A singular-free method and device for calibrating external parameters of a laser radar and an inertial measurement unit

Abstract

The present application relates to a kind of laser radar and inertial measurement unit external parameter calibration singularity-free method and device, for the inherent defect of singularity of the external parameter calibration analytical solution method between laser radar and inertial measurement unit proposed by D.Condurache, the present application gives a kind of laser radar and inertial measurement unit external parameter calibration singularity-free method.Problem is decomposed by dual transfer theorem, avoid the ill-conditioned problem in direct decomposition of dual tensor, significantly improve the stability and reliability of calibration result.Especially when there is small noise in rotation matrix or there is error in translation vector, still can keep higher calibration accuracy.The external parameter calibration method between laser radar and inertial measurement unit proposed in the present application improves the accuracy and safety of the external parameter calibration analytical solution method based on dual orthogonal tensor parameter.

Description

Technical Field

[0001] This invention relates to the field of multi-sensor calibration technology, and in particular to a non-singular method and apparatus for calibrating the extrinsic parameters of a lidar and inertial measurement unit. Background Technology

[0002] Currently, extrinsic parameter calibration between LiDAR and inertial measurement unit (IMU) is crucial for mobile robots. Essentially, it involves precisely aligning the high-precision, absolute environmental geometry information provided by the LiDAR point cloud with the high-frequency, relative motion information provided by the IMU in both space and time. Only through accurate extrinsic parameter calibration can the two be fused in a unified coordinate system. This allows the high-frequency data from the IMU to compensate for LiDAR scanning motion distortion, while the absolute observations from the LiDAR correct for the cumulative drift error of the IMU. This provides stable, continuous, and accurate state estimation for the robot's navigation and control system, which is the cornerstone of reliable autonomous movement. Without accurate extrinsic parameters, the advantages of multi-sensor fusion cannot be realized, and the overall system performance will deteriorate drastically.

[0003] As one of the main solutions to the extrinsic parameter calibration problem between lidar and inertial measurement units (IMU), discrete-time pose estimation (DST) has been proposed by many scholars. Its task is to solve for a 4th-order square matrix, simply called the "extrinsic parameter matrix." The 3x3 matrix in the upper left corner is called the attitude matrix, the vector formed by the elements in the first four columns and three rows is called the position matrix, and the elements in the fourth row are all known quantities, in the order of 0, 0, 0, 1. Currently, there are two main solutions to this extrinsic parameter calibration problem: numerical solutions and analytical solutions. Since numerical solutions heavily depend on the initial conditions, their accuracy and speed are difficult to guarantee. Therefore, analytical algorithms for lidar and IMU extrinsic parameter calibration remain an important research focus for many scholars. As a typical representative of analytical algorithms, D. Condurache et al. introduced dual orthogonal tensors into lidar and IMU extrinsic parameter calibration and proposed an analytical algorithm based on the singular value decomposition theory of matrices. However, since this method requires solving the inverse of a constructed coefficient matrix, experiments have shown that when the attitude matrix has small noise or the displacement vector has errors, the condition number of the coefficient matrix becomes very large, causing the inverse of the coefficient matrix to be almost ill-conditioned. This leads to the non-uniqueness of the analytical solution of the extrinsic parameter matrix or the amplification of errors, resulting in errors in the calibration results and seriously affecting the calibration accuracy and robustness. Summary of the Invention

[0004] In order to solve the above-mentioned technical problems, or at least partially solve the above-mentioned technical problems, and in view of the above-mentioned shortcomings, the present invention provides a non-singular method and apparatus for calibrating the extrinsic parameters of lidar and inertial measurement units.

[0005] In a first aspect, the present invention provides a method for non-singular extrinsic calibration of lidar and inertial measurement unit external parameters, comprising:

[0006] In a static indoor environment with no moving objects, during the full movement of the lidar and inertial measurement unit (IMU) carriers, J sets of extrinsic parameter calibration data between the lidar and IMU, with their relative poses remaining constant, are collected. These data include the relative homogeneous coordinate transformation matrix of the lidar between two moments in the world coordinate system. Homogeneous coordinate transformation matrix between adjacent moments of motion of the inertial measurement unit in its own coordinate system , ;

[0007] Random sampling group I and Obtain the homogeneous coordinate transformation matrix Homogeneous coordinate transformation matrix The corresponding dual orthogonal tensor; construct the homogeneous coordinate transformation matrix. Homogeneous coordinate transformation matrix The dual vector of the corresponding dual orthogonal tensor ;

[0008] Based on the dual vectors corresponding to the two homogeneous coordinate transformation matrices and The number of measurement data sets with non-parallel rotation axes is detected; if there are at least 3 sets of measurement data sets with non-parallel rotation axes, the dual vector is used as the basis for further analysis. and Construct dual orthogonal matrices :

[0009] ;

[0010] Dual orthogonal matrix transpose Singular value decomposition yields dual orthogonal tensors and dual orthogonal tensors : , It is a dual orthogonal tensor;

[0011] With 1,1 and dual orthogonal tensors and The determinant of the product is used to construct a 3x3 diagonal matrix from the diagonal elements. Then, the diagonal matrix is ​​compared with the dual orthogonal tensor. and The product matrix of the three components yields the dual orthogonal tensor corresponding to the estimated extrinsic parameter matrix between the lidar and the inertial measurement unit. The estimated extrinsic parameter matrix between the lidar and the inertial measurement unit is obtained by the inverse transformation based on the mapping relationship between the dual orthogonal tensor and the extrinsic parameter matrix.

