Mechanical arm repeated positioning precision index evaluation method based on normal random distribution

Abstract

The invention relates to a mechanical arm repeated positioning accuracy index evaluation method based on normal random distribution. According to the method, normal random distribution repeated positioning errors are given to all joints of the mechanical arm, calculation of index confidence is achieved, and then evaluation work of the repeated positioning precision index of the mechanical arm is completed, and the method comprises the following steps that firstly, a mechanical arm kinematics model is established based on an improved DH method, and then the constant working condition and the extreme working condition of the mechanical arm are determined; and calculating the tail end direction and position of the working condition under the error-free condition. Next, joint errors are set based on normal random distribution, a tail end pose matrix is calculated, and then corresponding positions and pose errors are obtained; and finally, defining the proportion meeting the index under the repeated positioning of the mechanical arm as the index confidence coefficient, and further realizing the evaluation of the repeated positioning precision index of the mechanical arm.

Description

Technical Field

[0001] The invention relates to the problem of evaluating the index of a mechanical arm, and in particular to a method for evaluating the index of repeated positioning accuracy of a mechanical arm based on normal random distribution. Background Art

[0002] At present, the acquisition and evaluation of the repeatability accuracy index of the robotic arm is obtained by using random methods such as Monte Carlo to uniformly input errors to each joint of the robotic arm and then find the maximum error. However, in actual applications, the joint output errors are normally distributed, especially for high-degree-of-freedom robotic arms. The index obtained by the existing method has a very small probability in actual application, which makes the index distorted in subsequent applications. Summary of the invention

[0003] In view of the above problems, the present invention provides a method for evaluating the repeatability accuracy index of a robotic arm with reliable results and complete strategies. The method inputs the joint angle error through the normal distribution method, and combines the introduction of the concept of indicator confidence to evaluate the given robotic arm repeatability accuracy index under normal working conditions and extreme working conditions. This helps to guide the formulation of the robotic arm repeatability accuracy index in the early stage of design.

[0004] The technical solution adopted by the present invention to achieve the above-mentioned purpose is: a method for evaluating the repeatability positioning accuracy index of a mechanical arm based on normal random distribution, comprising the following steps:

[0005] Step S1, establishing a kinematic model of the robot arm based on the improved DH method;

[0006] Step S2: determine the normal working conditions and extreme working conditions that the robot arm needs to pay attention to during task execution, and perform the following steps under each working condition:

[0007] S2a, calculate the reference end position and orientation R under the error-free condition of the current working condition g With reference space position p g ;

[0008] S2b, setting joint error Δθ based on normal random distribution i , calculate the terminal pose matrix T tr , and then obtain the corresponding posture deviation θ and position deviation S;

[0009] S2c, iteratively execute step S2b, define the proportion of indicators that meet the indicators under repeated positioning as the indicator confidence q of the current working condition, and then realize the evaluation of the robot arm's repeated positioning accuracy indicator.

[0010] The robotic arm is a cascade rigid system composed of rotating joints or moving joints; a joint coordinate system is established at the front end of each connecting rod, and a tool coordinate system is established at the end of the actuator. A kinematic model is established based on the improved DH method to calculate the end position and orientation of the robotic arm actuator.

[0011] The process of establishing the kinematic model based on the improved DH method is as follows:

[0012] S1a. Establish the joint coordinate system at the front end of each connecting rod:

[0013]

[0014] Where i=1,2,…,N is the joint number of the N-DOF robot arm. is the rotation transformation matrix from the joint i-1 coordinate system to the joint i coordinate system, α i-1 ,a i-1 ,d i ,θ i Respectively represent the connecting rod angle, connecting rod length, connecting rod offset and connecting rod angle in the MDH parameters, Δθ i Represents the repeated positioning error of joint i, and its upper and lower limits are

[0015] S1b. Establish the tool coordinate system at the end of the actuator:

[0016]

[0017] Step S1c, the kinematic model T established based on the improved DH method is obtained by multiplying the rotation transformation matrices of each joint, which includes the position and posture information of the end of the robotic arm;

[0018]

[0019] Among them, the matrix Represents the end position orientation, which is a 3×3 orthogonal matrix; matrix p = [xyz] T Represents the end position.

[0020] The normal working condition is the general situation of the robot arm in task execution, and the confidence of the robot arm meeting the repeatability index under normal conditions is evaluated; the extreme working condition is the situation where the robot arm is in a singular position, and the extreme working condition is selected as the situation where the robot arm is fully extended, and then the given repeatability index is evaluated under this working condition.

