CN114055477A - Anti-backlash control method for double-motor coaxial drive robot joint - Google Patents

Anti-backlash control method for double-motor coaxial drive robot joint Download PDF

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CN114055477A
CN114055477A CN202111534995.6A CN202111534995A CN114055477A CN 114055477 A CN114055477 A CN 114055477A CN 202111534995 A CN202111534995 A CN 202111534995A CN 114055477 A CN114055477 A CN 114055477A
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motor
double
backlash
control
robot joint
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CN114055477B (en
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房立金
许继谦
赵乾坤
王怀震
高跃
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Northeastern University China
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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
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • 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
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P5/00—Arrangements specially adapted for regulating or controlling the speed or torque of two or more electric motors
    • H02P5/46—Arrangements specially adapted for regulating or controlling the speed or torque of two or more electric motors for speed regulation of two or more dynamo-electric motors in relation to one another
    • H02P5/52—Arrangements specially adapted for regulating or controlling the speed or torque of two or more electric motors for speed regulation of two or more dynamo-electric motors in relation to one another additionally providing control of relative angular displacement
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P5/00—Arrangements specially adapted for regulating or controlling the speed or torque of two or more electric motors
    • H02P5/46—Arrangements specially adapted for regulating or controlling the speed or torque of two or more electric motors for speed regulation of two or more dynamo-electric motors in relation to one another
    • H02P5/52—Arrangements specially adapted for regulating or controlling the speed or torque of two or more electric motors for speed regulation of two or more dynamo-electric motors in relation to one another additionally providing control of relative angular displacement
    • H02P5/56—Speed and position comparison between the motors by electrical means

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  • Engineering & Computer Science (AREA)
  • Automation & Control Theory (AREA)
  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Power Engineering (AREA)
  • Feedback Control In General (AREA)
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Abstract

The invention relates to an anti-backlash control method for a double-motor coaxial drive robot joint, which designs an adaptive position compensator based on an admittance control strategy to ensure that double motors are always in an antagonistic state. The compensator comprises a contact force control mode, an anti-interference mode and switching conditions of the two modes; simplifying the dynamic model according to a double-motor gap elimination principle, and reconstructing the simplified dynamic model into a form of an extended state equation; designing a dual-motor position tracking controller based on an extended state equation; and fusing the self-adaptive position compensator and the double-motor linear active disturbance rejection position tracking controller to obtain the double-motor coaxial drive robot joint backlash elimination control method. On the premise of realizing load tracking, when external torque disturbance exists in a robot joint and machining and assembling errors are considered to cause uneven tooth gap size, the method can still eliminate the nonlinear influence of the tooth gap and reduce the energy consumption of double motors to the maximum extent.

Description

Anti-backlash control method for double-motor coaxial drive robot joint
Technical Field
The invention belongs to the technical field of electromechanical control, and relates to an anti-backlash control method for a double-motor coaxial drive robot joint.
Background
The robot is a complex dynamic system with non-linearity such as backlash and random disturbance. The robot is always in a state of frequent starting, acceleration and deceleration in the reciprocating motion process. The backlash is used as a non-smooth non-linear phenomenon and is coupled with other non-linear phenomena, so that the system buffeting is easily caused, and the abrasion of a transmission system is aggravated. The multi-motor coaxial driving technology is expected to relieve the unfavorable situation of core shortage caused by serious development delay of the Chinese precision speed reducer. The multi-motor drive means that a plurality of power input units jointly drive a load through connection of elastic materials such as rigid gears or belts. More importantly, the influence of transmission clearance and other nonlinear errors of a transmission system can be eliminated through the mutual matching (methods of loading bias torque and the like) of the motors, and the method is not dependent on an abnormally complex backlash model and is called as active backlash elimination control.
Four companies mainly have robots with motors coaxially driven abroad, namely kuka titan series, kawasaki MG15HL series and Fanuc M-2000iA series, and the field of the robots is still blank at home. Chinese patent application No.: 201610022004.9 discloses a dual-motor anti-backlash method, but the control structure is complex, the calculation amount is large, and the adjustment parameters are too much; chinese patent application No.: 201410169816.7, which is incorporated herein by reference, does not account for external torque disturbances and the effects of machining and assembly errors on backlash control.
