Robot modal identification method and system based on multi-directional random motion of joints

Abstract

This invention belongs to the field of industrial robot dynamics and specifically discloses a robot modal identification method and system based on multi-directional random motion of joints. The method comprises the following steps: applying an excitation force to the robot, causing each joint of the robot to perform random acceleration and deceleration motion, and collecting vibration signals from each joint of the robot during this process; the excitation force applied satisfies the following conditions: each excitation force has at least three non-collinear directions, and the excitation torque of each joint is non-linear. Under this excitation method, the modal vibration shapes of the robot in all directions can be fully excited; and then processing the vibration signals of each joint of the robot to identify each order of the robot's modes. The present invention can achieve complete, accurate, and effective identification of each order of the robot's modes.

Description

Technical Field

[0001] The present invention belongs to the field of industrial robot dynamics, and more specifically, relates to a robot modal identification method and system based on multi-directional random motion of joints. Background Art

[0002] The serial structure of industrial robots offers excellent machinability, strong redundancy, and high flexibility, playing an increasingly important role in the production and manufacturing of large and medium-sized parts in industries such as aviation, navigation, and automotive assembly. The robot's high flexibility and multi-position motion characteristics provide an effective way to process complex curved surfaces. The structure of an industrial robot mainly consists of a base, joints, an upper arm, a lower arm, and an end effector, which is usually composed of a tool spindle system. Because industrial robots have multiple rotary joints, they can provide a wider workspace during the milling process of large parts, and are not restricted by the work area and production shape during processing. However, this open serial structure reduces the overall rigidity of the industrial robot. During the milling process, the processing force applied to the end effector will cause excessive vibration, which will reduce the trajectory accuracy of the part processing process, resulting in insufficient manufacturing precision of the part processing surface, and may not meet the finishing requirements of parts with complex shapes. Therefore, it is necessary to study the dynamic characteristics of industrial robots in operation, accurately estimate the structural modal parameters, analyze the modal coupling chatter existing in the part processing process and suppress it. This is of great significance for reducing the vibration of the robot end effector, improving the surface quality such as the surface smoothness of complex parts, and reducing the trajectory error of the processing process.

[0003] Because industrial robots are composed of multiple flexible joints connected in series, each joint, linkage, and rotor at the front end influences the machining motion of the end effector. These complex kinematic characteristics also lead to complex dynamic characteristics of the end effector, resulting in a high degree of heterogeneity and difficulty in accurately locating the source of vibration. This makes vibration analysis and modal characterization of industrial robots challenging. Current methods for obtaining the structural modal parameters of industrial robots rely on model-based validation and experimental verification. For multimodal industrial robot systems, model-based validation methods cannot accurately predict all frequencies, and multi-joint serial systems of industrial robots also increase the computational load. Experimental-based modal analysis, in contrast, only requires the response signal to identify the system's modes. However, this requires white noise excitation, which is typically performed under well-controlled laboratory conditions. However, most robots do not meet these laboratory conditions during actual machining, making it difficult to fully excite the various modes of the robot itself. Consequently, this method has limited widespread application. Therefore, a method is needed to gain a deeper understanding of the overall structural dynamics of the robot.

[0004] Currently, the main vibration modal analysis of industrial robots pays little attention to the influence of the excitation direction. However, when the industrial robot is in different posture states, the overall mass distribution of the robot will change, causing changes in the stiffness distribution in different directions. At this time, if the direction of the excitation force applied to the robot is unreasonable, it may cause insufficient response of the frequency response function, resulting in incomplete identification results of the modal analysis. Therefore, it is particularly important to find a method that can accurately and effectively identify the modal parameters of the robot. Summary of the Invention

[0005] In response to the above-mentioned defects or improvement needs of the prior art, the present invention provides a robot modal identification method and system based on multi-directional random motion of joints, the purpose of which is to achieve complete, accurate and effective identification of various modes of the robot through the design of the excitation method.