[0012] Furthermore, in a static indoor environment without any moving objects, a planar calibration plate of a set size is used. The calibration plate is placed stably in the set position in the indoor environment to ensure that the calibration plate remains absolutely still throughout the entire data acquisition process. The position of the calibration plate should ensure that the lidar can scan the calibration plate from multiple different angles and distances involved in the experiment. The world coordinate system is determined using the calibration plate.

[0013] Furthermore, if there are only two sets of measurement data with non-parallel rotation axes, obtain the dual vectors corresponding to the two sets of measurement data with non-parallel rotation axes: { , }and{ , A virtual dual vector is constructed based on two sets of dual vectors whose rotation axes are not parallel: To satisfy the condition that there are at least 3 sets of measurement data where the rotation axes are not parallel, construct a dual orthogonal matrix by combining existing and virtual dual vectors:

[0014] .

[0015] Furthermore, the homogeneous coordinate transformation matrix Dual orthogonal tensors Taking the logarithm and then taking the column vectors corresponding to the skew-symmetric matrix yields its dual vector. : Homogeneous coordinate transformation matrix Dual orthogonal tensors Taking the logarithm and then taking the column vectors corresponding to the skew-symmetric matrix yields its dual vector. : ; This is the operator for taking the column vector corresponding to a skew-symmetric matrix.

[0016] Furthermore, if the extrinsic parameter matrix The corresponding dual orthogonal tensor Dual orthogonal tensor calibration equations A feasible solution, based on the dual transitivity theorem, is the extrinsic parameter matrix. The corresponding dual orthogonal tensor Dual vector equations A feasible solution will be the dual vector equation If the dual vector and dual orthogonal tensor in the vector are replaced by linear vectors and orthogonal tensors in Euclidean space respectively, then... The corresponding equation in the linear space is: ;in, , dual vector The real part of represents the unit direction vector of the lidar rotation axis under noisy conditions; , dual vector The real part of represents the unit direction vector of the rotation axis of the inertial measurement unit under noisy conditions. for The corresponding rotation matrix, ,satisfy , ;untie Corresponding equation in linear space Based on The solution and dual transitivity theorem lead to the solution in the dual space. The solution is obtained by:

[0017] With 1,1 and dual orthogonal tensors and The determinant of the product is used to construct a 3x3 diagonal matrix from the diagonal elements. Then, the diagonal matrix is ​​compared with the dual orthogonal tensor. and The product matrix of the three components yields the dual orthogonal tensor corresponding to the estimated extrinsic parameter matrix between the lidar and the inertial measurement unit.

[0018] Furthermore, to solve The cost function is:

[0019] ;

[0020] According to the linear minimum theory, the optimal solution of the cost function is:

[0021] ;

[0022] In the formula, and as well as Both are composed of dual orthogonal matrices The singular value decomposition is obtained, i.e. Dual orthogonal matrix From vector group as well as Build: ;

[0023] , ;

[0024] in, To construct a pure diagonal matrix by sequentially using the elements of a vector as the main diagonal elements, and It is the adjusted matrix, ensuring It is a true rotation matrix;

[0025] When the formula is obtained After solving the problem, the formula is derived based on the dual transitivity theorem. Solution:

[0026] When at least 3 sets of measurement data show that the rotation axes are not parallel The solution is:

[0027] ;

[0028] Dual orthogonal matrix transpose Dual orthogonal tensors obtained by performing singular value decomposition and dual orthogonal tensors : ;

[0029] and .

[0030] Furthermore, when there are only two sets of measurement data with non-parallel rotation axes, an additional virtual dual vector is introduced to construct a dual orthogonal matrix. Then on Solution:

[0031] ;

[0032] Dual orthogonal matrix The introduced virtual dual vector: , { , }and{ , } represents measurement data for two sets of non-parallel rotation axes;

[0033] ;

[0034] Dual orthogonal matrix transpose Dual orthogonal tensors obtained by performing singular value decomposition and dual orthogonal tensors : ;

[0035] and .

[0036] Furthermore, translation error metrics and rotation error metrics are constructed; the translation error metric is expressed as follows:

[0037] ;

[0038] in, This is the translation vector in the estimated extrinsic parameter matrix of this application. The actual translation vector of the extrinsic parameter matrix;

[0039] The rotational error metric is expressed as follows:

[0040] ;

[0041] Where logm is the matrix logarithm operator. Refers to the Frobenius norm operator. The matrix inversion operator. These are the homogeneous coordinate transformation matrices. and The rotation matrix part, It is the rotated part of the solved extrinsic parameter matrix;

[0042] Evaluation is conducted using translation error metrics and rotation error metrics.

