A force-position coordinated control method for compliant assembly of aircraft fuselage frames

Abstract

This invention relates to the field of force-position coordinated impedance control technology, and particularly to a force-position coordinated control method for compliant assembly of aircraft fuselage frames. The method includes steps such as kinematic calibration of a CNC positioner, calibration of the installation direction of the force sensor at the positioner's end effector, dynamic modeling of the fuselage bulkhead and linear response analysis of the fuselage web, trajectory planning for the fuselage bulkhead attitude adjustment and positioning process, design of the positioner control law for the fuselage bulkhead attitude adjustment and positioning process, and design of the positioner control law for the fuselage bulkhead and web mating process. Compared to traditional kinematic accuracy compensation strategies based on error differential transformation, this invention establishes a positioner kinematic model based on fitting the CNC positioner axis and hinge joint zero position using spatially measured points. This model requires no design information from the positioner, is applicable to any geometric error of the positioner, and achieves coordinated optimization of the positioning accuracy of the fuselage bulkhead during fine-tuning and the contact force between it and the fuselage web, possessing the ability to perform comprehensive optimal control of force and position.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of kinematics modeling and force-position collaborative impedance control, and particularly relates to a force-position collaborative control method for flexible assembly of an aircraft fuselage framework. BACKGROUND

[0002] The high maneuverability and long service life of a new generation of aircraft require strict standards for the impact resistance performance and fatigue life of the aircraft structure. Compared with traditional aircraft, the new generation of aircraft fuselage structure has the characteristic of using a large amount of composite materials. The fuselage framework structure of the composite materials is prone to hidden delamination and cracking damage under improper stress, and the load-carrying capacity and fatigue strength of the structure will be greatly reduced, which brings safety hazards to the normal service of the aircraft. The quality requirements for the mechanical properties of the aircraft body pose a challenge to the control of the assembly stress of the aircraft structure.

[0003] Traditional aircraft structure assembly takes single geometric accuracy as the guarantee target, and uses rigid assembly fixtures to position and clamp parts. In order to ensure the stability of positioning accuracy, the rigid fixture often has redundant positioners and clamps to over-position and over-constrain the parts. Under the influence of the pre-processing error of the parts and the slight deviation of the positioners and clamps, forced assembly and stress concentration often occur. Therefore, the industry and academia focus on flexible fixtures based on digital control, and carry out a lot of research work around the kinematics calibration of numerical control positioners and force-position collaborative control, in order to improve the positioning accuracy of the parts and reduce the assembly stress. However, there is still room for improvement.

[0004] On the one hand, the current kinematics calibration technology mainly follows the idea of error modeling→parameter identification→accuracy compensation. The error model represents the relationship between the parameter error and the end position error through approximate linear differential transformation near the theoretical kinematics parameters. When the actual kinematics parameters deviate greatly from the theoretical kinematics parameters, the error model will fail due to nonlinear effects, and the convergence of parameter identification cannot be guaranteed.

[0005] On the other hand, the existing force-position collaborative control strategy focuses on the force tracking control problem between the parts and the positioners, and sacrifices the position accuracy of the positioners to ensure the soft interaction between the positioners and the parts. In the actual demand of aircraft assembly, the contact force between the parts and the parts, the contact force between the parts and the positioners, and the positioning accuracy of the parts are all control targets. Therefore, in view of the positioning accuracy and stress state control targets of the aircraft fuselage framework in the assembly process, it is expected to propose a tracking control method considering the contact force between the parts and the parts, the contact force between the parts and the positioners, and to realize the collaborative optimization of the part position accuracy and the stress state. SUMMARY

[0006] The problem to be solved by this invention is to address the shortcomings of existing digital flexible assembly of aircraft. It provides a force-position coordination control method for compliant assembly of aircraft fuselage frames, which is aimed at the 4-PPPS type parallel attitude adjustment system commonly used in engineering.

[0007] To solve the above-mentioned technical problems, the present invention provides the following technical solution: A force-position coordinated control method for compliant assembly of an aircraft fuselage frame, comprising the following steps: S1. Kinematic Calibration of CNC Positioner: First, the lead screw error of a single linear axis of the CNC positioner is calibrated. Several displacement commands are given to drive the single axis motion. The positioning error of the linear axis under each displacement command is measured using a grating ruler, and the lead screw error is identified using the least squares method. Then, a target ball is fixed at an arbitrary position at the end of the CNC positioner. With the other linear axes in a zero-position state, each linear axis is driven independently in sequence. A laser tracker is used to collect multiple position coordinates of the target point during the independent motion of each linear axis. Based on these position coordinates, principal component analysis is used to fit the direction of each linear axis. The process involves: setting each linear axis of the CNC positioner to its zero position; fixing the target ball at any position on the ball joint rod at the end of the CNC positioner; rotating the target around the joint center using the ball joint rod; recording multiple position coordinates of the target rotating around the joint center using a laser tracker; obtaining the center coordinates of the ball joint when each linear axis is at its zero position using a spherical fitting algorithm based on these position coordinates; and finally, establishing the kinematic relationship between the displacement and velocity of each linear axis of the CNC positioner and the center position and velocity of the end ball joint using a matrix based on the direction vectors of the linear axes and the center coordinates of the ball joint at its zero position. S2. Installation direction calibration of the force sensor at the end of the CNC positioner: Fix the ball joint of the ball joint at the end of the CNC positioner, drive the CNC positioner to make small movements along the three linear axes in sequence, obtain the three-dimensional force components of the force sensor under the pulling action in the three directions, combine with the direction vectors of the three linear axes of the CNC positioner calibrated in S1, establish a least squares optimization model to identify the vector representation of the three measurement coordinate axes of the force sensor in the global coordinate system, and thus establish the transformation relationship from the force sensor measurement coordinate system to the global coordinate system; S3. Dynamic Modeling of Fuselage Frame and Linear Response Analysis of Fuselage Web: In digital design software, the mass, center of mass position, and inertia tensor matrix of the fuselage frame are extracted using its digital model. Based on the Newton-Euler method, an attitude adjustment dynamic model of the fuselage frame is established to characterize the relationship between its motion velocity, acceleration, and posture and the net external force. Furthermore, a force distribution matrix is ​​designed to establish the mapping from the net external force of the fuselage frame to the desired contact force at the ends of four sets of CNC positioners. In finite element analysis software, a mesh model of the fuselage web is established. Under linear elastic and small deformation conditions, multiple sets of force and displacement data at the interface between the fuselage web and the fuselage frame are obtained. Based on multiple sets of force and displacement data samples, the stiffness parameters of the fuselage web are identified using the least squares method, realizing the characterization of the linear mapping relationship between force and displacement at the interface between the fuselage web and the fuselage frame. S4. Trajectory planning for the attitude adjustment and positioning process of the fuselage bulkhead: First, the attitude adjustment trajectory of the fuselage bulkhead is planned. The coordinates of the feature points of the fuselage bulkhead in the initial pose state are collected using a laser tracker. Combined with the coordinates of these points in the ideal pose given by the design model, the rotation matrix and translation vector characterizing the transformation relationship of the fuselage bulkhead from the initial pose to the ideal pose are calculated. The rotation matrix is ​​further decomposed into the corresponding RPY angles. A fifth-order polynomial is used to establish the function of the three RPY angles and three translational components with respect to time in the attitude adjustment process of the fuselage bulkhead. Then, using the geometric distribution relationship between the end of the CNC positioner and the hinge point of the fuselage bulkhead, the attitude adjustment trajectory of the fuselage bulkhead is transformed into the motion trajectory of the ball joint center of the end of the CNC positioner. S5. Design of the control law for the CNC positioner in the fuselage attitude adjustment and positioning process: Three of the four CNC positioners adopt a position control strategy, using the kinematic relationship established in S1 to accurately track the motion trajectory planned in S4; the remaining CNC positioner adopts variable parameter impedance control, using the attitude adjustment dynamics model in S3 combined with the current CNC positioner motion feedback to calculate the resultant external force of the fuselage frame, and then using the force distribution relationship designed in S3 to decompose the resultant external force of the fuselage frame into the desired force at the end of the CNC positioner, and further calculating the velocity and acceleration compensation of the end relative to the motion trajectory in S4 based on the current end force feedback, and using the kinematic relationship established in S1 to convert the end motion compensation command into motion commands for each axis, which are sent to the servo drive of the motor for inner loop motion control; S6. Design of CNC Positioner Control Law for the Fitting Process between the Fuselage Frame and the Fuselage Web: Aiming at smooth interaction between the CNC positioner and the fuselage frame, and between the fuselage frame and the fuselage web, a two-loop impedance control system is designed. The outer loop impedance controller is used for fine-tuning the position of the fuselage frame. Based on the estimated contact force between the fuselage frame and the fuselage web, it outputs the displacement, velocity, and acceleration of the overall translation of the fuselage frame to the inner loop impedance controller. The inner loop impedance controller uses the translational command of the fuselage frame output by the outer loop controller as a reference trajectory. Based on the contact force feedback between the fuselage frame and the end effector of the CNC positioner, it outputs the compensation trajectory of the end effector of the CNC positioner and inversely decomposes it into commands for each axis, sending them to the servo drive for inner loop motion control.