Disclosure of Invention
In order to solve the technical problems, the invention provides a backlash elimination control method for a double-motor coaxial drive robot joint, which can still eliminate the nonlinear influence of backlash when the robot joint has external torque disturbance and the backlash is not uniform due to machining and assembling errors on the premise of realizing load tracking, and can reduce the energy consumption of double motors to the maximum extent.
The invention provides an anti-backlash control method for a double-motor coaxial driving robot joint, which divides the same double motors into a main motor and a slave motor, and comprises the following steps:
step 1, considering that the gear backlash is not uniform due to external torque disturbance and robot joint machining and assembling errors, and designing a dual-motor backlash elimination principle;
step 2, designing an adaptive position compensator based on an admittance control strategy based on a dual-motor backlash elimination principle;
step 3, establishing a double-motor coaxial driving system dynamic model considering the backlash, simplifying the dynamic model according to a double-motor backlash elimination principle, and reconstructing the simplified dynamic model into a form of an extended state equation according to a linear active disturbance rejection control framework;
step 4, designing a dual-motor position tracking controller by utilizing a linear active disturbance rejection control method based on the formed extended state equation;
and 5, fusing the designed adaptive position compensator with a dual-motor linear active disturbance rejection position tracking controller to obtain the dual-motor coaxial drive robot joint backlash elimination control method.
Further, the dual-motor gap elimination principle in the step 1 specifically includes:
and a driving pinion connected with the double motors is always meshed with the opposite side tooth surface of the load gear. When external disturbance with unknown direction and unknown magnitude exists, the double motors work in a position ring, and the mode is called an anti-interference mode; in the rest case, the master motor is operated in the position loop, and the driving pinion connected with the slave motor should control the contact force with the load gear, which is called the contact force control mode.
Further, the adaptive position compensator based on the admittance control strategy in step 2 includes a contact force control mode, an anti-interference mode and a switching condition of the two modes, and obtains a position specification of the slave motor, specifically:
step 2.1: designing a contact force control mode through an admittance control strategy, wherein the admittance control strategy is defined as follows:
Figure BDA0003412283840000031
wherein parameters B and K are target damping and stiffness, respectively; q. q.seIs the position compensation value, T, of the update of the admittance control strategyhIs a target resisting torque, which is 5% -15% of the rated torque of the selected motor; t iscIs the torque of one of the double motors at the current moment; t ishAnd TcGiven by the following equation:
Figure BDA0003412283840000032
Figure BDA0003412283840000033
in the formula, Tf1And Tf2The torques of the main motor and the slave motor at the current moment are respectively filtered by a second-order Butterworth low-pass filter; t isratFor the rated torque, ω, of the selected motordGiven joint angular velocity, the output based on the admittance control strategy of equations (1) - (2) is:
Figure BDA0003412283840000034
in the formula, tsIs the sampling time;
Figure BDA0003412283840000035
is kthsGiving the position of the robot joint at a moment;
Figure BDA0003412283840000036
is kthsThe current position estimation of the motor 1 at the moment is given by a linear extended state observer of linear active disturbance rejection control;
Figure BDA0003412283840000037
is kthsTime of day admittance control policy updateThe position compensation value of (1);
Figure BDA0003412283840000038
is the (k +1) th tsA position compensation value updated by the time admittance control strategy; if the slave motors work in the mode, the counter torque between the motors is always kept at the target counter torque ThNearby;
step 2.2: the position compensation value under the interference rejection mode is constant and is always equal to the position compensation value at the time of entering the mode;
step 2.3: the state switching conditions for the two modes given based on the dual motor torque information are as follows:
Figure BDA0003412283840000039
in the formula (I), the compound is shown in the specification,
Figure BDA0003412283840000041
is at (k +1) tsThe position compensation of the position compensator is carried out at the moment; t istuAnd TtlUpper and lower torque limits, respectively; 0.1Trat＞Ttl＞0.05Trat，0.3Trat＞Ttu＞0.15Trat；
Obtaining the value of the slave motor at (k +1) tsPosition of time of day is given
Figure BDA0003412283840000042
Figure BDA0003412283840000043
In the formula (I), the compound is shown in the specification,
Figure BDA0003412283840000044
is the (k +1) th tsThe target position of the robot joint at the moment.
