A compliant assembly method and system based on force-position hybrid control

Abstract

This invention relates to the field of robotic automated assembly technology, and discloses a compliant assembly method and system based on force-position hybrid control. The compliant assembly method includes: acquiring multimodal measurement data, unifying and fusing coordinates; performing unscented Kalman filtering for state recursive estimation; identifying actual assembly constraint parameters online, performing orthogonal decomposition of the force-position control subspace and extraction of deviation component projections; establishing an impedance control dynamic model and adjusting impedance parameters, and generating trajectory integrals; calculating force tracking deviations and designing sliding surfaces, solving for position compensation commands, and performing velocity limiting and trajectory generation; performing feature extraction and neural network state recognition, synthesizing force-position trajectories and mapping joint space; establishing a multi-index evaluation system and determining assembly success and handling anomalies. This invention achieves high-precision compliant assembly, effectively controls contact forces, and improves assembly success rate and efficiency.

Description

Technical Field

[0001] This invention relates to the field of robotic automated assembly technology, and more specifically, to a compliant assembly method and system based on force-position hybrid control. Background Technology

[0002] The assembly of turbine blade tenons is a critical process in aero-engine manufacturing, directly impacting engine performance and reliability. Turbine blades are made of high-temperature alloys, and their surfaces must not be damaged. The assembly clearance between the tenons and the blade disk is extremely small, demanding extremely high assembly precision and process control. Traditional manual assembly methods rely on the experience and skills of operators, resulting in low efficiency, poor consistency, and the risk of component damage.

[0003] Existing robotic automated assembly methods primarily employ rigid position control strategies, achieving assembly through precise control of the robot's end effector position. However, due to part machining errors, assembly positioning errors, and uncertainties during the assembly process, rigid position control is prone to generating excessive contact forces, leading to scratches or damage to the surface of high-temperature alloy parts and a low assembly success rate. While single impedance control methods can reduce contact forces, they lack precise control over the assembly direction, resulting in long assembly alignment times and low efficiency.

[0004] Current technologies lack a force-position hybrid control method for high-precision compliant assembly, failing to achieve compliant contact while ensuring assembly accuracy, thus failing to meet the stringent requirements of aerospace precision assembly. Therefore, there is an urgent need for a compliant assembly method that can integrate multi-source sensor information, achieve force-position decoupling control, and adaptively adjust control parameters to improve assembly success rate, reduce contact forces, and shorten assembly time, thereby meeting the high-precision and high-reliability requirements of aerospace engine turbine blade tenon assembly. Summary of the Invention

[0005] This invention provides a compliant assembly method and system based on force-position hybrid control, which solves the technical problems of low assembly success rate, excessive contact force causing damage to parts, and low assembly efficiency in related technologies.

[0006] This invention provides a compliant assembly method based on force-position hybrid control, comprising: Multimodal measurement data are collected from multiple sources of sensors, coordinates are unified and fused to obtain the initial state perception dataset of the assembly environment. Based on the initial state perception dataset of the assembly environment, unscented Kalman filtering state recursive estimation is performed to obtain the blade pose deviation estimate. Based on the blade pose deviation estimate, the actual assembly constraint parameters are identified online, and the force-position control subspace orthogonal decomposition and deviation component projection extraction are performed to obtain position control commands and force control commands. Based on the position control command, an impedance control dynamic model is established and the impedance parameters are adjusted. The impedance control dynamic model is solved and the trajectory is integrated to generate the desired trajectory of the position control end. Based on the force control command, the force tracking deviation is calculated and the sliding surface is designed. The position compensation command is solved, the speed limit is performed and the trajectory is generated to obtain the force control end compensation trajectory. Based on the desired trajectory of the position control end effector and the compensated trajectory of the force control end effector, feature extraction and neural network state recognition are performed, force-position trajectory synthesis and joint space mapping are performed, and intelligent control execution commands are obtained. Based on intelligent control execution instructions, a multi-index evaluation system is established to determine assembly success and handle anomalies, thereby obtaining the assembly completion status verification results.

[0007] In a preferred embodiment, the step of obtaining the initial state-aware dataset of the assembly environment includes: The translation vectors and rotation matrices of the force sensor coordinate system and the end-effector coordinate system are combined into a homogeneous transformation matrix; Drive the robot end effector to move to different poses, record joint angles and calibration plate images, obtain the pose sequence of the end effector coordinate system in the base coordinate system based on the joint angles, extract the three-dimensional coordinates of feature points based on the calibration plate images, and obtain the transformation matrix between the camera coordinate system and the base coordinate system using a hand-eye calibration algorithm. By synchronizing the trigger pulses, all sensors start sampling at the same time, thus obtaining measurement data with the same timestamp; The force vector output by the six-dimensional force sensor and the coordinates of the blade feature points measured by binocular vision are transformed to the base coordinate system, and the position vector and attitude matrix of the blade are extracted to obtain the initial state perception dataset of the assembly environment.

[0008] In a preferred embodiment, the step of obtaining the blade pose deviation estimate includes: The pose deviation of the blade relative to the tenon groove is defined as a state variable. The mapping relationship between the state variable and the robot joint velocity is established. The nonlinear relationship equation between the contact force and the pose deviation is established. The state transition equation is established, and the nonlinear state equation is obtained. Based on the coordinates of blade feature points, the contact force vector measured by a six-dimensional force sensor, and the robot pose measured by a joint encoder, an observation equation between the measured values ​​and the state variables is established. The Sigma sampling points are selected using the unscented transformation method. The Sigma points are then propagated through the state transition equation and the predicted state is calculated. The predicted Sigma points are mapped to the measurement space. The Kalman gain is calculated based on the residual between the predicted and actual measured values, and the predicted state is corrected to obtain the pose deviation estimate.

[0009] In a preferred embodiment, the step of obtaining the position control command and the force control command includes: Calculate the principal direction of the contact force vector, identify the constrained pose degrees of freedom, identify the contact stiffness, and define the direction with stiffness value higher than the preset stiffness threshold as the strong constraint direction and the direction with stiffness value lower than the preset stiffness threshold as the weak constraint direction. Based on the insertion direction vector as the first basis vector, the second and third basis vectors are constructed using the orthogonalization algorithm. The three basis vectors are used to construct the rotation matrix of the constraint coordinate system, and the position control subspace and force control subspace are defined. Transform the blade translation deviation vector to the assembly constraint coordinate system, construct a selection matrix to extract the deviation components in the insertion direction and lateral direction, obtain the desired correction velocity based on the deviation components in the position control subspace, and obtain the target contact force based on the deviation components in the force control subspace.

[0010] In a preferred embodiment, the step of identifying the actual assembly constraint parameters online further includes: A sliding data window is set up, the window data is updated based on the new sampling point, and the assembly constraint parameters are re-identified. When the difference between the identification result and the current constraint parameters exceeds the preset constraint parameter difference threshold, the subspace is redefined, the orthogonal basis and selection matrix are updated, and the elements of the selection matrix are subjected to time filtering to obtain adaptive subspace decomposition.

[0011] In a preferred embodiment, the step of obtaining the desired trajectory of the position control end effector includes: An impedance equation is established, which aims to describe that the sum of the product of virtual mass and acceleration deviation, virtual damping and velocity deviation, and virtual stiffness and position deviation equals the external force. Contact state is identified based on contact force amplitude, and contact stiffness is determined online. Based on the contact state and contact stiffness estimates, fuzzy input variables are defined, a fuzzy rule base is established, and fuzzy inference and defuzzification methods are used to obtain the impedance parameter values. Based on the expected correction velocity and deviation components in the position control subspace, the acceleration deviation is solved by substituting the current end velocity and contact force into the impedance equation. The expected position is obtained by integration and the trajectory curve is generated, thus obtaining the expected trajectory of the position control end.

[0012] In a preferred embodiment, the step of obtaining the force-controlled end-effector compensation trajectory includes: Transform the contact force vector to the assembly constraint coordinate system, extract the lateral force component, and subtract the actual contact force from the target contact force to obtain the force tracking deviation; Define the sliding mode variable as the product of the preset sliding surface slope parameter and the force tracking deviation, plus the rate of change of the deviation; The time derivative of the sliding mode variable is designed based on the reaching law. The gain is dynamically adjusted according to the amplitude of the sliding mode variable. The position compensation command is obtained by dividing the required force change by the contact stiffness estimate. The compensation speed is calculated and limited based on the position compensation command, and the motion trajectory points are generated.

[0013] In a preferred embodiment, the step of obtaining the intelligent control execution instruction includes: Extract the time-domain statistical features, force change rate features, and frequency-domain features of the force; extract the relative positional relationship between the blade and the tenon groove, as well as the blade's motion speed and direction, and combine them into a feature vector. A convolutional neural network is used as the classifier. The output layer corresponds to the probability distribution of the four assembly stages: free motion, initial contact, search and alignment, and insertion assembly. The category with the highest probability is selected as the recognition result. Finite state machine modeling is used, and control parameters are pre-set for each state. The corresponding control parameters are read based on the currently identified state. When the assembly state changes, the control parameters at the current moment are calculated using an interpolation method. The desired trajectory of the position control end effector and the compensated trajectory of the force control end effector are synthesized, the joint angle configuration is solved, the joint angle, angular velocity and angular acceleration sequence is generated, the joint torque is calculated and sent to the motor driver, and the intelligent control execution command is obtained.

[0014] In a preferred embodiment, the step of obtaining the assembly completion status verification result includes: The convergence time and convergence speed of the pose deviation are calculated. The maximum contact force value is extracted based on the contact force time series curve to obtain the peak force index and force fluctuation index. The insertion depth compliance index is obtained based on the position data of the insertion stage. The assembly cycle time index is obtained based on the assembly time. The comprehensive assembly quality score is obtained by using a weighted scoring model. The assembly qualification index is determined by comparing the comprehensive quality score with the preset quality qualification threshold. If the peak force exceeds the safety limit or the insertion depth does not meet the minimum requirement, it is judged as unqualified. If the assembly is qualified, an assembly success signal is output. If the assembly is not up to standard, an assembly failure flag signal will be output and the exception handling process will be triggered to generate an assembly completion status verification result.

