Industrial robot load parameter static identification and identification pose optimization method

Abstract

The application discloses a kind of industrial robot load parameter static identification method, belong to industrial robot technical field.The application is dedicated to solving the problem of complex design identification trajectory and big dynamic identification measurement error in industrial robot load dynamics parameter identification.According to the kinematic model of industrial robot and the force and torque balance equation, a joint driving torque-load parameter model is established to solve the identification pose group with the identification matrix condition number as the optimization objective.According to the optimization calculation, the industrial robot is controlled to move to the specified pose, and the joint torque and joint angle information is collected.According to the experimental measurement data and the established mathematical model, the load parameters are estimated using the weighted least squares method.This method reduces the complexity of load parameter identification and improves the identification accuracy.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of industrial robots, in particular to a static identification method of load dynamics parameters of an industrial robot. BACKGROUND

[0002] In the fields of intelligent manufacturing and precise measurement, industrial robots are often used in combination with actuators or sensors, as shown in the figure. Figure 1 At present, harmonic reducers are widely used in small and medium-sized industrial robots due to their advantages of large transmission ratio, small volume, small mass and high motion precision. However, harmonic reducers have the disadvantage of low stiffness, which makes the influence of joint flexible deformation cannot be ignored. Especially with the increase of the load-to-weight ratio of industrial robots, it is difficult to meet the precision requirements of milling, drilling and robot measurement in application scenarios by ignoring the flexible deformation caused by the load.

[0003] Obtaining the dynamics parameters of the load is an important prerequisite for compensating the flexible deformation caused by the load. There are mainly two methods for obtaining the dynamics parameters of the load. The first method is to obtain the parameters through the CAD model designed at the time, but it is difficult to obtain the parameters of the load with complex structure or assembly relationship through this method. The second method is to obtain the mass, center of gravity and inertia tensor of the load through a dynamic identification experiment by designing an identification trajectory. The current identification experiment method has the following problems: when the industrial robot is in a low-speed working condition or only needs to meet the positioning accuracy, the flexible deformation caused by the inertia tensor can be ignored, so the identified load dynamics parameters are redundant and cannot identify all the parameters; the identification trajectory is relatively complex and needs to optimize a large number of trajectory parameters, so it is difficult to obtain good results by optimizing the identification trajectory with the coefficient matrix condition number as the target; the experiment using the identification trajectory needs a large workspace and has certain requirements for the working space of the application environment; finally, the data collected under dynamic conditions are additionally affected by time-varying errors, which affects the accuracy of parameter estimation.

[0004] The present application obtains the dynamics parameters of the load through a static identification experiment, and identifies the center of gravity and mass of the load by designing and optimizing the identification pose, which can be used to improve the positioning accuracy of the robot. SUMMARY

[0005] The present application provides a static identification method of load parameters of an industrial robot, which establishes the relationship between the load driving torque and the load mass and center of gravity, selects an identification pose group with the identification matrix condition number as the optimization target, and identifies the load mass and center of gravity parameters using the weighted least squares method. The identification complexity is reduced and the identification accuracy is improved.

[0006] The present application aims to provide a static identification method of load parameters of an industrial robot, which comprises the following steps:

[0007] Step 1: Establish the kinematics model of industrial robot using modified DH model. Compared with the standard DH model, the output axis coordinate system is replaced by the driving axis coordinate system, which overcomes the problem of ambiguity in the modeling of robots with tree structure or closed chain. Define the link coordinate system for each link, and the transformation matrix between each link coordinate system is

[0008]

[0009] The first three rows and three columns of the rotation matrix R 3×3 describe the rotation relationship between the link coordinate system C i-1 and C i .

[0010] Step 2: Derive the relationship between the load driving torque and the load mass, center of gravity parameters. Calculate the acceleration recursive relationship of industrial robot in static state through the rotation matrix R

[0011]

[0012] where represents the acceleration of the origin of the coordinate system in the link coordinate system C i .

[0013] From the force and torque balance equation, the force and torque exerted by the load on the robot flange can be obtained:

[0014]

[0015] M load = r m × F load

[0016] where m load represents the mass of the load, r m = [r x , r y , r z ] T represents the center of gravity coordinates of the load in the robot end coordinate system.

