Cooperative error monitoring system, method and equipment for double-robot mirror image milling

Abstract

The invention discloses a collaborative error monitoring system for double-robot mirror image milling. The collaborative error monitoring system is used for monitoring the relative pose between a milling cutter and a supporting head. The collaborative error monitoring system comprises a data processing system, a permanent magnet fixedly connected with the tail end of a supporting side robot and a sensor array fixedly connected with the tail end of a machining side robot. The permanent magnet is used for generating a space magnetic field signal, the magnetic sensor array is used for measuring the magnetic induction intensity of the permanent magnet at each magnetic sensor, the magnetic sensor array comprises a plurality of three-axis magnetic sensors arranged in an array, and the axis of the permanent magnet coincides with the axis of the tail end of the supporting side robot; a pose and magnetic field forward model and a magnetic field and pose reverse model are arranged in the data processing system; the data processing system collects magnetic induction intensity detection data of the magnetic sensor array and pose data of the tail end of the machining side robot. And calculating to obtain a collaborative error oriented to double-robot mirror image milling. The machining quality and efficiency of cooperative machining of the large thin-wall component are improved.

Description

Technical Field

[0001] The present invention relates to the field of dual-robot collaborative error measurement, and in particular to a collaborative error monitoring system, method and equipment for dual-robot mirror milling. Background Art

[0002] At present, in high-end equipment fields such as aerospace and shipbuilding, mirror milling of large thin-walled components has become a core manufacturing process. The mirror milling system consists of two robots, one with a milling cutter mounted on the end, called the machining side robot, and the other with a support head mounted on the end, called the support side robot. The machining side milling cutter is used to remove material, and the support head on the support side moves in coordination with the milling cutter. The coordinated movement should maintain position and posture synchronization so that the milling cutter and the support head form point-to-point local normal support, thereby improving the rigidity of the process system. Therefore, the magnitude of the coordination error is one of the key indicators for measuring the machining performance of the mirror milling system. Due to geometric errors such as link length error, joint clearance, transmission error, and calibration error of the dual robot base coordinate system, as well as control errors such as communication delay, control algorithm, and dynamic response difference, coordination errors always exist in the coordinated movement of the dual robots during mirror milling, which directly affects the machining quality and even causes chatter. The existing dual-robot collaborative motion control strategy is to collaboratively control the position and posture of the tool and the robot body where the support is located. The final collaborative accuracy depends on the accuracy of the robot itself, and there is a lack of a link to measure the collaborative error for feedback adjustment. Therefore, the present invention intends to apply for a collaborative error magnetic measurement method for dual-robot mirror milling to measure the dual-robot collaborative error to improve the collaborative accuracy of the dual robots during the mirror milling process.

[0003] Patent CN118809306A discloses a method for measuring the synchronous coaxial error of a dual five-axis box-bottom mirror milling machine. Through kinematic modeling and synchronous coaxial constraints based on screw theory, high-precision measurement of the tool tip position error and tool axis direction error is achieved. Five displacement sensors are used to collect the spatial coordinate deviation of the tool tip and tool axis points in real time. Combined with the closed-loop motion chain model and coordinate system calibration algorithm, the synchronous position error and coaxial error are directly calculated. This method effectively measures quasi-static and dynamic errors, but there are still limitations: the dynamic error is treated as a fixed value, ignoring the cumulative effect of time-varying factors in the processing process, and it is difficult to meet the accuracy requirements of high-dynamic collaborative scenarios; the contact measurement relies on physical displacement sensors, which is difficult to meet online real-time measurement.

[0004] The existing collaborative error measurement method for dual-machine mirror milling systems can well measure quasi-static errors, but generally regards dynamic errors as constant values. There is a lack of means to measure the collaborative errors of dual machines in real time during the dual-robot mirror milling process. Summary of the Invention

[0005] The present invention aims to solve the technical problems existing in the known technology and provides a collaborative error monitoring system, method and equipment for dual-robot mirror milling.

[0006] The technical solution adopted by the present invention to solve the technical problems existing in the known technology is:

[0007] A collaborative error monitoring system for dual-robot mirror milling includes a processing-side robot end, a support-side robot end, and a collaborative error monitoring system; the processing-side robot end is provided with a milling cutter; the support-side robot end is provided with a support head for supporting a thin-walled workpiece; the collaborative error monitoring system is used to monitor the relative position between the milling cutter and the support head; the collaborative error monitoring system includes: a data processing system, a permanent magnet fixed to the support-side robot end, and a sensor array fixed to the processing-side robot end; the permanent magnet is used to generate a spatial magnetic field signal, and the magnetic sensor array is used to measure the magnetic induction intensity of the permanent magnet at each magnetic sensor. The magnetic sensor array includes multiple three-axis magnetic sensors arranged in an array, and the axis of the permanent magnet coincides with the axis of the support-side robot end;

[0008] The data processing system is equipped with a forward model of posture and magnetic field and an inverse model of magnetic field and posture; among which:

[0009] The posture and magnetic field forward model is used to reflect the mapping relationship between the relative posture of the permanent magnet and the magnetic sensor array and the magnetic induction intensity detection value of the magnetic sensor array;

[0010] The magnetic field and posture inverse model is used to reflect the mapping relationship between the magnetic induction intensity detection value of the magnetic sensor array and the relative posture of the permanent magnet and the magnetic sensor array;

[0011] The data processing system collects the magnetic induction intensity detection data of the magnetic sensor array and the posture data of the end of the processing side robot; the relative posture of the processing side milling cutter and the support side support head is calculated in turn by the posture and magnetic field forward model and the magnetic field and posture inverse model; based on the terminal instruction posture of both the support side robot and the processing side robot, the collaborative error for dual-robot mirror milling is further calculated.

[0012] Furthermore, the permanent magnet is cylindrical or cylindrical.

[0013] Furthermore, the magnetic sensor array includes d three-axis magnetic sensors uniformly distributed circumferentially around the axis of the end of the processing-side robot, where d≥3.

[0014] Furthermore, the forward model of posture and magnetic field is established based on the Biot-Savart law; the inverse model of magnetic field and posture is established based on the neural network model.

[0015] The present invention also provides a collaborative error monitoring method for dual-robot mirror milling using the collaborative error monitoring system for dual-robot mirror milling. The forward model of the posture and magnetic field is established based on the Biot-Savart law; the inverse model of the magnetic field and posture is established based on the neural network model. Assume: the permanent magnet fixed coordinate system is {M}; the magnetic sensor array fixed coordinate system is {S};

[0016] Before machining, collect the pose data of the magnetic sensor array in the {M} coordinate system and the magnetic induction intensity data of the magnetic sensor array in the {S} coordinate system corresponding to the pose data; create a sample set with the collected data, train the inverse model of magnetic field and pose, and perform fitting and correction on the forward model of pose and magnetic field;

[0017] During machining, the data processing system synchronously collects the command pose data of the magnetic sensor array in the {M} coordinate system and the magnetic induction intensity detection data of the magnetic sensor array in the {S} coordinate system. The synchronously collected data are input into the pose and magnetic field forward model and the magnetic field and pose inverse model to obtain the actual relative pose and command relative pose of the machining side milling cutter and the supporting side support head. The collaborative error for dual-robot mirror milling is further calculated.

[0018] Furthermore, the method for establishing the posture and magnetic field forward model includes the following steps:

[0019] Step A1: establishing a permanent magnet fixed coordinate system and a magnetic sensor array fixed coordinate system;

[0020] Assume: the permanent magnet fixed coordinate system is {M}; the magnetic sensor array fixed coordinate system is {S}; the magnetic sensor serial number is i, i = 1, 2, ..., n; n is the number of magnetic sensors in the magnetic sensor array; the i-th magnetic sensor fixed coordinate system is {S i}; ξ represents the pose vector of the magnetic sensor array in the {M} coordinate system; ψ represents the magnetic induction intensity vector induced by the magnetic sensor array in the {S} coordinate system;

[0021] Let ξ=[x,y,z,a,b,c] T ;in:

[0022] x represents the offset of the origin of the magnetic sensor array fixed coordinate system on the X axis of the permanent magnet fixed coordinate system;

[0023] y represents the offset of the origin of the magnetic sensor array fixed coordinate system on the Y axis of the permanent magnet fixed coordinate system;

[0024] z represents the offset of the origin of the magnetic sensor array fixed coordinate system on the Z axis of the permanent magnet fixed coordinate system;

[0025] a represents the angle of rotation of the magnetic sensor array around the axis parallel to the X-axis of the permanent magnet fixed coordinate system;

