A unified variable force / variable admittance control method and system based on neural energy functions

Abstract

A unified variable force / variable admittance control method and system based on neural energy functions is disclosed. The method includes: 1. Correcting the force sensor measurements based on the solved zero-point offset, and performing gravity compensation on the force / torque data based on the end-effector's gravity and center of mass position; 2. Defining a unified force / admittance control model for the robot and performing stability analysis; 3. Introducing a variable stiffness encoded energy function and a variable proportional / differential encoded energy function to learn variable stiffness parameters and variable proportional / differential coefficients online; 4. Solving for the analytical expressions of state-dependent variable admittance parameters; 5. Solving for the analytical expressions of the unified variable force / variable admittance control formula; 6. Calculating the pose adjustment amount and correcting the robot's current trajectory based on the pose adjustment amount. This invention achieves compliant and precise control of contact forces, enabling the system to maintain compliance while ensuring the stability and consistency of force output when interacting with the external environment.

Description

Technical Field

[0001] This invention relates to the field of intelligent assembly technology, and in particular to a unified variable force / variable admittance control method and system based on neural energy functions. Background Technology

[0002] Aircraft paneling is a core component of large aircraft, typically assembled from multiple parts such as skin, bulkheads, and stringers. It is characterized by its large size, low rigidity, high manufacturing precision, and complex structure. As a major load-bearing component of the aircraft fuselage structure, its assembly quality directly determines the aircraft's aerodynamic characteristics and service life. Traditional aircraft paneling assembly relies primarily on manual positioning of components by workers and connection using pneumatic tools. Assembly quality is heavily influenced by the operator's experience and skill level. This manual operation method suffers from limitations such as low efficiency, poor consistency in assembly quality, and long assembly cycles, making it difficult to meet the demands of efficient, high-quality mass production of large-size, complex, thin-walled curved surfaces.

[0003] With the development of the robotics industry and intelligent manufacturing technology, intelligent manufacturing technology, represented by robots, is gradually becoming a new trend in the high-quality manufacturing of large and complex components. Robots possess advantages such as dexterity, flexible configuration, high efficiency, and parallel collaboration. Integrating multiple sensors, they can comprehensively acquire environmental information to complete complex manufacturing tasks. Therefore, combining robots with intelligent control technology can effectively improve the assembly accuracy and production efficiency of large and complex components. Through the fusion of advanced vision, force, and other multimodal sensors, robots can perceive the workpiece status in real time, autonomously adjust operating parameters, and achieve high-precision positioning and intelligent assembly.

[0004] However, during aircraft panel assembly, multi-faceted contact between the bulkhead lugs and the skin is involved. As the bulkhead is a critical component of the fuselage's load-bearing frame, the assembly of the bulkhead and skin requires controlling the contact forces at multiple lug-to-skin connection surfaces to ensure sufficient and uniform contact, keeping the contact gap below the allowable error range, and preventing excessive contact forces from damaging the structural strength. Force sensors mounted at the end effector of a robotic arm can indirectly adjust the contact forces at each surface. Since industrial robotic arms typically have open position control drive interfaces, admittance control can be used to indirectly adjust the end effector's pose based on the desired contact force to achieve constant force contact performance. However, the bulkhead and skin are weakly rigid components, and due to material deformation during assembly, the contact dynamics are uncertain. Fixed-parameter admittance control cannot handle assembly tasks with unknown contact dynamics. Summary of the Invention

[0005] This invention provides a unified variable force / variable admittance control method and system based on neural energy functions to solve the technical problems mentioned in the background art.

[0006] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0007] This invention provides a unified variable force / variable admittance control method based on neural energy functions, comprising the following steps:

[0008] S1. The zero-point offset of the force sensor, the gravity of the end tool, and the position of the center of mass are calculated by the force sensor calibration algorithm. Based on the zero-point offset obtained, the force sensor measurement value is corrected to eliminate zero drift error. Based on the calculated gravity of the end tool and the position of the center of mass, gravity compensation is performed on the force / torque data. The actual contact force after compensation is calculated to obtain the environmental contact force.

[0009] S2. By considering environmental contact forces, a unified force / admittance control model for the robot is defined. Stability analysis is performed based on state-related force control and admittance control strategies to obtain unstable terms.

[0010] S3. To eliminate unstable terms and ensure the stability of the unified variable force / variable admittance control system, a variable stiffness coding energy function and a variable proportional / derivative coding energy function are introduced to learn the variable admittance / variable force control coefficients online.

[0011] S4, Design Cost Function And based on the cost function Solve for the analytical expression of the state-dependent variable admittance parameter to achieve online optimization of the admittance parameter;

[0012] S5, Design Cost Function as well as And based on the cost function as well as The analytical expressions for the state-dependent proportional / differential coefficients are obtained, and combined with the analytical expressions for the variable admittance parameters, the analytical expressions for the unified variable force / variable admittance control equations are obtained to achieve online updates of the proportional / differential coefficients; wherein, the proportional / differential coefficients include the variable force control proportional coefficient and the variable force differential control coefficient.

[0013] S6. Based on the analytical calculation of the pose adjustment amount according to the unified variable force / variable admittance control, the robot's current trajectory is corrected according to the pose adjustment amount, and the corrected trajectory is sent to the industrial robot for execution, thereby achieving high-precision compliant contact operation.

