CN112476411A - Delta parallel robot trajectory control method and system - Google Patents

Delta parallel robot trajectory control method and system Download PDF

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CN112476411A
CN112476411A CN202011259482.4A CN202011259482A CN112476411A CN 112476411 A CN112476411 A CN 112476411A CN 202011259482 A CN202011259482 A CN 202011259482A CN 112476411 A CN112476411 A CN 112476411A
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control
linear
parallel robot
angle
active arm
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柳成
孙继元
崔杨
程艳明
苑广军
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Beihua 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
    • B25J9/003—Programme-controlled manipulators having parallel kinematics
    • B25J9/0045—Programme-controlled manipulators having parallel kinematics with kinematics chains having a rotary joint at the base
    • B25J9/0051—Programme-controlled manipulators having parallel kinematics with kinematics chains having a rotary joint at the base with kinematics chains of the type rotary-universal-universal or rotary-spherical-spherical, e.g. Delta type manipulators
    • 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

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Abstract

The invention relates to a Delta parallel robot track control method, which comprises the following steps: acquiring control voltage and output angle of a driving arm motor of the Delta parallel robot at the last moment; designing a linear extended state observer; the input of the linear extended state observer is the control voltage and the output angle of the active arm motor at the last moment, and the output is the calculated angle and the total disturbance of the active arm at the current moment; obtaining a linear control rate of the linear extended state observer according to the target angle and the calculation angle; obtaining the control voltage of the active arm motor at the current moment according to the total disturbance and the linear control rate; and controlling the motion trail of the robot active arm according to the control voltage of the active arm motor at the current moment. The invention designs a linear extended state observer, applies a linear active disturbance rejection control strategy to the Delta parallel robot dynamics control, and improves the robustness of the Delta parallel robot in tracking.

Description

Delta parallel robot trajectory control method and system
Technical Field
The invention relates to the technical field of robot track control, in particular to a Delta parallel robot track control method and system.
Background
The parallel robot has the advantages of high movement speed, light weight of a mechanical mechanism, strong flexibility and the like, and is complementary with the serial robot. At present, the parallel robot is not widely applied to the problems of difficult design of a parallel mechanism, difficult solving of kinematics, complex trajectory planning, difficult control of trajectory tracking and the like.
Three joints of the Delta parallel robot are mutually coupled, a control object has nonlinear characteristics, and the control of the Delta parallel robot is always a difficult point for research. The quality of the control strategy directly influences the quality of track tracking and influences the speed and the precision of the parallel robot. The control of the Delta parallel robot can be divided into two types, one type is kinematic control, the centripetal force, the Coriolis force and various disturbances of the robot are ignored, and the servo motor is controlled to rotate by a corresponding angle directly through planning a given rotating angle by a track. The method is mainly applied to the parallel robot which has lower control requirement and runs at low speed. The other type is dynamic control, and if centripetal force, Coriolis force and various disturbances of the robot are ignored under high-speed motion, the problems of robot precision reduction, machine joint buffeting and the like are caused, so that a dynamic control method is designed, and the method has important significance for improving the dynamic responsiveness of a robot system, controlling various forces and interferences under high-speed motion and realizing the control precision of the robot under the high-speed motion.
The control strategies applied to the parallel robot at present comprise PID control, calculation torque control, sliding mode variable structure control and the like. These methods are highly demanding on the model of the control object and the operating conditions and operating environment are determined. The classical PID control has good robustness and reliability, is easy to realize, and occupies an important position in single-input and single-output application occasions. However, three output joints of the Delta parallel robot are mutually coupled and controlled to have nonlinear characteristics, so that PID control is difficult to ensure high-precision and high-speed trajectory tracking and has poor robustness. Although some improvement methods are also provided, the method depends on models too much, has the defects of complex calculation, difficult realization and incapability of meeting the requirements of high-precision and high-speed control of the high-speed parallel robot.
Disclosure of Invention
The invention aims to provide a Delta parallel robot trajectory control method and a Delta parallel robot trajectory control system to improve robustness during Delta parallel robot trajectory tracking.
