Self-calibration method of space manipulator

Abstract

The embodiment of the invention provides a self-calibration method of a space manipulator. The self-calibration method comprises the following steps: establishing a kinematic model of the space manipulator based on an improved Denison-Hartberg method (MDH); a tail end pose error model of the space manipulator is obtained through the kinematic model; obtaining the motion range of the hand-eye camera according to the measurement precision, the field of view of the hand-eye camera and the visual target parameters; according to the motion range of the hand-eye camera, distribution information of all measurement sub-areas in the working space of the space manipulator is obtained; and kinematics parameter calibration values of the space manipulator are obtained according to the tail end pose error model and the distribution information of the measurement sub-areas. According to the self-calibration method provided by the embodiment of the invention, error data in a larger measurement range can be obtained, and the calibration precision of kinematics parameters and the globality of a calibration result are improved.

Description

[Technical field]

[0001] The present invention relates to the technical field of mechanical arms, and in particular to a self-calibration method for a space mechanical arm.

Technical Background

[0002] Space manipulators are highly flexible and autonomous and are widely used in important tasks such as the construction and maintenance of various large space stations, the capture and docking maintenance of satellites, etc. Their operating accuracy determines the ability of the manipulator to perform tasks and is an important indicator for measuring the working performance of the manipulator. Therefore, it is crucial to ensure the absolute positioning accuracy of the end of the manipulator. Due to the processing errors in manufacturing and assembly, joint clearance errors, etc. of space manipulators, there are small errors between their nominal kinematic parameters and actual kinematic parameters, which causes large errors in end positioning. At the same time, the space manipulator is subject to multiple unknown factors such as impact and collision during the launch process, deformation and wear caused by long-term service, etc., which causes the kinematic parameter errors to change continuously during its entire service cycle. Therefore, the calibration results on the ground or the results of a single calibration cannot be applied throughout its entire life cycle. It is necessary to continuously perform on-orbit self-calibration to meet the requirements of its operating accuracy.

[0003] Kinematic parameter self-calibration is an effective means to improve the operating accuracy of space manipulators. This method uses the manipulator assembly measurement equipment to autonomously collect positioning errors for calibration, obtain the actual values ​​of the manipulator's kinematic parameters, and achieve precise control of the manipulator. At present, vision-based self-calibration technology is relatively simple and mature, easy to carry, and more economical and applicable for on-orbit self-calibration of space manipulators. However, due to the characteristics of the long arm of the space manipulator, the radius of its working space can reach more than ten meters. When using a visual camera to measure the end position of the space manipulator, the traditional visual self-calibration is constrained by the position of the camera and the matching target. The end position can only be measured in the local working space of the space manipulator, which is not conducive to a comprehensive analysis of the mechanism of the error. [Summary of the invention]

[0004] In view of this, an embodiment of the present invention provides a self-calibration method for a space robot arm, which constructs distribution information of multiple measurement sub-areas to increase the measurement range of the camera and improve the calibration accuracy of the kinematic parameters of the robot arm.

[0005] On the one hand, an embodiment of the present invention provides a self-calibration method for a space robot arm, comprising:

[0006] The kinematic model of the space manipulator is established based on the modified Denison-Hartberg method (MDH);

[0007] Using the kinematic model, a terminal position and posture error model of the space manipulator is obtained;

[0008] According to the measurement accuracy, the field of view of the hand-eye camera and the visual target parameters, the motion range of the hand-eye camera is obtained;

[0009] According to the motion range of the hand-eye camera, distribution information of each measurement sub-area in the workspace of the space manipulator is obtained;

[0010] According to the terminal posture error model and the distribution information of each measurement sub-area, the kinematic parameter calibration values ​​of the space manipulator are obtained.

[0011] In the above method, the kinematic model of the space manipulator is:

[0012]

[0013] Where n is the number of degrees of freedom of the space manipulator, α i 、a i ,θ i d i , β i are the kinematic parameters of the robot arm link coordinate system, Represents the transformation matrix between the robot arm link coordinate systems, Represents the transformation matrix of the robot tool coordinate system relative to the base coordinate system; the K axis represents the X, Y or Z axis, and T rot (K,θ) represents the transformation matrix corresponding to the rotation angle θ around the K axis, T rot (K, d) represents the transformation matrix corresponding to the translation of distance d along the K axis of the coordinate system.