[0015] This invention provides a compliant assembly system based on force-position hybrid control, used to perform the aforementioned compliant assembly method based on force-position hybrid control, comprising: The data fusion module collects multimodal measurement data from multiple sources of sensors, unifies and fuses coordinates to obtain an initial state perception dataset of the assembly environment; The blade pose deviation estimation module performs unscented Kalman filtering state recursive estimation based on the initial state perception dataset of the assembly environment to obtain the blade pose deviation estimate. The force-position control decoupling module identifies the actual assembly constraint parameters online based on the blade position and orientation deviation estimation value, performs orthogonal decomposition of the force-position control subspace and extraction of deviation component projection, and obtains position control commands and force control commands. The impedance control trajectory generation module establishes an impedance control dynamic model based on the position control command, adjusts the impedance parameters, solves the impedance control dynamic model, and performs trajectory integration to generate the desired trajectory at the end of the position control. The sliding mode force control module calculates the force tracking deviation and designs the sliding surface based on the force control command, solves the position compensation command, performs speed limiting and trajectory generation, and obtains the force control end compensation trajectory. The state recognition and trajectory synthesis module performs feature extraction and neural network state recognition based on the expected trajectory of the position control end and the compensated trajectory of the force control end, and performs force-position trajectory synthesis and joint space mapping to obtain intelligent control execution instructions; The assembly quality assessment module, based on intelligent control execution instructions, establishes a multi-index evaluation system and performs assembly success determination and anomaly handling to obtain assembly completion status verification results.

[0016] The beneficial effects of this invention are as follows: This invention utilizes multi-source sensor fusion technology to unify and fuse measurement data from a six-dimensional force sensor, a binocular vision camera, and a joint encoder into a base coordinate system. Unscented Kalman filtering is employed to achieve high-precision pose estimation, providing accurate feedback for subsequent control. By identifying actual assembly constraint parameters online and performing orthogonal decomposition of the force-position control subspace, complete geometric decoupling of force and position control is achieved, avoiding overlap and interference in control directions. A strategy combining adaptive impedance control and sliding mode force control is adopted to dynamically adjust control parameters according to the assembly state, maintaining optimal dynamic characteristics at different assembly stages. A lightweight neural network enables intelligent identification of the assembly state, driving a finite state machine to smoothly switch control parameters, improving the adaptability and robustness of the control strategy.

[0017] This invention enables high-success-rate compliant assembly under harsh assembly conditions, effectively controlling peak contact forces, preventing surface damage to high-temperature alloy parts, shortening assembly cycle time, and improving the consistency and stability of assembly quality. Through assembly data mining and process optimization, it achieves continuous improvement in assembly performance, forming a closed-loop optimization system. This invention provides an efficient and reliable technical solution for aerospace precision assembly and has broad application prospects. Attached Figure Description

[0018] Figure 1This is a main flowchart of a compliant assembly method based on force-position hybrid control according to the present invention; Figure 2 This is a detailed flowchart of a compliant assembly method based on force-position hybrid control according to the present invention; Figure 3 This is a block diagram of a compliant assembly system based on force-position hybrid control according to the present invention. Detailed Implementation

[0019] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, some features described in the examples may be combined in other examples.

[0020] At least one embodiment of the present invention discloses a compliant assembly method based on force-position hybrid control, such as Figures 1 to 2 As shown, it includes: Step 1: Collect multimodal measurement data based on multi-source sensors, unify and fuse coordinates to obtain the initial state perception dataset of the assembly environment; Specifically, the following steps are included: Step 1.1, Mechanical connection and coordinate system calibration of the force sensor; This invention employs a six-degree-of-freedom serial articulated industrial robot as the assembly actuator, with a dedicated gripper at the robot's end effector for grasping turbine blades. The robot features dual modes of position and torque control, supports real-time force-position hybrid control, achieves end-effector repeatability better than 0.05 mm, and has a maximum load capacity of at least 10 kg to meet the requirements of high-precision, compliant assembly. The assembly system also includes multi-source sensors such as a six-dimensional force sensor, a binocular vision camera, and joint encoders, achieving multi-modal information fusion through a unified data acquisition and processing system.

[0021] A six-dimensional force sensor is inserted between the end effector flange and the gripper of a six-degree-of-freedom industrial robot. The sensor adopts a flange-type connection structure, and the flatness and perpendicularity of the mounting surface are ensured through precision machining. The position of the sensor coordinate system origin in the end effector coordinate system is measured using a three-dimensional measuring instrument to obtain the translation vector; the sensor mounting posture is obtained through angle measurement to obtain the rotation matrix. The translation vector and rotation matrix are combined into a homogeneous transformation matrix to establish the geometric relationship between the force sensor coordinate system and the end effector coordinate system.

[0022] After calibration, a standard force loading device is used for verification. A standard force of 10 Newtons is applied in the X, Y, and Z directions of the sensor coordinate system. After transformation to the base coordinate system through the transformation matrix, the error of the measured force vector direction should be less than 2 degrees and the error of the force amplitude should be less than 5% to ensure the accuracy of the coordinate transformation.

[0023] Step 1.2, Binocular vision camera extrinsic parameter calibration; A calibration board is placed within the robot's workspace, and the robot's end effector is driven to move to multiple different poses. At each pose, the robot's joint angles and images of the calibration board captured by the binocular vision camera are recorded simultaneously. Based on the joint angles, the robot's forward kinematics are calculated to obtain the pose sequence of the end effector coordinate system in the base coordinate system. Based on the calibration board images, a corner detection algorithm is used to extract feature points from the calibration board. The 3D coordinates of these feature points are obtained through stereo matching, establishing a point cloud in the camera coordinate system. Based on the correspondence between the point cloud in the camera coordinate system and the pose in the base coordinate system, a hand-eye calibration algorithm is used to solve for the extrinsic parameters, obtaining the rotation matrix and translation vector between the camera coordinate system and the base coordinate system. These form the transformation matrix. The hand-eye calibration algorithm specifically employs the Tsai-Lenz method or the Park-Martin method, obtaining the transformation matrix by solving the homogeneous equation system AX=XB, where A is the transformation of the robot's end effector motion, B is the transformation of the calibration board motion observed by the camera, and X is the hand-eye relationship matrix to be determined. At least 15 sets of calibration poses are performed, covering different areas and postures within the workspace. The reprojection error after calibration should be less than 0.5 pixels. It provides a coordinate transformation basis for the global positioning of visual measurement data.

[0024] Step 1.3: Multi-source sensor hardware synchronous triggering; A master clock is set in the robot controller, and synchronous trigger pulses are sent to the six-dimensional force sensor data acquisition card and the binocular vision camera via digital I / O interface, with the trigger frequency set to 200 Hz. Based on the rising edge of the trigger pulse, an interrupt response mechanism is used to ensure that all sensors start sampling at the same time, obtaining measurement data with the same timestamp. Based on the analog output signal of the force sensor, a 16-bit analog-to-digital converter is used for digitization to obtain six-dimensional force vector data. Based on the image sensor exposure of the binocular vision camera, the image acquisition card acquires left and right views to obtain stereo vision image pairs. Based on the robot joint encoder, the joint angles are read using a real-time Ethernet protocol to obtain joint position data. Based on a unified timestamp, a data packaging method is used to combine the force vector, image pairs, and joint angles to obtain a spatiotemporally synchronized multimodal measurement data stream, ensuring the temporal consistency of data from different sensors and eliminating fusion errors caused by asynchronous sampling.

[0025] Step 1.4: Fusion of state data under a unified coordinate system; Using the force sensor transformation matrix from step 1.1 and the current robot end-effector pose, a complete transformation relationship from the force sensor to the base coordinate system is established through matrix multiplication. The force vector output by the six-dimensional force sensor is then transformed to the base coordinate system using this transformation matrix to obtain the contact force vector in the global coordinate system.

[0026] Using the camera transformation matrix from step 1.2, the coordinates of the blade feature points measured by binocular vision are transformed to the base coordinate system. Through a pose calculation algorithm for multiple feature points, the position vector and attitude matrix of the blade are extracted to obtain complete blade pose information.

[0027] Based on force vector, pose, and joint angle data, a data structure encapsulation method is used to obtain the initial state perception dataset of the assembly environment, providing input data in a unified coordinate system for subsequent multi-source information fusion and state estimation.

[0028] Step 2: Based on the initial state perception dataset of the assembly environment, perform unscented Kalman filter state recursive estimation to obtain the blade pose deviation estimate. Specifically, the following steps are included: Step 2.1, Model the nonlinear state equations of the assembly system; The pose deviation of the blade relative to the tenon groove is defined as a state variable, including three translational components and three rotational components, for a total of six degrees of freedom. Based on the kinematic relationship of the robot's end effector, differential kinematic equations are used to establish the mapping relationship between the state variables and the robot's joint velocities.

[0029] Based on the contact dynamics between the blade and the bladed disk, Hertzian contact theory is used to establish a nonlinear equation relating contact force and orientation deviation. Specifically, when the blade tenon and tenon groove come into contact, the magnitude of the contact force is related to the local deformation at the contact point, which is determined by the orientation deviation of the blade relative to the tenon groove. The larger the orientation deviation, the greater the contact deformation and the greater the contact force, and this relationship exhibits nonlinear characteristics. The measured contact force and orientation deviation state variables are correlated through the force-deformation relationship of Hertzian contact theory.

[0030] Based on the end-effector velocity command generated by the compliant control strategy, a discretization method is used to establish a state transition equation to describe how the current state evolves to the next state. Specifically, the pose deviation at the next moment is equal to the pose deviation at the current moment plus the pose change within the control cycle. This change is determined by the robot's end-effector velocity and the control input. By using discrete time steps, the continuous motion process is transformed into a stepwise recursive state evolution process.

[0031] Based on the state transition equation, and considering uncertainties such as modeling errors, robot motion errors, and environmental disturbances in the actual assembly process, additive white Gaussian noise is used to model the process noise. This noise term characterizes the random disturbances in the state transition process, resulting in a nonlinear state equation containing the process noise term. The process noise covariance matrix is ​​a 6×6 diagonal matrix, with the diagonal elements set according to the system uncertainties. The standard deviation of the process noise in the translation direction is taken from 0.01 mm to 0.05 mm, and the standard deviation of the process noise in the rotation direction is taken from 0.05 degrees to 0.1 degrees. The specific values ​​are determined through offline experimental statistics. This equation describes the pose deviation state at the next moment as the result of the current pose deviation state and the control input mapped through the nonlinear state transition function, plus the process noise.

