CN111681279A - Driving suspension arm space pose measurement method based on improved lie group nonlinear optimization - Google Patents
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Abstract
The invention discloses a method for measuring the spatial pose of a crane jib based on improved lie group nonlinear optimization, which comprises the following steps: s1: acquiring four target points which are distributed in a rectangular shape by using a camera, and extracting four barycentric coordinates of an infrared cursor in an acquired image; s2: calibrating the internal and external parameters of the acquisition camera, determining an imaging center and a distortion coefficient, and correcting the image distortion parameters of the image acquired in the step S1; s3: converting the relative pose problem of the camera and the cooperative target into a minimized re-projection problem; s4: calculating an initial rotation matrix and translation amount of the relative pose of the camera by using an EPNP method; s5: and performing nonlinear iteration by using a Gauss-Newton method, and then finally converging to a real solution to obtain a rotation matrix and a translation amount. The invention not only improves the precision of the measurement result, but also improves the detection and calculation speed, can carry out rapid target detection and space parameter acquisition, and improves the real-time performance and the accuracy of the space angle measurement of the suspension arm of the unmanned vehicle.
Description
Technical Field
The invention relates to unmanned driving control of an industrial system, in particular to a method for measuring the spatial pose of a driving suspension arm.
Background
The unmanned traveling system is a complex system comprising a plurality of subsystems, and the anti-swing control system is one of the subsystems and is responsible for accurately controlling a traveling crane boom in the moving operation process and ensuring that a traveling crane can run stably. The premise of anti-swing control is to acquire real-time and accurate space pose parameters of the crane jib. At present, the difficulty of detecting the space angle parameters of the crane jib is that the crane jib needs to be acquired and calculated in real time and at high speed and then sent to a crane controller, so that efficient and rapid target detection and space parameter calculation are important. In the aspect of angle measurement, the angle measurement technology applied to unmanned vehicles mainly comprises the direct measurement of an inclinometer and the indirect measurement of a visual target. Compared with an inclinometer method, the method for visually measuring the swing angle of the crane jib has the advantages that the obtained data is more comprehensive and visual, and the optimization and calculation of an anti-swing control algorithm are facilitated. But in the real-time high-speed running process of the vehicle, the spatial pose parameters of the industrial crane jib are difficult to accurately measure.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects and shortcomings of the prior art, the invention provides a method for measuring the space pose of a crane jib based on improved lie group nonlinear optimization, the method can be used for quickly calculating the space pose parameters of the crane jib, and the problem that the space pose parameters of the industrial crane jib are difficult to accurately measure in real time is effectively solved.
The technical scheme is as follows: a method for measuring the spatial pose of a crane jib based on improved lie group nonlinear optimization comprises the following steps:
s1: a camera is adopted to collect a target point of a cooperative target, and the cooperative target is composed of four laser points which are distributed in a rectangular shape. Extracting four gravity center coordinates of an infrared cursor in the collected image;
s2: calibrating the internal and external parameters of the acquisition camera, determining an imaging center and a distortion coefficient, and correcting the image distortion parameters of the image acquired in the step S1;
s3: converting the relative pose problem of the camera and the cooperative target into a minimized re-projection problem;
s4: calculating an initial rotation matrix and a translation amount of the relative position of the camera by using an EPNP method;
s5: and performing nonlinear iteration by using a Gauss-Newton method, and then finally converging to a real solution to obtain a rotation matrix and a translation amount.
Further, in step S1, the process of extracting coordinates of four barycentric centers of the infrared cursor in the acquired image includes the following steps:
s11: performing mixed filtering operation on an original image, namely judging to adopt a method of combining Gaussian filtering and median filtering according to a set threshold value, and smoothing the image to eliminate noise;
s12: performing morphological binary open operation on the image by adopting an optimal threshold segmentation method, finding a connected domain and eliminating isolated noise points and burrs in the image background;
s13: and searching cursor connected domains in the image by adopting a gray scale gravity center method and solving gravity center coordinates one by one.