[0014] In the above method, the end position error model of the space manipulator is:

[0015]

[0016] Among them, D g is the position error vector of the end of the space manipulator caused by the kinematic parameter error, J e is the error transfer matrix between the kinematic parameter error of the space manipulator and the end position error, e = [e1 e2…e n+1 ] T is the kinematic parameter error vector of the space manipulator; It represents the transfer matrix between the link kinematic parameter error and the link coordinate system posture error, e i =[Δα i Δa i Δθ i Δd i Δβ i ] T Represents the kinematic parameter error vector between the links of the space manipulator.

[0017] In the above method, the transfer matrix between the connecting rod kinematic parameter error and the connecting rod coordinate system posture error is:

[0018]

[0019] Among them, Represents the transformation matrix between the coordinate systems of the space manipulator link, and defines By distinguishing the superscript u from the representation of the kinematic parameters of the space manipulator, the position vector can be obtained and the posture vector 0 represents the zero vector; sθ is the abbreviation of sinθ, cθ is the abbreviation of cosθ; α i 、a i ,θ i ,d i , β i are the kinematic parameters of the space manipulator link coordinate system.

[0020] In the above method, the motion range of the hand-eye camera is expressed as:

[0021]

[0022] Among them, α is the horizontal field of view of the camera, L m is the side length of the visual target, h max is the distance between the light spot of the hand-eye camera and the visual target, i.e. the maximum object distance, x c ,y c 、z c They respectively represent the three-dimensional coordinate values ​​of the optical center of the hand-eye camera in the visual target coordinate system.

[0023] In the above method, obtaining distribution information of each measurement sub-area in the workspace of the space manipulator according to the motion range of the hand-eye camera includes:

[0024] According to the motion range of the hand-eye camera under a single visual target, the maximum diameter of the total imaging plane of the hand-eye camera is calculated as:

[0025]

[0026] Among them, x cmax Indicates the maximum motion range of the hand-eye camera in the x direction; Indicates that the imaging distance of the hand-eye camera is h max , and the horizontal field of view angle is α, the maximum imaging plane width at a single position point;

[0027] L r represents the radius of the bottom circle of the space manipulator workspace. The origin of each visual target is located at a distance of 0 from the center of the bottom circle of the space manipulator workspace. According to the motion range of the hand-eye camera under a single visual target, the total imaging plane formed by the hand-eye camera at this position can be obtained. The tangent relationship between this plane and the center of the bottom circle of the space manipulator workspace is calculated, and the angle δ formed is:

[0028]

[0029] Taking the center O0 of the bottom circle of the space manipulator workspace as the starting point, the bottom circle is evenly divided into num sectors with equal angle value 2(δ+Δδ), and the angle range of each sector is [2(δ+Δδ)·(i-1),2(δ+Δδ)·i], where i=1,2,…,num, Δδ represents the threshold of the angle, and the calculation formula of the number num is:

[0030]

[0031] In each sector, the center of the circle is A visual target is placed at the position of and the position distribution information of each visual target is generated as As the distribution information of each measurement sub-area.

[0032] In the above method, the kinematic parameter calibration values ​​of the space manipulator are obtained according to the terminal posture error model and the distribution information of each measurement sub-area, including:

[0033] According to the distribution information of each measurement sub-area, multiple groups of measurement configurations are randomly selected in multiple measurement sub-areas, and the robot arm is driven to collect the actual pose set PE corresponding to each group of measurement configurations a ; And use the kinematic model of the space manipulator established by the MDH method to calculate the nominal pose set PE corresponding to each set of measurement configurations n ;

[0034] According to the actual posture set PE a and the nominal pose set PE n , the position error of the end of the space manipulator caused by the kinematic parameter error can be obtained for each set of measurement configurations The end position error model and the following formula are used to solve the kinematic parameter error of the spatial manipulator:

[0035]

[0036] in, It is the pseudo-inverse of the error transfer matrix between the kinematic parameter error and the terminal posture error;