[0043] Secondly, the present invention provides a singularity-free device for extrinsic parameter calibration of lidar and inertial measurement unit, comprising: at least one set of processing units, wherein the processing units are connected to a storage unit via a bus unit, the storage unit stores a computer program, and the processing units implement the singularity-free method for extrinsic parameter calibration of lidar and inertial measurement unit by running the computer program stored in the storage unit.

[0044] Thirdly, the present invention provides a computer-readable storage medium storing a computer program, which, when executed, implements the non-singularity method for extrinsic parameter calibration of the lidar and inertial measurement unit.

[0045] The technical solutions provided in the embodiments of the present invention have the following advantages compared with the prior art:

[0046] This invention addresses the inherent singularity flaw in the analytical solution method for extrinsic parameter calibration proposed by D. Condurache based on dual orthogonal tensor parameters, proposing a singularity-free method for extrinsic parameter calibration between lidar and inertial measurement units. This invention decomposes the problem using the duality transitivity theorem, avoiding ill-conditioned problems in direct decomposition of dual tensors and D. Condurache's singularity, thus improving the security of extrinsic parameter calibration between robot lidar and inertial measurement units based on dual orthogonal tensor parameters. Attached Figure Description

[0047] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0048] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0049] Figure 1 A flowchart illustrating a singularity-free method for calibrating extrinsic parameters of a lidar and inertial measurement unit, provided as an embodiment of the present invention;

[0050] Figure 2 A schematic diagram showing the comparison of rotation error values ​​of the estimated extrinsic parameter matrix;

[0051] Figure 3 A schematic diagram showing the comparison of translation error values ​​of the estimated extrinsic parameter matrix;

[0052] Figure 4 This is a schematic diagram of a singular device for calibrating the external parameters of a lidar and inertial measurement unit provided in an embodiment of the present invention. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0055] To clearly illustrate the content of this application, firstly, the analytical solution method for extrinsic parameter calibration between lidar and inertial measurement unit proposed by D. Condurache is analyzed, and for the first time, it is pointed out that there is an inherent defect of singularity in some cases.

[0056] During multiple movements, the homogeneous coordinate transformation matrix between the lidar coordinate system and the inertial measurement unit coordinate system is acquired between two adjacent movements. and Then the equivalent equation for the external parameter calibration problem between the lidar and the inertial measurement unit is: .in, The unknown extrinsic parameter matrix between the lidar and the inertial measurement unit represents the relative pose between the lidar and the inertial measurement unit.

[0057] The goal is to utilize the measured data through multiple movements (i=1,2,…,N). and Seeking a solution .

[0058] To simplify the solution process, since there is an invertible mapping between the dual orthogonal tensor and the homogeneous coordinate transformation matrix, the equivalent equation for the external parameter calibration problem between the lidar and the inertial measurement unit is derived. The homogeneous coordinate transformation matrix in the equation is described using a dual orthogonal tensor, which gives us the dual orthogonal tensor calibration equation:

[0059] ;

[0060] in, , as well as In order , as well as The corresponding dual orthogonal tensor , , This is the dual orthogonal tensor operator for taking the pose matrix. A dual orthogonal tensor can simultaneously represent rotation and translation, where the real part corresponds to rotation and the imaginary part corresponds to translation.

[0061] According to D. Condurache's analytical method for extrinsic parameter calibration, if N sets of measurement data are given... and The condition is met if and only if at least two of the N sets of data contain data whose rotation axes are not parallel. Only then can the following unique solution be found:

[0062] ;

[0063] In the formula, This is the tensor product operator; for The dual vector, ; , , ; For obtaining the logarithmic operator of dual orthogonal tensors, The operator for retrieving the column vector of a skew-symmetric matrix. For inverting dual orthogonal tensors, The adjoint operator for dual orthogonal tensors.

[0064] Solve for the extrinsic parameter matrix The corresponding dual orthogonal tensor Then, the extrinsic parameter matrix can be obtained by inverting the dual orthogonal tensors. : .

[0065] Equation is valid only if the measurement data is free from external noise interference. Only then can it be established.

[0066] For noisy data, D. Condurache proposed an extrinsic parameter matrix based on SVD decomposition filtering. Solution methods include:

[0067] Solve Then, external parameter matrix The corresponding dual orthogonal tensor Perform singular value decomposition: ;

[0068] in, The singular value decomposition yields dual orthogonal tensors. as well as , It is a diagonal matrix.

[0069] To ensure It is an effective rotation matrix, utilizing The singular value decomposition results are adjusted as follows to ensure The determinant is 1:

[0070] ;

[0071] In the formula, This is the determinant operator for matrices;

[0072] according to The effective extrinsic parameter matrix is ​​calculated as follows: .

[0073] To explain the inherent singularity of the calibration analytical solution algorithm proposed by D. Condurache, we will focus on the case where "only the translation column vector of the measured data has an error, while its rotation part has no error".

[0074] When only the translation column vector of the measured data has an error, while its rotation part has no error, let... The given optimal solution is From the properties of dual orthogonal tensors, we know that... middle rotation matrix and The real part is only with as well as The rotation matrix is ​​related to the rotation matrix but not to the translation vectors of either, since the optimal solution If the real part is determined solely by the rotated portion of the external measurement data, then the optimal solution... The real part will be a strictly rotation matrix (noise-free), satisfying ;

[0075] in, The operator for retrieving the real part of the dual orthogonal tensor. The transpose operator for taking dual orthogonal tensors. It is a third-order identity matrix.

