A robot calibration method based on FIS theory

Abstract

The present invention discloses a robot calibration method based on FIS theory, comprising the following steps: measuring the robot end position error screw based on a laser tracker; establishing the robot's kinematic error model based on FIS theory; identifying the joint axis parameters based on the least squares method; converting the joint axis error into the active joint angle error for error compensation. In view of the problems existing in the existing kinematic calibration methods, such as the unintuitive interpretation of the error source, unclear error identification influencing mechanism, and inconvenient kinematic calibration process, the present invention systematically conducts research on error modeling and identification based on the finite instantaneous screw theory, and establishes a robot error model that meets the conditions of completeness, continuity, and minimization. In the error compensation stage, the present invention converts the identified joint axis error into the driving joint motion, thereby realizing efficient error compensation without changing the control system model. The present invention has high calibration accuracy, simple operation, and strong applicability.

Description

Technical Field

[0001] The invention belongs to the field of robot calibration, and in particular relates to a robot calibration method based on FIS theory. Background Art

[0002] The end positioning accuracy of the robot is a core technology in the field of robot processing applications. It is also a key indicator for the robot to extend from innovative design to engineering applications. It directly determines the robot's operating ability and product quality in processing applications.

[0003] Therefore, accuracy is defined as the primary operating indicator of robots in the industrial robot standard R15.05-1. For the geometric dimension errors of robots themselves, the existing solutions generally include error prevention and parameter calibration. Compared with the shortcomings of error prevention such as low efficiency and high cost, kinematic calibration is one of the effective methods to solve the geometric errors of robots.

[0004] The kinematic calibration of the robot first establishes the mapping relationship between the robot joint error and the terminal output error, then measures the actual position and posture of the terminal to calculate the terminal output error, then solves the joint error through the terminal output error and the mapping relationship, and finally corrects the control model according to the results of the error identification solution.

[0005] The above kinematic calibration process can be summarized into four parts: error measurement, error modeling, error identification and error compensation.

[0006] The kinematic calibration problems of robots are manifested in the following aspects:

[0007] First, in the error modeling link, there is still a lack of parallel mechanism error models that meet the error completeness and continuity conditions, can clearly realize error traceability and interpretation, and intuitively express the error transmission and accumulation characteristics.

[0008] Second, in the error identification link, the influence mechanism of the coupling relationship caused by the mutual constraints between parallel branches on error identification is still unclear.

[0009] In response to the above problems and challenges, the present invention carries out research on error modeling, error identification and error compensation based on FIS theory, which is of great significance to improving the absolute positioning accuracy of the robot and realizing rapid on-site calibration of the robot. Summary of the invention

[0010] The present invention is proposed to solve the problems existing in the prior art, and its purpose is to provide a robot calibration method based on FIS theory.

[0011] The technical solution of the present invention is: a robot calibration method based on FIS theory, comprising the following steps:

[0012] ⅰ. Measure the error rotation of the robot end position based on the laser tracker;

[0013] ⅱ. Establish the robot's kinematic error model based on FIS theory;

[0014] ⅲ. Identify joint axis parameters based on least squares method;

[0015] ⅳ. Convert the joint axis error into active joint angle error for error compensation.

[0016] Furthermore, step i measures the error rotation of the robot end position based on the laser tracker, including the acquisition process and the calculation process.

[0017] Step i includes the acquisition process of measuring the robot end position error rotation based on the laser tracker. The specific process is as follows:

[0018] First, several points are evenly selected in the robot's workspace, the robot's end is driven to these points, and the robot's joint motion is recorded;

[0019] Then, a laser tracker is used to record the spatial coordinates of the end point as the actual end position of the robot.

[0020] Furthermore, step i includes a calculation process based on the laser tracker to measure the error rotation of the robot end position, and the specific process is as follows:

[0021] The laser tracker is used to record the end coordinate system, the spatial coordinates in the base coordinate system and the joint motion of the robot to calculate the actual end finite rotation of the coordinate system.

