An error prediction method for online error compensation of robots

Abstract

The present invention discloses an error prediction method for online error compensation of a robot, and belongs to the technical field related to industrial robot processing. The present invention is divided into two parts: robot coordinate system calibration and online error prediction model construction. The coordinate system calibration method of the present invention can make the robot positioning error meet the stability conditions required by the prediction model within a specific workspace. On this basis, an online error prediction model is constructed, and the model is used to predict the robot positioning error in real time. The error prediction method of the present invention can overcome the internal time lag of the system, improve the real-time performance of online error compensation, and thus improve the accuracy and quality of robot processing. Moreover, the method does not rely on the system model, is simple and easy to implement, and has strong versatility.

Description

Technical Field

[0001] The invention relates to the field of robot control, and in particular to an error prediction method for overcoming the time lag of an online error compensation system of a robot. Background Art

[0002] As intelligent manufacturing becomes the main development direction of modern industry, industrial robots, as one of the representative equipment in the field of intelligent manufacturing, have been widely studied and applied in high-end manufacturing, especially in the field of aerospace manufacturing. Compared with traditional manufacturing equipment, industrial robots have the advantages of high task flexibility, large working space, relatively low cost, and high openness. On the other hand, due to its open-chain structure and low rigidity, the application of industrial robots in high-precision processing scenarios is subject to certain restrictions, especially when there is a large load at the end.

[0003] In order to overcome the limitation of low robot positioning accuracy, academia and industry have adopted a variety of solutions to optimize the robot's processing process. Calibration compensation for robots can be divided into two types: offline and online. Offline error compensation refers to correcting the robot's motion trajectory before processing, thereby improving the robot's positioning accuracy, such as CN114131611A. Online error compensation is to correct the positioning error caused by the robot's movement through the corresponding control algorithm combined with closed-loop control during the processing process. Examples of online error compensation can be found in CN115319743A and CN115229796A. Generally speaking, because of the introduction of a closed-loop feedback loop, online compensation can often achieve higher accuracy than offline compensation. However, online compensation is more difficult to implement, and the system stability is weaker than offline error compensation.

[0004] For online compensation, one of the prerequisites for a good closed-loop control effect is the high real-time performance of the feedback measurement system. However, the signal transmission, data processing and other links included in the measurement system will inevitably introduce time lag to the system. A large time lag in the system will make it impossible for online compensation to achieve any compensation effect, and in severe cases it will even cause the system to diverge; even if the time lag is not large, it will have an adverse effect on the compensation accuracy. At the same time, a smaller system time lag also means a higher hardware cost. Therefore, it is necessary to design a corresponding algorithm to overcome this time lag in order to achieve a good online accuracy compensation effect for the robot. Summary of the invention

[0005] The present invention aims to provide an error prediction method for overcoming the time lag of an online error compensation system of a robot during a closed-loop position control process of the robot. The method can overcome the time lag problem in the system and achieve high-precision control of the robot to improve the applicability of the robot in high-precision machining application scenarios. The method also has the advantages of low cost and easy implementation.

[0006] The present invention adopts the following technical solution:

[0007] An error prediction method for online error compensation of a robot comprises the following steps:

[0008] S1, calibrate the robot position according to the robot's maximum working space, and obtain the homogeneous transformation matrix of the robot relative to the world coordinate system The maximum workspace is the workspace that the robot will reach or pass through when performing a given task;

[0009] S2, error prediction during robot motion:

[0010] (1) Based on the homogeneous transformation matrix Compile the robot's initial motion program and formal motion program in the world coordinate system;

[0011] (2) The robot executes the initial motion program, compares the position data measured by the laser tracker with the theoretical position data, and obtains the error data sequence;

[0012] (3) Determine the order of the AR prediction model according to the AIC criterion;

[0013] (4) Construct an AR prediction model using the order and the linear coefficients of the AR model calculated during the order determination process;

[0014] (5) The robot executes the formal motion program and uses the AR prediction model and error time series to predict the error.