Further, the step S3 specifically includes the following steps:
s31: converting the relative pose problem of the camera and the cooperative target into a nonlinear optimization iteration, namely, minimizing the error between the real solution of the image coordinates and the image coordinates obtained in the step S1, as shown in the following formula:
2＝∑||qi′-f(M2Pi w)||2
in the formula (I), the compound is shown in the specification,2is an error term, q'iFor the coordinates of the measurement calibration point obtained in step S1,
as actual physical coordinates of the infrared cursor, M2A coordinate transformation matrix consisting of a rotation matrix and a translation quantity;
s32: the expression of step S31 is expressed by lie group method, i.e. rotation matrix and translation between camera coordinate and calibration object coordinate are expressed by lie algebra, ξ is a 6-dimensional vector, the first 3-dimensional represents translation, the last 3-dimensional represents rotation, i.e. 4 th order coordinate transformation matrix is expressed by ξ of 6-dimensional, the expression can be converted into:
xi is lie algebra and Λ is broadly expressed as "from vector to matrix".
Further, the step S4 specifically includes the following steps:
s41: representing three-dimensional control points of a cooperative target by a weighted sum of four virtual space coordinate points;
s42: calculating coordinates of the four virtual space points in a world coordinate system, converting the coordinates into a camera coordinate system by using a camera projection model, and calculating the coordinates in the camera coordinate system;
s43: and according to the 3D-3D matching, calculating a corresponding rotation matrix R and a corresponding translation amount t by adopting ICP (inductively coupled plasma), and taking the rotation matrix R and the translation amount t as initial values to be introduced into a lie group algorithm to carry out minimum optimization.
Further, the step S5 includes the following steps:
s51: find out
Calculating an advance as a Jacobian matrix and calculating an initial quantity as a subsequent Jacobian matrix, where A is
Is a kronecker product, wherein I in A is a unit matrix, R is a rotation matrix, and t is a translation amount;
s52: solving the derivative of the minimized re-projection error term about the optimization variable, namely linearizing the objective function under the K iteration, eliminating the secondary term information after first-order Taylor expansion, and iteratively converging the lie algebra left-times disturbance quantity exp (xi ^) to improve the convergence speed;
s53: merging the expression after the linearization expression in the step S52 and the nonlinear iterative error expression in the step S32, deriving the expression, performing vectorization calculation on the Jacobian matrix by using a Kernel product when solving the Jacobian matrix, and using the lead in the step S51 during each calculation;
s54, setting the derived expression obtained in the step S53 as 0, obtaining the variation lie algebra required by the next iteration, and setting the initial condition of the kth iteration as ξk、E(ξk) Substituting the following formula to obtain a lie algebra under the K +1 iteration;
exp(ξk∧)exp(Δξk∧)＝exp(ξk+1∧)
in the above formula, exp (^) represents a matrix index, ξkRepresenting lie algebra after the K iteration, ξk+1Represents the lie algebra, Δ, after the K +1 iterationξkRepresenting the variation of lie algebra;
s55 update f (exp (ξ)k+1∧）Ｐi w) Obtain new E (ξ)k+1) And judging whether a convergence termination condition is reached, if so, terminating the iteration, and if not, repeating S52 to S54 until the convergence reaches a true value.
Has the advantages that: the invention discloses a method for improving nonlinear optimization of a lie group and measuring the spatial pose of a crane jib. According to the method, through the corresponding relation between the geometric positions of the infrared coplanar four-point cursors and the imaging projection, the spatial pose parameters are solved by using a nonlinear optimization iteration method based on the lie group, and then the spatial pose parameters are converted into the attitude quantities of the four suspension arm models, so that the spatial pose parameters of the crane suspension arm can be rapidly calculated, and the real-time performance of the spatial pose parameter measurement of the industrial crane suspension arm is improved.
Drawings
FIG. 1 is a flow chart of an algorithm for solving spatial pose parameters in an embodiment of the present invention;
FIG. 2 is a block diagram of a monocular vision measuring system;
fig. 3 is a graph of the iterative error drop for the improved lie group.
Detailed Description
The technical solution of the present invention will be further described with reference to the following detailed description and accompanying drawings.
