Mechanical arm differential kinematics index comprehensive evaluation method under constant joint power

Abstract

The invention relates to a mechanical arm differential kinematics index comprehensive evaluation method under the constant joint power, and the method carries out the comprehensive evaluation of three differential kinematics indexes of the tail end force, the tail end torque and the tail end load speed of a mechanical arm based on the constant joint power. Comprising the following steps that firstly, a change matrix from all connecting rods to a tail end connecting rod of the mechanical arm is obtained based on an improved DH method, then working conditions needing to be concerned by the mechanical arm in task execution are determined, and a Jacobian matrix of the mechanical arm under the working conditions is calculated; and then, based on the given joint no-load and joint stalling output torque combined with a joint power constant hypothesis, the rotating speed condition of the joint when the mechanical arm meets the corresponding differential kinematics index is analyzed. And then, the rationality of the indexes is judged, the joint rotating speed range meeting the three indexes at the same time is analyzed, and finally, the index margin is introduced to conduct comprehensive evaluation on the mechanical arm differential kinematics indexes.

Description

Technical Field

[0001] The invention relates to the problem of evaluating indexes of a robot arm, and in particular to a comprehensive evaluation method of differential kinematic indexes of a robot arm under constant joint power. Background Art

[0002] At present, the differential kinematic indicators of the robot arm, such as the end force, end torque, and end load speed, are calculated by combining the maximum torque and maximum speed of the joint with the Jacobian matrix. At this time, the indicators are independent of each other. However, the existing method only considers the limit performance of the robot arm, and does not consider the correspondence between the torque and speed of the joint itself, that is, when the joint has the maximum output torque, it is in a continuous stalled state, and the joint speed is approximately zero; when the joint speed is the maximum, it is an unloaded joint, and the output torque is approximately zero. The above situation will cause the robot arm to fail when it needs to meet multiple differential kinematic indicators at the same time. Summary of the invention

[0003] In view of the above problems, the purpose of the present invention is to provide a method for evaluating differential kinematic indicators of a manipulator with reliable results, complete strategies and comprehensive evaluation. By assuming constant joint power and introducing indicator margin, a comprehensive evaluation is performed on the differential kinematic indicators of the given manipulator end force, end torque, end load speed, etc. under both normal and extreme working conditions, which helps to guide the formulation of differential kinematic indicators of the manipulator in the early stage of design.

[0004] The technical solution adopted by the present invention to achieve the above-mentioned purpose is: a comprehensive evaluation method of differential kinematic indicators of a manipulator under constant joint power, comprising the following steps:

[0005] Step S1: Establish the kinematic model of the robot arm based on the improved DH method and calculate the change matrix from each link to the end link Then obtain the Jacobian matrix J(θ);

[0006] Step S2: determine the working conditions that the robot arm needs to pay attention to during task execution, and calculate the Jacobian matrix J(θ g ) numerical solution and pseudo-inverse of its transposed matrix J -T (θ g );

[0007] Step S3: Based on the given joint no-load speed w max And the joint stall output torque τ max And its corresponding output resolution w e ,τ e , combined with the assumption that the joint power P of the robot arm is constant, the critical output values ​​of the joints when the corresponding differential kinematics indicators of the robot arm are met are calculated respectively, and the critical speed of the joints when the robot arm meets the corresponding differential kinematics indicators is analyzed;

[0008] Step S4, judge the rationality of the indicators and analyze the range of joint speeds that simultaneously meet the three indicators, and introduce the indicator margin r to comprehensively evaluate the above differential kinematic indicators.

[0009] 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 connecting rod, a tool coordinate system is established at the end of the actuator, and a kinematic model is completed based on an improved DH method.

[0010] The process of establishing the kinematic model based on the improved DH method is as follows:

[0011] S1a, establish a joint coordinate system at the front end of each link and calculate the change matrix of each link

[0012]

[0013] S1b, calculate the change matrix from each connecting rod to the end connecting rod

[0014]

[0015] S1c, according to the joint angles in the robot configuration, calculate the elements of each column of J(θ), where the i-th column Depend on OK, for the rotation matrix specifically:

[0016]

[0017] J(θ)=[J0(θ)J1(θ)…J6(θ)]

[0018] Where i = 1, 2, ..., N is the joint number of the N-DOF manipulator, 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; n i =[n xi ,n yi ,n zi ] T is the vector representation of the x-axis in the end link coordinate system in the i-th link coordinate system; where n xi is the mapping of the x-axis in the end link coordinate system to the x-axis in the i-th link coordinate system; n yi is the mapping of the x-axis in the end link coordinate system to the y-axis in the i-th link coordinate system; n zi is the mapping of the x-axis in the end link coordinate system to the z-axis in the i-th link coordinate system;i =[o xi ,o yi ,o zi ] T ,a i =[a xi ,a yi ,a zi ] T are the vector representations of the y and z axes in the coordinate system of the end link in the coordinate system of the i-th link; p i =[p xi ,p yi ,p zi ] T It represents the position of the origin of the end link coordinate system in the i-th link coordinate system.