[0015] Further, the step S1 includes the following sub-steps:

[0016] (1) Let the robot end TCP point be p, and its value in the world coordinate system {W} is W p(x,y,z); calculate the trajectory T that all robots need to walk R (x,y,z)=0, W The maximum and minimum values ​​of the three components x, y and z of p(x, y, z) in the corresponding directions are denoted by x max ,y max , z max , x min ,y min and z min ; Then in {W}, use x max x min ,y max y min , z max z min Build a cuboid for the edge, and call this cuboid the maximum workspace;

[0017] (2) Divide this maximum workspace into cubes of equal size: i ,i=1,2,...,N c ; At this time, if the maximum workspace volume constructed cannot be exactly divided by the cube, the cuboid is expanded to meet the division conditions;

[0018] (3) For each cube Cub i , calculate the trajectory T R The length of the journey is denoted as l i , and find min(l i ) is recorded as l min , l min The cube where the corresponding trajectory is located is denoted as Cub min ; For each l i , find [l i / l min ] as a multiple of the number of points to be sampled in each cube; if the trajectory T R If a cube is not passed, the sampling point multiple of the cube is 0; set Cub min The number of sampling points is N s , then any Cub i The number of sampling points is N s ·[l i / l min ], denoted as N c ;

[0019] (4) Control the robot to walk to Cub i In the random selection [l i / l min ] points i ,i=1,2,...,N c , measure its coordinate value in the laser tracker coordinate system {L}, recorded as L p i (i=1,2,...,N c );

[0020] Record each p i Coordinate values ​​in the robot coordinate system R p i (i=1,2,...,N c ), the coordinate value is read out through the robot coordinate system;

[0021] (5) Using the measured L p i (i=1,2,...,N c) to calibrate the coordinate system of the robot to the laser tracker, and use the singular value decomposition method or the least squares method to obtain the homogeneous transformation matrix of the robot coordinate system relative to the laser tracker coordinate system

[0022] Use a laser tracker to measure six or more fixed points in the world coordinate system {W}, and use the singular value decomposition method or the least squares method to obtain the homogeneous transformation matrix of the laser tracker coordinate system to the world coordinate system.

[0023] use and Using the formula:

[0024]

[0025] Obtain the homogeneous transformation matrix of the robot relative to the world coordinate system

[0026] Furthermore, in step S2, the position data measured by the laser tracker and the theoretical position data are compared to obtain the error data sequence: the robot moves, and the laser tracker is used to record the time sequence of the position of the robot TCP point in the world coordinate system {W} W p i , i = 1, 2, ..., N, where N is the total number of samples, and based on this the theoretical position of the TCP point i=1,2,...,N to obtain the positioning error sequence e i =[Δx i ,Δy i ,Δz i ] T , i=1,2,...,N; where, Using the robot theoretical trajectory T R (x,y,z)=0 and the laser tracker returns W p i The timestamp corresponding to each point is obtained, and the timestamp is the sampling data timestamp.

[0027] Furthermore, in step S2, the AR prediction model is ordered according to the AIC criterion as follows:

[0028] Propose a maximum order R max , for every n,o,p<R max , Represent the model order in the X, Y and Z directions respectively. The AR model linear coefficient Φ in the X, Y and Z directions is calculated using the following formula n =[φ1 φ2 ... φ n ] T , θp =[θ1 θ2 ... θ p ] T :

[0029] Φ n =[X T X] -1 X T x M,n

[0030]

[0031] θ p =[Z T Z] -1 Z T z M,p

[0032] In the formula, X, Y, and Z represent the matrices composed of time series in the three directions of X, Y, and Z in order, respectively. M,n ,y M,o 、z M,p Represents the vectors composed of time series in the three directions of X, Y, and Z respectively;

[0033] Calculate the AIC index under this order:

[0034]

[0035]

[0036]

[0037] In the formula, SSE is the residual sum of squares of the fitting; the order n, o, p corresponding to the smallest AIC index is selected as the best fitting order in the corresponding direction, that is, the order of the AR prediction model.

