CN116901069B - Robot modal identification method and system based on multi-direction random movement of joints - Google Patents
Robot modal identification method and system based on multi-direction random movement of jointsInfo
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- CN116901069B CN116901069B CN202310901585.3A CN202310901585A CN116901069B CN 116901069 B CN116901069 B CN 116901069B CN 202310901585 A CN202310901585 A CN 202310901585A CN 116901069 B CN116901069 B CN 116901069B
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Program-controlled manipulators
- B25J9/16—Program controls
- B25J9/1656—Program controls characterised by programming, planning systems for manipulators
- B25J9/1664—Program controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Program-controlled manipulators
- B25J9/16—Program controls
- B25J9/1628—Program controls characterised by the control loop
- B25J9/1633—Program controls characterised by the control loop compliant, force, torque control, e.g. combined with position control
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Abstract
The invention belongs to the field of industrial robot dynamics, and particularly discloses a robot modal identification method and system based on multi-directional random movement of joints, wherein the method comprises the following steps of applying exciting force to a robot to enable each joint of the robot to perform random acceleration and deceleration movement, and collecting vibration signals of each joint of the robot in the process; the applied excitation force meets the requirements that each excitation force has at least three non-collinear directions, meanwhile, the excitation moment of each joint is different, the mode shape of each direction of the robot can be completely excited under the excitation of the excitation mode, and then vibration signals of each joint of the robot are processed, so that each order mode of the robot is identified. The invention can realize complete, accurate and effective identification of each-order mode of the robot.
Description
Technical Field
The invention belongs to the field of industrial robot dynamics, and particularly relates to a robot modal identification method and system based on multi-directional random movement of joints.
Background
The serial structure of the industrial robot brings good processability, strong redundancy and high flexibility, plays an increasingly important role in the production and manufacture of large and medium-sized parts in the industries of navigation, automobile assembly and the like, and provides an effective way for the processing of complex curved surfaces due to the high flexibility and multi-pose movement characteristics of the robot. The structure of the industrial robot mainly comprises a base, joints, a big arm, a small arm and an end effector, which are usually a tool spindle system, and because the industrial robot is provided with a plurality of rotary joints, a wider working space can be provided in the milling process of large parts, the working area and the production shape can not be limited during the processing, but the whole rigidity of the industrial robot can be reduced due to the open serial structure, excessive vibration can be generated due to the processing force applied to the end effector in the milling process, the track precision of the part processing process can be reduced, the manufacturing precision of the part processing surface is insufficient, and the finish processing requirement of parts with complex shapes can not be met. Therefore, the dynamic characteristics of the industrial robot in the running state need to be researched, the structural modal parameters are accurately estimated, modal coupling flutter existing in the part machining process is analyzed and restrained, and the method has important significance for reducing the vibration of the robot end effector, improving the surface quality of complex parts such as surface smoothness and reducing the track error of the machining process.
Because the industrial robot is formed by combining a plurality of flexible joint industrial mechanical arms in series, each joint, connecting rod structure and rotor at the front end of the industrial robot affect the processing movement of the end effector, the complex movement characteristics also lead to the complex dynamic characteristics of the end effector, the mixing degree of the end effector is very high, and the vibration source of the end effector is difficult to accurately position, so that the vibration analysis and modal characterization of the industrial robot are difficult. The current method for acquiring the structural modal parameters of the industrial robot is based on a model verification method and an experiment verification method, for a multi-modal industrial robot system, the model verification method can not accurately predict the frequencies of all orders, meanwhile, the multi-joint serial system of the industrial robot can increase the calculation load, the working modal analysis in the experiment verification method can identify the modes of the system only according to response signals, but the requirements of white noise excitation are required to be met, the method is usually carried out under the laboratory condition with good control, and most robots can not meet the laboratory environment condition in the actual processing process, and the modes of the robot body are difficult to fully excite, so that the method is difficult to be widely applied. There is therefore a need for a method to gain insight into the structural dynamics of the robot as a whole.
