Rail-mounted stacker-reclaimer double-pitching laser radar external parameter calibration method and system

Abstract

The application provides a rail-mounted stacker-reclaimer double-pitch laser radar external parameter calibration method and system, relates to the sensing calibration technical field of large-scale mobile engineering machinery in port, mine bulk material yard, adopts RTK ground control points as absolute constraints, constructs a six-level kinematic chain model containing walking, rotation, double-pitch and laser radar system installation, realizes accurate modeling of the whole bottom surface installation mode of the cylindrical laser radar through joint optimization of 12-degree-of-freedom external parameters. The method effectively avoids the error accumulation problem caused by the traditional step-by-step calibration, and significantly improves the calibration accuracy and reliability of the laser radar system of the large-scale stacker-reclaimer in the complex operation environment.

Description

Technical Field

[0001] This invention relates to the field of sensing and calibration technology for large mobile engineering machinery in ports and mining bulk material storage yards, specifically to a method and system for calibrating the external parameters of a multi-line lidar mounted on an A-pillar gimbal under four degrees of freedom of motion: track walking, machine rotation, boom pitch, and gimbal pitch. Background Technology

[0002] As a core piece of equipment in modern bulk material yards, the bucket wheel stacker-reclaimer requires its onboard 3D lidar system to achieve accurate positioning of point cloud data within a fixed coordinate system across the entire yard through precise coordinate transformation. This positioning accuracy directly affects the accuracy of the 3D modeling of the material pile and the reliability of subsequent stacking and reclaiming operation path planning. From a mechanistic perspective, the bucket wheel stacker-reclaimer is a typical track-based serial mechanism. The entire equipment can move linearly along the laid track, the superstructure has rotational freedom around the central slewing bearing, and the cantilever carrying the lidar has vertical swing freedom around the pitch hinge point. Particularly noteworthy is that the lidar system is fixed to the front end of the cantilever via an A-pillar structure and mounted on a gimbal mechanism with independent pitch function, forming a four-stage kinematic chain structure.

[0003] In modern industrial applications, 32-line cylindrical lidar is commonly used as the main sensor. These sensors are typically mounted on a gimbal mounting plate with the entire bottom surface fixed to it. Since the lidar's factory coordinate system origin is generally located at the geometric center of its cylinder, while the actual mounting surface is located on the bottom of the device, there is a specific spatial positional deviation between the two. This characteristic necessitates that the lidar's measurement data undergo multiple stages of rigid body transformation when converted to the global coordinate system, and errors at any stage will directly affect the final positioning result.

[0004] Current calibration technologies in the industry suffer from several limitations. Traditional offline calibration methods rely heavily on specially designed planar calibration boards, which are often difficult to deploy and use in actual operating environments such as ports and power plants. While the combined calibration technology using global navigation satellite systems and inertial navigation systems is theoretically feasible, it fails to fully consider the motion relationships of multiple rigid body chains, such as the boom, A-pillar, and gimbal, within the actual equipment. Hand-eye calibration technology, originating from the field of industrial robots, is based on the assumption of a single kinematic chain and cannot adapt to complex mechanisms like bucket wheel stacker-reclaimers, which simultaneously possess walking, rotation, and dual pitch degrees of freedom. Segmented calibration or methods that directly use nominal values ​​from design drawings inevitably lead to error accumulation, potentially resulting in positioning deviations at the centimeter or even decimeter level. Furthermore, calibration methods relying solely on point cloud registration, lacking external absolute positioning references, are prone to significant position drift after prolonged operation.

[0005] An existing patent (authorized patent CN115840217B - A parameter calibration method and system for an airborne lidar of a bucket wheel stacker-reclaimer) proposes a calibration method for lidar on bucket wheel stacker-reclaimers. This method constructs a three-level coordinate system encompassing the machine's movement, upper rotation, and boom pitch, and establishes a sensor coordinate system with the lidar's optical center. Its core technology lies in using a random sampling consensus algorithm to extract effective data from the collected ground point cloud. By making the transformed ground point height approach zero and maintaining planarity, an optimization objective function is constructed. Finally, a genetic algorithm is used to solve for the six-dimensional installation parameters of the lidar relative to the machine. While this approach avoids the use of specialized measuring instruments, it still has significant shortcomings. It fails to fully consider the impact of the unique bottom-mounted design of cylindrical lidar on parameter estimation, and it does not fully consider the additional transformation relationships brought about by the gimbal pitch mechanism. More importantly, this method relies entirely on the self-constraint of the ground point cloud, lacking external absolute position references, making it difficult to guarantee the consistency of global positioning accuracy in large-scale operational scenarios.

