaction data mainly includes the end effector position coordinates (in meters), attitude angles (in degrees), motion speeds (in meters per second), torques (in Newton-meters), and the shortest spatial distance between the two arms (in meters). All data are in a continuous temporal structure.

[0082] Time series segmentation is performed on the collected device interaction data. The core of the time series segmentation method is to divide a long, continuous data sequence into equal-length segments at fixed time intervals, each segment being called a time window or time segment. Specifically, starting from the current time, the subsequent data is divided into multiple segments in 500-millisecond windows. The number of data entries in each segment is determined by the sampling frequency. For example, if sampling is performed 20 times per second, each segment contains 10 data records, corresponding to the state changes within the 500-millisecond window.

[0083] Each time segment is organized into a data structure unit called a segmented interactive dataset. Each segmented interactive dataset contains the following fields: start timestamp, end timestamp, corresponding sliding mode control target path point, position sequence, attitude sequence, velocity sequence, torque sequence, and spatial distance sequence between the two arms. This transforms the continuous device state change information throughout the control process into structured, time-stable segmented data, providing fundamental data support for subsequent interference identification, frequency domain analysis, and path reconstruction. This processing method enables precise time-based localization and anomaly analysis of the dynamic behavior of the two arms during task execution.

[0084] After constructing the segmented interactive dataset, path interference was identified sequentially for each time segment. The criteria for determining the presence of path interference were as follows: First, the Euclidean distance between the actual execution position of each data point in the time segment and its corresponding target path point in the contour adjustment sequence was calculated, forming a continuous position deviation sequence; second, the maximum deviation value in this sequence was calculated. If the maximum deviation value was greater than a set threshold of 0.02 meters, the time segment was marked as having path interference. The threshold of 0.02 meters was set based on the task accuracy requirements of typical industrial collaborative robots, i.e., a deviation greater than 2 centimeters may lead to assembly failure or collision risk; therefore, this value was chosen as the error judgment threshold.

[0085] For time segments marked as having path interference, a time series of position deviation values ​​is extracted from these segments. This series is arranged chronologically, with each data point representing the difference (in meters) between the actual position and the desired path point. The length is typically 10 (assuming a sampling frequency of 20 Hz and a segment duration of 500 milliseconds). This deviation time series is used as the signal input for Fourier transform analysis to identify the frequency components contained in the interference. After identifying path interference in a given time segment, a "position deviation time series" is extracted from that segment. This series consists of deviation values ​​at several consecutive time points, each representing the spatial offset (in meters) between the actual end effector position and the target position in the contour adjustment sequence. For example, with a sampling period of 500 milliseconds and a sampling frequency of 20 Hz, this sequence contains 10 data points, corresponding to a time interval of one data point every 50 milliseconds. Next, this position deviation sequence is input as a one-dimensional discrete signal into the Fourier transform module, where it undergoes frequency domain transformation using the Fast Fourier Transform (FFT) algorithm. The purpose of the Fourier transform is to convert a signal representation in the time domain into a frequency domain representation, thereby revealing the energy distribution of the signal across its various frequency components. The transform result is a complex vector array, where each complex number corresponds to a specific frequency component, and its magnitude (i.e., the amplitude of the complex number) represents the intensity of that frequency in the original signal. The amplitude of each element in this complex array is calculated, resulting in a sequence of corresponding real-valued amplitudes. Then, the amplitude sequences of all frequency components are traversed, and the three frequency points with the largest amplitudes are selected as representative frequency components. The frequency values ​​(in Hertz) and corresponding amplitudes (in meters) of these frequency components are recorded and compiled into an "interference frequency feature set." This set reflects the frequency range where the energy is most concentrated in the path interference signal; typically, high-frequency components indicate sudden disturbances, while low-frequency components indicate persistent trajectory deviations. Finally, this interference frequency feature set is used as input parameters and passed to subsequent path variation, support vector machine conflict detection, and gain adjustment modules, providing a basis for path optimization and control compensation, thereby achieving dynamic identification and accurate response to path interference.