[0037] According to the kinematic parameter error, the nominal kinematic parameters are corrected using the following formula:

[0038] E C =EN +e

[0039] Among them, E C is the corrected kinematic parameter, E N is the nominal kinematic parameter, e is the kinematic parameter error;

[0040] Determine whether the corrected kinematic parameters meet the accuracy requirements. If not, iterate the correction steps a finite number of times, wherein the iteration method is: Among them, E i+1 represents the kinematic parameters of the space manipulator in the i+1th iteration, E i represents the kinematic parameters of the space manipulator in the i-th iteration, represents the kinematic parameter error of the spatial manipulator obtained in the i-th iteration.

[0041] The space robot arm self-calibration method designed in the embodiment of the present invention expands the measurement range of errors, realizes the globality of error characterization, effectively solves the current problems of small measurement range based on visual calibration, poor ability to characterize the influence of errors, and poor robustness to interference, and improves the operating accuracy of the space robot arm.

Brief Description of the Drawings

[0042] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0043] Figure 1 It is a schematic diagram of the flow chart of the space manipulator self-calibration method provided by an embodiment of the present invention;

[0044] Figure 2 is a schematic diagram of MDH system establishment rules provided in an embodiment of the present invention;

[0045] Figure 3 is the spatial shape of the field of view of the hand-eye camera provided by the example of the present invention at a fixed point and a fixed posture;

[0046] Figure 4 is a positional relationship diagram of the maximum imaging plane of the hand-eye camera and the visual target plane provided by an example of the present invention;

[0047] Figure 5 is a diagram showing the relationship between the total imaging plane of the hand-eye camera and the local working space of the robot arm provided by an example of the present invention;

[0048] Figure 6 It is a schematic diagram of the kinematic parameter iteration process provided by an example of the present invention;

[0049] Figure 7 It is a schematic diagram of establishing a seven-DOF space robot arm link coordinate system based on the MDH method provided by an example of the present invention;

[0050] Figure 8 It is a point cloud diagram of the movable range of the optical center point of the hand-eye camera field of view under a single visual target provided by an example of the present invention;

[0051] Fig. 9 It is a distribution position diagram of multiple visual targets provided by an example of the present invention and a point cloud diagram of the movable range of the optical center point of the field of view of the corresponding hand-eye camera;

[0052] Fig.10 It is a comparison diagram of the three-axis composite position and attitude errors of the verification configuration group provided by the example of the present invention before and after calibration in a single measurement area and in multiple measurement areas. [Specific implementation method]

[0053] In order to better understand the technical solution of the present invention, the embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0054] It should be clear that 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 ordinary technicians in this field without creative work are within the protection scope of the present invention.

[0055] The embodiment of the present invention provides a self-calibration method for a space robot arm. Figure 1 , which is a schematic flow chart of a space manipulator self-calibration method provided by an embodiment of the present invention, the method comprising the following steps:

[0056] Step 101: Establish a kinematic model of a space manipulator based on a modified Denison-Hartberg method (MDH). The object of this embodiment is a space manipulator.

[0057] Specifically, the MDH method is used to establish the MDH coordinate system of the space manipulator. The MDH method adopts α i 、a i ,θ i d i , β i These five parameters describe the transformation relationship between the connecting rod coordinate systems. For the i-th connecting rod coordinate system Σ i For specific system building rules, please refer to the attached Figure 2 As shown:

[0058] ①Z i The axis is along the axis of joint i;

[0059] ②Origin O iThe intersection of the i+1 axis and the i axis or the common perpendicular line and the Z axis. i The intersection of the axes;

[0060] ③X i Axis along the common perpendicular line a i The direction of the common perpendicular line is from the joint i axis to the joint i+1 axis. If the joint i axis and the joint i+1 axis intersect, then X is specified. i The axis is perpendicular to the plane where the two joint axes lie;

[0061] ④Y i The axis is determined according to the right-hand rule;

[0062] ⑤When the first joint variable is 0, the coordinate system Σ0 and Σ1 coincide. n , whose origin and X n The direction can be chosen arbitrarily, but usually the connecting rod parameter is kept at 0.