[0008] Furthermore, in order to reduce the contact force between the fuselage bulkhead and the fuselage web while avoiding the displacement of the fuselage bulkhead exceeding the positioning tolerance, a linear quadratic regulator is used to dynamically adjust the reference trajectory and desired force of the outer loop impedance controller based on the state feedback of the fuselage bulkhead displacement, velocity and contact force with the fuselage web, so as to achieve the comprehensive minimization of the fuselage bulkhead displacement and the contact force between the fuselage bulkhead and the fuselage web.

[0009] This invention establishes a kinematic model of the CNC positioner based on the spatial measured point fitting of the axis and hinge joint zero position. It does not require any design information of the CNC positioner and is applicable to any geometric error of the CNC positioner, thereby greatly reducing the requirements for the machining and assembly accuracy of the CNC positioner.

[0010] This invention addresses the assembly and connection process between the fuselage bulkhead and the fuselage web. The proposed dual-loop impedance control architecture ensures smooth multi-point interaction between the fuselage bulkhead and the fuselage web, and between the fuselage bulkhead and the CNC positioner. By using a linear quadratic regulator to adjust the parameters of the outer loop impedance controller, it achieves coordinated optimization of the positioning accuracy of the fuselage bulkhead during fine-tuning and the contact force between it and the fuselage web. Compared to most current impedance controllers that focus solely on force tracking, this invention possesses the ability to comprehensively and optimally control both force and position.

[0011] By employing the above technical solution, the present invention provides a force-position coordination control method for compliant assembly of aircraft fuselage frames, which has at least the following beneficial effects: This invention addresses the kinematic calibration problem of CNC positioners, abandoning the traditional strategy of error modeling → parameter identification → accuracy compensation, and proposing a novel kinematic calibration method for CNC positioners. Unlike calibration methods based on the differential transformation between kinematic parameter errors and end-effector position errors, this invention utilizes multiple measurement points to fit the drive shaft direction and the zero position of the ball joint center, directly establishing a kinematic model of the CNC positioner based on this. It can be applied to CNC positioners with arbitrary geometric errors, even when the design values ​​of kinematic parameters are unknown, thereby significantly reducing the manufacturing and installation accuracy requirements of CNC positioners and greatly saving the development cost of flexible tooling.

[0012] This invention proposes an inner and outer dual-loop impedance control system architecture to simultaneously achieve multi-point compliant interaction between the fuselage bulkhead and the fuselage web plate, as well as between the fuselage bulkhead and the CNC positioner, during the digital assembly of the aircraft fuselage frame. The outer loop impedance controller is used for adjusting the position of the fuselage bulkhead to ensure the compliant fit between it and the fuselage web plate; the inner loop impedance controller is used to ensure the compliant contact between the adjusted fuselage bulkhead and the end of the CNC positioner during movement.

[0013] To address the issue of coordinating the positional accuracy of the fuselage bulkhead and the interaction force between it and the fuselage web, unlike most impedance controllers that are simply used for force tracking, this invention innovatively uses a linear quadratic regulator to dynamically adjust the reference position of the fuselage bulkhead and the desired contact force between the fuselage bulkhead and the fuselage web in the outer-loop impedance controller. By rationally setting the weights of the fuselage bulkhead displacement and contact force in the cost function of the linear quadratic regulator, a reasonable trade-off is achieved between the positioning accuracy of the fuselage bulkhead and the interaction force between the fuselage bulkhead and the fuselage web.

[0014] The high-precision kinematic calibration and dual-loop impedance control method proposed in this invention can be used for kinematic modeling of other CNC equipment such as machine tools and robots, and for multi-point, multi-target force-position cooperative compliant control, and has broad potential application value. Attached Figure Description

[0015] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of the assembly force-position coordinated control method of the present invention; Figure 2 A schematic diagram of the prototype of the fuselage frame and the flexible assembly tooling; Figure 3 A schematic diagram illustrating the kinematic calibration method for CNC positioners; Figure 4 This is a schematic diagram of the calibration of the end force sensor of a CNC positioner. Figure 5 A schematic diagram of the dynamic model of the fuselage bulkhead and the linear response analysis of the fuselage web; Figure 6 Schematic diagram of trajectory planning and CNC positioner control scheme for the attitude adjustment and positioning process of the fuselage frame; Figure 7 This is a schematic diagram of the dual-loop impedance control principle during the assembly process of the fuselage bulkhead and fuselage web. Figure 8 A comparison diagram of the end-effector motion error before and after the kinematic calibration experiment of the CNC positioner; Figure 9 A comparison chart of measured force signals for the fuselage bulkhead during attitude adjustment and positioning using position control; Figure 10 A comparison of measured force signals of the fuselage frame during attitude adjustment and positioning using impedance control; Figure 11 This represents the measured signals of contact force and displacement of the fuselage bulkhead during its mating with the fuselage web. Detailed Implementation

[0016] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This will allow for a full understanding of how the present application uses technical means to solve technical problems and achieve technical effects, and to facilitate its implementation.

