CN107398903B - Track control method for industrial mechanical arm execution end - Google Patents

Track control method for industrial mechanical arm execution end Download PDF

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CN107398903B
CN107398903B CN201710787000.4A CN201710787000A CN107398903B CN 107398903 B CN107398903 B CN 107398903B CN 201710787000 A CN201710787000 A CN 201710787000A CN 107398903 B CN107398903 B CN 107398903B
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execution end
constraint condition
mechanical arm
position variable
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CN107398903A (en
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吴占雄
李忠伟
曾毓
杨宇翔
高明煜
何志伟
黄继业
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Hangzhou Dianzi University
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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—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/40—Robotics, robotics mapping to robotics vision
    • G05B2219/40523—Path motion planning, path in space followed by tip of robot

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Abstract

The invention provides aThe method comprises the steps of obtaining mechanical structure parameters of the industrial mechanical arm execution end, determining a Jacobian matrix according to the mechanical structure parameters and initializing a gridding precision epsilon; determining the motion track of the execution end of the industrial mechanical arm according to the processing requirement; calculating reference position variable of k +1 moment of operation space according to Jacobian matrix
Figure DDA0001398319020000011
To manipulate the reference position variable at the time k +1 in space
Figure DDA0001398319020000012
Carrying out constrained quadratic optimization approximation on the objective function for the parameters to obtain the actual operation space position variable X at the moment of k +1k+1And input control quantity u of joint space at time kk(ii) a The execution end of the industrial mechanical arm actually operates a space position variable X according to the k +1 momentk+1And input control quantity u of joint space at time kkPerforming a trajectory movement.