[0076] According to the dual tensor singular value decomposition theory, for The first step in performing singular value decomposition is to... Perform eigenvalue decomposition. The eigenvalues ​​and eigenvectors of can be given by the following equations.

[0077]

[0078]

[0079] Even numbers With dual vector Representing orthogonal dual tensors The eigenvalues ​​and eigenvectors.

[0080] Will Substitution We can obtain, ;

[0081] It can be further rewritten as ;

[0082] because If the vector is a unit-length column vector, then if and only if , Established;

[0083] Will Substitution We can obtain,

[0084] ,

[0085] ;

[0086] In the formula, The operator for extracting the imaginary part of the dual orthogonal tensor; obviously, the matrix The rank of the expression is equal to 1. The condition number of the coefficient matrix of the defined linear system of equations will tend to infinity, therefore there is no solution. The eigenvalue decomposition is incorrect, which leads to an error in the optimal solution. The occurrence of singularities demonstrates the singularity of the extrinsic calibration method proposed by D. Condurache.

[0087] Example 1

[0088] like Figure 1 As shown, to address the singularity problem in the extrinsic calibration solution of D. Condurache, this invention provides a non-singularity method for extrinsic calibration of lidar and inertial measurement units. This method mainly includes the following steps:

[0089] A non-singular method for calibrating the extrinsic parameters of a lidar and inertial measurement unit, such as... Figure 1 As shown, the method mainly includes the following steps:

[0090] S10: Collect paired extrinsic parameter calibration data between the lidar and inertial measurement unit (IMU) of group J, maintaining a constant relative pose. This includes the relative homogeneous coordinate transformation matrix of the lidar between two time points in the "world coordinate system". Homogeneous transformation matrix values ​​between adjacent moments of motion of the inertial measurement unit in its own coordinate system , .

[0091] S101: The lidar and inertial measurement unit are rigidly fixed to the same fixed structure of the mobile robot to ensure that the relative pose X between the lidar and the inertial measurement unit, i.e. the external parameter matrix to be determined, remains absolutely unchanged throughout the entire process.

[0092] Using a synchronization cable, the master device (such as a computer or LiDAR) sends a synchronization pulse signal to the inertial measurement unit, ensuring that each LiDAR scan frame and inertial measurement unit data packet has a timestamp accurate to the microsecond level.

[0093] S102: Select a static indoor environment without moving objects for the experiment to avoid interference from irrelevant point clouds. Use a planar calibration plate of a predetermined size and place it stably in the designated location within the indoor environment. Ensure that the calibration plate remains absolutely stationary throughout the data acquisition process, and that its position allows the lidar to scan the calibration plate from multiple different angles and distances involved in the experiment. The calibration plate is used to determine the world coordinate system of the lidar.

[0094] S103: Control the mobile robot equipped with a LiDAR and inertial measurement unit to perform full and large-amplitude 3D movements around the calibration board, saving the LiDAR point cloud sequence and inertial measurement unit data sequence synchronized with all timestamps. Filter each frame of the acquired LiDAR point cloud to remove outliers and irrelevant distant points. Calculate the relative homogeneous coordinate transformation matrix of the LiDAR between two moments in the "world coordinate system (determined by the calibration board)" using the planar parameters fitted to the point cloud. This refers to the position and attitude of the lidar in the "world coordinate system." The raw data from the acquired inertial measurement units (IMUs) are denoised and zero-biased. Using the lidar's frame rate as the time node, the moment when pose calculation is required is determined. For two consecutive lidar point cloud frames, all IMU data within this time interval are extracted and aligned with the lidar point cloud frame timestamps. This yields the homogeneous coordinate transformation matrix value between adjacent moments in the IMU's own coordinate system. .

[0095] S20: Randomly select group I from the above group J external parameter calibration data. and ( Based on the mapping relationship between the homogeneous coordinate transformation matrix and the dual orthogonal tensor, the homogeneous coordinate transformation matrix of the lidar between two adjacent motions is solved. The corresponding dual orthogonal tensor The homogeneous coordinate transformation matrix of the inertial measurement unit between two adjacent motions The corresponding dual orthogonal tensor value ;

[0096] Based on this, construct the dual orthogonal tensor values ​​of the two homogeneous coordinate transformation matrices. and The corresponding dual vector. Specifically, the homogeneous coordinate transformation matrix. Dual orthogonal tensors Taking the logarithm and then taking the column vectors corresponding to the skew-symmetric matrix yields its dual vector. : Homogeneous coordinate transformation matrix Dual orthogonal tensors Taking the logarithm and then taking the column vectors corresponding to the skew-symmetric matrix yields its dual vector. : .

[0097] S30: Dual orthogonal tensor values ​​based on two homogeneous coordinate transformation matrices and The corresponding dual vector and The number of non-parallel rotating axes detected and measured.