[0017] This embodiment proposes a force-position coordination control method for compliant assembly of aircraft fuselage frames. It is applicable to situations where the geometric errors of CNC positioners are arbitrary or even the design values ​​of their kinematic parameters are unknown. This significantly reduces the manufacturing and installation accuracy requirements of the CNC positioners, greatly saves the development cost of flexible tooling, and achieves balanced stress control and positioning accuracy assurance in aircraft fuselage frame assembly. The overall technical process is as follows: Figure 1 As shown, the assembly objects targeted and the flexible tooling used are as follows: Figure 2 As shown. The fuselage frame includes three fuselage frames (front, middle, and rear) and two fuselage webs. During assembly, each fuselage frame is first adjusted and positioned using four sets of PPPS-type CNC positioners. Then, the two fuselage webs are connected to the fuselage frames using the fuselage frames as positioning references. To avoid the fuselage frames being subjected to the squeezing and pulling effects of the CNC positioners during the adjustment and positioning process, and to achieve a smooth fit between the fuselage frames and the fuselage webs, the method includes the following steps: S1, Kinematic calibration of CNC positioner.

[0018] First, the lead screw error of a single axis of the CNC positioner is calibrated. Several displacement commands are given to drive the single axis movement. The positioning error of the linear axis under each displacement command is measured using a linear scale. The lead screw error is then identified using the least squares method. Figure 3As shown in (a). Then, the target ball is fixed at an arbitrary position at the end of the CNC positioner. With the other linear axes in a zero-position state, each linear axis is driven independently and sequentially. A laser tracker is used to collect multiple position coordinates of the target ball during its independent movement along each linear axis. Based on these position coordinates, principal component analysis is used to fit the direction vector of each linear axis, as shown in (a). Figure 3 As shown in (b). With each linear axis of the CNC positioner in its zero-position state, the target ball is fixed at any position on the ball joint rod at the end of the CNC positioner. The ball joint rod drives the target ball to rotate around the joint center. A laser tracker is used to record multiple position coordinates of the target ball rotating around the joint center. Based on these position coordinates, a spherical fitting algorithm is used to obtain the center coordinates of the ball joint when each linear axis is in its zero-position state (i.e., the zero-position center coordinates of the ball joint). Figure 3 As shown in (c). Finally, based on the direction vector of the linear axes and the coordinates of the zero-position center of the ball joint, a matrix is ​​used to establish the kinematic relationship between the displacement and velocity of each linear axis of the CNC positioner and the position and velocity of the center of the end ball joint, as follows: Figure 3 As shown in (d).

[0019] For calibrating the lead error of a single linear axis leadscrew, suppose there are n sets of linear axis displacement commands d1, d2, ..., dn. n The corresponding positional errors obtained using a grating ruler are Δd1, Δd2, …, Δd n If the nominal value of the lead screw is h, then the lead screw lead error Δh theoretically needs to satisfy the following overdetermined linear equation system: ; Due to factors such as measurement errors, this system of equations cannot be strictly true. Therefore, we consider using the following optimization objective to find the best approximate solution for the lead screw error Δh, namely: ; By setting the derivative of the objective function f with respect to the lead screw error Δh to zero in the above equation, the optimal estimate of the lead screw error Δh can be easily obtained. ,Right now: ; Using the identified best estimate The mapping relationship between the displacement of a single linear axis and the motor rotation angle is corrected, thereby improving the motion control accuracy of the linear axis.

[0020] For the orientation calibration of the linear axis, suppose the target ball collects m points under the independent motion of a certain linear axis: p l1 =(x l1 , y l1 , z l1 ) T , p l2 = (xl2 , y l2 , z l2 ) T ,…, p lm = (x lm , y lm , z lm ) T The direction vector of the linear axis to be calibrated is n = (n x , n y , n z ) T The closest point on the linear axis to the centroid of the measurement point set is p. l0 =(x l0 , y l0 , z l0 ) T The objective is to minimize the sum of the squared distances from the measurement point to the linear axis, with respect to the direction vector n of the linear axis and the nearest point p. l0 The optimization model is as follows: ; The above optimization model can be solved using principal component analysis. It can be easily proven that the nearest point p... l0 That is, the measurement point p l1 ~ p lm The centroid of the line axis, and the solution for the direction vector n of the line axis can be transformed into finding the centroid of point p. l1 ~ p lm The covariance matrix is ​​orthogonally decomposed, i.e.: ; In the formula, λ1~λ m These are the eigenvalues ​​of the covariance matrix on the right side of the equation, arranged in descending order; e1~e m It is the corresponding unit orthogonal eigenvector. Then the direction vector n of the line axis is the eigenvector e1 corresponding to the largest eigenvalue λ1.

[0021] For fitting the center coordinates of the ball joint at the end of the CNC positioner when each linear axis is in the zero position, let's assume that m point coordinates were collected: p s1 =(x s1 , y s1 , z s1 ) T , p s2 = (x s2 , y s2 , z s2 ) T , …, p sm = (x sm , y sm , z sm ) TThe coordinates of the ball joint center to be calibrated are p. sc =(x sc , y sc , z sc ) T The radius is r. The center coordinate p of the ball joint is taken as the sum of the squares of the differences between the squares of the distances from each measurement point to the center of the ball joint and the radius. sc The optimization objective for radius r is: ; Therefore, the aforementioned optimization model has a certain relationship with x. sc , y sc , z sc The analytical solution is: ; The parameter c in the above formula x , c y , c z , c xx , c yy , c zz , c xz , c xy , c yz Based on measurement point p s1 ~ p sm The coordinates were calculated to yield: ; Regarding the kinematic relationship between the displacement and velocity of each linear axis of the CNC positioner and the position and velocity of the end ball joint center, let the displacement of the three linear axes of the CNC positioner be d. x , d y , d z The current coordinate of the center position of the distal ball joint during the motion is p. m =(x m , y m , z m ) T Then, based on the fitted direction vector n and the coordinate x of the ball joint center in the zero position state... sc , y sc , z sc The positive kinematic mapping between the displacement and velocity of the linear axis and the position and velocity of the end ball joint center is as follows: ; In the above formula, n x =(n xx , n xy , n xz ) T , n y =(n yx , n yy, n yz ) T , n z =(n zx , n zy , n zz ) T These are the fitted direction vectors of the three linear axes. Since the direction vectors n of these three linear axes are necessarily non-parallel, the inverse kinematic mapping relationship between the center position and velocity of the ball joint at the end of the CNC positioner and the displacement and velocity of each linear axis can be expressed using an inverse matrix as follows: ; In the above formula, Represents the displacement d of the three linear axes x , d y , d z The first derivative with respect to time; Indicates the current coordinate p m =(x m , y m , z m ) T The first derivative with respect to time. The above equation forms the basis for subsequent steps S4 and S5, which convert the end-point trajectory command of the CNC positioner into motion commands for each linear axis and send them to the servo drive for inner-loop motion control.

[0022] S2. Installation direction calibration of the force sensor at the end of the CNC positioner.

