A multi-robot coordinate system calibration method, device, equipment and medium

Abstract

The application relates to a multi-robot coordinate system calibration method, device, equipment and medium. A calibration equipment coordinate system, a calibration object coordinate system and a robot coordinate system are constructed, a rotation matrix between the robot coordinate system and the calibration equipment coordinate system is constructed, and optimization is performed, the multi-robot coordinate system is unified to the calibration equipment coordinate system, and the relative relationship between different robot coordinate systems is converted, cumulative errors caused by multiple data collection are avoided, the calibration efficiency is improved, and a large number of steps are saved. The existing calibration method has the problems of large cumulative error, high algorithm difficulty, repeated data collection multiple times, long time consumption and inconvenient implementation.

Description

Technical Field

[0001] This invention relates to the field of robot calibration technology, and in particular to a calibration method, apparatus, equipment and medium for multiple robot base coordinate systems. Background Technology

[0002] Coordinate system calibration is crucial in multi-robot systems. It is essential for ensuring collaborative work, accurate perception, and precise control among multiple robots, guaranteeing consistency in position and orientation information across different robots during shared tasks. This helps avoid error accumulation and inconsistencies. However, existing calibration methods suffer from several common problems and limitations, including: complexity and time consumption (coordinate system calibration typically requires multiple experiments and data acquisitions, as well as precise measurements and calibrations, making the process complex and time-consuming); error accumulation (each robot in a multi-arm system can introduce errors, which accumulate during calibration, leading to inaccurate final results); and sensor noise (when using sensors for coordinate system calibration, sensor noise and uncertainties can affect the accuracy of the calibration results).

[0003] Therefore, how to provide a simpler, more convenient, and more accurate calibration method is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0004] Based on this, the purpose of this application is to provide a calibration method, apparatus, device and medium for multiple robot base coordinate systems to solve at least one of the technical problems mentioned in the background art.

[0005] In a first aspect, the present invention provides a method for calibrating a multi-robot base coordinate system, the method comprising:

[0006] Install calibration equipment and install several calibration objects at the end of the robotic arm of each robot;

[0007] Construct the coordinate system for the calibration equipment, the coordinate system for the calibration object, and the robot coordinate system respectively;

[0008] Based on the positions of the calibration equipment, calibration object, and robot in each coordinate system, determine the measurement equations for the relative positional relationships among the three; the measurement equations include the rotation matrix between the calibration equipment and the robot.

[0009] The positions of the calibration equipment, calibration object, and robot are measured several times, and the results are substituted into the measurement equation to determine the rotation matrix between the calibration equipment and the robot.

[0010] Determine if the rotation matrix is ​​an orthogonal matrix; if it is, do nothing; otherwise, optimize it to be an orthogonal matrix.

[0011] Determine the positional relationship between any two robot coordinate systems based on the orthogonal matrix.

[0012] Furthermore, the positions of the calibration equipment, calibration object, and robot, measured in several measurements, are substituted into the measurement equations to determine the rotation matrix between the calibration equipment and the robot, including:

[0013] Multiple measurement equations were obtained by measuring the positions of the calibration equipment, calibration objects, and robot several times.

[0014] The difference equation is obtained by successively subtracting multiple measurement equations.

[0015] The difference equation is transposed, and the rotation matrix between the calibration device and the robot is determined using the least squares method.

[0016] Alternatively, the measurement equation is:

[0017]

[0018] Where R represents the rotation matrix, △P represents the relative position, m represents the calibration equipment coordinate system, b represents the robot coordinate system, t represents the calibration object coordinate system, i represents the i-th robot, 1≤i≤A, A represents the number of robots, and n represents the number of differences.