[0021] S2a includes: based on the kinematic model calculated above and the angles θ of each joint under normal working conditions without error g , calculate the actuator end pose orientation and spatial position as the reference pose R gand the reference position p g ; Among them, the end posture is a 3×3 orthogonal matrix, and the end position is a 3×1 matrix. Each element in the matrix represents the coordinate value of the end of the robotic arm actuator in the Cartesian coordinate system.

[0022] In S2b, when simulating the repeated positioning of the robot arm using different joint errors, the error range of the given joint repeated positioning is Assign normal distribution characteristics to joint errors and use the kinematic model to calculate the end position of the robot arm and pointing

[0023] The transformation matrix of the terminal posture from the posture with error to the corresponding reference posture state is as follows:

[0024]

[0025] In S2b, define the end position with joint error With reference position p g =[x g y g z g ] T The spatial distance is the position error S, which is obtained by the distance formula between two points in space The minimum angle from the end of the robot arm with joint error to the corresponding reference pose along the rotation axis is defined as the pose error θ, which is indirectly obtained from the trace of the rotation transformation matrix θ = arccos((trace(T tr )-1) / 2).

[0026] The proportion of indicators that meet the criteria in repeated positioning calculations is defined as the indicator confidence q: Θ =1-m Θ / n,q S =1-m S / n; respectively calculate the index evaluation standards under normal working conditions and extreme working conditions, and then realize the evaluation of the repeatability positioning accuracy index of the robot arm under the above working conditions.

[0027] The present invention has the following beneficial effects and advantages:

[0028] 1. Reliable results: The normal distribution method is used to input the joint angle error, combined with the introduction of the indicator confidence concept, to make the final indicator evaluation result more realistic.

[0029] 2. Complete strategy: The given robot arm repeatability positioning accuracy indicators are evaluated under normal working conditions and extreme working conditions respectively, and the evaluation strategy is complete. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 is a flow chart of an embodiment of the present invention;

[0031] Figure 2 is a schematic diagram of a seven-degree-of-freedom robotic arm configuration in an embodiment of the present invention;

[0032] Figure 3 Schematic diagram of a seven-degree-of-freedom robotic arm coordinate system in an embodiment of the present invention;

[0033] Figure 4 Schematic diagram of the configuration of a seven-degree-of-freedom robotic arm under normal working conditions in an embodiment of the present invention;

[0034] Figure 5 is a schematic diagram of the configuration of a seven-degree-of-freedom robotic arm under extreme working conditions in an embodiment of the present invention;

[0035] Among them, 0 is the base, 1 is the first link of the shoulder joint, 2 is the second link of the shoulder joint, 3 is the first link of the arm joint, 4 is the second link of the arm joint, 5 is the first link of the wrist joint, 6 is the second link of the wrist joint, and 7 is the actuator. DETAILED DESCRIPTION

[0036] In order to make the above-mentioned purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation method of the present invention is further described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the invention, so the present invention is not limited by the specific implementation disclosed below.

[0037] like Figure 1 As shown, the present invention proposes a method for evaluating the repeatability index of a mechanical arm based on normal random distribution, comprising the following steps:

[0038] 1) Based on the improved DH method, a kinematic model of the robotic arm with joint errors is established.

[0039] 2) Determine the normal and extreme working conditions of the robot arm.

[0040] 3) Calculate the terminal posture orientation and spatial position under the error-free conditions of the above working conditions.

[0041] 4) The joint error is set based on the normal random distribution to calculate the actuator end pose matrix, and then the corresponding position and attitude errors are obtained.

[0042] 5) The proportion of indicators that meet the robot arm's repeated positioning is defined as the indicator confidence level, thereby realizing the evaluation of the robot arm's repeated positioning accuracy indicator.

[0043] like Figure 2As shown, the robot arm evaluated in step 1 is a cascade rigid system composed of rotating joints or moving joints. The seven-degree-of-freedom robot arm in the embodiment includes a base 0, a first link 1 of a shoulder joint, a second link 2 of a shoulder joint, a first link 3 of an arm joint, a second link 4 of an arm joint, a first link 5 of a wrist joint, a second link 6 of a wrist joint, and an actuator 7. In the embodiment, all joints of the robot arm are rotating joints, and the repeatability is ±0.008°.