[0032] Based on the initial state perception dataset of the assembly environment obtained in step 1, the initial pose deviation of the blade relative to the tenon groove is extracted as the initial state value, and the initial covariance matrix is ​​set to reflect the initial uncertainty.

[0033] Step 2.2, Establishment of observation equations for multi-source sensors; Based on the coordinates of blade feature points measured by a binocular vision camera, a perspective projection model is used to establish a nonlinear observation equation relating the image plane coordinates to the blade's pose. Specifically, the positions of blade feature points in three-dimensional space are projected onto a two-dimensional image plane through the camera's optical system. The projection position is determined by the blade's pose. The three-dimensional coordinates of the feature points can be calculated in reverse using binocular stereo vision, thereby inferring the blade's pose. Binocular vision cameras can directly measure position and attitude, but their measurement accuracy is affected by illumination and occlusion.

[0034] Based on the contact force vector measured by a six-dimensional force sensor, an indirect observation equation for the contact force and pose deviation is established using contact geometry. Specifically, when the blade contacts the tenon groove, the direction of the contact force is perpendicular to the contact surface, and the magnitude of the contact force reflects the degree of contact. By analyzing the spatial distribution and direction of the contact force, the offset direction and amount of the blade relative to the tenon groove can be inferred. While the force sensor cannot directly measure pose, pose information can be deduced from the contact point location and the direction of the contact force. The measurement accuracy is affected by the accuracy of the contact model.

[0035] Based on robot pose measurements using joint encoders, forward kinematics is employed to establish the observation relationship between the end effector pose and the blade pose. Specifically, the end effector pose is calculated using joint angles and robot kinematic parameters. Since the blade is fixed to the end effector by the gripper, a fixed geometric relationship exists between the end effector pose and the blade pose, thus indirectly obtaining the observed value of the blade pose. Encoder measurements offer high accuracy but are subject to kinematic calibration errors.

[0036] The three measurement sources have complementary characteristics: visual measurement is intuitive but susceptible to occlusion; force measurement is robust but indirect; and encoders are highly accurate but limited by calibration errors. Fusion of these three sources can improve the accuracy and robustness of pose estimation. Based on the three measurement sources, a comprehensive observation equation is adopted. This equation describes the current measurement vector as the result of mapping the pose deviation state through a nonlinear observation function and superimposing measurement noise. This establishes a mapping relationship between the measured values ​​and state variables, providing an observation model for sensor fusion.

[0037] The measurement noise covariance matrix is ​​determined based on the accuracy of each sensor. The standard deviation of the force measurement noise of the six-dimensional force sensor is 0.1 Newtons, and the standard deviation of the torque measurement noise is 0.01 Newton-meters. The standard deviation of the position measurement noise of the binocular vision sensor is 0.1 millimeters, and the standard deviation of the attitude measurement noise is 0.2 degrees. The standard deviation of the angle measurement noise of the joint encoder is 0.001 degrees.

[0038] Step 2.3, Unscented transformation Sigma point propagation calculation; A set of Sigma sampling points is selected using an unscented transform method, with the number of points being twice the state dimension plus one. The Sigma points are propagated to the next time step through a nonlinear state transition equation. The predicted state mean and covariance matrix are calculated using a weighted average to complete the time update. The predicted Sigma points are mapped to the measurement space through an observation function, and the predicted measurement values ​​are calculated. Based on the residuals between the predicted and actual measurement values, and combined with the observation covariance, the Kalman gain is calculated to correct the predicted state, completing the measurement update and obtaining the optimal estimate of the pose deviation after fusing multi-source sensor information.

[0039] Based on the predicted Sigma points, an observation function is used to map the Sigma points in the state space to the measurement space, resulting in Sigma points in the observation space. Based on the Sigma points in the observation space, a weighted average is used to obtain the predicted measurement value, which is the expected sensor measurement value calculated based on the predicted state.

[0040] Based on the difference between the predicted measurement and the actual measurement from the multi-source sensors collected in step 1, and combined with the observation covariance, the Kalman gain is obtained. This gain reflects the degree of trust in the predicted and measured values. The larger the gain, the more trust the measured value is, and the smaller the gain, the more trust the predicted value is.

[0041] Based on Kalman gain, a state correction formula is used to correct the predicted state using measurement residuals, thereby obtaining the optimal estimate of the pose deviation and its covariance matrix after fusing multi-source sensor information, completing the measurement update step, which uses actual measurement values ​​to correct the prediction results.

[0042] Step 2.4, pose deviation recursive filtering estimation; The estimated positional deviation of the blade relative to the tenon groove at the current moment and the covariance matrix are used as the initial values ​​for filtering at the next moment. Based on the newly arrived multi-source sensor measurement data, the unscented Kalman filtering process in step 2.3 is used to perform a new round of time and measurement updates to obtain the estimated positional deviation of the blade relative to the tenon groove at the next moment. Based on recursive calculation, a real-time iterative method is used to continuously update the estimated positional deviation of the blade relative to the tenon groove throughout the assembly process. Based on the estimated covariance matrix, the confidence interval of the positional deviation is obtained using the three-standard-deviation criterion to evaluate the reliability of the estimation. Based on the time-series data of the positional deviation, a data recording method is used to obtain a complete positional deviation evolution curve from the start of assembly to the completion of assembly. This curve reflects the process of the blade gradually approaching and aligning with the tenon groove, providing the controller with high-precision, low-latency positional feedback information and providing data support for assembly quality assessment.

[0043] Through the above recursive filtering process, the estimated value of the blade position deviation during the entire assembly process is obtained. This estimated value integrates multi-source information from force, vision, and joint encoders, resulting in high accuracy and low delay, providing an accurate feedback signal for subsequent force-position hybrid control.

[0044] In some embodiments, since the contact stiffness changes abruptly during assembly, leading to variations in the system's dynamic characteristics, a multi-model adaptive estimation method can be employed to improve the filter's adaptability to dynamic changes. Specifically, multiple unscented Kalman filters are established in parallel, each corresponding to a different contact stiffness model, covering the stiffness range from free motion to complete contact. Based on the prediction residuals of each filter, the likelihood function is used to calculate the degree of matching between each model and the actual system. Based on the likelihood function values, a Bayesian update method is used to obtain the posterior probability of each model. Based on the posterior probabilities, a weighted fusion strategy is used to sum the estimation results of each filter according to probability weights, obtaining an adaptive pose deviation estimate. This method can automatically identify the current contact state and select the best-matching dynamic model, improving filtering accuracy and robustness, especially avoiding filter divergence at the moment of contact state transition.

[0045] Step 3: Based on the blade pose deviation estimate, identify the actual assembly constraint parameters online, perform orthogonal decomposition of the force-position control subspace and extraction of deviation component projection to obtain position control commands and force control commands; Specifically, the following steps are included: Step 3.1, Geometric analysis of theoretical assembly constraint directions; The tenon groove is a groove structure with a specific insertion direction and lateral constraints. Based on the three-dimensional model of the tenon groove, a geometric analysis method is used to determine that the insertion direction is the direction of the groove's central axis, defined as the normal direction of the constraint space. Based on the sidewall geometry of the groove, the constraint direction restricting the lateral movement of the blade is obtained by calculating the surface normal vector. The fit clearance between the blade tenon and the groove is 0.02 mm to 0.05 mm. A tolerance analysis method is used to determine that precise positional control is required in the normal direction to ensure the insertion depth, while compliant force control is required in the lateral direction to accommodate the fit clearance.

[0046] Based on theoretical geometric constraints, a coordinate system definition method is used to establish an assembly constraint coordinate system, where the Z-axis is along the insertion direction, and the X and Y axes are located within the cross-section of the groove. Based on the assembly constraint coordinate system, a direction decomposition method is used to obtain the Z-axis as the priority direction for position control and the X and Y-axis as the priority directions for force control, forming a preliminary force-position allocation strategy. However, this strategy is based on theoretical geometry and does not consider actual machining errors and assembly deviations.

[0047] Step 3.2, online identification of actual assembly constraint parameters; Due to machining errors, the insertion direction and sidewall direction of the actual tenon groove may deviate from the theoretical value. Based on the pose deviation time-series data output in step 2 and the contact force time-series data of the six-dimensional force sensor continuously collected in step 1, a data window selection method is used to extract the data segment of the initial contact stage of assembly. In this stage, the contact force gradient changes significantly and contains constraint information.

[0048] Based on the principal direction of the contact force vector, principal component analysis is used to calculate the first principal component of the force distribution. This principal component represents the direction of the main constraint reaction force, i.e., the actual normal to the groove sidewall. Based on the relationship between the direction of pose deviation change and the principal direction of the contact force, correlation analysis is used to identify which pose degrees of freedom are constrained.

[0049] Based on the constraint relationship, a linearized model of contact force and pose deviation is established using a recursive least squares algorithm, and the identified model parameters are the contact stiffness. Based on the identified contact stiffness distribution, a stiffness threshold judgment method is used. Directions with stiffness values ​​higher than the stiffness threshold are strong constraint directions, while directions with stiffness values ​​lower than the stiffness threshold are weak constraint directions. The stiffness threshold is determined based on material properties and assembly clearance. For high-temperature alloy tenon and tooth assembly, a typical stiffness threshold is 500 Newtons per meter. Directions higher than this value are determined to be strong constraint directions, where the environmental stiffness is high, and force control is used to achieve compliant contact and avoid excessive contact force. Directions lower than this value are determined to be weak constraint directions, where the environmental stiffness is low or there is no constraint, and position control is used to achieve precise positioning.

[0050] Based on strong and weak constraint directions, coordinate axis rotation transformation is used to correct the axial definition of the assembly constraint coordinate system, resulting in assembly constraint parameters that are adapted to actual geometric errors, including the corrected insertion direction unit vector and lateral constraint direction vector, thereby improving the accuracy of constraint modeling.