[0006] To achieve the above object, according to one aspect of the present invention, a robot modal identification method based on multi-directional random motion of joints is proposed, comprising the following steps:

[0007] Apply an excitation force to the robot, causing each joint of the robot to perform random acceleration and deceleration movements, and collect vibration signals from each joint of the robot during this process; the excitation force applied satisfies the following conditions: each excitation force has at least three non-collinear directions, and the excitation torque of each joint is non-linear during the robot's motion;

[0008] The vibration signals of each joint of the robot are processed to identify the various modes of the robot. As a further preferred embodiment, the excitation force applied satisfies:

[0009] di m(F)=dr≥3

[0010] Where F is the input force matrix composed of all input excitation forces, dim(·) represents the dimension, d is the number of input excitation forces, and r is the repeated direction excitation force acting on the robot.

[0011] As a further preferred embodiment, the excitation force applied satisfies:

[0012] dim(X(r))=3

[0013]

[0014] Among them, any spatial rectangular coordinate system is constructed, X(τ) is the projection of the robot force on the three axes, dim(·) represents the dimension; τ ax , τ ay , τ az They represent the projections of the excitation torque of the a-th joint in the x-axis, y-axis, and z-axis directions, respectively. a=1,2…A, where A is the total number of robot joints.

[0015] As a further preferred embodiment, an acceleration sensor is arranged on the robot, and vibration signals of various joints of the robot are obtained through the acceleration sensor.

[0016] As a further preferred embodiment, the acceleration sensors are arranged in a specific manner as follows: more than four acceleration sensors are arranged on the robot base, each joint, and each connecting rod.

[0017] As a further preference, the robot movement is controlled by a CNC program, and the interval time of the movement is set to a random sequence, so that the joints of the robot perform random acceleration and deceleration movements. During the start and stop process, the movement of each joint produces an inertial impact on the body, and the robot produces a corresponding vibration response.

[0018] As a further preferred embodiment, the vibration signals of each joint of the robot are processed by OMA analysis, so as to identify each order mode of the robot.

[0019] According to another aspect of the present invention, a robot modal identification system based on multi-directional random motion of joints is provided, comprising a control unit, a collection unit, and a processing unit, wherein:

[0020] The control unit is used to apply an excitation force to the robot so that each joint of the robot performs random acceleration and deceleration motion; the excitation force applied satisfies: each excitation force has at least three non-collinear directions, and the excitation torque of each joint is non-linear during the movement of the robot;

[0021] The acquisition unit is used to collect vibration signals of each joint of the robot during movement;

[0022] The processing unit is used to process the vibration signals of each joint of the robot and identify each order mode of the robot.

[0023] As a further preference, the acquisition unit includes a plurality of acceleration sensors arranged on the robot.

[0024] As a further preferred embodiment, the vibration signals of each joint of the robot are processed by OMA analysis, so as to identify each order mode of the robot.

[0025] In general, the above technical solutions conceived by the present invention have the following technical advantages compared with the existing technology:

[0026] 1. The present invention designs the robot excitation method to ensure that the excitation force is generated in all directions of the modal vibration mode, thereby completely, accurately and effectively identifying the various modes of the robot during the processing process. This method is also suitable for modal parameter identification of various forms of industrial robots in different postures.

[0027] 2. The present invention takes into account the problem of spatial redundancy of the robot. Specifically, during the processing of different postures, since the robot has certain additional degrees of freedom of movement (i.e., redundancy), there may be situations where the robot end is in the same position but the robot joint angles and postures are different. Based on this, the present invention proposes the conditions that the excitation torque must meet to avoid the influence of the robot redundancy and ensure that the different modal orders of the robot can be completely and effectively identified. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 Schematic diagram of cross-direction self-excitation of multiple joints of a six-degree-of-freedom robot according to an embodiment of the present invention;

[0029] Figure 2 (a) and (b) are schematic diagrams of the random motion sequence velocity and acceleration of each joint of the robot according to an embodiment of the present invention. DETAILED DESCRIPTION

[0030] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0031] The embodiment of the present invention provides a robot modal identification method based on multi-directional random motion of joints, which fully excites the robot structure from all directions to ensure that the different modal orders of the robot can be completely and effectively identified; specifically, Figure 1 Taking the six-degree-of-freedom industrial robot shown in the figure as an example, this embodiment includes the following steps:

[0032] S1. Arrange acceleration sensors evenly on the six-degree-of-freedom industrial robot body, ensuring that the robot base, each joint, and each connecting rod are equipped with acceleration sensors; preferably, at least four test points are symmetrically and evenly arranged on the robot base, six joints, and two connecting rods to capture vibration signals on each joint of the robot.