Further, the step 3 specifically includes:
step 3.1: the method comprises the following steps of establishing a dynamic model of the double-motor coaxial driving system considering the backlash:
Figure BDA0003412283840000045
in the formula, JLAnd JmRespectively a load end and a motor end rotational inertia; q. q.s1、q2And q isLThe angles of the main motor, the slave motor and the load end respectively; omega1、ω2And ωLThe angular velocities of the main motor, the slave motor and the load end are respectively; bmAnd bLRespectively, the motor end and the load end viscosity coefficients; t is1And T2Control inputs for the master and slave motors respectively; t isdAnd TFUnknown external disturbances and friction, respectively; r is the robot joint reduction ratio; t iss1And Ts2Is the transmitted torque of the equivalent drive shaft of the gear system; t iss1And Ts2Described by a backlash dead zone model:
Figure BDA0003412283840000046
wherein i is 1, 2 represents the number of the two motors, and Δ qi＝qi-qL/r is the difference between the motor position and the load position; q. q.sbIs the transmission system backlash; k is a radical ofsAnd csRespectively equivalent transmission shaft torsional rigidity and damping coefficient;
step 3.2: assuming that the joint of the double-motor coaxial drive robot has no backlash, the dynamic characteristic of a gear system is not considered, and q is1＝q2The dynamic model of the dual-motor coaxial driving system in the formula (7) is simplified into the following form:
Figure BDA0003412283840000047
in the formula, Ta，iIs each motor opposing torque; t isLIs the equivalent load torque;
step 3.3: reconstructing the simplified dynamic model of the double-motor coaxial driving system into a form of an extended state equation according to a linear active disturbance rejection control framework:
Figure BDA0003412283840000051
in the formula, the state variable x is [ q ]1 ω1 f1 q2 ω2 f2]TControl input u ═ T1 T2]TThe system matrix A, the input matrix gamma and the output matrix C are respectively as follows:
Figure BDA0003412283840000052
the total perturbation is defined as:
f＝[f1 f2]T＝[b0(Tu，1-buω1)b0(Tu，2-buw2)]T (12)
in the formula, b0＝1/(JL/r2+2Jm) As total inertia, bu＝bL/r2+2bmThe total viscous friction coefficient; t isu，i＝Tg+(Td+TF)/r+Ta，1+Ta，2，g＝1，2(g≠i)；
In addition, assuming that the total disturbance f is derivable, the total disturbance differential matrix h in the equation is defined as:
Figure BDA0003412283840000053
further, the dual-motor position tracking controller comprises a linear expansion observer and a state feedback control rate, and the step 4 specifically comprises:
step 4.1: designing a linear extended state observer to estimate the angle, the angular velocity and the total disturbance of the double motors based on a reconstructed extended state equation:
Figure BDA0003412283840000054
in the formula (I), the compound is shown in the specification,
Figure BDA0003412283840000055
for an estimate of the state variable x, L is the observer gain matrix:
Figure BDA0003412283840000056
in the formula, beta1，β2，β3Is the observer gain;
step 4.2: designing a state feedback control rate including an estimated total disturbance feedforward based on the obtained estimated value of the state variable:
Figure BDA0003412283840000061
in the formula, kp，kdIs the state feedback control rate gain.
Further, the step 5 specifically includes:
the position of the robot joint is given by qdAnd given angular velocity wdSetting the position and the angular speed of the main motor;
the position of the robot joint is given by qdAnd given angular velocity wdAs an input to an adaptive position compensator;
the output of the adaptive position compensator is given q from the position of the motorsThe position is input of the dual-motor linear active disturbance rejection position tracking controller;
the output of the double-motor linear active disturbance rejection position tracking controller is the actual control input T of the double motors at the next moment1And T2；
Actual control input T of the double motors at the next moment1And T2Will send into the motor servo driver;
finally, the motor servo driver is according to T1And T2And automatically finishing the motor control of the current control period.
Further, the input of the adaptive position compensator also comprises a dual-motor actual control input T1And T2And estimating from the position of the motor
Figure BDA0003412283840000062
Further, the input of the dual-motor linear active disturbance rejection position tracking controller further comprises a position specification q of the main motordActual position q of the double motor1And q is2Actual control input T of double motors1And T2The output also includes an estimate of the state variable x.
Further, the adaptive position compensator for backlash control and the linear active disturbance rejection controller for trajectory tracking are structurally independent of each other.
Further, the anti-backlash control algorithm is deployed in a special dual-motor servo driver or a robot upper controller.