Description

Track control method for industrial mechanical arm execution end
Technical Field
The invention relates to the field of industrial control, in particular to a track control method for an industrial mechanical arm execution end.
Background
The industrial mechanical arm has wide application in welding, painting, stacking and assembling, and becomes an essential intelligent device in industrial production. An industrial robot is a very complex multi-input multi-output nonlinear system with time-varying, strong coupling and nonlinear dynamics characteristics. The control is more complicated due to the influence of uncertain factors such as load change, mechanical disturbance and the like. The rapid development of industry 4.0 requires high quality industrial robot service. The control strategy aiming at stability and high efficiency becomes the difficulty of industrial robot research.
The motion discontinuity and the frequent switching of the control servo may cause the motion track of the execution end of the industrial robot to generate jitter, which may cause mechanical wear of the execution component and failure of the high frequency dynamic response. The control strategy of most industrial robots at present is to carry out PID control on independent joints, and the main defect of the control method is that the feedback gain is a predetermined constant and cannot be changed under the condition of change of a payload, and the dynamic effect of the robot joint is obvious when the robot joint rotates at a high speed.
Disclosure of Invention
The invention provides a control method of a motion track of an execution end of an industrial mechanical arm, which has high control precision and no jitter, and aims to overcome the obvious dynamic effect of the existing industrial robot control strategy.
In order to achieve the above object, the present invention provides a method for controlling a trajectory of an execution end of an industrial robot arm, the method comprising:
s1, obtaining mechanical structure parameters of the industrial mechanical arm execution end, determining a Jacobian matrix according to the mechanical structure parameters and initializing a gridding precision epsilon;
step S2, determining the motion track of the executing end of the industrial mechanical arm according to the processing requirement, wherein the starting point is XstartEnd point is XterminalWhere X ═ { X, y, z, ωx,ωy,ωzThe position variable of k time of the operation space is used as the position variable;
step S3, calculating the reference position variable of the operating space at the time k +1 according to the Jacobian matrix
Figure GDA0002433809690000021
Step S4 to manipulate the reference position variable at time k +1 in space
Figure GDA0002433809690000022
Constrained quadratic optimization approximation of the objective function for the parameters to find the k +1 time realSpace position variable X of inter-operationk+1And input control quantity u of joint space at time kk；
Step S5, the execution end of the industrial mechanical arm actually operates the space position variable X according to the k +1 momentk+1And input control quantity u of joint space at time kkCarrying out track motion;
wherein the objective function is:
Figure GDA0002433809690000023
the constraint conditions include:
the first constraint condition is:
Figure GDA0002433809690000024
the second constraint condition is as follows:
Figure GDA0002433809690000025
the third constraint condition is as follows: q. q.smin≤q≤qmax(ii) a And
the fourth constraint condition is as follows: u. ofmin≤uk≤umax；
Wherein,
Figure GDA0002433809690000026
for the actual operating space position variable X at the time k +1k+1The differential of (a) is determined,
Figure GDA0002433809690000027
reference position variable at time k +1
Figure GDA0002433809690000028
Differentiation of (1); t issIs the state feedback interval time, the input control quantity of the joint space
Figure GDA0002433809690000029
The acceleration of the angular velocity of the joint motor in the execution end is obtained; discrete Jacobian matrix Jk＝J(qk)；
Figure GDA00024338096900000210
The upper limit of the motion speed of the execution end of the industrial mechanical arm is set; q. q.sminThe lower limit value of the motion angle of the joint motor; q. q.smaxThe upper limit value of the motion angle of the joint motor; u. ofminFor actuation of lower limit of end acceleration, umaxIs an execution end acceleration upper limit value.
According to an embodiment of the invention, a binary grid optimization algorithm is adopted to perform optimization approximation on an objective function, and the specific steps are as follows:
step S41, substituting the first constraint condition into the objective function
Figure GDA00024338096900000211
Finally obtain the product ofkIs an objective function of
Figure GDA00024338096900000212
Step S42, under the constraint of the fourth constraint condition, the u is paired at the interval delta ukPerforming equal-interval division;
step S43, calculating
Figure GDA0002433809690000031
Traversing and finding all lattice points which accord with the second constraint condition and the third constraint condition; if the two-dimensional gridding is not found, continuously carrying out two-dimensional gridding again at the interval of delta u/2;
step S44, calculating an objective function psi (u) according to the searched lattice points meeting the second constraint condition and the third constraint conditionk) To obtain the target function psi (u)k) Grid point corresponding to the minimum value of (1)
Figure GDA0002433809690000032
Step S45 to
Figure GDA0002433809690000033
At the center, in the range
Figure GDA0002433809690000034
At an interval of delta u/2lPerforming gridding, wherein l is a half grid number, re-executing the steps S43 to S44 when
Figure GDA0002433809690000035
Will control the quantity
Figure GDA0002433809690000036
As the controlled variable u at the time k +1kAnd (6) outputting.
According to an embodiment of the present invention, the Jacobian matrix is:
Figure GDA0002433809690000037
wherein q ═ { q ═ q1,q2,…,qiThe variable is a joint space angle variable, (x, y, z) is an execution end coordinate, (omega)x,ωy,ωz) Is the actuation end rotation angle.
According to an embodiment of the present invention, the mechanical structure parameters include a degree of freedom of an industrial robot arm execution end, a joint rotation angle, and an arm length.
According to an embodiment of the invention, the motion track of the executing end of the industrial mechanical arm is an arc line or a straight line.
In summary, the trajectory control method for the execution end of the industrial robot provided by the present invention predicts the position of the execution end at the next time by modeling the mechanical structure parameters of the execution end of the industrial robot and combining the motion trajectory determined by the processing requirement, and finally performs constraint optimization of the objective function with the predicted position as a parameter to obtain the input control quantity of the execution end. The control mode takes the mechanical structure parameters of the execution end and the current position as variables to calculate the parameters of the next spatial position in real time, the calculation real-time performance is very strong, the conformity with the actual motion track is very high, the control precision of the mechanical arm is high, the dynamic effect of the execution end of the mechanical arm in the motion process is effectively reduced, and the motion is more stable and efficient.