[0051] Step 3.3, orthogonal decomposition of the force-position control subspace; Based on the unit vector of the insertion direction identified in step 3.2, it is normalized and used as the first basis vector of the position control subspace. Based on the lateral constraint direction vector, the Gram-Schmidt orthogonalization algorithm is used to construct a vector orthogonal to the first basis vector, which is then normalized to obtain the first basis vector of the force control subspace, i.e., the second basis vector. Based on the first and second basis vectors, a cross product operation is used to obtain a vector that is perpendicular to both of the first two basis vectors, which is then normalized to obtain the third basis vector.

[0052] Based on three orthogonal basis vectors, a matrix assembly method is used to construct a constraint coordinate system rotation matrix by arranging the three basis vectors column-wise. The column vectors of this matrix are orthonormal bases, defining the attitude of the assembly constraint coordinate system relative to the base coordinate system. Based on the constraint coordinate system rotation matrix, the concept of subspace projection is adopted. The position control subspace is defined as a one-dimensional subspace spanned by the first basis vector, and the force control subspace is defined as a two-dimensional subspace spanned by the second and third basis vectors. The two subspaces are orthogonal and span the entire three-dimensional space, ensuring that force control and position control are geometrically completely decoupled, with no overlap or interference in control directions.

[0053] Step 3.4, Subspace bias component projection extraction; Extract the blade translation deviation vector output in step 2, and transform it from the base coordinate system to the assembly constraint coordinate system using the constraint coordinate system rotation matrix to obtain the insertion direction deviation and lateral deviation components.

[0054] Construct position control selection matrices and force control selection matrices, and extract the deviation components in the insertion direction and lateral direction, respectively. The position control selection matrix is ​​set to 1 only in the insertion direction and 0 in all other directions; the force control selection matrix is ​​set to 1 in the lateral direction and 0 in the insertion direction. By multiplying the selection matrices by the deviation vector, the deviation components of the position control subspace and force control subspace are obtained, respectively.

[0055] Based on the complementary force control selection matrix, which is a diagonal matrix with diagonal elements of 0, 1, and 1 respectively, the selection matrix is ​​multiplied with the deviation vector in the constrained coordinate system in the same way to obtain the deviation component of the force control subspace. This component contains two lateral deviations, which need to be corrected by force control guidance.

[0056] Based on the two deviation components, an inverse coordinate transformation is used to transform them back to the base coordinate system, obtaining the position control deviation vector and force control deviation vector in the base coordinate system, which provides decoupled input signals for the subsequent independent design of the position controller and force controller.

[0057] Step 3.5: Perform adaptive evolutionary subspace decomposition; Since the subspace definition needs to be dynamically adjusted to adapt to constraint changes during assembly, a sliding data window with a length of 1 second is set, containing pose and force data of 200 sampling points. Based on the arrival of each new sampling point, a first-in-first-out (FIFO) strategy is used to update the window content, discarding the oldest data point and adding the latest. Based on the updated window data, the recursive least squares algorithm in step 3.2 is used to re-identify the assembly constraint parameters. Based on the difference between the identification result and the current constraint parameters, a threshold judgment is used. If the difference exceeds the constraint parameter difference threshold (typically a constraint direction deviation of 5 degrees or a contact stiffness change of 30%), a subspace redefinition is triggered. Based on the new constraint parameters, the orthogonalization method in step 3.3 is used to update the standard orthogonal basis and selection matrix. Based on the requirement for smooth transition, a first-order low-pass filter (time constant 0.1 to 0.3 seconds) is used to perform time filtering on the selection matrix elements to avoid abrupt changes in control commands caused by sudden changes in subspace definition, resulting in a smoothly evolving adaptive subspace decomposition. This method enables the system to track changes in constraint conditions during assembly and automatically adjust the force-position allocation strategy at different assembly stages, maintaining decoupling effects.

[0058] Step 3.6, Decoupling control command generation; Based on the deviation component of the position control subspace, a proportional control term is used, multiplying the deviation by the position proportional gain to obtain the proportional correction speed. Based on the time derivative of the deviation, a differential control term is used, multiplying the rate of change of the deviation by the position differential gain to obtain the differential correction speed. Based on the proportional and differential terms, a summation operation is performed to obtain the desired correction speed of the position control subspace. This speed command is used to drive the robot to move along the insertion direction to eliminate position deviation. The control gain is selected according to the response speed and stability requirements of the assembly task. A larger gain improves the response speed but may reduce stability, while a smaller gain improves stability but slows down the response. The appropriate gain value is determined through experimental debugging.

[0059] Based on the deviation component of the force control subspace, an impedance relationship is used to convert the position deviation into the desired contact force. The impedance relationship is defined as the contact force being proportional to the position deviation, with the proportionality coefficient being the virtual stiffness. Based on the virtual stiffness, a multiplication operation is used to multiply the virtual stiffness by the deviation component of the force control subspace to obtain the target contact force of the force control subspace. This target force is used to guide the blades to make compliant adjustments laterally, achieving automatic alignment through contact force feedback. The choice of virtual stiffness determines the degree of compliance; a smaller stiffness makes the system more compliant but slows down the alignment speed, while a larger stiffness speeds up alignment but may generate excessive contact force. The choice is made based on a trade-off between material tolerance and assembly efficiency requirements.

[0060] Based on the desired correction velocity of the position control subspace and the target contact force of the force control subspace, data packaging is used to obtain decoupled position control commands and force control commands, which are then input to the position controller and force controller respectively to achieve coordinated execution of force-position hybrid control.

[0061] Step 4: Based on the position control command, establish an impedance control dynamic model and adjust the impedance parameters, solve the impedance control dynamic model and perform trajectory integration to obtain the desired trajectory of the position control end. Specifically, the following steps are included: Step 4.1, Establish the impedance control dynamic model; Impedance control establishes a desired force-position relationship, enabling the robot's end effector to exhibit virtual mechanical impedance characteristics. Based on Newton's second law, a mass-spring-damped model is used to establish an impedance equation. This equation describes how the sum of the products of the desired virtual mass and acceleration deviation, the desired virtual damping and velocity deviation, and the desired virtual stiffness and position deviation equals the external force applied by the environment. This equation describes how the end effector responds under external forces. By adjusting the three parameters—desired virtual mass, desired virtual damping, and desired virtual stiffness—different dynamic characteristics can be designed.

[0062] Based on the assembly task requirements, during the free movement phase, a rapid system response is desired. A larger virtual stiffness and smaller virtual damping are employed to give the system rigid characteristics and quickly eliminate positional deviations. During the contact phase, to sense contact and ensure a smooth transition, moderate virtual stiffness and moderate virtual damping are used, allowing the system to maintain a certain response speed while exhibiting moderate compliance. During the insertion phase, to avoid excessive contact force damaging parts, smaller virtual stiffness and larger virtual damping are used to give the system compliant characteristics, with adaptive adjustment achieved through force feedback. By dynamically adjusting impedance parameters at different assembly stages, the robot end effector maintains dynamic characteristics that match the task requirements throughout the entire assembly process.

[0063] Step 4.2, adaptive adjustment of impedance parameters based on fuzzy logic; Based on the contact force amplitude measured by a six-dimensional force sensor, a dual-threshold judgment method is used to identify the contact state. A low contact force threshold and a high contact force threshold are set. When the contact force is less than the low contact force threshold, it is determined to be a free motion state; when the contact force is between the low and high contact force thresholds, it is determined to be a soft contact state; and when the contact force exceeds the high contact force threshold, it is determined to be a hard contact state. Based on the relationship between contact force and pose deviation, a recursive least squares algorithm is used to identify the contact stiffness online.

[0064] Based on contact state identifiers, fuzzy linguistic variables are defined, including three fuzzy states: free motion, soft contact, and hard contact. Based on contact stiffness estimates, fuzzy input variables are defined, fuzzifying the stiffness values ​​into three fuzzy sets: low, medium, and high. The low-stiffness fuzzy set uses a descending half-trapezoidal membership function, with a membership degree of 1 in the range of 0 to 300 N / m, and linearly decreasing to 0 in the range of 300 to 600 N / m; the medium-stiffness set uses a triangular membership function, with a peak at 600 N / m and a triangular distribution in the range of 300 to 900 N / m; the high-stiffness set uses an ascending half-trapezoidal membership function, linearly increasing to 1 in the range of 900 to 1200 N / m, and having a membership degree of 1 above 1200 N / m.

[0065] Based on assembly experience, a fuzzy rule base was established. The rule format is: if the contact state is a certain state and the contact stiffness is a certain value, then the impedance parameter is a certain value. Specific rules include: if it is a free motion state, then set high virtual stiffness and low virtual damping to achieve fast tracking; if it is a soft contact state and the contact stiffness is low, then set medium virtual stiffness and medium virtual damping to maintain a certain response speed and compliance; if it is a hard contact state and the contact stiffness is high, then set low virtual stiffness and high virtual damping to enhance compliance and avoid damage.

[0066] Based on the current contact state and stiffness estimate, a fuzzy inference mechanism is used to calculate the activation degree of each rule. Based on the activation degree, a weighted average defuzzification method is used to obtain real-time impedance parameter values, including the current virtual mass, current virtual damping, and current virtual stiffness. These parameters can be dynamically adjusted according to the assembly process, so that the system maintains optimal dynamic characteristics at different stages.

[0067] Step 4.3, solving the impedance equation and calculating the acceleration; Based on the desired correction velocity and deviation components of the position control subspace output from step 3, and combined with the current actual end-effector velocity and contact force, the acceleration deviation is solved by substituting them into the impedance equation. The desired end-effector velocity and acceleration correction are obtained through integration.

[0068] The trapezoidal integral method is used to numerically integrate acceleration and velocity within the control cycle to obtain the desired position at the current moment. A smooth trajectory curve is generated through cubic spline interpolation to ensure continuous acceleration. A sequence of trajectory points is extracted at control cycle intervals to obtain the desired trajectory at the end of the position control process.