[0086] After obtaining the interference frequency feature set, it serves as a crucial input for path adjustment. First, the three-dimensional coordinates (in meters) of each control point in the current contour adjustment sequence are read to construct the original path. Based on the main frequency components and amplitudes contained in the interference frequency feature set, it is determined whether the interference characteristics are high-frequency or low-frequency. If the main frequency is greater than 5 Hz and the amplitude is greater than 0.005 meters, it is classified as a high-frequency disturbance; otherwise, it is a low-frequency disturbance. In high-frequency disturbance scenarios, finer-grained and smoother path variations are prioritized; in low-frequency disturbance scenarios, the path variation amplitude is relatively larger. The variation path generation method includes the following steps: selecting key control points from the original path, typically one key point every two points; generating disturbance points around each key point, with disturbance directions including up, down, left, right, forward, and backward, and the disturbance amplitude set according to the interference frequency. For example, when the frequency is greater than 7 Hz, the disturbance amplitude is ±0.003 meters; when the frequency is less than 3 Hz, the disturbance amplitude is ±0.01 meters. Six disturbance points are generated for each key point, and a path is formed by combining all the disturbed control points. Ten distinct paths are generated, forming a candidate path set. Each path is stored as a sequence of three-dimensional coordinates with a path number. Next, conflict detection is performed on the candidate path set using a Support Vector Machine (SVM) algorithm for path classification. To this end, multi-dimensional features are extracted for each candidate path, including: total path offset (i.e., the average Euclidean distance from the original path), minimum control point spacing (used to assess potential collision risk), path smoothness index (i.e., the variance of distance changes between consecutive points), and arm synchronization deviation (i.e., the temporal and spatial coordination difference between the left and right arm trajectories). Each path is encoded into a 4-dimensional feature vector. The SVM model uses the RBF kernel function and has been trained using historical path data, enabling it to classify paths into "safe paths" and "conflicting paths." The feature vector corresponding to each candidate path is input into the SVM classifier for judgment. If a path is determined to be a "conflicting path," its output value is greater than a set conflict detection threshold of 0.7, indicating that the classification model's confidence level is higher than 70% before considering the path to have potential conflict risk. Finally, all path numbers identified as conflicting paths are grouped into a conflicting path subset for subsequent path filtering and adjustment.

[0087] After completing conflict detection for candidate paths, a subset of conflicting paths is evaluated. If this subset is not empty, it indicates that some candidate paths have potential control conflicts or spatial collision risks and cannot be directly used to replace the original paths. In this case, an optimal path parameter configuration that balances robustness and coordination needs to be calculated from all candidate paths, considering both control safety and collaborative execution efficiency. This is specifically achieved through a weighted average method to adjust the path parameters. First, two types of evaluation indicators are defined: one is the "control conflict indicator," including path offset magnitude, minimum distance between end effectors, and path smoothness; the other is the "collaborative operation mode indicator," including dual-arm trajectory synchronization, load balancing degree, and command response delay difference. Each indicator is standardized, with values ​​normalized to between 0 and 1. Then, weights are assigned to these two types of indicators, with the control conflict indicator weighted at 0.6 and the collaborative operation indicator weighted at 0.4, based on the safety-first principle in standard industrial tasks. Next, a comprehensive score is calculated for each path in the non-conflicting path subset. The scoring formula is as follows: For each path, calculate the weighted total score of its control conflict index and coordination index, and then sum the two weighted values ​​to obtain the overall path score. The path with the highest score is used as the "reference path" at the current moment, and its control point coordinates constitute the "adjusted path parameter set". To further improve the stability of the path in actual execution, a linear interpolation method is applied to the coordinates of each control point in this parameter set to generate a smooth path sequence. Specifically, several intermediate points are inserted between every two adjacent control points, arranged at equal intervals in space, thereby eliminating possible jumps and abrupt changes in the path. The number of interpolation points is determined based on the Euclidean distance between the two points: if the distance is greater than 0.01 meters, two intermediate points are inserted; if it is between 0.005 meters and 0.01 meters, one intermediate point is inserted; if it is less than 0.005 meters, no interpolation is performed. The coordinate values ​​of each intermediate point are calculated using linear interpolation, that is, using a linear proportional distribution between the coordinates of the start and end points. The resulting smooth path sequence consists of multiple continuous control points, exhibiting spatial continuity and velocity stability. It can be directly input into dual-arm cooperative control for trajectory tracking, ensuring the dynamic stability and control response accuracy of the path during actual operation.

[0088] The smoothed path sequence is renumbered according to the control cycle, with each control point corresponding to a specific timestamp, and the control cycle remains at 500 milliseconds. For the dual arms, the smoothed path sequence is matched in the control modules of the left and right arms respectively. The matching principle is: at each time point, the spatial distance between the control points of the left and right arms must not be less than 0.05 meters, and the target motion directions of the two points should maintain a cooperative relationship, i.e., the difference in position vector direction is less than 15 degrees. Coordination is judged by calculating the relative position and motion trend angle between the control points. If the control points of the left and right arms at a certain time point do not meet the above coordination criteria, the control points at that time point are fine-tuned. The method is to keep the left arm control point stationary and finely adjust the right arm control point along the trajectory projection line that maintains the cooperative direction. The adjustment range should not exceed 0.01 meters to ensure that no new control conflicts are introduced. After completing the coordination correction of each pair of path points, a global verification is performed on the entire path sequence to confirm that the dual-arm control targets at each time point meet the spatial cooperative constraints and dynamic continuity. Then, the processed dual-arm path sequences are integrated into a unified data structure. Each record includes a timestamp, target position of the left arm end effector, target position of the right arm end effector, target attitude angle, target velocity command, and required control gain parameters. All data is arranged in task order, forming a complete set of cooperative operation path configurations. This set is directly used as the input command set for dual-arm control, enabling synchronous control and path tracking of the left and right arms.