[0006] Therefore, developing a novel calibration method that can comprehensively utilize the absolute constraints of ground control points, fully express the multi-level rigid body motion relationships, and accurately describe the sensor installation characteristics has significant engineering application value. Summary of the Invention

[0007] In view of this, the present invention provides a method and system for calibrating the extrinsic parameters of a dual-pitch lidar for a track-mounted stacker-reclaimer, in order to solve the technical problems in the prior art of being unable to accurately calibrate the extrinsic parameters of multi-level kinematic chains under the condition of no calibration target, having difficulty in accurately modeling the mounting characteristics of the bottom surface of a cylindrical lidar, and lacking an effective calibration attitude planning scheme.

[0008] Therefore, the present invention adopts the following technical solution: On one hand, the present invention provides a method for calibrating the extrinsic parameters of a dual-elevation lidar for a track-mounted stacker-reclaimer, comprising: A six-level coordinate transformation chain is established, which includes a system coordinate system with the starting point of the track as the origin, a base system with the rotation center, a pitch system with the pitch center and fixed to the A-pillar, a gimbal system, a bottom mounting system with the bottom center of the lidar and its axis along the cylinder axis, and a sensor system. Based on the travel displacement, rotation angle, boom pitch angle, gimbal pitch angle, and mechanical dimensions, calculate the first transformation matrix from the system coordinate system to the base system, the second transformation matrix from the base system to the pitch system, and the rotation matrix of the gimbal around the pitch axis. The constant rigid body transformation from the pitch system to the gimbal system, the constant rigid body transformation from the gimbal system to the bottom mounting system, and the constant rigid body transformation from the bottom mounting system to the sensor system are taken as external parameters to be calibrated. Among them, the constant rigid body transformation from the bottom mounting system to the sensor system includes the axial translation and the mounting yaw angle. The first coordinates of multiple ground feature points in the system coordinate system are measured by a real-time dynamic measurement device. The stacker-reclaimer is operated to multiple poses, and the second coordinates of each feature point in the sensor system and the state of each joint are recorded. The poses cover the working range of each joint. Establish a forward kinematics equation, minimize the residual between the first coordinate and the predicted coordinate calculated based on the second coordinate, the state of each joint and the external parameters to be calibrated, and jointly solve the external parameters to be calibrated. Write the calibrated extrinsic parameters into the configuration, and transform the point cloud from the sensor coordinate system to the system coordinate system according to the current joint state.

[0009] Furthermore, the joint solution of the extrinsic parameters to be calibrated includes: A nonlinear least squares algorithm is used for optimization.

[0010] Furthermore, the nonlinear least squares algorithm is the Levenberg-Marquardt nonlinear least squares algorithm.

[0011] Furthermore, the cost function for minimizing the residual employs a robust kernel function to suppress gross errors.

[0012] Furthermore, the forward kinematic equations are established as follows:

[0013] Where p_W is the coordinate of the ground feature point in the system coordinate system {W}, i.e., the first coordinate; p_R is the coordinate of the same feature point in the sensor system {R}, i.e., the second coordinate; x This represents the displacement during walking; It is the rotation angle; The pitch angle of the upper arm; Let T_{W←B}(x) be the gimbal pitch angle; T_{W←B}(x) be the translation transformation matrix from the system coordinate system to the base system. T_{P←G} is the transformation matrix from the base system to the pitch system; T_{P←G} is the constant rigid body transformation from the pitch system to the gimbal system; Rot_y(ψ) is the rotation matrix of the gimbal about the pitch axis; T_{G←M} is the constant rigid body transformation from the gimbal system to the bottom mounting system; T_{M←R} is the constant rigid body transformation from the bottom mounting system to the sensor system.

[0014] Furthermore, the rotation matrix of the gimbal around the Y-axis is expanded to be the product of the rotation matrix of the gimbal around the Y-axis and the fixed small deviation of the gimbal pitch axis. The fixed small deviation of the gimbal pitch axis is optimized together with the constant rigid body transformation from the pitch system to the gimbal system.

[0015] Furthermore, operating the stacker-reclaimer to multiple positions includes: The plan marks the positioning posture so that the walking displacement, turning angle, boom pitch angle, and gimbal pitch angle each cover their respective working range.