[0044] like Figure 3 As shown, in order to complete the kinematic model establishment based on the improved DH method, a joint coordinate system is established at the front end of each connecting rod, and a tool coordinate system is established at the end of the actuator to display the end position and orientation of the robot arm actuator. The MDH parameters of the robot arm of the embodiment are shown in Table 1:

[0045] Table 1 Example robot arm MDH parameters

[0046]

[0047] The kinematic model T of the robot arm with joint errors in the embodiment described in step 1 can be obtained by the following equations, specifically:

[0048]

[0049] Wherein, i=1, 2, ..., 7 are the joint numbers of the seven-degree-of-freedom robotic arm in the embodiment, is the rotation transformation matrix from the joint i-1 coordinate system to the joint i coordinate system, α i-1 ,a i-1 ,d i ,θ i Respectively represent the connecting rod angle, connecting rod length, connecting rod offset and connecting rod angle in the MDH parameters. i Represents the repeated positioning error of joint i, and its upper and lower limits are is the rotation change matrix from the joint 7 coordinate system to the end of the robot. Finally, the kinematic model T of the robot is obtained by multiplying the rotation transformation matrices of each joint, which contains the position and posture information of the end of the robot. Matrix

[0050] Represents the end position orientation, which is a 3×3 orthogonal matrix. Matrix p = [xyz] T Represents the end position.

[0051] like Figure 4 As shown in FIG. 1 , it is a schematic diagram of the configuration of the seven-degree-of-freedom robot arm in normal working conditions in the embodiment, and the corresponding joint angle is θ g=[180°,-150°,150°,-130°,-130°,180°,0°], based on Δθ=0, solve the reference end position orientation R under the error-free working condition g With reference space position p g , the results are:

[0052]

[0053] Further, as shown in step 3, the joint input repeatability error is calculated. It is worth noting that the joint error is normally distributed, which is equivalent to a normal distribution with a mean of 0.5 and a standard deviation of 0.5 / 3. This also means that 99.7% of the data points of a single joint error will fall within the given joint repeatability error. The joint input error can be defined as

[0054]

[0055] Substituting the result into the kinematic model, we can get the terminal position and orientation at this time. and spatial position Furthermore, the rotation change matrix T of the robot arm’s current error posture to the reference posture is solved. tr , specifically:

[0056]

[0057] Next, we calculate the repeated positioning posture deviation θ and position deviation S of the manipulator under this joint positioning error, where the repeated positioning posture deviation θ of the manipulator is related to the rotation transformation matrix T tr The rank correlation of the robot arm's repeated positioning position deviation S can be solved by the distance between two points in space:

[0058] trace(T tr )=a 11 +a 22 +a 33 =1+2cos(θ)

[0059] Θ=arccos((trace(T tr )-1) / 2)

[0060]

[0061] For a given robot arm repetitive positioning accuracy index, define the index confidence q, that is, through n repeated positioning calculations, define the proportion of the index that is satisfied in the repeated positioning calculations as the index confidence, and then realize the evaluation of the repetitive positioning accuracy index of the robot arm under the working conditions of interest. In the embodiment, given the robot arm repetitive position accuracy of ±0.4mm and repetitive posture accuracy of ±0.025°, in n = 300,000 repeated positionings, record the number of abnormalities m of each index data gΘ =0,m gS =81, the confidence evaluation of each indicator under normal working conditions can be completed, including:

[0062] q gΘ =1-m gΘ / n=100%

[0063] q gS =1-m gS / n=99.97%

[0064] like Figure 5 As shown in FIG. 1 , it is a schematic diagram of the configuration of the seven-degree-of-freedom robot arm in an extreme working condition in the embodiment, and the corresponding joint angle is θ k =[0°, 0°, 0°, -180°, -90°, 180°, 0°], similar to the above discussion, input the joint error with normal distribution in the given n = 300000 repeated positioning, and record the number of abnormalities m of each indicator data kΘ =7,m kS =1283, the confidence level of each indicator under extreme working conditions can be obtained.

[0065] q kΘ =1-m kΘ / n=99.99%

[0066] q kS =1-m kS / n=99.57%

[0067] In summary, the confidence of the repetitive positioning index of the robot arm in the embodiment under normal working conditions and extreme working conditions is obtained, and the results are shown in Table 2. In the evaluation process, when the confidence of the index under normal working conditions of the robot arm is higher than 99.95% and the confidence of the index under extreme working conditions is higher than 99.5%, it is considered that the proposed index is credible and has a certain margin. In the embodiment, the repetitive positioning accuracy index of the robot arm with a repetitive position accuracy of ±0.4mm and a repetitive posture accuracy of ±0.025° can be considered credible.