[0089] S6 includes: extracting key features from a set of quantified indicators using principal component analysis to generate a set of feature vectors; dividing the data into groups using cluster analysis based on the feature vector set to obtain a dynamic interactive data subset; if abnormal fluctuations exist in the dynamic interactive data subset, extracting signal frequency features using Fourier transform to generate a set of frequency features; calculating the probability distribution of mutation operations using Bayesian inference based on the frequency feature set to obtain a set of probability distributions; generating a path adjustment strategy and constructing a mitigation mapping set using the probability distribution set; optimizing the parameters of the dual-arm control law using linear interpolation based on the mitigation mapping set to generate a set of control parameters; and updating the contour sequence adjustment using the control parameter set to generate an optimized collaborative instruction set.

[0090] In this implementation, during the path control task, real-time device interaction feedback data is collected to extract a set of quantitative indicators characterizing dynamic behavior. This set includes at least the following six specific indicators: control delay time (in milliseconds), path deviation error (in meters), relative position error of the two arm ends (in meters), execution speed change rate (in meters per second), feedback torque change gradient (in Newton-meters per second), and two-arm coordination error (in seconds). Each indicator is statistically analyzed through a fixed-length sampling window, with the sampling window set to 1 second and the sampling frequency set to 20 Hz. Twenty sets of data are sampled within each window, and the mean and standard deviation are calculated to express the stability and representativeness of the indicator within the current control cycle. The collected quantitative indicator data are normalized, converting all values ​​to dimensionless values ​​between 0 and 1, forming a multidimensional quantitative indicator vector set. Subsequently, this set is input into the principal component analysis module to construct a covariance matrix, and the eigenvalues ​​and corresponding eigenvectors of each principal component are obtained through eigenvalue decomposition. The eigenvalues ​​are sorted from highest to lowest, and the top three principal components are selected, with a cumulative contribution rate of at least 85%. Based on these three principal components, the projection values ​​of the original index vectors onto these three eigenvectors are extracted, forming a new set of eigenvectors. This set retains most of the original data information but significantly reduces dimensionality, facilitating subsequent clustering analysis. Next, K-means clustering is used to cluster this eigenvector set. The number of clusters K is set to 3, representing normal working state, mild abnormal state, and severe abnormal state, respectively. The initial cluster centers are obtained through historical data statistics during the initialization phase. Each eigenvector is assigned to the nearest cluster based on its Euclidean distance to the current three cluster centers. The cluster center positions are updated in each clustering iteration until the assignment of all samples no longer changes or the change is less than a set threshold of 0.01. After clustering, three subsets are obtained, collectively referred to as dynamic interactive data subsets. In each dynamic interactive data subset, volatility analysis is performed based on each index sequence, mainly by calculating the moving standard deviation to identify the existence of abnormal volatility. If more than 30% of the samples in a subset have any indicator whose standard deviation exceeds 0.15 times its mean over three consecutive sliding windows, then that subset is marked as exhibiting abnormal fluctuations. For the subsets marked as abnormal, a Fourier transform operation is further performed. Specifically, the Fourier transform process involves performing a Fast Fourier Transform on the time series of each indicator (e.g., the path offset error series) to transform it from the time domain to the frequency domain, calculating the amplitude of each frequency component in the spectrum. The top three frequency components with the largest amplitudes are retained as the dominant frequency features, and their frequency values ​​and corresponding amplitudes are recorded, forming a frequency feature set. This set reflects the frequency structure when abnormal fluctuations exist and is one of the fundamental inputs for subsequent probabilistic inference and control strategy selection.