[0022] Furthermore, step ii establishes the kinematic error model of the robot based on FIS theory. The specific process is as follows:

[0023] Firstly, the terminal posture error is calculated from the theoretical terminal posture finite rotation and the actual terminal posture finite rotation;

[0024] Then, a differential error mapping model based on FIS theory is established to obtain the mapping relationship between the kinematic parameters to be calibrated, namely the joint axis error and the end position error.

[0025] Furthermore, step iii identifies the joint axis parameters based on the least squares method, and the specific process is as follows:

[0026] First, the joint angle values ​​of the robot joint motion in step i and the end point space coordinates of the actual end position in step ii are brought into the differential error mapping model to establish the identification equation group of the robot error parameters;

[0027] Then, the least squares algorithm is used to quickly and efficiently identify the error parameters to be identified.

[0028] Furthermore, step iv converts the joint axis error into the active joint angle error for error compensation. The specific process is as follows:

[0029] First, the calibrated error parameters are substituted into the error compensation model;

[0030] Then, the joint axis error is converted into the active joint error;

[0031] Finally, the active joints are driven to achieve error compensation.

[0032] Furthermore, step iii establishes the identification equation group of the robot error parameters, which requires the introduction of a filter matrix for construction.

[0033] The beneficial effects of the present invention are as follows:

[0034] In order to solve the problems existing in existing kinematic calibration methods, such as the unintuitive interpretation of error tracing, unclear error identification influencing mechanism, and inconvenient kinematic calibration process, the present invention systematically carries out research on error modeling and identification based on the finite instantaneous spinor theory, and establishes a robot error model that meets the conditions of completeness, continuity and minimization.

[0035] In the error compensation stage, the present invention converts the identified joint axis error into the driving joint motion amount, thereby realizing efficient error compensation without changing the control system model.

[0036] The present invention has high calibration accuracy, simple operation and strong applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 is a flow chart of the serial mechanism calibration method of the present invention;

[0038] Figure 2 is a flow chart of the parallel mechanism calibration method of the present invention;

[0039] Figure 3 This is a comparison chart of the accuracy of the UR3 serial robot before and after calibration in the present invention;

[0040] Figure 4 This is a comparison chart of the accuracy of the Helix parallel robot before and after calibration in the present invention. DETAILED DESCRIPTION

[0041] Hereinafter, the present invention will be described in detail with reference to the accompanying drawings and embodiments:

[0042] like Figures 1 to 4 As shown, a robot calibration method based on FIS theory includes the following steps:

[0043] ⅰ. Measure the error rotation of the robot end position based on the laser tracker;

[0044] ⅱ. Establish the robot's kinematic error model based on FIS theory;

[0045] ⅲ. Identify joint axis parameters based on least squares method;

[0046] ⅳ. Convert the joint axis error into active joint angle error for error compensation.

[0047] Step i measures the robot end position error rotation quantity based on the laser tracker, including the acquisition process and the calculation process.

[0048] Step i includes the acquisition process of measuring the robot end position error rotation based on the laser tracker. The specific process is as follows:

[0049] First, several points are evenly selected in the robot's workspace, the robot's end is driven to these points, and the robot's joint motion is recorded;

[0050] Then, a laser tracker is used to record the spatial coordinates of the end point as the actual end position of the robot.

[0051] Step i includes the calculation process of measuring the robot end position error rotation based on the laser tracker. The specific process is as follows:

[0052] The laser tracker is used to record the end coordinate system, the spatial coordinates in the base coordinate system and the joint motion of the robot to calculate the actual end finite rotation of the coordinate system.

[0053] Step ii: Establish the robot's kinematic error model based on FIS theory. The specific process is as follows:

[0054] Firstly, the terminal posture error is calculated from the theoretical terminal posture finite rotation and the actual terminal posture finite rotation;

[0055] Then, a differential error mapping model based on FIS theory is established to obtain the mapping relationship between the kinematic parameters to be calibrated, namely the joint axis error and the end position error.