[0069] In some embodiments, since abrupt changes in impedance parameters may lead to discontinuous control commands, a parameter smoothing transition strategy can be adopted to improve control stability. Specifically, when the difference between the new impedance parameter output by fuzzy inference and the currently used parameter exceeds a parameter change threshold, the system does not directly switch to the new parameter but instead uses a first-order inertial element for transition. Based on the transfer function of the first-order inertial element, the time constant is set to 0.1 to 0.3 seconds. Based on the new and old parameters, an exponentially weighted moving average method is used to gradually adjust the parameter values ​​over multiple control cycles to obtain a smoothly changing impedance parameter curve. Based on the smoothed parameters, the impedance equation is substituted to calculate the continuously changing acceleration correction, avoiding abrupt changes in control commands, reducing the impact on the robot drive system, and improving system stability and assembly quality.

[0070] Step 5: Based on the force control command, calculate the force tracking deviation and design the sliding surface, solve the position compensation command, perform speed limiting and trajectory generation, and obtain the force control end compensation trajectory. Specifically, the following steps are included: Step 5.1, Calculation of tracking deviation in force control subspace; Based on the target contact force in the force control subspace output in step 3, this force vector is defined in the two lateral directions of the assembly constraint coordinate system. Using the contact force vector measured in real-time by the six-dimensional force sensor, the coordinate transformation relationship established in step 1 is used to transform the measured force to the assembly constraint coordinate system, obtaining the force vector in the constraint coordinate system. Based on the definition of the force control subspace, the force components in the two lateral directions are extracted using the force control selection matrix; these components represent the actual contact force within the force control subspace.

[0071] Based on the target force and the actual force, a vector subtraction method is used to subtract the actual contact force from the target contact force, yielding the force tracking deviation. This deviation signal serves as the input to the force controller, reflecting the difference between the current contact force and the desired contact force. A positive deviation indicates that the actual force is less than the target force, requiring an increase in contact pressure; a negative deviation indicates that the actual force is greater than the target force, requiring a decrease in contact pressure. Based on the force tracking deviation, amplitude calculation is used to determine the magnitude of the deviation, which is then used for subsequent control gain adjustment.

[0072] Step 5.2, Sliding surface design and sliding variable definition; Sliding mode control designs a sliding surface that allows the system state to slide along the surface and converge to the desired state. A linear sliding surface design is used, defining the sliding variable as the product of the sliding surface slope parameter and the force tracking deviation, plus the rate of change of the deviation. The sliding surface slope parameter is determined based on the force control response speed requirements of the assembly task; a larger parameter results in faster convergence but increased chattering, while a smaller parameter provides a smoother response but reduces speed. By adjusting the sliding surface slope parameter, the system's force tracking response time is made to meet the assembly requirements.

[0073] Based on sliding mode variables, the system state relative to the sliding surface is determined. A sliding mode variable greater than zero indicates the system is above the sliding surface, less than zero indicates the system is below the sliding surface, and equal to zero indicates the system is on the sliding surface. The goal of sliding mode control is to drive the system towards zero and maintain this position, achieving force tracking. Based on the sign of the sliding mode variables, a switching control law is designed to obtain the control action that causes the system to move towards the sliding surface.

[0074] Step 5.3, Design of adaptive gain sliding mode control law; The reaching law defines how a sliding mode variable approaches zero, determining the dynamic quality of the system. Based on the exponential reaching law, the time derivative of the sliding mode variable is designed to be equal to the product of the negative switching gain and the sign function, minus the product of the exponential reaching velocity and the sliding mode variable, where the switching gain and the exponential reaching velocity are control parameters. The switching gain needs to be large enough to overcome system uncertainties and disturbances, but too large a gain can lead to chattering. Based on an adaptive strategy, the gain is dynamically adjusted according to the amplitude of the sliding mode variable. When the amplitude is large, the switching gain is increased to accelerate the reaching process; when the amplitude is small, the switching gain is decreased to suppress chattering.

[0075] The adaptive law is designed, and the switching gain consists of a base gain and an adaptive adjustment term. The base gain ensures basic robustness, while the adaptive adjustment term dynamically adjusts based on the amplitude of the sliding mode variable. When the deviation is large, the gain is increased to speed up the response; when the deviation is small, the gain is decreased to suppress chattering. The control parameters are determined based on the robustness and stability requirements of the assembly task. The required control input is derived by back-calculating the reaching law, and in force control, the contact force is changed by adjusting the end position.

[0076] Based on the contact stiffness model, the contact force equals the product of the contact stiffness and the position change, which leads to the derivation that the position change equals the contact force divided by the contact stiffness. Using the approach law to calculate the required force change, the inverse operation of contact stiffness is employed, dividing the force change by the online identified contact stiffness estimate to obtain the position compensation command. Based on the position compensation command, a direction transformation is used to transform the compensation amount in the force control subspace back to the base coordinate system, resulting in the position compensation command output by the sliding mode control. This command is used to correct the end-effector position to achieve force tracking.

[0077] Step 5.4, force control compensation trajectory generation; Based on the position compensation command, a differential method is used to calculate the change in compensation position relative to the current position. Based on the control cycle, a division operation is used to divide the position change by the time step to obtain the required compensation speed. Based on the compensation speed, a speed limiting method is used to restrict the speed to a safe range to avoid impact caused by excessively rapid compensation movement. The speed limit value is determined based on contact safety; under contact conditions, the compensation speed should be controlled on the order of a few millimeters per second. Based on the limited compensation speed, a trajectory generation method is used to generate motion trajectory points based on the current position and in the direction of the compensation speed. Based on continuous trajectory points, smooth interpolation is used to obtain the force control end compensation trajectory. This trajectory reflects the corrective motion generated by the force controller to eliminate force deviation and is independent of the position control trajectory. The two operate in different subspaces without interfering with each other.

[0078] In some embodiments, since the sign function of sliding mode control can cause chattering that affects assembly quality, a continuous function can be used instead of the sign function to smooth the control output and suppress chattering. Specifically, a saturated function is used instead of the sign function. The saturated function is defined as follows: when the absolute value of the sliding mode variable is greater than the boundary layer thickness, the function value is equal to the sign function value; when the absolute value of the sliding mode variable is less than the boundary layer thickness, the function value is equal to the sliding mode variable divided by the boundary layer thickness, exhibiting a linear change. Based on the saturated function, the reaching law becomes that the time derivative of the sliding mode variable is equal to the product of the negative switching gain and the saturated function minus the product of the exponential reaching velocity and the sliding mode variable. The choice of boundary layer thickness balances chattering and robustness; a larger boundary layer thickness reduces chattering but decreases robustness, while a smaller boundary layer thickness maintains robustness but increases chattering. A suitable value is selected through experiments. Based on the improved reaching law, using the same derivation method as in step 5.3, a smooth position compensation command is obtained. This command no longer switches at high frequency after the sliding mode variable enters the boundary layer, but changes continuously, reducing chattering and improving the stability of the contact force and the quality of the assembly surface.

[0079] Step 6: Based on the desired trajectory of the position control end effector and the compensation trajectory of the force control end effector, perform feature extraction and neural network state recognition, synthesize the force-position trajectory and map it into joint space to obtain the intelligent control execution command; Specifically, the following steps are included: Step 6.1, Multi-scale feature extraction of assembly state; The assembly process includes four main stages: free movement, initial contact, search and alignment, and insertion assembly. Each stage has different force signals and visual characteristics.

[0080] Based on the time-series data output by the six-dimensional force sensor, a sliding window method is used to extract 100 force sampling points within the most recent 0.5 seconds to form a force time-series matrix. Based on the force time-series matrix, statistical feature extraction is performed to calculate the mean, variance, maximum, and minimum values ​​of the force, thereby obtaining the time-domain statistical features.

[0081] Based on the rate of change of the force signal, a gradient calculation method is used to obtain the force change rate characteristics, which show abrupt changes at the moment of contact. Based on the force signal, a fast Fourier transform is used to convert the time-domain signal to the frequency domain, extract the main frequency components and energy distribution, and obtain the frequency domain characteristics. Different contact states have different spectral characteristics.

[0082] Based on images from a binocular vision camera, an edge detection algorithm is used to extract the relative positional relationship between the blade and the tenon groove, and the minimum distance between the blade edge and the groove edge is calculated to obtain visual distance features. Based on motion estimation of the visual images, an optical flow method is used to calculate the blade's motion speed and direction, obtaining visual motion features.

[0083] Based on the above multi-source, multi-scale features, a feature concatenation method is used to combine them into a high-dimensional feature vector, which comprehensively reflects the current assembly status information.

[0084] Step 6.2, Lightweight Neural Network State Recognition; Traditional support vector machine (SVM) classifiers, while accurate, are computationally complex and difficult to run in real time. Step 6.1 extracts 32-dimensional feature vectors, including 8 force temporal statistical features, 4 force frequency domain features, 6 force gradient features, 8 visual distance and motion features, and 6 pose deviation features. The training dataset contains labeled data from at least 500 assembly processes, with approximately 10,000 data points sampled for each process, divided into training, validation, and test sets in a 7:2:1 ratio.

[0085] A lightweight one-dimensional convolutional neural network is used as the classifier. The network contains three convolutional layers for feature abstraction: the first convolutional layer contains 16 kernels, the second contains 32 kernels, and the third contains 64 kernels. Each layer is followed by batch normalization and ReLU activation functions, and dimensionality reduction is achieved through max pooling layers. The network structure parameters are determined based on the feature dimension and classification accuracy requirements, with the total number of parameters controlled within 50,000, ensuring that the single inference time is less than 5 milliseconds, and meeting the real-time control requirements at a 200 Hz control frequency.

[0086] The network data flow process is as follows: The input 32-dimensional feature vector passes through the first convolutional layer with a kernel size of 3 and a stride of 1, outputting a 16-channel feature map; after batch normalization, it passes through the ReLU activation function, and then through a max pooling layer with a kernel size of 2 for dimensionality reduction; the pooling output enters the second convolutional layer with a kernel size of 3 and a stride of 1, outputting a 32-channel feature map, which also undergoes batch normalization, ReLU activation, and max pooling; the third convolutional layer receives the pooling output with a kernel size of 3 and a stride of 1, outputting a 64-channel feature map, which undergoes batch normalization and ReLU activation, followed by global average pooling to compress the feature map into a 64-dimensional feature vector; this feature vector is input into a fully connected layer, which contains 128 neurons and uses ReLU activation, connecting to the 4 neurons of the output layer, and outputting the probability distribution of the four assembly stages through the softmax function.

[0087] The network training process followed these steps: The features of the training set were preprocessed by normalization, with the mean set to zero and the variance to one; a mini-batch training method with a batch size of 64 was used, and the initial learning rate was set to 0.001; the training process was divided into two phases: the first phase trained for 50 epochs with the learning rate remaining constant, and the second phase trained for 30 epochs, with the learning rate decreasing to 0.5 times its original value every 10 epochs; after each epoch, the accuracy was evaluated on the validation set, and the weights of the model with the highest validation accuracy were saved; an early stopping strategy was adopted, terminating training if the validation accuracy did not improve for 10 consecutive epochs; after training, the results were evaluated on the test set, achieving a final classification accuracy of 97.5% and recall rates above 95% for each category.

[0088] Based on the high-level features output by the convolutional layers, a fully connected layer is used for classification. The output layer has four neurons corresponding to four assembly stages, and a softmax activation function is used to obtain the probability distribution of each stage. Based on the probability distribution, the maximum probability criterion is used to select the category with the highest probability as the recognition result, and this maximum probability value is used as the recognition confidence level.

[0089] Based on the assembly dataset collected offline, a supervised learning method was used to train the network, with cross-entropy as the training loss function and the Adam algorithm as the optimizer. The network parameters were fixed after training, and only forward inference was performed during online runtime, with a single inference time of less than 5 milliseconds, meeting real-time requirements.

[0090] Based on the recognition results and confidence levels, a confidence threshold is used for judgment. When the confidence level is higher than the threshold, the recognition result is accepted; when the confidence level is lower than the threshold, the previous state is maintained to avoid incorrect switching due to misrecognition. The confidence threshold is determined through validation set performance, typically ranging from 0.7 to 0.9, balancing recognition reliability and response speed. To improve training efficiency and model generalization ability, data augmentation strategies are employed during training. Gaussian noise with an amplitude of 1 to 2 times the standard deviation of the measurement noise is added to the force signal. Visual features are randomly scaled (scaling factor 0.9 to 1.1) and randomly offset (offset within 5% of the feature value) to expand the diversity of training samples. Model regularization uses L2 weight decay with a decay coefficient of 0.0001 to prevent overfitting. The training loss function is class-weighted cross-entropy, with weights set according to the reciprocal of the number of samples in each class to balance the imbalanced sample problem.

[0091] Step 6.3: Switching control parameters driven by the state machine; Based on the transition rules of the assembly state, a finite state machine is used for modeling, defining state nodes and transition conditions. The state transition sequence is: free motion → initial contact → search for alignment → insertion of assembly → assembly completion. Based on the state machine model, a set of optimal control parameters is pre-set for each state, including impedance parameters such as virtual mass, virtual damping, and virtual stiffness, sliding mode control gains such as switching gain and exponentially approaching velocity, and trajectory synthesis weighting coefficients.

[0092] In the free motion state, high stiffness and high speed parameters are used to quickly approach the target position; in the initial contact state, medium stiffness and damping are used to sense contact and decelerate; in the search and centering state, low stiffness, high damping and large force control weights are used to emphasize compliance and centering capability; in the insertion and assembly state, balanced parameters are used to take into account both insertion depth control and lateral force control.

[0093] Based on the currently identified state, a lookup table method is used to retrieve the corresponding set of control parameters from the parameter library. Based on state transition triggering, a smooth parameter switching strategy is adopted, specifically implemented as follows: When step 6.2 identifies a state transition, the transition time is recorded as the state transition start time. A transition time window is set to 1 to 2 seconds, the length of which is determined according to the state transition type. The transition window from free movement to initial contact is shorter (1 second), and the transition window from search alignment to insertion into the assembly is longer (2 seconds) to ensure smoothness. Within the transition time window, the S-curve interpolation method is used to calculate the control parameters at the current moment. This method has a zero derivative at the beginning and end of the window, ensuring continuous acceleration of parameter changes. Specifically, let the old state parameter be the initial parameter value, the new state parameter be the final parameter value, the time from the current moment to the start of the switch be the elapsed time, and the total duration of the transition window be the window duration. Then, the current parameter value is equal to the initial parameter value plus the difference between the final parameter value and the initial parameter value multiplied by the S-curve function, where the S-curve function is a cubic polynomial, and the function value smoothly increases from 0 to 1. This smooth transition strategy ensures that control parameters do not jump during state transitions, thus avoiding abrupt changes in robot motion and impacts from contact forces.

[0094] Step 6.4, Force trajectory synthesis and joint space mapping; Based on the desired position control trajectory output in step 4 and the compensated force control trajectory output in step 5, the two trajectories are defined in different subspaces. To meet the trajectory synthesis requirements, a weighted summation method is used to synthesize the two trajectories in the base coordinate system. The weighting coefficients are provided by the control parameter set in step 6.3, including position control weights and force control weights, with the sum of the two weights being one. Based on the weighting coefficients, a weighted average formula is used to multiply the position control weight by the position control trajectory and the force control weight by the force control trajectory, and the sum of the two yields the synthesized desired end-point trajectory. The weighting coefficients differ at different assembly stages, reflecting the changing priorities of force control and position control.

[0095] Based on the synthesized trajectory, the desired end-effector pose at the current moment is extracted, including position and orientation. Based on the robot's kinematic model, a numerical iterative inverse kinematics algorithm is used to solve for the joint angle configuration that satisfies the desired end-effector pose. Since inverse kinematics often has multiple solutions, the minimum joint motion criterion is used to select the optimal solution, i.e., the solution with the smallest change in joint angles, ensuring smooth motion.

[0096] Based on the solved joint angles, joint space trajectory planning is employed to generate sequences of joint angles, angular velocities, and angular accelerations. Using the robot's dynamics model, inverse dynamics calculations are employed to calculate the required joint torques based on joint acceleration, velocity, and position. Simultaneously, gravity compensation, friction compensation, and inertia compensation are performed to obtain the driving torque commands for each joint. Based on these torque commands, a servo driver interface protocol is used to send the torque commands to the motor drivers of each joint, driving the robot to perform compliant assembly actions. This yields intelligent control execution commands, enabling the adaptive application of force-position hybrid control throughout the assembly process.

[0097] In some embodiments, since the generalization ability of neural network classifiers may be insufficient when facing new assembly scenarios, an online incremental learning method can be adopted to continuously improve the accuracy of state recognition. Specifically, after each assembly is completed, the feature vectors and state sequences of this assembly process are labeled using manual annotation or automatic annotation based on whether the assembly was successful or not, resulting in new training samples. Based on the new training samples, the neural network weights are fine-tuned and updated using a mini-batch gradient descent algorithm, with the learning rate set to one-tenth of the initial training rate to maintain the stability of the learned knowledge. Based on the updated network, a validation set is used for testing. If the recognition accuracy improves, the new weights are retained; if it decreases, the old weights are reverted. Through continuous online learning, the network can adapt to the slight differences between different batches of parts and changes in the assembly environment, gradually improving the recognition accuracy from the initial 95% to over 98%, improving the correctness of control strategy switching, and reducing assembly failures caused by misidentification.

[0098] Step 7: Based on the intelligent control execution instructions, establish a multi-index evaluation system and perform assembly success determination and anomaly handling to obtain the assembly completion status verification result; Specifically, the following steps are included: Step 7.1, Multi-index evaluation system for assembly quality; Based on the pose deviation time-series curve of the unscented Kalman filter output, a convergence analysis method is used to calculate the time and convergence rate of the pose deviation from the initial value to the final value, thus obtaining the centering efficiency index. The centering time reflects the efficiency of the search and centering stage; the shorter the time, the better the performance of the force-position hybrid control.

[0099] Based on the contact force time-series curve recorded by a six-dimensional force sensor, a peak detection algorithm is used to extract the maximum contact force value throughout the assembly process, thus obtaining the peak force index. The peak force should be controlled within the allowable range of the material. For tenon and tooth assembly, the peak force should not exceed 20 Newtons; exceeding this value may cause surface damage.

[0100] Based on the fluctuation of the contact force curve, using the standard deviation calculation method, a force fluctuation index is obtained to reflect the stability of the assembly process. The smaller the fluctuation, the more stable the control. Based on the position data in the insertion stage, using the depth measurement method, calculate whether the blade insertion depth reaches the design value to obtain the insertion depth compliance index. Based on the time difference of the timestamps from the start to the end of the assembly, obtain the assembly cycle time index, which is required to be controlled between 45 seconds and 60 seconds.

[0101] Based on the above multiple indicators, using a weighted scoring model, weights are assigned to each indicator. The force peak value and the insertion depth are key indicators with relatively large weights, and the assembly time is a secondary indicator with a relatively small weight. Based on the weighted sum, a comprehensive assembly quality score is obtained, and the score range is from 0 to 100. The weight distribution of each indicator is as follows: the weight of the force peak value indicator is 0.30, the weight of the insertion depth compliance indicator is 0.30, the weight of the force fluctuation indicator is 0.20, the weight of the centering efficiency indicator is 0.10, and the weight of the assembly cycle time indicator is 0.10. Each indicator is scored on a 100-point scale. If the force peak value is less than 15 Newtons, the full score of 100 points is obtained; it linearly decreases from 60 points when it is between 15 and 20 Newtons; and it is 0 points when it is greater than 20 Newtons. If the insertion depth error is less than 0.05 millimeters, the full score is obtained, and 10 points are deducted for each increase of 0.01 millimeter in the error.

[0102] Step 7.2, determination of assembly success and exception handling; Based on the comprehensive quality score, set the quality pass threshold as 80 points. Using the comparison of the quality score threshold, if the score is higher than the quality pass threshold, it is determined that the assembly is qualified; if it is lower than the quality pass threshold, it is determined that the assembly is unqualified. Based on the individual inspection of the key indicators, even if the comprehensive score meets the standard, if the force peak value exceeds the safety upper limit or the insertion depth does not reach the minimum requirement, it is still determined as unqualified. A one-vote veto mechanism is adopted to ensure the key quality requirements.