[0023] like Figure 4 As shown, the ball joint at the end of the CNC positioner is fixed, and the CNC positioner is driven to make small movements along three linear axes in sequence to obtain the three-dimensional force components of the force sensor under the pulling action in the three directions. Combined with the three linear axis vectors of the CNC positioner calibrated in S1, a least squares optimization model is established to identify the vector representation of the three measurement coordinate axes of the force sensor in the global coordinate system, thereby establishing the transformation relationship from the force sensor measurement coordinate system to the global coordinate system.

[0024] Let the CNC positioner be along the three axes with vectors n respectively. x , n y , n z Under independent motion, the force vectors collected by the end effector force sensor and normalized in the sensor coordinate system are f. x , f y , f z And assume that the direction vectors of the three coordinate axes of the force sensor to be calibrated in the global coordinate system are s x , s y , s z Let matrix S = [s x s y sz The least squares optimization model used for sensor coordinate axis calibration is as follows: ; Similar to linear axis fitting, matrix S can be obtained through orthogonal decomposition: ;

[0025] In the formula, U and V are both orthogonal matrices; D is a diagonal matrix. Based on the identified sensor coordinate system matrix S, for the three-dimensional force vector f directly measured by the force sensor... m Its vector representation in the global coordinate system is: f g =Sf m .

[0026] S3. Dynamic modeling of fuselage bulkhead and linear response analysis of fuselage web.

[0027] In digital design software, the mass, center of mass position, and inertia tensor matrix of the fuselage bulkhead are extracted using its digital model. Based on the Newton-Euler method, the attitude adjustment dynamics equations of the fuselage bulkhead are established to characterize the relationship between its velocity, acceleration, and pose and the net external force. Furthermore, a force distribution matrix is ​​designed to establish the mapping from the net external force of the fuselage bulkhead to the desired contact force at the ends of the four sets of CNC positioners. Figure 5 As shown in (a), a mesh model of the fuselage web is created in finite element analysis software. Fixed constraints are applied to the surfaces where the fuselage web mates with the midframe, and concentrated forces are applied to the surfaces where the fuselage web contacts the front and rear frames, as shown in (a). Figure 5 As shown in (b). Multiple sets of force and displacement data at the interface between the fuselage web and the fuselage bulkhead were obtained under linear elastic and small deformation conditions. Based on these force and displacement data samples, the stiffness parameters of the fuselage web were identified using the least squares method, thus representing the linear mapping relationship between force and displacement at the interface between the fuselage web and the front and rear fuselage bulkheads. Figure 5 As shown in (c), the dynamic model of the fuselage bulkhead and the stiffness parameter identification process of the fuselage web are as follows: 1. Design of attitude adjustment dynamics model and force distribution matrix for fuselage bulkhead.

[0028] The attitude adjustment dynamics model of the fuselage bulkhead based on the Newton-Euler method described above is as follows: ;

[0029] In the formula, p c ω and ω represent the position of the center of mass of the fuselage frame in the global coordinate system and the rotational angular velocity, respectively; f1~f4 represent the three-dimensional contact forces between the ends of the four sets of CNC positioners and the fuselage frame; r1~r4 represent the line vectors connecting the center of mass of the fuselage frame to the center of the ball joint at the ends of the four sets of CNC positioners, such as... Figure 5As shown in (a); M and J are the 3×3 mass matrix and inertia matrix, respectively, and g is the three-dimensional gravitational acceleration vector, expressed as follows: ;

[0030] In the formula, m is the total mass of the fuselage frame; I xx , I yy , I zz It is the moment of inertia of the fuselage frame rotating around the center of mass and along three coordinate axes parallel to the global coordinate system; I xy , I xz , I yz This is the corresponding inertia product. The total mass m is obtained directly from the digital model, while the moment of inertia, the inertia product, and the vectors r1~r4 connecting the center of mass of the fuselage frame to the hinge center at the end of the CNC positioner all change with the attitude of the fuselage frame during the attitude adjustment process. Let R be the rotation matrix of the fuselage frame from the current attitude to the target attitude, then the current inertia matrix J and the vectors r1~r4 can be expressed as: ;

[0031] In the formula, J0 and r i0 These are the inertia matrix of the fuselage bulkhead relative to the center of mass, obtained from the digital model in the global coordinate system, and the vector from the center of mass to the center of the ball joint at the end of the CNC positioner. The rotation matrix R is obtained through the attitude adjustment trajectory planning of the fuselage bulkhead in subsequent step S4.

[0032] For the design of the force distribution matrix of the fuselage bulkhead, let the resultant external force vector of the fuselage bulkhead be f. c The resultant torque relative to the center of mass is m c The force distribution matrix is ​​W + Then the net external force f c , m c The mapping relationship between the contact forces f1~f4 between the machine frame and the four sets of CNC positioners can be expressed as: ; In the formula, W represents the sum of the contact forces f1~f4 and the net external force f. c , m c The mapping matrix is ​​determined by the geometric distribution of the four ball joint center points; A is a manually designed matrix that determines how the net external force of the fuselage frame is distributed to the four sets of CNC positioners. To ensure that there is no redundant compressive or tensile internal force between the four sets of CNC positioners and the fuselage frame, the value of matrix A should be such that the mapping matrix W and the force distribution matrix are both W + They are generalized inverses of each other, that is, they satisfy: W + W=I. The expression for the mapping matrix W and the appropriate values ​​for a matrix A are: ; In the expression for the mapping matrix W, It is an antisymmetric matrix constructed by connecting vectors r1 to r4, that is: .

[0033] 2. Identification of fuselage web stiffness.

[0034] For the identification of fuselage web stiffness parameters, assume that N concentrated forces f are applied along the x, y, and z directions on the mating surfaces between the fuselage web and the front and rear fuselage bulkheads. (1) p,x~f (N) p,x, f (1) p,y~f (N) p,y, f (1) p,z~f (N) p,z, the displacement of the mating surface obtained through linear finite element analysis is ΔT (1) p,x~ΔT (N) p,x, ΔT (1) p,y~ΔT (N) p,y, ΔT (1) p,z~ΔT If (N) p,z, then the stiffness parameters k of the fuselage web mating surfaces bending in three directions are identified by the least squares method. p,x , k p,y , k p,z for: ;

[0035] The stiffness parameter k identified above p,x , k p,y , k p,z That is, the proportionality coefficient between the displacement of the mating surface along the coordinate direction and the load in the same direction, which is used for the design of the outer loop impedance controller in the subsequent step S6.

[0036] S4. Trajectory planning for the attitude adjustment and positioning process of the fuselage frame.

[0037] First, the attitude adjustment trajectory of the fuselage bulkhead is planned. A laser tracker is used to collect the coordinates of feature points of the fuselage bulkhead in its initial pose. Combining these coordinates with the coordinates of these points in the ideal pose given by the design model, the rotation matrix and translation vector characterizing the transformation relationship of the fuselage bulkhead from the initial pose to the ideal pose are calculated. The rotation matrix is ​​further decomposed into corresponding RPY angles. A fifth-order polynomial is used to establish the functions of the three RPY angles and three translational components with respect to time during the attitude adjustment process of the fuselage bulkhead. Then, using the geometric distribution relationship between the end effector of the CNC positioner and the hinge points of the fuselage bulkhead, the attitude adjustment trajectory of the fuselage bulkhead is transformed into the trajectory of the centers of the ball joints at the ends of the four CNC positioners. The details are as follows: 1. Solving the rotation and translation transformation of the fuselage frame from the initial pose to the target pose.