[0016] Furthermore, before writing the calibrated extrinsic parameters into the configuration, the parameters are re-measured on an independent pose that is not involved in optimization, and the deviation between the transformed coordinates and the RTK measurement coordinates is checked until the engineering accuracy requirements are met.

[0017] Furthermore, the first transformation matrix T_{W←B}(x): ; The position of the rotation center along the track direction is determined by the readings of the travel encoder. The vertical track direction and vertical position are given in real time by the fixed offsets y0 and z0 of the machine. When the rotation angle θ=0, the axes of the base system {B} are parallel to the axes of the system coordinate system {W}. The rotational motion is reflected by Rot_z(θ) in the subsequent T_{B←P}. Therefore, this matrix is ​​a pure translation transformation. The second transformation matrix T_{B←P}(θ, φ):

[0018] From the center of rotation to the center of boom pitch, first rotate θ around the vertical Z-axis, then translate r in the horizontal direction and rise h in the vertical direction, and finally pitch φ around the pitch hinge point Y-axis; Rotation matrix Rot_y(ψ):

[0019] The gimbal has only one pitch degree of freedom about its pitch axis Y_G, and the rotation angle ψ is read by the gimbal encoder. Therefore, this matrix is ​​a standard homogeneous rotation matrix about the Y-axis.

[0020] In another aspect, the present invention also provides a method for calibrating the extrinsic parameters of a dual-elevation lidar for a track-mounted stacker-reclaimer, for implementing the above method, comprising: The joint status acquisition module is used to acquire the walking displacement of the walking encoder, the rotation angle and boom pitch angle of the PLC, and the gimbal pitch angle of the gimbal encoder. The RTK measurement module is used to measure the first coordinates of multiple ground feature points in the system coordinate system; record the second coordinates of each feature point in the sensor system and the state of each joint under multiple poses, wherein the poses cover the working range of each joint; The point cloud acquisition module is used to acquire point cloud data collected by the lidar. The kinematic modeling module is used to establish the six-level coordinate transformation chain and calculate each transformation matrix; establish the forward kinematic equations, minimize the residual between the first coordinate and the predicted coordinates calculated based on the second coordinate, the joint states and the extrinsic parameters to be calibrated, and jointly solve for the extrinsic parameters to be calibrated. The extrinsic parameter solving module is used to jointly solve the extrinsic parameters to be calibrated with the goal of minimizing the residuals. The online registration module is used to transform the point cloud from the sensor coordinate system to the system coordinate system in real time based on the extrinsic parameters obtained from calibration and the current joint state.

[0021] The above technical solution has the following beneficial effects: This invention provides a method and system for calibrating the extrinsic parameters of a dual-pitch lidar on a track-mounted stacker-reclaimer. It employs real-time dynamic differential positioning (RTK) ground control points as absolute constraints to construct a six-level kinematic chain model encompassing travel, rotation, dual pitch, and lidar system installation. Through joint optimization of the 12-DOF extrinsic parameters, accurate modeling of the cylindrical lidar's full-surface mounting configuration is achieved. Compared to existing technologies, this solution eliminates the need for a dedicated calibration plate, requiring only RTK ground points for on-site calibration. By introducing a bottom-mounted coordinate system and embedding structural constraints of the cylindrical lidar, the physical authenticity of the geometric parameters is ensured. A specially designed calibration attitude planning effectively covers the working range of each joint, guaranteeing the observability and calibration stability of the extrinsic parameters. It supports configuration-based operation, facilitating system debugging and online registration. This method effectively avoids the error accumulation problem caused by traditional step-by-step calibration, significantly improving the calibration accuracy and reliability of lidar systems in large stacker-reclaimers operating in complex environments. Attached Figure Description

[0022] 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, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 This is a flowchart illustrating a method for calibrating the extrinsic parameters of a dual-elevation lidar for a track-mounted stacker-reclaimer, as described in an embodiment of the present invention. Figure 2 This is a block diagram of a six-level coordinate transformation chain in an embodiment of the present invention; Figure 3 This is a schematic diagram of the stacker-reclaimer and the three-dimensional structure of the six-level coordinate system in an embodiment of the present invention; Figure 4 This is a flowchart of the positioning pose planning process in an embodiment of the present invention. Detailed Implementation

[0024] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0025] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0026] like Figure 1 As shown, this embodiment takes a port rail-mounted stacker-reclaimer as an example. A 32-line cylindrical lidar (H_cyl=146 mm) is mounted on the bottom of the pan-tilt unit. Its external parameter calibration method includes: S1. Establish a six-level coordinate transformation chain; like Figure 2 As shown, the six-level coordinate transformation chain includes a system coordinate system {W} established with the starting point of the track as the origin, a base system {B} established with the rotation center, a pitch system {P} established with the pitch center and fixed to column A, a gimbal system {G}, a bottom mounting system {M} established with the center of the bottom surface of the lidar and its axis along the cylindrical axis, and a sensor system {R}; the positive direction of the vertical axis of the bottom mounting system is along the cylindrical axis of the lidar, and its horizontal axis is located in the bottom circular plane.