[0056] Among them, FIS theory is finite instantaneous spinor theory.

[0057] Step iii: Identify the joint axis parameters based on the least squares method. The specific process is as follows:

[0058] First, the joint angle values ​​of the robot joint motion in step i and the end point space coordinates of the actual end position in step ii are brought into the differential error mapping model to establish the identification equation group of the robot error parameters;

[0059] Then, the least squares algorithm is used to quickly and efficiently identify the error parameters to be identified.

[0060] Step iv: convert the joint axis error into the active joint angle error for error compensation. The specific process is as follows:

[0061] First, the calibrated error parameters are substituted into the error compensation model;

[0062] Then, the joint axis error is converted into the active joint error;

[0063] Finally, the active joints are driven to achieve error compensation.

[0064] Step iii: To establish the identification equations of the robot error parameters, a filter matrix needs to be introduced for construction.

[0065] Embodiment 1

[0066] Take the serial robot as an example to illustrate this embodiment

[0067] Step 1. Measure the robot end position error rotation based on the laser tracker

[0068] Select several points evenly in the robot's workspace, drive the robot end to these points, and use a laser tracker to record the spatial coordinates of the end coordinate system {T} in the base coordinate system {B} and the robot's joint motion.

[0069] The actual finite motion of the coordinate system {T} is calculated from the measured end point coordinates as S f,a .

[0070] Specifically, the dynamic and static platform posture transformation matrix R st It is expressed as:

[0071]

[0072] When trace(R st )≠1, we can get:

[0073]

[0074]

[0075]

[0076] In the formula,

[0077] in, Yes st The skew-symmetric matrix, b st is the position matrix of {T} relative to {B}, R st is the attitude matrix of {T} relative to {B}.

[0078] sf,st =ω st / ||ω st ||

[0079]

[0080]

[0081] Therefore, the actual finite rotation of the robot end is:

[0082]

[0083] In the formula, S f,a It is the actual finite rotation of the terminal calculated from the actual posture of the terminal.

[0084] Step ii. Establish the robot's kinematic error model based on FIS theory

[0085] The actual finite rotation of the robot end is calculated from the actual position of the robot end measured in step ⅰ as S f,a , the theoretical finite rotation at the end of the branch chain is calculated from the joint rotation angle:

[0086] S f,serial =S f,st ΔS f,n Δ…ΔS f,1

[0087] In the formula, Δ represents the triangular product operation, S f,st represents the finite motion between the end coordinate system {T} of the mechanism and the world coordinate system {B} in the initial state, S f,n To S f,1 They represent the limited motion of the corresponding joints in sequence, and the joint numbers are set to increase from 1 to n in the direction from the base to the end.

[0088] The end position error of the robot is obtained by quasi-differential operation Qd(·):

[0089] δS t =Qd(-S f,serial ΔS f,a )

[0090] The kinematic error mapping relationship of the series branch chain is as follows:

[0091]

[0092] In the formula, is the instantaneous axis of the current state of the j-th joint.

[0093] The series branch error map can be organized into the following format:

[0094] Qd(-Sf,serial ΔS f,a )=y=CDS e +Fδq

[0095] in,

[0096] C=[J0 J1 … J n-1 J n ],

[0097]

[0098] In the formula, is the joint axis error of the kth joint,

[0099] is the initial end axis error,

[0100] δq k is the kth joint motion error.

[0101] Step iii. Identify joint axis parameters based on least squares method

[0102] In the serial mechanism, the joint is the active joint, δq k It is considered to be directly understandable as sensor noise or encoder offset, which can be directly read from the corresponding sensor, so all joint zero position errors should be eliminated from the error model. The composite error model containing N identified measurement point pose data can be expressed as follows:

[0103]

[0104] From the composition of the above formula, the error parameter vector S L The coefficient matrix of is obtained from the matrix μ.

