CN114434450A

CN114434450A - Flexible joint jitter suppression method and system based on track optimization control

Info

Publication number: CN114434450A
Application number: CN202210364782.1A
Authority: CN
Inventors: 甘中学; 黄尧; 谢云斌
Original assignee: Zhichang Technology Group Co ltd
Current assignee: Zhichang Technology Group Co ltd
Priority date: 2022-04-08
Filing date: 2022-04-08
Publication date: 2022-05-06
Anticipated expiration: 2042-04-08
Also published as: CN114434450B

Abstract

The invention relates to the technical field of flexible joint jitter suppression, and discloses a flexible joint jitter suppression method and system based on track optimization control, wherein the track optimization-based jitter suppression method provided by the invention belongs to the field of active control; the method is a limited Laplace track optimization method for carrying out track design based on key track information and a flexible joint model, wherein the key track information is the starting position, the target position and the running time from the starting position to the target position, and compared with the traditional input shaping, the method has no problem of running delay; the method carries out the limited Laplace track optimization method based on the initial position, the target position and the running time required by reaching the target position, can realize the optimization of acceleration, improves the residual shake of the flexible joint of the robot, and improves the running stability.

Description

Flexible joint jitter suppression method and system based on track optimization control

Technical Field

The invention relates to the technical field of flexible joint jitter suppression, in particular to a method and a system for suppressing flexible joint jitter based on track optimization control.

Background

The flexibility of the robot is mainly divided into connecting rod flexibility and joint flexibility, and due to the existence of the flexibility, the robot can generate process jitter and residual jitter after stopping in the operation process, and for improving the control performance, the two flexible jitter suppression methods are mainly divided into an active suppression method and a passive suppression method. Because passive restraint optimizes the structure of design flexible robot through selecting various power consumption or energy storage materials for use to reach the purpose that reduces the shake, passive restraint is not considered at this application for the moment.

Currently, most commonly used input shaping methods of ZV and ZVD are adopted. The conventional trajectory shaping method causes a problem of running lag due to lag of the zv (zvd) shaper after processing the trajectory, the lag time depends on the number of pulses for convolution and the pulse application time, the lag is more serious when the number is larger, and the lag is more serious when the pulse application time interval is larger. However, in practical engineering applications, efficient production efficiency is essential, and therefore the plant operation lag caused by conventional input shapers is unacceptable.

The problem of serious tail end shaking is often caused by flexible joints of the serial robot, if each joint is flexible, serious tail end shaking and residual shaking after stopping can be caused by flexible accumulation, and the shaking problem is a method which needs to be solved urgently;

the traditional trajectory shaping method is easy to cause the phenomenon of delay of running time, and especially for point-to-point running, if delay exists in each section of trajectory, efficient operation cannot be realized finally.

Disclosure of Invention

The invention mainly provides a flexible joint jitter suppression method and system based on track optimization control.

In order to solve the technical problems, the invention adopts the following technical scheme:

the flexible joint shake suppression method based on the track optimization control comprises the following steps:

acquiring an original track and motion data of the robot flexible joint motion, extracting key track information based on the original track on a track motion coordinate system, and establishing a flexible joint model based on the motion data;

and obtaining the optimized track of the flexible joint of the robot by utilizing limited Laplace transformation based on the key track information and the flexible joint model.

Further, the obtaining of the optimized track of the flexible joint of the robot by using the limited Laplace transform based on the key track information and the flexible joint model includes:

calculating transformation constraint boundary conditions by combining limited Laplace transformation based on the key track information and the flexible joint model;

and optimizing the track of the flexible joint of the robot based on the transformation constraint boundary conditions.

Further, the acquiring an original track and motion data of the robot flexible joint motion, extracting key track information based on the original track on a track motion coordinate system, and establishing a flexible joint model based on the motion data includes:

acquiring an original track and motion data of the motion of a flexible joint of the robot;

constructing a track motion coordinate system, extracting the initial position, the target position and the running time of the flexible joint of the robot based on the spatial position of the original track distributed on the track motion coordinate system, and acquiring track boundary conditions based on the initial position, the target position and the running time;

and equivalently establishing the flexible joint model for the effect generated by the flexible joint based on the motion data.

Further, calculating transformation constraint boundary conditions based on the key track information and the flexible joint model by combining with finite Laplace transformation, wherein the method comprises the following steps:

decoupling the track boundary condition and the flexible joint model in a simultaneous mode to obtain a state equation under a modal coordinate system;

acquiring a Jordan standard form of the state equation and calculating an initial solution of the Jordan standard form;

and carrying out limited Laplace transformation on the initial solution to obtain a transformation constraint boundary condition.