[0027] S2. Based on the travel displacement x, rotation angle θ, boom pitch angle φ, gimbal pitch angle ψ, and mechanical dimensions r, h, y0, z0, calculate the first transformation matrix T_{W←B}(x) from the system coordinate system to the base system, the second transformation matrix T_{B←P}(θ,φ) from the base system to the pitch system, and the rotation matrix Rot_y(ψ) of the gimbal around the pitch axis. Where r is the horizontal eccentricity of the boom pitch center relative to the slewing center, h is the height difference between the boom pitch center and the slewing center, y0 is the lateral offset of the slewing center relative to the track centerline, and z0 is the height of the slewing center relative to the system coordinate system elevation datum; all the above parameters are given by CAD drawings or installation measurements, are fixed geometric constants of the machine, and are not involved in calibration optimization.

[0028] The calculation process and principle of the above transformation matrices are as follows: (1) The first transformation matrix T_{W←B}(x): ; The origin of the system coordinate system {W} is taken as the starting point of the track, and the origin of the base system {B} is the center of rotation; the position of the center of rotation along the track direction is determined by the reading of the travel encoder. The vertical track direction and vertical position are given in real time by the fixed offsets y0 and z0 of the machine. When the rotation angle θ=0, the axes of {B} are parallel to the axes of {W}. The rotational motion is reflected by Rot_z(θ) in the subsequent T_{B←P}. Therefore, this matrix is ​​a pure translation transformation.

[0029] (2) The second transformation matrix T_{B←P}(θ, φ):

[0030] From the center of rotation to the center of boom pitch, first rotate θ around the vertical Z-axis, then translate r horizontally and rise h vertically, and finally pitch φ around the pitch hinge point Y-axis; using the body-fixed base system ({B} rotates with the rotation), i.e., first rotate, then translate, then pitch. Its equivalent ground-fixed axial notation is T_{B←P}(θ,φ) = Trans(r·cosθ, r·sinθ, h) · Rot_z(θ) · Rot_y(φ), and the two notations are physically equivalent.

[0031] (3) Rotation matrix Rot_y(ψ) of the gimbal around the pitch axis:

[0032] The gimbal has only one pitch degree of freedom about its pitch axis Y_G, and the rotation angle ψ is read by the gimbal encoder. Therefore, this matrix is ​​a standard homogeneous rotation matrix about the Y-axis. In an optional embodiment, it can be extended to R_y(ψ)·R_axis, where R_axis is a fixed small deviation of the gimbal pitch axis, and is jointly optimized with T_{P←G} to compensate for axis system errors under large pitch angle conditions.

[0033] Preferably, Rot_y(ψ) can be extended to R_y(ψ)·R_axis, where R_axis is a fixed small deviation of the gimbal pitch axis, and optimized together with T_{P←G} to improve the registration effect under large pitch angle conditions.

[0034] S3. The constant rigid body transformation T_{P←G} from the pitch system to the gimbal system, the constant rigid body transformation T_{G←M} from the gimbal system to the ground mounting system, and the constant rigid body transformation T_{M←R} from the ground mounting system to the sensor system are taken as external parameters to be calibrated. The external parameters to be calibrated have a total of 12 degrees of freedom, which are composed as follows: the constant rigid body transformation T_{P←G} from the pitch system to the gimbal system contributes 6 degrees of freedom (3 translational components and 3 rotational components); the constant rigid body transformation T_{G←M} from the gimbal system to the bottom mounting system and the constant rigid body transformation T_{M←R} from the bottom mounting system to the sensor system are combined into a combined constant rigid body transformation T_{G←R} from the gimbal system to the sensor system, contributing 6 degrees of freedom (3 translational components and 3 rotational components). Among them, the translation h_ref along the cylindrical axis of T_{M←R} is known from the product manual and does not participate in the optimization. Only its mounting yaw angle α_mount is incorporated into the rotational component of the combined transformation for optimization; therefore, 12 degrees of freedom = 6(T_{P←G}) + 6(T_{G←R}).