[0098] If there are at least 3 sets of measurement data with non-parallel rotation axes, construct a dual orthogonal matrix based on the dot product rule of dual vectors:

[0099] ;

[0100] If there are only two sets of measurement data where the rotation axes are not parallel, let { , }and{ , When dealing with two sets of measurement data whose rotation axes are not parallel, a virtual dual vector with non-parallel rotation axes is constructed based on the cross product rule of dual vectors: To satisfy the condition that there are at least 3 sets of measurement data where the rotation axes are not parallel, a dual orthogonal matrix is ​​constructed by combining existing and new virtual dual vectors:

[0101] .

[0102] S40: The dual orthogonal matrix obtained from S30 Based on the transpose theorem of dual orthogonal tensors, we obtain the dual orthogonal matrix. transpose And by using the singular value decomposition theory of dual orthogonal tensors, the transpose dual orthogonal matrix is... Perform singular value decomposition. Among them, the dual orthogonal tensors obtained by singular value decomposition The column dual vectors form a set of orthogonal dual bases for the output space, and the dual orthogonal tensors obtained from singular value decomposition... The column dual vectors form a set of orthogonal dual bases in the input space, and the dual orthogonal tensors... The diagonal elements are, in order, the transpose dual orthogonal matrices. The singular values ​​of .

[0103] S50: with 1, 1 and dual orthogonal tensor and Determinant value of the product Construct a 3x3 diagonal matrix for the diagonal elements This diagonal matrix and its dual orthogonal tensor and The product matrix of the three components yields the dual orthogonal tensor corresponding to the estimated extrinsic parameter matrix between the lidar and the inertial measurement unit. ,Right now:

[0104] ;

[0105] in, This refers to the dual orthogonal tensor corresponding to the estimated extrinsic parameter matrix between the lidar and the inertial measurement unit.

[0106] S60: The dual orthogonal tensor corresponding to the estimated external parameter matrix between the lidar and the inertial measurement unit obtained from S50. The analytical solution for the unknown extrinsic matrix of the lidar and inertial measurement unit is obtained by inverse transformation based on the mapping relationship between the dual orthogonal tensor and the extrinsic parameter matrix: .

[0107] This application will be compared and evaluated with the D. Condurache solution:

[0108] To evaluate the accuracy of the extrinsic parameter matrix estimates, this application introduces the following translation error metrics and rotation error metrics.

[0109] The translation error metric is expressed as follows:

[0110] ;

[0111] in, This is the translation vector in the estimated extrinsic parameter matrix of this application. The actual translation vector of the extrinsic parameter matrix;

[0112] The rotational error metric is expressed as follows:

[0113] ;

[0114] Where logm is the matrix logarithm operator. Refers to the Frobenius norm operator. The matrix inversion operator. These are the homogeneous coordinate transformation matrices. and The rotation matrix part, It is the rotated part of the solved extrinsic parameter matrix.

[0115] Record the analytical solution of the unknown extrinsic parameter matrix of the lidar and inertial measurement unit in this application. The corresponding translation error value and the logarithmic value of rotational error .

[0116] Then, the dual orthogonal tensor values ​​corresponding to the pose matrix between the lidar and the inertial measurement unit selected in S20 are... and ( Substitute the values ​​into the extrinsic parameter calibration method proposed by D. Condurache to obtain the analytical solution, and obtain the corresponding translation error value and rotation error constant logarithmic value based on the translation metric and rotation metric.

[0117] like Figure 2 and Figure 3 As shown, the rotation and translation errors of the extrinsic parameter matrices of 150 sets of analytical solutions of this application and the D. Condurache scheme were obtained.

[0118] Preferred, by Figure 2 It can be seen that although the rotation error values ​​given by D. Condurache's solution are all higher than those of the solution proposed in this application, both are very small (less than 10). -11 This is within the normal range. However, due to... Figure 3 Therefore, for the 150 sets of simulation results mentioned above, the translation error values ​​of the unknown extrinsic parameter matrix estimates given by D. Condurache are all very large, while the translation error values ​​corresponding to the solutions proposed in this application are all very small (within the normal range). Thus, the extrinsic parameter calibration solution for the lidar and inertial measurement unit proposed in this paper will not exhibit singularities, while D. Condurache's solution will definitely exhibit singularities, thereby verifying the singularity of the solution proposed by D. Condurache and the correctness of the extrinsic parameter calibration solution for the lidar and inertial measurement unit proposed in this application.

[0119] The principle of this application is as follows:

[0120] Based on the duality transitivity theorem, this application proposes a singularity-free method for calibrating the extrinsic parameters of lidar and inertial measurement units. The duality transitivity theorem states that "for all formulas and theorems determined by the unit concurrent vectors in a linear space, if the unit concurrent vectors in the linear space are replaced with the unit dual vectors in the dual space, then all the above formulas and theorems still hold."

[0121] Therefore, based on the duality transitivity theorem, if the extrinsic parameter matrix... The corresponding dual orthogonal tensor Dual orthogonal tensor calibration equations A feasible solution is then the extrinsic parameter matrix. The corresponding dual orthogonal tensor Dual vector equations A feasible solution if the dual vector equations If the dual vector and dual orthogonal tensor in the equation are replaced by linear vectors and orthogonal tensors in Euclidean space, respectively, then... The corresponding equation in the linear space is: .in, , dual vector The real part of represents the unit direction vector of the lidar rotation axis under noisy conditions; , dual vector The real part of represents the unit direction vector of the rotation axis of the inertial measurement unit under noisy conditions. for The corresponding rotation matrix, ,satisfy , .