[0105] The intra-chain redundancy of the series branch chain exists in the μ matrix. From the perspective of the spinor axis error, the redundant error of the R pair corresponds to the error vector The 3rd and 6th items of the P pair correspond to the error vector The 1st, 2nd, 3rd, and 6th items of can be used to eliminate the redundant errors within the branch chain by constructing a null space matrix.

[0106] To simplify the format of the culling matrix, the axis error in the world system is Axis error converted to local system

[0107]

[0108] Among them, A dg,jRepresenting the 6-dimensional transformation matrix from the local system to the world system, the error identification equation that eliminates the redundancy within the chain can be obtained:

[0109] y=CDA dgs δS lc =(CDA dgs U)δS lc

[0110] in,

[0111]

[0112] The matrix U is a filter matrix that eliminates the intra-chain redundancy of the series branch chain. The u in the diagonal position j The matrix corresponds to the filter matrix that eliminates the redundancy of the j-th joint.

[0113] As shown in the following formula, according to the different types of joints j, u j The matrix can be divided into the filter matrix u for R pairs R and the filter matrix u for P pairs P .

[0114]

[0115] The redundancy in the chain is eliminated by introducing the filter matrix U in the branch chain model. The full-rank μ matrix is ​​obtained from the μ matrix containing redundancy. u Matrix, axis error S L After removing the redundant items in the chain and transferring to the local coordinate system, it changes to S LU . Through μ u Matrix The format to obtain the minimum error model is as follows:

[0116]

[0117] S LU =(μ u T μ u ) -1 μ u T Y

[0118] In the formula, μ u To obtain a μ matrix with full column rank from a μ matrix containing redundancy u matrix;

[0119] Step iv. Convert the joint axis error into the active joint angle error for error compensation

[0120] The purpose of error compensation is to improve the operation accuracy of the robot end. The compensation idea proposed in the present invention is to set an additional drive joint motion δq aOffset the influence of joint axis error on the robot end error, thereby achieving zero end error.

[0121] For a serial mechanism, when we expect the robot to move to a certain point in the workspace, the actual finite rotation of the robot end at that point can be expressed as

[0122]

[0123] In the formula,

[0124]

[0125]

[0126] in,

[0127]

[0128] Through the above error parameter identification, the robot axis parameter error δS can be obtained t,k And the initial pose error δS t,st , while keeping the actual finite motion unchanged, the finite motion contributed by each joint is transformed into

[0129]

[0130] Then the corresponding joint rotation error of the robot at this point can be obtained as

[0131]

[0132] δθ k ′ is the amount of motion that needs to be compensated for each joint. The series mechanism is driven to compensate for the corresponding joint rotation error, and the robot can be moved to the ideal position.

[0133] Embodiment 2

[0134] Take the parallel robot as an example to illustrate this embodiment

[0135] Step 1. Measure the robot end position error rotation based on the laser tracker

[0136] Select several points evenly in the robot's workspace, drive the robot end to these points, and use a laser tracker to record the spatial coordinates of the end coordinate system {T} in the base coordinate system {B} and the robot's joint motion.

[0137] The actual finite motion of the coordinate system {T} is calculated from the measured end point coordinates as S f,a .

[0138] Specifically, the dynamic and static platform posture transformation matrix R st It is expressed as:

[0139]

[0140] When trace(R st )≠1, we can get:

[0141]

[0142]

[0143]

[0144] In the formula, in, Yes st The skew-symmetric matrix, b st is the position matrix of {T} relative to {B}, R st is the attitude matrix of {T} relative to {B}.

[0145] s f,st =ω st / ||ω st ||

[0146]

[0147]

[0148] Therefore, the actual finite rotation of the robot end is:

[0149]

[0150] In the formula, S f,a It is the actual finite rotation of the terminal calculated from the actual posture of the terminal.