[0026] b represents the angle of the magnetic sensor array after rotating around an axis parallel to the X-axis of the permanent magnet fixed coordinate system and then rotating around an axis parallel to the Y-axis of the permanent magnet fixed coordinate system;

[0027] c represents the angle of the magnetic sensor array rotating around the axes parallel to the X and Y axes of the permanent magnet fixed coordinate system and then rotating around the axis parallel to the Z axis of the permanent magnet fixed coordinate system;

[0028] Step A2: generate m discrete pose sample points in the {M} coordinate system to form a sampling space, and make the magnetic sensor array traverse the sampling space to collect magnetic induction intensity detection data of the magnetic sensor array at each pose sample point; D mea Represents the magnetic induction intensity detection data set at each posture sample point;

[0029] Assume D mea ={ψ mea_1 ,ψ mea_2 ,…,ψ mea_m};in:

[0030] ψ mea_1 ,ψ mea_2 ,…,ψ mea_m Correspondingly represents the magnetic induction intensity detection data at the 1st, 2nd, ..., mth pose sample points; m represents the number of pose sample points;

[0031] Step A3: Establish the following permanent magnet magnetic field model taking into account practical factors: B(H,P)=B x (H,x,y,z)u+B y (H,x,y,z)v+B z (H,x,y,z)w;H={h1,h2,h3,…,h k}, P = [x, y, z] T ;in:

[0032] B(H,P) represents the permanent magnet magnetic field model containing actual factor variables;

[0033] H represents the actual factor parameter vector;

[0034] P represents the position vector parameter vector;

[0035] B x Indicates the magnetic induction intensity of the permanent magnet in the X-axis direction;

[0036] B y Indicates the magnetic induction intensity of the permanent magnet in the Y-axis direction;

[0037] Bz Indicates the magnetic induction intensity of the permanent magnet in the Z-axis direction;

[0038] u represents the unit vector of the X axis;

[0039] v represents the unit vector of the Y axis;

[0040] w represents the unit vector of the Z axis;

[0041] h1,h2,h3,…,h k Represents the 1st, 2nd, 3rd, ..., kth actual factor parameters in the permanent magnet magnetic field model;

[0042] k represents the number of actual factor parameters in the permanent magnet magnetic field model;

[0043] Step A4: Construct a forward model of the position and magnetic field. Assume that the position of the magnetic sensor array in the {M} coordinate system is ξ = [x, y, z, a, b, c] T When , the position of the i-th sensor in the {M} coordinate system is in:

[0044]

[0045]

[0046]

[0047]

[0048] Will M P i Substitute the permanent magnet magnetic field model B(H,P) to obtain the magnetic induction intensity B(H, M P i ), i=1,2,…,n; through coordinate transformation, [B(H, M P1),B(H, M P2),…,B(H, M P n )] T Transformed to the {S} coordinate system, we get The following posture and magnetic field forward model are obtained: The input of the posture and magnetic field forward model is the posture of the magnetic sensor array relative to the permanent magnet, and the output is the magnetic induction intensity value sensed by the magnetic sensor array in the {S} coordinate system;

[0049] Where:

[0050] Rot(X,a) represents the rotation matrix of the magnetic sensor array around an axis parallel to the X-axis of the permanent magnet fixed coordinate system by an angle a;

[0051] Rot(Y,b) represents the rotation matrix of the magnetic sensor array around an axis parallel to the Y axis of the permanent magnet fixed coordinate system by an angle b;

[0052] Rot(Z,c) represents the rotation matrix of the magnetic sensor array around an axis parallel to the Z axis of the permanent magnet fixed coordinate system by an angle c;

[0053] represents the rotation matrix of the magnetic sensor array fixed coordinate system {S} relative to the permanent magnet fixed coordinate system {M};

[0054] represents the rotation matrix of the permanent magnet fixed coordinate system {M} relative to the magnetic sensor array fixed coordinate system {S};

[0055] M P i represents the position of the i-th magnetic sensor in the coordinate system {M}; i = 1, 2, ..., n;

[0056] S P i represents the position of the i-th magnetic sensor in the coordinate system {S}; i = 1, 2, ..., n;

[0057] S B i represents the magnetic induction intensity at the i-th magnetic sensor in the coordinate system {S};

[0058] B(H, M P i ) represents the calculated value of the magnetic induction intensity containing actual factor variables at the i-th magnetic sensor in the coordinate system {M}, i = 1, 2, ..., n;

[0059] f(ξ) represents the forward model of posture and magnetic field with ξ as the independent variable;

[0060] Representation matrix With the matrix B(H, M P i )Multiply the two matrices.

[0061] Furthermore, the actual factor parameter H in the posture and magnetic field forward model is optimized as follows:

[0062] Substitute the posture data of the magnetic sensor array relative to the permanent magnet at each posture sample point into the posture and magnetic field forward model to calculate the magnetic induction intensity value sensed by the magnetic sensor array at each posture sample point in the {S} coordinate system;

[0063] Let ψ mea_j represents the magnetic induction intensity detection value of the magnetic sensor array at the j-th pose sample point; ψcal_j represents the calculated value of the magnetic induction intensity of the magnetic sensor array at the jth pose sample point; j = 1, 2, ..., m; j represents the sequence number of the pose sample point; let H* represent the optimal actual factor parameter vector corresponding to the actual factor parameter vector H;

[0064] Construct the following objective function: The optimization algorithm is used to perform nonlinear least square optimization to obtain the optimal actual factor parameter vector H*.

[0065] Furthermore, the method for training the magnetic field and posture inverse model includes the following steps:

[0066] Using the posture sampling strategy of the Monte Carlo method, the posture data of each posture sample point of the magnetic sensor array in the {M} coordinate system is substituted into the posture and magnetic field forward model to obtain the calculated value of the magnetic induction intensity at each posture sample point of the magnetic sensor array in the {S} coordinate system. The posture data of the magnetic sensor array at the posture sample point in the {M} coordinate system is combined with the corresponding calculated value of the magnetic induction intensity in the {S} coordinate system to obtain several groups of sample data, and the following sample data set D is generated:

[0067] D={(ξ 1, ψ cal_1 ),(ξ 2, ψ cal_2 ),…,(ξ g, ψ cal_g )};

[0068] ξ j Represents the pose data of the j-th pose sample point in the {M} coordinate system; j = 1, 2, …, g;

[0069] g represents the number of pose sample points in the sample data set D;

[0070] (ξ 1, ψ cal_1 ),(ξ 2, ψ cal_2 ),…,(ξ g, ψ cal_g ) corresponds to the 1st, 2nd, ..., gth group of sample data in the sample data set D;

[0071] Collect the magnetic induction intensity detection values ​​at each pose sample point in the {S} coordinate system, combine the pose data of the magnetic sensor array at the pose sample point in the {M} coordinate system with the corresponding magnetic induction intensity detection value in the {S} coordinate system, and obtain several groups of sample data to form the following sample data set E:

[0072] E={(ξ 1, ψ mea_1 ,(ξ 2, ψmea_2 ),…,(ξ g, ψ mea_q )}; q represents the number of pose sample points in the sample dataset E;

[0073] The magnetic field and posture inverse model is trained using samples from the sample data set D. The calculated magnetic induction intensity of the magnetic sensor array at a certain posture sample point in the {S} coordinate system is input into the magnetic field and posture inverse model. The magnetic field and posture inverse model then outputs the posture data of the magnetic sensor array at the posture sample point in the {M} coordinate system.

[0074] The samples in the sample data set E are used to verify and test the magnetic field and posture inverse model. The magnetic induction intensity detection value of the magnetic sensor array at a certain posture sample point in the {S} coordinate system is input into the magnetic field and posture inverse model, and the magnetic field and posture inverse model outputs the posture data of the magnetic sensor array at the posture sample point in the {M} coordinate system.

[0075] Furthermore, n magnetic sensors are evenly distributed around the axis of the end of the processing robot; the position of the i-th magnetic sensor in the {S} coordinate system is as follows:

[0076]

[0077] Where:

[0078] r represents the radius of the circle where the magnetic sensors are distributed;

[0079] The three-axis magnetic induction intensity detection values ​​of n magnetic sensors are transformed by the following coordinate transformation formula: Transformed to the {S} coordinate system; the three-axis magnetic induction intensity detection values ​​of n magnetic sensors in the {S} coordinate system form a 3n×1 magnetic sensor array detection value column vector ψ, ψ=[ S B1 S B2… S B n ] T ;

[0080] Where:

[0081] S B i represents the magnetic induction intensity detected by the i-th magnetic sensor in the coordinate system {S}; i = 1, 2, ..., n;

[0082] represents the i-th magnetic sensor fixed coordinate system {S i} Rotation matrix relative to the magnetic sensor array fixed coordinate system {S}; i = 1, 2, ..., n;

[0083] represents the rotation matrix of the magnetic sensor array fixed coordinate system {S} relative to the permanent magnet fixed coordinate system {M};

[0084] Si B i In the coordinate system {S i}The magnetic induction intensity detected by the i-th magnetic sensor under ; i = 1, 2,…, n.