The anti-backlash control method for the double-motor coaxial drive robot joint at least has the following beneficial effects:
1. the double-motor backlash eliminating method does not need to know information such as backlash, external torque disturbance and the like, has good robustness on the non-uniform backlash caused by machining and assembling errors of a mechanical structure, and is small in calculated amount, easy to adjust parameters and quite easy to carry out engineering practice.
2. The method can reduce the precision requirement of the system on other speed reduction and transmission links, make the selection of a domestic speed reducer possible, greatly prolong the service life of the speed reducer, eliminate the occurrence of tooth clearance or tooth clearance increase by an active clearance elimination technology, and reduce the maintenance times in the operation process of the equipment.
3. The technology greatly improves the reusability and product consistency of power units such as servo motors, speed reducers and the like. Therefore, the overall economy and reliability can be ensured.
Drawings
FIG. 1 is a schematic block diagram of a backlash elimination control method for a dual-motor coaxial drive robot joint according to the present invention;
FIG. 2 shows the sinusoidal trajectory response of the robot joint applying three control methods in this embodiment;
FIG. 3 shows sinusoidal track tracking errors for three control methods in this embodiment;
FIG. 4 is a dual-motor torque for the anti-backlash control method for the dual-motor coaxial drive robot joint according to the present invention;
FIG. 5 is a dual motor torque for a conventional dual motor anti-backlash method in an embodiment.
Detailed Description
As shown in the figure, the invention is a functional block diagram of an anti-backlash control method for a double-motor coaxial driving robot joint. The invention discloses a gap elimination control method for a double-motor coaxial driving robot joint, which divides the same double motors into a main motor and a slave motor, and specifically comprises the following steps:
step 1, considering that the gear backlash is not uniform due to external torque disturbance and robot joint machining and assembling errors, designing a dual-motor backlash eliminating principle, specifically comprising the following steps of:
and a driving pinion connected with the double motors is always meshed with the opposite side tooth surface of the load gear. When external disturbance with unknown direction and unknown magnitude exists, the double motors work in a position ring, and the mode is called an anti-interference mode; in the rest case, the master motor is operated in the position loop, and the driving pinion connected with the slave motor should control the contact force with the load gear, which is called the contact force control mode.
Step 2, designing an adaptive position compensator based on an admittance control strategy based on a dual-motor backlash elimination principle;
in specific implementation, the adaptive position compensator based on the admittance control strategy includes a contact force control mode, an anti-interference mode and a conversion condition of the two modes, and obtains a position specification of the motor, specifically:
step 2.1: designing a contact force control mode through an admittance control strategy, wherein the admittance control strategy is defined as follows:
Figure BDA0003412283840000081
wherein parameters B and K are target damping and stiffness, respectively; q. q.seIs the position compensation value, T, of the update of the admittance control strategyhIs a target resisting torque, which is 5% -15% of the rated torque of the selected motor; t iscIs the torque of one of the double motors at the current moment; t ishAnd TcGiven by the following equation:
Figure BDA0003412283840000082
Figure BDA0003412283840000083
in the formula, Tf1And Tf2The torques of the main motor and the slave motor at the current moment are respectively filtered by a second-order Butterworth low-pass filter; t isratFor the rated torque, ω, of the selected motordGiven joint angular velocity, the output based on the admittance control strategy of equations (1) - (2) is:
Figure BDA0003412283840000084
in the formula, tsIs the sampling time;
Figure BDA0003412283840000085
is kthsGiving the position of the robot joint at a moment;
Figure BDA0003412283840000086
is kthsThe current position estimation of the motor 1 at the moment is given by a linear extended state observer of linear active disturbance rejection control;
Figure BDA0003412283840000091
is kthsA position compensation value updated by the time admittance control strategy;
Figure BDA0003412283840000092
is the (k +1) th tsA position compensation value updated by the time admittance control strategy; if the slave motors work in the mode, the counter torque between the motors is always kept at the target counter torque ThNearby;
step 2.2: designing an anti-interference mode: the position compensation value under the interference rejection mode is constant and is always equal to the position compensation value at the time of entering the mode;
step 2.3: the state switching conditions for the two modes given based on the dual motor torque information are as follows:
Figure BDA0003412283840000093
in the formula (I), the compound is shown in the specification,
Figure BDA0003412283840000094
is at (k +1) tsThe position compensation of the position compensator is carried out at the moment; t istuAnd TtlUpper and lower torque limits, respectively; 0.1Trat＞Ttl＞0.05Trat，0.3Trat＞Ttu＞0.15Trat；
Obtaining the value of the slave motor at (k +1) tsPosition of time of day is given
Figure BDA0003412283840000095
Figure BDA0003412283840000096
In the formula (I), the compound is shown in the specification,
Figure BDA0003412283840000097
is the (k +1) th tsThe target position of the robot joint at the moment.