[0151] Step ii. Establish the robot's kinematic error model based on FIS theory

[0152] The actual finite rotation of the robot end is calculated from the actual position of the robot end measured in step ⅰ as S f,a , the theoretical finite rotation at the end of the branch chain is calculated from the joint rotation angle:

[0153] S f,serial =S f,st ΔS f,n Δ…ΔS f,1

[0154] In the formula, Δ represents the triangular product operation, S f,st represents the finite motion between the end coordinate system {T} of the mechanism and the world coordinate system {B} in the initial state, S f,n To S f,1They represent the limited motion of the corresponding joints in sequence, and the joint numbers are set to increase from 1 to n in the direction from the base to the end.

[0155] The end position error of the robot is obtained by quasi-differential operation Qd(·):

[0156] δS t =Qd(-S f,serial ΔS f,a )

[0157] The kinematic error mapping relationship of the series branch chain is as follows:

[0158]

[0159] In the formula, is the instantaneous axis of the current state of the j-th joint.

[0160] The series branch error map can be organized into the following format:

[0161] Qd(-S f,serial ΔS f,a )=y=CDS e +Fδq

[0162] in,

[0163] C=[J0 J1 … J n-1 J n ],

[0164]

[0165] In the formula, is the joint axis error of the kth joint,

[0166] is the initial end axis error,

[0167] δq k is the kth joint motion error.

[0168] The series branches form a parallel mechanism by sharing the same moving platform. Assuming that there are l branches in the parallel mechanism, the kinematic error mapping relationship of the parallel branches is as follows:

[0169]

[0170] By sorting out the different parameters in the above formula, we can preliminarily get the error model of the parallel mechanism as follows:

[0171] E L y=ΦΨS L +Hδq L

[0172] in,

[0173]

[0174]

[0175] In order to improve the practicality of the error model, the model needs to be adjusted to reduce the proportion of passive joints while ensuring the correctness of the model.

[0176] Based on the special arrangement of the F matrix in the above formula, the driving force spinor S wa and the constraint force screw S wc As the basic element, the passive joint screening matrix is ​​defined as follows:

[0177]

[0178] in,

[0179] W i =[S wa,i S wc,i ],

[0180] S wa,i =[S wa,1,i … S wa,m,i ],S wc,i =[S wc,1,i … S wc,d,i ]

[0181] W i The matrix represents the aggregate matrix of all the force spins inside the i-th branch, including all the driving force spins S in the i-th branch wa,i and the total constraint force screw S wc,i .

[0182] By multiplying both sides of the above equation by matrix Γ, the error model of the parallel mechanism can be transformed into the following format:

[0183] ΓE L y=S F y=ΓΦΨS L +Kδq a

[0184] in,

[0185]

[0186]

[0187] Step iii. Identify joint axis parameters based on least squares method

[0188] The composite error model containing N identified measurement point pose data can be expressed as follows:

[0189]

[0190] From the composition of the above formula, the error parameter vector S L The coefficient matrix of is obtained by multiplying the diagonal block matrix τ with the matrix μ.

[0191] The matrix μ is a combination of the internal information of each branch chain, while the matrix τ is an additional matrix introduced through the reciprocal product relationship to eliminate the error of passive joint motion.

[0192] The redundancy within the series branch chain exists in the μ matrix. From the perspective of the spinor axis error, the redundant error of the R pair corresponds to the error vector The 3rd and 6th items of the P pair correspond to the error vector The 1st, 2nd, 3rd, and 6th items of can be used to eliminate the redundant errors within the branch chain by constructing a null space matrix.