[0033] S2, use CNC program to control multiple joint components to do random acceleration and deceleration motion, specifically by changing the interval time of joint motion, setting it into a random sequence, such as Figure 2 As shown in the figure, during the process of controlling the start and stop of the robot, the joint movement generates an inertial impact on the body, and the robot structure will produce a corresponding vibration response, and the vibration signal is collected by the acceleration sensor.

[0034] At the same time, the conditions that the excitation force applied to the robot by each joint during random motion should meet are: the excitation force has no less than three non-collinear directions, and the excitation torque of each joint is non-linear.

[0035] S3. Process the collected vibration signals based on OMA analysis theory to fully identify the various modes of the robot.

[0036] The principle and effectiveness of the method of the present invention are further explained below.

[0037] By simultaneously controlling multiple joints to perform random inertial impacts, and meeting the requirement of generating excitation in intersecting directions (i.e., three or more non-collinear directions), the various components of the robot structure will produce a vibration response under the action of inertial forces. During the process of random inertial impacts on the robot, the robot's structural dynamic parameters can be assumed to be unchanged. During the milling process, industrial robots need to be in different positions and postures, which will cause the robot's mass distribution to change, thereby changing the robot's overall stiffness distribution. Therefore, modal identification of the industrial robot's structure during motion is necessary.

[0038] (1) Dynamic principles of multi-directional excitation

[0039] Based on the basic theory of OMA, when the robot is subjected to random inertial impact, the input and output relationship of the industrial robot system is:

[0040] Y(ω)=X(ω)H(ω) (1)

[0041] Where X(ω) is the input response signal to the system in the frequency domain, Y(ω) is the system output response signal in the frequency domain, and H(ω) is the system transfer function matrix in the frequency domain, where each element represents the dynamic characteristic information from the input point to the output point.

[0042] Assuming that n measuring points are evenly arranged on the entire industrial robot body, the relationship between input and output can be written as:

[0043]

[0044] Where, X i (ω) is the actual response measured by the i-th sensor, F j (ω) is the jth generalized force component, H ij (ω) is the transfer function between the external force at the i-th measurement point and the j-th excitation point, that is:

[0045]

[0046] Assuming the robot is a linear system, the response at a point in the structure is affected by the superposition of all excitation forces, and predicting the structural deformation requires understanding multiple transfer function equations. However, in most tests, only H ij A row or column of (ω) can identify the dynamic parameters of the structure under test. The differential equation of motion of the multi-degree-of-freedom system is:

[0047]

[0048] Written in matrix form as follows:

[0049]

[0050] Now use a set of generalized coordinates η j (t)(j=1,2,…,n) to replace x in the equation i (t)(i=1,2,…,n), the transformation relationship is:

[0051] {x(t)}=[U]{η(t)} (6)

[0052] Therefore, formula (6) can be written as:

[0053]

[0054] Where [U] is the mode shape matrix, is the acceleration matrix in the natural coordinate system, is the velocity matrix in the natural coordinate system, {η(t)} is the displacement matrix in the natural coordinate system, and {F(t)} is the generalized force vector. [U] T [m][U] represents the modal mass matrix M, [U] T [c][U] represents the modal damping matrix, [U] T [k][U] represents the modal stiffness matrix, and the expanded formula (7) is:

[0055]

[0056] In the above formula, in order to clearly illustrate the role of the mode vibration shape, one of the elements on the right side of the equation can be expanded as follows:

[0057]

[0058] Among them, u r，s represents the observed value of the sth point in the rth order mode shape, F j represents the input force vector at point j. The above formula illustrates the influence of the excitation position on the test results. In order to further illustrate the role of the excitation direction in the vibration process, formula (9) is expanded to:

[0059]

[0060] According to the above formula, in the weak excitation direction, for example, {u r} T {f}, u r，sx It represents the component of the observation value of the sth point in the rth order modal vibration shape in the x direction. If its value is close to 0, the excitation force {f} will not produce the effect of exciting the modal vibration shape in this direction. When unidirectional excitation is performed, {f} can be combined with {u r} T Calculating only one row in the matrix can easily cause the mode to not appear in the vibration, resulting in incomplete identification results.