[0038] Let q be the measured coordinates of the four feature points of the fuselage frame in the initial pose. m1 , q m2 , q m3 , q m4 ,like Figure 6 As shown in (a); their coordinates in the given target pose in the digital model are q r1 , q r2 , q r3 , q r4 The rotation matrix of the fuselage frame from the initial pose to the target pose. Translation vector It can be estimated as follows: ; In the formula, S and Q are orthogonal matrices.

[0039] Further, the rotation matrix from the initial pose to the target pose. It is decomposed into three RPY angles that rotate sequentially around the global coordinate axes x, y, and z. ,Right now: .

[0040] 2. Motion trajectory planning during the attitude adjustment and positioning process of the fuselage frame.

[0041] Let the three RPY angular and translational components of the fuselage frame at any time t during attitude adjustment be respectively... Under the boundary conditions where the initial and final velocities and accelerations are zero, the fifth-order polynomial interpolation is used. The expression is: ; In the formula, and It is composed of rotation matrix Translation vector The decomposed fuselage bulkhead yields the total RPY angle and total translational components from the initial pose to the target pose; t f It is the attitude adjustment time, which is obtained by a simple binary search method with the goal of minimizing it and combining the maximum velocity and acceleration constraints.

[0042] After planning the RPY angle and translation components for the attitude adjustment of the fuselage frame, for the trajectory of the ball joint center of the four sets of CNC positioners, let the ball joint center point of the i-th set of CNC positioners be... ,like Figure 6 As shown in (a), its function with respect to time t can be expressed as: ; In the formula, p c R(t) is the position vector of the fuselage frame in the target pose in the global coordinate system; R(t) and T(t) are the rotation matrix and translation vector constructed from the RPY angle and translation components as functions of time t, respectively, representing the transformation relationship between the current pose of the fuselage frame and the target pose; r i This represents the line vector connecting the center of mass of the fuselage frame to the center of the ball joint at the end of the four sets of CNC positioners.

[0043] S5. Design of the control law for the CNC positioner during the body attitude adjustment and positioning process.

[0044] like Figure 6 As shown in (b), three of the four sets of CNC positioners employ a position control strategy, using the kinematic relationships established in S1 to accurately track the motion trajectory planned in S4. The remaining set of CNC positioners uses variable parameter impedance control, calculating the resultant external force on the fuselage frame using the attitude adjustment dynamics model in S3 combined with the current motion feedback of the CNC positioner. Then, using the force distribution relationship designed in S3, the resultant external force on the fuselage frame is decomposed into the desired force at the end of this set of CNC positioners. Furthermore, based on the current end force feedback, the velocity and acceleration compensation amount of the end relative to the predetermined motion trajectory in S4 is calculated. Using the kinematic relationships established in S1, the end motion compensation command is converted into motion commands for each axis and sent to the servo drive of the motor for inner-loop motion control. The architecture of the control system is as follows: Figure 6 As shown in (c). The specific model design of the controller is as follows: For the three sets of CNC positioners using position control, the trajectory of the end ball joint center planned in S4 is discretized in the time domain into several displacement and velocity commands, namely: ; In the formula, Δt is the communication cycle between the PLC motion control program and the servo driver; t jThis represents the j-th time point in the discretized posture adjustment process; the superscript "i" indicates the displacement or velocity command at the end of the i-th group of CNC positioners. Based on this, using the inverse kinematics model of the CNC positioner established by S1, the motion command of the end ball joint center is converted into displacement and velocity commands for the three linear axes of each group of CNC positioners, which are then sent by the motion control program to the servo driver for inner-loop PID motion control.

[0045] For a single-group CNC positioner using variable parameter impedance control, the time-domain equation of its impedance controller is: ; In the formula, and These are the trajectory correction command for the ball joint center at the end of the CNC positioner and the predetermined motion trajectory given in S4; f I4 It is the internal force component where the end of the CNC positioner contacts the machine frame, i.e., the force sensor feedback quantity and the force distribution matrix W based on the attitude adjustment dynamics model and force distribution matrix in S3. + The calculated difference in expected force; v(t) is the velocity compensation term dynamically adjusted based on force feedback, which acts on the predetermined trajectory at the center of the ball joint in any time-varying environment. The deviation from its true trajectory causes the internal force component f to... I4 Converging to zero; σ is the parameter that determines the adjustment rate of the velocity compensation term v(t); M d C d These are diagonal matrices containing the impedance controller's inertia and damping parameters, respectively: ; In the impedance control equation, m d , c d σ is a positive parameter that needs to be designed manually. It can be proven that σ is true if and only if the positive parameter m... d , c d When σ satisfies the following constraint, under the assumption of a linearly elastic environment model, the internal force component f of the controller is asymptotically stable and the CNC positioner is in contact with the machine frame. I4 It converges to zero, that is: ; Based on the time-domain equations of the impedance controller, they are discretized over time into several displacement, velocity, and acceleration commands related to the center of the ball joint, namely: ; The displacement and velocity commands in the above formula are converted into displacement and velocity commands for each linear axis through the inverse kinematic model of the CNC positioner established by S1, and sent to the servo drive for inner loop motion control.

[0046] S6. Design of the control law for the CNC positioner during the mating process of the fuselage frame and the fuselage web.

[0047] To achieve a smooth interaction between the fuselage bulkhead and the fuselage web during assembly, the central fuselage bulkhead is kept stationary while the positions of the front and rear frames are fine-tuned. For example... Figure 7 As shown in (a), during the fine-tuning of the front and rear frames, a two-loop impedance control system is designed with the goal of smooth interaction between the CNC positioner and the body frame, and between the body frame and the body web, respectively. The outer loop impedance controller is used for fine-tuning the position of the body frame. Based on the estimated value of the contact force between the body frame and the body web, it outputs the displacement, velocity, and acceleration of the overall translation of the body frame to the inner loop impedance controller. The inner loop impedance controller uses the translation command of the body frame output by the outer loop controller as a reference trajectory. Based on the contact force feedback between the body frame and the end of the CNC positioner, it outputs the compensation trajectory of the end of the CNC positioner and decomposes it into commands for each axis to the servo drive for inner loop motion control. To reduce the contact force between the fuselage bulkhead and the fuselage web while preventing the bulkhead displacement from exceeding the positioning tolerance, a linear quadratic regulator is used to dynamically adjust the reference trajectory and desired force of the outer loop impedance controller based on the state feedback of the bulkhead displacement, velocity, and contact force with the fuselage web. This achieves a comprehensive minimization of the bulkhead displacement and the contact force between the bulkhead and the fuselage web. The architecture of the entire control system is as follows: Figure 7 As shown in (b), the specific design process of the outer loop impedance controller model is as follows: The time-domain equations for the outer-loop impedance controller used for fine-tuning the fuselage bulkhead position and the linear response of the fuselage web are as follows: ; In the formula, T r This is the reference position for the fuselage bulkhead, that is, the initial position after the fuselage bulkhead has been positioned and before fine-tuning; T c It is the fuselage frame position correction command output by the controller; T p and These are the positions of the left and right fuselage belly plates that mate with the fuselage bulkhead; f p It is the combined force between the fuselage bulkhead and the two fuselage plates, f d It is its expected value; M d,o C d,o , K d,o These are the controller's inertia, damping, and stiffness matrices, K. p These are the stiffness matrices of the fuselage web, represented as follows: ; In the formula, k p,x , k p,y k p,z These are the stiffness parameters identified in step S3, and m d,x , m d,y m d,z , cd,x ,c d,y c d,z , k d,x , k d,y k d,z These are the inertia, damping, and stiffness parameters that are manually designed by the controller.