[0035] The aforementioned extrinsic parameters to be calibrated are all 4×4 homogeneous constant rigid body transformation matrices, whose general form is:

[0036] The three values ​​are obtained by using the CAD-defined installation dimensions and product manual geometry as initial values, and then by joint optimization through multi-pose RTK point-by-point residual minimization in steps S4 and S5 below. The specific form and physical meaning of each matrix are as follows: (1) : Represents the fixed rigid body relationship from the pitch hinge point on column A (fixed to {P}) to the center of the pitch axis of the gimbal, including 3 attitude angles and 3 translation components. The initial value is taken from the installation dimensions of column A to the gimbal in the CAD drawing.

[0037] (2) : Characterizes the rigid body relationship between the gimbal's pitch axis O_G and the center of the lidar's bottom surface O_M; when the gimbal's pitch angle ψ≠0, That is, the mounting surface rotates with the entire gimbal.

[0038] (3) Where h_ref is the distance from the center O_M of the bottom surface along the cylindrical axis Z_M to the sensor origin O_R (given in the product manual, typically h_ref ≈ H_cyl / 2, in this embodiment H_cyl = 146 mm); α_mount is the mounting yaw angle about Z_M, initially determined by the connector orientation or the zero-position alignment of the wiring harness. This matrix explicitly encodes the structural constraints for full-surface mounting of the cylindrical lidar.

[0039] Figure 3 illustrates the spatial layout and connection relationship of the stacker-reclaimer and its six-level coordinate system in this embodiment of the invention: the system coordinate system {W} (originating at the starting point of the track) and the base system {B} (originating at the center of rotation, moving along the track with the traveling mechanism) are shown along the track laying direction; the upper rotating structure rotates around the center of rotation, showing the rotation angle θ; the boom swings around the pitch center, showing the pitch system {P} (fixed to column A) and the boom pitch angle φ; the gimbal at the front end of column A swings around its pitch axis, showing the gimbal system {G} and the gimbal pitch angle ψ; a cylindrical laser radar is fixed on the gimbal mounting surface, showing the bottom mounting system {M} (originating at the center of the bottom of the cylinder, Z_M along the cylinder axis upwards) and the sensor system {R} (originating at the geometric center of the cylinder). The six-level coordinate systems are connected sequentially by the first transformation matrix T_{W←B}, the second transformation matrix T_{B←P}, the constant rigid body transformation T_{P←G}, the gimbal rotation matrix Rot_y(ψ) around the pitch axis, the constant rigid body transformation T_{G←M}, and T_{M←R}, forming the six-level coordinate transformation chain shown in Figure 2.

[0040] S4. Measure the first coordinates of multiple ground feature points in the system coordinate system using a real-time dynamic measurement device (RTK), operate the stacker-reclaimer to multiple poses, record the second coordinates of each feature point in the sensor system and the state of each joint, and cover the working range of each joint in the pose. In practice, about 15 evenly distributed ground feature points are selected in the storage yard. The coordinates of these ground feature points under {W} are determined using RTK and denoted as the first coordinate p_W^i, which serves as the absolute reference for calibration.

[0041] Here, multiple poses refer to several combinations of poses selected by the stacker-reclaimer across four joint dimensions: travel displacement x, rotation angle θ, boom pitch angle φ, and gimbal pitch angle ψ. Each pose corresponds to a defined set of (x, θ, φ, ψ) joint states. The pose selection principle is that each joint covers representative values ​​within its respective working range, and there are significant variations between different poses across each joint dimension, ensuring sufficient observability of the extrinsic parameters to be calibrated during joint optimization. In this embodiment, according to... Figure 4The pose planning process plans eight calibration poses, ensuring that the walking x, rotation θ, boom pitch φ, and gimbal pitch ψ each cover their respective working ranges. Point clouds are acquired at each pose, picking the same set of feature points corresponding to the RTK, and simultaneously recording x, θ, φ, and ψ at that moment. Specifically, the walking displacement x is taken from at least two positions at least 5 m apart, the rotation angle θ covers a range of ±30°, the boom pitch angle φ covers a range of ±15°, and the gimbal pitch angle ψ is between 0° and... At least three different angles are taken within a 60° range. The eight calibration poses specifically planned in this embodiment are shown in Table 1.