[0103] Based on the determination result, using logical branching, if the assembly is qualified, an assembly success flag signal is output to trigger the assembly completion process, and the robot exits and prepares for the next assembly; if the assembly is unqualified, an assembly failure flag signal is output to trigger the exception handling process. Based on the analysis of the specific reasons for the failure situation, if the insertion depth is insufficient, it may be that the centering is not completed, and the exit and retry strategy is adopted, and the robot returns to the search centering stage to execute again; if the force peak value is too large, it may be that the control parameters are improper, and the parameter adjustment strategy is adopted to reduce the movement speed or increase the compliance and then retry; if there are consecutive failures, the manual intervention strategy is adopted to pause the automatic assembly and notify the operator to check the part and equipment status.

[0104] Based on the determination of assembly success or failure, the comprehensive quality score, the inspection results of key indicators, and the exception handling records, generate the verification result of the assembly completion status. This result includes information such as whether the assembly is successful, the quality score, the compliance of each indicator, the exception type, and the handling measures, providing a complete record for the traceability of the assembly process and quality management.

[0105] Step 7.3, Assembly data mining and process optimization; Based on complete data from each assembly, including initial pose deviation, force-position timing curve, state transition sequence, control parameter sequence, and final quality score, a structured storage method is used to save the data to the assembly database.

[0106] Based on a large number of assembly cases accumulated in the database, data mining techniques were used to analyze the relationship between initial conditions and assembly results. Cluster analysis identified typical initial condition patterns that lead to assembly failures; for example, a high failure rate is observed when initial deviations in a certain direction are too large. Association rule mining revealed the correlation between certain combinations of control parameters and high-quality assembly; for instance, using specific impedance parameters during the alignment search phase resulted in faster alignment speeds and lower peak force.

[0107] Based on regression analysis, a quantitative relationship model is established between initial deviation, control parameters, and quality score to predict the optimal control parameters under given initial conditions. Based on optimization algorithms, control parameter configurations that maximize the quality score are searched for common initial deviation ranges. Based on the optimization results, assembly process optimization suggestions are generated, including suggested impedance parameter adjustment directions, suggested motion speed settings, and suggested force control weight configurations. Based on the optimization suggestions, a parameter update mechanism is adopted to write the optimized parameters into the controller's parameter library, enabling subsequent assembly tasks to apply the improved process parameters, achieving continuous optimization of assembly performance, obtaining assembly process optimization feedback, and forming a closed-loop improvement system.

[0108] Step 7.4, System Fault Diagnosis and Security Protection; Based on the self-test function of the sensors, a periodic triggering mechanism is adopted to send self-test commands to the six-dimensional force sensor, vision sensor, and joint encoder every 10 seconds. Based on the self-test status codes returned by the sensors, a status parsing method is used to determine whether the sensors are working properly. If the sensors return abnormal states, such as force sensor overload, camera lens damage, or encoder communication failure, a fault marking method is used to record the fault type and time.

[0109] Based on current and temperature monitoring of robot joints, a current-temperature threshold judgment is used. If the current of a joint continuously exceeds the current safety threshold or the temperature exceeds the temperature safety threshold, it is judged as an overload or overheating fault. Based on the fault diagnosis results, a graded response strategy is adopted. For minor faults, such as increased sensor noise, a warning is issued but operation continues; for serious faults, such as sensor failure or joint overload, an emergency stop is immediately triggered, the robot stops moving and maintains its current position. Based on the emergency stop trigger, a brake activation method is used to apply brakes to each joint to prevent the robot from falling or moving in the event of a power outage, protecting the safety of parts and equipment.

[0110] Based on the fault information, an alarm output method is adopted to prompt operators through audible and visual signals and a human-machine interface, explaining the fault type and location, and guiding maintenance operations. Based on the system recovery condition judgment, after the fault is eliminated, a reset procedure is used to reinitialize the sensors and controllers, restore the system to the standby state, obtain system health status assessment and protection action commands, and ensure the safe and reliable operation of the assembly system.

[0111] Through the above-mentioned real-time assembly quality assessment and anomaly handling mechanism, the assembly completion status verification results are obtained, including assembly success determination, quality score, key indicator compliance status, anomaly handling records, and system health status. Process optimization feedback is also obtained, including process parameter optimization suggestions, control strategy improvement directions, and assembly performance improvement feedback, thereby realizing closed-loop monitoring and continuous improvement of assembly quality.

[0112] In some embodiments, where parts may become stuck during assembly, preventing further assembly, an intelligent unblocking strategy can be employed to autonomously resolve the jamming and resume assembly. Specifically, based on abnormal contact force pattern recognition, a jamming state is identified when a sudden increase in resistance in the insertion direction is detected and its duration exceeds the jamming determination time threshold. Based on the jamming determination, the current insertion motion is stopped, and a vibration unblocking method is used to control the robot's end effector to perform small-amplitude, high-frequency vibrations laterally, with an amplitude of 0.1 mm to 0.3 mm and a frequency of 5 Hz to 10 Hz. Based on the force feedback during the vibration process, a resistance monitoring method is used to determine whether the resistance has decreased. If the resistance decreases, the jamming is relieved, and the insertion motion is resumed to continue assembly; if the resistance does not decrease after a certain period of vibration, a withdrawal and re-insertion strategy is adopted, controlling the robot to withdraw a certain distance, readjust its posture, and attempt insertion again. Through the intelligent unblocking strategy, the assembly failure rate caused by jamming is reduced from 15% to below 3%, improving the assembly success rate and reducing the need for manual intervention.

[0113] A compliant assembly system based on force-position hybrid control is used to execute the aforementioned compliant assembly method based on force-position hybrid control, such as... Figure 3 As shown, it includes: The data fusion module collects multimodal measurement data from multiple sources of sensors, unifies and fuses coordinates to obtain an initial state perception dataset of the assembly environment; The blade pose deviation estimation module performs unscented Kalman filtering state recursive estimation based on the initial state perception dataset of the assembly environment to obtain the blade pose deviation estimate. The force-position control decoupling module identifies the actual assembly constraint parameters online based on the blade position and orientation deviation estimation value, performs orthogonal decomposition of the force-position control subspace and extraction of deviation component projection, and obtains position control commands and force control commands. The impedance control trajectory generation module establishes an impedance control dynamic model based on the position control command, adjusts the impedance parameters, solves the impedance control dynamic model, and performs trajectory integration to generate the desired trajectory at the end of the position control. The sliding mode force control module calculates the force tracking deviation and designs the sliding surface based on the force control command, solves the position compensation command, performs speed limiting and trajectory generation, and obtains the force control end compensation trajectory. The state recognition and trajectory synthesis module performs feature extraction and neural network state recognition based on the expected trajectory of the position control end and the compensated trajectory of the force control end, and performs force-position trajectory synthesis and joint space mapping to obtain intelligent control execution instructions; The assembly quality assessment module, based on intelligent control execution instructions, establishes a multi-index evaluation system and performs assembly success determination and anomaly handling to obtain assembly completion status verification results.

[0114] In one embodiment of the present invention, a specific example is provided: A 15-day field test was conducted in the precision assembly workshop of an aero-engine manufacturing company. During the test, a six-axis industrial robot assembly workstation was deployed, equipped with a German ATI Mini40 six-dimensional force sensor (measurement accuracy 0.1 Newtons, sampling frequency 200 Hz), a Basler binocular vision system (resolution 1920×1200 pixels, frame rate 60 frames per second), and a real-time control system. The test area was approximately 25 square meters, with the ambient temperature controlled at 20±2 degrees Celsius and relative humidity between 45% and 55%. The test object was the tenon and tooth assembly of a certain type of high-temperature alloy turbine blade and titanium alloy bladed disk. The tenon and tooth groove depth was 22 mm, the assembly clearance was 0.03 mm, and the assembly tolerance grade was IT6. A total of 50 assembly tasks were completed, each including multiple repeated experiments.

[0115] In the initial assembly stage, through synchronous acquisition by multiple sensors in step 1, the initial blade pose was found to have translational deviations of 0.45 mm in the X direction, 0.62 mm in the Y direction, and 0.38 mm in the Z direction, and angular deviations of 0.8 degrees around the X-axis, 1.2 degrees around the Y-axis, and 0.6 degrees around the Z-axis. Through unscented Kalman filtering fusion in step 2, the pose estimation accuracy was improved to 0.02 mm and 0.1 degrees, providing accurate feedback for subsequent control.

[0116] Table 1 shows examples of initial state data collected by multiple sensors during a typical assembly process: Table 1: Initial state data collected by multi-source sensors during a typical assembly process; Through assembly space decoupling in step 3, the force control subspace dominates during the search and alignment phase, with a weighting coefficient of 0.75, while the position control subspace has a weighting coefficient of 0.25, achieving efficient alignment. Through variable parameter impedance control in step 4, the impedance stiffness is dynamically adjusted from 1200 N / m in the free motion phase to 300 N / m in the insertion phase, and the damping coefficient is adjusted from 80 N / s / m to 180 N / s / m, improving system compliance. Through adaptive sliding mode force control in step 5, the contact force tracking error is controlled within 1.5 N, with a response time of 0.3 seconds. Through neural network state recognition in step 6, the recognition accuracy across the four assembly phases reaches 97.5%, with a state transition delay of less than 0.05 seconds.

[0117] Table 2 shows an example of the assembly result data collected by the quality assessment system after assembly is completed: Table 2: Assembly result data collected by the quality assessment system after assembly; Experimental results show that the force-position hybrid control compliant assembly method proposed in this invention performs excellently in demanding tenon and tooth assembly tasks, achieving a 100% assembly success rate. Assembly time is controlled between 48 and 56 seconds, meeting the requirement of 45 to 60 seconds. The peak maximum contact force is consistently controlled below 20 Newtons, effectively protecting the surface of expensive high-temperature alloy parts. Insertion depth accuracy reaches within 0.03 mm, meeting assembly tolerance requirements. Assembly quality scores are all above 88 points, far exceeding the 80-point passing mark.

[0118] Compared to traditional rigid position control methods, the traditional method achieves an assembly success rate of only 65% ​​under the same initial deviation conditions, with a peak contact force of 45 Newtons, often resulting in scratches on the tenon surface. Assembly time exceeds 120 seconds due to multiple retries. Compared to single impedance control methods, while single impedance control can reduce the contact force to around 25 Newtons, the lack of a force-position decoupling mechanism results in an assembly alignment time exceeding 40 seconds, a total assembly time exceeding 80 seconds, and an assembly success rate of only 82%. This invention, through the comprehensive application of assembly space decoupling, multi-source information fusion, adaptive control, and intelligent state recognition, comprehensively outperforms existing technologies in key indicators such as assembly success rate, assembly time, and contact force control, providing an efficient and reliable technical solution for precision assembly in aerospace.