[0085] The present invention also provides a device for a collaborative error monitoring method for dual-robot mirror milling, comprising a memory and a processor, wherein the memory is used to store a computer program; the processor is used to execute the computer program and implement the steps of the collaborative error monitoring method for dual-robot mirror milling as described above when executing the computer program.

[0086] The advantages and positive effects of the present invention include: A collaborative error monitoring system and method for dual-robot mirror milling can measure collaborative errors during mirror milling, even when magnetic materials and external magnetic fields are absent from the dual-robot end-point's moving space. This provides a foundation for real-time error feedback closed-loop control in collaborative machining scenarios, helping to enhance precision control capabilities in dynamic scenarios and improve the machining quality and efficiency of large, thin-walled components. The system is lightweight, easy to integrate, low-cost, and convenient to deploy. The permanent magnet and magnetic sensor array can be directly attached to the robot end-point without modifying the mechanical structure, making it compatible with existing mirror milling systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] Figure 1 This is a structural schematic diagram of a collaborative error magnetic measurement system for dual-robot mirror milling according to the present invention.

[0088] Figure 2 This is a schematic diagram of the working principle of a collaborative error magnetic measurement system for dual-robot mirror milling according to the present invention.

[0089] In the figure: 1. Processing side robot; 2. Milling cutter; 3. Sensor bracket; 4. Magnetic sensor array; 5. Support head; 6. Permanent magnet; 7. Permanent magnet bracket; 8. Thin-walled workpiece; 9. Support side robot.

[0090] M represents the permanent magnet fixed coordinate system;

[0091] S represents the fixed coordinate system of the magnetic sensor array;

[0092] x s represents the X-axis of the magnetic sensor array fixed coordinate system;

[0093] y s represents the Y axis of the magnetic sensor array fixed coordinate system;

[0094] zs represents the Z axis of the magnetic sensor array fixed coordinate system;

[0095] x m represents the X-axis of the permanent magnet fixed coordinate system;

[0096] y m represents the Y axis of the permanent magnet fixed coordinate system;

[0097] z m represents the Z axis of the permanent magnet fixed coordinate system;

[0098] x s1 Indicates the X-axis of the first magnetic sensor fixed coordinate system;

[0099] y s1 Indicates the Y axis of the first magnetic sensor fixed coordinate system;

[0100] z s1 Indicates the Z axis of the first magnetic sensor fixed coordinate system;

[0101] x s2 represents the X-axis of the second magnetic sensor fixed coordinate system;

[0102] y s2 represents the Y axis of the second magnetic sensor fixed coordinate system;

[0103] z s2 represents the Z axis of the second magnetic sensor fixed coordinate system;

[0104] x s3 represents the X-axis of the third magnetic sensor fixed coordinate system;

[0105] y s3 represents the Y axis of the third magnetic sensor fixed coordinate system;

[0106] z s3 represents the Z axis of the fixed coordinate system of the third magnetic sensor;

[0107] θ represents the Euler angle between the Z axis of the permanent magnet fixed coordinate system and the Z axis of the magnetic sensor array fixed coordinate system. DETAILED DESCRIPTION

[0108] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention and are not used to limit the present invention.

[0109] In the description of the present invention, the terms "upper", "lower", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", etc., indicating directions or positional relationships, are based on the directions or positional relationships shown in the accompanying drawings. They are only for the convenience of describing the present invention and do not require that the present invention must be constructed and operated in a specific direction. Therefore, they should not be understood as limitations on the present invention. The terms "connected" and "connection" used in the present invention should be understood in a broad sense. For example, it can be a fixed connection or a detachable connection; it can be a direct connection or an indirect connection through an intermediate component; it can also be an electrical connection or signal transmission. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to the specific circumstances.

[0110] See Figures 1 to 2 , a collaborative error monitoring system for dual-robot mirror milling, including the end of a processing-side robot 1, the end of a supporting-side robot 9 and a collaborative error monitoring system; the end of the processing-side robot 1 is provided with a milling cutter 2; the end of the supporting-side robot 9 is provided with a supporting head 5 for supporting a thin-walled workpiece 8; the collaborative error monitoring system is used to monitor the relative posture between the milling cutter 2 and the supporting head 5; the collaborative error monitoring system includes: a data processing system, a permanent magnet 6 fixed to the end of the supporting-side robot 9, and a sensor array fixed to the end of the processing-side robot 1; the permanent magnet 6 is used to generate a spatial magnetic field signal, and the magnetic sensor array 4 is used to measure the magnetic induction intensity of the permanent magnet 6 at each magnetic sensor, and the magnetic sensor array 4 includes a plurality of three-axis magnetic sensors arranged in an array, and the axis of the permanent magnet 6 coincides with the axis of the end of the supporting-side robot 9.

[0111] A magnetic sensor is a device that detects corresponding physical quantities by converting changes in the magnetic properties of sensitive components caused by external factors such as magnetic field, current, stress and strain, temperature, and light into electrical signals.

[0112] A magnetic sensor, also known as a magnetometer, is a sensor that measures magnetic fields. It detects the direction and strength of a magnetic field and converts it into an electrical signal. Magnetometers are often used in robotics, aerospace, navigation, and other fields for navigation, positioning, and motion control.

[0113] A three-axis magnetic sensor (or three-axis magnetometer) consists of three mutually perpendicular magnetic field sensors that measure the three axial components of the magnetic field. The measurement result can be expressed as a three-dimensional vector. A three-axis magnetic sensor accurately measures the magnetic field vector in three dimensions, providing more precise magnetic field data. The magnetic sensor can be a Hall effect sensor.

[0114] The working principle of the three-axis magnetic sensor is to utilize the Hall Effect, that is, carriers moving in a magnetic field are deflected by the Lorentz force, generating a voltage difference within the material, thereby measuring the direction and strength of the magnetic field.

[0115] The data processing system is equipped with a forward model of posture and magnetic field and an inverse model of magnetic field and posture; among which:

[0116] The posture and magnetic field forward model is used to reflect the mapping relationship between the relative posture of the permanent magnet 6 and the magnetic sensor array 4 and the magnetic induction intensity detection value of the magnetic sensor array 4.

[0117] The magnetic field and posture inverse model is used to reflect the mapping relationship between the magnetic induction intensity detection value of the magnetic sensor array 4 and the relative posture of the permanent magnet 6 and the magnetic sensor array 4.

[0118] The data processing system collects the magnetic induction intensity detection data of the magnetic sensor array 4 and the posture data of the end of the processing side robot 1; the relative posture of the processing side milling cutter 2 and the support side support head 5 is calculated in turn by the posture and magnetic field forward model and the magnetic field and posture inverse model; based on the end command postures of both the support side robot 9 and the processing side robot 1, the collaborative error for dual robot mirror milling is further calculated.

[0119] Figure 1 In the figure, in order to show the relative positions of the processing side robot 1, the thin-walled workpiece 8, and the supporting side robot 9, the thin-walled workpiece 8 is shown as translucent; the ends of the processing side robot 1 and the supporting side robot 9 are located on both sides of the thin-walled workpiece and are mirror-imaged relative to the thin-walled workpiece.

[0120] The end of the processing-side robot 1 is fixedly connected to the sensor bracket 3 , and the sensor array is installed on the sensor bracket 3 ; the end of the supporting-side robot 9 is fixedly connected to the permanent magnet bracket 7 , and the permanent magnet 6 is installed on the permanent magnet bracket 7 .

[0121] Preferably, the permanent magnet 6 may be cylindrical or cylindrical. The permanent magnet 6 may also be in the shape of a cube with a square end face.

[0122] Preferably, the magnetic sensor array 4 may include d three-axis magnetic sensors uniformly distributed circumferentially around the axis of the end of the processing-side robot 1, where d≥3.

[0123] The permanent magnet 6 may also be in the shape of a cube with a square end face. The magnetic sensor array 4 may also be a matrix with a square layout, that is, the row spacing and column spacing between sensors are equal, and the number of sensors in rows and columns is also equal.

[0124] Preferably, the forward model of posture and magnetic field can be established based on the Biot-Savart law; the inverse model of magnetic field and posture can be established based on the neural network model.