Further, the trajectory optimization of the flexible joint of the robot based on the transformation constraint boundary conditions comprises:

determining a linear expression of an optimized track based on the transformation constraint boundary condition;

substituting the linear expression into the transformation constraint boundary condition to determine a linear state formula input by a system input curve;

acquiring a final track expression based on the linear state expression and the track boundary condition;

and acquiring an optimized track of the flexible joint of the robot based on the final track expression.

A flexible joint vibration suppression system based on track optimization control comprises:

the data acquisition module is used for acquiring an original track and motion data of the robot flexible joint motion, extracting key track information based on the original track on a track motion coordinate system, and establishing a flexible joint model based on the motion data;

and the track optimization module is used for acquiring the optimized track of the flexible joint of the robot by utilizing limited Laplace transformation based on the key track information and the flexible joint model.

Further, the trajectory optimization module includes:

the transformation constraint boundary condition calculation submodule is used for calculating a transformation constraint boundary condition by combining limited Laplace transformation based on the key track information and the flexible joint model;

and the track optimization submodule is used for optimizing the track of the flexible joint of the robot based on the transformation constraint boundary condition.

Further, the data acquisition module includes:

the data acquisition submodule is used for acquiring the original track and the motion data of the motion of the flexible joint of the robot;

the track boundary condition acquisition submodule is used for constructing a track motion coordinate system, extracting the initial position, the target position and the running time of the flexible joint of the robot based on the spatial position of the original track distributed on the track motion coordinate system, and acquiring a track boundary condition based on the initial position, the target position and the running time;

and the flexible joint model establishing submodule is used for equivalently establishing the flexible joint model for the effect generated by the flexible joint based on the motion data.

Further, the transformation constraint boundary condition calculation submodule includes:

the state equation calculation unit is used for decoupling the track boundary condition and the flexible joint model in a simultaneous mode to obtain a state equation under a modal coordinate system;

the initial solution calculation unit is used for acquiring a Jordan standard form of the state equation and calculating an initial solution of the Jordan standard form;

and the limited Laplace transformation unit is used for carrying out limited Laplace transformation on the initial solution to acquire a transformation constraint boundary condition.

Further, the trajectory optimization submodule includes:

the linear expression computing unit is used for determining a linear expression of the optimized track based on the transformation constraint boundary condition;

the linear state formula computing unit is used for substituting the linear expression into the linear state formula input by the transformation constraint boundary condition determination system input curve;

the final expression computing unit is used for acquiring a final track expression based on the linear state expression and the track boundary condition;

and the track optimization unit is used for acquiring the optimized track of the flexible joint of the robot based on the final track expression.

Has the beneficial effects that: the invention provides a track optimization-based jitter suppression method, which belongs to the field of active control; the method is a limited Laplace track optimization method for carrying out track design based on key track information and by combining a flexible joint model, wherein the key track information is the starting position, the target position and the running time from the starting position to the target position, and compared with the traditional input shaping, the method has no problem of running delay; the method carries out the limited Laplace track optimization method based on the initial position, the target position and the running time required by reaching the target position, can realize the optimization of acceleration, improves the residual shake of the flexible joint of the robot, and improves the running stability.

The invention redesigns the track on the basis of the original track, optimizes the acceleration based on the energy minimum theory, and breaks the problem of operation time delay caused by the traditional track shaping method by the re-optimized track, so that residual vibration and jitter are not generated when the device is operated to a target point and the same jitter is inhibited, and the operation efficiency of the device is improved.

Drawings

FIG. 1 is a flow chart of a method for suppressing flexible joint jitter based on trajectory optimization control;

FIG. 2 is a flowchart of step S2;

FIG. 3 is a flowchart of step S1;

FIG. 4 is a flowchart of step S21;

FIG. 5 is a flowchart of step S22;

FIG. 6 is a block diagram of a flexible joint jitter suppression system based on trajectory optimization control;

FIG. 7 is a simplified model diagram of a flexible joint;

FIG. 8 is a comparison of four different traces;

FIG. 9 is a graphical representation of the actual position of the flexible joint tip;

fig. 10 is a current waveform diagram at the motor end for four different traces.

Detailed Description

The following describes the technical solutions of the method and system for suppressing flexible joint jitter based on trajectory optimization control according to the present invention in further detail with reference to the embodiments.