[0063] According to the establishment rules of the coordinate system, the transformation matrix between the intermediate link coordinate systems of the manipulator can be obtained respectively, and then the transformation matrix of the tool coordinate system relative to the base coordinate system can be obtained, that is, the kinematic model of the spatial manipulator is obtained.

[0064] The transformation matrix between the robot arm link coordinate systems obtained by the MDH kinematic modeling method can be expressed as

[0065]

[0066] Where n is the number of degrees of freedom of the space manipulator, α i 、a i ,θ i ,d i , β i are the kinematic parameters of the robot arm link coordinate system, Represents the transformation matrix between the robot arm link coordinate systems, Represents the transformation matrix of the robot tool coordinate system relative to the base coordinate system; the K axis represents the X, Y or Z axis, and T rot (K,θ) represents the transformation matrix corresponding to the rotation angle θ around the K axis, T rot (K, d) represents the transformation matrix corresponding to the translation of distance d along the K axis of the coordinate system.

[0067] For an n-DOF space manipulator, the transformation relationship from the base coordinate system to the tool coordinate system, that is, the kinematic model of the space manipulator is:

[0068]

[0069] Step 102: using the kinematic model to obtain an end position error model of the space robot.

[0070] Specifically, according to the characteristics of the MDH method, the error model of the intermediate link coordinate system is derived, and then the end position error model of the spatial manipulator is derived.

[0071] In an embodiment of the present invention, a specific method for deriving a space manipulator error model based on the obtained space manipulator kinematic model includes:

[0072] 1) Derivation of the pose error model between the intermediate link coordinate systems

[0073] Assuming coordinate system Σ i With coordinate system Σ i-1 The nominal transformation matrix between The actual transformation matrix is Then the deviation between the nominal and actual transformation matrices of the coordinate system is

[0074]

[0075] The deviation dT i It can also be expressed as the partial differential of the link transformation matrix with respect to the kinematic parameters

[0076]

[0077] From formula (4), the pose error matrix of the adjacent link coordinate system can be obtained as follows:

[0078]

[0079] At the same time, in formula (5) is the posture error matrix of the adjacent link coordinate system. This matrix is ​​a differential operator, which consists of a differential rotation matrix and a differential translation vector. Its expression can be defined as

[0080]

[0081] in, are the attitude error and position error of coordinate system {i} relative to coordinate system {i-1} respectively.

[0082] From equations (3) to (6), the pose error vector between the intermediate link coordinate systems can be calculated as:

[0083]

[0084] Among them, sθ is the abbreviation of sinθ, and cθ is the abbreviation of cosθ.

[0085] 2) Derivation of the manipulator end position error model

[0086] by and Represent the tool coordinate system Σ tThe nominal transformation matrix and the actual transformation matrix relative to the base coordinate system Σ0, with dT representing the deviation between the nominal and actual transformation matrices, ignoring high-order infinitesimals, can be obtained:

[0087]

[0088] make U n+2 =I4 (i.e., 4×4 unit matrix), then U i is a homogeneous transformation matrix, and its general formula can be expressed as

[0089]

[0090] Among them, the superscript u is used to distinguish the kinematic parameters of the space manipulator. represents the position vector, represents the attitude vector; 0 represents the zero vector;

[0091] Formula (8) can be expressed as

[0092]

[0093] From this, we can deduce that the position error vector of the end of the space manipulator is:

[0094]

[0095] Substituting equation (7) into equation (11), we can get D g represents the end position error vector of the space manipulator caused by the kinematic parameter error, that is, the end position error model of the space manipulator; J e is the error transfer matrix between the kinematic parameter error of the space manipulator and the end position error; e = [e1 e2…e n+1 ] T is the kinematic parameter error vector of the space manipulator; represents the transfer matrix between the link kinematic parameter error and the link coordinate system position error; e i =[Δα i Δa i Δθ i Δd i Δβ i ] T represents the kinematic parameter error vector between the links of the space manipulator, and equation (11) can be expressed as

[0096]

[0097] Among them, J i The specific expression is

[0098]

[0099] Step 103, obtaining the motion range of the hand-eye camera according to the measurement accuracy, the field of view of the hand-eye camera and the visual target parameters.