[0038] Further, in step S2, the AR prediction model is:

[0039]

[0040] In the formula, Respectively represent the predicted values ​​of the errors in the three directions of X, Y, and Z at time M+1; Δx i (i=1,2,...,M-n+1), Δy i (i=1,2,...,,M-o+1),Δz i (i=1,2,...,M-p+1) respectively represent the positioning error values ​​in the X, Y and Z directions at the corresponding time.

[0041] The beneficial effects of the present invention compared to the prior art are as follows:

[0042] (1) No complex system model is required, and the robot positioning error can be predicted by relying only on the error time series.

[0043] (2) The prediction process itself has a certain lead time, and the system delay can be overcome through advance control.

[0044] (3) Except for the laser tracker, no additional sensors are required, the structure is simple and the operability is strong. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 101 is a robot, 102 is an end effector (schematic), and 103 is a laser tracker.

[0046] Figure 2 The calibration flow chart is shown in Figure 2.

[0047] Figure 3 This is a schematic diagram of the spatial grid division during the calibration process. The space enclosed by the dotted line is the robot's maximum working space, and the solid line is the division and expansion of the space.

[0048] Figure 4 This is the flow chart of robot trajectory error prediction.

[0049] Figure 5 It is a step-by-step flow chart. DETAILED DESCRIPTION

[0050] The present invention is further described below in conjunction with the accompanying drawings. The specific implementation methods described here are only for explanation and do not impose any limitation on the present invention.

[0051] See also Figure 1 The hardware system of the present invention includes an industrial robot 101, an end effector 102, a laser tracker 103 and a system controller (not shown in the figure). The industrial robot is used as the actuator of the system, and the end effector is fixed on the flange of the sixth axis of the robot; the laser tracker cooperates with the target ball placed on the end effector to measure the three-dimensional position of the end effector; the system controller is used to run the control algorithm, receive the return data of the laser tracker and the robot, and send control instructions to the laser tracker and the robot.

[0052] The error prediction method for online error compensation of a robot of the present invention is mainly divided into two parts: 1. Calibrate the robot position according to the maximum working space of the robot. 2. During the robot movement, predict and compensate the error according to the provided autoregressive (AR) error prediction method. They will be described below respectively.

[0053] It should be noted that in the robot position calibration step, the so-called "maximum workspace" does not refer to all possible workspaces of the robot, but refers to "the workspace that the robot will reach or pass through when performing its given work". The reason for calibrating the coordinate system only in this space is that the AR error prediction method requires weak stability of the time series. It is necessary to calibrate the maximum workspace of the robot to meet the error stability of the robot when executing its motion instructions.

[0054] like Figure 2 As shown in the figure, the robot calibration process is as follows:

[0055] 1. Let the robot end TCP point be p, and its value in the world coordinate system {W} is W p(x,y,z). Calculate the trajectory T that all robots need to walk R (x,y,z)=0, W The maximum and minimum values ​​of the three components x, y and z of p(x, y, z) in the corresponding directions are denoted by x max ,y max , z max , x min ,y min and z min Then in {W}, use x max x min ,y max y min , z max z min Build a cuboid for the edge, and call this cuboid the maximum working space.

[0056] 2. Divide this maximum workspace into cubes of equal size i (i=1,2,...,N c ). At this time, if the maximum workspace volume constructed cannot be exactly divided by the cube, the cuboid can be expanded appropriately, such as Figure 3 As shown, the space enclosed by the dotted line is the robot's maximum working space, and the solid line is the division and expansion of the space.