[0125] The present invention also provides a collaborative error monitoring method for dual-robot mirror milling using the collaborative error monitoring system for dual-robot mirror milling. The forward model of posture and magnetic field is established based on the Biot-Savart law; the inverse model of magnetic field and posture is established based on a neural network model.

[0126] Assume that the fixed coordinate system of the permanent magnet 6 is {M}; the fixed coordinate system of the magnetic sensor array 4 is {S}.

[0127] Before the processing operation, the posture data of the magnetic sensor array 4 in the {M} coordinate system and the magnetic induction intensity data of the magnetic sensor array 4 in the {S} coordinate system corresponding to the posture data are collected; a sample set is made with the collected data, the magnetic field and posture inverse model is trained, and the posture and magnetic field forward model is fitted and corrected.

[0128] During the machining operation, the data processing system synchronously collects the command posture data of the magnetic sensor array 4 in the {M} coordinate system and the magnetic induction intensity detection data of the magnetic sensor array 4 in the {S} coordinate system; the synchronously collected data are input into the posture and magnetic field forward model and the magnetic field and posture inverse model to obtain the actual relative posture and command relative posture of the machining side milling cutter 2 and the supporting side support head 5; the collaborative error for dual robot mirror milling is further calculated.

[0129] Preferably, the method for establishing a posture and magnetic field forward model may include the following steps:

[0130] Step A1: establishing a fixed coordinate system of the permanent magnet 6 and a fixed coordinate system of the magnetic sensor array 4.

[0131] Assume: the fixed coordinate system of the permanent magnet 6 is {M}; the fixed coordinate system of the magnetic sensor array 4 is {S}; the magnetic sensor serial number is i, i = 1, 2, ..., n; n is the number of magnetic sensors in the magnetic sensor array 4; the fixed coordinate system of the i-th magnetic sensor is {S i}; ξ represents the posture vector of the magnetic sensor array 4 in the {M} coordinate system; ψ represents the magnetic induction intensity vector sensed by the magnetic sensor array 4 in the {S} coordinate system.

[0132] Let ξ=[x,y,z,a,b,c] T ;in:

[0133] x represents the offset of the origin of the fixed coordinate system of the magnetic sensor array 4 on the X axis of the fixed coordinate system of the permanent magnet 6;

[0134] y represents the offset of the origin of the fixed coordinate system of the magnetic sensor array 4 on the Y axis of the fixed coordinate system of the permanent magnet 6;

[0135] z represents the offset of the origin of the fixed coordinate system of the magnetic sensor array 4 on the Z axis of the fixed coordinate system of the permanent magnet 6;

[0136] a represents the angle of rotation of the magnetic sensor array 4 around an axis parallel to the X-axis of the coordinate system fixed to the permanent magnet 6;

[0137] b represents the angle of the magnetic sensor array 4 after rotating around an axis parallel to the X-axis of the coordinate system fixed to the permanent magnet 6 and then rotating around an axis parallel to the Y-axis of the coordinate system fixed to the permanent magnet 6;

[0138] c represents the angle of the magnetic sensor array 4 rotating around the axis parallel to the X and Y axes of the coordinate system fixed to the permanent magnet 6 and then rotating around the axis parallel to the Z axis of the coordinate system fixed to the permanent magnet 6;

[0139] Step A2: generate m discrete pose sample points in the {M} coordinate system to form a sampling space, and allow the magnetic sensor array 4 to traverse the sampling space to collect magnetic induction intensity detection data of the magnetic sensor array 4 at each pose sample point; D mea Represents the magnetic induction intensity detection data set at each posture sample point;

[0140] Assume D mea ={ψ mea_1 ,ψ mea_2 ,…,ψ mea_m};in:

[0141] ψ mea_1 ,ψ mea_2 ,…,ψ mea_m It corresponds to the magnetic induction intensity detection data at the 1st, 2nd, ..., mth pose sample points; m represents the number of pose sample points.

[0142] Step A3: Establish the following magnetic field model of the permanent magnet 6 taking into account practical factors: B(H,P)=B x (H,x,y,z)u+B y (H,x,y,z)v+B z (H,x,y,z)w;H={h1,h2,h3,…,h k}, P = [x, y, z] T ;in:

[0143] B(H,P) represents the magnetic field model of permanent magnet 6 containing actual factor variables;

[0144] H represents the actual factor parameter vector;

[0145] P represents the position vector parameter vector;

[0146] B x represents the magnetic induction intensity of the permanent magnet 6 in the X-axis direction;

[0147] B yrepresents the magnetic induction intensity of the permanent magnet 6 in the Y-axis direction;

[0148] B z represents the magnetic induction intensity of the permanent magnet 6 in the Z-axis direction;

[0149] u represents the unit vector of the X axis;

[0150] v represents the unit vector of the Y axis;

[0151] w represents the unit vector of the Z axis;

[0152] h1,h2,h3,…,h k Represents the 1st, 2nd, 3rd, ..., kth actual factor parameters in the permanent magnet magnetic field model;

[0153] k represents the number of actual factor parameters in the magnetic field model of the permanent magnet 6.

[0154] Step A4: Construct a forward model of posture and magnetic field. Assume that the posture of the magnetic sensor array 4 in the {M} coordinate system is ξ=[x, y, z, a, b, c] T When , the position of the i-th sensor in the {M} coordinate system is in:

[0155]

[0156]

[0157]

[0158]

[0159] Will M P i Substitute the magnetic field model B(H, P) of the permanent magnet 6 to obtain the magnetic induction intensity B(H, M P i ), i=1,2,…,n; through coordinate transformation, [B(H, M P1),B(H, M P2),…,B(H, M P n )] T Transformed to the {S} coordinate system, we get The following posture and magnetic field forward model are obtained: The input of the posture and magnetic field forward model is the posture of the magnetic sensor array 4 relative to the permanent magnet 6, and the output is the magnetic induction intensity value sensed by the magnetic sensor array 4 in the {S} coordinate system.

[0160] Where:

[0161] Rot(X,a) represents the rotation matrix of the magnetic sensor array 4 around an axis parallel to the X axis of the coordinate system fixed to the permanent magnet 6 by an angle a;

[0162] Rot(Y, b) represents the rotation matrix of the magnetic sensor array 4 around an axis parallel to the Y axis of the coordinate system fixed to the permanent magnet 6 by an angle b;

[0163] Rot(Z, c) represents the rotation matrix of the magnetic sensor array 4 around an axis parallel to the Z axis of the coordinate system fixed to the permanent magnet 6 by an angle c;

[0164] represents the rotation matrix of the magnetic sensor array fixed coordinate system {S} relative to the permanent magnet 6 fixed coordinate system {M};

[0165] represents the rotation matrix of the permanent magnet 6 fixed coordinate system {M} relative to the magnetic sensor array fixed coordinate system {S};

[0166] M P i represents the position of the i-th magnetic sensor in the coordinate system {M}; i = 1, 2, ..., n;

[0167] S P i represents the position of the i-th magnetic sensor in the coordinate system {S}; i = 1, 2, ..., n;

[0168] S B i represents the magnetic induction intensity at the i-th magnetic sensor in the coordinate system {S};

[0169] B(H, M P i ) represents the calculated value of the magnetic induction intensity containing actual factor variables at the i-th magnetic sensor in the coordinate system {M}, i = 1, 2, ..., n;

[0170] f(ξ) represents the forward model of posture and magnetic field with ξ as the independent variable;

[0171] Representation matrix With the matrix B(H, M P i )Multiply the two matrices.

[0172] Preferably, the actual factor parameter H in the posture and magnetic field forward model can be optimized as follows:

[0173] The posture data of the magnetic sensor array 4 relative to the permanent magnet 6 at each posture sample point is substituted into the posture and magnetic field forward model to calculate the magnetic induction intensity value sensed by the magnetic sensor array 4 at each posture sample point in the {S} coordinate system.

[0174] Let ψ mea_j represents the magnetic induction intensity detection value of the magnetic sensor array 4 at the j-th posture sample point; ψ cal_j represents the calculated value of the magnetic induction intensity of the magnetic sensor array 4 at the jth posture sample point; j = 1, 2, ..., m; j represents the sequence number of the posture sample point; let H* represent the optimal actual factor parameter vector corresponding to the actual factor parameter vector H.

[0175] Construct the following objective function: The optimization algorithm is used to perform nonlinear least square optimization to obtain the optimal actual factor parameter vector H*.