[0119] After assembly, through quality assessment and data analysis in step 7, an optimized parameter library for the assembly of this type of blade was established. The assembly time of subsequent blades in the same batch was further shortened to 42 to 50 seconds, and the assembly success rate was increased to 99.2%, demonstrating the system's continuous learning and self-optimization capabilities.

[0120] The embodiments of the present invention have been described above. However, the embodiments are not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make more equivalent embodiments under the guidance of the present embodiments, and all of them are within the protection scope of the present embodiments.

Claims

1. A compliant assembly method based on a force-position hybrid control, characterized in that, Includes the following steps: Multimodal measurement data are collected from multiple sources of sensors, coordinates are unified and fused to obtain the initial state perception dataset of the assembly environment. Based on the initial state perception dataset of the assembly environment, unscented Kalman filtering state recursive estimation is performed to obtain the blade pose deviation estimate. Based on the blade pose deviation estimate, the actual assembly constraint parameters are identified online, and the force-position control subspace orthogonal decomposition and deviation component projection extraction are performed to obtain position control commands and force control commands. Based on the position control command, an impedance control dynamic model is established and the impedance parameters are adjusted. The impedance control dynamic model is solved and the trajectory is integrated to generate the desired trajectory of the position control end. Based on the force control command, the force tracking deviation is calculated and the sliding surface is designed. The position compensation command is solved, the speed limit is performed and the trajectory is generated to obtain the force control end compensation trajectory. Based on the desired trajectory of the position control end effector and the compensated trajectory of the force control end effector, feature extraction and neural network state recognition are performed, force-position trajectory synthesis and joint space mapping are performed, and intelligent control execution commands are obtained. Based on intelligent control execution instructions, a multi-index evaluation system is established to determine assembly success and handle anomalies, thereby obtaining the assembly completion status verification results.

2. The compliant assembly method based on the hybrid control of force and position according to claim 1, wherein, The steps for obtaining the initial state-aware dataset of the assembly environment include: The translation vectors and rotation matrices of the force sensor coordinate system and the end-effector coordinate system are combined into a homogeneous transformation matrix; Drive the robot end effector to move to different poses, record joint angles and calibration plate images, obtain the pose sequence of the end effector coordinate system in the base coordinate system based on the joint angles, extract the three-dimensional coordinates of feature points based on the calibration plate images, and obtain the transformation matrix between the camera coordinate system and the base coordinate system using a hand-eye calibration algorithm. By synchronizing the trigger pulses, all sensors start sampling at the same time, thus obtaining measurement data with the same timestamp; The force vector output by the six-dimensional force sensor and the coordinates of the blade feature points measured by binocular vision are transformed to the base coordinate system, and the position vector and attitude matrix of the blade are extracted to obtain the initial state perception dataset of the assembly environment.

3. The compliant assembly method based on the hybrid control of force and position according to claim 1, wherein, The steps for obtaining the blade pose deviation estimate include: The pose deviation of the blade relative to the tenon groove is defined as a state variable. The mapping relationship between the state variable and the robot joint velocity is established. The nonlinear relationship equation between the contact force and the pose deviation is established. The state transition equation is established, and the nonlinear state equation is obtained. Based on the coordinates of blade feature points, the contact force vector measured by a six-dimensional force sensor, and the robot pose measured by a joint encoder, an observation equation between the measured values ​​and the state variables is established. The Sigma sampling points are selected using the unscented transformation method. The Sigma points are then propagated through the state transition equation and the predicted state is calculated. The predicted Sigma points are mapped to the measurement space. The Kalman gain is calculated based on the residual between the predicted and actual measured values, and the predicted state is corrected to obtain the pose deviation estimate.

4. The compliant assembly method based on force-position hybrid control according to claim 1, characterized in that, The steps for obtaining position control commands and force control commands include: Calculate the principal direction of the contact force vector, identify the constrained pose degrees of freedom, identify the contact stiffness, and define the direction with stiffness value higher than the preset stiffness threshold as the strong constraint direction and the direction with stiffness value lower than the preset stiffness threshold as the weak constraint direction. Based on the insertion direction vector as the first basis vector, the second and third basis vectors are constructed using the orthogonalization algorithm. The three basis vectors are used to construct the rotation matrix of the constraint coordinate system, and the position control subspace and force control subspace are defined. Transform the blade translation deviation vector to the assembly constraint coordinate system, construct a selection matrix to extract the deviation components in the insertion direction and lateral direction, obtain the desired correction velocity based on the deviation components in the position control subspace, and obtain the target contact force based on the deviation components in the force control subspace.

5. A compliant assembly method based on force-position hybrid control according to claim 4, characterized in that, Following the step of online identification of actual assembly constraint parameters, the following is also included: A sliding data window is set up, the window data is updated based on the new sampling point, and the assembly constraint parameters are re-identified. When the difference between the identification result and the current constraint parameters exceeds the preset constraint parameter difference threshold, the subspace is redefined, the orthogonal basis and selection matrix are updated, and the elements of the selection matrix are subjected to time filtering to obtain adaptive subspace decomposition.

6. The compliant assembly method based on force-position hybrid control according to claim 1, characterized in that, The step of obtaining the desired trajectory of the position control terminal includes: An impedance equation is established, which aims to describe that the sum of the product of virtual mass and acceleration deviation, virtual damping and velocity deviation, and virtual stiffness and position deviation equals the external force. Contact state is identified based on contact force amplitude, and contact stiffness is determined online. Based on the contact state and contact stiffness estimates, fuzzy input variables are defined, a fuzzy rule base is established, and fuzzy inference and defuzzification methods are used to obtain the impedance parameter values. Based on the expected correction velocity and deviation components in the position control subspace, the acceleration deviation is solved by substituting the current end velocity and contact force into the impedance equation. The expected position is obtained by integration and the trajectory curve is generated, thus obtaining the expected trajectory of the position control end.

7. The compliant assembly method based on force-position hybrid control according to claim 1, characterized in that, The steps for obtaining the force control end-compensation trajectory include: Transform the contact force vector to the assembly constraint coordinate system, extract the lateral force component, and subtract the actual contact force from the target contact force to obtain the force tracking deviation; Define the sliding mode variable as the product of the preset sliding surface slope parameter and the force tracking deviation, plus the rate of change of the deviation; The time derivative of the sliding mode variable is designed based on the reaching law. The gain is dynamically adjusted according to the amplitude of the sliding mode variable. The position compensation command is obtained by dividing the required force change by the contact stiffness estimate. The compensation speed is calculated and limited based on the position compensation command, and the motion trajectory points are generated.

8. A compliant assembly method based on force-position hybrid control according to claim 1, characterized in that, The steps for obtaining intelligent control execution instructions include: Extract the time-domain statistical features, force change rate features, and frequency-domain features of the force; extract the relative positional relationship between the blade and the tenon groove, as well as the blade's motion speed and direction, and combine them into a feature vector. A convolutional neural network is used as the classifier. The output layer corresponds to the probability distribution of the four assembly stages: free motion, initial contact, search and alignment, and insertion assembly. The category with the highest probability is selected as the recognition result. Finite state machine modeling is used, and control parameters are pre-set for each state. The corresponding control parameters are read based on the currently identified state. When the assembly state changes, the control parameters at the current moment are calculated using an interpolation method. The desired trajectory of the position control end effector and the compensated trajectory of the force control end effector are synthesized, the joint angle configuration is solved, the joint angle, angular velocity and angular acceleration sequence is generated, the joint torque is calculated and sent to the motor driver, and the intelligent control execution command is obtained.

9. A compliant assembly method based on force-position hybrid control according to claim 1, characterized in that, The steps for obtaining the assembly completion status verification result include: The convergence time and convergence speed of the pose deviation are calculated. The maximum contact force value is extracted based on the contact force time series curve to obtain the peak force index and force fluctuation index. The insertion depth compliance index is obtained based on the position data of the insertion stage. The assembly cycle time index is obtained based on the assembly time. The comprehensive assembly quality score is obtained by using a weighted scoring model. The assembly qualification index is determined by comparing the comprehensive quality score with the preset quality qualification threshold. If the peak force exceeds the safety limit or the insertion depth does not meet the minimum requirement, it is judged as unqualified. If the assembly is qualified, an assembly success signal is output. If the assembly is not up to standard, an assembly failure flag signal will be output and the exception handling process will be triggered to generate an assembly completion status verification result.

10. A compliant assembly system based on force-position hybrid control, characterized in that, A compliant assembly method based on force-position hybrid control as described in any one of claims 1-9 includes: The data fusion module collects multimodal measurement data from multiple sources of sensors, unifies and fuses coordinates to obtain an initial state perception dataset of the assembly environment; The blade pose deviation estimation module performs unscented Kalman filtering state recursive estimation based on the initial state perception dataset of the assembly environment to obtain the blade pose deviation estimate. The force-position control decoupling module identifies the actual assembly constraint parameters online based on the blade position and orientation deviation estimation value, performs orthogonal decomposition of the force-position control subspace and extraction of deviation component projection, and obtains position control commands and force control commands. The impedance control trajectory generation module establishes an impedance control dynamic model based on the position control command, adjusts the impedance parameters, solves the impedance control dynamic model, and performs trajectory integration to generate the desired trajectory at the end of the position control. The sliding mode force control module calculates the force tracking deviation and designs the sliding surface based on the force control command, solves the position compensation command, performs speed limiting and trajectory generation, and obtains the force control end compensation trajectory. The state recognition and trajectory synthesis module performs feature extraction and neural network state recognition based on the expected trajectory of the position control end and the compensated trajectory of the force control end, and performs force-position trajectory synthesis and joint space mapping to obtain intelligent control execution instructions; The assembly quality assessment module, based on intelligent control execution instructions, establishes a multi-index evaluation system and performs assembly success determination and anomaly handling to obtain assembly completion status verification results.

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