[0019] Based on the kinematic model calculated above, for the non-six-degree-of-freedom manipulator, the Jacobian matrix under the target working condition is calculated; including: calculating the Jacobian matrix J(θ g )'s transposed pseudo-inverse J -T (θ g )=pinv(J T (θ g )), which satisfies J T J -T J T =J T ,J -T J T J -T =J -T .

[0020] Step S3 analyzes the rotation speed of the joint when the corresponding index is met, including:

[0021] a) Initially set the joint torque τ as the joint continuous stall output torque τ = τ max ;

[0022] b) Use the Jacobian matrix transpose pseudo-inverse J -T (θ g ) The end force f and torque T of the manipulator are obtained through the joint torque τ, specifically:

[0023] F g =[f1 f2 f3 T1 T2 T3] T =J -T (θ g )τ

[0024]

[0025] c) Calculate the joint output torque critical value τ that meets the end force and end torque indicators of the robot arm * ;

[0026] d) Initially set the joint torque w to the joint no-load speed w = w mzs ;

[0027] e) Using the Jacobian matrix J(θ g ) Obtain the end velocity v of the robot arm through the joint speed w;

[0028] V g =[v1 v2 v3 w1 w2 w3] T = J(θ g )

[0029]

[0030] f) Calculate the critical value w of the joint speed that satisfies the load speed at the end of the robot arm * ;

[0031] g) Based on the assumption that the joint is constant P = τ·w, calculate the joint output speed under the condition of minimum joint output torque This is the maximum output speed of the joint that simultaneously meets the index end force and torque.

[0032] c) Calculate the critical value τ of the joint output torque that meets the end force and end torque indicators of the robot arm * include:

[0033] When the following conditions are met at the same time: the end force f of the manipulator under the joint output force τ in this cycle> the end force f of the manipulator z , in this cycle, the torque T of the robot arm under the joint output force τ> the end torque T z When τ is updated to τ-τ e ; Return to execution process b and continue the loop;

[0034] Finally, after jumping out of the loop, the minimum joint output torque τ that satisfies the indicators of end force, torque, and joint output torque resolution is obtained. * =τ+τ e .

[0035] f) calculates the critical value w of the joint speed that satisfies the load speed at the end of the robot arm * ,include:

[0036] When the following conditions are met: the end load speed v of the robot arm under the joint speed w of this link> the end load speed v z When w=ww e ; Then return to the execution process e to continue the loop;

[0037] Finally, after jumping out of the loop, the minimum joint output speed w that meets the load speed at the end of the robot and the joint speed resolution is obtained. * =w+w e .

[0038] By analyzing the critical joint speed under different index requirements, the rationality of the index is judged, and the ratio between the maximum and minimum values ​​in the joint speed range that simultaneously meets the three indexes is defined as the index margin. Then, a comprehensive evaluation of the differential kinematic indicators of the robot arm under the above working conditions can be achieved.

[0039] The present invention has the following beneficial effects and advantages:

[0040] 1. Reliable results: The joint speed resolution and joint output torque resolution are used to find the joint critical speed and torque output values ​​that meet the corresponding differential kinematic indicators of the robot arm. The results can be implemented in practical applications with high reliability.

[0041] 2. Comprehensive evaluation: The concept of indicator margin is proposed. By analyzing the range of joint speeds of the robot arm under the premise of meeting the three indicators, the end force, end torque, and end load speed of the robot arm are comprehensively evaluated to make the indicators clearer. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 is a flow chart of an embodiment of the present invention;

[0043] Figure 2 is a schematic diagram of a seven-degree-of-freedom robotic arm configuration in an embodiment of the present invention;

[0044] Figure 3 Schematic diagram of a seven-degree-of-freedom robotic arm coordinate system in an embodiment of the present invention;

[0045] 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;

[0046] 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

[0047] 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.