[0048] Now, we are considering using a linear quadratic regulator to dynamically adjust the fuselage frame reference position T in the outer loop impedance control. r and expectation f d These two parameters determine the fuselage frame displacement and contact force f. p To achieve comprehensive minimization, a state-space model of the closed-loop system needs to be established first. Since the fuselage web remains stationary during the fuselage frame fine-tuning process, therefore... Let ΔT = T c –T r Taking the first derivative of both sides of the time-domain equation for the linear response of the fuselage web with respect to time and then... Substituting these values ​​and combining them with the time-domain equations of the controller, we have: ; The above equation is the state equation of the closed-loop system. Define the state vector. Given state matrix A, input matrix B, and input vector u, then: ; The state equation can then be simplified as: ; Based on this, in order to realize the state vector by designing the input vector u(t) Contact force f between mid-fuselage bulkhead and fuselage web p The displacement ΔT of the fuselage frame relative to the reference position and the reference position T of the fuselage frame in the input vector u. r The overall minimization of the adjustment amount is defined by the following quadratic optimization model with respect to the input vector u(t) and the control law based on state feedback: ; In the formula, Q e Q and H are the corresponding representation state vectors. The diagonal matrix of loss weights for each element in the input vector u(t); G is the time-varying gain matrix to be solved; t e It is a given adjustment time.

[0049] The first quadratic term in the loss function of the control law represents the requirement to minimize each element in the state vector at the final adjustment time. This is because the displacement ΔT of the fuselage frame relative to the reference position and the contact force f between it and the fuselage web in the state vector represent the factors in the state vector . pThese are the main optimization variables, and they are in the diagonal matrix Q. e The weights in the input vector u(t) should be relatively large. The integral term in the loss function represents the requirement to minimize the mean of each element of the state vector ẋ and the input vector u(t) throughout the entire adjustment process. To reduce the adjustment amount of the fuselage frame reference position during the entire adjustment process, thereby reducing the total displacement of the fuselage frame, the rate of change of the reference position in the input vector u should be [value missing]. The integral over the entire adjustment period should be minimized, and its loss weight in the diagonal matrix H should be relatively large. Since the value of the state vector 𝜂 during the adjustment process is not the focus of the optimization, the elements of the diagonal matrix Q can take small values ​​but should not be zero to avoid drastic changes in the state variables. Through the above reasonable weight settings, the optimization model can achieve a trade-off between the fuselage bulkhead displacement and the fuselage bulkhead-fuselage web contact force.

[0050] Based on the quadratic optimization model, the optimal solution for the state gain G(t) is: ; The constraint on P(t) on the right-hand side of the above equation is a first-order nonlinear differential equation, also known as the Riccati equation. It is independent of state feedback and can be calculated using the Euler method from the final time t. e Offline iterative solutions are performed at the initial time t=0, thus not affecting the delay of online control. Since solving the Riccati equation is a well-established technique, the specific solution process for P(t) will not be elaborated here.

[0051] Based on the above equation, the optimal solution G for the state gain G(t) is... * The optimal input vector is (t), which is: Thus, the rate of change of the reference position of the fuselage bulkhead in the outer loop impedance control is obtained. and expectation f d The optimal time-domain equation is obtained. Based on this, the time-domain equation of the outer-loop impedance controller is discretized into several equations relating to the translational acceleration of the fuselage frame. ,speed and displacement The instruction is sent to the impedance controller of the inner loop, namely: ; The motion commands for the fuselage bulkhead in the above formula The inner loop impedance controller serves as the reference trajectory for the CNC positioner. Based on the difference between the CNC positioner end-effector force feedback and the desired force obtained in step S3, the inner loop impedance controller outputs the CNC positioner end-effector trajectory compensation amount, achieving smooth interaction between the machine frame and the CNC positioner end-effector during fine-tuning. The inner loop controller employs the same variable-parameter impedance control law used in the machine frame orientation and positioning process in step S5, which has already been described in step S5 and will not be repeated here.

[0052] Experimental verification of kinematic calibration of CNC positioner: To verify the effect of the kinematic calibration method proposed in step S1 on improving the positioning accuracy of the CNC positioner, a calibration experiment was conducted based on a constructed flexible tooling platform. A laser tracker was used to collect the fitting points of the linear axis and the center of the ball joint, such as... Figure 8 (a) and Figure 8 As shown in (b), the comparison of the positioning errors of the end point before and after calibration under circular and straight-line trajectories is as follows: Figure 8 As shown in (c), the error of the CNC positioner after calibration decreased from 0.3~0.5mm to less than 0.05mm.

[0053] Impedance control experiment verification during fuselage frame attitude adjustment and positioning process: To verify the effect of variable parameter impedance control on the force control between the end effector and the machine frame in step S5 using a single CNC positioner, the time-domain signals of the end effector force sensor were recorded under both variable impedance and position control. The force signal components in the three directions under the two control strategies are shown below. Figure 9 (a) Figure 9 (b) Figure 9 (c) and Figure 10 (d) Figure 10 (e) Figure 10 As shown in (f), compared to position control, the force signal amplitudes in all three directions decrease significantly under impedance control.

[0054] Impedance control experiment verification during the mating process between the fuselage bulkhead and the fuselage web: To verify the coordinated control effect of the outer loop controller on the contact force between the fuselage bulkhead and the fuselage web and the displacement of the fuselage bulkhead under dual-loop impedance control in step S6, the time-domain signals of the displacement of the fuselage bulkhead and the estimated contact force between it and the fuselage web were recorded during the fine-tuning process. Figure 11 (a) and Figure 11 As shown in (b), while the contact force between the fuselage bulkhead and the fuselage web plate decreased significantly, the displacement of the fuselage bulkhead was controlled within a range that met the tolerance requirements, verifying that the outer loop impedance control based on the linear quadratic regulator has the ability to achieve multi-objective optimal control of force and position.