[0100] Specifically, the field of view spatial shape of the hand-eye camera at a fixed point and fixed posture is referenced in the attached Figure 3 As shown, it is composed of the optical center point O of the field of view. c (x c ,y c ,z c ) is formed by a tetrahedron radiating outward, which is centrally symmetrical about the Z axis. Its size is determined by the horizontal field of view angle α and the vertical field of view angle β. The bottom rectangle of the tetrahedron is the imaging plane of the hand-eye camera.

[0101] Assume that the horizontal field of view angle of the camera is the same as the vertical field of view angle, that is, α = β. When the imaging distance between the hand-eye camera and the target is h m When L c Indicates the length of the maximum imaging plane in the horizontal and vertical directions, and its value is

[0102]

[0103] Set the visual target size to L m ×L m , fixed imaging distance is h m When the maximum imaging plane of the hand-eye camera and the visual target plane are shown in the attached figure Figure 4 In order to ensure the measurement accuracy of the hand-eye camera, the imaging direction of the hand-eye camera is limited to the measurement when the vertical visual target is facing downward, and the imaging distance is no greater than h. max The circumscribed circle of the visual target plane is defined as S m , the diameter is The inscribed circle of the maximum imaging plane of the hand-eye camera is S c , diameter is R c =L c When the circumscribed circle S of the visual target plane m The inscribed circle S that is inscribed or contained in the maximum imaging plane of the hand-eye camera c When the hand-eye camera is turned around its own z-axis, the optical center of the hand-eye camera field of view is in the target coordinate system Σ m The position constraint relationship is

[0104]

[0105] Among them, x c ,y c 、z cThey represent the optical center of the hand-eye camera in the target coordinate system Σ m The coordinate value below.

[0106] According to formula (15), the motion range of the hand-eye camera can be calculated.

[0107] Step 104: Obtain distribution information of each measurement sub-area in the workspace of the spatial manipulator according to the motion range of the hand-eye camera.

[0108] Specifically, since the arm of the space robot can reach more than ten meters in its straight state, only one visual target is configured in its entire workspace, and the measurement space range is small, which cannot fully characterize the influencing mechanism of errors. Therefore, it is necessary to design the target distribution position and number to form multiple feasible measurement sub-areas in the workspace of the space robot to expand the measurement range.

[0109] 1) The total imaging plane size formed by the hand-eye camera under a single visual target

[0110] The length of the space robot arm in the straight state is L r , then its ideal working space is L r The base coordinate system Σ0 is established, and the origin of each visual target is placed at a distance of 0 from the center of the bottom circle of the space manipulator workspace. Position, establish visual target systemΣ m At this time, the position relationship between the origin O0 of the visual target system and the origin O0 of the robot base is

[0111] |O0-O m |=L r / 2 (16)

[0112] Combining formula (15), we can know that when the imaging distance z cmax =h max When , the imaging plane of the hand-eye camera is the largest, and its side length is

[0113]

[0114] Since the point can rotate around its own z-axis direction at any angle, the imaging plane of the hand-eye camera forms a diameter of According to the motion range of the hand-eye camera under a single visual target, the total imaging plane formed is approximately a circular imaging plane with a diameter of R I The circle is expressed as

[0115]

[0116] in, When the imaging distance z c =h maxThe maximum distance along the x-axis of the target coordinate system is also the range of motion of the hand-eye camera perpendicular to the visual target within the target Σ m The maximum circle radius of the xoy plane projection of the system.

[0117] 2) Distribution scheme of multiple visual targets

[0118] According to the motion range of the hand-eye camera under a single visual target, the total imaging plane formed by the hand-eye camera at this position can be obtained. Figure 5 The relationship between the total imaging plane of the hand-eye camera and the local fan-shaped workspace of the manipulator, calculate the tangent relationship between the total imaging plane and the center O0 of the bottom circle of the spatial manipulator workspace, and the angle δ formed is:

[0119]

[0120] In order to ensure that the total imaging planes of the hand-eye camera under each visual target do not overlap, that is, only one visual target image can be obtained in each total imaging plane, the bottom circle of the space manipulator workspace is divided into num sectors evenly with the same angle value 2(δ+Δδ) with the center O0 as the starting point, and the angle range of each sector is [2(δ+Δδ)·(i-1),2(δ+Δδ)·i], where i=1,2,…,num, Δδ represents the threshold of the angle, and the calculation formula of the number of targets num is:

[0121]

[0122] Where num is an integer.