[0057] 3. For each cube Cub i , calculate the trajectory T R The length of the journey is denoted as l i , and find min(l i ) is recorded as l min , l min The cube where the corresponding trajectory is located is denoted as Cub min For each l i , find [l i / l min] ([·] is a floor function) as a multiple of the number of sampling points in each cube. If the trajectory T R If a cube is not passed, the sampling point multiple of the cube is 0. Set Cub min The number of sampling points is N s , then any Cub i The number of sampling points is N s ·[l i / l min ], denoted as N c .

[0058] 4. Operate the robot to walk to Cub i In the random selection [l i / l min ] points i (i=1,2,...,N c ), measure its coordinate value in the laser tracker coordinate system {L}, and record it as L p i (i=1,2,...,N c ). L p i The elements in are represented as:

[0059]

[0060] In addition, it is necessary to record each p i Coordinate values ​​in the robot coordinate system R p i (i=1,2,...,N c ), the coordinate value can be read out through the robot coordinate system. L p i similar, R p i The elements in are represented as:

[0061]

[0062] 5. Use the measured L p i (i=1,2,...,N c ) to calibrate the coordinate system from the robot to the laser tracker. The calibration method can refer to the singular value decomposition method or the least squares method to obtain the homogeneous transformation matrix of the robot coordinate system relative to the laser tracker coordinate system

[0063] Similarly, a laser tracker is used to measure six or more fixed points in the world coordinate system {W}, and the homogeneous transformation matrix of the laser tracker coordinate system to the world coordinate system can be obtained by using the singular value decomposition method or the least squares method:

[0064] use and Using the formula:

[0065]

[0066] Obtain the homogeneous transformation matrix of the robot relative to the world coordinate system

[0067] The robot's motion program is based on That is, it is compiled in the world coordinate system. At this point, the robot coordinate system calibration is completed, and the online error compensation work begins.

[0068] During the robot motion, the robot trajectory error is predicted and compensated according to the provided self-AR error prediction method. Figure 4 As shown in Figure 2, the robot trajectory error prediction process is as follows:

[0069] 1. The robot executes the initial motion program;

[0070] Compile the robot program in the world coordinate system. In addition to the normal operation program of the robot, it is also necessary to insert a robot initial motion program at the beginning of the program for AR model initialization, so as to determine the order and coefficient of the AR model.

[0071] 2. Compare the position data measured by the laser tracker with the theoretical position data to obtain the positioning error data sequence;

[0072] During the initialization phase, the laser tracker is used to record the time series of the robot TCP point position in the world coordinate system {W} when the robot performs additional movements. W p i (i=1,2,...,N), where N is the total number of samples, and based on this the theoretical position of the TCP point Obtain the positioning error sequence e i =[Δx i ,Δy i ,Δz i ] T (i=1,2,...,N). Among them, The robot theoretical trajectory T R (x,y,z)=0 and the laser tracker returns W p i(i=1,2,...,N) The timestamps corresponding to each point are obtained. It should be noted that the theoretical position should be calculated based on the timestamp of the sampled data at this time. This is because there is a system time lag in the time of receiving the sampled data, and the theoretical position cannot be calculated based on the time when the sampled data is received.

[0073] 3. Determine the order of AR prediction model according to AIC criterion;

[0074] The present invention adopts the AR model prediction error, and the mathematical expression of the model is as follows:

[0075]

[0076] Among them, x i (i=0,1,2,...,n-1,n,n+1,...,M-1,M) represents the observation data of the system at the corresponding time intervals. The interval time is recorded as Δt. The selection of the time interval needs to take into account the system delay and the prediction lead time. In this example, x i (i=0,1,2,...,n-1,n,n+1,...,M-1,M) represents the positioning error of the robot in the three directions of X, Y, and Z, that is, the difference between the theoretical position and the actual position. ε t is the noise interference term, φ i (i=1,2,...,n) represents the model linear parameters, and n is the model order in the X direction. Arranged in matrix form:

[0077] x M,n =X M-1,n-1 Φ n +ε t (5)

[0078] For predictions based on the AR model, the noise interference term is expected to be 0, so it is ignored. The expression is:

[0079]

[0080] The methods for solving the prediction expressions in the Y and Z directions are the same as those in the X direction and will not be repeated here.