[0176] Preferably, the method for training the magnetic field and posture inverse model may include the following method steps:

[0177] Using the posture sampling strategy of the Monte Carlo method, the posture data of each posture sample point of the magnetic sensor array 4 in the {M} coordinate system is substituted into the posture and magnetic field forward model to obtain the calculated value of the magnetic induction intensity of the magnetic sensor array 4 at each posture sample point in the {S} coordinate system. The posture data of the magnetic sensor array 4 at the posture sample point in the {M} coordinate system is combined with the corresponding calculated value of the magnetic induction intensity in the {S} coordinate system to obtain several groups of sample data, and the following sample data set D is generated:

[0178] D={(ξ 1, ψ cal_1 ),(ξ 2, ψ cal_2 ),…,(ξ g, ψ cal_g )};

[0179] ξ j Represents the pose data of the j-th pose sample point in the {M} coordinate system; j = 1, 2, …, g;

[0180] g represents the number of pose sample points in the sample data set D;

[0181] (ξ 1, ψ cal_1 ),(ξ 2, ψ cal_2 ),…,(ξ g, ψ cal_g ) corresponds to the 1st, 2nd, ..., gth group of sample data in the sample data set D;

[0182] Collect the magnetic induction intensity detection values ​​at each pose sample point in the {S} coordinate system, combine the pose data of the magnetic sensor array at the pose sample point in the {M} coordinate system with the corresponding magnetic induction intensity detection value in the {S} coordinate system, and obtain several groups of sample data to form the following sample data set E:

[0183] E={(ξ 1, ψ mea_1 ,(ξ 2, ψ mea_2 ),…,(ξ g, ψ mea_q )}; q represents the number of pose sample points in the sample dataset E.

[0184] The samples in the sample data set D are used to train the magnetic field and posture inverse model, and the calculated value of the magnetic induction intensity of the magnetic sensor array 4 at a certain posture sample point in the {S} coordinate system is input into the magnetic field and posture inverse model. The magnetic field and posture inverse model outputs the posture data of the magnetic sensor array 4 at the posture sample point in the {M} coordinate system.

[0185] The samples in the sample data set E are used to verify and test the magnetic field and posture inverse model. The magnetic induction intensity detection value of the magnetic sensor array 4 at a certain posture sample point in the {S} coordinate system is input into the magnetic field and posture inverse model, and the magnetic field and posture inverse model outputs the posture data of the magnetic sensor array 4 at the posture sample point in the {M} coordinate system.

[0186] Preferably, n magnetic sensors can be evenly distributed around the axis of the end of the processing side robot 1; the position of the i-th magnetic sensor in the {S} coordinate system is as follows:

[0187]

[0188] Where:

[0189] r represents the radius of the circle where the magnetic sensors are distributed;

[0190] The three-axis magnetic induction intensity detection values ​​of n magnetic sensors can be obtained through the following coordinate transformation formula: Transformed to the {S} coordinate system; the three-axis magnetic induction intensity detection values ​​of n magnetic sensors in the {S} coordinate system form a 3n×1 magnetic sensor array 4 detection value column vector ψ, ψ=[ S B1 S B2… S B n ] T ;

[0191] Where:

[0192] S B i represents the magnetic induction intensity detected by the i-th magnetic sensor in the coordinate system {S}; i = 1, 2, ..., n;

[0193] represents the i-th magnetic sensor fixed coordinate system {S i} Rotation matrix relative to the magnetic sensor array fixed coordinate system {S}; i = 1, 2, ..., n;

[0194] Si B i In the coordinate system {S i}The magnetic induction intensity detected by the i-th magnetic sensor under ; i = 1, 2,…, n.

[0195] The present invention also provides a device for a collaborative error monitoring method for dual-robot mirror milling, comprising a memory and a processor, wherein the memory is used to store a computer program; the processor is used to execute the computer program and implement the steps of the collaborative error monitoring method for dual-robot mirror milling as described above when executing the computer program.

[0196] The structure, working process and working principle of the present invention are further explained below with reference to the preferred embodiments of the present invention:

[0197] A collaborative error monitoring system for dual-robot mirror milling, comprising an end of a processing-side robot 1, an end of a supporting-side robot 9 and a collaborative error monitoring system; the end of the processing-side robot 1 is provided with a milling cutter 2 for milling a workpiece, and the end of the supporting-side robot 9 is provided with a supporting head 5 for supporting a thin-walled workpiece 8; the collaborative error monitoring system is used to monitor the relative posture between the milling cutter 2 and the supporting head 5; the collaborative error monitoring system comprises: a data processing system, a permanent magnet 6 fixed to the end of the supporting-side robot 9, and a sensor array fixed to the end of the processing-side robot 1; the permanent magnet 6 is used to generate a spatial magnetic field signal, and the magnetic sensor array 4 is used to measure the magnetic induction intensity of the permanent magnet 6 at each magnetic sensor, and the magnetic sensor array 4 comprises a plurality of three-axis magnetic sensors arranged in an array, and the axis of the permanent magnet 6 coincides with the axis of the end of the supporting-side robot 9.

[0198] The data processing system is equipped with a forward model of posture and magnetic field and an inverse model of magnetic field and posture; among which:

[0199] The posture and magnetic field forward model is used to reflect the mapping relationship between the relative posture of the permanent magnet 6 and the magnetic sensor array 4 and the magnetic induction intensity detection value of the magnetic sensor array 4.

[0200] The magnetic field and posture inverse model is used to reflect the mapping relationship between the magnetic induction intensity detection value of the magnetic sensor array 4 and the relative posture of the permanent magnet 6 and the magnetic sensor array 4.

[0201] The data processing system collects the magnetic induction intensity detection data of the magnetic sensor array 4 and the posture data of the end of the processing side robot 1; the relative posture of the processing side milling cutter 2 and the support side support head 5 is calculated in turn by the posture and magnetic field forward model and the magnetic field and posture inverse model; based on the end command postures of both the support side robot 9 and the processing side robot 1, the collaborative error for dual robot mirror milling is further calculated.

[0202] The present application provides a collaborative error monitoring system for dual-robot mirror milling. By virtue of the one-to-one correspondence between the position of the permanent magnet 6 and the magnetic induction intensity in space, the relative positions between multiple magnetic sensors and the permanent magnet 6 can be obtained, and then the posture of the magnetic sensor array 4 relative to the permanent magnet 6 can be obtained; a mathematical model representing the relationship between the relative posture of the permanent magnet 6 and the magnetic sensor array 4 and the magnetic induction intensity detected by the magnetic sensor array 4 is provided in the data processing system; the magnetic induction intensity data detected by the magnetic sensor array 4 is input into the data processing system to obtain the posture of the magnetic sensor array 4 relative to the permanent magnet 6, that is, the posture of the machining side milling cutter 2 relative to the supporting side support head 5, thereby realizing the measurement of the collaborative error in the dual-robot mirror milling process.

[0203] The position information of the magnetic sensor array 4 relative to the permanent magnet 6 is calculated based on the measured magnetic field value of the magnetic sensor array 4 and the magnetic field inverse model of the permanent magnet 6. The magnetic field measurement value in the {S} coordinate system is input, and the position in the {M} coordinate system, that is, the relative position between the two objects, is output.

[0204] Based on the movement trajectory instructions of the end of the processing side robot 1 and the end of the supporting side robot 9, several discrete points of the posture trajectory of the end of the processing side robot 1 and the end of the milling cutter 2, and the end of the supporting side robot 9 and the end of the permanent magnet 6 can be obtained, and then the ideal value of the relative posture of the end of the milling cutter 2 and the end of the permanent magnet 6 can be obtained.

[0205] The actual position of the magnetic sensor array 4 relative to the permanent magnet 6 obtained by the data processing system is compared with the ideal relative position of the end of the milling cutter 2 and the end of the permanent magnet 6 to obtain the collaborative error for dual robot mirror milling.

[0206] The permanent magnet 6 is cylindrical. The magnetic sensor array 4 includes d three-axis magnetic sensors uniformly distributed circumferentially around the axis of the end of the processing robot 1, where d≥3.

[0207] The axis of the permanent magnet 6 coincides with the axis of the supporting head 5 on the supporting side, and the axis of the magnetic sensor array 4 coincides with the axis of the machining side milling cutter 2 .

[0208] A collaborative error monitoring method for dual-robot mirror milling using the collaborative error monitoring system for dual-robot mirror milling includes the following steps:

[0209] 1) Posture and magnetic field forward model construction stage: Based on the Biot-Savart law, a magnetic field model of the permanent magnet 6 is established that takes practical factors into account. Based on the magnetic field model of the permanent magnet 6 that takes practical factors into account, a mathematical model f: ξ→ψ is established to represent the relationship between the relative posture of the permanent magnet 6 and the magnetic sensor array 4 and the magnetic induction intensity detected by the magnetic sensor array 4, where ξ = [x, y, z, a, b, c] T Indicates the position of the magnetic sensor array 4 relative to the permanent magnet 6, including the three-dimensional position offset [x, y, z] T and Euler angle pose [a,b,c] T ,ψ=[B1 T ,…,B n T ] T represents a set of magnetic induction intensities detected by the magnetic sensor array 4, B n ∈R 3×1 represents the spatial magnetic induction intensity of the i-th sensor.