[0055] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0056] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. Since the above embodiments are substantially similar to the method embodiments, their descriptions are relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0057] The above embodiments provide a detailed description of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A force-position coordination control method for compliant assembly of an aircraft fuselage frame, characterized in that, The method includes the following steps: Kinematic calibration was performed on multiple CNC positioners used to support and adjust the machine frame, and the kinematic relationship between the linear axis displacement and velocity of each CNC positioner and the center position and velocity of its end effector was established. The CNC positioner is driven to make small movements along each of its calibrated linear axes in sequence, and the multidimensional force signals of the force sensor installed at its end are collected under each movement. Combined with the direction vector of the linear axis, the transformation relationship between the measurement coordinate system of the force sensor and the global coordinate system is established. Based on the digital model of the fuselage frame, an attitude adjustment dynamic model is established to characterize the relationship between the motion state of the fuselage frame and the resultant external force it is subjected to. Linear response analysis is performed on the fuselage web to obtain stiffness parameters that characterize the force and displacement relationship between the fuselage web and the fuselage frame at the mating interface. Plan the attitude adjustment trajectory of the fuselage frame from the initial pose to the target pose, and convert the attitude adjustment trajectory into the motion trajectory of each CNC positioner end through geometric relationships; During the attitude adjustment and positioning stage of the fuselage frame, the first part of the multiple CNC positioners is controlled to perform position tracking based on kinematic relationships, and at least one second part of the multiple CNC positioners is controlled to output motion compensation based on the attitude adjustment dynamics model and its end contact force feedback, using an impedance control strategy. This is to collaboratively achieve the attitude accuracy control of the fuselage frame and the compliant force control of the CNC positioners on the fuselage frame. During the connection phase between the fuselage bulkhead and the fuselage web, a dual-loop impedance control architecture is adopted to output the pose adjustment command of the fuselage bulkhead and the motion control command of the CNC positioner, so as to realize multi-point smooth interaction between the fuselage bulkhead and the fuselage web, and between the fuselage bulkhead and the CNC positioner.

2. The force-position coordinated control method according to claim 1, characterized in that, Establishing the kinematic relationship includes: First, the lead screw error of a single linear axis of the CNC positioner is calibrated. Several displacement commands are given to drive the single linear axis to move. The positioning error of the linear axis under each displacement command is measured by a grating ruler. The lead screw error is identified by the least squares method. Then, fix the target ball at any position at the end of the CNC positioner, and drive each linear axis to move independently in sequence while the other linear axes are in the zero position state. Use a laser tracker to collect multiple position coordinates of the target ball when it moves independently on each linear axis, and use principal component analysis to fit the direction vector of each linear axis based on these position coordinates. Set each linear axis of the CNC positioner to the zero position, fix the target ball at any position of the ball joint rod at the end of the CNC positioner, and let the ball joint drive the target ball to rotate around the center of the joint. Use a laser tracker to record multiple position coordinates of the target rotating around the center of the ball joint. Use a spherical fitting algorithm to obtain the center coordinates of the ball joint when each linear axis is in the zero position. Finally, based on the direction vector and center coordinates of the linear axes, a matrix is ​​used to establish the kinematic relationship between the displacement and velocity of each linear axis of the CNC positioner and the center position and velocity of the end ball joint.

3. The force-position coordinated control method according to claim 2, characterized in that, The lead error of a single linear axis includes: Suppose we have n sets of linear axis displacement commands d1, d2, ..., dn. n The corresponding positional errors obtained using a grating ruler are Δd1, Δd2, ..., Δd n The nominal value of the lead screw is h. The lead screw error Δh, satisfying the overdetermined linear equation system, is established as: ； The optimal approximate solution for the lead screw error Δh is obtained using the following optimization objective: ； Set the derivative of the objective function f with respect to the lead screw error Δh to zero, and solve for the best estimate of the lead screw error Δh. ,Right now: ； Using the identified best estimate The mapping relationship between the displacement of the linear axis and the rotation angle of the motor is corrected to improve the motion control accuracy of a single linear axis; The direction of the linear axis is calibrated as follows: Suppose that the target ball collects m points under independent motion along a certain linear axis: p l1 =(x l1 , y l1 , z l1 ) T , p l2 =(x l2 , y l2 , z l2 ) T ,…, p lm = (x lm , y lm , z lm ) T The direction vector of the linear axis to be calibrated is n = (n x , n y , n z ) T The closest point on the linear axis to the centroid of the measurement point set is p. l0 =(x l0 , y l0 , z l0 ) T The objective is to minimize the sum of the squared distances from the measurement point to the linear axis, with respect to the direction vector n of the linear axis and the nearest point p. l0 The optimization model is as follows: ； Principal component analysis was used to solve the optimization model to obtain the nearest point p. l0 Then it is the measurement point p l1 ~ p lm The centroid; Solving for the direction vector n of the line axis is transformed into solving for the point p. l1 ~ p lm If we perform orthogonal decomposition on the covariance matrix, then the direction vector n of the linear axis is the eigenvector e1 corresponding to the largest eigenvalue λ1, expressed as: ； In the formula, λ1~λ m These are the eigenvalues ​​of the covariance matrix on the right side of the equation, arranged in descending order; e1~e m These are the corresponding orthogonal eigenvectors; Calibrating the zero position of the end joint center includes: Suppose we collect the coordinates of m points: p s1 =(x s1 , y s1 , z s1 ) T , p s2 = (x s2 , y s2 , z s2 ) T , …, p sm = (x sm ,y sm , z sm ) T The coordinates of the ball joint center to be calibrated are p. sc =(x sc , y sc , z sc ) T The radius is r; The center coordinate p of the ball joint is defined as the sum of the squares of the differences between the squares of the distances from each measurement point to the center of the ball joint and the radius. sc The optimization objective for radius r is: ； The optimization objective has a relation to x sc , y sc , z sc The analytical solution is: ； The parameter c in the above formula x , c y , c z , c xx , c yy , c zz , c xz , c xy , c yz Based on measurement point p s1 ~ p sm The coordinates were calculated to yield: ； In the above formula, .

4. The force-position coordinated control method according to claim 2, characterized in that, Establishing the kinematic relationship includes: Let the displacement of the three linear axes of the CNC positioner be d. x , d y , d z The current coordinate of the center position of the distal ball joint during the motion is p. m =(x m , y m , z m ) T Then, based on the fitted direction vector n and the coordinate x of the ball joint center in the zero position state... sc , y sc , z sc The positive kinematic mapping between the displacement and velocity of the linear axis and the position and velocity of the center of the end ball joint is as follows: ； In the above formula, n x =(n xx , n xy , n xz ) T , n y =(n yx , n yy , n yz ) T , n z =(n zx , n zy , n zz ) T These are the three linear axis direction vectors obtained from the fitting; Since the direction vectors n of these three linear axes are necessarily not parallel, the inverse kinematic mapping relationship between the center position and velocity of the ball joint at the end of the CNC positioner and the displacement and velocity of each linear axis can be expressed using an inverse matrix as follows: ； In the above formula, Represents the displacement d of the three linear axes x , d y , d z The first derivative with respect to time; Indicates the current coordinate p m =(x m , y m , z m ) T The first derivative with respect to time.

5. The force-position coordinated control method according to claim 1, characterized in that, Establishing the transformation relationship includes: Let the CNC positioner be along the three axes with vectors n respectively. x , n y , n z Under independent motion, the force vectors collected by the end effector force sensor and normalized in the sensor coordinate system are f. x , f y , f z And assume that the direction vectors of the three coordinate axes of the force sensor to be calibrated in the global coordinate system are s x , s y , s z ; Let matrix S = [s x s y s z The least squares optimization model used for sensor coordinate axis calibration is as follows: ； Then, matrix S can be obtained through orthogonal decomposition as follows: ； In the formula, U and V are both orthogonal matrices; D is a diagonal matrix; Based on the identified sensor coordinate system matrix S, the three-dimensional force vector f directly measured by the force sensor... m The transformation relationship representing its vector representation in the global coordinate system is: f g =Sf m .