[0042] Table 1

[0043] Where x is the walking displacement from the starting point of the track, θ is the rotation angle, φ is the boom pitch angle, and ψ is the gimbal pitch angle.

[0044] The coverage of the above 8 poses is as follows: the walking displacement x takes two positions {0 m, 10 m} that are 10 m apart (≥5 m), and the translational component along the track is constrained; the rotation angle θ covers... 30°~+30° (±30°) to ensure considerable slewing component; boom pitch angle φ covers 15°~+15° (±15°) to ensure a considerable boom pitch component; gimbal pitch angle ψ is within 0°~ Within a 60° range, take {0°, 30° Three angles, 60°, decouple T_{P←G} and T_{G←R}; at least 4 ground feature points are observed for each pose, and the total number of observation equations is ≥ 3×(12+1), which meets the overdetermined solution requirements.

[0045] S5. Based on the first transformation matrix, the second transformation matrix, the rotation matrix, and the constant rigid body transformation, establish the forward kinematic equations, minimize the residual between the first coordinate and the predicted coordinate calculated based on the second coordinate, the state of each joint, and the external parameters to be calibrated, and jointly solve for the external parameters to be calibrated. The principle for establishing the forward kinematics equations is as follows: Based on multi-level rigid body kinematics, the lidar point cloud is transformed step by step from the sensor system {R} to the system coordinate system {W}. Each time a coordinate system is passed, a corresponding 4×4 homogeneous transformation matrix is ​​multiplied on the left. The transformation sequence is consistent with the six-level coordinate transformation chain: first, T_{M←R} transforms the point from {R} to the base mounting system {M}; then, T_{G←M} transforms it to the gimbal system {G}; after gimbal pitch and rotation Rot_y(ψ), T_{P←G} transforms it to the pitch system {P}; then, T_{B←P}(θ,φ) transforms it to the base system {B} (including rotation and boom pitch); finally, T_{W←B}(x) transforms it to the system coordinate system {W}. Multiplying the matrices in this order yields the forward kinematics equations of the point cloud from {R} to {W} (rewritten in standard mathematical form in the above equation). The equation takes the joint states (x, θ, φ, ψ) at each level and the extrinsic parameters to be calibrated as inputs, predicts the coordinates of feature points in {W}, and forms a residual with the RTK measured coordinates p_W, which serves as the joint optimization objective.

[0046] The established forward kinematic equations are as follows:

[0047] Where p_W is the coordinate of the ground feature point in the system coordinate system {W} (measured by RTK, serving as an absolute reference); p_R is the coordinate of the same feature point in the sensor system {R} (picked from the lidar point cloud); x is the walking displacement (reading from the PLC walking encoder, measured from the starting point of the track); θ is the rotation angle (PLC encoder); φ is the boom pitch angle (PLC encoder); ψ is the gimbal pitch angle (gimbal encoder); T_{W←B}(x) is the translation transformation matrix from the system coordinate system to the base system; T_{B←P}(θ,φ) is the transformation matrix from the base system to the pitch system (including rotation and boom pitch); T_{P←G} is the constant rigid body transformation from the pitch system to the gimbal system (external parameters to be calibrated); Rot_y(ψ) is the rotation matrix of the gimbal about the pitch axis; T_{G←M} T_{M←R} is the constant rigid body transformation from the gimbal system to the bottom mounting system (external parameters to be calibrated); T_{M←R} is the constant rigid body transformation from the bottom mounting system to the sensor system (external parameters to be calibrated).

[0048] In practice, Levenberg-Marquardt nonlinear least squares can be used for the solution; the cost function can be optimized using the Huber robust kernel to suppress gross errors. Using the nominal CAD installation dimensions as initial values, LM nonlinear least squares are used to jointly optimize T_{P←G}, T_{G←M}, and T_{M←R} to minimize the residuals between the forward kinematics prediction and the RTK measurement. Re-measurements are then performed on independent poses not involved in the optimization, and the deviations from RTK after transformation to {W} are checked until the engineering accuracy requirements are met.

[0049] S6. Write the calibrated extrinsic parameters into the configuration, and synthesize the transformation matrix in real time according to the current joint state and kinematic chain to transform the point cloud from the sensor coordinate system to the system coordinate system.

[0050] Write the calibrated T_{P←G}, T_{G←M}, and T_{M←R} into the configuration; synthesize T_{W←R} online in real time based on the current x, θ, φ, ψ and the kinematic chain, and transform the point cloud from {R} to {W}.

[0051] In another embodiment, the present invention also provides a dual-elevation lidar extrinsic parameter calibration system for a track-mounted stacker-reclaimer, used to implement the method described in the above embodiments, including: The joint status acquisition module is used to acquire the walking displacement of the walking encoder, the rotation angle and boom pitch angle of the PLC, and the gimbal pitch angle of the gimbal encoder. The RTK measurement module is used to measure the first coordinates of multiple ground feature points in the system coordinate system. The point cloud acquisition module is used to acquire point cloud data collected by the lidar. The kinematic modeling module is used to establish the six-level coordinate transformation chain and calculate each transformation matrix. The extrinsic parameter solving module is used to jointly solve the extrinsic parameters to be calibrated with the goal of minimizing the residuals. The online registration module is used to transform the point cloud from the sensor coordinate system to the system coordinate system in real time based on the extrinsic parameters obtained from calibration and the current joint state.

[0052] In the above embodiments, RTK ground control points are used as absolute constraints to construct a six-level kinematic chain model including walking, rotation, dual pitch, and lidar system installation. Through joint optimization of 12-DOF extrinsic parameters, accurate modeling of the cylindrical lidar's full-surface mounting method is achieved. Compared with existing technologies, this solution does not require a dedicated calibration plate; on-site calibration can be achieved using only RTK ground points. By introducing a bottom-mounted coordinate system and embedding the structural constraints of the cylindrical lidar, the physical authenticity of the geometric parameters is ensured. The specially designed calibration attitude planning effectively covers the working range of each joint, ensuring the observability of extrinsic parameters and calibration stability. It supports configuration-based operation, facilitating system debugging and online registration. This method effectively avoids the error accumulation problem caused by traditional step-by-step calibration, significantly improving the calibration accuracy and reliability of the lidar system in complex operating environments for large stacker-reclaimers.

[0053] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calibrating the extrinsic parameters of a dual-elevation lidar for a track-mounted stacker-reclaimer, characterized in that, include: A six-level coordinate transformation chain is established, which includes a system coordinate system with the starting point of the track as the origin, a base system with the rotation center, a pitch system with the pitch center and fixed to the A-pillar, a gimbal system, a bottom mounting system with the bottom center of the lidar and its axis along the cylinder axis, and a sensor system. Based on the travel displacement, rotation angle, boom pitch angle, gimbal pitch angle, and mechanical dimensions, calculate the first transformation matrix from the system coordinate system to the base system, the second transformation matrix from the base system to the pitch system, and the rotation matrix of the gimbal around the pitch axis. The constant rigid body transformation from the pitch system to the gimbal system, the constant rigid body transformation from the gimbal system to the bottom mounting system, and the constant rigid body transformation from the bottom mounting system to the sensor system are taken as external parameters to be calibrated. Among them, the constant rigid body transformation from the bottom mounting system to the sensor system includes the axial translation and the mounting yaw angle. The first coordinates of multiple ground feature points in the system coordinate system are measured by a real-time dynamic measurement device. The stacker-reclaimer is operated to multiple poses, and the second coordinates of each feature point in the sensor system and the state of each joint are recorded. The poses cover the working range of each joint. Establish a forward kinematics equation, minimize the residual between the first coordinate and the predicted coordinate calculated based on the second coordinate, the state of each joint and the external parameters to be calibrated, and jointly solve the external parameters to be calibrated. Write the calibrated extrinsic parameters into the configuration, and transform the point cloud from the sensor coordinate system to the system coordinate system according to the current joint state.

2. The method for calibrating the extrinsic parameters of a dual-elevation lidar for a track-mounted stacker-reclaimer according to claim 1, characterized in that, The joint solution of the extrinsic parameters to be calibrated includes: A nonlinear least squares algorithm is used for optimization.

3. The method for calibrating the extrinsic parameters of a dual-elevation lidar for a track-mounted stacker-reclaimer according to claim 2, characterized in that, The nonlinear least squares algorithm is the Levenberg-Marquardt nonlinear least squares algorithm.

4. The method for calibrating the extrinsic parameters of a dual-elevation lidar for a track-mounted stacker-reclaimer according to claim 3, characterized in that, The cost function for minimizing the residuals employs a robust kernel function to suppress gross errors.