Step 3, establishing a double-motor coaxial driving system dynamic model considering the backlash, simplifying the dynamic model according to a double-motor backlash elimination principle, and reconstructing the simplified dynamic model into a form of an extended state equation according to a linear active disturbance rejection control framework, wherein the form specifically comprises the following steps:
step 3.1: the method comprises the following steps of establishing a dynamic model of the double-motor coaxial driving system considering the backlash:
Figure BDA0003412283840000098
in the formula, JLAnd JmRespectively a load end and a motor end rotational inertia; q. q.s1、q2And q isLThe angles of the main motor, the slave motor and the load end respectively; omega1、ω2And ωLThe angular velocities of the main motor, the slave motor and the load end are respectively; bmAnd bLRespectively, the motor end and the load end viscosity coefficients; t is1And T2Control inputs for the master and slave motors respectively; t isdAnd TFUnknown external disturbances and friction, respectively; r is the robot joint reduction ratio; t iss1And Ts2Is the transmitted torque of the equivalent drive shaft of the gear system; t iss1And Ts2Described by a backlash dead zone model:
Figure BDA0003412283840000101
wherein i is 1, 2 represents the number of the two motors, and Δ qi＝qi-qL/r is the difference between the motor position and the load position; q. q.sbIs the transmission system backlash; k is a radical ofsAnd csRespectively equivalent transmission shaft torsional rigidity and damping coefficient;
step 3.2: if the double motors drive the load according to the double-motor backlash elimination principle, the system is ensured to run without backlash. Based on the fact that the joint of the double-motor coaxial drive robot has no backlashIrrespective of the dynamics of the gear system, and q1＝q2The dynamic model of the dual-motor coaxial driving system in the formula (7) is simplified into the following form:
Figure BDA0003412283840000102
in the formula, Ta，iIs each motor opposing torque; t isLIs the equivalent load torque;
step 3.3: reconstructing the simplified dynamic model of the double-motor coaxial driving system into a form of an extended state equation according to a linear active disturbance rejection control framework:
Figure BDA0003412283840000103
in the formula, the state variable x is [ q ]1 ω1 f1 q2 ω2 f2]TControl input u ═ T1 T2]TThe system matrix A, the input matrix gamma and the output matrix C are respectively as follows:
Figure BDA0003412283840000104
the total perturbation is defined as:
f＝[f1 f2]T＝[b0(Tu，1-buω1)b0(Tu，2-buω2)]T (12)
in the formula, b0＝1/(JL/r2+2Jm) As total inertia, bu＝bL/r2+2bmThe total viscous friction coefficient; t isu,i＝Tg+(Td+TF)/r+Ta,1+Ta,2，g＝1，2(g≠i)；
In addition, assuming that the total disturbance f is derivable, the total disturbance differential matrix h in the equation is defined as:
Figure BDA0003412283840000111
step 4, designing a dual-motor position tracking controller by utilizing a linear active disturbance rejection control method based on the formed extended state equation;
in specific implementation, the dual-motor position tracking controller comprises a linear expansion observer and a state feedback control rate, and the step 4 specifically comprises:
step 4.1: designing a linear extended state observer to estimate the angle, the angular velocity and the total disturbance of the double motors based on a reconstructed extended state equation:
Figure BDA0003412283840000112
in the formula (I), the compound is shown in the specification,
Figure BDA0003412283840000113
for an estimate of the state variable x, L is the observer gain matrix:
Figure BDA0003412283840000114
in the formula, beta1，β2，β3Is the observer gain;
step 4.2: designing a state feedback control rate including an estimated total disturbance feedforward based on the obtained estimated value of the state variable:
Figure BDA0003412283840000115
in the formula, kp，kdIs the state feedback control rate gain.