Referring to fig. 1 and 2, the present embodiment discloses a method for measuring a crane jib spatial pose with improved lie group nonlinear optimization, comprising the following steps:
and step S1, a camera is adopted to collect a target point of the cooperation target, and the cooperation target is composed of four laser points which are distributed in a rectangular shape. And extracting the barycentric coordinates of the light spots of the collected image infrared cursor by using a gray scale barycentric method. The process of solving the barycentric coordinate of the infrared cursor in the collected image comprises the following steps:
s11: the mixed filtering operation is firstly carried out on the original image, namely, the method of combining Gaussian filtering and median filtering is adopted according to the set threshold value judgment, and the image is subjected to smoothing processing to eliminate noise.
Specifically, based on the characteristics of mixed noise, a noise model in a filtering window is judged first, the variance of pixels in the window is calculated, if the variance is larger than a preset threshold, the window is polluted by salt and pepper noise, median filtering is needed, and otherwise, Gaussian filtering is directly performed.
S12: and (3) adopting an optimal threshold segmentation method, taking 30 of the nearest distance between two peaks, carrying out morphological binary open operation on the image, finding a connected domain and eliminating isolated noise points and burrs in the image background.
S13: and searching cursor connected domains in the image by adopting a gray scale gravity center method and solving gravity center coordinates one by one.
Specifically, by adopting a gray scale gravity center method, only a circular ring part of a light spot from an edge to a certain position in a circle is obtained to search cursor connected domains in an image and gradually obtain gravity center coordinates, through a previous gray scale threshold segmentation method, a lower limit value of the gray scale of the circular ring can be determined, namely, a gray scale value of the edge of the light spot is used as Thresh1, and a maximum light intensity amplitude value of the gray scale distribution of the light spot can be found to be H, so that the upper limit Thresh2 can be obtained by the following formula:
Thresh2＝H-tc
wherein, tcIs a value that can be changed appropriately for light intensity. The barycentric coordinate standard deviation can be controlled to be within 0.1 pixel.
Step S2, calibrating the internal and external parameters of the acquisition camera, determining the imaging center, calculating the radial distortion coefficient by adopting two-step calibration, and correcting the image distortion parameter of the image acquired in the step S1;
step S3, transforming the relative pose problem of the camera and the cooperative target into a minimized reprojection problem, specifically including the steps of:
s31: converting the relative pose problem of the camera and the cooperative target into a nonlinear optimization iteration, namely, minimizing the error between the real solution of the image coordinates and the image coordinates obtained in the step S1, as shown in the following formula:
2＝∑||q′i-f(M2Pi w)||2
in the formula (I), the compound is shown in the specification,2is an error term，q′iFor the coordinates of the measurement calibration point obtained in step S1,
as actual physical coordinates of the infrared cursor, M2A coordinate transformation matrix consisting of rotation matrix and translation amount, f represents image coordinate with respect to M2And
the functional relationship of (a);
s32: the expression of step S31 is expressed by lie group method, i.e. rotation matrix and translation between camera coordinate and calibration object coordinate are expressed by lie algebra, ξ is a 6-dimensional vector, the first 3-dimensional represents translation, the last 3-dimensional represents rotation, i.e. 4 th order coordinate transformation matrix is expressed by ξ of 6-dimensional, the expression can be converted into:
xi is lie algebra and Λ is broadly expressed as "from vector to matrix".
Step S4, calculating the initial rotation matrix and translation of the relative pose of the camera by using an EPNP method, which comprises the following steps:
s41: the three-dimensional control point of a cooperative target is represented by a weighted sum of four virtual coordinate points in space, which is specifically represented as follows:
wherein, Pi wRepresenting the coordinates of a three-dimensional control point,
as virtual space point coordinates, αijAnd (3) the uniquely determined mean barycentric coordinate satisfies the following conditions:
s42: calculating coordinates of the four virtual space points in a world coordinate system, converting the coordinates into a camera coordinate system by using a camera projection model, and calculating the coordinates in the camera coordinate system;
s43: and according to the matching of 3D and 3D, calculating a corresponding rotation matrix R and a corresponding translation quantity T by adopting ICP (inductively coupled plasma), and taking the rotation matrix R and the translation quantity T as initial values to be introduced into a lie group algorithm to carry out minimum optimization.