[0193] To simplify the format of the culling matrix, the axis error in the world system is Axis error converted to local system

[0194]

[0195] Among them, A dg,j Representing the 6-dimensional transformation matrix from the local system to the world system, the error identification equation that eliminates the redundancy within the chain can be obtained:

[0196] y=CDA dgs δS lc =(CDA dgs U)δS lc

[0197] in,

[0198]

[0199] The matrix U is a filter matrix that eliminates the intra-chain redundancy of the series branch chain. The u in the diagonal position j The matrix corresponds to the filter matrix that eliminates the redundancy of the j-th joint.

[0200] As shown in the following formula, according to the different types of joints j, u j The matrix can be divided into the filter matrix u for R pairs R and the filter matrix u for P pairs P .

[0201]

[0202] The redundancy in the chain is eliminated by introducing a local filter matrix U in the branch chain model. The full-rank μ matrix is ​​obtained from the μ matrix containing redundancy. u Matrix, axis error S L After removing the redundant items in the chain and transferring to the local coordinate system, it changes to S LU . Through μ u Matrix The format to obtain the minimum error model is as follows:

[0203] Y τ =τ T (ττ T ) -1 Y=μS L

[0204] S LU =(μ u T μ u ) -1 μ u T Y τ

[0205] In the formula, μ u To obtain a μ matrix with full column rank from a μ matrix containing redundancy u matrix;

[0206] τ is the force screw matrix containing the posture point information, that is, the set of force screw matrices at different measurement points:

[0207]

[0208] Step iv. Convert the joint axis error into the active joint angle error for error compensation

[0209] The purpose of error compensation is to improve the operation accuracy of the robot end. The compensation idea proposed in the present invention is to set an additional drive joint motion δq a Offset the influence of joint axis error on the robot end error, thereby achieving zero end error.

[0210] Introducing the filter matrix L, the error compensation equation is as follows:

[0211]

[0212] in,

[0213]

[0214] Based on the above equivalent conversion idea, the equivalent drive joint compensation can be obtained as follows:

[0215] δq a =K-1 ΓΦΨLS LU

[0216] In actual use, the compensation amount δq can be obtained in real time through the above formula according to the end position of the mechanism and the axis error obtained by identification. a . a By adding the motion of the driving joint obtained by inverse solution of the mechanism, the end operation accuracy of the parallel mechanism can be improved.

[0217] Based on the present invention, the UR3 serial robot and the Helix parallel robot are calibrated.

[0218] Figure 2 This is a comparison chart of the accuracy of the UR3 serial robot before and after calibration. Figure 3 This is a comparison chart of the accuracy of the Helix parallel robot before and after calibration.

[0219] In order to solve the problems existing in existing kinematic calibration methods, such as the unintuitive interpretation of error tracing, unclear error identification influencing mechanism, and inconvenient kinematic calibration process, the present invention systematically carries out research on error modeling and identification based on the finite instantaneous spinor theory, and establishes a robot error model that meets the conditions of completeness, continuity and minimization.

[0220] In the error compensation stage, the present invention converts the identified joint axis error into the driving joint motion amount, thereby realizing efficient error compensation without changing the control system model.

[0221] The present invention has high calibration accuracy, simple operation and strong applicability.