In order to achieve the purpose, the invention provides the following scheme:
a Delta parallel robot track control method comprises the following steps:
acquiring control voltage and output angle of a driving arm motor of the Delta parallel robot at the last moment;
designing a linear extended state observer; the input of the linear extended state observer is the control voltage and the output angle of the active arm motor at the previous moment, and the output is the calculated angle and the total disturbance of the active arm at the current moment;
obtaining the linear control rate of the linear extended state observer according to the target angle and the calculated angle;
obtaining the control voltage of the active arm motor at the current moment according to the total disturbance and the linear control rate;
and controlling the motion track of the active arm of the Delta parallel robot according to the control voltage of the active arm motor at the current moment.
Optionally, the linear extended state observer is:
Figure BDA0002774156160000021
wherein e is the deviation between the calculated angle of the master arm at the current moment and the output angle of the master arm at the last moment, and z1Is the calculated angle of the active arm at the current moment, y is the output angle of the active arm at the last moment,
Figure BDA0002774156160000022
is z1Derivative of (a), z2For the differential of the calculated angle of the active arm at the present moment, f1(e)＝z1-y，
Figure BDA0002774156160000023
Is z2Derivative of (a), z3As total disturbance，f2(e)＝z2-y，b0To be an approximate value of the uncertain control gain, u' is the control voltage of the driving arm motor at the last moment,
Figure BDA0002774156160000024
wherein u isoIn order to control the rate of the linear control,
Figure BDA0002774156160000025
is z3Derivative of f3(e)＝z3-y，β1、β2And beta3For the linear extended state observer parameters, [ beta ]1 β2 β3]TL, where T is transpose and L is observer gain.
Optionally, the linear control rate is calculated by the following formula:
Figure BDA0002774156160000026
wherein k ispIs a proportionality coefficient, gamma is a target angle, kdIn order to be the differential coefficient,
Figure BDA0002774156160000031
the derivative of gamma.
Optionally, the calculation formula of the control voltage of the active arm motor at the current moment is as follows:
Figure BDA0002774156160000032
wherein u is the control voltage of the active arm motor at the current moment, and s is the time in the complex frequency domain.
A Delta parallel robot trajectory control system comprising:
the obtaining module is used for obtaining the control voltage and the output angle of the driving arm motor of the Delta parallel robot at the last moment;
the design module is used for designing a linear extended state observer; the input of the linear extended state observer is the control voltage and the output angle of the active arm motor at the previous moment, and the output is the calculated angle and the total disturbance of the active arm at the current moment;
the linear control rate acquisition module is used for obtaining the linear control rate of the linear extended state observer according to the target angle and the calculation angle;
the control voltage acquisition module is used for obtaining the control voltage of the active arm motor at the current moment according to the total disturbance and the linear control rate;
and the track control module is used for controlling the motion track of the active arm of the Delta parallel robot according to the control voltage of the active arm motor at the current moment.
Optionally, the linear extended state observer is:
Figure BDA0002774156160000033
wherein e is the deviation between the calculated angle of the master arm at the current moment and the output angle of the master arm at the last moment, and z1Is the calculated angle of the active arm at the current moment, y is the output angle of the active arm at the last moment,
Figure BDA0002774156160000034
is z1Derivative of (a), z2For the differential of the calculated angle of the active arm at the present moment, f1(e)＝z1-y，
Figure BDA0002774156160000035
Is z2Derivative of (a), z3To total disturbance, f2(e)＝z2-y，b0To be an approximate value of the uncertain control gain, u' is the control voltage of the driving arm motor at the last moment,
Figure BDA0002774156160000041
wherein u isoIn order to control the rate of the linear control,
Figure BDA0002774156160000042
is z3Derivative of f3(e)＝z3-y，β1、β2And beta3For the linear extended state observer parameters, [ beta ]1 β2 β3]TL, where T is transpose and L is observer gain.
Optionally, the linear control rate is calculated by the following formula:
Figure BDA0002774156160000043
wherein k ispIs a proportionality coefficient, gamma is a target angle, kdIn order to be the differential coefficient,
Figure BDA0002774156160000044
the derivative of gamma.