At present, the influence of the excitation direction is seldom focused on the main vibration mode analysis of the industrial robot, however, when the industrial robot is in different pose states, the overall mass distribution of the robot can be changed, so that the rigidity distribution in different directions is changed, and at the moment, if the direction of the exciting force applied to the robot is unreasonable, the response of a frequency response function is possibly insufficient, so that the identification result of the mode analysis is incomplete, and therefore, the method for accurately and effectively identifying the mode parameters of the robot is particularly important.
Disclosure of Invention
Aiming at the defects or improvement demands of the prior art, the invention provides a robot mode identification method and a system based on multi-directional random movement of joints, which aim to realize complete, accurate and effective identification of each-order mode of a robot through the design of an excitation mode.
In order to achieve the above object, according to an aspect of the present invention, a robot modal identification method based on multi-directional random motion of joints is provided, including the following steps:
applying exciting 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 in the process, wherein the applied exciting force meets the conditions that each exciting force has at least three non-collinear directions and excitation moment of each joint is different in the motion process of the robot;
And processing vibration signals of each joint of the robot so as to identify and obtain each-order mode of the robot. As a further preference, the applied excitation force satisfies:
di m(F)=d-r≥3
Wherein F is an input force matrix formed by all input excitation forces, dim (·) represents dimensions, d is the number of input excitation forces, and r is the excitation force acting on the robot in the repetition direction.
As a further preference, the applied excitation force satisfies:
dim(X(r))=3
The method comprises the steps of optionally constructing a space rectangular coordinate system, wherein X (tau) is the projection of the robot stress on three axes, dim (·) represents dimensions, tau ax、τay、τaz represents the projection of excitation moment of an a-th joint in the directions of an X axis, a y axis and a z axis, and a=1, 2..A, A is the total number of the robot joints.
As a further preferred option, an acceleration sensor is arranged on the robot, by means of which acceleration sensor vibration signals of the individual joints of the robot are acquired.
As a further preferable method, the arrangement method of the acceleration sensors is specifically that more than 4 acceleration sensors are arranged on the robot base, each joint and each connecting rod.
As a further preferable mode, the robot is controlled to move through a numerical control program, the interval time of the movement is set to be a random sequence, each joint of the robot is enabled to perform random acceleration and deceleration movement, in the starting and stopping process, inertial impact on a machine body is generated by each joint movement, and the robot generates corresponding vibration response.
Further preferably, vibration signals of each joint of the robot are processed by OMA analysis, and each order mode of the robot is identified.
According to another aspect of the present invention, there is provided a robot modal identification system based on multi-directional random movement of joints, comprising a control unit, an acquisition unit and a processing unit, wherein:
the control unit is used for applying exciting force to the robot to enable each joint of the robot to perform random acceleration and deceleration movements, wherein the applied exciting force meets the requirements that each exciting force has at least three non-collinear directions, and meanwhile, exciting moment of each joint is different in the movement process of the robot;
the acquisition unit is used for acquiring vibration signals of each joint of the robot in the motion process;
The processing unit is used for processing vibration signals of all joints of the robot and identifying to obtain all orders of modes of the robot.
As a further preferred feature, the acquisition unit comprises a plurality of acceleration sensors arranged on the robot.
Further preferably, vibration signals of each joint of the robot are processed by OMA analysis, and each order mode of the robot is identified.
In general, compared with the prior art, the above technical solution conceived by the present invention mainly has the following technical advantages:
1. According to the method, the excitation mode of the robot is designed, so that the excitation force can be guaranteed to be generated in all directions of the mode shape, the modes of each order of the robot in the processing process can be completely, accurately and effectively identified, and the method is suitable for identifying the mode parameters of various industrial robots in different positions and postures.
2. The invention considers the problem of space redundancy of robots, in particular, in the processing process of different poses, as the robots have a certain extra degree of freedom of movement (namely redundancy), the conditions that the tail ends of the robots are positioned at the same position but the angles and the poses of the joints of the robots are different are existed, and the invention provides the conditions that the excitation moment needs to meet based on the conditions, thereby avoiding the influence of the redundancy of the robots and ensuring that the different modal orders of the robots can be completely and effectively identified.