[0014] Another aspect of the present invention provides a unified variable force / variable admittance control system based on neural energy functions, including an industrial robot, a digital photogrammetry system, a force sensor, an end effector, and a control unit. The industrial robot, the digital photogrammetry system, the force sensor, and the end effector are all electrically connected to the control unit. The digital photogrammetry system is mounted on one side of the industrial robot to provide measurement data for the industrial robot. The force sensor and the end effector are both installed at the end of the industrial robot. The end effector is used to grasp the bulkhead. The industrial robot assembles the bulkhead and skin according to the above unified variable force / variable admittance control method.

[0015] The beneficial effects of this invention are:

[0016] 1. This invention discloses a unified variable force / variable admittance control method based on a neural energy function. Internally, it utilizes a state-dependent neural energy function that satisfies the conditions of being positive definite, continuously differentiable, radially unbounded, and possessing a unique minimum. Based on this, analytical expressions for the state-dependent variable admittance parameters and the unified variable force / variable admittance control formula are derived. Compared to traditional variable admittance / variable force PD parameter adjustment methods that rely on time variables, this design uses the actual physical state of the system instead of a single time variable, containing more contact dynamic information. This allows the variable force / variable admittance control model to respond more directly and sensitively to complex contact dynamics based on the real-time state dynamics of the system, improving the adaptability and accuracy of the control.

[0017] 2. The unified variable force / variable admittance control method based on neural energy function in this invention also discloses a unified variable admittance / variable force control activation function. This activation function achieves a smooth transition of the robot from free space motion to complex contact operation scenarios by dynamically adjusting the control behavior, and can effectively avoid abrupt or discontinuous control responses.

[0018] 3. The unified variable force / variable admittance control system based on neural energy function disclosed in this invention integrates the advantages of compliance of variable admittance control and force uniformity of variable force control, realizing compliant and precise control of contact force, enabling the system to maintain compliance when interacting with the external environment, while ensuring the stability and consistency of force output. Attached Figure Description

[0019] Figure 1 This is a logic block diagram of the unified variable force / variable admittance control method in this invention;

[0020] Figure 2 This is a structural diagram of the unified variable force / variable admittance control system in this invention. Detailed Implementation

[0021] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Preferred embodiments of the invention are shown in the drawings. However, the invention can be implemented in many other different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a thorough and complete understanding of the disclosure of the invention.

[0022] Reference Figure 1 This application provides a unified variable force / variable admittance control method based on neural energy functions, comprising the following steps:

[0023] S1. The robot end effector is equipped with a force sensor (six-dimensional force sensor) and an end effector tool. The zero-point offset of the force sensor, the gravity of the end effector tool, and the position of the center of mass are calculated by the force sensor calibration algorithm. Based on the zero-point offset obtained, the force sensor measurement value is corrected to eliminate zero drift error. Based on the calculated gravity of the end effector tool and the position of the center of mass, gravity compensation is performed on the force / torque data. The actual contact force after compensation is calculated to obtain the environmental contact force.

[0024] S2. By considering environmental contact forces, a unified force / admittance control model for the robot is defined. Stability analysis is performed based on state-related force control and admittance control strategies to obtain unstable terms.

[0025] S3. To eliminate instability terms and ensure the stability of the unified variable force / variable admittance control system, a variable stiffness coding energy function and a variable proportional / derivative coding energy function are introduced to learn the variable stiffness parameters and variable proportional / derivative coefficients online.

[0026] S4, Design Cost Function And based on the cost function The analytical expressions for state-dependent variable admittance parameters are solved to achieve online optimization of the admittance parameters; the variable admittance parameters include variable stiffness parameters and variable damping parameters.

[0027] S5, Design Cost Function as well as And based on the cost function as well as The analytical expressions for the state-dependent proportional / differential coefficients are obtained, and combined with the analytical expressions for the variable admittance parameters, the analytical expressions for the unified variable force / variable admittance control equations are obtained to achieve online updates of the proportional / differential coefficients; wherein, the proportional / differential coefficients include the variable force control proportional coefficient and the variable force differential control coefficient.

[0028] S6. Based on the analytical calculation of the pose adjustment amount according to the unified variable force / variable admittance control, the robot's current trajectory is corrected according to the pose adjustment amount, and the corrected trajectory is sent to the industrial robot for execution, thereby achieving high-precision compliant contact operation.

[0029] In some embodiments, S1 specifically includes the following steps:

[0030] S11. Install the force sensor between the robot end effector and the end tool, and put the robot in a known stationary pose. Maintain this state and record the pose of the end tool and the six-dimensional force / torque data of the force sensor.

[0031] S12. Optimize the readings of the six-dimensional force sensor using the Kalman filter algorithm to filter out sensor reading jitter, and record the pose of the end tool and the filtered force / torque data of the six-dimensional force sensor at this time.

[0032] S13. Adjust the robot end effector pose to ensure that the range of changes covers the influence of force / torque in different directions. Under the new pose, keep the robot stationary and record the current pose of the end effector and the force / torque data measured by the six-dimensional force sensor.

[0033] S14. Repeat S12 to S13 for a total of N times, record the pose of the end effector and the corresponding values ​​of the six-dimensional force sensor, and construct a dataset.

[0034] S15. Combine the dataset and use the force sensor calibration algorithm to calculate the zero-point offset of the six-dimensional force sensor, the gravity of the end tool, and the center of mass of the end tool; the zero-point offset is the measurement error under no-load conditions.

[0035] S16. Based on the zero-point offset obtained by the solution, the measurement value of the six-dimensional force sensor is corrected to eliminate zero drift error. Based on the calculated end tool gravity and center of mass position, gravity compensation is performed on the force / torque data to eliminate the additional influence introduced by the tool's own weight. The actual contact force after compensation is calculated.