[0061] The method of the present invention can drive the random motion of multiple joints to generate forces in the cross directions, ensuring that there will be {f} in multiple directions. In this case, it has the ability to excite various modal vibration modes of the structure.

[0062] (2) Fully identified modal judgment matrix based on excitation direction

[0063] First, consider the excitation force on a joint. Assume that the input force is d and the components of the input force in the x, y, and z directions are F x , F y , F z The input force matrix composed of all input forces is:

[0064]

[0065] According to formula (11), when the excitation force with the same direction acts on the structure under test, its projection vector is proportional in the matrix. At this time, only one of the multiple force vectors with the same excitation direction has a valid meaning, and F is not a full row rank matrix. Assuming that there are r repeated direction excitation forces acting on the robot structure, then:

[0066] dim(F)=dr (12)

[0067] When dim(F) = 3, the excitation force applied to the robot structure must meet the multi-directional requirements. At this time, the proposed method of driving multiple joints to move randomly in cross directions can ensure that the excitation force is generated in all directions of the modal vibration shape. Therefore, dim(F) = 3 is a sufficient condition for exciting all modal parameters of the robot structure.

[0068] Furthermore, considering the spatial redundancy of industrial robots, during the processing of different postures, the robot's joints may be at different angles and postures for the same end position. In addition, during the robot's motion, the input form of the structure is not as simple as a unidirectional excitation force. Therefore, if only the direction of the excitation force in Equation (12) is considered, the direction of the input excitation force may be satisfied, but when the joint motor drives each joint to twist, the direction of the excitation force becomes collinear, making it impossible to fully identify the structural mode. Therefore, in the process of driving multiple joints to move randomly in cross directions, the excitation torque must also meet certain conditions.

[0069] In the process of industrial robot excitation, the robot's workspace is a Cartesian coordinate system established with the origin of the end effector coordinate system. All links are represented by a set of 6-variable joint vectors. The space composed of joint vectors is called the joint space. The interaction between the robot and the working environment will generate forces and torques at the end effector. The end effector will also generate forces on each joint during the processing process. Assume that the force and torque on the end effector of the robot is F = (F x , F y , F z , M x , M y , M z ) T , the joint vector composed of the driving force and torque of each joint is τ=(τ1,τ2,τ3,τ4,τ5,τ6) T , when the driving torque generated by the rotation of each joint of the robot causes the output of the end, the sum of the work done by each joint is:

[0070] W=τ T δq=τ1δq1+τ2δq2+…+τ6δq6 (13)

[0071] where δq represents the displacement in the joint space.

[0072] The work done by the robot's end effector is:

[0073] W=F T X=F x dx+F y dy+F z dz+M x δ x +M y δ y +M z δ z (14)

[0074] Where X is the displacement generated by the robot end effector. There is a kinematic correlation between the end effector and the robot joints. Therefore, the workspace displacement is assumed to be X = Jδq, where J is the Jacobian matrix. According to the principle of virtual work, the virtual work of the robot end effector is equal to the void created by the joints, that is:

[0075] τ T δq=F T X=F T Jδq (15)

[0076] That is:

[0077] τ=J T F (16)

[0078] The above formula represents the relationship between the external force and joint torque of the robot end effector. When the robot performs self-excitation motion based on the joint motor, the force on the robot system is equal to the driving torque of each joint. Therefore, the projection of the force on the robot on the three axes in any coordinate system can be expressed as:

[0079]

[0080] τ 6x represents the projection of the input torque of the sixth joint in the x-axis direction, τ 6y Represents the projection of the input torque of the sixth joint in the y-axis direction, τ 6z represents the projection of the input torque of the sixth joint in the z-axis direction. The above formula is not a square matrix, and its maximum number of linearly independent groups is the rank of formula (16). Therefore, one end effector position in the workspace corresponds to multiple solutions in the joint space, and the redundancy exhibited by the robot will also change in different processing processes.