Optionally, the calculation formula of the control voltage of the active arm motor at the current moment is as follows:
Figure BDA0002774156160000045
wherein u is the control voltage of the active arm motor at the current moment, and s is the time in the complex frequency domain.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention discloses a Delta parallel robot track control method, which comprises the following steps: acquiring control voltage and output angle of a driving arm motor of the Delta parallel robot at the last moment; designing a linear extended state observer; the input of the linear extended state observer is the control voltage and the output angle of the active arm motor at the previous moment, and the output is the calculated angle and the total disturbance of the active arm at the current moment; obtaining the linear control rate of the linear extended state observer according to the target angle and the calculated angle; obtaining the control voltage of the active arm motor at the current moment according to the total disturbance and the linear control rate; and controlling the motion track of the active arm of the Delta parallel robot according to the control voltage of the active arm motor at the current moment. The invention designs a linear extended state observer, namely, a linear active disturbance rejection control strategy is applied to the Delta parallel robot dynamics control, so that the robustness of the Delta parallel robot in tracking is improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
FIG. 1 is a flowchart of a Delta parallel robot trajectory control method provided in embodiment 1 of the present invention;
FIG. 2 is a schematic structural diagram of a Delta parallel robot provided in embodiment 1 of the invention;
FIG. 3 is a control structure diagram of a Delta parallel robot provided in embodiment 1 of the present invention;
fig. 4 is a control structure diagram of a Delta parallel robot based on linear active disturbance rejection control according to embodiment 1 of the present invention;
fig. 5 is a structure diagram of a single closed loop provided in embodiment 1 of the present invention;
fig. 6 is a structural diagram of a single-arm controller under the linear active disturbance rejection control strategy provided in embodiment 1 of the present invention;
fig. 7 is a general diagram of a controller structure under the linear active disturbance rejection control strategy provided in embodiment 1 of the present invention;
FIG. 8 is a graph showing the results of experiment one provided in example 1 of the present invention;
FIG. 9 is a diagram of a disturbance input waveform of experiment two according to embodiment 1 of the present invention;
fig. 10 is a comparison graph of a given trajectory and a tracking trajectory of experiment two provided in embodiment 1 of the present invention;
FIG. 11 is a waveform of a disturbance input for experiment three according to example 1 of the present invention;
FIG. 12 is a comparison graph of a given trajectory and a tracking trajectory of experiment three provided in embodiment 1 of the present invention;
fig. 13 is a side view of a comparison graph of a given trajectory and a tracking trajectory of experiment three provided in embodiment 1 of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a robot track control method and a robot track control system so as to improve the robustness of robot track tracking.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Example 1
Fig. 1 is a flowchart of a Delta parallel robot trajectory control method provided in embodiment 1 of the present invention, and as shown in fig. 1, the method includes:
step 101: and acquiring the control voltage and the output angle of the driving arm motor of the Delta parallel robot at the last moment.
Step 102: designing a linear extended state observer; and the input of the linear extended state observer is the control voltage and the output angle of the active arm motor at the previous moment, and the output is the calculated angle and the total disturbance of the active arm at the current moment.
Step 103: and obtaining the linear control rate of the linear extended state observer according to the target angle and the calculated angle.
Step 104: and obtaining the control voltage of the active arm motor at the current moment according to the total disturbance and the linear control rate.
Step 105: and controlling the motion track of the active arm of the Delta parallel robot according to the control voltage of the active arm motor at the current moment.
In this embodiment, the linear extended state observer is:
Figure BDA0002774156160000061
wherein e is the deviation between the calculated angle of the master arm at the current moment and the output angle of the master arm at the last moment, and z1Is the calculated angle of the active arm at the current moment, y is the output angle of the active arm at the last moment,
Figure BDA0002774156160000062
is z1Derivative of (a), z2For the differential of the calculated angle of the active arm at the present moment, f1(e)＝z1-y，
Figure BDA0002774156160000063
Is z2Derivative of (a), z3To total disturbance, f2(e)＝z2-y，b0To be an approximate value of the uncertain control gain, u' is the control voltage of the driving arm motor at the last moment,
Figure BDA0002774156160000064
wherein u isoIn order to control the rate of the linear control,
Figure BDA0002774156160000065
is z3Derivative of f3(e)＝z3-y，β1、β2And beta3For the linear extended state observer parameters, [ beta ]1 β2 β3]TL, where T is transpose and L is observer gain.
In this embodiment, the calculation formula of the linear control rate is:
Figure BDA0002774156160000066
wherein k ispIs a proportionality coefficient, gamma is a target angle, kdIn order to be the differential coefficient,
Figure BDA0002774156160000067
the derivative of gamma.
In this embodiment, the calculation formula of the control voltage of the active arm motor at the current time is as follows:
Figure BDA0002774156160000071
wherein u is the control voltage of the active arm motor at the current moment, and s is the time in the complex frequency domain.