In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, preferred embodiments accompanied with figures are described in detail below.
Drawings
Fig. 1 is a flowchart illustrating a trajectory control method for an industrial robot actuator according to an embodiment of the present invention.
Detailed Description
As shown in fig. 1, the method for controlling a trajectory of an industrial robot actuator provided in this embodiment starts with step S1, obtaining mechanical structure parameters of the industrial robot actuator, determining a jacobian matrix according to the mechanical structure parameters, and initializing a gridding precision ∈. In this embodiment, the mechanical structure parameters of the industrial robot actuator include the degree of freedom, the joint rotation angle, and the arm length of the industrial robot actuator. However, the present invention is not limited thereto. The Jacobian matrix determined from the mechanical structure parameters is as follows:
Figure GDA0002433809690000041
wherein q ═ { q ═ q1,q2,…,qiThe variable is a joint space angle variable, (x, y, z) is an execution end coordinate, (omega)x,ωy,ωz) Is the actuation end rotation angle.
Step S2, determining the motion track of the executing end of the industrial mechanical arm according to the processing requirement, wherein the starting point is XstartEnd point is XterminalWhere X ═ { X, y, z, ωx,ωy,ωzIs the position variable at the time instant of the operating space k. The motion trail of the execution end of the industrial mechanical arm is an arc line or a straight line, and is determined according to the shape of a product to be processed. In the present embodiment, after the step S1 is completed, the step S2 is executed. However, the present invention is not limited thereto. In other embodiments, step S2 may be performed first, and then step S1 may be performed; or steps S2 and S1 may be performed simultaneously.
Step S3 is executed to calculate the reference position variable at the time of k +1 in the operation space according to the Jacobian matrix
Figure GDA0002433809690000051
Step S4 is performed to manipulate the reference position variable at time k +1 in space
Figure GDA0002433809690000052
Carrying out constrained quadratic optimization approximation on the objective function for the parameters to obtain the actual operation space position variable X at the moment of k +1k+1And input control quantity u of joint space at time kk. In this embodiment, the objective function is:
Figure GDA0002433809690000053
the constraint conditions include:
the first constraint condition is:
Figure GDA0002433809690000054
the second constraint condition is as follows:
Figure GDA0002433809690000055
the third constraint condition is as follows: q. q.smin≤q≤qmax(ii) a And
the fourth constraint condition is as follows: u. ofmin≤uk≤umax；
Wherein,
Figure GDA0002433809690000056
for the actual operating space position variable X at the time k +1k+1The differential of (a) is determined,
Figure GDA0002433809690000057
reference position variable at time k +1
Figure GDA0002433809690000058
Differentiation of (1); t issIs the state feedback interval time, the input control quantity of the joint space
Figure GDA0002433809690000059
The acceleration of the angular velocity of the joint motor in the execution end is obtained; discrete Jacobian matrix Jk＝J(qk)；
Figure GDA00024338096900000510
The upper limit of the motion speed of the execution end of the industrial mechanical arm is set; q. q.sminThe lower limit value of the motion angle of the joint motor; q. q.smaxThe upper limit value of the motion angle of the joint motor; u. ofminFor actuation of lower limit of end acceleration, umaxIs an execution end acceleration upper limit value.
In this embodiment, a binary grid optimization algorithm is used to perform optimization approximation on the objective function, and the specific steps are as follows:
step S41, substituting the first constraint condition into the objective function
Figure GDA00024338096900000511
Finally obtain the product ofkIs an objective function of
Figure GDA00024338096900000512
Step S42, under the constraint of the fourth constraint condition, the u is paired at the interval delta ukAnd performing equal-interval division.
Step S43, calculating
Figure GDA0002433809690000061
And
Figure GDA0002433809690000062
traversing and finding all lattice points which accord with the second constraint condition and the third constraint condition; and if the binary grid is not found, continuously carrying out binary grid again at the interval of delta u/2.
Step S44, calculating an objective function psi (u) according to the searched lattice points meeting the second constraint condition and the third constraint conditionk) To obtain the target function psi (u)k) Grid point corresponding to the minimum value of (1)
Figure GDA0002433809690000063
Step S45 to
Figure GDA0002433809690000064
At the center, in the range
Figure GDA0002433809690000065
At an interval of delta u/2lPerforming gridding, wherein l is a half grid number, re-executing the steps S43 to S44 when
Figure GDA0002433809690000066
Will control the quantity
Figure GDA0002433809690000067
Input control quantity u as time k +1kAnd (6) outputting.
Such as when u is paired at intervals Δ u and Δ u/2 in step S43kWhen the equal-interval division is carried out, the lattice points meeting the conditions are not found, then the division is carried out by delta u/4, at the moment, the division frequency of the binary grid is 3 times, and therefore l is equal to 3 in the step S45.
Then, step S5 is executed, and the industrial robot execution end actually operates the spatial position variable X according to the time k +1k+1And input control quantity u of joint space at time kkPerforming a trajectory movement.
The trajectory control method for the execution end of the industrial mechanical arm provided by the embodiment calculates the input control quantity at the next moment by using the real-time data of the execution end, and the control has good real-time performance and accuracy. Furthermore, the binary grid optimization algorithm is accurate in calculation and small in calculation amount, can effectively avoid excessive CPU and memory resources, is suitable for being realized on an embedded control system, can meet the requirement of the existing industrial mechanical control system, and has good compatibility.
In summary, the trajectory control method for the execution end of the industrial robot provided by the present invention predicts the position of the execution end at the next time by modeling the mechanical structure parameters of the execution end of the industrial robot and combining the motion trajectory determined by the processing requirement, and finally performs constraint optimization of the objective function with the predicted position as a parameter to obtain the input control quantity of the execution end. The control mode takes the mechanical structure parameters of the execution end and the current position as variables to calculate the parameters of the next spatial position in real time, the calculation real-time performance is very strong, the conformity with the actual motion track is very high, the control precision of the mechanical arm is high, the dynamic effect of the execution end of the mechanical arm in the motion process is effectively reduced, and the motion is more stable and efficient.
Although the present invention has been described with reference to the preferred embodiments, it should be understood that various changes and modifications can be made therein by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (5)