[0210] 2) Magnetic field and posture inverse model construction stage: A magnetic field and posture inverse model h: ψ→ξ is constructed based on a neural network. The model establishes a mapping relationship between the spatial magnetic induction intensity detected by the magnetic sensor array 4 and the relative posture of the permanent magnet 6 and the magnetic sensor array 4.

[0211] 3) Dynamic error online solution stage: Establish the topological configuration of the magnetic measurement system for the collaborative error of the dual-robot mirror milling, wherein the end of the supporting-side robot 9 is fixed with a permanent magnet 6 as a magnetic field source, and the end of the processing-side robot 1 is fixed with a magnetic sensor array 4 to form a magnetic field detection unit. The data processing system is provided with a magnetic field and posture inverse model h; the magnetic induction intensity data detected by the magnetic sensor array 4 is input into the data processing system, and the posture of the magnetic sensor array 4 relative to the permanent magnet 6, that is, the posture of the end of the processing-side robot 1 relative to the end of the supporting-side robot 9, is solved, thereby realizing the measurement of the collaborative error in the dual-robot mirror milling process.

[0212] The method for establishing a posture and magnetic field forward model includes the following steps:

[0213] Step A1: establishing a fixed coordinate system of the permanent magnet 6 and a fixed coordinate system of the magnetic sensor array 4.

[0214] Assume: the fixed coordinate system of the permanent magnet 6 is {M}; the fixed coordinate system of the magnetic sensor array 4 is {S}; the magnetic sensor serial number is i, i = 1, 2, ..., n; n is the number of magnetic sensors in the magnetic sensor array 4; the fixed coordinate system of the i-th magnetic sensor is {S i}; ξ represents the posture vector of the magnetic sensor array 4 in the {M} coordinate system; ψ represents the magnetic induction intensity vector sensed by the magnetic sensor array 4 in the {S} coordinate system.

[0215] Let ξ=[x,y,z,a,b,c] T ;in:

[0216] x represents the offset of the origin of the fixed coordinate system of the magnetic sensor array 4 on the X axis of the fixed coordinate system of the permanent magnet 6;

[0217] y represents the offset of the origin of the fixed coordinate system of the magnetic sensor array 4 on the Y axis of the fixed coordinate system of the permanent magnet 6;

[0218] z represents the offset of the origin of the fixed coordinate system of the magnetic sensor array 4 on the Z axis of the fixed coordinate system of the permanent magnet 6;

[0219] a represents the angle of rotation of the magnetic sensor array 4 around an axis parallel to the X-axis of the coordinate system fixed to the permanent magnet 6;

[0220] b represents the angle of the magnetic sensor array 4 after rotating around an axis parallel to the X-axis of the coordinate system fixed to the permanent magnet 6 and then rotating around an axis parallel to the Y-axis of the coordinate system fixed to the permanent magnet 6;

[0221] c represents the angle of the magnetic sensor array 4 rotating around the axis parallel to the X and Y axes of the coordinate system fixed to the permanent magnet 6 and then rotating around the axis parallel to the Z axis of the coordinate system fixed to the permanent magnet 6;

[0222] Step A2: generate m discrete pose sample points in the {M} coordinate system to form a sampling space, and allow the magnetic sensor array 4 to traverse the sampling space to collect magnetic induction intensity detection data of the magnetic sensor array 4 at each pose sample point; D mea Represents the magnetic induction intensity detection data set at each pose sample point.

[0223] Assume D mea ={ψ mea_1 ,ψ mea_2 ,…,ψ mea_m};in:

[0224] ψ mea_1 ,ψ mea_2 ,…,ψ mea_m It corresponds to the magnetic induction intensity detection data at the 1st, 2nd, ..., mth pose sample points; m represents the number of pose sample points.

[0225] In step A2, the magnetic field values ​​are measured in the {S} coordinate system. Each set of magnetic field values ​​is measured by the three-axis magnetic induction intensity measured by n magnetic sensors through coordinate transformation. After being transformed into the {S} coordinate system, it forms a 3n×1 column vector ψ=[ S B1 S B2… S B n ] T .

[0226] Where:

[0227] S B i represents the magnetic induction intensity detected by the i-th magnetic sensor in the coordinate system {S}; i = 1, 2, ..., n;

[0228] represents the rotation matrix of the i-th magnetic sensor relative to the magnetic sensor array 4; i=1, 2, ..., n;

[0229] Si B i In the coordinate system {S i}The magnetic induction intensity detected by the i-th magnetic sensor under ; i = 1, 2,…, n.

[0230] Step A3: Establish the following magnetic field model of the permanent magnet 6 taking into account practical factors: B(H,P)=B x (H,x,y,z)u+B y (H,x,y,z)v+B z (H,x,y,z)w;H={h1,h2,h3,…,h k}, P = [x, y, z] T ;in:

[0231] B(H,P) represents the magnetic field model of permanent magnet 6 containing actual factor variables;

[0232] H represents the actual factor parameter vector;

[0233] P represents the position vector parameter vector;

[0234] B x represents the magnetic induction intensity of the permanent magnet 6 in the X-axis direction;

[0235] B y represents the magnetic induction intensity of the permanent magnet 6 in the Y-axis direction;

[0236] B z represents the magnetic induction intensity of the permanent magnet 6 in the Z-axis direction;

[0237] u represents the unit vector of the X axis;

[0238] v represents the unit vector of the Y axis;

[0239] w represents the unit vector of the Z axis;

[0240] h1,h2,h3,…,h k Represents the 1st, 2nd, 3rd, ..., kth actual factor parameters in the permanent magnet magnetic field model;

[0241] k represents the number of actual factor parameters in the magnetic field model of the permanent magnet 6.

[0242] Step A4: Construct a forward model of posture and magnetic field. Assume that the posture of the magnetic sensor array 4 in the {M} coordinate system is ξ=[x, y, z, a, b, c] T When , the position of the i-th sensor in the {M} coordinate system is in:

[0243]

[0244]

[0245]

[0246]

[0247] Will M P i Substitute the magnetic field model B(H, P) of the permanent magnet 6 to obtain the magnetic induction intensity B(H, M P i ), i=1,2,…,n; through coordinate transformation, [B(H, M P1),B(H, M P2),…,B(H, M P n )] T Transformed to the {S} coordinate system, we get The following posture and magnetic field forward model are obtained: The input of the posture and magnetic field forward model is the posture of the magnetic sensor array 4 relative to the permanent magnet 6, and the output is the magnetic induction intensity value sensed by the magnetic sensor array 4 in the {S} coordinate system.

[0248] Where:

[0249] Rot(X,a) represents the rotation matrix of the magnetic sensor array 4 around an axis parallel to the X axis of the coordinate system fixed to the permanent magnet 6 by an angle a;

[0250] Rot(Y, b) represents the rotation matrix of the magnetic sensor array 4 around an axis parallel to the Y axis of the coordinate system fixed to the permanent magnet 6 by an angle b;

[0251] Rot(Z, c) represents the rotation matrix of the magnetic sensor array 4 around an axis parallel to the Z axis of the coordinate system fixed to the permanent magnet 6 by an angle c;

[0252] represents the rotation matrix of the magnetic sensor array fixed coordinate system {S} relative to the permanent magnet 6 fixed coordinate system {M};

[0253] represents the rotation matrix of the permanent magnet 6 fixed coordinate system {M} relative to the magnetic sensor array fixed coordinate system {S};

[0254] M P i represents the position of the i-th magnetic sensor in the coordinate system {M}; i = 1, 2, ..., n;

[0255] S P i represents the position of the i-th magnetic sensor in the coordinate system {S}; i = 1, 2, ..., n;

[0256] S B i represents the magnetic induction intensity at the i-th magnetic sensor in the coordinate system {S};

[0257] B(H, M P i ) represents the calculated value of the magnetic induction intensity containing actual factor variables at the i-th magnetic sensor in the coordinate system {M}, i = 1, 2, ..., n;

[0258] f(ξ) represents the forward model of posture and magnetic field with ξ as the independent variable;

[0259] Representation matrix With the matrix B(H, M P i )Multiply the two matrices.

