Collaborative robot real-time modal analysis method combined with joint rotation

Abstract

The invention relates to a joint rotation combined collaborative robot real-time modal analysis method, which comprises the following steps of: 1, splitting a robot into a plurality of independent modules, and enabling each module to be equivalent to a super unit; step 2, obtaining a flexibility matrix Ci and a mass matrix Mi of each super-unit under an output coordinate system of the super-unit, and calculating and converting the Ci to obtain a flexibility matrix CJi of the super-unit under the output coordinate system when the super-unit rotates; 3, the flexibility matrix CJi and the mass matrix Mi obtained in the step 2 are converted to a robot end coordinate system, a robot whole machine flexibility matrix nC and a whole machine mass matrix nM are obtained, and the whole machine rigidity matrix nK is obtained by conducting inversion on nC; and 4, establishing an undamped free vibration equation of the robot, and substituting the complete machine flexibility matrix nC and the complete machine mass matrix nM obtained in the step 3 into the equation so as to solve the inherent frequency of the collaborative robot in real time. According to the method, the rigidity change condition during rotation of the joint module is considered, and the calculation amount is greatly simplified while the calculation error is reduced.

Description

Technical Field

[0001] The present invention relates to the field of collaborative robots, and in particular to a real-time modal analysis method of collaborative robots combined with joint rotation. Background Art

[0002] Collaborative robots are a new type of industrial robot that can interact with humans in a shared space. The main differences between them and traditional industrial robots are whether they are in a structured environment and whether they can work with humans. Due to the characteristics of collaborative robots, such as light weight, safety, and high interaction efficiency, they have become one of the current research hotspots in the field of robotics.

[0003] The design concept of lightweight and high load-to-weight ratio introduces a large number of flexible factors into collaborative robots, but this also causes the robot to inevitably vibrate during movement, affecting the robot's dynamic performance and motion accuracy, which is contrary to the performance of collaborative robots. Structural optimization is an effective means to improve its vibration and improve movement smoothness.

[0004] The dynamic characteristics such as natural frequency, amplitude and vibration mode obtained by modal analysis of robots are important parameters for robot structural optimization. Considering the multi-position dynamic performance of the robot structure, structural optimization requires the real-time solution of the robot's dynamic characteristics, and high-precision real-time modal analysis methods are an important theoretical basis for improving the dynamic performance and vibration suppression of collaborative robots.

[0005] The previous modal analysis methods mainly include analytical method, high-precision modal analysis finite element method and experimental modal method, such as vibration test method, etc. The analytical method is to obtain the undamped free vibration equation of the robot system by establishing the rigid-flexible coupling or flexible dynamics model of the robot, and then obtain the natural frequency and vibration mode of the robot. The analytical method can meet the real-time requirements of the dynamic performance structure optimization of the robot, and it is widely used in the dynamic performance structure optimization of parallel and serial robots. However, although this method greatly simplifies the robot model and reduces the amount of calculation, the simplification of joints and connecting rods also reduces the modeling accuracy. The finite element method is based on the finite element theory to model and analyze the robot, and then obtain the natural frequency and vibration mode of the robot. At present, the finite element method can be used to analyze the dynamic characteristics of the robot in typical positions and postures, and put forward suggestions for improving the robot structure. The vibration test method uses a frequency response function measurement device to excite the mechanical structure to obtain the system's modal parameters such as natural frequency, damping and vibration mode. However, although the finite element analysis method and the vibration test method can intuitively and truly reflect the dynamic performance of the mechanical structure, they both have the disadvantages of poor real-time performance and large workload. Each analysis result is only valid for the calculated posture and boundary conditions. Once the posture changes, it is necessary to re-model or arrange the test for calculation.

[0006] Patent CN112949104B discloses a real-time modal analysis method for a collaborative robot combined with joint rotation, which uses a method combining finite element and analytical methods to solve the dynamic performance of the collaborative robot, and has the advantages of small amount of calculation, high efficiency, and high precision, and can fully consider the elastic deformation of various components of the robot. However, in step 2, this method directly extracts the stiffness matrix and mass matrix of the super unit in its own coordinate system through finite element analysis software, and does not take into account the rotation of the joint module, so its subsequent solution process is still relatively cumbersome. Summary of the invention

[0007] The purpose of the present invention is to provide a real-time modal analysis method for a collaborative robot combined with joint rotation, which takes into account the stiffness change of the joint module when it rotates, further reducing the corresponding calculation error while also greatly simplifying the calculation amount.