1. A track control method for an industrial mechanical arm execution end is characterized by comprising the following steps:
s1, obtaining mechanical structure parameters of the industrial mechanical arm execution end, determining a Jacobian matrix according to the mechanical structure parameters and initializing a gridding precision epsilon;
step S2, determining the motion track of the executing end of the industrial mechanical arm according to the processing requirement, wherein the starting point is XstartEnd point is XterminalWhere X ═ { X, y, z, ωx,ωy,ωzThe position variable of k time of the operation space is used as the position variable;
step S3, calculating the reference position variable of the operating space at the time k +1 according to the Jacobian matrix
Figure FDA0002434219810000011
Step S4 to manipulate the reference position variable at time k +1 in space
Figure FDA0002434219810000012
Carrying out constrained quadratic optimization approximation on the objective function for the parameters to obtain the actual operation space position variable X at the moment of k +1k+1And input control quantity u of joint space at time kk；
Step S5,The execution end of the industrial mechanical arm actually operates a space position variable X according to the k +1 momentk+1And input control quantity u of joint space at time kkCarrying out track motion;
wherein the objective function is:
Figure FDA0002434219810000013
the constraint conditions include:
the first constraint condition is:
Figure FDA0002434219810000014
the second constraint condition is as follows:
Figure FDA0002434219810000015
the third constraint condition is as follows: q. q.smin≤q≤qmax(ii) a And
the fourth constraint condition is as follows: u. ofmin≤uk≤umax；
Wherein,
Figure FDA0002434219810000016
for the actual operating space position variable X at the time k +1k+1The differential of (a) is determined,
Figure FDA0002434219810000017
reference position variable at time k +1
Figure FDA0002434219810000018
Differentiation of (1); t issIs the state feedback interval time, the input control quantity of the joint space
Figure FDA0002434219810000019
Figure FDA00024342198100000110
For performing angular velocity of joint motor in endAcceleration; discrete Jacobian matrix Jk＝J(qk)；
Figure FDA00024342198100000111
The upper limit of the motion speed of the execution end of the industrial mechanical arm is set; q. q.sminThe lower limit value of the motion angle of the joint motor; q. q.smaxThe upper limit value of the motion angle of the joint motor; u. ofminFor actuation of lower limit of end acceleration, umaxIs an execution end acceleration upper limit value.
2. The method for controlling the trajectory of the execution end of the industrial mechanical arm according to claim 1, wherein a binary grid optimization algorithm is used for performing optimization approximation on the objective function, and the method comprises the following specific steps:
step S41, substituting the first constraint condition into the objective function
Figure FDA0002434219810000021
Finally obtain the product ofkIs an objective function of
Figure FDA0002434219810000022
Step S42, under the constraint of the fourth constraint condition, the u is paired at the interval delta ukPerforming equal-interval division;
step S43, calculating
Figure FDA0002434219810000023
And
Figure FDA0002434219810000024
traversing and finding all lattice points which accord with the second constraint condition and the third constraint condition; if the two-dimensional gridding is not found, continuously carrying out two-dimensional gridding again at the interval of delta u/2;
step S44, calculating an objective function psi (u) according to the searched lattice points meeting the second constraint condition and the third constraint conditionk) To obtain the target function psi (u)k) Grid point corresponding to the minimum value of (1)
Figure FDA0002434219810000025
Step S45 to
Figure FDA0002434219810000026
At the center, in the range
Figure FDA0002434219810000027
At an interval of delta u/2lPerforming gridding, wherein l is a half grid number, re-executing the steps S43 to S44 when
Figure FDA0002434219810000028
Will control the quantity
Figure FDA0002434219810000029
As the controlled variable u at the time k +1kAnd (6) outputting.
3. The method as claimed in claim 1, wherein the Jacobian matrix is:
Figure FDA00024342198100000210
wherein q ═ { q ═ q1,q2,…,qiThe variable is a joint space angle variable, (x, y, z) is an execution end coordinate, (omega)x,ωy,ωz) Is the actuation end rotation angle.
4. The method as claimed in claim 1, wherein the mechanical structure parameters include degrees of freedom, joint rotation angles, and arm lengths of the industrial robot.
5. The method as claimed in claim 1, wherein the motion trajectory of the industrial robot is an arc or a straight line.
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CN116141341B (en) * 2023-04-21 2023-08-08 之江实验室 Method for realizing pointing action of five-degree-of-freedom mechanical arm meeting Cartesian space constraint

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