[0036] S17. After each power-on, repeat steps S12 to S16 to obtain the compensated real contact force data. Take the average value to obtain the environmental contact force. .

[0037] In some embodiments, S2 specifically includes the following steps:

[0038] S21. Define a proportional / differential force controller for the robot's end effector in Cartesian space, as follows:

[0039] ;

[0040] in, , It is a positive definite diagonal gain matrix. Represents the set of real numbers; , These are the Cartesian space control input force and the desired environmental contact force, respectively. and These are the derivatives of the environmental contact force with respect to time and the derivatives of the desired environmental contact force with respect to time, respectively.

[0041] definition To address the end-effector contact force tracking error, the robot's end-effector force proportional / differential controller 1 was rewritten to obtain robot end-effector force proportional / differential controller 2, as detailed below: ;

[0042] in, It is the derivative of the end-contact force tracking error with respect to time;

[0043] S22. Combining the robot's end-effector proportional / differential force controller, a unified force / admittance control model for the robot in Cartesian space is defined as follows:

[0044] ;

[0045] in, This represents the pose tracking error, and ; and These are the end-effector pose velocity tracking error and the end-effector pose acceleration tracking error, respectively. and These represent the robot's current pose and desired pose, respectively. , , These represent the Cartesian space inertia matrix, damping coefficient matrix, and stiffness coefficient matrix, respectively.

[0046] S23. To ensure the robot's motion performance in free space and avoid interference from sensor measurement noise, sensor zero drift, and other factors, while ensuring a smooth switch to uniform force / admittance control during the contact phase to guarantee safe and compliant contact between the frame and the skin, design a variable admittance / variable force control activation function. , Let represent a diagonal matrix, where the _th __ in the variable admittance / variable force control activation function is _____. element The specific expression is as follows:

[0047] ;

[0048] in, It is a positive constant. Threshold for smooth transition interval The first in Each element value; Contact force The first variable One element, Contact force activation threshold The first in One element; e Represents the natural constant;

[0049] S24. Combine the variable admittance / variable force control activation function in S23 with the robot unified force / admittance control model in S22, and rewrite the unified force / admittance control model as follows:

[0050] ;

[0051] When the contact force is less than the contact force threshold hour, This means that at this point, the end-effector control input force is 0, and the robot performs closed-loop position control in free space based on high-precision vision detection; when the contact force... hour, The value gradually increases from 0 to 1, meaning the unified force / admittance control gradually opens, until... At that time, the unified force / admittance control is fully activated;

[0052] S25. Establish a unified variable force / variable admittance control model based on predetermined assumptions. The unified variable force / variable admittance control model is as follows:

[0053] ;

[0054] The specific assumptions are as follows:

[0055] Assuming the S24 unified force / admittance control model, the stiffness coefficient matrix... and damping coefficient matrix It is related to system state variables The relevant parameters, namely, the variable stiffness parameters that are expressed in matrix form under different states. and matrix form of variable damping parameters Allow admittance parameters to be adjusted based on system state variables. Online adjustment; assuming the S24 unified force / admittance control model and It is related to system state variables The relevant coefficient matrix, that is, the variable force control proportional coefficients in matrix form under different states. and matrix form of variable force differential control coefficients The proportional / derivative control coefficients are allowed to be based on the system state variables. Adjust online;

[0056] S26. To perform stability analysis on the unified variable force / variable admittance control model, an energy function is designed as follows:

[0057] ;

[0058] in, V Indicates the total energy of the system; superscript T Indicates transpose;

[0059] S27, to V Taking the derivative with respect to time, we obtain the following formula:

[0060] ;

[0061] in, for V Differentials with respect to time; For variable stiffness parameters Differentials with respect to time;

[0062] S28. Substituting the unified variable force / variable admittance control model from S25 into the formula in S27, we obtain the following formula:

[0063] ;

[0064] By analyzing the above equation, we obtain three unstable terms that violate system stability. These three unstable terms are as follows: , , .

[0065] In some embodiments, S3 specifically includes the following steps:

[0066] S31. To address the instability issues introduced by the three unstable terms in a unified variable force / variable admittance system, a variable stiffness encoding energy function is introduced. and variable proportional / differential coding energy function The second energy function is designed as follows: ;

[0067] in, This represents the total energy of energy function two;

[0068] S32. Taking the differential of the energy function with respect to time, we obtain the following formula:

[0069] ;

[0070] in, Indicates the partial derivative sign; This represents the differential of the total energy of energy function two with respect to time;

[0071] S33. Substitute the unified variable force / variable admittance control model from S25 into the formula obtained in S32, and rearrange to obtain the following formula:

[0072] ;

[0073] S34. Set the coding expressions for the variable force control proportional coefficient, the variable force differential control coefficient, and the variable stiffness parameter, as follows:

[0074] ;

[0075] Substituting the three encoded expressions into the formula in S25, we obtain the unified variable force / variable admittance control system equations after the control parameters are encoded.

[0076] ;

[0077] S35. Based on the Lassalle invariance principle, construct constraint condition one, which is as follows:

[0078] According to Lassalle's invariance principle, if the equations of the unified variable force / variable admittance control system after the control parameters are encoded in S34 satisfy global asymptotic stability, then the variable stiffness encoded energy function... and variable proportional / differential coding energy function It must satisfy the following conditions: positive definite, continuously differentiable, radially unbounded, and possess a unique minimum value.

[0079] Among them, the variable stiffness encoding energy function It satisfies the unique minimum property, specifically in the form of:

[0080] ;

[0081] Variable Proportional / Differential Encoding Energy Function It satisfies the unique minimum property, specifically in the form of:

[0082] ;

[0083] S36. Design an energy function that satisfies the variable stiffness coding in S35. Properties of neural energy functions The specific form is as follows:

[0084] ;

[0085] in, These are the weighting coefficients. Represent a A dimensional real vector space; These are the weighting coefficients. Represent a A dimensional real vector space; Let be the activation function, where Represents the natural exponential function; For bias, All are positive numbers; This represents the weighting function for the hidden layer output vectors. express The reference output at that time, Indicates about a quadratic function, This represents a vector consisting of all the outputs of the hidden layer. The hidden layer is represented by the first... The output of each neuron Denotes the Euclidean norm;

[0086] The above formula must satisfy the following constraint condition two, namely:

[0087] ;

[0088] in, It is a vector The One element, It is a vector The One element; In mathematics, it is a universal quantifier meaning "for all". H This indicates the number of neurons in the hidden layer;

[0089] S37, Design a variable proportional / differential coding energy function that satisfies S35. Properties of neural energy functions The specific form is as follows:

[0090] ;

[0091] in, , , , These represent the modified pose tracking error and force tracking error, respectively. and All are positive numbers;

[0092] The detailed expressions for each term in the above formula are as follows:

[0093] ;

[0094] in, The dot product symbol. as well as Each has a different weighting coefficient. , They represent peacekeeping A 3D real vector space, For bias, and All are normal numbers.

[0095] In some embodiments, the neural energy function in S36 It is positive definite, continuously differentiable, radially unbounded, and possesses a unique minimum property; among them, the neural energy function The specific form that satisfies the unique minimum property is:

[0096] ;

[0097] Simultaneously, neural energy function The following constraint condition two must be met:

[0098] ;

[0099] in, It is a vector The One element, It is a vector The One element; In mathematics, it is a universal quantifier meaning "for all". H This indicates the number of neurons in the hidden layer;

[0100] The neural energy function in S37 It is positive definite, continuously differentiable, radially unbounded, and possesses a unique minimum property; among them, the neural energy function The specific form that satisfies the unique minimum property is:

[0101] ;

[0102] Simultaneously, neural energy function The following constraint three must be met:

[0103] ;

[0104] in, It is a vector The One element; This represents the weighting coefficient.

[0105] In some embodiments, S4 specifically includes the following steps:

[0106] S41. Rewrite the variable stiffness parameter encoding expression in S34 to obtain the following equation;

[0107] ;

[0108] in, These are learnable parameter variables;

[0109] S42. To solve the parameter variables in equation S41 Design the cost function related to the coefficients of the variable stiffness parameter encoding expression. The format is:

[0110] ;

[0111] in, For the expected variable admittance dataset Dimension size, and Each dataset The first in Individual pose tracking error and desired stiffness samples, Represents the first in the dataset The derivative of the pose tracking error. Represents the first in the dataset One expected damping sample; Representative dataset The Middle One sample;

[0112] S43. To find the optimal parameter variables The problem of solving the objective function in S42 is transformed into an optimization problem, minimizing the cost function. The specific expression for the optimization problem is as follows:

[0113] ;

[0114] The above equation is subject to constraint condition two, as follows:

[0115] ;

[0116] S44. Solve for the minimum cost function based on constraint condition two. The optimization problem is to derive the optimal learning parameters. Based on the optimal learning parameters Calculate the energy function in S41 and variable stiffness parameters In order to obtain a state-dependent variable admittance control strategy;

[0117] S45. To improve the execution efficiency of the state-dependent variable admittance control strategy, solve for the state-dependent variable admittance parameters. The analytical expression is as follows:

[0118] ;

[0119] in, It is the identity matrix. and The specific expression is:

[0120] ;

[0121] in, It is by The vector formed by the second element to the last element;

[0122] Using variable stiffness parameters The analytical expression is used to construct the variable damping parameters. The analytical expression, specifically in the form of:

[0123] ;

[0124] Variable damping parameters Analytical expression and variable stiffness parameters The analytical combination of these is the analytical expression for the state-dependent variable admittance parameter;

[0125] Substitute the analytical expressions of the state-dependent variable admittance parameters into the unified variable force / variable admittance control system equations after the control parameter encoding in S34 to optimize the admittance parameters online.

[0126] In some embodiments, S5 specifically includes the following steps:

[0127] S51. To implement the variable proportional / derivative coefficients related to the online learning state, the encoding expressions for the variable force control proportional coefficient and the variable force differential control coefficient in S34 are rewritten to introduce the optimized parameter variables, as follows:

[0128] ;

[0129] in, These are the parameter variables that need to be learned;

[0130] S52. To implement the variable proportional / differential coefficients related to the online learning state, design a cost function related to the variable proportional / differential coefficients based on the formula in S51. as well as The details are as follows:

[0131] ;

[0132] in, , The functions representing the expected proportional coefficient and the expected differential coefficient are respectively expressed as follows: ; ; For the expected scale / differential dataset Dimension size, Representative dataset The Middle The time derivative of the force tracking error; and Each dataset The expected force control proportional coefficient and the expected force differential control coefficient are in the first place. One sample; Indicates the dataset The Middle Individual force tracking error;

[0133] S53. Consider the constraints in S37, and apply the cost function related to the variable proportional / differential coefficients. as well as Model 2 for the optimization problem is constructed as follows:

[0134] ;

[0135] The optimization problem model 2 must satisfy the following constraints:

[0136] ;

[0137] S54. Solving the optimization problem model two using the chain rule yields the following formula:

[0138] ;

[0139] S55, the neural energy function in S37 Substituting into the formula in S54 and rearranging, we get the following formula:

[0140] ;

[0141] in, and Let's call them simplified parameter one and simplified parameter two, respectively. The expressions for simplified parameter one and simplified parameter two are as follows:

[0142] ;

[0143] in, It is by The vector formed by the second element to the last element;

[0144] S56, according to The following formula is obtained:

[0145] ;

[0146] in, The simplified parameter three is represented by the following expression:

[0147] ;

[0148] In the formula, Representing vectors The dimension;

[0149] S57. Based on the formula in S56, the following formula is derived:

[0150] ;

[0151] in, The simplified parameter four is represented by the following expression:

[0152] ;

[0153] Solve according to the above formula. The analytical solution form is as follows:

[0154] ;

[0155] The neural energy function in S37 Substituting into the formula in S54, we get the following formula:

[0156] ;

[0157] in, and These are simplified parameters five and six, respectively. The expressions for simplified parameters five and six are as follows:

[0158] ;

[0159] S58, according to The following formula is obtained:

[0160] ;

[0161] in, Representing simplified parameter seven, the specific expression for simplified parameter seven is:

[0162] ;

[0163] S59. Based on the formula in S58, the following formula is derived:

[0164] ;

[0165] in, The simplified parameter eight has the following specific form:

[0166] ;

[0167] Based on the above formula, the solution is obtained. The analytical expression is as follows:

[0168] ;

[0169] The above formula must meet the following conditions ;

[0170] when When, solve for the values ​​of the variable proportional / differential coefficients respectively. and The expressions are as follows:

[0171] ;

[0172] in, and Represents the current moment The variable proportional / differential coefficient values, and This represents the updated proportional / differential coefficient value from the previous moment, i.e., in time The value of the proportional / differential coefficient at that time;

[0173] Based on the formulas in S3, S4, and S5, the analytical expression for the unified variable force / variable admittance control formula based on the neural energy function is obtained as follows: ;

[0174] Using the above formulas, and updating the variable stiffness parameters and variable proportional / differential coefficients online according to the system status, flexible frame skin assembly can be achieved.

[0175] In some embodiments, S6 specifically includes the following steps:

[0176] S61. Based on the analytical solution of the unified variable force / variable admittance control formula, the variable stiffness parameter, variable damping coefficient, and variable proportional / derivative coefficient values ​​are obtained, and then substituted into the unified variable force / variable admittance control model in S25 to obtain the pose adjustment amount in the contact force constraint direction. The details are as follows:

[0177] ;

[0178] in, and These are the velocity adjustment and pose adjustment amounts from the previous sampling time, respectively.

[0179] S62. Calculate the updated desired pose based on the velocity adjustment and pose adjustment. Specifically, the sampling period is as follows;

[0180] ;

[0181] In the above formula, For the desired pose of the frame planned based on the digital photography system, These are the updated pose correction values. The current pose of the frame captured by the digital photography system;

[0182] S63, Updated Pose Correction Values Send it to the robot to enable flexible and precise assembly by the industrial robot.

[0183] In aircraft panel assembly, the robot's absolute positioning accuracy is low due to accumulated errors caused by friction between joints and motor noise, environmental interference (such as temperature changes and vibration), and limitations in calibration accuracy. This makes it difficult to meet the stringent high-precision assembly requirements of the aerospace manufacturing industry. Particularly in the assembly of large, complex curved parts, error amplification further reduces assembly accuracy, leading to inaccurate fit between the frame and skin, affecting the final assembly quality. This invention utilizes a digital photography system to accurately measure the robot's end effector pose in real time and uses visual feedback signals to design a motion control algorithm to correct the robot's trajectory in real time, thus bringing the final positioning error within the accuracy range.

[0184] In aircraft panel assembly, due to part machining errors and minor deviations during assembly, the contact force during the robot's gripping of the bulkhead and skin is unknown. Furthermore, since the bulkhead and skin are weakly rigid components, their material properties cause deformation during compression, resulting in a nonlinear change in the contact force field. Therefore, the contact dynamics are complex and unknown, making precise control of the assembly clamping force difficult. This invention combines admittance control and direct force control strategies to design a state-based unified variable admittance / variable force control strategy.

[0185] Traditional constant-parameter admittance control possesses good compliance. Combined with direct force control, it forms a unified force / admittance control strategy, enabling the robot to maintain compliance while converging the contact force to the desired clamping force. However, due to the complex contact dynamics described above, admittance control and force control methods struggle to select appropriate parameters to adapt to real-time changing contact states. This can lead to excessive assembly force damaging components, or insufficient assembly force causing contact gaps to exceed tolerances, affecting assembly quality. Time-based variable admittance and variable force control strategies rely on preset time strategies to adjust parameters, failing to adjust nonlinear contact control parameters according to actual contact states. This can result in uneven contact, excessive localized forces, and even oscillations or instability. This invention designs a contact state-related neural energy function, utilizes this function to learn variable admittance and variable force behaviors, and solves for the analytical form of unified variable admittance / variable force control state-related parameters. This enables low-cost, online, real-time adjustment of unified variable admittance / variable force control parameters, ensuring compliant contact assembly while converging to the desired clamping force. The above strategy can effectively solve the problems caused by robot positioning errors, nonlinear contact force fields, assembly dynamic complexity and limitations of traditional control methods in the assembly of aircraft panels, and improve the accuracy, stability and adaptability of automated assembly.

[0186] Reference Figure 2 In another aspect, the present invention provides a unified variable force / variable admittance control system based on neural energy functions, including an industrial robot, a digital photogrammetry system, a force sensor, an end effector, and a control unit. The industrial robot, the digital photogrammetry system, the force sensor (i.e., a six-dimensional force sensor), and the end effector (i.e., a flexible tooling) are all electrically connected to the control unit. The digital photogrammetry system is mounted on one side of the industrial robot to provide measurement data for the industrial robot. The force sensor and the end effector are both installed at the end of the industrial robot. The end effector is used to grasp the bulkhead. The industrial robot assembles the bulkhead and skin according to the above unified variable force / variable admittance control method.

[0187] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A unified variable force / variable admittance control method based on neural energy functions, characterized in that, Includes the following steps: S1. The zero-point offset of the force sensor, the gravity of the end tool, and the position of the center of mass are calculated by the force sensor calibration algorithm. Based on the zero-point offset obtained, the force sensor measurement value is corrected to eliminate zero drift error. Based on the calculated gravity of the end tool and the position of the center of mass, gravity compensation is performed on the force / torque data. The actual contact force after compensation is calculated to obtain the environmental contact force. S2. By considering environmental contact forces, a unified force / admittance control model for the robot is defined. Stability analysis is performed based on state-related force control and admittance control strategies to obtain unstable terms. S3. To eliminate instability terms and ensure the stability of the unified variable force / variable admittance control system, a variable stiffness coding energy function and a variable proportional / derivative coding energy function are introduced to learn the variable stiffness parameters and variable proportional / derivative coefficients online. S4, Design Cost Function And based on the cost function Solve for the analytical expression of the state-dependent variable admittance parameter to achieve online optimization of the admittance parameter; S5, Design Cost Function as well as And based on the cost function as well as The analytical expressions for the state-dependent proportional / differential coefficients are obtained, and combined with the analytical expressions for the variable admittance parameters, the analytical expressions for the unified variable force / variable admittance control equations are obtained; where the proportional / differential coefficients include the variable force control proportional coefficient and the variable force differential control coefficient. S6. Calculate the pose adjustment amount analytically based on the unified variable force / variable admittance control method, correct the robot's current trajectory based on the pose adjustment amount, and send the corrected trajectory to the industrial robot for execution.

2. The unified variable force / variable admittance control method based on neural energy function according to claim 1, characterized in that, S1 specifically includes the following steps: S11. Install the force sensor between the robot's end effector and the end tool, and position the robot in a known stationary pose, maintaining this state. S12. Optimize the readings of the six-dimensional force sensor using the Kalman filter algorithm to filter out sensor reading jitter, and record the pose of the end tool and the filtered force / torque data of the six-dimensional force sensor at this time. S13. Adjust the robot end effector pose to ensure that the range of changes covers the influence of force / torque in different directions. Under the new pose, keep the robot stationary and record the current pose of the end effector and the force / torque data measured by the six-dimensional force sensor. S14. Repeat S12 to S13 for a total of N times, record the pose of the end effector and the corresponding values ​​of the six-dimensional force sensor, and construct a dataset. S15. Combine the dataset and use the force sensor calibration algorithm to calculate the zero-point offset of the six-dimensional force sensor, the gravity of the end tool, and the center of mass of the end tool. The zero-point offset is the measurement error under no-load conditions. S16. Based on the zero-point offset obtained by the solution, the measurement value of the six-dimensional force sensor is corrected to eliminate zero drift error. Based on the calculated tool weight and center of gravity position, the measurement value of the six-dimensional force sensor is compensated for gravity to eliminate the additional influence introduced by the end tool's own weight. The actual contact force after compensation is calculated. S17. Each time the robot is powered on, repeat steps S12 to S16 to obtain the compensated real contact force data, i.e., the environmental contact force. .

3. The unified variable force / variable admittance control method based on neural energy function according to claim 1, characterized in that, S2 specifically includes the following steps: S21. Define a proportional / differential force controller for the robot's end effector in Cartesian space, as follows: ； in, , It is a positive definite diagonal gain matrix. Represents the set of real numbers; , These are the Cartesian space control input force and the desired environmental contact force, respectively. and These are the derivatives of the environmental contact force with respect to time and the derivatives of the desired environmental contact force with respect to time, respectively. definition To address the end-effector contact force tracking error, the robot's end-effector force proportional / differential controller 1 was rewritten to obtain robot end-effector force proportional / differential controller 2, as detailed below: ; in, It is the derivative of the end-contact force tracking error with respect to time; S22. Combining the robot's end-effector proportional / differential force controller, a unified force / admittance control model for the robot in Cartesian space is defined as follows: ； in, This represents the pose tracking error, and ; and These are the end-effector pose velocity tracking error and the end-effector pose acceleration tracking error, respectively. and These represent the robot's current pose and desired pose, respectively. , , These represent the Cartesian space inertia matrix, damping coefficient matrix, and stiffness coefficient matrix, respectively. S23. To ensure the robot's motion performance in free space and to ensure a smooth transition to uniform force / admittance control during the contact phase, design a variable admittance / variable force control activation function. , Let represent a diagonal matrix, where the _th __ in the variable admittance / variable force control activation function is _____. element The specific expression is as follows: ； in, It is a positive constant. Threshold for smooth transition interval The first in Each element value; Contact force The first variable One element, Contact force activation threshold The first in One element; e Represents the natural constant; S24. Combine the variable admittance / variable force control activation function in S23 with the robot unified force / admittance control model in S22, and rewrite the unified force / admittance control model as follows: ； S25. Establish a unified variable force / variable admittance control model based on predetermined assumptions. The unified variable force / variable admittance control model is as follows: ； The specific assumptions are as follows: Assuming the S24 unified force / admittance control model, the stiffness coefficient matrix... and damping coefficient matrix It is related to system state variables The relevant parameters, namely, the variable stiffness parameters that are expressed in matrix form under different states. and matrix form of variable damping parameters Allow admittance parameters to be adjusted based on system state variables. Online adjustment; assuming the S24 unified force / admittance control model and It is related to system state variables The relevant coefficient matrix, that is, the variable force control proportional coefficients in matrix form under different states. and matrix form of variable force differential control coefficients The proportional / derivative control coefficients are allowed to be based on the system state variables. Adjust online; S26. To perform stability analysis on the unified variable force / variable admittance control model, an energy function is designed as follows: ； in, V Indicates the total energy of the system; superscript T Indicates transpose; S27, to V Taking the derivative with respect to time, we obtain the following formula: ； in, for V Differentials with respect to time; For variable stiffness parameters Differentials with respect to time; S28. Substituting the unified variable force / variable admittance control model from S25 into the formula in S27, we obtain the following formula: ； By analyzing the above equation, we obtain three unstable terms that violate system stability. These three unstable terms are as follows: , , .

4. The unified variable force / variable admittance control method based on neural energy function according to claim 3, characterized in that, S3 specifically includes the following steps: S31. To address the instability issues introduced by the three unstable terms in a unified variable force / variable admittance system, a variable stiffness encoding energy function is introduced. and variable proportional / differential coding energy function The second energy function is designed as follows: ; in, This represents the total energy of energy function two; S32. Taking the differential of the energy function with respect to time, we obtain the following formula: ； in, Indicates the sign of the partial derivative; This represents the differential of the total energy of energy function two with respect to time; S33. Substitute the unified variable force / variable admittance control model from S25 into the formula obtained in S32, and rearrange to obtain the following formula: ； S34. Set the coding expressions for the variable force control proportional coefficient, the variable force differential control coefficient, and the variable stiffness parameter, as follows: ； Substituting the three encoded expressions into the formula in S25, we obtain the unified variable force / variable admittance control system equations after the control parameters are encoded. ； S35. Based on the Lassalle invariance principle, construct constraint condition one, which is as follows: According to Lassalle's invariance principle, if the equations of the unified variable force / variable admittance control system after the control parameters are encoded in S34 satisfy global asymptotic stability, then the variable stiffness encoded energy function... and variable proportional / differential coding energy function It must satisfy the following conditions: positive definite, continuously differentiable, radially unbounded, and possess a unique minimum value. Among them, the variable stiffness encoding energy function It satisfies the unique minimum property, specifically in the form of: ； Variable Proportional / Differential Encoding Energy Function It satisfies the unique minimum property, specifically in the form of: ； S36. Design an energy function that satisfies the variable stiffness coding in S35. Properties of neural energy functions The specific form is as follows: ； in, These are the weighting coefficients. Represent a A dimensional real vector space; These are the weighting coefficients. Represent a A dimensional real vector space; Let be the activation function, where Represents the natural exponential function; This is the bias value. All are positive numbers; This represents the weighting function for the hidden layer output vectors. express The reference output at that time, Indicates about a quadratic function, This represents a vector consisting of all the outputs of the hidden layer. The hidden layer is represented by the first... The output of each neuron Denotes the Euclidean norm; S37, Design a variable proportional / differential coding energy function that satisfies S35. Properties of neural energy functions The specific form is as follows: ； in, , , , These represent the modified pose tracking error and force tracking error, respectively. and All are positive numbers; The detailed expressions for each term in the above formula are as follows: ； in, The dot product symbol. as well as Each has a different weighting coefficient. , They represent peacekeeping A 3D real vector space, This is the bias value. and All are normal numbers.

5. The unified variable force / variable admittance control method based on neural energy function according to claim 4, characterized in that, The neural energy function in S36 It is positive definite, continuously differentiable, radially unbounded, and possesses a unique minimum property; among them, the neural energy function The specific form that satisfies the unique minimum property is: ； Simultaneously, neural energy function The following constraint condition two must be met: ； in, It is a vector The One element, It is a vector The One element; In mathematics, it is a universal quantifier meaning "for all". H This indicates the number of neurons in the hidden layer; The neural energy function in S37 It is positive definite, continuously differentiable, radially unbounded, and possesses a unique minimum property; among them, the neural energy function The specific form that satisfies the unique minimum property is: ； Simultaneously, neural energy function The following constraint three must be met: ； in, It is a vector The One element; This represents the weighting coefficient.