[0048] like Figure 1As 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:

[0049] 1) Based on the improved DH method, the change matrix from each link of the robot arm to the end link is calculated to obtain the Jacobian matrix.

[0050] 2) Determine the working conditions that the robot arm needs to pay attention to during task execution, and calculate the numerical solution of the Jacobian matrix of the robot arm and the pseudo-inverse of its transposed matrix under the above working conditions.

[0051] 3) Based on the given joint no-load speed, joint stall output torque and output resolution, combined with the assumption of constant joint power of the robot arm, the critical speed of the joint is analyzed when the robot arm meets the corresponding differential kinematic indicators.

[0052] 4) Determine the rationality of the indicators and analyze the range of joint speeds that simultaneously meet the three indicators, and introduce indicator margins to conduct a comprehensive evaluation of the above differential kinematic indicators.

[0053] like Figure 2 As 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 shoulder joint link 1, a second shoulder joint link 2, a first arm joint link 3, a second arm joint link 4, a first wrist joint link 5, a second wrist joint link 6, and an actuator 7. In the embodiment, each joint of the robot arm is a rotating joint.

[0054] 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 obtained as shown in Table 1:

[0055] Table 1 Example robot arm MDH parameters

[0056]

[0057] Wherein, i=1, 2, ..., 7 are the joint numbers of the seven-degree-of-freedom robotic arm in the embodiment, 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. The Jacobian matrix of the embodiment described in step 1 is solved in the following process:

[0058] a) Calculate the change matrix of each connecting rod

[0059]

[0060] b) Calculate the change matrix from each link to the end link

[0061]

[0062] Among them, n i =[n xi ,n yi ,n zi ] T is the vector representation of the x-axis in the end link coordinate system in the i-th link coordinate system. Specifically, n xi is the mapping of the x-axis in the end link coordinate system to the x-axis in the i-th link coordinate system; n yi is the mapping of the x-axis in the end link coordinate system to the y-axis in the i-th link coordinate system; n zi is the mapping of the x-axis in the end link coordinate system to the z-axis in the i-th link coordinate system. Similar to the above definition, o i =[o xi ,o yi ,o zi ] T ,a i =[a xi ,a yi ,a zi ] T are the vector representations of the y and z axes in the end link coordinate system in the i-th link coordinate system. i =[p xi ,p yi ,p zi ] T It represents the position of the origin of the end link coordinate system in the i-th link coordinate system.

[0063] c) According to the joint angles in the robot configuration, calculate the column elements of J(θ), where the i-th column Depend on OK, for the rotation matrix specifically:

[0064]

[0065] J(θ)=[J0(θ) J1(θ) … J6(θ)]

[0066] 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°], solve the numerical solution of the Jacobian matrix in step 2.

[0067]

[0068] Then, the Jacobian matrix J(θ g )'s transposed pseudo-inverse J -T (θ g )=pinv(J T (θ g )), which satisfies J T J -T J T =J T ,J -T J T J -T =J -T , the results are:

[0069]

[0070] Further, as shown in step 3, using the above Jacobian matrix J(θ g ) and its corresponding transposed pseudo-inverse J -T (θ g ), based on the given joint no-load speed w max And the joint stall output torque τ max And its corresponding output resolution w e ,τ e , combined with the assumption that the joint power P of the robot arm is constant, the critical speed of the joint is analyzed when the corresponding indicators are met. The specific process is as follows:

[0071] a) Initially set the joint torque τ as the joint continuous stall output torque τ = τ max ;

[0072] b) Use the Jacobian matrix transpose pseudo-inverse J -T (θ g ) The end force f and torque T of the manipulator are obtained through the joint torque τ, specifically:

[0073] F g =[f1 f2 f3 T1 T2 T3] T =J -T (θ g )τ

[0074]

[0075] Among them, F g is the end force rotation quantity; f1, f2, f3, T1, T2, T3 are the components of the end force f and torque T of the robot arm in the x, y, z axis directions of the end coordinate system respectively.

[0076] c) Calculate the joint output torque critical value τ that meets the end force and end torque indicators of the robot arm * First, determine the end force f and torque T of the manipulator under the joint output force τ in this cycle. Then, determine its relationship with the end force f of the manipulator. z =100N, terminal torque T z =30N·m. When f>f z , T>T z When τ = τ - τ e , and then return to the execution process b to continue the loop. Finally, after jumping out of the loop, the minimum joint output torque τ that satisfies the index end force, torque, and joint output torque resolution can be obtained. * =τ+τ e .