6. The force-position coordinated control method according to claim 1, characterized in that, Obtaining the stiffness parameters includes: In digital design software, the mass, center of mass position and inertia tensor matrix of the fuselage frame are extracted using the digital model. The attitude adjustment dynamic equation of the fuselage frame is established based on the Newton-Euler method to characterize the relationship between its motion velocity, acceleration and posture and the resultant external force. The force distribution matrix is ​​designed and the mapping of the resultant external force of the fuselage frame to the expected contact force at the end of the four sets of CNC positioners is established. A mesh model of the fuselage web is established in the finite element analysis software. Fixed constraints are applied to the surfaces where the fuselage web mates with the mid-frame, and concentrated forces are applied to the surfaces where the fuselage web contacts the front and rear frames. Under online elastic and small deformation conditions, multiple sets of force and displacement data of the interface between the fuselage web and the fuselage bulkhead are obtained. Based on the multiple sets of force and displacement data samples, the stiffness parameters of the fuselage web are identified using the least squares method, thereby representing the linear mapping relationship between force and displacement at the interface between the fuselage web and the front and rear fuselage bulkheads.

7. The force-position coordinated control method according to claim 6, characterized in that, The attitude adjustment dynamics model, force distribution matrix design, and stiffness parameter identification of the fuselage frame include: The attitude adjustment dynamics model of the fuselage bulkhead based on the Newton-Euler method is as follows: ； In the formula, p c ω and ω represent the position of the center of mass and the rotational angular velocity of the fuselage frame in the global coordinate system, respectively; f1~f4 represent the three-dimensional contact forces between the ends of the four sets of CNC positioners and the fuselage frame; r1~r4 represent the line vectors connecting the center of mass of the fuselage frame to the center of the ball joint at the ends of the four sets of CNC positioners; M and J are the 3×3 mass matrix and inertia matrix, respectively, and g is the three-dimensional gravitational acceleration vector; The design of the force distribution matrix includes: Let f be the resultant external force vector of the fuselage frame. c The resultant torque relative to the center of mass is m c The force distribution matrix is ​​W + Then the net external force f c , m c The mapping relationship between the contact forces f1~f4 between the machine frame and the four sets of CNC positioners is expressed as follows: ； In the formula, W represents the sum of the contact forces f1~f4 and the net external force f. c , m c The mapping matrix is ​​determined by the geometric distribution of the four ball joint center points; A is a manually designed matrix that determines how the resultant external force of the fuselage frame is distributed to the four sets of CNC positioners. Identifying the stiffness parameters of the fuselage web includes: Suppose that N concentrated forces f(1) p,x~f(N) p,x, f(1) p,y~f(N) p,y, f(1) p,z~f(N) p,z are applied along the x, y, and z directions to the mating surfaces of the fuselage web and the front and rear fuselage bulkheads, respectively. The displacements of the mating surfaces obtained through linear finite element analysis are ΔT(1) p,x~ΔT(N) p,x, ΔT(1) p,y~ΔT(N) p,y, ΔT(1) p,z~ΔT(N)p,z. Then, the stiffness parameter k of the bending of the fuselage web mating surfaces along the three directions is identified by the least squares method. p,x , k p,y , k p,z for: ； The stiffness parameter k identified above p,x , k p,y , k p,z That is, the proportionality coefficient between the displacement of the mating surface along the coordinate direction and the load in the same direction.

8. The force-position coordinated control method according to claim 6, characterized in that, The conversion of the motion trajectory to the end of each CNC positioner includes: The coordinates of multiple feature points of the fuselage frame in the initial pose are measured using a laser tracker. Combined with the design coordinates of the feature points in the target pose, the pose transformation matrix of the fuselage frame from the initial pose to the target pose is calculated. The pose transformation matrix is ​​decomposed into translational and rotational components, and a polynomial function is used to plan the trajectory of the translational and rotational components.

9. The force-position coordinated control method according to claim 1, characterized in that, The dual-loop impedance control architecture includes an outer-loop impedance controller that outputs a position adjustment command for the fuselage bulkhead based on the feedback of the contact force between the fuselage bulkhead and the fuselage web; and... The inner loop impedance controller outputs motion control commands for the CNC positioner based on the posture adjustment command and the contact force feedback between the end of the CNC positioner and the machine frame. The outer loop impedance controller is used for fine-tuning the position of the fuselage bulkhead. Based on the estimated value of the contact force between the fuselage bulkhead and the fuselage web, it outputs the displacement, velocity and acceleration of the overall translation of the fuselage bulkhead to the inner loop impedance controller. The inner loop impedance controller uses the translation command of the machine frame output by the outer loop controller as the reference trajectory. Based on the contact force feedback between the machine frame and the end of the CNC positioner, it outputs the compensation trajectory of the end of the CNC positioner and decomposes it into commands for each axis to the servo drive for inner loop motion control.

10. The force-position coordinated control method according to claim 1, characterized in that, It also includes state feedback based on fuselage bulkhead displacement, velocity, and contact force with the fuselage web, using a linear quadratic regulator to dynamically adjust the reference trajectory and desired force of the outer loop impedance controller. Specific methods include: Establish the state-space model of the closed-loop system with outer-loop impedance control, the expression of which is: ； In the formula, A represents the output state; A is the state matrix; B is the state vector; B is the input matrix; u is the input vector. Establish the loss function for the linear quadratic regulator: Based on the state-space model, the contact force f between the fuselage bulkhead and the fuselage web in the state vector 𝜂 is realized by designing the input vector u(t). p The displacement ΔT of the fuselage frame relative to the reference position and the reference position T of the fuselage frame in the input vector u. r To minimize the overall adjustment, we define the following quadratic optimization model for u(t) and the control law based on state feedback: ； In the formula, Q e Q and H are the corresponding representation state vectors. The diagonal matrix of loss weights for each element in the input vector u(t); G is the time-varying gain matrix to be solved; t e It is a given adjustment time; Solve for the optimal control law for the input vector u(t): Based on the loss function of the linear quadratic regulator, the optimal solution for the state gain G(t) is: ； The optimal solution G based on gain G(t) * The optimal input vector is (t), which is: Thus, the rate of change of the reference position of the fuselage bulkhead in the outer loop impedance control is obtained. and expectation f d The optimal time-domain equation; Instructions for fine-tuning the fuselage frame trajectory are obtained based on the outer loop impedance controller: The time-domain equations of the outer-loop impedance controller are discretized into several equations relating to the translational acceleration of the fuselage frame. ,speed and displacement The instruction is sent to the impedance controller of the inner loop, namely: ； The motion commands for the fuselage frame in the above formula As a reference trajectory for the inner loop impedance controller, it enables smooth interaction between the machine body frame and the end of the CNC positioner during the fine-tuning process.

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