6. The unified variable force / variable admittance control method based on neural energy function according to claim 5, characterized in that, S4 specifically includes the following steps: S41. Rewrite the variable stiffness parameter encoding expression in S34 to obtain the following equation; ； in, These are learnable parameter variables; S42. To solve the parameter variables in equation S41 Design the cost function related to the coefficients of the variable stiffness parameter encoding expression. The format is: ； in, For the expected variable admittance dataset Dimension size, and Each dataset The first in Individual pose tracking error and desired stiffness samples, Represents the first in the dataset The derivative of the pose tracking error. Represents the first in the dataset One expected damping sample; Representative dataset The Middle One sample; S43. To find the optimal parameter variables The problem of solving the objective function in S42 is transformed into an optimization problem, minimizing the cost function. The specific expression for the optimization problem is as follows: ； The above equation is subject to constraint condition two, as follows: ； S44. Solve for the minimum cost function based on constraint condition two. The optimization problem is to derive the optimal learning parameters. Based on the optimal learning parameters Calculate the energy function in S41 and variable stiffness parameters In order to obtain a state-dependent variable admittance control strategy; S45. To improve the execution efficiency of the state-dependent variable admittance control strategy, solve for the state-dependent variable admittance parameters. The analytical expression is as follows: ； in, It is the identity matrix. and The specific expression is: ； in, It is by The vector formed by the second element to the last element; Using variable stiffness parameters The analytical expression is used to construct the variable damping parameters. The analytical expression, specifically in the form of: ； Variable damping parameters Analytical expression and variable stiffness parameters The analytical combination of these is the analytical expression for the state-dependent variable admittance parameter; Substitute the analytical expressions of the state-dependent variable admittance parameters into the unified variable force / variable admittance control system equations after the control parameter encoding in S34 to optimize the admittance parameters online.

7. The unified variable force / variable admittance control method based on neural energy function according to claim 6, characterized in that, S5 specifically includes the following steps: S51. To implement the variable proportional / derivative coefficients related to the online learning state, the encoding expressions for the variable force control proportional coefficient and the variable force differential control coefficient in S34 are rewritten as follows: ； in, These are the parameter variables that need to be learned; S52. To implement the variable proportional / differential coefficients related to the online learning state, design a cost function related to the variable proportional / differential coefficients based on the formula in S51. as well as The details are as follows: ； in, , The functions representing the expected proportional coefficient and the expected differential coefficient are respectively expressed as follows: ; ; For the expected scale / differential dataset Dimension size, Representative dataset The Middle The time derivative of the force tracking error; and Each dataset The expected force control proportional coefficient and the expected force differential control coefficient are in the first place. One sample; Indicates the data set The Middle Individual force tracking error; S53. Consider the constraints in S37, and apply the cost function related to the variable proportional / differential coefficients. as well as Model 2 for the optimization problem is constructed as follows: ； The optimization problem model 2 must satisfy the following constraints: ； S54. Solving the optimization problem model two using the chain rule yields the following formula: ； S55, the neural energy function in S37 Substituting into the formula in S54 and rearranging, we get the following formula: ； in, and Let's call them simplified parameter one and simplified parameter two, respectively. The expressions for simplified parameter one and simplified parameter two are as follows: ； in, It is by The vector formed by the second element to the last element; S56, according to The following formula is obtained: ； in, The simplified parameter three is represented by the following expression: ； In the formula, Representing vectors The dimension; S57. Based on the formula in S56, the following formula is derived: ； in, The simplified parameter four is represented by the following expression: ； Solve according to the above formula. The analytical solution form is as follows: ； The neural energy function in S37 Substituting into the formula in S54, we get the following formula: ； in, and These are simplified parameters five and six, respectively. The expressions for simplified parameters five and six are as follows: ； S58, according to The following formula is obtained: ； in, Representing simplified parameter seven, the specific expression for simplified parameter seven is: ； S59. Based on the formula in S58, the following formula is derived: ; in, The simplified parameter eight has the following specific form: ； Based on the above formula, the solution is obtained. The analytical expression is as follows: ； The above formula must meet the following conditions ; when When, solve for the values ​​of the variable proportional / differential coefficients respectively. and The expressions are as follows: ； in, and Represents the current moment The variable proportional / differential coefficient values, and This represents the updated proportional / differential coefficient value from the previous moment, i.e., in time The value of the proportional / differential coefficient at that time; Based on the formulas in S3, S4, and S5, the analytical expression for the unified variable force / variable admittance control formula based on the neural energy function is obtained as follows: ； Using the above formulas, and updating the variable stiffness parameters and variable proportional / differential coefficients online according to the system status, flexible frame skin assembly can be achieved.

8. The unified variable force / variable admittance control method based on neural energy function according to claim 7, characterized in that, S6 specifically includes the following steps: S61. Based on the analytical solution of the unified variable force / variable admittance control formula, the variable stiffness parameter, variable damping coefficient, and variable proportional / derivative coefficient values ​​are obtained, and then substituted into the unified variable force / variable admittance control model in S25 to obtain the pose adjustment amount in the contact force constraint direction. The details are as follows: ； in, and These are the velocity adjustment and pose adjustment amounts from the previous sampling time, respectively. S62. Calculate the updated desired pose based on the velocity adjustment and pose adjustment. Specifically, the sampling period is as follows; ； In the above formula, For the desired pose of the frame planned based on the digital photography system, These are the updated pose correction values. The current pose of the frame captured by the digital photography system; S63, Updated Pose Correction Values Send it to the robot to enable flexible and precise assembly by the industrial robot.

9. A unified variable force / variable admittance control system based on neural energy functions, characterized in that, The system includes an industrial robot, a digital photogrammetry system, a force sensor, an end effector, and a control unit. The industrial robot, the digital photogrammetry system, the force sensor, and the end effector are all electrically connected to the control unit. The digital photogrammetry system is mounted on one side of the industrial robot to provide measurement data for the industrial robot. The force sensor and the end effector are both installed at the end of the industrial robot. The end effector is used to grasp the bulkhead. The industrial robot assembles the bulkhead and skin according to the unified variable force / variable admittance control method described in any one of claims 1 to 8.

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