[0260] A5. Optimize the actual factor parameter H in the posture and magnetic field forward model as follows:

[0261] The posture data of the magnetic sensor array 4 relative to the permanent magnet 6 at each posture sample point is substituted into the posture and magnetic field forward model to calculate the magnetic induction intensity value sensed by the magnetic sensor array 4 at each posture sample point in the {S} coordinate system.

[0262] Let ψ mea_j represents the magnetic induction intensity detection value of the magnetic sensor array 4 at the j-th posture sample point; ψ ca l _j represents the calculated value of the magnetic induction intensity of the magnetic sensor array 4 at the jth posture sample point; j = 1, 2, ..., m; j represents the sequence number of the posture sample point; let H* represent the optimal actual factor parameter vector corresponding to the actual factor parameter vector H.

[0263] Construct the following objective function: The optimization algorithm is used to perform nonlinear least square optimization to obtain the optimal actual factor parameter vector H*.

[0264] The magnetic field and posture inverse model construction phase includes the following steps:

[0265] B1. Generate a data set. Using the Monte Carlo method's posture sampling strategy, substitute the posture data of each posture sample point of the magnetic sensor array 4 in the {M} coordinate system into the posture and magnetic field forward model to obtain the calculated magnetic induction intensity value of the magnetic sensor array 4 at each posture sample point in the {S} coordinate system. Combine the posture data of the magnetic sensor array 4 at the posture sample point in the {M} coordinate system with the corresponding calculated magnetic induction intensity value in the {S} coordinate system to obtain several groups of sample data, and create the following sample data set D:

[0266] D={(ξ 1, ψ cal_1 ),(ξ 2, ψ cal_2 ),…,(ξ g, ψ cal_g )};

[0267] ξ j Represents the pose data of the j-th pose sample point in the {M} coordinate system; j = 1, 2, …, g;

[0268] g represents the number of pose sample points in the sample data set D;

[0269] (ξ 1, ψ cal_1 ),(ξ 2, ψ cal_2 ),…,(ξ g, ψ cal_g ) corresponds to the 1st, 2nd,…, gth group of sample data in the sample data set D.

[0270] B2. Train the magnetic field and posture inverse model based on the data in sample dataset D: g(ψ) = [x, y, z, a, b, c] T , the input is the magnetic field measurement value detected by the magnetic sensor array 4, and the output is the position of the magnetic sensor array 4 relative to the permanent magnet 6.

[0271] n magnetic sensors are evenly distributed on a circle with a diameter of r around the axis of the end of the processing robot 1; the position of the i-th magnetic sensor in the {S} coordinate system is as follows:

[0272]

[0273] Where:

[0274] r represents the radius of the circle where the magnetic sensors are distributed.

[0275] The position information of the magnetic sensor array 4 relative to the permanent magnet 6 is calculated based on the measured magnetic field value of the magnetic sensor array 4 and the magnetic field inverse model of the permanent magnet 6. The magnetic field measurement value in the {S} coordinate system is input, and the position in the {M} coordinate system, that is, the relative position between the two objects, is output.

[0276] The above-mentioned nonlinear least squares optimization algorithm, Monte Carlo method, neural network model, permanent magnet 6, and magnetic sensor array 4 can all adopt devices, algorithms or software modules in the existing technology, or adopt devices, algorithms or software modules in the existing technology and construct them using conventional technical means.

[0277] The above embodiments are only used to illustrate the technical ideas and features of the present invention. Their purpose is to enable those skilled in the art to understand the contents of the present invention and implement them accordingly. The patent scope of the present invention cannot be limited by these embodiments alone. That is, any equivalent changes or modifications made to the spirit disclosed by the present invention still fall within the patent scope of the present invention.

Claims

1. A collaborative error monitoring system for dual-robot mirror milling, characterized in that: It includes a processing-side robot end, a support-side robot end and a collaborative error monitoring system; the processing-side robot end is provided with a milling cutter; the support-side robot end is provided with a support head for supporting a thin-walled workpiece; the collaborative error monitoring system is used to monitor the relative posture between the milling cutter and the support head; the collaborative error monitoring system includes: a data processing system, a permanent magnet fixed to the support-side robot end, and a sensor array fixed to the processing-side robot end; the permanent magnet is used to generate a spatial magnetic field signal, and the magnetic sensor array is used to measure the magnetic induction intensity of the permanent magnet at each magnetic sensor. The magnetic sensor array includes a plurality of three-axis magnetic sensors arranged in an array, and the axis of the permanent magnet coincides with the axis of the support-side robot end; The data processing system is equipped with a forward model of posture and magnetic field and an inverse model of magnetic field and posture; among which: The posture and magnetic field forward model is used to reflect the mapping relationship between the relative posture of the permanent magnet and the magnetic sensor array and the magnetic induction intensity detection value of the magnetic sensor array; The magnetic field and posture inverse model is used to reflect the mapping relationship between the magnetic induction intensity detection value of the magnetic sensor array and the relative posture of the permanent magnet and the magnetic sensor array; The data processing system collects the magnetic induction intensity detection data of the magnetic sensor array and the posture data of the end of the processing side robot; the relative posture of the processing side milling cutter and the support side support head is calculated in turn by the posture and magnetic field forward model and the magnetic field and posture inverse model; based on the terminal instruction posture of both the support side robot and the processing side robot, the collaborative error for dual-robot mirror milling is further calculated.

2. The collaborative error monitoring system for dual-robot mirror milling according to claim 1 is characterized in that: The permanent magnet is cylindrical or cylindrical.

3. The collaborative error monitoring system for dual-robot mirror milling according to claim 1, characterized in that: The magnetic sensor array includes d three-axis magnetic sensors uniformly distributed circumferentially around the axis of the robot end at the processing side, where d≥3.

4. The collaborative error monitoring system for dual-robot mirror milling according to any one of claims 1 to 3, characterized in that: The forward model of posture and magnetic field is established based on the Biot-Savart law; the inverse model of magnetic field and posture is established based on the neural network model.

5. A collaborative error monitoring method for dual-robot mirror milling using the collaborative error monitoring system for dual-robot mirror milling according to claim 1, characterized in that: The forward model of posture and magnetic field is established based on the Biot-Savart law; the inverse model of magnetic field and posture is established based on the neural network model. Let: the fixed coordinate system of the permanent magnet be {M}; the fixed coordinate system of the magnetic sensor array be {S}; Before the processing operation, the pose data of the magnetic sensor array in the {M} coordinate system and the magnetic induction intensity data of the magnetic sensor array in the {S} coordinate system corresponding to the pose data are collected; The collected data is used to create a sample set, to train the inverse model of magnetic field and posture, and to fit and correct the forward model of posture and magnetic field; During machining, the data processing system synchronously collects the command pose data of the magnetic sensor array in the {M} coordinate system and the magnetic induction intensity detection data of the magnetic sensor array in the {S} coordinate system. The synchronously collected data are input into the pose and magnetic field forward model and the magnetic field and pose inverse model to obtain the actual relative pose and command relative pose of the machining side milling cutter and the supporting side support head. The collaborative error for dual-robot mirror milling is further calculated.