[0091] After obtaining the frequency feature set, it is necessary to evaluate the correlation between these frequency components and potential abnormal operations in equipment control (such as path deviation, synchronization failure, control jumps, etc.). To this end, a probabilistic modeling process based on Bayesian inference is constructed. First, during the training phase, a prior model is established using historical task execution data samples. This data sample includes: different frequency component features (dominant frequency, frequency amplitude), control state labels (whether an abnormal operation occurred), and execution feedback data. During modeling, each type of frequency feature is grouped and statistically analyzed, and its probability of occurrence under different control states is calculated, thus obtaining the prior distribution of each control state. During the actual operation phase, when the dominant frequency feature set appearing in the current cycle is detected, the current dominant frequency and its corresponding amplitude are extracted from the spectrum analysis results and input as observation data into the Bayesian inference module. Based on the prior distribution and conditional probability model obtained during the training phase, combined with Bayes' theorem, the posterior probability of each type of potential control anomaly under the current observed frequency conditions is calculated. For example, if a certain dominant frequency appears frequently in past abnormal offset events but rarely in normal samples, this frequency feature will significantly improve the posterior estimate of the current offset. This method ultimately generates a set of probability distributions that clearly indicates the probability of each abnormal operation occurring within the current control cycle. The values ​​range from 0 to 1, and the sum of the probabilities of each abnormal type is 1.

[0092] Subsequently, based on the high-probability anomalous operation types in the probability distribution set, the path adjustment strategy generation process is initiated. The specific strategy responds in tiers according to probability intensity: if the posterior probability of an anomalous operation is higher than 0.6, it is considered that immediate path adjustment is required; operations with probabilities between 0.3 and 0.6 are considered minor disturbances, requiring only early warning and parameter fine-tuning; if all anomalous probabilities are lower than 0.3, the existing path remains unchanged. For cases requiring adjustment, a set of predefined path adjustment templates is matched based on the anomaly type, frequency component directionality, and characteristics of the controlled object (e.g., left or right arm actuator). These templates are preset based on experience and historical data, and each template includes parameters such as path offset vector, correction step size, and duration of action. The current frequency features are used as input and mapped to the parameter space in the matching templates. A customized path adjustment strategy is generated using a linear weighting method, including specific correction direction, magnitude, and target point. All generated path adjustment strategies are combined into a mitigation mapping set. This set is essentially an input-output mapping library, with frequency features and anomaly types as inputs and a set of corresponding path control vectors as outputs.

[0093] After inferring the anomaly probability distribution based on Bayesian inference and generating a path adjustment strategy and constructing a mitigation mapping set accordingly, the next step is to transform the mapping result into a direct adjustment of the dual-arm cooperative control law. Each entry in the mitigation mapping set includes input frequency characteristics, anomaly operation type, and corresponding control correction parameters. These correction parameters include path offset, control response time delay correction value, control gain correction direction, and boundary layer thickness adjustment. Upon receiving this set, based on the frequency characteristics of the current execution state, the corresponding entry is matched from the mitigation mapping set to extract the target control law parameter adjustment direction and target value. In the actual generation of the control parameter set, a linear interpolation method is used to achieve a smooth transition from the current control parameter value to the target correction value. Specifically, for each control law parameter, such as sliding mode gain, switching gain, boundary layer thickness, and cooperative compensation coefficient, the measured value and target adjustment value of the current cycle are first extracted, and a fixed adjustment cycle is set, typically 3 control cycles (i.e., 150 milliseconds). Then, this transition time is divided into 3 interpolation points, and the intermediate parameter value to be reached at each time point is calculated. The linear interpolation formula consists of two endpoint values, ensuring a smooth and continuous parameter adjustment path and avoiding oscillations or actuator load instability caused by abrupt changes in the control law. Each interpolation result is loaded into the controller at the beginning of the control cycle, allowing it to be updated in real time with each small adjustment step. After obtaining the complete set of control parameters, new control instructions are jointly calculated based on the current task state, path sequence, and parameter set, updating the contour adjustment sequence. The contour adjustment sequence is the actual path point sequence output to the actuator, containing the target position, attitude angle, velocity value, and updated control law parameter configuration at each critical moment. The compensation amount and control input value of each control point are recalculated using the interpolated parameter values, and these new values ​​are written into the contour sequence. Each contour point, while containing position information, also includes real-time control law parameter configuration, achieving synchronous adjustment of position control and control strategy. Finally, an optimized cooperative instruction set is generated through this updated contour adjustment sequence. This instruction set is used to coordinate the collaborative execution of the two arms, containing the precise trajectory points, velocity values, attitude directions, and robust control parameters that the left and right arms should execute in the next time period.

[0094] S7 includes acquiring real-time feedback data, extracting dynamic change features from the data using time series analysis to obtain a dynamic feature set; using the dynamic feature set, classifying whether the data meets the task requirements using a support vector machine method to determine the classification result; if the classification result meets the task requirements, generating an initial sliding surface configuration based on the dynamic feature set to obtain sliding surface parameters; calculating the joint torque commands of the left and right arms using the sliding surface parameters to generate a torque command set; optimizing the commands using a linear programming method based on the torque command set and geometric constraints to obtain an optimized command set; generating a control strategy adapted to geometric constraints using the optimized command set to determine the final control output; if the classification result does not meet the task requirements, adjusting the dynamic feature set using real-time feedback data and regenerating the sliding surface configuration.

[0095] In this implementation scheme, real-time feedback data generated by various sensors of the dual-arm collaborative robot is continuously acquired during task execution. The collected data mainly includes: end-effector position error, end-effector velocity error, current angle change rate of each joint, applied external load change, control delay, and trajectory tracking error. These data are recorded sequentially at fixed intervals (e.g., every 100 milliseconds) based on timestamps, forming a data window of length 10, which constitutes a time-series data block covering the most recent second.

[0096] The above data was processed using time series analysis. The specific steps included: first, constructing a time series for each physical quantity; then, performing differencing on each series to capture its trend; next, calculating the statistical characteristics of each differencing series, including seven indicators: mean, standard deviation, maximum value, minimum value, maximum amplitude of change, series skewness, and kurtosis, representing the dynamic behavior of the physical quantity within the selected window; with each physical quantity corresponding to seven statistical indicators, if five physical dimensions are involved, a total of 35-dimensional dynamic feature vectors are obtained, and this set of feature vectors is the dynamic feature set.

[0097] Then, this dynamic feature set is input into a pre-trained support vector machine model for classification. This model uses radial basis functions as its kernel function and is trained in advance using supervised learning. The training samples consist of dynamic feature sets recorded over multiple task cycles and manually labeled "task accomplished" or "task not accomplished" status tags. During model training, cross-validation is used to optimize the kernel function parameters and penalty factors, and the model configuration with the highest classification accuracy is ultimately retained as the online discrimination criterion.

[0098] During online operation, the support vector machine model is invoked based on the dynamic feature set of the current task stage, and the judgment result is output. If the classification result is "meets task requirements", the initial configuration of the sliding surface is constructed based on the current dynamic feature values. This configuration process includes three key steps: First, the normal vector of the sliding surface is generated based on the weighted average of the position error and velocity error, with the weights typically set as 0.6 for position error and 0.4 for velocity error; second, the switching gain is set after normalization based on the physical quantity with the largest standard deviation, as the one with the largest standard deviation represents the largest fluctuation in the current state and should be given a higher control response speed; third, the boundary layer thickness is determined based on the control input delay and the mean of the trajectory tracking error. Specifically, if the delay is less than 10 milliseconds and the error is less than 0.01 meters, the boundary layer thickness is set to 0.02 meters; otherwise, it is 0.04 meters. Finally, the above three parameters together constitute the sliding surface parameters, providing a stable and environmentally adaptable control basis for subsequent control law calculations.