Step S5, carrying out nonlinear iteration by using a Gauss Newton method, and then finally converging to a real solution to obtain a rotation matrix and a translation amount, wherein the method specifically comprises the following steps:
s51: find out
Calculating an advance as a Jacobian matrix and calculating an initial quantity as a subsequent Jacobian matrix, where A is
Is a kronecker product, wherein I in A is a unit matrix, R is a rotation matrix, and t is a translation amount;
s52: solving the derivative of the minimized re-projection error term about the optimization variable, namely linearizing the objective function under the K iteration, eliminating the secondary term information after first-order Taylor expansion, and iteratively converging the lie algebra left-times disturbance quantity exp (xi ^) to improve the convergence speed;
s53: merging the expression after the linearization expression in the step S52 and the nonlinear iteration error expression in the step S32, deriving the expression, performing vectorization calculation on the Jacobian matrix by using a Kernel product when solving the Jacobian matrix, and using the lead in the step S51 during each calculation;
s54, setting the derived expression obtained in the step S53 as 0, obtaining the variation lie algebra required by the next iteration, and setting the initial condition of the kth iteration as ξk、E(ξk) And (4) obtaining a lie algebra under the K +1 iteration after the following formula is substituted:
exp(ξk∧)exp(Δξk∧)＝exp(ξk+1∧)
in the above formula, exp (^) represents a matrix index, ξkRepresenting lie algebra after the K iteration, ξk+1Denotes the lie algebra after the K +1 iteration, Δ ξkRepresenting the variation of lie algebra;
s55 update f (exp (ξ)k+1∧)Pi w) Obtain new E (ξ)k+1) And judging whether a convergence termination condition is reached, if so, terminating iteration, otherwise, repeating the steps from S52 to S54 until the convergence reaches a true value, generally requiring 6 steps of iteration, and increasing the speed by about 3 ms.
In terms of the convergence rate of the nonlinear iteration, the iteration number and projection error descending curve of the improved lie group iteration method is shown in fig. 3. And the real solution can be converged basically through 6 iteration steps. Through platform experiments, the iterative algorithm is short in time consumption, completely meets the requirement of the real-time performance of the system, and can quickly calculate three Euclidean angles and three translation amounts of the space pose of the target.
Taking this example as an example, the comparison result of the image plane reprojection error with the original lie group nonlinear optimization method after the test by the monocular vision measurement method for vehicle driving space pose parameters is shown in table 1.
TABLE 1 image plane reprojection error contrast for different algorithms
The improved lie group nonlinear optimization method is compared with the original lie group method in terms of the calculation time consumption of the algorithm, and is shown in table 2.
TABLE 2 comparison of the computation time consumption (ms) for the different algorithms
As can be seen from the analysis of tables 1 and 2, the improved lie group algorithm provided by the invention has better precision and real-time performance than the pose estimation method based on the original lie group.
Claims (5)
1. A method for measuring the spatial pose of a crane jib based on improved lie group nonlinear optimization is characterized by comprising the following steps:
s1: acquiring a target point of a cooperation target by using a camera, wherein the cooperation target consists of four laser points which are distributed in a rectangular shape, and extracting four barycentric coordinates of an infrared cursor in an acquired image;
s2: calibrating the internal and external parameters of the acquisition camera, determining an imaging center and a distortion coefficient, and correcting the image distortion parameters of the image acquired in the step S1;
s3: converting the relative pose problem of the camera and the cooperative target into a minimized re-projection problem;
s4: calculating an initial rotation matrix and translation amount of the relative pose of the camera by using an EPNP method;
s5: and performing nonlinear iteration by using a Gauss-Newton method, and then finally converging to a real solution to obtain a rotation matrix and a translation amount.