[0019] Furthermore, the step of determining whether the rotation matrix is ​​an orthogonal matrix, if yes, no processing is performed; otherwise, it is optimized to be an orthogonal matrix, including:

[0020] When the rotation matrix is ​​not an orthogonal matrix, set the cost matrix and transform it into a constrained extremum problem;

[0021] When solving constrained extrema problems, Lagrange multipliers are introduced;

[0022] Find the extreme points of a problem with constrained extrema after introducing Lagrange multipliers, and determine the orthogonal matrix.

[0023] Optionally, the cost matrix is:

[0024]

[0025] Where C is the cost function, Let q0, q1, q2, and q3 be the orthogonal matrices to be determined, F be the metric, Rot() be the function to convert quaternions into rotation matrices, and let q0, q1, q2, and q3 satisfy the relation

[0026] Furthermore, determining the positional relationship between any two robot coordinate systems based on the orthogonal matrix specifically includes:

[0027] Calculate the rotation components of an orthogonal matrix;

[0028] Substitute the rotation matrix into the measurement equation to obtain the position components of the orthogonal matrix;

[0029] Coordinate system transformation is performed based on position components to determine the positional relationship between any two robot coordinate systems.

[0030] Furthermore, the method also includes:

[0031] Calculate the attitude error and position error between the base coordinate systems;

[0032] The accuracy of the calibration results is determined based on the attitude error and position error.

[0033] Secondly, the present invention provides an apparatus for a calibration method of a multi-robot base coordinate system, comprising:

[0034] Install the module, install the calibration equipment, and install several calibration objects at the end of the robotic arm of each robot;

[0035] The coordinate system construction module, connected to the installation module, is used to construct the coordinate system of the calibration equipment, the coordinate system of the calibration object, and the robot coordinate system, respectively.

[0036] The equation module, connected to the coordinate system construction module, is used to determine the measurement equations for the relative positional relationship between the calibration equipment, calibration object, and robot in each coordinate system. The measurement equations include the rotation matrix between the calibration equipment and the robot.

[0037] The rotation matrix construction module, connected to the equation module, is used to measure the positions of the calibration equipment, calibration object, and robot several times. By substituting these positions into the measurement equation, the rotation matrix between the calibration equipment and the robot is determined.

[0038] The judgment module, connected to the rotation matrix construction module, is used to determine whether the rotation matrix is ​​an orthogonal matrix. If it is, no processing is performed; otherwise, it is optimized to be an orthogonal matrix.

[0039] The position relationship acquisition module, connected to the judgment module, is used to determine the position relationship between any two robot coordinate systems based on an orthogonal matrix.

[0040] Thirdly, the present invention provides an electronic device, the device comprising: a processor, and a memory coupled to the processor; the memory storing a program for a multi-robot coordinate system calibration method that can run on the processor, wherein when the program for the multi-robot coordinate system calibration method is executed by the processor, the steps of the multi-robot coordinate system calibration method as described in the first aspect above are implemented.

[0041] Fourthly, the present invention provides a computer storage medium storing a program for a calibration method of a multi-robot coordinate system, wherein when the program for the calibration method of the multi-robot coordinate system is executed by a processor, the steps of the calibration method of the multi-robot coordinate system as described in the first aspect are implemented.

[0042] This invention provides a calibration method, apparatus, device, and medium for multiple robot coordinate systems. By constructing a calibration device coordinate system, a calibration object coordinate system, and a robot coordinate system, and then constructing and optimizing the rotation matrix between the robot coordinate system and the calibration device coordinate system, the multi-robot coordinate system is transformed into the calibration device coordinate system and then converted into relative relationships between different robot coordinate systems. This avoids the cumulative errors caused by multiple data acquisitions, improves calibration efficiency, and saves a significant number of steps. It solves the problems of large cumulative errors, complex algorithms, and the need for repeated data acquisition in existing calibration methods, which result in long processing times and inconvenient implementation. Attached Figure Description

[0043] Figure 1 This is a flowchart of a multi-robot base coordinate system calibration method according to an embodiment of the present invention;

[0044] Figure 2 This is a schematic diagram of the apparatus for a multi-robot base coordinate system calibration method according to an embodiment of the present invention;

[0045] Figure 3 This is a schematic diagram of the structure of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without inventive effort are within the scope of protection of this invention.