The principle of the invention is illustrated below:
FIG. 2 is a simplified structural diagram of a Delta parallel robot provided in embodiment 1 of the present invention, and as shown in FIG. 2, the Delta parallel robot is composed of a movable platform (i.e. a regular triangle Δ B)1B2B3) Static platform (namely regular triangle delta A)1A2A3) Three driving arms A1C1、A2C2、A3C3And three slave arms C1B1、C2B2、C3B3And (4) forming. A. the1、A2And A3Is a rotary joint, B1、B2、B3、C1、C2And C3Is a ball joint. O is the center of the static platform, P is the center of the movable platform, R is the radius of the circumscribed circle of the static platform, and R is the radius of the circumscribed circle of the movable platform.
The Delta parallel robot has a complicated mechanical structure, three joints are coupled with each other, and fig. 3 is a control structure diagram of the Delta parallel robot provided by the embodiment 1 of the invention. As shown in FIG. 3, G11(S) is the transfer function of the slave arm 1, G12(S) is the coupling transfer function of the slave arm 1 and the slave arm 2, G13(S) is the coupling transfer function of the follower arm 1 and the follower arm 3, G21(S) is the coupling transfer function of the slave arm 2 and the slave arm 1, G22(S) is the transfer function of the slave arm 2, G23For coupling transfer functions of the slave arm 2 and slave arm 3, G31(S) is the coupling transfer function of the slave arm 3 and the slave arm 1, G32(S) isCoupling transfer function, G, of the slave arm 3 and slave arm 233(S) is the slave arm 3 transfer function. X1(S)、X2(S) and X3(S) three inputs to the robot, Y1(S)、Y2(S) and Y3(S) is the output of the robot, when any one input Xi(S) when changed, Yi(S) are all changed, and another 2 inputs X are changedi(S). Therefore, to realize the Delta high-speed parallel robot trajectory tracking control, three joints are required to be input simultaneously and are required to be controlled in a mutual decoupling mode.
The linear active disturbance rejection control strategy (LADRC) adopted by the invention has strong robustness, because many variable factors are omitted in the dynamic modeling, and in the actual control, the variable factors are all controlled. And the linear active disturbance rejection control strategy does not depend on the establishment of a dynamic model, so that the problem of errors of the dynamic model of the parallel robot is solved. The control idea is that each joint is controlled independently, coupling parameters among the joints, omission factors during modeling and disturbance in actual operation are processed into interference in a unified mode to compensate, and finally the control of high-precision trajectory tracking of the Delta parallel robot is achieved. Fig. 4 is a structure diagram of a Delta parallel robot control based on linear active disturbance rejection control according to embodiment 1 of the present invention.
The specific control strategy is as follows:
obtaining a Delta parallel robot kinetic equation:
Figure BDA0002774156160000081
wherein M (theta) is an inertia matrix of the Delta parallel robot, and M (theta) belongs to Rmxn，RmxnThe number of rows is m, the number of columns is n, theta is the calculated angle of the active arm of the Delta parallel robot, and theta belongs to Rk，RkA matrix of real numbers with a number of rows k,
Figure BDA0002774156160000082
is the second derivative of the value of theta,
Figure BDA0002774156160000083
in order to provide the centripetal and coriolis forces,
Figure BDA0002774156160000084
is the first derivative of theta, G (theta) is gravity, G (theta) is belonged to RnAnd τ is the servo input.
Adding friction and turbulence in equation (4) yields:
Figure BDA0002774156160000085
wherein the content of the first and second substances,
Figure BDA0002774156160000086
is friction force, τdIs a perturbation.
Equation (5) further translates to:
Figure BDA0002774156160000087
wherein M ═ M (θ).
The formula further translates to:
Figure BDA0002774156160000088
wherein the content of the first and second substances,
Figure BDA0002774156160000089
a2＝M-1G，
Figure BDA00027741561600000810
the modeling dynamics are known for the object and,
Figure BDA00027741561600000811
modeling the sum of dynamic state and external disturbance for the unknown object, where ω is angular velocity, t is ω θ, b is uncertain control gain, and u is system input, i.e. control voltage of the active arm motor at the current moment, and let
Figure BDA00027741561600000812
x1＝θ，
Figure BDA00027741561600000813
x3F (·), the state equation of the second-order object shown in equation (7) is:
Figure BDA00027741561600000814
where f (-) is a non-linear function in the active disturbance rejection controller, b0Is an approximation of b.