[0122] Referring to the duality transitivity theorem, the dual vector equations The necessary and sufficient condition for a solution is that, Corresponding equation in Euclidean space There is a solution. Therefore, if you want to obtain... To find the solution, the following two steps are required:

[0123] Let's solve it first. Corresponding equation in linear space ;

[0124] Based on The solution and dual transitivity theorem lead to the solution in the dual space. The solution.

[0125] Solve Equivalent to, given I vector groups as well as Find a rotation matrix This makes the vector group In the rotation matrix Under the action of the vector group, it moves to the vector group The cost function for the best overlap or degree of overlap is:

[0126] ;

[0127] According to the linear minimization theory, the optimal solution that minimizes the cost function is:

[0128] ;

[0129] In the formula, and as well as Both are composed of dual orthogonal matrices The singular value decomposition is obtained, i.e. Dual orthogonal matrix From vector group as well as Build: ;

[0130] , ;

[0131] in, To construct a pure diagonal matrix by sequentially using the elements of a vector as the main diagonal elements, and It is the adjusted matrix, ensuring It is a true rotation matrix (determinant is 1).

[0132] When the formula is obtained After solving the problem, based on the duality transitivity theorem, the formula can be directly derived. The solution.

[0133] Given the formula The necessary and sufficient condition for a unique solution is that at least two sets of measurement data with non-parallel rotation axes are required. Therefore, we will discuss the following two cases:

[0134] There are at least 3 sets of measurement data where the rotation axes are not parallel. The solution is:

[0135] ;

[0136] Dual orthogonal matrix transpose Dual orthogonal tensors obtained by performing singular value decomposition and dual orthogonal tensors : The dual orthogonal matrix The dual orthogonal tensor values ​​based on two homogeneous coordinate transformation matrices and The corresponding dual vector and Calculation yielded: ;

[0137] and ;

[0138] With only two sets of measurement data where the rotation axes are not parallel, an additional virtual dual vector is introduced to construct a dual orthogonal matrix. :

[0139] ;

[0140] Dual orthogonal matrix The introduced virtual dual vector is: , .

[0141] The estimated value of the extrinsic parameter matrix between the lidar and the inertial measurement unit is obtained by inverse transformation based on the mapping relationship between the dual orthogonal tensor and the extrinsic parameter matrix:

[0142] .

[0143] Example 2

[0144] See Figure 4 As shown, this embodiment of the invention provides a singularity-free device for extrinsic parameter calibration of a lidar and inertial measurement unit, comprising: at least one set of processing units, wherein the processing units are connected to a storage unit via a bus unit, and the storage unit serves as a computer-readable storage medium for storing software programs, computer-executable programs, and modules, such as the software program, computer-executable program, and module corresponding to a singularity-free extrinsic parameter calibration method for a lidar and inertial measurement unit according to this embodiment of the invention. The processing units implement the aforementioned singularity-free extrinsic parameter calibration method for a lidar and inertial measurement unit by running the software program, computer-executable program, and module stored in the storage unit, including:

[0145] In a static indoor environment with no moving objects, during the full movement of the lidar and inertial measurement unit (IMU) carriers, J sets of extrinsic parameter calibration data between the lidar and IMU, with their relative poses remaining constant, are collected. These data include the relative homogeneous coordinate transformation matrix of the lidar between two moments in the world coordinate system. Homogeneous coordinate transformation matrix between adjacent moments of motion of the inertial measurement unit in its own coordinate system , ;

[0146] Random sampling group I and Obtain the homogeneous coordinate transformation matrix Homogeneous coordinate transformation matrix The corresponding dual orthogonal tensor; construct the homogeneous coordinate transformation matrix. Homogeneous coordinate transformation matrix The dual vector of the corresponding dual orthogonal tensor ;

[0147] Based on the dual vectors corresponding to the two homogeneous coordinate transformation matrices and The number of measurement data sets with non-parallel rotation axes is detected; if there are at least 3 sets of measurement data sets with non-parallel rotation axes, the dual vector is used as the basis for further analysis. and Construct dual orthogonal matrices :

[0148] ;

[0149] Dual orthogonal matrix transpose Singular value decomposition yields dual orthogonal tensors and dual orthogonal tensors : , It is a dual orthogonal tensor;

[0150] With 1,1 and dual orthogonal tensors and The determinant of the product is used to construct a 3x3 diagonal matrix from the diagonal elements. Then, the diagonal matrix is ​​compared with the dual orthogonal tensor. and The product matrix of the three components yields the dual orthogonal tensor corresponding to the estimated extrinsic parameter matrix between the lidar and the inertial measurement unit. The estimated extrinsic parameter matrix between the lidar and the inertial measurement unit is obtained by the inverse transformation based on the mapping relationship between the dual orthogonal tensor and the extrinsic parameter matrix.

[0151] Of course, the computer program stored in the storage unit of the non-singularity calibration device for lidar and inertial measurement unit provided in the embodiments of the present invention is not limited to the method operation described above, and can also execute related operations in the non-singularity calibration method for lidar and inertial measurement unit provided in any embodiment of the present invention.

[0152] Example 3

[0153] This invention provides a computer-readable storage medium storing a computer program. When executed, the computer program implements the singularity-free extrinsic calibration method for lidar and inertial measurement unit, comprising:

[0154] In a static indoor environment with no moving objects, during the full movement of the lidar and inertial measurement unit (IMU) carriers, J sets of extrinsic parameter calibration data between the lidar and IMU, with their relative poses remaining constant, are collected. These data include the relative homogeneous coordinate transformation matrix of the lidar between two moments in the world coordinate system. Homogeneous coordinate transformation matrix between adjacent moments of motion of the inertial measurement unit in its own coordinate system , ;

[0155] Random sampling group I and Obtain the homogeneous coordinate transformation matrix Homogeneous coordinate transformation matrix The corresponding dual orthogonal tensor; construct the homogeneous coordinate transformation matrix. Homogeneous coordinate transformation matrix The dual vector of the corresponding dual orthogonal tensor ;

[0156] Based on the dual vectors corresponding to the two homogeneous coordinate transformation matrices and The number of measurement data sets with non-parallel rotation axes is detected; if there are at least 3 sets of measurement data sets with non-parallel rotation axes, the dual vector is used as the basis for further analysis. and Construct dual orthogonal matrices :

[0157] ;

[0158] Dual orthogonal matrix transpose Singular value decomposition yields dual orthogonal tensors and dual orthogonal tensors : , It is a dual orthogonal tensor;

[0159] With 1,1 and dual orthogonal tensors and The determinant of the product is used to construct a 3x3 diagonal matrix from the diagonal elements. Then, the diagonal matrix is ​​compared with the dual orthogonal tensor. and The product matrix of the three components yields the dual orthogonal tensor corresponding to the estimated extrinsic parameter matrix between the lidar and the inertial measurement unit. The estimated extrinsic parameter matrix between the lidar and the inertial measurement unit is obtained by the inverse transformation based on the mapping relationship between the dual orthogonal tensor and the extrinsic parameter matrix.

[0160] The computer-readable storage medium provided in the embodiments of the present invention stores a computer program that is not limited to the method operation described above, but can also execute related operations in the non-singularity calibration method for external parameters of lidar and inertial measurement unit provided in any embodiment of the present invention.

[0161] In the embodiments provided by this invention, it should be understood that the disclosed structures and methods can be implemented in other ways. For example, the structural embodiments described above are merely illustrative. For instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection through some interfaces, structures, or units, and may be electrical, mechanical, or other forms.

[0162] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0163] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0164] The above description is merely a specific embodiment of the present invention, enabling those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A method for calibrating the extrinsic parameters of a lidar and inertial measurement unit without singularities, characterized in that, include: In a static indoor environment with no moving objects, during the full movement of the lidar and inertial measurement unit (IMU) carriers, J sets of extrinsic parameter calibration data between the lidar and IMU, with their relative poses remaining constant, are collected. These data include the relative homogeneous coordinate transformation matrix of the lidar between two moments in the world coordinate system. Homogeneous coordinate transformation matrix between adjacent moments of motion of the inertial measurement unit in its own coordinate system , ; Random sampling group I and Obtain the homogeneous coordinate transformation matrix Homogeneous coordinate transformation matrix The corresponding dual orthogonal tensor; construct the homogeneous coordinate transformation matrix. Homogeneous coordinate transformation matrix The dual vector of the corresponding dual orthogonal tensor ; Based on the dual vectors corresponding to the two homogeneous coordinate transformation matrices and The number of measurement data sets with non-parallel rotation axes is detected; if there are at least 3 sets of measurement data sets with non-parallel rotation axes, the dual vector is used as the basis for further analysis. and Construct dual orthogonal matrices : ； Dual orthogonal matrix transpose Singular value decomposition yields dual orthogonal tensors and dual orthogonal tensors : , It is a dual orthogonal tensor; With 1,1 and dual orthogonal tensors and The determinant of the product is used to construct a 3x3 diagonal matrix from the diagonal elements. Then, the diagonal matrix is ​​compared with the dual orthogonal tensor. and The product matrix of the three components yields the dual orthogonal tensor corresponding to the estimated extrinsic parameter matrix between the lidar and the inertial measurement unit. The estimated extrinsic parameter matrix between the lidar and the inertial measurement unit is obtained by the inverse transformation based on the mapping relationship between the dual orthogonal tensor and the extrinsic parameter matrix.

2. The non-singularity method for calibrating the extrinsic parameters of a lidar and inertial measurement unit according to claim 1, characterized in that, For a static indoor environment without moving objects, a flat calibration plate of a set size is used. The calibration plate is placed stably in the set position in the indoor environment to ensure that the calibration plate is absolutely stationary throughout the data acquisition process. The position of the calibration plate should ensure that the lidar can scan the calibration plate from multiple different angles and distances involved in the experiment. The world coordinate system is determined using the calibration plate.

3. The non-singularity method for calibrating the extrinsic parameters of a lidar and inertial measurement unit according to claim 1, characterized in that, If there are only two sets of measurement data with non-parallel rotation axes, obtain the dual vectors corresponding to the two sets of measurement data with non-parallel rotation axes: { , }and{ , A virtual dual vector is constructed based on two sets of dual vectors whose rotation axes are not parallel: To satisfy the condition that there are at least 3 sets of measurement data where the rotation axes are not parallel, construct a dual orthogonal matrix by combining existing and virtual dual vectors: 。 4. The non-singularity method for calibrating the extrinsic parameters of a lidar and inertial measurement unit according to claim 1, characterized in that, Homogeneous coordinate transformation matrix Dual orthogonal tensors Taking the logarithm and then taking the column vectors corresponding to the skew-symmetric matrix yields its dual vector. : Homogeneous coordinate transformation matrix Dual orthogonal tensors Taking the logarithm and then taking the column vectors corresponding to the skew-symmetric matrix yields its dual vector. : ; This is the operator for taking the column vector corresponding to a skew-symmetric matrix.

5. The non-singularity method for calibrating the extrinsic parameters of a lidar and inertial measurement unit according to claim 1, characterized in that, If the extrinsic parameter matrix The corresponding dual orthogonal tensor Dual orthogonal tensor calibration equations A feasible solution, based on the dual transitivity theorem, is the extrinsic parameter matrix. The corresponding dual orthogonal tensor Dual vector equations A feasible solution will be the dual vector equation If the dual vector and dual orthogonal tensor in the vector are replaced by linear vectors and orthogonal tensors in Euclidean space respectively, then... The corresponding equation in the linear space is: ;in, , dual vector The real part of represents the unit direction vector of the lidar rotation axis under noisy conditions; , dual vector The real part of represents the unit direction vector of the rotation axis of the inertial measurement unit under noisy conditions. for The corresponding rotation matrix, ,satisfy , ;untie Corresponding equation in linear space Based on The solution and dual transitivity theorem lead to the solution in the dual space. The solution is obtained by: With 1,1 and dual orthogonal tensors and The determinant of the product is used to construct a 3x3 diagonal matrix from the diagonal elements. Then, the diagonal matrix is ​​compared with the dual orthogonal tensor. and The product matrix of the three components yields the dual orthogonal tensor corresponding to the estimated extrinsic parameter matrix between the lidar and the inertial measurement unit.

6. The non-singularity calibration method for external parameters of lidar and inertial measurement units according to claim 5, characterized in that, Solve The cost function is: ； According to the linear minimum theory, the optimal solution of the cost function is: ； In the formula, and as well as Both are composed of dual orthogonal matrices The singular value decomposition is obtained, i.e. Dual orthogonal matrix From vector group as well as Build: ; ， ； in, To construct a pure diagonal matrix by sequentially using the elements of a vector as the main diagonal elements, and It is the adjusted matrix, ensuring It is a true rotation matrix; When the formula is obtained After solving the problem, the formula is derived based on the dual transitivity theorem. Solution: When at least 3 sets of measurement data show that the rotation axes are not parallel The solution is: ； Dual orthogonal matrix transpose Dual orthogonal tensors obtained by performing singular value decomposition and dual orthogonal tensors : ; and .

7. The non-singularity method for calibrating the extrinsic parameters of a lidar and inertial measurement unit according to claim 6, characterized in that, When there are only two sets of measurement data with non-parallel rotation axes, an additional virtual dual vector is introduced to construct a dual orthogonal matrix. Then on Solution: ； Dual orthogonal matrix The introduced virtual dual vector: , { , }and{ , } represents measurement data for two sets of non-parallel rotation axes; ； Dual orthogonal matrix transpose Dual orthogonal tensors obtained by performing singular value decomposition and dual orthogonal tensors : ; and .

8. The non-singularity method for calibrating the extrinsic parameters of a lidar and inertial measurement unit according to claim 1, characterized in that, Construct translation error metrics and rotation error metrics; wherein, the translation error metrics are expressed as: ； in, This is the translation vector in the estimated extrinsic parameter matrix of this application. The actual translation vector of the extrinsic parameter matrix; The rotational error metric is expressed as follows: ； Where logm is the matrix logarithm operator. Refers to the Frobenius norm operator. The matrix inversion operator. These are the homogeneous coordinate transformation matrices. and The rotation matrix part, It is the rotated part of the solved extrinsic parameter matrix; Evaluation is conducted using translation error metrics and rotation error metrics.

9. A singularity-free device for calibrating the extrinsic parameters of a lidar and inertial measurement unit, comprising: At least one set of processing units, wherein the processing units are connected to a storage unit and an acquisition unit via a bus unit, wherein the storage unit stores a computer program and data acquired by the acquisition unit, and the processing unit processes the acquired data by running the computer program stored in the storage unit, thereby implementing the non-singularity method for extrinsic parameter calibration of lidar and inertial measurement unit as described in any one of claims 1-8.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed, it implements the non-singularity method for extrinsic parameter calibration of lidar and inertial measurement unit as described in any one of claims 1-8.

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