[0008] The objective of the present invention is achieved through the following technical solutions:

[0009] A real-time modal analysis method for a collaborative robot combined with joint rotation comprises the following steps:

[0010] Step 1: Split the robot into multiple independent modules, and each module is equivalent to a super unit;

[0011] Step 2: Obtain the flexibility matrix C of each super-element in its own output coordinate system i and the mass matrix M i , and C i Calculate the transformation to obtain the flexibility matrix C of the output coordinate system when the super element rotates itself Ji :

[0012] Step 3: Substitute the flexibility matrix C obtained in step 2 Ji and the mass matrix M i Convert to the robot end coordinate system and obtain the robot's overall flexibility matrix n C and the machine mass matrix n M, where the superelement mass matrix M i In the robot end coordinate system, it is expressed as:

[0013]

[0014] The flexibility matrix C of the superelement Ji In the robot end coordinate system, it is expressed as:

[0015]

[0016] Machine stiffness matrix n K is for n C is inverted to obtain:

[0017] n K= n C -1 (13);

[0018] Step 4: Establish the undamped free vibration equation of the robot and transform the whole machine flexibility matrix obtained in step 3 into n C and the machine mass matrix n M is substituted into the equation to achieve real-time solution of the collaborative robot's natural frequency, providing a basis for the real-time modal analysis of the collaborative robot.

[0019] In step one, the robot module includes a link module and a joint module.

[0020] In step 2, the connecting rod module does not need to be further processed because it does not rotate and has no effect on the calculation.

[0021] For the joint module, the flexibility matrix C is calculated and transformed according to the following formula (1): Ji :

[0022]

[0023] In the above formula (1), It is T i The adjoint transformation, T i It is the mapping between the output coordinate system and the input coordinate system when the joint rotates, where:

[0024]

[0025] In the above formulas (2) and (3), R i is the rotation matrix, By p i The 3×3 antisymmetric matrix of vectors is:

[0026]

[0027] In step 3, the joint module needs to consider the change in stiffness after its own angle rotation. For the link module, since it does not rotate, it has no effect on the calculation. Therefore, the flexibility matrix C of all super units is Ji In the robot end coordinate system, they are expressed as:

[0028]

[0029] In step three, n The process of obtaining M is as follows:

[0030] First, obtain the mapping of the input coordinate system of the robot's next module to the input coordinate system of the previous module i-1 T i :

[0031]

[0032] In the above formula (5), i-1 R i represents the rotation matrix from the input coordinate system of the i-th module to the input coordinate system of the i-1-th module, p i =[x i ,y i , z i ] T They respectively represent the positions of the origin of the input coordinate system of the i-th module in the X, Y, and Z directions of the input coordinate system of the i-1-th module;

[0033] The mapping of the robot end coordinate system to the coordinate system of each super unit is obtained by multiplying the transformation matrix of each super unit:

[0034]

[0035] The transformation matrix from the i-th superunit's own coordinate system to the robot's end coordinate system is obtained by inverting the above formula (6):

[0036]

[0037] According to the mapping relationship in equation (7), the mass transformation matrix S from the i-th super unit to the robot end coordinate system is obtained: i :

[0038]

[0039] So each super-element mass matrix M i The expression in the robot end coordinate system is:

[0040] n M i =ST i ·M i ·S i (9).

[0041] The advantages and positive effects of the present invention are:

[0042] 1. The present invention obtains the flexibility matrix of the joint module in its own output coordinate system at any rotation angle through the screw transformation matrix. In this way, the present invention takes into account the stiffness change of the joint module when it rotates, and the corresponding calculation error can be further reduced in subsequent processing.

[0043] 2. The present invention is based on the flexibility matrix C of the super unit in its own output coordinate system when it rotates Ji and the superelement mass M i Obtain the robot's overall flexibility matrixn C and the machine mass matrix n M, and n C is inverted to obtain the robot's entire stiffness matrix n K, where the above machine flexibility matrix n C and the machine mass matrix n The dimensions of the M results are all 6×6. Compared with the prior art (CN112949104B patent), the present invention can directly use MATLAB software to calculate the results without cyclically extracting elements and adding them, which greatly simplifies the amount of calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is a schematic diagram of the collaborative robot model and various coordinate systems involved in the present invention.

[0045] Figure 2 This is a schematic diagram of a module equivalent model involved in the present invention.

[0046] Figure 3 for Figure 2 Schematic diagram of the super unit model obtained after simplifying the equivalent model of the middle module.

[0047] Figure 4 This is a schematic diagram of the joint module and its coordinate system conversion involved in the present invention.

[0048] Figure 5 This is a schematic diagram of the connecting rod module coordinate system involved in the present invention.

[0049] Figure 6 It is a flowchart of the present invention. DETAILED DESCRIPTION

[0050] The present invention will be further described below in conjunction with the accompanying drawings.

[0051] The present invention is a further improvement on the basis of the CN112949104B patent.

[0052] like Figures 1 to 6 As shown, the method of the present invention comprises the following steps:

[0053] Step 1: Establish a robot model and split the robot model into multiple independent modules, and then equate each module to a super unit. The robot module includes a link module and a joint module.

[0054] In this step, the substructure method is used to split the model into several sub-models, and the finite element models of each sub-model are established respectively. Each sub-model must be condensed into a unit, that is, a super unit, using the static condensation technology.

[0055] The specific steps of this step are as follows: Figure 1The figure shows a complex large model, which can be regarded as a number of independent module units connected in series in sequence. The substructure method can be used to split the model into several sub-models, and the finite element model of each sub-model can be established separately. Each sub-model must be condensed into a unit, that is, a super unit, using static condensation technology. Then, these super units are combined on the specified interface to obtain a greatly simplified model of the whole machine. The present invention uses static condensation and super unit technology to condense the module into a super unit, and then directly extracts the stiffness matrix relative to the output coordinate system of the module. Due to the special serial structure of the collaborative robot and the connection form between the modules, each module is only mutually constrained with other modules at the output and input flanges, and the constraint relationship is defined by the nodes on the flange end faces.

[0056] In order to reduce the amount of calculation and improve the calculation efficiency, the present invention uses structural mass point units to simulate the constraint relationship between modules, and the mass point units are respectively located at the input end and the output end center of the module. Through multi-point constraints (MPC), a rigid beam can be established between the structural mass point unit and the end face node, and finally two rigid regions are formed at the output end and the input end of the module respectively. The structural mass point unit is defined as the main node, so each module can be simplified into a super unit with two main nodes, and each super unit has 12 degrees of freedom. The super units corresponding to many robot modules are connected in series in sequence to be equivalent to a finite element substructure model of a robotic arm. The super units corresponding to these modules are connected in series in sequence to construct an equivalent finite element model of the instantaneous rigidification treatment of the robotic arm.

[0057] In actual operation, in order to further simplify the operation process, a fixed constraint can be applied to the input end of the module. At this time, the main degrees of freedom of the super unit are only the degrees of freedom corresponding to the mass point unit at the output port, such as Figure 2 As shown, the corresponding simplified representation of the super unit is as follows Figure 3 As shown. Figure 1 The 6-DOF collaborative robot shown in the figure can be equivalent to 13 super units, 14 master nodes ( Figure 1 The finite element model is composed of a series of nodes (where n is the 14th main node).

[0058] The above process is a well-known technology in the art, for example, see CN112949104B patent, but the difference between the present invention and CN112949104B patent is: Figure 3 As shown, the present invention simplifies the fixing of one end of the beam because the joint rotation is taken into consideration.

[0059] Step 2: Simplify the module model and use the finite element substructuring method to obtain the flexibility matrix C of each super-element in its own output coordinate system. i and the mass matrix M i , where for C iThe flexibility matrix C of each joint superunit in the output coordinate system when it rotates needs to be obtained through conversion calculation Ji , the change of the output coordinate system compared to the initial position will cause the stiffness characteristics to change, and the present invention obtains the flexibility matrix of the output coordinate system of the joint module at any rotation angle through the screw transformation matrix, so that the present invention takes into account the change of stiffness when the joint module rotates, and the corresponding calculation error can be further reduced in subsequent processing. Then the present invention uses C Ji and M i Obtain the robot's overall flexibility matrix n C and the machine mass matrix n M, and n C is inverted to obtain the robot's entire stiffness matrix n K, which is different from the prior art CN112949104B patent that directly extracts the stiffness matrix and solves it through software.