[0068] Table 2 Calculation results of confidence level of indicators in the embodiment

[0069]

[0070] The embodiments described in the above description will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

Claims

1. A method for evaluating the repeatability index of a robot arm based on normal random distribution, characterized in that: The following steps are involved: Step S1, establishing a kinematic model of the robot arm based on the improved DH method; Step S2: determine the normal working conditions and extreme working conditions that the robot arm needs to pay attention to during task execution, and perform the following steps under each working condition: S2a, calculate the reference end position and orientation R under the error-free condition of the current working condition g With reference space position p g ; S2b, setting joint error Δθ based on normal random distribution i , calculate the terminal pose matrix T tr , and then obtain the corresponding posture deviation θ and position deviation S; S2c, iteratively execute step S2b, define the proportion of indicators that meet the indicators under repeated positioning as the indicator confidence q of the current working condition, and then realize the evaluation of the robot arm's repeated positioning accuracy indicator.

2. The method for evaluating the repeatability index of a robot arm based on normal random distribution according to claim 1 is characterized in that: The robot arm is a cascade rigid system composed of rotating joints or moving joints; A joint coordinate system is established at the front end of each link, and a tool coordinate system is established at the end of the actuator. A kinematic model is established based on the improved DH method to calculate the end position and orientation of the robotic arm actuator.

3. A method for evaluating the repeatability of a robot positioning accuracy index based on normal random distribution according to claim 1 or 2, characterized in that: The process of establishing the kinematic model based on the improved DH method is as follows: S1a. Establish the joint coordinate system at the front end of each connecting rod: Where i=1,2,…,N is the joint number of the N-DOF robot arm. is the rotation transformation matrix from the joint i-1 coordinate system to the joint i coordinate system, α i-1 ,a i-1 ,d i ,θ i Respectively represent the connecting rod angle, connecting rod length, connecting rod offset and connecting rod angle in the MDH parameters, Δθ i Represents the repeated positioning error of joint i, and its upper and lower limits are S1b. Establish the tool coordinate system at the end of the actuator: Step S1c, the kinematic model T established based on the improved DH method is obtained by multiplying the rotation transformation matrices of each joint, which includes the position and posture information of the end of the robotic arm; Among them, the matrix Represents the end position orientation, which is a 3×3 orthogonal matrix; matrix p = [xyz] T Represents the end position.

4. The method for evaluating the repeatability index of a mechanical arm based on normal random distribution according to claim 1 is characterized in that: The normal working condition is the general situation of the robot arm in task execution, and the confidence of the robot arm meeting the repeatability index under normal conditions is evaluated; the extreme working condition is the situation where the robot arm is in a singular position, and the extreme working condition is selected as the situation where the robot arm is fully extended, and then the given repeatability index is evaluated under this working condition.

5. The method for evaluating the repeatability index of a mechanical arm based on normal random distribution according to claim 1 is characterized in that: S2a includes: based on the kinematic model calculated above and the angles θ of each joint under normal working conditions without error g , calculate the actuator end pose orientation and spatial position as the reference pose R g and the reference position p g ; Among them, the end posture is a 3×3 orthogonal matrix, and the end position is a 3×1 matrix. Each element in the matrix represents the coordinate value of the end of the robotic arm actuator in the Cartesian coordinate system.

6. The method for evaluating the repeatability index of a mechanical arm based on normal random distribution according to claim 1, characterized in that: In S2b, when simulating the repeated positioning of the robot arm using different joint errors, the error range of the given joint repeated positioning is Assign normal distribution characteristics to joint errors and use the kinematic model to calculate the end position of the robot arm and pointing 7. The method for evaluating the repeatability index of a robot arm based on normal random distribution according to claim 1 or 6, characterized in that: The transformation matrix of the terminal posture from the posture with error to the corresponding reference posture state is as follows:

8. The method for evaluating the repeatability index of a robot arm based on normal random distribution according to claim 1, characterized in that: In S2b, define the end position with joint error With reference position p g =[x g y g z g ] T The spatial distance is the position error S, which is obtained by the distance formula between two points in space The minimum angle from the end of the robot arm with joint error to the corresponding reference pose along the rotation axis is defined as the pose error θ, which is indirectly obtained from the trace of the rotation transformation matrix θ = arccos((trace(T tr )-1) / 2).

9. The method for evaluating the repeatability index of a mechanical arm based on normal random distribution according to claim 1, characterized in that: The proportion of indicators that meet the criteria in repeated positioning calculations is defined as the indicator confidence q: Θ =1-m Θ / n,q S =1-m S / n; respectively calculate the index evaluation standards under normal working conditions and extreme working conditions, and then realize the evaluation of the repeatability positioning accuracy index of the robot arm under the above working conditions.

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