[0123] Thus, the position distribution information of each visual target is generated, that is, the center point P of the visual target in each measurement sub-area i The coordinate position distribution information is

[0124]

[0125] Where i=1,2,…num represents the target number.

[0126] Step 105: obtaining kinematic parameter calibration values ​​of the space manipulator according to the terminal posture error model and the distribution information of each measurement sub-area.

[0127] Specifically, according to the distribution information of each measurement sub-area, m groups of measurement configurations are randomly generated in multiple measurement sub-areas, and the manipulator is driven to collect the actual pose set PE corresponding to each group of measurement configurations a ; And use the kinematic model of the space manipulator established by the MDH method to calculate the nominal pose set PE corresponding to each set of measurement configurations n ; According to the actual posture set PEa and the nominal pose set PE n , the position error of the end of the space manipulator caused by the kinematic parameter error can be obtained for each set of measurement configurations

[0128] The MDH model of the n-DOF space manipulator has a total of 5 (n+1) kinematic parameters. To solve the errors of all kinematic parameters, we take these m groups of configurations and substitute them into equation (12) to construct the overdetermined equations as follows:

[0129]

[0130] remember Then formula (22) can be written as

[0131]

[0132] Using the least squares method to solve equation (22)

[0133]

[0134] in, The error transfer matrix The pseudo-inverse.

[0135] The kinematic parameter error of the robot arm obtained by formula (24) can be used to correct the nominal kinematic parameters. According to the kinematic parameter error, the nominal kinematic parameters are corrected using the following formula:

[0136] E C =E N +e (25)

[0137] Among them, E C is the corrected kinematic parameter, E N is the nominal kinematic parameter, e is the kinematic parameter error;

[0138] Determine whether the corrected kinematic parameters meet the accuracy requirements. If not, a finite number of iterations is required to make the error converge to the allowable range. i represents the kinematic parameters of the robot in the i-th iteration, represents the kinematic parameter error of the robot arm solved in the i-th iteration, then the kinematic parameter of the robot arm in the i+1-th iteration is

[0139]

[0140] Please refer to the attached iterative flow chart Figure 6 .

[0141] According to the above method provided by the example of the present invention, a self-calibration method of a space robot arm is simulated.

[0142] In this embodiment, the MDH system diagram of the seven-degree-of-freedom spatial robot arm of the research object is shown in the attached Figure 7 , MDH parameters are shown in Table 1

[0143] Table 1 MDH parameters of space manipulator

[0144]

[0145]

[0146] At the same time, the geometric dimension parameters of the arm of the given space robot are shown in Table 2

[0147] Table 2 Geometric parameters of space manipulator

[0148]

[0149] Assume that the horizontal and vertical field of view angles of the camera are α = β = 60°, and the target size is L m = 20cm, and in order to ensure the measurement accuracy, the vertical distance between the center point of the camera field of view and the target is constrained to be no greater than h max =1.5m. According to formula (15), the optical center point P of the hand-eye camera field of view is plotted under the given size and position of a single visual target. c The motion range point cloud diagram is attached Figure 8 As shown, the plane imaging area size R of the hand-eye camera can be obtained from formula (18): I ≈3.90m.

[0150] From the geometric dimensions of the space manipulator, we know that the radius of the straightened state is L r =11m, and Δδ=5°, the number of targets calculated by formula (20) is num=6. According to the distribution scheme of multiple measurement sub-areas, multiple visual target configurations and their corresponding kinematic range point cloud diagrams of the optical center point of the hand-eye camera field of view can be simulated. Fig. 9 shown.