[0077] d) Initially set the joint torque w to the joint no-load speed w = w max ;

[0078] e) Using the Jacobian matrix J(θ g ) Obtain the end velocity v of the robot arm through the joint speed w;

[0079] V g =[v1 v2 v3 w1 w2 w3] T = J(θ g )

[0080]

[0081] Among them, V g is the terminal velocity spinor; v1, v2, v3, w1, w2, w3 are the terminal velocity v and the terminal angular velocity w of the manipulator respectively m Components in the x, y, and z directions of the end coordinate system.

[0082] f) Calculate the critical value w of the joint speed that satisfies the load speed at the end of the robot arm * First, determine the end load speed v of the robot arm under the joint speed w of this link. Then, determine its difference with the end load speed v of the robot arm. z =0.2m / s. When v>v z When w=ww e , and then return to the execution process e to continue the loop. Finally, after jumping out of the loop, the minimum joint output speed w that meets the load speed at the end of the robot and the joint speed resolution can be obtained. * =w+w e .

[0083] g) Based on the assumption that the joint is constant P = τ·w, calculate the joint output speed under the condition of minimum joint output torque This is the maximum output speed of the joint that simultaneously meets the index end force and torque.

[0084] In step 4, we first need to judge the rationality of the indicators. When , it means that the robot arm is still greater than the joint no-load speed under the premise of meeting the end force and torque indicators, which means that the assumed joint power is too large and the indicator design is incorrect. When the robot arm reaches the end force and torque indicators, it cannot meet the end load indicators. The joint power design is too small and the indicator design is incorrect.

[0085] In the embodiment, the robot arm posture is θ g =[180°,-150°,150°,-130°,-130°,180°,0°]. Given the constant joint power P = 3W, the end force of the robot arm f z =100N, terminal torque T z =50N·m, load speed v at the end of the robot arm z =0.2m / s, the maximum output torque of the joint when it is continuously blocked is τ max =216N·m, output torque resolution is τ w =0.01N·m, maximum speed of joint without load w max =5rpm, output resolution w e =0.01rpm, the analysis results are shown in the following table:

[0086] Table 1 Calculation results of normal working conditions

[0087]

[0088]

[0089]

[0090] The above results show that under the premise of the joint rated power of 3W, the end load speed is in the range of 0.2 to 0.43m / s, and the index requirements of the operating arm end force of 100N and the end torque of 50N·m can still be guaranteed. At this time, the joint speed range is 0.465 to 0.999rpm. During the evaluation process, when the margin r of the differential kinematics index of the manipulator is higher than 1.5, the proposed index is considered to be credible. In the embodiment, the comprehensive index margin of the manipulator end force of 100N, the end torque of 50N·m, and the end load speed of 0.2m / s is r=2.148>1.5, then the above three indicators can be considered to be comprehensive and credible.

[0091] 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 comprehensive evaluation method for differential kinematics indicators of a manipulator under constant joint power, characterized in that: The following steps are involved: Step S1: Establish the kinematic model of the robot arm based on the improved DH method and calculate the change matrix from each link to the end link Then obtain the Jacobian matrix H(θ); Step S2: determine the working conditions that the robot arm needs to pay attention to during task execution, and calculate the Jacobian matrix H(θ g ) numerical solution and pseudo-inverse of its transposed matrix J -T (θ g ); Step S3: Based on the given joint no-load speed w max And the joint stall output torque τ max And its corresponding output resolution w e ,τ e , combined with the assumption that the joint power P of the robot arm is constant, the critical output values ​​of the joints when the corresponding differential kinematics indicators of the robot arm are met are calculated respectively, and the critical speed of the joints when the robot arm meets the corresponding differential kinematics indicators is analyzed; Step S4, judge the rationality of the indicators and analyze the range of joint speeds that simultaneously meet the three indicators, and introduce the indicator margin r to conduct a comprehensive evaluation of the above differential kinematic indicators.

2. The comprehensive evaluation method of differential kinematics indicators of a manipulator under constant joint power according to claim 1 is characterized in that: The robot arm is a cascade rigid system consisting of rotating joints or moving joints; A joint coordinate system is established at the front end of each connecting rod, a tool coordinate system is established at the end of the actuator, and the kinematic model is completed based on the improved DH method.