[0060] The specific steps of this step are:

[0061] Step 2.1: Use SolidWorks software to simplify the module model, and use ANSYS finite element software workbench platform to analyze and obtain the flexibility matrix C of each super unit in its own output coordinate system. i and the mass matrix M i .

[0062] Step 2.2: If Figure 5 As shown, for the connecting rod module, since it does not rotate itself, it only has a conversion of coordinate position, and the rotation attitude transformation matrix is ​​the unit matrix, which has no effect on the calculation, so the connecting rod module does not need further processing;

[0063] And as Figure 4 As shown in the figure, for the joint module, it is necessary to calculate the flexibility matrix C of each joint super unit in the output coordinate system when it rotates. Ji , specifically: the flexibility matrix C of joint i obtained in step 2.1 i The reference is when joint i is in zero position, such as Figure 4 As shown, when the joint variable qi is not zero, that is, the joint is {Ji 2-0}Zero position moves to {J i1}, the output coordinate system of the joint {J i2} and {Ji 2-0} do not overlap, which produces a relative rotation of a certain angle. At this time, the expression of the flexibility matrix in the joint output coordinate system {Ji2} is C Ji for:

[0064]

[0065] In the above formula (1), It is T i The adjoint transformation, T i is the mapping between the output coordinate system {Ji2} and the input coordinate system when the joint rotates, where

[0066]

[0067]

[0068] In the above formulas (2) and (3), R i is the rotation matrix, By p i The 3×3 antisymmetric matrix of vectors is:

[0069]

[0070] Step 3: Substitute the flexibility matrix C obtained in step 2 Ji and the mass matrix M i Convert to the robot end coordinate system and integrate to get the instantaneous rigid robot flexibility matrix n C and the machine mass matrix n M.

[0071] The specific steps of this step are:

[0072] Step 3.1: Obtain the mapping of the input coordinate system of the robot's next module to the input coordinate system of the previous module i-1 T i :

[0073]

[0074] In the above formula (5), i-1 R i represents the rotation matrix from the input coordinate system of the i-th module to the input coordinate system of the i-1-th module, p i =[x i ,y i , z i ] T They respectively represent the positions of the origin of the input coordinate system of the i-th module in the X, Y, and Z directions of the input coordinate system of the i-1-th module;

[0075] In this embodiment, the mapping of each module input coordinate system to the previous module input coordinate system is:

[0076]

[0077] Step 3.2: Obtain the transformation matrix from the i-th (i>1) super unit's own coordinate system to the robot's end coordinate system.

[0078] The mapping of the robot end coordinate system to the coordinate system of each super unit (the robot end coordinate system coincides with the end flange output coordinate system) is obtained by multiplying the transformation matrices of each super unit:

[0079]

[0080] In the above formula (6), i p n represents the position of the origin of the whole coordinate system in the i-th superunit's own coordinate system, i R n Represents the rotation matrix from the robot end coordinate system to the i-th super unit's own coordinate system;

[0081] The transformation matrix from the i-th (i>1) super unit's own coordinate system to the robot's end coordinate system is obtained by inverting the above formula (6):

[0082]

[0083] Step 3.3: According to the mapping relationship in equation (7), obtain the mass transformation matrix S from the i-th super unit to the robot end coordinate system: i :

[0084]

[0085] This step is the same as that of patent CN112949104B;

[0086] So each super-element mass matrix M i The expression in the robot end coordinate system is:

[0087]

[0088] As mentioned above, the flexibility of each module is expressed in the robot terminal coordinate system using a screw transformation. The joint module needs to consider the change in stiffness after its own angle rotation. For the link module, there is no rotation itself, and only the coordinate position is transformed. The rotation attitude transformation matrix is ​​the unit matrix and has no effect on the calculation. Therefore, the flexibility matrix C of all super units is Ji In the robot end coordinate system, it can be expressed as:

[0089]

[0090] Step 3.4: Since all the links in the robot stiffness model are assembled in series, the overall flexibility matrix of the robot can be obtained. n C and the machine mass matrix n M:

[0091]

[0092] The machine stiffness matrix n K inverts equation (11) to obtain:

[0093] n K= n C -1 (13);

[0094] The above steps are all calculated by MATLAB software, where the above formula (11) can be further expressed as:

[0095]

[0096] The above formula (12) can be further expressed as:

[0097]

[0098] Taking the above formula (14) as an example, n C i-11 is the first row and first column element of the flexibility matrix of the i-th module converted to the end of the robot, is the sum of the first row and first column elements of the flexibility matrix of all modules after conversion. Similarly, the dimension of the flexibility matrix of the whole machine is 6×6.