Claims

1. A robot calibration method based on FIS theory, characterized by: The following steps are involved: (i) Measuring the error rotation of the robot end position based on the laser tracker; (ii) Establish the robot's kinematic error model based on FIS theory; (iii) Identify joint axis parameters based on the least squares method; (iv) converting the joint axis error into the active joint angle error for error compensation; Step (ii) Establish the robot's kinematic error model based on FIS theory. The specific process is as follows: Firstly, the terminal posture error is calculated from the theoretical terminal posture finite rotation and the actual terminal posture finite rotation; Then, a differential error mapping model based on FIS theory is established to obtain the mapping relationship between the kinematic parameters to be calibrated, namely the joint axis error and the terminal posture error; The actual finite rotation of the robot end is calculated from the actual position of the robot end measured in step (i) as S f,a , the theoretical finite rotation at the end of the branch chain is calculated from the joint rotation angle: S f,serial =S f,st ΔS f,n Δ…ΔS f,1 In the formula, Δ represents the triangular product operation, S f,st represents the finite motion between the end coordinate system {T} of the mechanism and the world coordinate system {B} in the initial state, S f,n To S f,1 In turn, they represent the limited motion of the corresponding joints, and the joint numbers are set to increase from 1 to n in the direction from the base to the end; The end position error of the robot is obtained by quasi-differential operation Qd(·): δS t =Qd(-S f,serial ΔS f,a ) The kinematic error mapping relationship of the series branch chain is as follows: In the formula, is the instantaneous axis of the current state of the j-th joint; The series branch error map can be organized into the following format: Qd(-S f,serial ΔS f,a )=y=CDS e +Fδq in, C=[J0 J1…J n-1 J n ], In the formula, is the joint axis error of the kth joint, is the initial end axis error, δq k is the kth joint motion error; The series branches form a parallel mechanism by sharing the same moving platform. Assuming that there are L branches in the parallel mechanism, the kinematic error mapping relationship of the parallel branches is as follows: By sorting out the different parameters in the above formula, we can preliminarily get the error model of the parallel mechanism as follows: E L y=ΦΨS L +Hδq L in, In order to improve the practicality of the error model, it is necessary to adjust the model and reduce the proportion of passive joints while ensuring the correctness of the model; Based on the special arrangement of the F matrix in the above formula, the driving force spinor S wa and the constraint force screw S wc As the basic element, the passive joint screening matrix is ​​defined as follows: in, W i =[S wa,i S wc,i ], S wa,i =[S wa,1,i …S wa,m,i ],S wc,i =[S wc,1,i …S wc,d,i ] W i The matrix represents the aggregate matrix of all the force spins inside the i-th branch, including all the driving force spins S in the i-th branch wa,i and the total constraint force screw S wc,i ; By multiplying both sides of the above equation by matrix Γ, the error model of the parallel mechanism can be transformed into the following format: GE L y=S F y=ΓΦΨS L +Kδq a in, 2. The robot calibration method based on FIS theory according to claim 1, characterized in that: Step (i) measures the robot end position error rotation quantity based on the laser tracker, including the acquisition process and the calculation process.

3. The robot calibration method based on FIS theory according to claim 1, characterized in that: Step (i) includes the acquisition process of measuring the robot end position error rotation quantity based on the laser tracker, and the specific process is as follows: First, several points are evenly selected in the robot's workspace, the robot's end is driven to these points, and the robot's joint motion is recorded; Then, a laser tracker is used to record the spatial coordinates of the end point as the actual end position of the robot.

4. The robot calibration method based on FIS theory according to claim 3, characterized in that: Step (i) includes a calculation process for measuring the robot end position error rotation based on the laser tracker. The specific process is as follows: The laser tracker is used to record the end coordinate system, the spatial coordinates in the base coordinate system and the joint motion of the robot to calculate the actual end finite rotation of the coordinate system.

5. The robot calibration method based on FIS theory according to claim 1, characterized in that: Step (iii) identifies the joint axis parameters based on the least squares method. The specific process is as follows: First, the joint angle values ​​of the robot joint motion in step (i) and the end point spatial coordinates of the actual end position in step (ii) are brought into the differential error mapping model to establish the identification equation group of the robot error parameters; Then, the least squares algorithm is used to quickly and efficiently identify the error parameters to be identified.

6. The robot calibration method based on FIS theory according to claim 1, characterized in that: Step (iv) converts the joint axis error into the active joint angle error for error compensation. The specific process is as follows: First, the calibrated error parameters are substituted into the error compensation model; Then, the joint axis error is converted into the active joint error; Finally, the active joints are driven to achieve error compensation.

7. The robot calibration method based on FIS theory according to claim 5, characterized in that: Step (iii) establishes the identification equation group of the robot error parameters, which requires the introduction of a filter matrix for construction.

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