[0151] In order to verify the feasibility of the self-calibration method of the space manipulator proposed in this paper, the kinematic parameter error values ​​caused by geometric errors are randomly generated, where the angle error is randomly selected in the interval [-0.5°, 0.5°], and the length error is randomly selected in the interval [-0.005m, 0.005m]. The preset values ​​of the kinematic parameter errors of the space manipulator are shown in Table 3.

[0152] Table 3 Preset values ​​of kinematic parameter errors of space manipulator

[0153]

[0154]

[0155] At the same time, in order to simulate the actual self-calibration experimental environment, the measurement errors generated by the measuring equipment, namely the joint angle δj measured by the measuring sensor, the end position δp and the end posture δe measured by the hand-eye camera, and the non-geometric error caused by temperature and other reasons generally account for about 10% of the total error. Therefore, uniformly distributed measurement noise is added to the measurement error and non-geometric error respectively as shown in Table 4.

[0156] Table 4 Distribution settings of measurement interference error terms

[0157]

[0158] In the single measurement area formed by a single visual target and the multi-measurement area formed by multiple visual targets, a set of measurement configurations that meet the measurement area restrictions are randomly generated, and the kinematic parameter error calibration values ​​are calculated respectively. At the same time, a verification configuration group is randomly generated in the manipulator workspace, and the kinematic parameter error calibration values ​​of the single measurement area and the multi-measurement area are used to calculate the terminal posture error of the verification configuration group before and after calibration. The comparison diagram of the three-axis synthetic position and posture error before and after calibration is obtained. See the attached figure for reference. Fig.10 shown.

[0159] By processing the experimental data, the maximum, minimum and average values ​​of the three-axis synthetic total error of the terminal position and posture before and after calibration can be obtained as shown in Table 5.

[0160] Table 5 Comparison of terminal pose error data before and after calibration

[0161]

[0162]

[0163] From the analysis of the data in Table 5, it can be seen that the average values ​​of the terminal position and posture errors after calibration of the two methods are significantly reduced compared with those before calibration. Among them, the average position error of the single vision target method is reduced by 77.87%, and the average posture error is reduced by 81.83%. The average position error of the multi-vision target method is reduced by 92.26%, and the average posture error is reduced by 98.33%. The experimental results show that the calibration results of the multi-vision target method are better than those of the single vision target method and are more robust.

[0164] The technical solution of the embodiment of the present invention has the following beneficial effects:

[0165] The technical solution of the embodiment of the present invention provides a general space manipulator self-calibration method. By adopting the self-calibration method proposed in the technical solution of the embodiment of the present invention, error data of a larger measurement range can be obtained, and the kinematic parameter calibration accuracy and the globality of the calibration results can be improved.

[0166] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A self-calibration method for a space manipulator, characterized in that: The method comprises: The kinematic model of the space manipulator is established based on the modified Denison-Hartberg method (MDH); Using the kinematic model, a terminal position and posture error model of the space manipulator is obtained; According to the measurement accuracy, the field of view of the hand-eye camera and the visual target parameters, the motion range of the hand-eye camera is obtained; According to the motion range of the hand-eye camera, distribution information of each measurement sub-area in the workspace of the space manipulator is obtained; According to the terminal posture error model and the distribution information of each measurement sub-area, the kinematic parameter calibration values ​​of the space manipulator are obtained.

2. The method according to claim 1, characterized in that The kinematic model of the space manipulator is: Where n is the number of degrees of freedom of the space manipulator, α i 、a i ,θ i ,d i , β i are the kinematic parameters of the robot arm link coordinate system, Represents the transformation matrix between the robot arm link coordinate systems, Represents the transformation matrix of the robot tool coordinate system relative to the base coordinate system; the K axis represents the X, Y or Z axis, and T rot (K,θ) represents the transformation matrix corresponding to the rotation angle θ around the K axis, T rot (K, d) represents the transformation matrix corresponding to the translation of distance d along the K axis of the coordinate system.

3. The method according to claim 1, characterized in that The end position error model of the space manipulator is: Among them, D g is the position error vector of the end of the space manipulator caused by the kinematic parameter error, J e is the error transfer matrix between the kinematic parameter error of the space manipulator and the end position error, e=[e1 e2 … e n+1 ] T is the kinematic parameter error vector of the space manipulator; It represents the transfer matrix between the link kinematic parameter error and the link coordinate system posture error, e i =[Δα i Δa i Δθ i Δd i Δβ i ] T Represents the kinematic parameter error vector between the links of the space manipulator.