[0081] Then the AIC criterion is used to determine the order, such as Figure 5 As shown, a maximum order R is proposed max , for every n,o,p<R max , Represent the model order in the X, Y and Z directions respectively. The linear coefficient Φ of the AR model in the X, Y and Z directions is calculated by the least square method, i.e., formula (7): n =[φ1 φ2 ... φ n ] T, θ p =[θ1 θ2 ...θ p ] T :

[0082]

[0083] In the formula, X is the X in formula (5) M-1,n-1 , whose dimensions depend on the model order n and the total number of samples N; the same is true for Y and Z, whose dimensions depend on the model order o, p and the total number of samples N respectively.

[0084] And calculate the AIC index under this order according to formula (8):

[0085]

[0086] In the formula, SSE is the residual sum of squares of the fitting, that is, x n ,x n+1 ,x n+2 ...x M The sum of the squares of the differences between the theoretical value and the calculated value.

[0087] Then, the order n, o, p corresponding to the smallest AIC index is selected as the best fitting order in the corresponding direction.

[0088] 4. Use the order and the linear coefficients of the AR model calculated in the order determination process to build an AR prediction model:

[0089]

[0090] In the formula, Respectively represent the predicted values ​​of the errors in the three directions of X, Y, and Z at time M+1. i (i=1,2,...,n) represents the linear coefficient of the AR prediction model in the X direction. Similarly, and θ i (i=1,2,...,p) represent the AR prediction model coefficients in the Y and Z directions respectively. Δx i (i=1,2,...,M-n+1), Δy i (i=1,2,...,M-o+1), Δz i (i=1,2,...,M-p+1) respectively represent the positioning error values ​​in the X, Y and Z directions at the corresponding time.

[0091] 5. The robot executes the formal motion program and predicts the error using the AR prediction model and the error time series;

[0092] Finally, the laser tracker samples the current motion position of the robot according to the sampling time interval Δt mentioned above and transmits the data to the controller. The controller calculates the robot positioning error sequence based on the robot theoretical position, e i =[Δx i ,Δy i ,Δz i ] T (max(i)=M), the error value at time i=M+1 can be calculated according to formula (9) Then at time i=M+1, the robot is controlled according to Apply compensation for the reverse motion or corresponding control rate.

Claims

1. An error prediction method for online error compensation of a robot, characterized in that: The following steps are involved: S1, calibrate the robot position according to the robot's maximum working space, and obtain the homogeneous transformation matrix of the robot relative to the world coordinate system The maximum workspace is the workspace that the robot will reach or pass through when performing a given task; S2, error prediction during robot motion: (1) Based on the homogeneous transformation matrix Compile the robot's initial motion program and formal motion program in the world coordinate system; (2) The robot executes the initial motion program, compares the position data measured by the laser tracker with the theoretical position data, and obtains the error data sequence; (3) Determine the order of the AR prediction model according to the AIC criterion; (4) Construct an AR prediction model using the order and the linear coefficients of the AR model calculated during the order determination process; (5) The robot executes the formal motion program and predicts the error using the AR prediction model and the error time series; The step S1 comprises the following sub-steps: (1) Let the robot end TCP point be p, and its value in the world coordinate system {W} is W p(x,y,z); calculate the trajectory T that all robots need to walk R (x,y,z)=0, W The maximum and minimum values ​​of the three components x, y and z of p(x, y, z) in the corresponding directions are denoted by x max ,y max , z max , x min ,y min and z min ; Then in {W}, use x max x min ,y max y min , z max z min Build a cuboid for the edge, and call this cuboid the maximum workspace; (2) Divide this maximum workspace into cubes of equal size: i ,i=1,2,K,N c ; At this time, if the maximum workspace volume constructed cannot be exactly divided by the cube, the cuboid is expanded to meet the division conditions; (3) For each cube Cub i , calculate the trajectory T R The length of the journey is denoted as l i , and find min(l i ) is recorded as l min , l min The cube where the corresponding trajectory is located is denoted as Cub min ; For each l i , find [l i / l min ] as a multiple of the number of points to be sampled in each cube; if the trajectory T R If a cube is not passed, the sampling point multiple of the cube is 0; set Cub min The number of sampling points is N s , then any Cub i The number of sampling points is N s ·[l i / l min ], denoted as N c ; (4) Control the robot to walk to Cub i In the random selection [l i / l min ] points i ,i=1,2,K,N c , measure its coordinate value in the laser tracker coordinate system {L}, recorded as L p i (i=1,2,K,N c ); Record each p i Coordinate values ​​in the robot coordinate system R p i (i=1,2,K,N c ), the coordinate value is read out through the robot coordinate system; (5) Using the measured L p i (i=1,2,K,N c ) to calibrate the coordinate system of the robot to the laser tracker, and use the singular value decomposition method or the least squares method to obtain the homogeneous transformation matrix of the robot coordinate system relative to the laser tracker coordinate system Use a laser tracker to measure six or more fixed points in the world coordinate system {W}, and use the singular value decomposition method or the least squares method to obtain the homogeneous transformation matrix of the laser tracker coordinate system to the world coordinate system. use and Using the formula: Obtain the homogeneous transformation matrix of the robot relative to the world coordinate system 2. The error prediction method for online error compensation of a robot according to claim 1, characterized in that: The step S2 compares the position data measured by the laser tracker with the theoretical position data to obtain the error data sequence: the robot moves and the laser tracker is used to record the time sequence of the position of the robot TCP point in the world coordinate system {W} W p i , i = 1, 2, K, N, where N is the total number of samples, and based on this the theoretical position of the TCP point i=1,2,K,N to obtain the positioning error sequence e i =[Δx i ,Δy i ,Δz i ] T , i=1,2,K,N; where, Using the robot theoretical trajectory T R (x,y,z)=0 and the laser tracker returns W p i The timestamp corresponding to each point is obtained, and the timestamp is the sampling data timestamp.

3. The error prediction method for online error compensation of a robot according to claim 2, characterized in that: The step S2, determining the order of the AR prediction model according to the AIC criterion, is specifically as follows: Propose a maximum order R max , for each n,o,p <R max ,n,o,p∈￥ + , respectively represent the model order in the X, Y and Z directions, and use the following formula to calculate the AR model linear coefficient Φ in the X, Y and Z directions respectively n =[φ1 φ2 K φ n ] T , θ p =[θ1 θ2 K θ p ] T : Φ n =[X T X] -1 X T x M,n θ p =[From T WITH] -1 WITH T With M,p In the formula, X, Y, and Z represent the matrices composed of time series in the three directions of X, Y, and Z in order, respectively. M,n ,y M,o 、z M,p Represents the vectors composed of time series in the three directions of X, Y, and Z respectively; Calculate the AIC index under this order: In the formula, SSE is the residual sum of squares of the fitting; the order n, o, p corresponding to the smallest AIC index is selected as the best fitting order in the corresponding direction, that is, the order of the AR prediction model.

4. The error prediction method for online error compensation of a robot according to claim 3, characterized in that: In step S2, the AR prediction model is: In the formula, Respectively represent the predicted values ​​of the errors in the three directions of X, Y, and Z at time M+1; Δx i (i=1,2,K,M-n+1),Δy i (i=1,2,K,M-o+1),Δz i (i=1, 2, K, M-p+1) respectively represent the positioning error values ​​in the X, Y, and Z directions at the corresponding moments.

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