[0081] The velocity Jacobian matrix can be written as

[0082]

[0083] in, represents the joint velocity vector, Denotes the operating velocity vector, let q s is a special solution of it, q a represents any vector in the null space of the velocity Jacobian matrix, then:

[0084]

[0085] Where k is an arbitrary constant. The above formula shows that there are countless inverse solutions for the robot structure. Therefore, considering the scope of the excitation direction determination problem for the redundant robot, when the robot is in different posture states, there may be a situation where the tool center point has the same position in the corresponding base coordinates, but its joint torque vector τ = (τ1, τ2, τ3, τ4, τ5, τ6) T There are differences; in formula (17), when the excitation directions are not collinear, the three-axis projections in any Cartesian coordinate system are greater than zero, and X(τ) is full rank; on the contrary, when the excitation directions are consistent, X(τ) is not full rank.

[0086] Therefore, the conditions for determining the sufficiency of the direction of the robot during self-excitation are:

[0087] dim(X(τ))=3 (20)

[0088] When the excitation direction of the torque in the workspace satisfies the above formula, it can be ensured that sufficient excitation is carried out in all directions of the body structure, ensuring that the different modal orders of the robot can be completely and effectively identified.

[0089] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A robot modal identification method based on multi-directional random motion of joints, characterized in that: The steps include: Apply excitation force to the robot to make each joint of the robot perform random acceleration and deceleration motion, and collect vibration signals of each joint of the robot during this process; the excitation force applied satisfies: each excitation force has at least three non-collinear directions, and the excitation torque of each joint is non-collinear during the robot motion process, specifically: dim(F)=dr≥3 Where F is the input force matrix composed of all input excitation forces, dim(·) represents the dimension, d is the number of input excitation forces, and r is the repeated direction excitation force acting on the robot; The vibration signals of each joint of the robot are processed to identify the various modes of the robot.

2. The robot modal identification method based on multi-directional random motion of joints according to claim 1, characterized in that: The excitation force applied satisfies: dim(X(τ))=3 Among them, any spatial rectangular coordinate system is constructed, X(τ) is the projection of the robot force on the three axes, dim(·) represents the dimension; τ ax , τ ay , τ az They represent the projections of the excitation torque of the a-th joint in the x-axis, y-axis, and z-axis directions, respectively. a=1,2…A, where A is the total number of robot joints.

3. The robot modal identification method based on multi-directional random motion of joints according to claim 1, characterized in that: An acceleration sensor is arranged on the robot to obtain vibration signals of each joint of the robot.

4. The robot modal identification method based on multi-directional random motion of joints according to claim 3, characterized in that: The specific arrangement method of the acceleration sensors is as follows: more than four acceleration sensors are arranged on the robot base, each joint and each connecting rod.

5. The robot modal identification method based on multi-directional random motion of joints according to claim 1, characterized in that: The robot's movement is controlled by a CNC program, and the movement intervals are set to a random sequence, so that the robot's joints perform random acceleration and deceleration movements. During the start and stop process, the movement of each joint produces an inertial impact on the body, and the robot produces a corresponding vibration response.

6. The robot modal identification method based on multi-directional random motion of joints according to any one of claims 1 to 5, characterized in that: The vibration signals of each joint of the robot are processed through OMA analysis to identify the various modes of the robot.

7. A robot modal identification system based on multi-directional random motion of joints, characterized in that: It includes a control unit, a collection unit and a processing unit, wherein: The control unit is used to apply an excitation force to the robot so that each joint of the robot performs random acceleration and deceleration motion; the excitation force applied satisfies: each excitation force has at least three non-collinear directions, and the excitation torque of each joint is non-collinear during the movement of the robot, specifically: dim(F)=dr≥3 Where F is the input force matrix composed of all input excitation forces, dim(·) represents the dimension, d is the number of input excitation forces, and r is the repeated direction excitation force acting on the robot; The acquisition unit is used to collect vibration signals of each joint of the robot during movement; The processing unit is used to process the vibration signals of each joint of the robot and identify each order mode of the robot.

8. The robot modal identification system based on multi-directional random motion of joints according to claim 7, characterized in that: The acquisition unit includes a plurality of acceleration sensors arranged on the robot.

9. The robot modal identification system based on multi-directional random motion of joints according to claim 7 or 8, characterized in that: The vibration signals of each joint of the robot are processed through OMA analysis to identify the various modes of the robot.

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