5. The method for calibrating the extrinsic parameters of a dual-elevation lidar for a track-mounted stacker-reclaimer according to claim 1, characterized in that, The established forward kinematic equations are as follows: Where p_W is the coordinate of the ground feature point in the system coordinate system {W}, i.e., the first coordinate; p_R is the coordinate of the same feature point in the sensor system {R}, i.e., the second coordinate; x This represents the displacement during walking; It is the rotation angle; The pitch angle of the upper arm; Let T_{W←B}(x) be the gimbal pitch angle; T_{W←B}(x) be the translation transformation matrix from the system coordinate system to the base system. T_{P←G} is the transformation matrix from the base system to the pitch system; T_{P←G} is the constant rigid body transformation from the pitch system to the gimbal system; Rot_y(ψ) is the rotation matrix of the gimbal about the pitch axis; T_{G←M} is the constant rigid body transformation from the gimbal system to the bottom mounting system; T_{M←R} is the constant rigid body transformation from the bottom mounting system to the sensor system.

6. The method for calibrating the extrinsic parameters of a dual-elevation lidar for a track-mounted stacker-reclaimer according to claim 1, characterized in that, The rotation matrix of the gimbal around the Y-axis is expanded to be the product of the rotation matrix of the gimbal around the Y-axis and the fixed small deviation of the gimbal pitch axis. The fixed small deviation of the gimbal pitch axis is optimized together with the constant rigid body transformation from the pitch system to the gimbal system.

7. The method for calibrating the extrinsic parameters of a dual-elevation lidar for a track-mounted stacker-reclaimer according to claim 1, characterized in that, The operation of the stacker-reclaimer to multiple positions includes: The plan marks the positioning posture so that the walking displacement, turning angle, boom pitch angle, and gimbal pitch angle each cover their respective working range.

8. The method for calibrating the extrinsic parameters of a dual-elevation lidar for a track-mounted stacker-reclaimer according to claim 1, characterized in that, Before writing the calibrated extrinsic parameters into the configuration, the parameters are re-measured on an independent pose that is not involved in optimization, and the deviation between the transformed coordinate system and the RTK measurement coordinates is checked until the engineering accuracy requirements are met.

9. The method for calibrating the extrinsic parameters of a dual-elevation lidar for a track-mounted stacker-reclaimer according to claim 1, characterized in that, The first transformation matrix T_{W←B}(x): ； The position of the rotation center along the track direction is determined by the readings of the travel encoder. The vertical track direction and vertical position are given in real time by the fixed offsets y0 and z0 of the machine. When the rotation angle θ=0, the axes of the base system {B} are parallel to the axes of the system coordinate system {W}. The rotational motion is reflected by Rot_z(θ) in the subsequent T_{B←P}. Therefore, this matrix is ​​a pure translation transformation. The second transformation matrix T_{B←P}(θ, φ): From the center of rotation to the center of boom pitch, first rotate θ around the vertical Z-axis, then translate r in the horizontal direction and rise h in the vertical direction, and finally pitch φ around the pitch hinge point Y-axis; Rotation matrix Rot_y(ψ): The gimbal has only one pitch degree of freedom about its pitch axis Y_G, and the rotation angle ψ is read by the gimbal encoder. Therefore, this matrix is ​​a standard homogeneous rotation matrix about the Y-axis.

10. A method for calibrating the extrinsic parameters of a dual-elevation lidar for a track-mounted stacker-reclaimer, characterized in that, To implement the method according to any one of claims 1 to 9, comprising: The joint status acquisition module is used to acquire the walking displacement of the walking encoder, the rotation angle and boom pitch angle of the PLC, and the gimbal pitch angle of the gimbal encoder. The RTK measurement module is used to measure the first coordinates of multiple ground feature points in the system coordinate system; record the second coordinates of each feature point in the sensor system and the state of each joint under multiple poses, wherein the poses cover the working range of each joint; The point cloud acquisition module is used to acquire point cloud data collected by the lidar. The kinematic modeling module is used to establish the six-level coordinate transformation chain and calculate each transformation matrix; establish the forward kinematic equations, minimize the residual between the first coordinate and the predicted coordinates calculated based on the second coordinate, the joint states and the extrinsic parameters to be calibrated, and jointly solve for the extrinsic parameters to be calibrated. The extrinsic parameter solving module is used to jointly solve the extrinsic parameters to be calibrated with the goal of minimizing the residuals. The online registration module is used to transform the point cloud from the sensor coordinate system to the system coordinate system in real time based on the extrinsic parameters obtained from calibration and the current joint state.

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