According to the formulae (8) and z1＝θ，
Figure BDA00027741561600000815
z3Design Linear Extended State Observer (LESO):
Figure BDA0002774156160000091
wherein e is the deviation between the calculated angle of the master arm at the current moment and the output angle of the master arm at the previous moment, y is the output angle of the master arm at the previous moment, and f1(e)＝z1-y，f2(e)＝z2-y，b0To be an approximate value of the uncertain control gain, u' is the control voltage of the driving arm motor at the last moment,
Figure BDA0002774156160000092
Figure BDA0002774156160000093
wherein u isoFor linear control rate, f3(e)＝z3-y，β1、β2And beta3For the linear extended state observer parameters, [ beta ]1β2β3]TL, where T is transpose and L is observer gain.
Linear control rate uoThe calculation formula of (2) is as follows:
Figure BDA0002774156160000094
wherein k ispIs a proportionality coefficient, gamma is a target angle, kdIn order to be the differential coefficient,
Figure BDA0002774156160000095
the derivative of gamma.
From formula (9):
Figure BDA0002774156160000096
Figure BDA0002774156160000097
Figure BDA0002774156160000098
wherein u is the control voltage of the active arm motor at the current moment, and s is the time in the complex frequency domain.
Then, according to the formula (10), it can be obtained:
Figure BDA0002774156160000099
will be z derived from formula (9)1、z2And z3Substituting equation (11) yields the final controller:
Figure BDA00027741561600000910
the stability of the present controller was analyzed as follows:
fig. 5 is a structure diagram of a single closed loop provided in embodiment 1 of the present invention, wherein:
G1(s)＝kp+kds (13)
Figure BDA0002774156160000101
Figure BDA0002774156160000102
wherein G is1(s)、G2(s), H(s) are intermediate parameters for simplifying the controller, the closed-loop transfer function G of which can be obtained from FIG. 5b(s) is:
Figure BDA0002774156160000103
theorem 1: when the controlled object model is accurately known, the Delta high-speed parallel robot has stability by using the method. The differential tracker of the linear active disturbance rejection control strategy does not influence the system stability, only influences the system zero point, and reasonably selects (or presets) b0、kp、kd、β1、β2And beta3The system can be stabilized.
The following was demonstrated:
if the controlled object model is precisely known, the transfer function (obtained) is:
Figure BDA0002774156160000104
substituting equations (13), (14), (15), and (17) into equation (16) can result:
Figure BDA0002774156160000105
the closed-loop characteristic equation (i.e., denominator) of equation (18) is:
Figure BDA0002774156160000106
order:
D0＝b0，D1＝b0(β1+kd+a1)，D2＝b0(β2+kp+kdβ1+a1β1+a1kd+a2)
D3＝[b0a1(β2+kp+kdβ1)+b0a2(β1+kd)+k0(kpβ1+kdβ2+β3)]
D4＝[b0a2(β2+kp+kdβ1)+k0(kpβ2+kdβ3)]
D5＝k0kpβ3
the criterion of the Laus can be obtained as follows:
s5 D0 D2 D4
s4 D1 D3 D5
s3 B31 B32
s2 B41 B42
s1 B51
s0 B61
Figure BDA0002774156160000111
B42＝D5，
Figure BDA0002774156160000112
B51＝D5
and (5) finishing the certification. The whole system is proved to be stable under the external interference. The Delta parallel robot has good stability when using the invention.
Theorem 2: when a controlled object model is unknown (when the Delta high-speed parallel robot runs at a high speed, the joints are coupled, and during modeling, the parallel robot cannot omit the action of the rotational inertia and the friction force between the joints, otherwise, the system generates shake in the running process, and the stability of the system and the track tracking performance are finally damaged.
The following was demonstrated:
let the nominal model of the object be GnThen the actual object G(s) G (G) ═ Gn(1+ δ G (s)), wherein δ G is the perturbation of the nominal model and satisfies
Figure BDA0002774156160000113
Wherein
Figure BDA0002774156160000114
There is a bounded uncertainty for the multiplicative norm.
According to closed-loop characteristic equation
Figure BDA0002774156160000115
The following can be obtained:
Figure BDA0002774156160000121
according to a robust stability criterion, for any omega, an inequality of an equation (4-27) is satisfied:
b0+G2(s)Gn(s)H(s)+G2(s)Gn(s)H(s)δG(s)＝0 (21)
Figure BDA0002774156160000122
deriving equation (22) from equations (21) and (4-27) stabilizes the system.
Deducing the expression of delta G(s) according to the formula (20), and substituting the delta G(s)
Figure BDA0002774156160000123
The formula (22) can be obtained. Equation (22) holds for any ω, based on the robust stability criterion. Therefore, it is not only easy to use
Figure BDA0002774156160000124
Is a multiplicative norm bounded uncertainty. Thus indicating that the system is stable.
It can be seen that b is selected (or preset) reasonably0、kp、kd、β1、β2And beta3The system can be stable and has certain robustness.
The stability proves that the linear active disturbance rejection control strategy can realize the dynamic control of the trajectory tracking of the Delta high-speed parallel robot, and the stability of the system is not influenced because the unknown parameters of the object model do not have parameters representing uncertain factors during high-speed operation.
Fig. 6 is a structural diagram of a single-arm controller under the linear active disturbance rejection control strategy provided in embodiment 1 of the present invention, and as can be seen from fig. 6, the linear active disturbance rejection controller only needs to set β1、β2And beta3. The linear extended state observer equation (9) is stable with β1、β2And beta3Are all greater than zero, and beta1β2＞β3。
As can be seen from FIG. 3, X1(s)、X2(s)、X3(s) is the three inputs to the system, Y1(s)、Y2(s)、Y3(s) is the output of the system when any one input Xi(s) change, Yi(s) outputs all change, and another 2 inputs X changei(s). Delta high-speed parallel robots are coupled in quantity with three inputs and three outputs, and formula (23) can be constructed through FIG. 5:
Figure BDA0002774156160000125
Figure BDA0002774156160000126
combining equation (7) yields equation (24):
Figure BDA0002774156160000131
wherein the content of the first and second substances,
Figure BDA0002774156160000132
in order to achieve an equivalent comprehensive disturbance,
Figure BDA0002774156160000133
is the coupling term between the three axes,
Figure BDA0002774156160000134
for the uncertain item in the high-speed movement,
Figure BDA0002774156160000135
is a comprehensive function of various disturbance terms in the field.
Fig. 7 is a general diagram of a controller structure under a linear active disturbance rejection control strategy according to embodiment 1 of the present invention, and is a general diagram of a controller structure under a linear active disturbance rejection control strategy constructed based on fig. 6.
The embodiment also carries out simulation experiment design to further verify the invention:
the nominal parameters in the experiment are shown in table 1.
TABLE 1
Parameter(s) Numerical value
Rated output power of servo motor 750W
Rated speed of servo motor 3000rpm
Rated torque of servo motor 2.39N·m
Rotational inertia of servo motor 1.59*10-4kg·m2
Reduction ratio 20:01
Active arm mass 2.35kg
Mass of driven arm 0.9kg
Driving arm 400mm
Length of driven arm 1000mm
The method comprises the steps of setting circular given tracks, 8-shaped given tracks and the like respectively, firstly verifying the non-disturbance condition and then verifying the disturbance condition for each track, and removing angle limitation, time (speed) limitation and space limitation of the robot in order to better verify the control effect in the control.
Experiment one: circular trajectory input without disturbance
Setting the tracking track of the Delta high-speed parallel robot as a circle with the radius of 250 mm. The given trajectories of the movement of the joints 1, 2 and 3 are respectively:
Figure BDA0002774156160000141
linear extended state observer parameter beta controlled by linear active disturbance rejection control strategy1＝1，β2＝65000，β3A trace tracking control simulation curve is obtained as shown in fig. 8 at 600.
Experiment two: inputting circular track, adding triangular wave disturbance after 5 seconds in simulation
In order to verify the robustness of the controller for the circular track input, when the robot runs for 5s, a triangular wave external interference with the amplitude of 500mm and the period of 0.1Hz is added, and the experimental result is shown in FIG. 10. It can be known that, because the added disturbance amplitude is large, the three-dimensional trajectory graph (fig. 9) fluctuates unobviously after the triangular wave disturbance is added by adopting the linear active disturbance rejection control strategy control. The decoupling control of the three joints can be realized by adopting linear active disturbance rejection, and the method has stronger robustness for triangular wave disturbance.