[0017] The force and torque exerted by the load on the robot flange can be converted to the driving torque of the load in the joint space by the force Jacobian matrix. According to the principle of virtual work, the force Jacobian matrix is the transpose of the Jacobian matrix. Since the Jacobian matrix does not destroy the linear relationship of the equation, the inertia parameters can still be linearly separated after the Jacobian matrix conversion:

[0018]

[0019] where A load is the coefficient matrix of the identification parameters, and pload = [m load r x ,m load r y ,m load r z ,m load ] T is the load inertia parameter to be identified.

[0020] The joint driving torque has a linear relationship with the motor current, and the corresponding joint driving torque can be obtained by reading the motor current. The joint driving torque includes the driving torque required by the robot body and the driving torque required by the load, and the two do not have a coupling relationship and are linearly superimposed, so the load driving torque can be obtained through two experiments. The specific method is: under the condition of carrying a load and under the condition of no load, respectively control the robot to move to the same position, i.e. linkload,i = q link,i , measure the joint torque. The difference between the two measured torques is the load driving torque, so the identification equation corresponding to joint i is obtained:

[0021] τ load,i = τ linkload,i - τ link,i = A load,i p load

[0022] Select N identification poses for measurement, and the load driving torque equation of 6 joints can be listed for each identification pose, so the identification equation set can be represented as:

[0023]

[0024] Step 3: Select the load parameter identification pose. Control the first, second and fifth joints to be fixed at a certain angle and always unchanged, and the third, fourth and sixth joints to rotate to different angles each time to select the identification pose. Under the condition of meeting the joint angle limit, select the identification pose set with the minimum condition number of the regression matrix as the target, and the formula is as follows:

[0025] min(cond(A load,A ))

[0026] q i,min ≤ q i (t) ≤ q i,max , i = 3, 4, 6

[0027] q i (t) = const, i = 1, 2, 5

[0028] Step 4: Perform identification experiment and data processing. According to the optimized identification pose, the robot is controlled to reach each identification pose to collect joint torque data. The collected torque data is averaged to obtain the torque data at each identification pose.

[0029] According to the load parameter identification model, a statically indeterminate linear equation can be obtained, and the optimal solution of the parameters is estimated by the weighted least square method:

[0030]

[0031] Wherein, W is the weight matrix.

[0032] The beneficial effects of the present application are: the present application establishes a linear model of the joint torque of the industrial robot and the load mass and the center of gravity parameters, reducing the complexity of parameter identification. The identification process only needs to control the rotation of the 3rd, 4th and 6th joints, the space required for the identification experiment is small, and the load and the body or base of the industrial robot are not easy to interfere. The selection of the identification pose is simple, the optimized pose is used for the experiment, the sensitivity to measurement error is low, the parameter solving accuracy is high. No additional external measuring instruments are needed, only the motion and torque data provided by the industrial robot itself are collected, and the identification cost is low. The method can be used for industrial robots of different models and configurations.

[0033] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the following briefly introduces the drawings: BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 Fig. 1 is a schematic diagram of a serial six-degree-of-freedom industrial robot with load

[0035] Figure 2 Fig. 5 is a D-H model diagram of a KUKA KR6 R700 sixx robot.

[0036] Figure 3 Fig. 8 is a flow chart of identification pose optimization

[0037] Figure 4 Fig. 11 is an optimization result taking the condition number as an index DETAILED DESCRIPTION

[0038] The present application provides a static identification method to obtain the mass and center of gravity of the load, aiming at the problems of parameter redundancy, complex design of identification trajectory and large dynamic identification measurement error in the identification of load dynamics parameters of industrial robots without obtaining the inertia tensor. The method can reduce the measurement error, only needs to design the identification pose without designing the identification trajectory, requires a small experimental space suitable for industrial field environment, and the identification result can be used for improving the positioning accuracy of the industrial robot.

[0039] In order to achieve the above object, the application adopts an industrial robot load parameter static identification method, comprising the following steps:

[0040] Step 1: using the modified DH model to establish the kinematics model of the industrial robot. First, define the link coordinate system on each link, and then express the transformation relationship between the coordinate systems of each link of the serial industrial robot through four parameters, i.e. link length a i , link torsion angle α i , link offset d i , and joint angle θ i . Among the four DH parameters, the link length, the link torsion angle and the link offset are fixed quantities, and the joint angle is obtained by reading the encoder data at each joint of the robot.

[0041] The embodiment object of the application is a KUKA KR6 R700 sixx type industrial robot. The modified D-H model diagram of the robot is shown in Figure 2 , and the D-H parameter table is shown in Table 1. The initial joint angles of the robot at the origin are 0, -90°, 90°, 0, 0, and 0, respectively.