[0099] Upon entering the current control cycle, the sliding surface parameters are first read, including the normal direction, switching gain, boundary layer thickness, and membership slope. Simultaneously, the current position, current angular velocity, output torque of the previous cycle, instantaneous position and velocity errors of the end effector relative to the desired path, and the current estimated end effector load are read for each joint of the left and right arms, with a sampling interval of 100 milliseconds. Then, the raw torque calculation process is executed joint-by-joint. First, the end effector position and velocity errors are projected onto the motion contribution direction of each joint along the sliding surface normal direction to obtain the error share and velocity share for each joint. The error share is used to generate the tracking term, and the velocity share is used to generate the damping term. The coefficient of the tracking term is determined by a linear mapping of the switching gain within the range of 0.3 to 1.0; the higher the gain, the greater the correction torque for the error. The coefficient of the damping term is determined by the membership slope. The slope is determined between 0.5 and 1.0, with a larger slope resulting in stronger suppression of angular velocity. To suppress chattering, a smoothing term is introduced based on a boundary layer thickness between 0.02 and 0.04 meters. The greater the thickness, the stronger the smoothing of the switching term, resulting in less chattering but a slightly slower response. To ensure consistent load bearing, a load compensation term is introduced, the magnitude of which is directly obtained from the end load estimate and the calibration table of the transmission ratio of each joint, and mapped to the compensation torque of each joint. The sum of the four terms yields the original torque command for each joint, and physical upper and lower limits are imposed on it. The upper limit is set to 150 Nm and the lower limit is set to 0 Nm, with any excess being directly truncated. After completing the above steps for all joints of the left and right arms, a torque command set is formed, and the difference between the torque of the corresponding joint in the previous cycle is recorded for use in subsequent optimization rate of change constraints.After completing the initial set, the linear programming optimization stage begins. The decision variable is the torque value that each joint of the left and right arms needs to output in this cycle. The objective function is "weighted minimization of trajectory tracking error and torque change". The weights are set as 0.7 for error and 0.3 for torque change, based on the principle of prioritizing trajectory accuracy while also considering actuator stability. The constraints are divided into five categories: joint torque boundary constraints, torque change rate constraints, geometric constraints, safety distance constraints, and synchronization constraints. The joint torque boundary constraints require that each torque value be within the range of 0 to 150 Nm and consistent with the physical cutoff. The torque change rate constraints require that the torque difference of the same joint in the previous cycle does not exceed 20 Nm, and this threshold is determined based on the motor overcurrent safety margin and vibration reduction requirements. The geometric constraints require that the angle of each joint does not exceed the mechanical limit, which is set to ±180 degrees according to the upper limit of the equipment parameters, and the path point generated by the end effector pose must be within the reachable working area. Within the spatial grid; the safety distance constraint requires that the distance between the closest points of the two ends be no less than 0.05 meters, and this threshold is determined according to the actual safety clearance between the machinery and the tooling; the synchronization constraint requires that the speed difference between the ends of the two arms at the same time point do not exceed 0.1 meters per second to ensure coordination consistency, and this threshold is determined according to the minimum feasible bandwidth for synchronization during historical collaborative assembly; after loading the objective and all constraints into the linear programming solver, the optimized solution for all joints is obtained. If individual joints touch the boundary, the constraint takes effect actively and the solver redistributes the torque of other joints within the feasible region to maintain the minimum error; after the solution is completed, the optimized instruction set is output, which includes the final torque values ​​of each joint of the left and right arms in the current cycle and the deviation from the original values ​​for auditing. The optimized instruction set immediately replaces the original torque instruction set and enters the issuance queue for execution in this cycle, thereby achieving high-precision tracking of the sliding surface target with minimal torque change under the premise of satisfying geometric and safety constraints.

[0100] After completing the linear programming optimization of the torque commands, an optimized instruction set is obtained. This optimized instruction set contains the final target torque values ​​for all joints of the left and right arms in the current control cycle, and records the corresponding execution timestamps and sliding surface configuration parameters. A control strategy adapted to geometric constraints is then generated based on this optimized instruction set. The control strategy generation process is as follows: First, check whether the joint angle corresponding to the torque of each joint in the optimization instruction set meets the geometric boundary conditions of the robotic arm, such as the angle not exceeding ±180 degrees and the end-effector pose remaining within the workspace. If the limits are exceeded, automatic correction is performed within the feasible region to adjust the torque value to the maximum feasible solution allowed by the boundary. Second, check whether the spatial distance between the ends of the two arms meets the safety clearance requirement (minimum distance 0.05 meters). If not, select an intervention point in the path and finely adjust the end positions of the two arms in opposite directions along the normal vector. The adjustment range should not exceed 0.01 meters to eliminate potential collision risks while maintaining cooperation. Third, check the speed synchronization of the ends of the two arms to ensure that the speed difference does not exceed 0.1 meters per second. If it exceeds this, introduce a speed compensation factor into the control strategy to lower the speed of the fast arm and raise the speed of the slow arm to near the middle value until the synchronization requirement is met. After the above three checks and corrections, the final output control strategy is a complete set of collaborative control instructions. This set of instructions includes the final torque output of all joints of both arms, joint angle limit information, end position correction information, and synchronization compensation factor, ensuring that the two arms move continuously, safely, and meet geometric constraints when working together.

[0101] If the classification result is "does not meet task requirements," the current optimized instruction set will not be used directly. Instead, the process will return to the dynamic feature set adjustment stage. Specifically: First, real-time feedback data will be reacquired, and the error change rate, trajectory deviation, and control delay will be checked. Dimensions with abnormally large values ​​in the dynamic feature set will be removed. For example, if the standard deviation of a certain dimension exceeds a set threshold of 0.2 or the trajectory deviation exceeds 0.05 meters, that dimension will be marked as an abnormal dimension. The marked abnormal dimensions will be smoothed by recalculating their mean and standard deviation using a moving average method and replacing the original abnormal values. At the same time, the maximum absolute difference and features such as skewness and kurtosis of the difference sequence will be updated to obtain an adjusted dynamic feature set. Subsequently, the sliding surface configuration will be regenerated based on this new dynamic feature set, and the four key parameters of normal direction, switching gain, boundary layer thickness, and membership slope will be recalculated. Based on this, the joint torque instruction generation and optimization process will be re-executed.