6. The collaborative error monitoring method for dual-robot mirror milling according to claim 5, characterized in that: The method for establishing a posture and magnetic field forward model includes the following steps: Step A1: establishing a permanent magnet fixed coordinate system and a magnetic sensor array fixed coordinate system; Assume: the permanent magnet fixed coordinate system is {M}; the magnetic sensor array fixed coordinate system is {S}; the magnetic sensor serial number is i, i = 1, 2, ..., n; n is the number of magnetic sensors in the magnetic sensor array; the i-th magnetic sensor fixed coordinate system is {S i }; ξ represents the pose vector of the magnetic sensor array in the {M} coordinate system; ψ represents the magnetic induction intensity vector induced by the magnetic sensor array in the {S} coordinate system; Let ξ=[x,y,z,a,b,c] T ;in: x represents the offset of the origin of the magnetic sensor array fixed coordinate system on the X axis of the permanent magnet fixed coordinate system; y represents the offset of the origin of the magnetic sensor array fixed coordinate system on the Y axis of the permanent magnet fixed coordinate system; z represents the offset of the origin of the magnetic sensor array fixed coordinate system on the Z axis of the permanent magnet fixed coordinate system; a represents the angle of rotation of the magnetic sensor array around the axis parallel to the X-axis of the permanent magnet fixed coordinate system; b represents the angle of the magnetic sensor array after rotating around an axis parallel to the X-axis of the permanent magnet fixed coordinate system and then rotating around an axis parallel to the Y-axis of the permanent magnet fixed coordinate system; c represents the angle of the magnetic sensor array rotating around the axes parallel to the X and Y axes of the permanent magnet fixed coordinate system and then rotating around the axis parallel to the Z axis of the permanent magnet fixed coordinate system; Step A2: generate m discrete pose sample points in the {M} coordinate system to form a sampling space, and make the magnetic sensor array traverse the sampling space to collect magnetic induction intensity detection data of the magnetic sensor array at each pose sample point; D mea Represents the magnetic induction intensity detection data set at each posture sample point; Let D mea ={ψ mea_ 1 , ψ mea_ 2 , …, ψ mea_m}; where: ψ mea_ 1 ,ψ mea_ 2 ,…,ψ mea_m Correspondingly represents the magnetic induction intensity detection data at the 1st, 2nd, ..., mth pose sample points; m represents the number of pose sample points; Step A3: Establish the following permanent magnet magnetic field model taking into account practical factors: B(H,P)=B x (H,x,y,z)u+B y (H,x,y,z)v+B z (H,x,y,z)w;H={h1,h2,h3,…,h k }, P = [x, y, z] T ;in: B(H,P) represents the permanent magnet magnetic field model containing actual factor variables; H represents the actual factor parameter vector; P represents the position vector parameter vector; B x Indicates the magnetic induction intensity of the permanent magnet in the X-axis direction; B y Indicates the magnetic induction intensity of the permanent magnet in the Y-axis direction; B z Indicates the magnetic induction intensity of the permanent magnet in the Z-axis direction; u represents the unit vector of the X axis; v represents the unit vector of the Y axis; w represents the unit vector of the Z axis; h1,h2,h3,…,h k Represents the 1st, 2nd, 3rd, ..., kth actual factor parameters in the permanent magnet magnetic field model; k represents the number of actual factor parameters in the permanent magnet magnetic field model; Step A4: Construct a forward model of the position and magnetic field. Assume that the position of the magnetic sensor array in the {M} coordinate system is ξ = [x, y, z, a, b, c] T When , the position of the i-th sensor in the {M} coordinate system is in: Will M P i Substitute the permanent magnet magnetic field model B(H,P) to obtain the magnetic induction intensity B(H, M P i ), i=1,2,…,n; through coordinate transformation, [B(H, M P1),B(H, M P2),…,B(H, M P n )] T Transformed to the {S} coordinate system, we get The following posture and magnetic field forward model are obtained: The input of the posture and magnetic field forward model is the posture of the magnetic sensor array relative to the permanent magnet, and the output is the magnetic induction intensity value sensed by the magnetic sensor array in the {S} coordinate system; Where: Rot(X,a) represents the rotation matrix of the magnetic sensor array around an axis parallel to the X-axis of the permanent magnet fixed coordinate system by an angle a; Rot(Y,b) represents the rotation matrix of the magnetic sensor array around an axis parallel to the Y axis of the permanent magnet fixed coordinate system by an angle b; Rot(Z,c) represents the rotation matrix of the magnetic sensor array around an axis parallel to the Z axis of the permanent magnet fixed coordinate system by an angle c; represents the rotation matrix of the magnetic sensor array fixed coordinate system {S} relative to the permanent magnet fixed coordinate system {M}; represents the rotation matrix of the permanent magnet fixed coordinate system {M} relative to the magnetic sensor array fixed coordinate system {S}; M P i represents the position of the i-th magnetic sensor in the coordinate system {M}; i = 1, 2, ..., n; S P i represents the position of the i-th magnetic sensor in the coordinate system {S}; i = 1, 2, ..., n; S B i represents the magnetic induction intensity at the i-th magnetic sensor in the coordinate system {S}; B(H, M P i ) represents the calculated value of the magnetic induction intensity containing actual factor variables at the i-th magnetic sensor in the coordinate system {M}, i = 1, 2, ..., n; f(ξ) represents the forward model of posture and magnetic field with ξ as the independent variable; Representation matrix With the matrix B(H, M P i )Multiply the two matrices.

7. The collaborative error monitoring method for dual-robot mirror milling according to claim 6, characterized in that: The actual factor parameter H in the posture and magnetic field forward model is optimized as follows: Substitute the posture data of the magnetic sensor array relative to the permanent magnet at each posture sample point into the posture and magnetic field forward model to calculate the magnetic induction intensity value sensed by the magnetic sensor array at each posture sample point in the {S} coordinate system; Let ψ mea_j represents the magnetic induction intensity detection value of the magnetic sensor array at the j-th pose sample point; ψ ca l _j represents the calculated value of the magnetic induction intensity of the magnetic sensor array at the jth pose sample point; j = 1, 2, ..., m; j represents the sequence number of the pose sample point; let H* represent the optimal actual factor parameter vector corresponding to the actual factor parameter vector H; Construct the following objective function: The optimization algorithm is used to perform nonlinear least square optimization to obtain the optimal actual factor parameter vector H*.

8. The collaborative error monitoring method for dual-robot mirror milling according to claim 6, characterized in that: The method for training the magnetic field and posture inverse model includes the following steps: Using the posture sampling strategy of the Monte Carlo method, the posture data of each posture sample point of the magnetic sensor array in the {M} coordinate system is substituted into the posture and magnetic field forward model to obtain the calculated value of the magnetic induction intensity at each posture sample point of the magnetic sensor array in the {S} coordinate system. The posture data of the magnetic sensor array at the posture sample point in the {M} coordinate system is combined with the corresponding calculated value of the magnetic induction intensity in the {S} coordinate system to obtain several groups of sample data, and the following sample data set D is generated: D={(ξ 1, ψ ca l _ 1 ),(ξ 2, ψ ca l _ 2 ),…,(ξ g, ψ ca l _g )}; ξ j Represents the pose data of the j-th pose sample point in the {M} coordinate system; j = 1, 2, …, g; g represents the number of pose sample points in the sample data set D; (ξ 1, ψ ca l _ 1 ),(ξ 2, ψ ca l _ 2 ),…,(ξ g, ψ ca l _g ) corresponds to the 1st, 2nd, ..., gth group of sample data in the sample data set D; Collect the magnetic induction intensity detection values ​​at each pose sample point in the {S} coordinate system, combine the pose data of the magnetic sensor array at the pose sample point in the {M} coordinate system with the corresponding magnetic induction intensity detection value in the {S} coordinate system, and obtain several groups of sample data to form the following sample data set E: E={(ξ 1, ψ mea_ 1 ,(ξ 2, ψ mea_ 2 ),…,(ξ g, ψ mea_q )}; q represents the number of pose sample points in the sample dataset E; The magnetic field and posture inverse model is trained using samples from the sample data set D. The calculated magnetic induction intensity of the magnetic sensor array at a certain posture sample point in the {S} coordinate system is input into the magnetic field and posture inverse model. The magnetic field and posture inverse model then outputs the posture data of the magnetic sensor array at the posture sample point in the {M} coordinate system. The samples in the sample data set E are used to verify and test the magnetic field and posture inverse model. The magnetic induction intensity detection value of the magnetic sensor array at a certain posture sample point in the {S} coordinate system is input into the magnetic field and posture inverse model, and the magnetic field and posture inverse model outputs the posture data of the magnetic sensor array at the posture sample point in the {M} coordinate system.

9. The collaborative error monitoring method for dual-robot mirror milling according to claim 6, characterized in that: n magnetic sensors are evenly distributed around the axis of the robot end at the processing side; the position of the i-th magnetic sensor in the {S} coordinate system is as follows: Where: r represents the radius of the circle where the magnetic sensors are distributed; The three-axis magnetic induction intensity detection values ​​of n magnetic sensors are transformed by the following coordinate transformation formula: Transformed to the {S} coordinate system; the three-axis magnetic induction intensity detection values ​​of n magnetic sensors in the {S} coordinate system form a 3n×1 magnetic sensor array detection value column vector ψ, ψ=[ S B1 S B2… S B n ] T ; Where: S B i represents the magnetic induction intensity detected by the i-th magnetic sensor in the coordinate system {S}; i = 1, 2, ..., n; represents the i-th magnetic sensor fixed coordinate system {S i } Rotation matrix relative to the magnetic sensor array fixed coordinate system {S}; i = 1, 2, ..., n; represents the rotation matrix of the magnetic sensor array fixed coordinate system {S} relative to the permanent magnet fixed coordinate system {M}; Si B i In the coordinate system {S i }The magnetic induction intensity detected by the i-th magnetic sensor under ; i = 1, 2,…, n.

10. A device for collaborative error monitoring method for dual-robot mirror milling, comprising a memory and a processor, characterized in that: The memory is used to store a computer program; the processor is used to execute the computer program and implement the steps of the collaborative error monitoring method for dual-robot mirror milling as described in any one of claims 5 to 9 when executing the computer program.

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