Drawings
FIG. 1 is a schematic diagram of multi-joint cross direction self-excitation of a six-degree-of-freedom robot according to an embodiment of the present invention;
Fig. 2 (a) and (b) are schematic diagrams of random motion sequence speeds and accelerations of each joint of the robot according to the embodiment of the invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
The embodiment of the invention provides a robot modal identification method based on multi-directional random movement of joints, which fully excites a robot structure from all directions to ensure that different modal orders of a robot can be completely and effectively identified, specifically, taking a six-degree-of-freedom industrial robot as shown in fig. 1 as an example, the embodiment comprises the following steps:
S1, uniformly arranging acceleration sensors on a six-degree-of-freedom industrial robot body, ensuring that the acceleration sensors are arranged on a robot base, each joint and each connecting rod, and preferably, uniformly arranging at least 4 test points on the robot base, 6 joints and 2 connecting rods symmetrically for capturing vibration signals on each joint of the robot.
S2, controlling a plurality of joint components to perform random acceleration and deceleration movements by using a numerical control program, specifically, setting the joint components to be random sequences by changing the interval time of the joint movements, and acquiring vibration signals by using an acceleration sensor, wherein in the process of controlling the start and stop of the robot, the joint movements generate inertial impact on a machine body, and the robot structure generates corresponding vibration response, as shown in fig. 2.
Meanwhile, the condition that the excitation force applied to the robot by each joint in the random motion process is that the excitation force has no less than three non-collinear directions and the excitation moment of each joint is different in line.
S3, processing the collected vibration signals based on an OMA analysis theory to realize full identification of each-order mode of the robot.
The principle and effectiveness of the method of the present invention are further described below.
Meanwhile, the joints are controlled to perform random inertial impact, so that the requirement of excitation in the cross direction (namely, three or more directions which are not collinear) is met, and each part of the robot structure can generate vibration response under the action of inertial force. The structural dynamics of the robot may be considered to be constant during random inertial impaction of the robot. In the milling process of the industrial robot, the industrial robot needs to be in different positions and postures, so that the mass distribution of the robot is changed, the overall rigidity distribution of the robot is changed, and the structure of the industrial robot in the motion process needs to be subjected to modal identification.
(1) Dynamics principle of multidirectional excitation
Based on OMA basic theory, under the action of random inertia impact, the input and output relation of the industrial robot system is that
Y(ω)=X(ω)H(ω) (1)
Where X (ω) is an input response signal to the system in the frequency domain, Y (ω) is a system output response signal in the frequency domain, and H (ω) is a system transfer function matrix in the frequency domain, each element of which represents kinetic characteristic information from an input point to an output point.
Assuming that n measuring points are uniformly arranged on the whole industrial robot body, the relationship between input and output can be written as:
Where X i (ω) is the actual response measured by the ith sensor, F j (ω) is the jth generalized force component, and H ij (ω) is the transfer function between the external force at the ith measurement point and the jth excitation point, i.e.:
Assuming that the robot is a linear system, the response generated at a point in the structure is affected by the superposition of all excitation forces, and predicting structural deformation requires knowledge of multiple transfer function equations. In most tests, however, the kinetic parameters of the structure being tested can be identified by calculating only one row or column of H ij (ω). The motion differential equation of the multi-degree-of-freedom system is as follows:
written in matrix form as follows:
Now replace x i (t) (i=1, 2., n) in the equation with a set of generalized coordinates η j (t) (j=1, 2., n) with the transformation relationship:
{x(t)}=[U]{η(t)} (6)
Thus formula (6) can be written as:
Wherein [ U ] is a mode shape matrix, Is an acceleration matrix under a natural coordinate system,Is a velocity matrix under a natural coordinate system, { η (t) } is a displacement matrix under the natural coordinate system, { F (t) } is a generalized force vector. [ U ] T [ M ] [ U ] represents a modal mass matrix M, [ U ] T [ c ] [ U ] represents a modal damping matrix, [ U ] T [ k ] [ U ] represents a modal stiffness matrix, and expansion (7) is performed to obtain:
in the above equation, to clearly illustrate the effect of the mode shape, one element on the right side of the equation can be expanded to:
wherein u r,s represents the observed value of the s-th point in the mode shape of the r-th order, F j represents the input force vector of the j-th point, the above equation describes the influence of the excitation position on the test result, and in order to further describe the effect of the excitation direction in the vibration process, the equation (9) is extended to:
As can be seen from the above equation, in the weak excitation direction, for example, { u r}T { f }, u r,sx represents the component of the observed value of the s-th point in the r-th order mode shape in the x direction, and if the value is close to 0, the excitation force { f } does not produce the effect of exciting the mode shape in this direction, and when unidirectional excitation is performed, { f } can be calculated with one row in the { u r}T matrix, which is extremely easy to cause that the order mode does not appear in the vibration, causing the problem that the recognition result is incomplete.