[0102] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A fuzzy adaptive sliding mode control calculation method for dual-arm collaborative robots, characterized by, Comprise: S1, obtain real-time sensor data in the environment, determine geometric constraint conditions by analyzing the data, generate geometric initialization of left arm sliding surface, right arm sliding surface and collaborative constraint sliding surface by using population diversity coding processing initial parameter randomization, obtain environment variable set under current task demand; S2, according to the environment variable set, adopt fitness function to calculate and evaluate the initial design, combine constraint condition embedding processing coding bit string representation, determine the preliminary adjustment parameter under the setting of population size, obtain the optimized shape framework; S3, through the optimized shape framework, obtain the historical data sample of contour characteristics, if the sample matching degree with task demand is lower than the preset threshold, then generate and process the sample by using the initialization iteration number, obtain the adaptive correction coefficient of contour characteristics, the correction coefficient is used as the initial value of gain and parameter setting, the correction coefficient is used for initializing fuzzy rule weight and fuzzy gain; S4, according to the adaptive correction coefficient, determine the dynamic contour updating rule of sliding surface, fuse the design robustness evaluation detection path interference signs, construct fuzzy inference, take sliding surface and sliding surface change rate as input, online set switching gain and boundary layer thickness, obtain contour adjustment sequence for variable environment; S5, through the contour adjustment sequence, obtain the equipment interaction data in collaborative operation, if the data shows path interference signs, then fuse the variable path to generate conflict detection threshold judgment, obtain the quantitative index calculation result of control conflict; The S1 comprises: Obtain real-time sensor data in the environment, remove noise by using preset filtering algorithm, obtain clean sensor data set; By analyzing the clean sensor data set, adopt clustering algorithm to determine geometric constraint conditions, obtain environment geometric parameter set; For environment geometric parameter set, adopt population diversity coding method to randomize initial parameters, generate parameter initialization set; According to the parameter initialization set, build geometric model of left arm sliding surface and right arm sliding surface, obtain independent sliding surface set; If the independent sliding surface set meets the preset collaborative constraint threshold, then generate collaborative constraint sliding surface by using geometric optimization algorithm, obtain collaborative sliding surface model; By analyzing the matching degree of collaborative sliding surface model and task demand analysis, adjust the environment variable set, obtain the optimized environment variable set; According to the optimized environment variable set, update sliding surface generation parameters, obtain the final task adaptive sliding surface set.

2. The method of claim 1, wherein the method is a fuzzy adaptive sliding mode control method for a dual-arm collaborative robot. The S2 comprises: Obtain environment variable set, process data by using preset feature extraction algorithm, generate feature vector set; According to the feature vector set, adopt genetic algorithm to calculate individual fitness, obtain fitness evaluation result; If the fitness evaluation result meets the preset threshold, then generate coding bit string set by using constraint condition embedding method, otherwise adjust the feature vector set; According to the coding bit string set, adopt simulated annealing algorithm to optimize parameter configuration, obtain preliminary parameter set; Through the preliminary parameter set, build geometric representation of shape framework, obtain initial shape model; If the initial shape model meets the task constraint threshold, then adjust geometric parameters by using iterative optimization method, obtain optimized shape framework; According to the optimized shape framework, generate task adaptive environment variable update set. 3.The fuzzy adaptive sliding mode control calculation method for the dual-arm collaborative robot according to claim 1, wherein: The S3 comprises: Obtaining a historical sample data of contour features from an optimized shape framework, removing outliers in the sample data by a data cleaning method to obtain a cleaned sample data set; If the matching degree of the cleaned sample data set with the task requirement is lower than a preset threshold, grouping the sample data set by a k-means clustering algorithm to obtain a feature grouping set; According to the feature grouping set, extracting main feature vectors by a principal component analysis algorithm to obtain a dimension-reduced feature vector set; If the feature expression capability of the dimension-reduced feature vector set is lower than a preset threshold, adjusting the feature vector weights by a gradient boosting method to obtain an optimized feature weight set; According to the optimized feature weight set, generating an adaptive correction coefficient, and applying the correction coefficient to the fuzzy rule weight by a linear mapping method to obtain an updated fuzzy rule set; Using the updated fuzzy rule set, adjusting the initial parameter configuration by a fuzzy gain algorithm to obtain an optimized parameter configuration set; Updating the geometric expression of the shape framework by the optimized parameter configuration set to obtain a final shape model adapted to the task requirement.