[0047] It should be noted that if the embodiments of the present invention involve directional indications, such as up, down, left, right, front, back, etc., these directional indications are only used to explain the relative positional relationships and movement of the components in a specific posture. If the specific posture changes, the directional indications will also change accordingly. Furthermore, if the embodiments of the present invention involve descriptions such as "first," "second," "S1," "S2," "step one," "step two," etc., these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance, or implicitly indicating the number of technical features indicated or the order of method execution. Those skilled in the art will understand that anything that does not violate the inventive concept and is within the scope of the present invention should be included in the protection scope of the present invention.

[0048] like Figure 1 As shown, the present invention provides a calibration method for a multi-robot base coordinate system, the method comprising:

[0049] Step S101: Install calibration equipment and install several calibration objects at the end of the robotic arm of each robot.

[0050] Specifically, the calibration equipment can be, but is not limited to, cameras, lidar, laser trackers, coordinate measuring machines, etc.; the installation location of the calibration equipment should be able to detect all the robots to be inspected.

[0051] More specifically, the calibration objects can be, but are not limited to, camera markers, spherically mounted retroreflectors (SMRs), calibration spheres, etc. Depending on the number of robots, a preset number of calibration objects can be installed at the end of the robot's robotic arm, ensuring that each robot's end has at least one calibration object.

[0052] Preferably, a laser tracker with a long measurement distance, small target size, and wide field of view, along with a corresponding spherical reflector as the calibration device and calibration object, can be used.

[0053] Step S102: Construct the coordinate system of the calibration equipment, the coordinate system of the calibration object, and the robot coordinate system respectively;

[0054] Specifically, but not limited to, the coordinate systems of the calibration equipment, the calibration object, and each robot can be constructed with the positions of the calibration equipment, the calibration object, and each robot as the origin, such as the center point of the calibration equipment, the center point of the calibration object, the center point or vertex of the robot base, etc.

[0055] Step S103: Determine the measurement equations for the relative positional relationship between the calibration equipment, calibration object, and robot in each coordinate system; the measurement equations include the rotation matrix between the calibration equipment and the robot.

[0056] Specifically, since the calibration device, calibration object, and robot satisfy certain spatial constraints in space, a measurement equation for their positional relationship can be constructed. It is possible, but not limited to, using the three coordinate systems established in step S102, with their respective origins as the basis, to obtain the positions of the calibration device, calibration object, and robot, and construct a measurement equation for their relative positional relationship.

[0057] Based on this, during measurement, the position of the calibration device can be selected, but is not limited to, using a point such as its center point or vertex as a reference; the position of the robot can be selected, but is not limited to, using a point on its base as a reference; the position of the calibration object can be selected, but is not limited to, using its center point as a reference, which reflects the tool center point of the robot's robotic arm. TCP calibration is performed on this object to confirm the positional relationship between the tool center point and the robot coordinate system. Since the relative positional relationships of these three elements satisfy certain spatial constraints, measurement equations for all three can be constructed.

[0058] In one embodiment, the spatial constraint, i.e., the measurement equation satisfied by the relative positions of the three, can be, but is not limited to, expressed as Equation 1-1:

[0059] p mtij =R mbij P btij +P mbij 1-1

[0060] Where R represents the rotation matrix, P represents the relative position, m represents the calibration equipment coordinate system, b represents the robot coordinate system, t represents the calibration object coordinate system, i represents the i-th robot, 1≤i≤A, and A represents the number of robots; j represents the j-th measurement, 1≤j≤B, and B represents the number of measurements.

[0061] It is worth noting that the spatial constraint, namely the measurement equation satisfied by the relative positions of the three, is illustrated only by Equation 1-1 above, which is simple and clear; however, the measurement equation can also be selected, but is not limited to, the triangular relationship satisfied by the relative positions of the three, etc., and is not limited to this.

[0062] Step S104: Measure the positions of the calibration equipment, calibration object, and robot several times, substitute them into the measurement equation, and determine the rotation matrix between the calibration equipment and the robot;

[0063] Specifically, optional, but not limited to, the following:

[0064] S1041: Several measurements were taken to calibrate the positions of the calibration equipment, calibration object, and robot, resulting in multiple measurement equations;

[0065] Specifically, according to step S103, multiple measurements can be performed on the positions of the calibration device, the calibration object, and the robot, and multiple measurement equations can be constructed based on the relative positional relationship of the three and the spatial constraints they satisfy. Specifically, the number of measurements can be arbitrarily set by those skilled in the art based on accuracy requirements, time requirements, etc., with four or more measurements being preferred.

[0066] Preferably, the center point of the calibration equipment, the calibration object, and the robot base is used as the reference during measurement.

[0067] S1042: Obtain the difference equation by successively subtracting multiple measurement equations;

[0068] Specifically, any two of the multiple measurement equations constructed in step S1041 are selected and their differences are calculated.

[0069] To Equation 1-2:

[0070]

[0071] Where R represents the rotation matrix, ΔP represents the relative position, m represents the calibration equipment coordinate system, b represents the robot coordinate system, t represents the calibration object coordinate system, i represents the i-th robot, 1≤i≤A, and A represents the number of robots; n represents the number of differences. In any two differences above, each measurement equation may or may not be repeated. For example, if the difference is taken pairwise for j measurements, then n = j / 2; if the difference is taken between the later and earlier measurements for j measurements, then n = j-1; if the difference is taken between every pair of j measurements, then n = C j 2 .

[0072] S1043: Transpose the difference equation and use the least squares method to determine the rotation matrix between the calibration device and the robot.

[0073] Specifically, the difference equations 1-2 obtained in step S1041 are transposed, and then the least squares method is used to calculate the rotation matrix between the calibration device and the robot.

[0074] Transpose equation 1-2 calculated in step S1041 to obtain equation 1-3:

[0075]

[0076] R is then obtained using the least squares method. mbi .

[0077] Step S105: Determine whether the rotation matrix is ​​an orthogonal matrix. If it is, do nothing; otherwise, optimize it to an orthogonal matrix.

[0078] Preferably, when the rotation matrix is ​​not an orthogonal matrix, the step of optimizing the rotation matrix into an orthogonal matrix may optionally include, but is not limited to, the following:

[0079] S1051: Set the cost matrix as shown in Equation 1-4;

[0080]

[0081] Here, the F-norm is used as the metric, Rot() represents the function that converts a quaternion into a rotation matrix, and the constraint equation is a unit quaternion, i.e., Equation 1-5:

[0082]

[0083] Therefore, the problem of minimizing equation 1-4 is transformed into a constrained extremum problem;

[0084] S1052: When solving constrained extrema problems, introducing Lagrange multipliers yields Equation 1-6:

[0085]

[0086] S1053: Find the extreme points of Equation 1-6 and determine the orthogonal matrix.

[0087] Specifically, the rotation matrix corresponding to q0 to q3 at the extreme points can be chosen, but is not limited to, as the one with respect to R. mbi The closest identity orthogonal matrix.

[0088] Step S106: Determine the positional relationship between any two robot coordinate systems based on the orthogonal matrix.

[0089] Specifically, optional, but not limited to, the following:

[0090] S1061: Calculate the rotation components of an orthogonal matrix;

[0091] Specifically, when the rotation matrix is ​​an orthogonal matrix, taking the partial derivative of equation 1-6 yields equation system 1-7:

[0092]

[0093] Then solve the system of equations q * Convert to rotation matrix R in quaternion form mbi =R ot (q * ), which is determined to be the rotation component of the calibration matrix.

[0094] S1062: Substitute the rotation matrix into the measurement equation to obtain the position components of the orthogonal matrix;

[0095] Specifically, substituting the rotation matrix into Equation 1-1 yields the position components of the calibrated orthogonal matrix.

[0096] S1063: Perform coordinate system transformation based on position components to determine the positional relationship between any two robot coordinate systems.

[0097] Specifically, step S1061 determines the rotation matrix R of each robot coordinate system relative to the calibration device coordinate system. mbi By transforming the coordinate system, the rotation matrix between any two robot coordinate systems can be obtained. For example, the rotation matrices of the first and second robots relative to the calibration device coordinate system are R and R, respectively. mb1 and R mb2 The rotation matrix between the two is R. b1b2 =R mb1 -1 R mb2 .

[0098] Preferably, the calibration method for the multi-robot coordinate system of the present invention further includes: calculating the calibration error between each pair of coordinate systems and determining the accuracy of the calibration result.

[0099] Specifically, this calibration error is divided into attitude error and position error. The formula for calculating attitude error can be, but is not limited to, Equation 1-8:

[0100]

[0101] The formula for calculating position error can be, but is not limited to, Equation 1-9:

[0102]

[0103] In this formula, the infinite norm of the vector is used, that is, only the component with the largest error is considered. Euler(·) represents the function that converts the rotation component of the transformation matrix into Euler angles, and Tran(·) represents the function that obtains the position component in the transformation matrix.

[0104] This invention proposes a multi-robot coordinate system calibration method. By installing several calibration objects at the end effector of the robot's arm, and constructing coordinate systems for the calibration device, calibration objects, and the robot based on the calibration equipment, the calibration objects, and the robot, a rotation matrix is ​​built between the robot coordinate system and the calibration device coordinate system. This transforms the multi-robot coordinate system into the calibration device coordinate system and then into the relative relationships between different robot coordinate systems, reducing accumulated errors and eliminating the need for repeated data collection. This solves the problems of existing calibration methods, such as large accumulated errors, complex algorithms, and the need for repeated data collection, leading to long processing times and inconvenient implementation.

[0105] On the other hand, such as Figure 2 As shown, the present invention provides an apparatus for a multi-robot coordinate system calibration method, used to perform the above-mentioned multi-robot coordinate system calibration method, comprising:

[0106] Install module 201, install calibration equipment, and install several calibration objects at the end of the robotic arm of each robot;

[0107] The coordinate system construction module 202 is connected to the installation module 201 and is used to construct the calibration equipment coordinate system, the calibration object coordinate system, and the robot coordinate system respectively.

[0108] The equation module 203, connected to the coordinate system construction module 202, is used to determine the measurement equations of the relative positional relationship between the calibration device, calibration object, and robot in each coordinate system; the measurement equations include the rotation matrix between the calibration device and the robot.

[0109] The rotation matrix construction module 204 is connected to the equation module 203. It is used to measure the positions of the calibration equipment, calibration object and robot several times, and substitute them into the measurement equation to determine the rotation matrix between the calibration equipment and the robot.

[0110] Optionally, the rotation matrix construction module 204 includes:

[0111] The measurement unit is used to measure and calibrate the position of the calibration equipment, calibration object, and robot multiple times, and obtains multiple measurement equations.

[0112] Difference units are used to obtain difference equations by successively subtracting multiple measurement equations.

[0113] The computational unit is used to transpose the difference equation and determine the rotation matrix between the calibration device and the robot using the least squares method.

[0114] Alternatively, the measurement equation is:

[0115]

[0116] Where R represents the rotation matrix, △P represents the relative position, m represents the calibration equipment coordinate system, b represents the robot coordinate system, t represents the calibration object coordinate system, i represents the i-th robot, 1≤i≤A, A represents the number of robots, and n represents the number of differences.

[0117] The judgment module 205 is connected to the rotation matrix construction module 204. It is used to determine whether the rotation matrix is ​​an orthogonal matrix. If it is, no processing is performed. Otherwise, it is optimized to be an orthogonal matrix.

[0118] Optionally, the determination module 205 includes:

[0119] A setting unit is used to set the cost matrix and transform it into a constrained extremum problem when the rotation matrix is ​​not an orthogonal matrix;

[0120] Transformation unit, used to introduce Lagrange multipliers when solving constrained extrema problems;

[0121] The evaluation unit is used to find the extreme points of problems with constrained extrema after introducing Lagrange multipliers and to determine the orthogonal matrix.

[0122] Optionally, the cost matrix is:

[0123]

[0124] Where C is the cost function, Let q0, q1, q2, and q3 be the orthogonal matrices to be determined, F be the metric, Rot() be the function to convert quaternions into rotation matrices, and let q0, q1, q2, and q3 satisfy the relation

[0125] The position relationship acquisition module 206 is connected to the judgment module 205 and is used to determine the position relationship between any two robot coordinate systems based on the orthogonal matrix.

[0126] Optionally, the position relationship acquisition module 206 includes:

[0127] Rotation component calculation unit, used to calculate the rotation components of orthogonal matrices;

[0128] The position component calculation unit is used to substitute the rotation matrix into the measurement equation to obtain the position components of the orthogonal matrix;

[0129] The coordinate system transformation unit is used to perform coordinate system transformation based on the position components to determine the positional relationship between any two robot coordinate systems.

[0130] Optionally, the device further includes:

[0131] The error calculation module is used to calculate the attitude error and position error between the base coordinate systems.

[0132] The accuracy assessment module is used to determine the accuracy of the calibration results based on the attitude error and position error.

[0133] On the other hand, reference Figure 3 The present invention provides an electronic device, characterized in that the device includes: a processor 301 and a memory 302 coupled to the processor 301; the memory 302 stores a program of a multi-robot coordinate system calibration method that can be run on the processor 301, and when the program of the multi-robot coordinate system calibration method is executed by the processor 301, it implements the steps of the multi-robot coordinate system calibration method as described in the embodiment.

[0134] On the other hand, the present invention provides a computer storage medium storing a program for a calibration method of a multi-robot coordinate system. When the program for the calibration method of the multi-robot coordinate system is executed by a processor, it implements the steps of the calibration method of the multi-robot coordinate system as described in the embodiments.

[0135] The computer-readable storage medium includes volatile or non-volatile, removable or non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, computer program modules, or other data). Computer-readable storage media include, but are not limited to, RAM (Random Access Memory), ROM (Read-Only Memory), EEPROM (Electrically Erasable Programmable Read-Only Memory), flash memory or other memory technologies, CD-ROM (Compact Disc Read-Only Memory), DVD or other optical disc storage, cartridges, magnetic tapes, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and is accessible to a computer.

[0136] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0137] The above embodiments are merely illustrative of several implementation methods of this application, and their descriptions are relatively specific and detailed. However, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for calibrating a multi-robot base coordinate system, characterized in that, include: Install calibration equipment and install several calibration objects at the end of the robotic arm of each robot; Construct the coordinate system for the calibration equipment, the coordinate system for the calibration object, and the robot coordinate system respectively; Based on the positions of the calibration equipment, calibration object, and robot in each coordinate system, determine the measurement equations for the relative positional relationships among the three; the measurement equations include the rotation matrix between the calibration equipment and the robot; The positions of the calibration equipment, calibration object, and robot are measured several times, and the results are substituted into the measurement equation to determine the rotation matrix between the calibration equipment and the robot. Determine if the rotation matrix is ​​an orthogonal matrix; if it is, do nothing; otherwise, optimize it to be an orthogonal matrix. Determine the positional relationship between any two robot coordinate systems based on the orthogonal matrix.

2. The method according to claim 1, characterized in that, The positions of the calibration equipment, calibration object, and robot, measured in several measurements, are substituted into the measurement equations to determine the rotation matrix between the calibration equipment and the robot, including: Multiple measurement equations were obtained by measuring the positions of the calibration equipment, calibration objects, and robot several times. The difference equation is obtained by successively subtracting multiple measurement equations. The difference equation is transposed, and the rotation matrix between the calibration device and the robot is determined using the least squares method.

3. The method according to claim 2, characterized in that, The measurement equation is: ； Where R represents the rotation matrix, △P represents the relative position, m represents the calibration equipment coordinate system, b represents the robot coordinate system, t represents the calibration object coordinate system, i represents the i-th robot, 1≤i≤A, A represents the number of robots, and n represents the number of differences.

4. The method according to claim 1, characterized in that, The process of determining whether the rotation matrix is ​​an orthogonal matrix, if yes, no processing is performed; otherwise, it is optimized to be an orthogonal matrix, including: When the rotation matrix is ​​not an orthogonal matrix, set the cost matrix and transform it into a constrained extremum problem; When solving constrained extrema problems, Lagrange multipliers are introduced; Find the extreme points of a problem with constrained extrema after introducing Lagrange multipliers, and determine the orthogonal matrix.

5. The method according to claim 4, characterized in that, The cost matrix is: ； Where C is the cost function, Let be the orthogonal matrix to be determined, F be the metric, and Rot() be the function that converts the quaternion into a rotation matrix. Let q0, q1, q2, and q3 satisfy the relation .

6. The method according to claim 1, characterized in that, The step of determining the positional relationship between any two robot coordinate systems based on an orthogonal matrix specifically includes: Calculate the rotation components of an orthogonal matrix; Substituting the rotation component into the measurement equation, the position component of the orthogonal matrix is ​​obtained; Coordinate system transformation is performed based on position components to determine the positional relationship between any two robot coordinate systems.

7. The method according to claim 1, characterized in that, The method further includes: Calculate the attitude error and position error between the base coordinate systems; The accuracy of the calibration results is determined based on the attitude error and position error.

8. An apparatus for calibrating a multi-robot base coordinate system, characterized in that, include: Install the module, install the calibration equipment, and install several calibration objects at the end of the robotic arm of each robot; The coordinate system construction module, connected to the installation module, is used to construct the coordinate system of the calibration equipment, the coordinate system of the calibration object, and the robot coordinate system, respectively. The equation module, connected to the coordinate system construction module, is used to determine the measurement equations for the relative positional relationship between the calibration device, calibration object, and robot in each coordinate system. The measurement equations include the rotation matrix between the calibration device and the robot. The rotation matrix construction module, connected to the equation module, is used to measure the positions of the calibration equipment, calibration object, and robot several times. By substituting these positions into the measurement equation, the rotation matrix between the calibration equipment and the robot is determined. The judgment module, connected to the rotation matrix construction module, is used to determine whether the rotation matrix is ​​an orthogonal matrix. If it is, no processing is performed; otherwise, it is optimized to be an orthogonal matrix. The position relationship acquisition module, connected to the judgment module, is used to determine the position relationship between any two robot coordinate systems based on an orthogonal matrix.

9. An electronic device, characterized in that, The device includes: a processor, and a memory coupled to the processor; the memory stores a program for a multi-robot coordinate system calibration method that can run on the processor, wherein when the program for the multi-robot coordinate system calibration method is executed by the processor, the program for the multi-robot coordinate system calibration method implements the steps of the multi-robot coordinate system calibration method as described in any one of claims 1 to 7.

10. A computer storage medium, characterized in that, The program stores a calibration method for a multi-robot coordinate system, which, when executed by a processor, implements the steps of the calibration method for a multi-robot coordinate system as described in any one of claims 1 to 7.

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