[0042] Table 1 D-H parameter table of KUKA KR6 R700 sixx robot

[0043]

[0044] The link coordinate system C i-1 is converted to the link coordinate system C i through the four parameters describing two rotations around the axis and two translations along the axis. The conversion matrix is

[0045]

[0046] Trans(x, a i ) represents the translation of a mm along the x-axis of the coordinate system C i-1 , Rot(x, α i ) represents the rotation of α° around the x-axis of the coordinate system C i-1 , Trans(z, d i ) represents the translation of d mm along the z-axis of the coordinate system C i , and Rot(z, θ i ) represents the rotation of θ° around the z-axis of the coordinate system C i . The first three rows and three columns of the matrix are the rotation matrix R 3×3 , which describes the rotation relationship between the link coordinate system C i-1 and C i .

[0047] Step 2: Derive the relationship between the load driving torque and the load mass, center of gravity. Calculate the acceleration recursive relationship of the industrial robot in the static case through the rotation matrix R:

[0048]

[0049] wherein represents the acceleration of the origin of the coordinate system in the coordinate system C i .

[0050] The initial value of the base coordinate system acceleration in this embodiment is the gravitational acceleration, specifically [0, 0, 9.81] m / s 2 .

[0051] From the force and torque balance equation, the force and torque exerted by the load on the flange of the robot can be listed:

[0052]

[0053] M load = r m x F load

[0054] wherein m load represents the mass of the load, r m = [r x , r y , r z ] T represents the coordinates of the center of gravity of the load in the coordinate system of the robot end.

[0055] The force Jacobian matrix can convert the force and torque exerted by the load on the flange of the robot into the load driving torque in the joint space. According to the principle of virtual work, the force Jacobian matrix is the transpose of the Jacobian matrix. Since the Jacobian matrix does not destroy the linear relationship of the equation, the inertia parameters can still be linearly separated after the Jacobian matrix conversion:

[0056]

[0057] wherein A load is the coefficient matrix of the identification parameters, p load = [m load r x , m load r y , m load r z , m load ] T are the load inertia parameters to be identified.

[0058] The joint driving torque has a linear relationship with the motor current, and the corresponding joint driving torque can be obtained by reading the motor current. The joint driving torque includes the driving torque required by the robot body and the driving torque required by the load, and the two do not have a coupling relationship and are linearly superimposed, so the load driving torque can be obtained through two experiments. The specific method is: under the condition of carrying a load and under the condition of no load, the robot is controlled to move to the same position, i.e. linkload,i q link,i , and the joint torque is measured. The difference between the two measured torques is the load driving torque, so the identification equation corresponding to joint i is obtained:

[0059] τ load,i i linkload,i =τ link,i i load,i -τ load i

[0060] N identification poses are selected for measurement, and the load driving torque equation of 6 joints can be listed for each identification pose, so the identification equation set can be expressed as:

[0061]

[0062] Step 3: Select the load parameter identification pose. The 1st, 2nd and 5th joints are fixed at a certain angle and do not change, and the 3rd, 4th and 6th joints are rotated to different angles each time to select the identification pose. Under the condition of meeting the joint angle limit, the identification pose set is selected with the minimum condition number of the regression matrix as the target, and the formula is as follows:

[0063] min(cond(A load,A ))

[0064] q i,min ≤q i (t)≤q i,max ,i=3,4,6

[0065] q i (t)=const,i=1,2,5

[0066] Table 2 Joint angle movement range

[0067]

[0068] The range of joint motion of the embodiment is shown in Table 2. In order to avoid interference between the load and the robot body and the base with the end effector, the range of joint angle motion can be further constrained when selecting the identified pose. Specifically, the joint angles of the 1st, 2nd and 5th axes are kept at 0°, -90° and 0° respectively. The range of joint angle motion of the 2nd, 3rd and 6th axes is -90°-120°, -160°-160° and -180°-180° respectively. The optimization flowchart is shown in Figure 3 In the embodiment, 27000 poses are first randomly selected within the range of joint motion to create a candidate pose library. Then 30 poses are selected from the candidate pose library as an initial pose library, and the remaining 26970 poses are referred to as a remaining pose library. Then a pose P A is selected from the remaining pose library. The pose P D satisfies the condition that the condition number is minimum after the initial pose library is added with the pose P A . The pose library composed of the 31 poses is referred to as an added pose library. Then a pose P D is selected from the added pose library. The pose P D satisfies the condition that the condition number is minimum after the added pose library is deleted with the pose P A . The pose library is referred to as a deleted pose library. The above adding and deleting process is repeated until the current cycle satisfies P D . At this time, the deleted pose library is the 30 poses in the entire candidate pose library that satisfy the minimum condition number. The optimization result is shown in Figure 4 . The condition number of the identification matrix is reduced from 7526.9002 to 9.9315 after optimization, with a reduction of 99.87%. It can be seen that the optimization method can select the 30 poses with the best identification effect from the created candidate pose library.