3. 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 process of establishing the kinematic model based on the improved DH method is as follows: S1a, establish a joint coordinate system at the front end of each link and calculate the change matrix of each link S1b, calculate the change matrix from each connecting rod to the end connecting rod S1c, according to the joint angles in the robot configuration, calculate the elements of each column of J(θ), where the i-th column Depend on OK, for the rotation matrix specifically: J(θ)=[J0(θ)J1(θ)…J6(θ)] Where i = 1, 2, ..., N is the joint number of the N-DOF manipulator, 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; n i =[n xi ,n yi ,n zi ] T is the vector representation of the x-axis in the end link coordinate system in the i-th link coordinate system; where n xi is the mapping of the x-axis in the end link coordinate system to the x-axis in the i-th link coordinate system; n yi is the mapping of the x-axis in the end link coordinate system to the y-axis in the i-th link coordinate system; n zi is the mapping of the x-axis in the end link coordinate system to the z-axis in the i-th link coordinate system; i =[o xi ,o yi ,o zi ] T ,a i =[a xi ,a yi ,a zi ] T are the vector representations of the y and z axes in the coordinate system of the end link in the coordinate system of the i-th link; p i =[p xi ,p yi ,p zi ] T It represents the position of the origin of the end link coordinate system in the i-th link coordinate system.

4. The comprehensive evaluation method of differential kinematics indexes of a manipulator under constant joint power according to claim 1, characterized in that: Based on the kinematic model calculated above, for the non-six-degree-of-freedom manipulator, the Jacobian matrix under the target working condition is calculated; including: calculating the Jacobian matrix J(θ g )'s transposed pseudo-inverse J -T (θ g )=pinv(J T (θ g )), which satisfies J T J -T J T =J T ,J -T J T J -T =J -T .

5. The comprehensive evaluation method of differential kinematics indicators of a manipulator under constant joint power according to claim 1 is characterized in that: Step S3 analyzes the rotation speed of the joint when the corresponding index is met, including: a) Initially set the joint torque τ to the joint continuous stall output torque τ = τ max ; b) Use the Jacobian matrix transpose pseudo-inverse J -T (θ g ) The end force f and torque T of the manipulator are obtained through the joint torque τ, specifically: F g =[f1 f2 f3 T1 T2 T3] T =J -T (i g )t c) Calculate the joint output torque critical value τ that meets the end force and end torque indicators of the robot arm * ; d) Initially set the joint torque w to the joint no-load speed w = w max ; e) Using the Jacobian matrix J(J g ) Obtain the end velocity v of the robot arm through the joint speed w; V g =[v1 v2 v3 w1 w2 w3] T =J(θ g )w f) Calculate the critical value w of the joint speed that satisfies the load speed at the end of the robot arm * ; g) Based on the assumption that the joint is constant P = τ·w, calculate the joint output speed under the condition of minimum joint output torque This is the maximum output speed of the joint that simultaneously meets the index end force and torque.

6. The comprehensive evaluation method of differential kinematics indexes of a manipulator under constant joint power according to claim 5 is characterized in that: c) Calculate the joint output torque critical value τ that meets the end force and end torque indicators of the robot arm * include: When the following conditions are met at the same time: the end force f of the manipulator under the joint output force τ in this cycle> the end force f of the manipulator z , in this cycle, the torque T of the robot arm under the joint output force τ> the end torque T z When τ is updated to τ-τ e ; Return to execution process b and continue the loop; Finally, after jumping out of the loop, the minimum joint output torque τ that satisfies the indicators of end force, torque, and joint output torque resolution is obtained. * =τ+τ e .

7. The comprehensive evaluation method of differential kinematics indexes of a manipulator under constant joint power according to claim 5 is characterized in that: f) Calculate the critical value w of the joint speed that satisfies the load speed at the end of the robot arm * ,include: When the following conditions are met: the end load speed v of the robot arm under the joint speed w of this link> the end load speed v z When w=ww e ; Then return to the execution process e to continue the loop; Finally, after jumping out of the loop, the minimum joint output speed w that meets the load speed at the end of the robot and the joint speed resolution is obtained. * =w+w e .

8. A comprehensive evaluation method for differential kinematics indicators of a manipulator under constant joint power according to claim 5, 6 or 7, characterized in that: By analyzing the critical joint speed under different index requirements, the rationality of the index is judged, and the ratio between the maximum and minimum values ​​in the joint speed range that simultaneously meets the three indexes is defined as the index margin. Then, a comprehensive evaluation of the differential kinematic indicators of the robot arm under the above working conditions can be achieved.

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