And 5, fusing the designed self-adaptive position compensator with a dual-motor linear active disturbance rejection position tracking controller to obtain the dual-motor coaxial drive robot joint backlash elimination control method, which specifically comprises the following steps:
the position of the robot joint is given by qdAnd given angular velocity wdSetting the position and the angular speed of the main motor;
the position of the robot joint is given by qdAnd given angular velocity wdAs an input to an adaptive position compensator;
the output of the adaptive position compensator is given q from the position of the motorsThe position is input of the dual-motor linear active disturbance rejection position tracking controller;
the output of the double-motor linear active disturbance rejection position tracking controller is the actual control input T of the double motors at the next moment1And T2；
Actual control input T of the double motors at the next moment1And T2Will send into the motor servo driver;
finally, the motor servo driver is according to T1And T2And automatically finishing the motor control of the current control period.
In specific implementation, the input of the adaptive position compensator also comprises a double-motor actual control input T1And T2And estimating from the position of the motor
Figure BDA0003412283840000122
In specific implementation, the input of the dual-motor linear active disturbance rejection position tracking controller further comprises a position specification q of the main motordActual position q of the double motor1And q is2Actual control input T of double motors1And T2The output also includes an estimate of the state variable x.
In particular, the adaptive position compensator for backlash control and the linear active disturbance rejection controller for trajectory tracking are structurally independent from each other.
In specific implementation, the anti-backlash control algorithm is deployed in a special dual-motor servo driver or a robot upper controller.
The double-motor coaxial drive robot joint selected by the embodiment has rated torque TratTwo identical AC permanent magnet servo motors with the rated rotation speed of 3500rpm of 1.27Nm and two identical planetary reducers with the reduction ratio of 66. The robot joint drags an inertia of 2 kg.m2The load of (a) is oscillated sinusoidally and a pulsed external disturbance is applied for around 5.5 s.
The sinusoidal signals are:
Figure BDA0003412283840000121
to further illustrate the superiority of the proposed anti-backlash control method, the control method of the present invention is compared with the conventional two-motor anti-backlash method based on a fixed-value position compensator and the single-motor driven semi-closed-loop control method. In addition, the position tracking controllers of all the methods adopt a linear active disturbance rejection control design, and the control gains are the same.
The gain of the linear active disturbance rejection controller is: k is a radical ofp＝2500，kd＝100，β1＝720，β2＝172800，β31382400; the value of the position compensation of the constant value position compensator is required to meet the requirement that the resisting torque of the double motors at the zero position of the joint is 0.1Trat(ii) a The parameters of the adaptive position compensator take values as follows: t istu＝0.2Trat，Ttl＝0.2TratK is 0.002, B is 1, and the cut-off frequency of the second order butterworth low pass filter is 100 Hz.
Figure 2 shows the sinusoidal signal tracking response for three control methods. Fig. 3 shows the tracking error of the three control methods. As can be seen from fig. 2 and 3, the backlash elimination control method provided by the present invention is superior to the existing motor backlash elimination method in tracking errors in the stages of initialization, joint commutation, external disturbance, etc. Since the backlash is not treated by the single-motor semi-closed loop control, which is only regarded as a disturbance, the anti-disturbance response is delayed and the impact caused by the backlash is the most severe. And the conventional method for controlling the double-motor backlash eliminates a part of backlash, so that the tracking performance is improved. Fig. 4 shows the dual-motor torque of the anti-backlash method proposed by the present invention. FIG. 5 is a torque for a conventional dual motor anti-backlash control method. Wherein, the motor 1 is a main motor, and the motor 2 is a slave motor. From fig. 4 and 5, it can be concluded that both algorithms respond to external disturbances in time. However, comparing fig. 4 and 5, the conventional dual motor anti-backlash method is much larger in resistance to torque ripple than the method proposed in the present patent due to the influence of machining and assembly errors. This results in insufficient backlash at certain positions where the counteracting torque is too small and unnecessary energy consumption at certain positions where the counteracting torque is too large. In conclusion, the dual-motor anti-backlash method provided by the invention has obvious advantages in tracking, anti-backlash, anti-interference, energy consumption and the like.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the scope of the present invention, which is defined by the appended claims.

Claims (10)

1. An anti-backlash control method for a double-motor coaxial drive robot joint, characterized in that the same double motors are divided into a master motor and a slave motor, the control method comprising the steps of:
step 1, considering that the gear backlash is not uniform due to external torque disturbance and robot joint machining and assembling errors, and designing a dual-motor backlash elimination principle;
step 2, designing an adaptive position compensator based on an admittance control strategy based on a dual-motor backlash elimination principle;
step 3, establishing a double-motor coaxial driving system dynamic model considering the backlash, simplifying the dynamic model according to a double-motor backlash elimination principle, and reconstructing the simplified dynamic model into a form of an extended state equation according to a linear active disturbance rejection control framework;
step 4, designing a dual-motor position tracking controller by utilizing a linear active disturbance rejection control method based on the formed extended state equation;
and 5, fusing the designed adaptive position compensator with a dual-motor linear active disturbance rejection position tracking controller to obtain the dual-motor coaxial drive robot joint backlash elimination control method.