As shown in fig. 1, the method for suppressing flexible joint shake based on trajectory optimization control of this embodiment includes: S1-S2

S1, acquiring an original track and motion data of the robot flexible joint motion, extracting key track information based on the original track on a track motion coordinate system, and establishing a flexible joint model based on the motion data;

and S2, acquiring the optimized track of the flexible joint of the robot by using limited Laplace transformation based on the key track information and the flexible joint model.

Further, as shown in fig. 2, the step S2 of obtaining an optimized trajectory of a flexible joint of a robot by using a limited Laplace transformation based on the key trajectory information and the flexible joint model includes:

s21, calculating transformation constraint boundary conditions by combining limited Laplace transformation based on the key track information and the flexible joint model;

and S22, optimizing the track of the flexible joint of the robot based on the transformation constraint boundary conditions.

Further, as shown in fig. 3, the acquiring of the original trajectory and the motion data of the robot flexible joint motion in step S1, extracting key trajectory information based on the original trajectory on the trajectory motion coordinate system, and establishing a flexible joint model based on the motion data includes:

s11, acquiring the original track and motion data of the robot flexible joint motion;

s12, constructing a track motion coordinate system, extracting the initial position, the target position and the running time of the flexible joint of the robot based on the spatial position of the original track distributed on the track motion coordinate system, and acquiring track boundary conditions based on the initial position, the target position and the running time;

acquiring an original track, and extracting key track information from the original track; the final control is also reverted to controlling the motor, and thus equals to extracting the trajectory information from the motor side, such as the motor side start position

Motor end target position

Length of operation

。

Wherein it is assumed that the initial position is 0, i.e.

Upon acquisition of the target position

And expected operation time length

Later, if it is desired that the flexible joint not undergo residual wobble at the end of its movement

The position of the motor end can be determined at any time

Position of end of output end

Are considered equal; i.e. assuming no reduction ratio

And the speed of the starting time and the speed of the ending time of the two are both 0; t is a time variable. Namely, obtaining a trajectory boundary condition in the following formula (1):

（1）

in the formula (1), the reaction mixture is,

、

is the position and speed of the motor terminal motor,

、

is the position and velocity of the output end.

And S13, equivalently establishing the flexible joint model according to the motion data and the effect generated by the flexible joint.

In order to derive the flexible joint dynamics model, the following assumptions are further made:

1) in a dynamic model, the effect generated by the flexibility of the flexible joint is equivalent to a linear spring, and the elastic coefficient of the linear spring represents the stiffness coefficient of the flexible joint;

2) the motor rotor is regarded as a whole integrated on the rotating shaft, and the motor rotor cannot bring additional influence on the rotation of the motor when rotating;

3) the electrical dynamics of the flexible joint are faster than the mechanical dynamics, so that the influence of the motor dynamics can be neglected in the flexible joint modeling.

This is a typical spring-mass system with a flexural mode, and the flexural joint model can be described as shown in equation (2):

（2）

wherein, the first and the second end of the pipe are connected with each other,

and

respectively a motor driving moment and a motor rotation angle,

i.e. the position of the motor end, the two are identical.

Is the equivalent moment of the flexible element,

and

the turning angles of the moment applied to the load end of the flexible connecting rod and the actual load end are respectively;

and

respectively the equivalent stiffness coefficient and the equal damping coefficient of the flexible connecting rod;

is the inertia of the motor and is,

is the output end equivalent inertia;

defined as the motor end speed

，

Is defined as the output rotation speed

；

Is an angular acceleration at the motor end,

is the angular acceleration of the output.

Further, as shown in fig. 4, in step S21, the calculating a transformation constraint boundary condition based on the key trajectory information and the flexible joint model and combined with a finite Laplace transformation includes:

s211, decoupling the track boundary condition and the flexible joint model in a simultaneous mode to obtain a state equation under a modal coordinate system;

the track boundary condition formula (1) and the flexible joint model formula (2) are combined to obtain the relation between the input and state variables of the flexible joint and the boundary condition; further decoupling and carrying out equivalent transformation to obtain a state equation under a modal coordinate system:

（3）

wherein the content of the first and second substances,

state variables in the modal coordinate system

Represents the position of the rigid body and represents the position of the rigid body,

which represents the amount of elastic deformation,

is the equivalent mass of the motor end,

is the equivalent mass at the output end of the mass,

is the equivalent mass of the flexible body mode of the system.

Wherein the boundary condition change after decoupling is as shown in equation (4):

（4）

from the formula (4), it is shown that at the end of the operation, the position of the flexible joint is operated to

However, the elastic deformation of the flexibility is 0, and the kinetic energy and the potential energy of the flexibility and the elastic deformation are both 0, namely the kinetic energy and the elastic potential energy are 0.