2. The method for measuring the spatial pose of the crane boom based on the improved lie group nonlinear optimization as claimed in claim 1, wherein the step S1 of extracting barycentric coordinates of the infrared cursor in the acquired image comprises the following steps:
s11: performing mixed filtering operation on an original image, namely judging to adopt a method of combining Gaussian filtering and median filtering according to a set threshold value, and smoothing the image to eliminate noise;
s12: performing morphological binary open operation on the image by adopting an optimal threshold segmentation method, finding a connected domain and eliminating isolated noise points and burrs in the image background;
s13: and searching cursor connected domains in the image by adopting a gray scale gravity center method and solving gravity center coordinates one by one.
3. The method for measuring the spatial pose of the crane boom based on the improved lie group nonlinear optimization as claimed in claim 1, wherein the step S3 specifically comprises the following steps:
s31: converting the relative pose problem of the camera and the cooperative target into nonlinear optimization iteration, namely solving the error minimization of the image coordinate real solution and the image coordinate obtained in the step S1:
2＝∑||qi′-f(M2Pi w)||2
in the formula (I), the compound is shown in the specification,2is an error term, q'iFor the coordinates of the measurement calibration point obtained in step S1,
as actual physical coordinates of the infrared cursor, M2The coordinate transformation matrix is composed of a rotation matrix and a translation quantity, and f represents a functional relation;
s32: the expression of step S31 is expressed by the lie group method, i.e., the rotation matrix and the translation amount between the camera coordinates and the calibration object coordinates are expressed by the lie algebra:
xi is lie algebra and Λ is broadly expressed as "from vector to matrix".
4. The method for measuring the spatial pose of the crane boom based on the improved lie group nonlinear optimization as claimed in claim 3, wherein the step S4 specifically comprises the following steps:
s41: representing three-dimensional control points of a cooperative target by a weighted sum of four virtual space coordinate points;
s42: calculating coordinates of the four virtual space points in a world coordinate system, converting the coordinates into a camera coordinate system by using a camera projection model, and calculating the coordinates in the camera coordinate system;
s43: and according to the 3D-3D matching, calculating a corresponding rotation matrix R and a corresponding translation t by adopting an ICP (inductively coupled plasma) method, and taking the rotation matrix R and the translation t as initial values to be introduced into a lie group algorithm to carry out minimum optimization.
5. The method for measuring the spatial pose of the crane boom based on the improved lie group nonlinear optimization as claimed in claim 3, wherein the step S5 specifically comprises the following steps:
s51: find out
Calculating an advance as a Jacobian matrix and calculating an initial quantity as a subsequent Jacobian matrix, where A is
The method comprises the following steps of (1) representing a kronecker product, wherein R is a rotation matrix, t is a translation amount, I is a unit matrix, and a lie algebra is used for representing the rotation matrix and the translation amount between a camera coordinate and a calibration object coordinate;
s52: solving the derivative of the minimized re-projection error term about the optimization variable, namely linearizing the objective function under the K iteration, eliminating the secondary term information after first-order Taylor expansion, and iteratively converging the lie algebra left-times disturbance quantity exp (xi ^);
s53: combining the expression after the linearization expression in the step S52 with the nonlinear iteration error expression, deriving the expression, and carrying out vectorization calculation on the Jacobian matrix by using a Kernel product when solving the Jacobian matrix, wherein the lead in the step S51 is used in each calculation;
s54, setting the derived expression obtained in the step S53 as 0, obtaining the variation lie algebra required by the next iteration, and setting the initial condition of the kth iteration as ξk、E(ξk) Substituting the following formula to obtain a lie algebra under the K +1 iteration;
exp(ξk∧)exp(Δξk∧)＝exp(ξk+1∧)
in the above formula, exp (^) represents a matrix index, ξkRepresenting lie algebra after the K iteration, ξk+1Denotes the lie algebra after the K +1 iteration, Δ ξkRepresenting the variation of lie algebra;
s55 update f (exp (ξ)k+1 ∧)Pi w) Obtain new E (ξ)k+1) And judging whether a convergence termination condition is reached, if so, terminating the iteration, and if not, repeating S52 to S54 until the convergence reaches a true value.
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