2. The anti-backlash control method for the double-motor coaxial drive robot joint as claimed in claim 1, wherein the principle of the double-motor anti-backlash in the step 1 is specifically as follows:
and a driving pinion connected with the double motors is always meshed with the opposite side tooth surface of the load gear. When external disturbance with unknown direction and unknown magnitude exists, the double motors work in a position ring, and the mode is called an anti-interference mode; in the rest case, the master motor is operated in the position loop, and the driving pinion connected with the slave motor should control the contact force with the load gear, which is called the contact force control mode.
3. The anti-backlash control method for the joint of the two-motor coaxial drive robot according to claim 1, wherein the adaptive position compensator based on the admittance control strategy in the step 2 includes a contact force control mode, an anti-interference mode and a switching condition of the two modes, and is given by the position of the motor, specifically:
step 2.1: designing a contact force control mode through an admittance control strategy, wherein the admittance control strategy is defined as follows:
Figure FDA0003412283830000021
wherein parameters B and K are target damping and stiffness, respectively; q. q.seIs the position compensation value, T, of the update of the admittance control strategyhIs a target resisting torque, which is 5% -15% of the rated torque of the selected motor; t iscIs the torque of one of the double motors at the current moment; t ishAnd TcGiven by the following equation:
Figure FDA0003412283830000022
Figure FDA0003412283830000023
in the formula, Tf1And Tf2The torques of the main motor and the slave motor at the current moment are respectively filtered by a second-order Butterworth low-pass filter; t isratFor the rated torque, ω, of the selected motordGiven joint angular velocity, the output based on the admittance control strategy of equations (1) - (2) is:
Figure FDA0003412283830000024
in the formula, tsIs the sampling time;
Figure FDA0003412283830000025
is kthsGiving the position of the robot joint at a moment;
Figure FDA0003412283830000026
is kthsThe current position estimation of the motor 1 at the moment is given by a linear extended state observer of linear active disturbance rejection control;
Figure FDA0003412283830000027
is kthsA position compensation value updated by the time admittance control strategy;
Figure FDA0003412283830000028
is the (k +1) th tsA position compensation value updated by the time admittance control strategy; if the slave motors work in the mode, the counter torque between the motors is always kept at the target counter torque ThNearby;
step 2.2: the position compensation value under the interference rejection mode is constant and is always equal to the position compensation value at the time of entering the mode;
step 2.3: the state switching conditions for the two modes given based on the dual motor torque information are as follows:
Figure FDA0003412283830000029
in the formula (I), the compound is shown in the specification,
Figure FDA0003412283830000031
is at (k +1) tsThe position compensation of the position compensator is carried out at the moment; t istuAnd TtlUpper and lower torque limits, respectively; 0.1Trat＞Ttl＞0.05Trat，0.3Trat＞Ttu＞0.15Trat；
Obtaining the value of the slave motor at (k +1) tsPosition of time of day is given
Figure FDA0003412283830000032
Figure FDA0003412283830000033
In the formula (I), the compound is shown in the specification,
Figure FDA0003412283830000034
is the (k +1) th tsThe target position of the robot joint at the moment.