S212, acquiring a Jordan standard form of the state equation, and calculating an initial solution of the Jordan standard form;

wherein, the Jordan standard type of the state equation is shown as the formula (5):

（5）

is recorded as:

input of

In the above formula (5)

And

is the root of the characteristic equation of the flexible joint model, i.e. a pair of conjugate poles of the system. Variable of state

、

、

、

Redefined separately

. And the initial solution of equation (5) when the system initial condition is 0 can be obtained as equation (6), that is, the solution of the Jordan standard equation:

（6）

wherein the content of the first and second substances,

in order to have a long time period of operation,

。

and S213, performing limited Laplace transformation on the initial solution to obtain a transformation constraint boundary condition.

Wherein, considering the integration time variable t as s, that is, s is a complex frequency domain, the part in parentheses of the initial solution formula (6) can be defined as Laplace transform formula (7) of the finite time variable:

（7）

wherein, define

Is to input

In that

A limited Laplace transform between the two,

is the term that results after the solution.

Further, solving to obtain a transformation constraint boundary condition of the system flexible joint input limited Laplace transformation as shown in the formula (8): the solving method is to carry out mathematical derivation by the left and right side equivalence principle of the formula (6).

（8）

Wherein the content of the first and second substances,

，

，

。

further, as shown in fig. 5, the performing of the trajectory optimization of the flexible joint of the robot based on the transformation constraint boundary conditions in step S22 includes:

s221, determining a linear expression of the optimized track based on the transformation constraint boundary condition;

the method comprises the following steps of (1) determining flexible joint input, namely a linear expression of an optimized track, based on a transformation constraint boundary condition of an equation (8), and adopting an independent basic linear function to form the flexible joint input, wherein the equation (9) is as follows:

（9）

wherein the content of the first and second substances,

in order to constitute a substantially linear function,

in order to be a function coefficient of the image,

the number of basic linear functions forming the input of the system is related to the number of flexible body modes of the system.

S222, substituting the linear expression into the transformation constraint boundary condition to determine a linear state formula input by a system input curve;

wherein, substituting formula (9) into (8) yields:

（10）

wherein, the characteristic equation root

And

consistent with the foregoing;

、

etc. are linear basis functions.

The result obtained after the final linearization is shown in formula (11):

（11）

wherein coefficients corresponding thereto are determined by means of a substantially linear function

Form an input function

。

S223, acquiring a final track expression based on the linear state expression and the track boundary condition;

after the basic linear functions forming the input curve of the system are determined in the linear state mode, the coefficient of each basic linear function can be uniquely determined through the formula (1), and therefore the goal position can be achieved

The target movement time is

The final trajectory expression of the optimized trajectory of the zero residual vibration motion is shown as the formula (12):

（12）

wherein the content of the first and second substances,

，

the first and last two items in (1) are not modifiable, intermediate

Can follow the coefficient

Is increased correspondingly.

Is a function of time t and is also a function of the trajectory after final optimization.

And S224, acquiring an optimized track of the flexible joint of the robot based on the final track expression.

And (3) experimental verification:

four different trajectories are given below, namely a ramp trajectory, a cubic polynomial trajectory, an S-shaped trajectory, and a Laplace optimization trajectory, as shown in fig. 8. As can be seen from the figure, the Laplace optimized track is relatively gentle at the starting time and the stopping time, and indirectly proves that the Laplace carries out re-optimization on the acceleration of the track.

And respectively comparing the position response waveforms of the tail end of the mechanical arm under the four tracks. The obtained result is shown in fig. 9, and it can be seen from the figure that the jitter amplitude of the output end of the flexible joint of the motor under the Laplace track is minimum, and the problem of running time lag does not exist.

The size of the residual jitter after the motor terminal is operated to the target position can also be represented by the current waveform of the motor terminal, as shown in fig. 10, at the starting time, although the jitter of the cubic polynomial locus is minimum, at the time of reaching the target position, the current fluctuation under the Laplace locus is minimum, and the Laplace locus has an obvious suppression effect on the residual jitter.