The method can drive the random motion of the multiple joints to generate force in the cross direction, ensure that { f } in multiple directions are certain, and has the capability of exciting the mode shape of each stage of the structure under the condition.
(2) Full recognition mode judgment matrix based on excitation direction
Considering the excitation force condition of one joint, the input force quantity is assumed to be d, and the components of the input force in the x, y and z directions are respectively F x,Fy,Fz. The input force matrix composed of all input forces is:
As can be seen from the equation (11), when the exciting force with the same direction acts on the structure to be measured, the projection vectors thereof are in a proportional relationship in the matrix, and only one of the force vectors with the same exciting direction has an effective meaning, and F is not a full-line matrix. Assuming that there are r repetitive direction excitation forces acting on the robot structure, then:
dim(F)=d-r (12)
When dim (F) =3, the excitation force applied to the robot structure must meet the requirement of multiple directions, and the method for driving the multi-joints to randomly move in the cross direction can ensure that the excitation force is generated in all directions of the mode shape, so dim (F) =3 is a sufficient condition for exciting all mode parameters of the robot structure.
Further, considering the problem of spatial redundancy of the industrial robot, the condition that the joints of the robot are at different angles and postures for the same end position may exist in the processing process of different postures, and in addition, the input form of the structure of the robot is not as simple as that of unidirectional excitation force in the moving process of the robot. Therefore, if only the direction of the excitation force in the formula (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 is collinear, so that the problem that the structural mode cannot be completely identified can occur. The excitation moment therefore also needs to meet certain conditions during the random movement of the drive multi-joint in the crossing direction.
In the excitation process of an industrial robot, the working space of the robot is a Cartesian coordinate system established by an origin of a coordinate system of an end effector, all connecting rods are represented by a set of joint vectors of 6 variables, the space formed by the joint vectors is called a joint space, the interaction between the robot and the working environment can generate force and moment at the end effector, and the end effector can also generate force on each joint in the processing process. Assuming that the force and moment applied to the actuator at the end of the robot are f= (F x,Fy,Fz,Mx,My,Mz)T, and the joint vector formed by combining the driving forces and moments of the joints is τ= (τ 1,τ2,τ3,τ4,τ5,τ6)T), when the driving moment generated by the rotation of the joints of the robot causes the output of the end, the sum of the works performed by the joints is:
W=τTδq＝τ1δq1+τ2δq2+…+τ6δq6 (13)
where δq represents the displacement in joint space.
The work done by the robot end effector is:
W＝FTX＝Fxdx+Fydy+Fzdz+Mxδx+Myδy+Mzδz (14)
Wherein X is the displacement generated by the end effector of the robot, and the end effector and each joint of the robot have motion correlation characteristics, so that the working space displacement is assumed to be x=jδq, where J is Jacobian matrix, and according to the virtual work principle, the virtual work of the end effector of the robot is equal to the virtual work done by the joint, namely:
τTδq＝FTX＝FTJδq (15)
That is:
τ=JTF (16)
the relationship between the external force and the joint moment of the robot end effector is shown, and when the robot performs self-excitation motion based on the joint motor, the force of the robot system is equal to the driving moment of each joint, so the projection of the force of the robot on three axes under any coordinate system can be shown as:
τ 6x represents the projection of the input torque of the 6 th joint in the x-axis direction, τ 6y represents the projection of the input torque of the 6 th joint in the y-axis direction, and τ 6z represents the projection of the input torque of the 6 th joint in the z-axis direction. The above formula is not a square matrix, and the maximum linear independent group number is the rank number of formula (16), so that one end effector position in the working space corresponds to solutions in multiple joint spaces, and redundancy represented by the robot also changes in different machining processes.
The velocity Jacobian matrix can be written as
Wherein, the The velocity vector of the joint is represented,Representing the operational speed vector, let q s be a special solution thereof, and q a represent any vector of the speed Jacobian matrix null space, then:
In the formula, k is any constant, and the above formula shows that the inverse solution of the robot structure is numerous, so that when the robot is in different pose states, the positions of the tool center points in the corresponding base coordinates may be the same in consideration of the action range of the excitation direction judging problem on the redundancy robot, but the joint moment vectors tau= (tau 1,τ2,τ3,τ4,τ5,τ6)T are different, in the formula (17), when the excitation directions are not collinear, the triaxial projection in any Cartesian coordinate system is larger than zero, and when the excitation directions are consistent, the X (tau) is not full of rank.
Therefore, the conditions for judging the directional sufficiency of the robot at the time of self-excitation are:
dim(X(τ))=3 (20)
when the excitation direction of the moment in the working space meets the above formula, the robot can be fully excited in all directions of the machine body structure, and different mode orders of the robot can be completely and effectively identified.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (9)
1. The robot modal identification method based on the multi-directional random movement of the joints is characterized by comprising the following steps of:
Applying exciting 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 in the process, wherein the applied exciting force meets the conditions that each exciting force has at least three non-collinear directions and excitation moment of each joint is different in the motion process of the robot, and the method specifically comprises the following steps:
dim(F)=d-r≥3
Wherein F is an input force matrix formed by all input excitation forces, dim (·) represents dimensions, d is the number of input excitation forces, and r is the excitation force acting on the robot in the repetition direction;
And processing vibration signals of each joint of the robot so as to identify and obtain each-order mode of the robot.
2. The robot modal identification method based on multi-directional random motion of joints as claimed in claim 1, wherein the applied excitation force satisfies:
dim(X(τ))=3
The method comprises the steps of optionally constructing a space rectangular coordinate system, wherein X (tau) is the projection of the robot stress on three axes, dim (·) represents dimensions, tau ax、τay、τaz represents the projection of excitation moment of an a-th joint in the directions of an X axis, a y axis and a z axis, and a=1, 2..A, A is the total number of the robot joints.
3. The robot modal identification method based on multi-directional random motion of joints according to claim 1, wherein an acceleration sensor is arranged on the robot, and vibration signals of each joint of the robot are acquired through the acceleration sensor.
4. The method for identifying the robot modal based on the multidirectional random movement of the joints according to claim 3, wherein the arrangement method of the acceleration sensors is characterized in that more than 4 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 movement of joints according to claim 1, wherein the robot is controlled to move through a numerical control program, the interval time of the movement is set to be a random sequence, each joint of the robot is enabled to perform random acceleration and deceleration movement, in the start-stop process, each joint movement generates inertial impact on a machine body, and the robot generates corresponding vibration response.
6. The method for recognizing the modes of the robot based on the multidirectional random movement of the joints according to any one of claims 1 to 5, wherein vibration signals of the joints of the robot are processed through OMA analysis, thereby recognizing the modes of the steps of the robot.
7. The robot modal identification system based on the multi-directional random movement of the joints is characterized by comprising a control unit, an acquisition unit and a processing unit, wherein:
The control unit is used for applying exciting force to the robot to enable each joint of the robot to perform random acceleration and deceleration movement, and the applied exciting force meets the conditions that each exciting force has at least three non-collinear directions, and exciting moment of each joint is different in the moving process of the robot, and specifically comprises the following steps:
dim(F)=d-r≥3
Wherein F is an input force matrix formed by all input excitation forces, dim (·) represents dimensions, d is the number of input excitation forces, and r is the excitation force acting on the robot in the repetition direction;
the acquisition unit is used for acquiring vibration signals of each joint of the robot in the motion process;
The processing unit is used for processing vibration signals of all joints of the robot and identifying to obtain all orders of modes of the robot.
8. The robot-modality identification system based on multi-directional random motion of joints of claim 7, wherein the acquisition unit includes a plurality of acceleration sensors disposed on the robot.
9. The robot modal identification system based on multi-directional random motion of joints as set forth in claim 7 or 8, wherein vibration signals of each joint of the robot are processed by OMA analysis to identify each order of the robot.
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