Experiment three: inputting 8-shaped trace, inputting triangular wave disturbance after 5 seconds
And setting an 8-shaped tracking track of the Delta high-speed parallel robot. Linear extended state observer parameter beta controlled by linear active disturbance rejection control strategy1＝1，β2＝65000，β 3600. The given trajectories of the movement of the joints 1, 2 and 3 are respectively:
Figure BDA0002774156160000142
to verify the robustness of the controller against the figure-8 trajectory input, a triangular wave external disturbance was added when the robot ran to 5s, as shown in fig. 11. The results of the experiment of the external interference of the triangular wave with the input amplitude of 50mm and the period of 0.1Hz are shown in FIGS. 12-13.
By adopting a linear active disturbance rejection control strategy, in fig. 12-13, the fluctuation of the three-dimensional trajectory graph is not obvious, and the controlled 8-shaped trajectory has slight vibration. The decoupling control of the three joints can be realized by adopting a linear active disturbance rejection control strategy, and the method has stronger robustness under the triangular wave disturbance aiming at the 8-shaped input track.
The first experiment to the third experiment are integrated, and the decoupling control of three joints can be realized by verifying a linear active disturbance rejection control strategy through circular track tracking control, circular track tracking anti-interference control and 8-shaped track tracking anti-interference control in the experiments, so that the accurate real-time tracking of a given track can be realized, and the robustness is good.
Example 2
The embodiment provides a Delta parallel robot track control system, which comprises:
and the acquisition module is used for acquiring the control voltage and the output angle of the driving arm motor of the Delta parallel robot at the last moment.
The design module is used for designing a linear extended state observer; and the input of the linear extended state observer is the control voltage and the output angle of the active arm motor at the previous moment, and the output is the calculated angle and the total disturbance of the active arm at the current moment.
And the linear control rate acquisition module is used for obtaining the linear control rate of the linear extended state observer according to the target angle and the calculation angle.
And the control voltage acquisition module is used for acquiring the control voltage of the active arm motor at the current moment according to the total disturbance and the linear control rate.
And the track control module is used for controlling the motion track of the active arm of the Delta parallel robot according to the control voltage of the active arm motor at the current moment.
In this embodiment, the linear extended state observer is:
Figure BDA0002774156160000151
wherein e is the current timeDeviation of the calculated angle of the master arm from the output angle of the master arm at the previous moment, z1Is the calculated angle of the active arm at the current moment, y is the output angle of the active arm at the last moment,
Figure BDA0002774156160000152
is z1Derivative of (a), z2For the differential of the calculated angle of the active arm at the present moment, f1(e)＝z1-y，
Figure BDA0002774156160000153
Is z2Derivative of (a), z3To total disturbance, f2(e)＝z2-y，b0To be an approximate value of the uncertain control gain, u' is the control voltage of the driving arm motor at the last moment,
Figure BDA0002774156160000154
wherein u isoIn order to control the rate of the linear control,
Figure BDA0002774156160000155
is z3Derivative of f3(e)＝z3-y，β1、β2And beta3For the linear extended state observer parameters, [ beta ]1 β2 β3]TL, where T is transpose and L is observer gain.
In this embodiment, the calculation formula of the linear control rate is:
Figure BDA0002774156160000161
wherein k ispIs a proportionality coefficient, gamma is a target angle, kdIn order to be the differential coefficient,
Figure BDA0002774156160000162
the derivative of gamma.
In this embodiment, the calculation formula of the control voltage of the active arm motor at the current time is as follows:
Figure BDA0002774156160000163
wherein u is the control voltage of the active arm motor at the current moment, and s is the time in the complex frequency domain.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
aiming at the movement requirement, nonlinear characteristics and model omission of the Delta high-speed parallel robot, the linear active disturbance rejection control strategy is applied to the dynamics control of the Delta high-speed parallel robot, and through stability analysis, the linear active disturbance rejection control strategy can realize the dynamics control of the trajectory tracking of the Delta high-speed parallel robot, and in high-speed operation, the uncertain factors of the model cannot influence the stability of the system. Namely, the invention has good track tracking effect and strong robustness.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (8)

1. A Delta parallel robot track control method is characterized by comprising the following steps:
acquiring control voltage and output angle of a driving arm motor of the Delta parallel robot at the last moment;
designing a linear extended state observer; the input of the linear extended state observer is the control voltage and the output angle of the active arm motor at the previous moment, and the output is the calculated angle and the total disturbance of the active arm at the current moment;
obtaining the linear control rate of the linear extended state observer according to the target angle and the calculated angle;
obtaining the control voltage of the active arm motor at the current moment according to the total disturbance and the linear control rate;
and controlling the motion track of the active arm of the Delta parallel robot according to the control voltage of the active arm motor at the current moment.