4. The anti-backlash control method for the double-motor coaxial drive robot joint as claimed in claim 1, wherein the step 3 is specifically:
step 3.1: the method comprises the following steps of establishing a dynamic model of the double-motor coaxial driving system considering the backlash:
Figure FDA0003412283830000035
in the formula, JLAnd JmRespectively a load end and a motor end rotational inertia; q. q.s1、q2And q isLThe angles of the main motor, the slave motor and the load end respectively; omega1、ω2And ωLThe angular velocities of the main motor, the slave motor and the load end are respectively; bmAnd bLRespectively, the motor end and the load end viscosity coefficients; t is1And T2Control inputs for the master and slave motors respectively; t isdAnd TFUnknown external disturbances and friction, respectively; r is the robot joint reduction ratio; t iss1And Ts2Is the transmitted torque of the equivalent drive shaft of the gear system; t iss1And Ts2Described by a backlash dead zone model:
Figure FDA0003412283830000036
wherein i is 1, 2 represents the number of the two motors, and Δ qi＝qi-qL/r is the difference between the motor position and the load position; q. q.sbIs the transmission system backlash; k is a radical ofsAnd csRespectively equivalent transmission shaft torsional rigidity and damping coefficient;
step 3.2: assuming that the joint of the double-motor coaxial drive robot has no backlash, the dynamic characteristic of a gear system is not considered, and q is1＝q2The dynamic model of the dual-motor coaxial driving system in the formula (7) is simplified into the following form:
Figure FDA0003412283830000041
in the formula, Ta，iIs each motor opposing torque; t isLIs the equivalent load torque;
step 3.3: reconstructing the simplified dynamic model of the double-motor coaxial driving system into a form of an extended state equation according to a linear active disturbance rejection control framework:
Figure FDA0003412283830000042
in the formula, the state variable x is [ q ]1 ω1 f1 q2 ω2 f2]TControl input u ═ T1 T2]TThe system matrix A, the input matrix gamma and the output matrix C are respectively as follows:
Figure FDA0003412283830000043
the total perturbation is defined as:
f＝[f1 f2]T＝[b0(Tu，1-buω1) b0(Tu，2-buω2)]T (12)
in the formula, b0＝1/(JL/r2+2Jm) As total inertia, bu＝bL/r2+2bmThe total viscous friction coefficient; t isu,i＝Tg+(Td+TF)/r+Ta,1+Ta,2，g＝1，2(g≠i)；
In addition, assuming that the total disturbance f is derivable, the total disturbance differential matrix h in the equation is defined as:
Figure FDA0003412283830000044
5. the anti-backlash control method for the double-motor coaxial drive robot joint as claimed in claim 1, wherein the double-motor position tracking controller comprises a linear expansion observer and a state feedback control rate, and the step 4 is specifically:
step 4.1: designing a linear extended state observer to estimate the angle, the angular velocity and the total disturbance of the double motors based on a reconstructed extended state equation:
Figure FDA0003412283830000045
in the formula (I), the compound is shown in the specification,
Figure FDA0003412283830000046
for an estimate of the state variable x, L is the observer gain matrix:
Figure FDA0003412283830000051
in the formula, beta1，β2，β3Is the observer gain;
step 4.2: designing a state feedback control rate including an estimated total disturbance feedforward based on the obtained estimated value of the state variable:
Figure FDA0003412283830000052
in the formula, kp，kdIs the state feedback control rate gain.
6. The anti-backlash control method for the double-motor coaxial drive robot joint as claimed in claim 5, wherein the step 5 is specifically:
the position of the robot joint is given by qdAnd given angular velocity wdSetting the position and the angular speed of the main motor;
the position of the robot joint is given by qdAnd given angular velocity wdAs an input to an adaptive position compensator;
the output of the self-adaptive position compensator is qs given from the position of the motor, namely the output of the double-motor linear active disturbance rejection position tracking controller;
the output of the double-motor linear active disturbance rejection position tracking controller is the actual control input T of the double motors at the next moment1And T2；
Actual control input T of the double motors at the next moment1And T2Will send into the motor servo driver;
finally, the motor is servoDriver according to T1And T2And automatically finishing the motor control of the current control period.
7. The anti-backlash control method for a dual motor coaxial drive robot joint as claimed in claim 6, wherein said adaptive position compensator input further comprises a dual motor actual control input T1And T2And estimating from the position of the motor
Figure FDA0003412283830000053
8. The anti-backlash control method for a two-motor coaxial drive robot joint as claimed in claim 6, wherein the input of said two-motor linear auto-disturbance-rejection position tracking controller further comprises a position specification q of a master motordActual position q of the double motor1And q is2Actual control input T of double motors1And T2The output also includes an estimate of the state variable x.
9. The anti-backlash control method for a dual motor coaxial drive robot joint as claimed in claim 1, wherein said adaptive position compensator for anti-backlash control and said linear auto-disturbance-rejection controller for trajectory tracking are structurally independent from each other.
10. The anti-backlash control method for the double-motor coaxial driving robot joint as claimed in claim 1, wherein the anti-backlash control algorithm is deployed in a proprietary double-motor servo driver or in an upper controller of the robot.
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