[0069] Step 4: Identification experiment and data processing. According to the identified pose obtained by optimization, the robot is controlled to reach each identified pose to continuously collect joint torque data. The collected torque data is averaged to obtain the torque data at each identified pose. The formula is as follows:

[0070]

[0071] τ j,k represents the jth pose kth sampling, and K represents the number of torque sampling at each identified pose.

[0072] The super statically indeterminate linear equation can be obtained according to the load parameter identification model established in step 2, and the optimal solution of the parameter is estimated by the weighted least square method:

[0073]

[0074] The weight matrix W can be calculated from the variance matrix determined by the joint torque noise, and the formula is as follows:

[0075]

[0076]

[0077] This example is illustrative only and is not intended to limit the scope of the application. Other embodiments can be apparent to those skilled in the art from consideration of the specification and can be practiced within the spirit and principles of the application. For example, the specification can be used to learn how to make and use other embodiments of the application.

Claims

1. A method for industrial robot load parameter static identification and identification pose optimization, characterized in that, The method comprises the following steps: Step 1: Establish the kinematics model of industrial robot using improved DH model, first define the link coordinate system, and then through the link length a i , link torsion angle α i , link offset d i , joint angle θ i These four parameters describe the conversion relationship of the link coordinate system C i to the link coordinate system C i+1 , and the conversion relationship expression is as follows: Trans(x,a i ) represents the translation distance amm along the x-axis of the coordinate system, Rot(x,α i ) represents a rotation of α° around the x-axis of the coordinate system, Trans(z,d i ) represents the translation distance dmm along the z-axis of the coordinate system, Rot(z,θ i ) represents the rotation θ° around the z-axis of the coordinate system; Step 2: Derive the relationship between the driving torque, load gravity, and center of gravity, and calculate the recursive relationship for the static acceleration of the industrial robot: wherein denotes the acceleration of the origin of the coordinate system C i the acceleration of the origin of the coordinate system C The force and torque balance equation can be used to list the force and torque exerted on the flange of the robot by the load: M load = r m x F load where m load represents the mass of the load, r m x y z T represents the coordinates of the center of gravity of the load in the robot end coordinate system,​​​​ The force and torque balance equation can be used to list the force and torque exerted on the flange of the robot by the load: where A load is a coefficient matrix of the identification parameters, p load = [m load r x , m load r y , m load r z , m load ] T is a load inertia parameter to be identified, By collecting multiple identification pose data, an identification equation set is listed: Step 3: Select the load parameter identification pose, and select the pose by optimizing the condition number of the regression matrix as the target, and the formula is as follows: min(cond(A load,A )) q i,min ≤q i (t)≤q i,max i = 3, 4, 6 q i (t) = const, i = 1,2,5 Step 4: Perform the load identification motion according to the optimized measurement points, collect the joint torque and joint position, and estimate the load parameters according to the load parameter model established in step 2.

2. The method according to claim 1, wherein, In step 3, the pose is selected by optimizing the condition number of the regression matrix, comprising the following steps: (1) Create a candidate pose library; (2) Select an initial pose library, and the remaining poses are used as a remaining pose library; (3) Select a pose in the remaining pose library to minimize the condition number after adding the pose to the initial pose library, and the pose library is an added pose library; (4) Delete a pose in the added pose library to minimize the condition number, and the pose library is called a deleted pose library, and the deleted pose is returned to the remaining pose library; (5) Repeat (3) and (4) until the added pose and the deleted pose are consistent, and the optimal pose set is obtained.

3. The method according to claim 1, wherein, In step 3, the load identification motion is performed according to the optimized identification pose, and the joint torque is continuously collected at each identification pose, comprising two identification motions: (1) Industrial robot empty load motion; (2) Industrial robot load installation motion.

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