2. The Delta parallel robot trajectory control method of claim 1, wherein the linear extended state observer is:
Figure FDA0002774156150000011
wherein e is the deviation between the calculated angle of the master arm at the current moment and the output angle of the master arm at the last moment, and z1Is the calculated angle of the active arm at the current moment, y is the output angle of the active arm at the last moment,
Figure FDA0002774156150000012
is z1Derivative of (a), z2For the differential of the calculated angle of the active arm at the present moment, f1(e)＝z1-y，
Figure FDA0002774156150000013
Is z2Derivative of (a), z3To total disturbance, f2(e)＝z2-y，b0To be an approximate value of the uncertain control gain, u' is the control voltage of the driving arm motor at the last moment,
Figure FDA0002774156150000014
wherein u isoIn order to control the rate of the linear control,
Figure FDA0002774156150000015
is z3Derivative of f3(e)＝z3-y，β1、β2And beta3For the linear extended state observer parameters, [ beta ]1 β2 β3]TL, where T is transpose and L is observer gain.
3. The Delta parallel robot trajectory control method of claim 2, wherein the linear control rate is calculated as:
Figure FDA0002774156150000021
wherein k ispIs a proportionality coefficient, gamma is a target angle, kdIn order to be the differential coefficient,
Figure FDA0002774156150000022
the derivative of gamma.
4. The Delta parallel robot trajectory control method of claim 3, wherein the calculation formula of the control voltage of the active arm motor at the current time is:
Figure FDA0002774156150000023
wherein u is the control voltage of the active arm motor at the current moment, and s is the time in the complex frequency domain.
5. A Delta parallel robot trajectory control system, comprising:
the obtaining module is used for obtaining the control voltage and the output angle of the driving arm motor of the Delta parallel robot at the last moment;
the design module is used for designing a linear extended state observer; the input of the linear extended state observer is the control voltage and the output angle of the active arm motor at the previous moment, and the output is the calculated angle and the total disturbance of the active arm at the current moment;
the linear control rate acquisition module is used for obtaining the linear control rate of the linear extended state observer according to the target angle and the calculation angle;
the control voltage acquisition module is used for obtaining the control voltage of the active arm motor at the current moment according to the total disturbance and the linear control rate;
and the track control module is used for controlling the motion track of the active arm of the Delta parallel robot according to the control voltage of the active arm motor at the current moment.
6. The Delta parallel robot trajectory control system of claim 5, wherein the linear extended state observer is:
Figure FDA0002774156150000024
wherein e is the deviation between the calculated angle of the master arm at the current moment and the output angle of the master arm at the last moment, and z1Is the calculated angle of the active arm at the current moment, y is the output angle of the active arm at the last moment,
Figure FDA0002774156150000031
is z1Derivative of (a), z2For the differential of the calculated angle of the active arm at the present moment, f1(e)＝z1-y，
Figure FDA0002774156150000032
Is z2Derivative of (a), z3To total disturbance, f2(e)＝z2-y，b0To be an approximate value of the uncertain control gain, u' is the control voltage of the driving arm motor at the last moment,
Figure FDA0002774156150000033
wherein u isoIn order to control the rate of the linear control,
Figure FDA0002774156150000034
is z3Derivative of f3(e)＝z3-y，β1、β2And beta3For the linear extended state observer parameters, [ beta ]1 β2 β3]TL, where T is transpose and L is observer gain.
7. The Delta parallel robot trajectory control system of claim 6, wherein the linear control rate is calculated as:
Figure FDA0002774156150000035
wherein k ispIs a proportionality coefficient, gamma is a target angle, kdIn order to be the differential coefficient,
Figure FDA0002774156150000036
the derivative of gamma.
8. The Delta parallel robot trajectory control system of claim 7, wherein the calculation formula of the control voltage of the active arm motor at the current time is:
Figure FDA0002774156150000037
wherein u is the control voltage of the active arm motor at the current moment, and s is the time in the complex frequency domain.
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