4. The method according to claim 3, characterized in that The transfer matrix between the connecting rod kinematic parameter error and the connecting rod coordinate system posture error is: Among them, Represents the transformation matrix between the coordinate systems of the space manipulator link, and defines By distinguishing the superscript u from the representation of the kinematic parameters of the space manipulator, the position vector can be obtained and the posture vector 0 represents the zero vector; sθ is the abbreviation of sinθ, cθ is the abbreviation of cosθ; α i 、a i ,θ i ,d i , β i are the kinematic parameters of the space manipulator link coordinate system.

5. The method according to claim 1, characterized in that The motion range of the hand-eye camera is expressed as: Among them, α is the horizontal field of view of the camera, L m is the side length of the visual target, h max is the distance between the light spot of the hand-eye camera and the visual target, i.e. the maximum object distance, x c ,y c 、z c They respectively represent the three-dimensional coordinate values ​​of the optical center of the hand-eye camera in the visual target coordinate system.

6. The method according to claim 1, characterized in that According to the motion range of the hand-eye camera, the distribution information of each measurement sub-area in the workspace of the space manipulator is obtained, including: According to the motion range of the hand-eye camera under a single visual target, the maximum diameter of the total imaging plane of the hand-eye camera is calculated as: Among them, x cmax Indicates the maximum motion range of the hand-eye camera in the x direction; Indicates that the imaging distance of the hand-eye camera is h max , and the maximum imaging plane width at a single position when the horizontal field of view angle is α; L r represents the radius of the bottom circle of the space manipulator workspace. The origin of each visual target is located at a distance of 0 from the center of the bottom circle of the space manipulator workspace. According to the motion range of the hand-eye camera under a single visual target, the total imaging plane formed by the hand-eye camera at this position can be obtained. The tangent relationship between this plane and the center of the bottom circle of the space manipulator workspace is calculated, and the angle δ formed is: Taking the center O0 of the bottom circle of the space manipulator workspace as the starting point, the bottom circle is evenly divided into num sectors with equal angle value 2(δ+Δδ), and the angle range of each sector is [2(δ+Δδ)·(i-1),2(δ+Δδ)·i], where i=1,2,…,num, Δδ represents the threshold of the angle, and the calculation formula of the number num is: In each sector, the center of the circle is A visual target is placed at the position of and the position distribution information of each visual target is generated as As the distribution information of each measurement sub-area.

7. The method according to claim 1, characterized in that According to the end position error model and the distribution information of each measurement sub-area, the kinematic parameter calibration value of the space manipulator is obtained, including: According to the distribution information of each measurement sub-area, multiple groups of measurement configurations are randomly selected in multiple measurement sub-areas, and the robot arm is driven to collect the actual pose set PE corresponding to each group of measurement configurations a ; And use the kinematic model of the space manipulator established by the MDH method to calculate the nominal pose set PE corresponding to each set of measurement configurations n ; According to the actual posture set PE a and the nominal pose set PE n , the position error of the end of the space manipulator caused by the kinematic parameter error can be obtained for each set of measurement configurations The end position error model and the following formula are used to solve the kinematic parameter error of the spatial manipulator: in, It is the pseudo-inverse of the error transfer matrix between the kinematic parameter error and the terminal posture error; According to the kinematic parameter error, the nominal kinematic parameters are corrected using the following formula: AND C =And N +e Among them, E C is the corrected kinematic parameter, E N is the nominal kinematic parameter, e is the kinematic parameter error; Determine whether the corrected kinematic parameters meet the accuracy requirements. If not, iterate the correction steps a finite number of times, wherein the iteration method is: Among them, E i+1 represents the kinematic parameters of the space manipulator in the i+1th iteration, E i represents the kinematic parameters of the space manipulator in the i-th iteration, e i represents the kinematic parameter error of the spatial manipulator obtained in the i-th iteration.

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