[0099] Since the whole machine of the present invention only retains two nodes, the base and the end, and the base node is fixed, compared with the assembly calculation in CN112949104B (step 3.6) (the corresponding result dimension of this method is 72×72), the present invention can directly calculate the result using MATLAB software without the need to cyclically extract and add elements, which greatly simplifies the amount of calculation.

[0100] Step 4: Establish the undamped free vibration equation of the robot and transform the whole machine flexibility matrix obtained in step 3 into n C and the machine mass matrix n Substitute M into the equation to achieve real-time solution of the natural frequency of the collaborative robot, providing a basis for real-time modal analysis of the collaborative robot. This step is the same as that of the CN112949104B patent.

Claims

1. A real-time modal analysis method for a collaborative robot combined with joint rotation, characterized in that: The steps include: Step 1: Split the robot into multiple independent modules, and each module is equivalent to a super unit; Step 2: Obtain the flexibility matrix C of each super-element in its own output coordinate system i and the mass matrix M i , and C i Calculate the transformation to obtain the flexibility matrix C of the output coordinate system when the super element rotates itself Ji : Step 3: Substitute the flexibility matrix C obtained in step 2 Ji and the mass matrix M i Convert to the robot end coordinate system and obtain the robot's overall flexibility matrix n C and the machine mass matrix n M, where the superelement mass matrix M i In the robot end coordinate system, it is expressed as: The flexibility matrix C of the superelement Ji In the robot end coordinate system, it is expressed as: Machine stiffness matrix n K is for n C is inverted to obtain: n K= n C -1 (13); Step 4: Establish the undamped free vibration equation of the robot and transform the whole machine flexibility matrix obtained in step 3 into n C and the machine mass matrix n M is substituted into the equation to achieve real-time solution of the collaborative robot's natural frequency, providing a basis for the real-time modal analysis of the collaborative robot.

2. The real-time modal analysis method of a collaborative robot combined with joint rotation according to claim 1, characterized in that: In step one, the robot module includes a link module and a joint module.

3. The real-time modal analysis method of a collaborative robot combined with joint rotation according to claim 2, characterized in that: In step 2, the connecting rod module does not need to be further processed because it does not rotate and has no effect on the calculation. For the joint module, the flexibility matrix C is calculated and transformed according to the following formula (1): Ji : In the above formula (1), It is T i The adjoint transformation, T i It is the mapping between the output coordinate system and the input coordinate system when the joint rotates, where: In the above formulas (2) and (3), R i is the rotation matrix, By p i The 3×3 antisymmetric matrix of vectors is:

4. The real-time modal analysis method of a collaborative robot combined with joint rotation according to claim 3 is characterized in that: In step 3, the joint module needs to consider the change in stiffness after its own angle rotation. For the link module, since it does not rotate, it has no effect on the calculation. Therefore, the flexibility matrix C of all super units is Ji In the robot end coordinate system, they are expressed as:

5. The real-time modal analysis method of a collaborative robot combined with joint rotation according to claim 1 or 5, characterized in that: In step three, n The process of obtaining M is as follows: First, obtain the mapping of the input coordinate system of the robot's next module to the input coordinate system of the previous module i-1 T i : In the above formula (5), i-1 R i represents the rotation matrix from the input coordinate system of the i-th module to the input coordinate system of the i-1-th module, p i =[x i ,y i , z i ] T They respectively represent the positions of the origin of the input coordinate system of the i-th module in the X, Y, and Z directions of the input coordinate system of the i-1-th module; The mapping of the robot end coordinate system to the coordinate system of each super unit is obtained by multiplying the transformation matrix of each super unit: The transformation matrix from the i-th superunit's own coordinate system to the robot's end coordinate system is obtained by inverting the above formula (6): According to the mapping relationship in equation (7), the mass transformation matrix S from the i-th super unit to the robot end coordinate system is obtained: i : So each super-element mass matrix M i The expression in the robot end coordinate system is:

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