4. The method of claim 1, wherein the method is a fuzzy adaptive sliding mode control method for a dual-arm collaborative robot. The S4 comprises: Extracting dynamic features from the adaptive correction coefficient, and decomposing the coefficient matrix by a principal component analysis algorithm to obtain a main feature vector set; According to the main feature vector set, constructing a sliding mode surface update rule, and generating an initial dynamic rule set by a weighted linear combination method; If the matching degree of the initial dynamic rule set with the path interference sign is lower than a preset threshold, classifying the rule set by a support vector machine algorithm to obtain an optimized dynamic rule set; Fusing robustness evaluation detection by the optimized dynamic rule set, processing the interference sign data by a mean filtering method to obtain a smooth interference feature set; According to the smooth interference feature set, constructing a fuzzy inference engine, taking the sliding mode surface change rate as the input, adjusting the switching gain by a membership function mapping to obtain an updated gain parameter set; Using the updated gain parameter set, combining the boundary layer thickness adjustment rule, and adjusting the thickness parameter online by a linear interpolation method to obtain a parameter configuration set adapted to the environment; Generating a contour adjustment sequence by the parameter configuration set, and predicting the stability of the adjustment sequence by a time series analysis method to obtain a final contour adjustment sequence.

5. The method of claim 1, wherein the method is a fuzzy adaptive sliding mode control method for a dual-arm collaborative robot. The S5 comprises: Extracting device interaction data by the contour adjustment sequence, dividing the data into multiple time segments by a time series segmentation method to obtain a segmented interaction data set; If there is a path interference sign in the segmented interaction data set, analyzing the interference signal strength by a Fourier transform method to obtain an interference frequency feature set; According to the interference frequency feature set, constructing multiple candidate paths by a variant path generation method to obtain a candidate path set; Using a support vector machine algorithm to detect conflicts by the candidate path set, and judging whether the candidate path exceeds a preset conflict detection threshold to obtain a conflict path subset; If the conflict path subset is not empty, generating an adjusted path parameter set by fusing the control conflict indicator and the collaborative operation mode by a weighted average method; According to the adjusted path parameter set, a linear interpolation method is used to optimize the dynamic change trend of the device interaction data, and a smooth path sequence is obtained; Through the smooth path sequence, the contour adjustment sequence is updated, and a final collaborative work path configuration set is generated. 6.The fuzzy adaptive sliding mode control calculation method for dual-arm collaborative robot according to claim 1, wherein, It also includes S6, according to the quantitative index calculation result, using path adjustment fusion iteration contour adjustment sequence, combining interference sign identification to determine the variation operation probability under the relief mapping, calculating the double-arm control law, and obtaining the optimized collaborative control instruction set, specifically including: Through the quantitative index set, the principal component analysis method is used to extract the key features, and the feature vector set is generated; According to the feature vector set, the clustering analysis method is used to divide the data groups, and the dynamic interaction data subset is obtained; If there is an abnormal fluctuation in the dynamic interaction data subset, the signal frequency characteristics are extracted by the Fourier transform method, and a frequency characteristic set is generated.

7. The method of claim 6, wherein the method is a fuzzy adaptive sliding mode control method for a dual-arm collaborative robot. The S6 also includes: According to the frequency characteristic set, the Bayesian inference method is used to calculate the variation operation probability distribution, and a probability distribution set is obtained; Through the probability distribution set, the path adjustment strategy is generated, and the relief mapping set is constructed; According to the relief mapping set, the linear interpolation method is used to optimize the double-arm control law parameters, and a control parameter set is generated; Through the control parameter set, the contour sequence adjustment is updated, and the optimized collaborative instruction set is generated.

8. The method of claim 1, wherein the method is a fuzzy adaptive sliding mode control method for a dual-arm collaborative robot. It also includes S7, through the optimized collaborative control instruction set, real-time feedback data is obtained, if the data meets the task demand, the final sliding mode surface configuration is output, and the left arm and right arm joint torque instruction or joint speed instruction is generated, the control strategy adapted to the geometric constraint is obtained, specifically including: Obtain real-time feedback data, use time series analysis method to extract dynamic change characteristics in data, get dynamic characteristic set; Through the dynamic characteristic set, the support vector machine method is used to classify whether the data meets the task demand, and the classification result is determined; If the classification result meets the task demand, according to the dynamic characteristic set, the initial sliding mode surface configuration is generated, and the sliding mode surface parameters are obtained.

9. The method of claim 8, wherein the method is for a dual-arm cooperative robot. The S7 also includes: Through the sliding mode surface parameters, the joint torque instructions of the left arm and the right arm are calculated, and a torque instruction set is generated; According to the torque instruction set, combined with the geometric constraint condition, the linear programming method is used to optimize the instruction, and the optimized instruction set is obtained; Through the optimized instruction set, the control strategy adapted to the geometric constraint is generated, and the final control output is determined; If the classification result does not meet the task demand, the dynamic characteristic set is adjusted through the real-time feedback data, and the sliding mode surface configuration is regenerated.

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