As an embodiment to which the present application is applied, a home position

Is 0, target position

1050 degrees, run length

Is 0.6ms, and the track boundary condition has the formula (1) of

Time =0.6 ms:

and is

；

And the flexible joint model is established in a SIMULINK simulation environment by means of an SIMMECHANICS tool box, and the motor driving torque, the flexible element equivalent torque, the flexible connecting rod load torque, the flexible connecting rod equivalent stiffness coefficient, the equal damping coefficient and the motor inertia are all obtained by means of SIMMECHANICS tool kit simulation. Using run time

And position

The final optimized trajectory represented is expressed as:

after the track optimization is carried out by the flexible joint jitter suppression method, after the operation time length is 0.6ms along the optimized track, the jitter amplitude value of the track relative to the target position does not exceed +/-0.5 degrees, is reduced by 87.5 percent relative to the jitter amplitude value (+/-4 degrees) of the original slope track, is reduced by 83.3 percent relative to the jitter amplitude value (+/-3 degrees) of the existing cubic polynomial track, and is reduced by 68.2 percent relative to the jitter amplitude value (+/-1 degree) of the existing S-shaped track.

As shown in fig. 6, the flexible joint shake suppression system based on trajectory optimization control according to the present embodiment includes:

the data acquisition module 61 is used for acquiring an original track and motion data of the robot flexible joint motion, extracting key track information based on the original track on a track motion coordinate system, and establishing a flexible joint model based on the motion data;

and a track optimization module 62, configured to obtain an optimized track of the flexible joint of the robot by using a limited Laplace transform based on the key track information and the flexible joint model.

Further, the trajectory optimization module 62 includes:

the transformation constraint boundary condition calculation submodule 621 is used for calculating a transformation constraint boundary condition by combining limited Laplace transformation based on the key track information and the flexible joint model;

and the track optimization submodule 622 is used for optimizing the track of the flexible joint of the robot based on the transformation constraint boundary conditions.

Further, the data acquisition module 61 includes:

the data acquisition sub-module 611 is used for acquiring the original track and the motion data of the motion of the flexible joint of the robot;

the trajectory boundary condition obtaining submodule 612 is configured to construct a trajectory motion coordinate system, extract an initial position, a target position, and an operation time of a flexible joint of the robot based on a spatial position of the original trajectory distributed on the trajectory motion coordinate system, and obtain a trajectory boundary condition based on the initial position, the target position, and the operation time;

and a flexible joint model establishing submodule 613, configured to equivalently establish the flexible joint model according to the motion data and an effect generated by the flexible joint.

Further, the transformation constraint boundary condition calculation sub-module 621 includes:

the state equation calculation unit 6211 is configured to combine the trajectory boundary condition and the flexible joint model for decoupling, and obtain a state equation in a modal coordinate system;

an initial solution calculation unit 6212 configured to obtain a Jordan standard form of the state equation and calculate an initial solution of the Jordan standard form;

and a limited Laplace transformation unit 6213, configured to perform limited Laplace transformation on the initial solution to obtain a transformation constraint boundary condition.

Further, the trajectory optimization submodule 622 includes:

a linear expression calculation unit 6221, configured to determine a linear expression of the optimized trajectory based on the transformation constraint boundary condition;

a linear state formula calculating unit 6222, configured to bring the linear expression into the linear state formula input by the transformation constraint boundary condition determination system;

a final expression calculation unit 6223, configured to obtain a final trajectory expression based on the linear state expression and the trajectory boundary condition;

a trajectory optimization unit 6224, configured to obtain an optimized trajectory of the flexible joint of the robot based on the final trajectory expression.

Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims

1. The flexible joint shake suppression method based on track optimization control is characterized by comprising the following steps:

2. The method of claim 1, wherein the obtaining an optimized trajectory of a flexible joint of a robot based on the key trajectory information and a flexible joint model using a limited Laplace transform comprises:

3. The method of claim 2, wherein the obtaining of the original track and the motion data of the robot flexible joint motion, extracting key track information based on the original track on a track motion coordinate system, and establishing a flexible joint model based on the motion data comprises:

4. The method of claim 3, wherein computing transformation constraint boundary conditions in combination with a finite Laplace transform based on the key trajectory information and a flexible joint model comprises:

5. The method of claim 4, wherein the trajectory optimization of the flexible joints of the robot based on the transformation constraint boundary conditions comprises:

and acquiring the optimized track of the flexible joint of the robot based on the final track expression.

6. A flexible joint vibration suppression system based on track optimization control is characterized by comprising:

7. The system of claim 6, wherein the trajectory optimization module comprises:

8. The system of claim 7, wherein the data acquisition module comprises:

9. The system of claim 8, wherein the transformation constraint boundary condition computation submodule comprises:

and the limited Laplace transformation unit is used for carrying out limited Laplace transformation on the initial solution to obtain a transformation constraint boundary condition.

10. The system of claim 9, wherein the trajectory optimization submodule comprises: