CN105137764B - A kind of parallel robot motion control method with quick response and robust performance - Google Patents
A kind of parallel robot motion control method with quick response and robust performance Download PDFInfo
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Abstract
The invention discloses a kind of parallel robot motion control method with quick response and robust performance, belong to electromechanical control field.The desired displacement that this method obtains each drive shaft according to parallel robot desired trajectory against solution first is instructed；Utilize fractional order PDμController, by selecting preferable cut-off frequency, phase margin and Robustness Design criterion Guarantee control system stable and with capability of fast response.Each drive shaft actual motion state, PD are fed back by grating scale in motion processμController provides motion control amount according to desired displacement instruction with feedback states, is sent to the rotation of motor driver drive motor；The kinetic model of parallel robot is set up simultaneously, calculated according to the model and obtain driving moment instruction, thermal compensation signal is sent to driver by driving moment instruction by dynamics feedforward compensation controller, compensate parallel robot suffered disturbance torque in linkage process, strengthening system robustness, it is ensured that parallel robot completes programming movement.
Description
Technical field
The invention belongs to technical field of electromechanical control, more particularly to parallel robot it is practical during control problem.
Background technology
Compared to traditional serial manipulator, parallel robot has higher movement velocity, acceleration, quality of loads ratio
And more preferable rigidity, it has been widely used in industrial circle at present, typical case's application includes：Lathe, conveyer, quick pick-up machine
Device people, medical robot, large-scale radio telescope supporting construction.With continuing to develop for parallel robot, to its motion index
And precision proposes higher requirement, but during actual use, parallel robot occurs in that kinematic accuracy is low and asked
Topic, even occurs vibration, steady-state error in the acceleration and deceleration stage, the popularization and application of serious restriction parallel robot.
Parallel robot is complex electromechanical systems, because of the design feature of its branched link coupling, and parallel robot is being moved through
Dynamics significantly, particularly can bear larger disturbance torque in the acceleration and deceleration stage, relative to conventional serial machine in journey
People, parallel robot control problem is increasingly complex, therefore the high-speed, high precision moving target of parallel robot is carried to control method
Higher performance requirement is gone out.Parallel robot is in the case of different movement positions, different speed and acceleration, dynamics
Obvious change can all occur for characteristic, under high speed, high acceleration moving, and moving platform and each side chain will produce larger inertia force,
So as to cause overall poor dynamic, control is difficult, is difficult to realize high speed, high acceleration moving, and therefore, it is difficult to ensure motion essence
Degree.To improve parallel robot kinematic accuracy, control method must have fast-response energy, to meet parallel robot at a high speed
Demand for control during motion, should also have robustness with period control method and consider dynamics, it is ensured that parallel robot exists
Bear that there is preferable dynamic property during disturbance torque.Traditional kinematics control method can not provide preferably response and robust
Performance, the influence produced by being moved because of dynamics to parallel robot can not be compensated using such control method, and
Due in the presence of non-linear factors such as friction, gaps, causing, the effect of control is poor, and tracking accuracy is low.
At present, parallel robot generally uses conventional motion control method.Conventional motion control method is by each driving
Motor corner is instructed make the difference with value of feedback after, scaling obtain motion control amount by simple with differential process and sent out
Give driver drives motor movement.Kinematics control method ensures that parallel robot has necessarily by itself response performance
Control accuracy, with it is simple in construction the characteristics of.But traditional kinematics control method response performance is limited, while the control method
Disturbance torque suffered in parallel robot motion process is not accounted for, this disturbance torque is in parallel robot acceleration and deceleration motion
Stage becomes apparent, and traditional kinematics control method robust performance is poor in addition, and this will cause kinematic accuracy to decline.Therefore make
The kinematic accuracy of parallel robot can not be further improved with conventional motion control method.
There is presently no the control method with quick response and robust performance for being generally applicable to parallel robot, for
The characteristics of parallel robot, propose that a kind of control method with quick response and robust performance is answered promoting parallel robot
With significant.
The content of the invention
The purpose of the present invention is to overcome the weak point of prior art, it is proposed that one kind has quick response and robustness
The parallel robot motion control method of energy, is mainly used to the solution existing control method of parallel robot and is deposited in motion process
Response performance it is not enough, robust performance is poor, the low problem of kinematic accuracy.
Technical scheme is as follows：
A kind of parallel robot motion control method with quick response and robust performance, this method includes following step
Suddenly：
1) parallel robot desired trajectory is planned according to duty requirements, each drive shaft sliding block is obtained by Inverse Kinematics Solution
Desired displacement is instructed, and calculates the preferable corner instruction of respective drive motor, and corner instruction will be used to obtain parallel manipulator
The control instruction of each motor of people；
2) using fractional order PDμController is handled the control instruction of motor, and its expression is：
Gp(s)=Kp(1+Kdsμ)
G in formulap(s) it is controller transfer function, KpFor controller proportional gain factor, KdFor controller differential gain system
Number, s is differential operator, and μ is a positive non-integer；Preferable ω is selected firstcWith φM, ω herecFor control system cutoff frequency
Rate, φMFor control system phase margin；To make control system that there is quick response and robust performance, while utilizing three frequency domains
Design constraint：
(a) cut-off frequency design constraint：
|G(jωc)|dB=| Gp(jωc)P(jωc)|dB=0
ω in formulacFor control system cut-off frequency, cut-off frequency directly determines control system responding ability, is managed by designing
The cut-off frequency thought, it is ensured that system has fast-response energy；G (j ω) is open-loop transfer function, | | it is modulus computing, j is single
Position imaginary number, ω is frequency；P (j ω) is control object, including driver and motor model, and its expression is：
A=K in formulatKpiKpvTiiTiv, b=KtKpiKpv(Tii+Tiv), c=KtKpiKpv, A=JLTiiTiv, B=J (R+Kpi)
TiiTivC=JKpiTiv+KtKeTiiTiv+KtKpiKpvTiiTiv, D=KtKpiKpv(Tii+Tiv), E=KtKpiKpv.L it is armature electricity
Sense, R is armature resistance, KtIt is motor electromagnetic moment coefficient, KeIt is back emf coefficient, KpiIt is the ratio of driver current ring
Gain coefficient, KpvIt is the proportional gain factor of drivers velocity ring, TiiIt is the time of integration coefficient of driver current ring, TivIt is
The time of integration coefficient of drivers velocity ring；
(b) phase margin design constraint：
Arg[G(jωc)]=Arg [Gp(jωc)P(jωc)]=φM-π
φ in formulaMFor control system phase margin, phase margin directly determines the stability and robustness of control system；
Arg [] is phase operation, represents to solve the phase of respective transfer functions；
(c) Robustness Design constraints：
D () is derivative operation in formula, by phase margin to frequencies omega derivation；
3) the actual motion state of each drive shaft sliding block is detected and fed back by grating scale, and resolving obtains motor
Actual motion corner state；
4) parallel manipulator human occupant dynamic model is set up, for obtaining corresponding driving moment instruction；
5) dynamics feedforward compensation controller is used, for the disturbance torque during compensation campaign；
6) the preferable corner instruction of each driving spindle motor is made the difference with actual motion corner value and obtains motion control amount, by this
Motion control amount passes through the fractional order PDμController is sent to the motion of motor driver drive motor；Power will be passed through simultaneously
Model calculates obtained driving moment instruction and is compensated controlled quentity controlled variable by dynamics feedforward compensation controller, by this compensation control
Amount processed is sent to the disturbance torque during driver compensation campaign, final control parallel robot movement locus, meets operating mode
Demand.
The present invention the above method in, step 4) described in parallel manipulator human occupant dynamic model use following expression：
τ represents the driving moment of parallel robot each motor in motion process in formula, and M is inertia matrix, and C is section
Family name's power/centrifugal force matrix, G is gravity,For the nominal speed of each drive shaft slide block movement,For each drive shaft slide block movement
Nominal acceleration.
The present invention the above method in, step 5) described in dynamics feedforward controller use following expression：
G in formulaf(s) it is dynamics feedforward compensation controller transmission function, L is armature inductance, KtIt is that motor electromagnetic turns
Moment coefficient, KpiIt is the proportional gain factor of driver current ring, TiiIt is the time of integration coefficient of driver current ring, R is motor
Armature resistance, NcFor a small arithmetic number, s is differential operator.
The present invention combines fractional order PD firstμController and dynamics feedforward compensation controller, and use it for parallel machine
Device people controls, and it has the technique effect of advantages below and high-lighting：By using fractional order PDμController, makes control system
With fast-response energy, while improving its robust performance；Binding kineticses feedforward compensation controller, reduces disturbance torque power
The influence of square, eliminates the error peak and steady-state error during following, and finally realizes high speed, the high accuracy control of parallel robot
System；The control method can be widely used in the motion control of parallel robot.
Brief description of the drawings
The present invention is described in further detail below in conjunction with drawings and the specific embodiments.
Fig. 1 is a kind of canonical parallel robot.
Fig. 2 is a kind of parallel robot motion control method principle frame with quick response and robust performance of the invention
Figure.
Fig. 3 flows for a kind of parallel robot motion control method design with quick response and robust performance of the present invention
Cheng Tu.
Fig. 4 is the α directions motion tracking error under existing control system.
Fig. 5 is the β directions motion tracking error under existing control system.
Fig. 6 is the α directions motion tracking error under control system of the present invention.
Fig. 7 is the β directions motion tracking error under control system of the present invention.
Embodiment
A kind of parallel robot motion control method with quick response and robust performance that Fig. 2 show the present invention is former
Block diagram is managed, a kind of parallel robot motion control method with quick response and robust performance that Fig. 3 show the present invention is set
Count flow chart.First according to parallel robot desired trajectory, the desired displacement of each drive shaft sliding block is obtained by Inverse Kinematics Solution
Instruction, and calculate the corner instruction of respective drive motor；Secondly, the selection preferable cut-off frequency of system and phase margin, profit
Fractional order PD is designed with three Domain Design constraintssμController；Each drive shaft sliding block actual motion is fed back by grating scale
State, and resolve the actual rotational angle state for obtaining motor, it would be desirable to the instruction of motor corner is entered with real electrical machinery motion state
Row, which makes the difference, obtains motion control amount；Set up the kinetic model of parallel robot；Then design motivation feedforward compensation controller；
Motion control amount is passed through into fractional order PDμController feeds motor driver, drive motor motion；Utilize kinetic model simultaneously
Calculating obtains driving moment and is compensated signal by dynamics feedforward compensation controller, and this thermal compensation signal is also fed into driving
Device, for compensating the disturbance torque in parallel robot linkage process, it is ensured that kinematic accuracy.Specific method step is as follows：
1) parallel robot desired trajectory, is planned according to duty requirements, each drive shaft sliding block is obtained by Inverse Kinematics Solution
Desired displacement instruction xd, xdIt can be exchanged into the preferable corner instruction θ of each driving spindle motord, specific formula is as follows：
P in formulahFor guide screw lead, θd(unit rad) refers to the preferable corner that spindle motor is respectively driven as parallel robot
Order, while angular speed can be expected in the hope of motor(unit rad/s) expects angular acceleration (unit rad/s with motor2)；
2), design fractional order PDμController, its expression is：
Gp(s)=Kp(1+Kdsμ) (2)
G in formulap(s) it is controller transfer function, KpFor controller proportional gain factor, KdFor controller differential gain system
Number, s is differential operator, and μ is a positive non-integer.Preferable ω is selected firstcWith φM, ω herecFor control system cutoff frequency
Rate, φMFor control system phase margin.It is simultaneously as follows using three Domain Design constraintss：
(a) cut-off frequency design constraint：
|G(jωc)|dB=| Gp(jωc)P(jωc)|dB=0 (3)
ω in formulacFor control system cut-off frequency, G (j ω) is open-loop transfer function, | | it is modulus computing, j is that unit is empty
Number, ω is frequency；P (j ω) is control object, including driver and motor model, and its expression is：
A=K in formulatKpiKpvTiiTiv, b=KtKpiKpv(Tii+Tiv), c=KtKpiKpv, A=JLTiiTiv, B=J (R+Kpi)
TiiTivC=JKpiTiv+KtKeTiiTiv+KtKpiKpvTiiTiv, D=KtKpiKpv(Tii+Tiv), E=KtKpiKpv.L it is armature electricity
Sense, R is armature resistance, KtIt is motor electromagnetic moment coefficient, KeIt is back emf coefficient, KpiIt is the ratio of driver current ring
Gain coefficient, KpvIt is the proportional gain factor of drivers velocity ring, TiiIt is the time of integration coefficient of driver current ring, TivIt is
The time of integration coefficient of drivers velocity ring；
(b) phase margin design constraint：
Arg[G(jωc)]=Arg [Gp(jωc)P(jωc)]=φM-π (5)
φ in formulaMFor control system phase margin；Arg [] is phase operation, represents to solve the phase of respective transfer functions；
(c) Robustness Design constraints：
D () is derivative operation in formula；
Equation below group can be obtained according to (3)-(6)：
tan-1(B1/A1)+Arg(P(jωc))+π-φM=0 (8)
In formula, A1=1+KdωμCos (π μ/2), B1=KdωμSin (π μ/2),Each ginseng
Number physical significance is as previously described.By solving this Nonlinear System of Equations, you can obtain one group of [Kp Kdμ] meet design condition；
3) the actual motion state of each drive shaft, is detected and fed back by grating scale, and it is real that feedback obtains each drive shaft sliding block
Border displacement xc, and clearing obtain driving spindle motor actual rotational angle θc, solution formula is as follows：
P in formulahFor guide screw lead, and then angular errors can be obtained：
E=θd-θc (11)
The angular errors will enter fractional order PD as controlled quentity controlled variableμController；
4) parallel manipulator human occupant dynamic model, is set up as follows：
τ represents the driving moment of parallel robot each motor in motion process in formula, and M is inertia matrix, and C is section
Family name's power/centrifugal force matrix, G is gravity,For the nominal movement velocity of drive shaft sliding block,For the name fortune of drive shaft sliding block
Dynamic acceleration；
5), design motivation feedforward compensation controller is used for the influence for eliminating disturbance torque, dynamics feedforward controller
Input instruction is the result of calculation τ of kinetic model in 4, and τ is by the corresponding compensation letter of dynamics feedforward compensation controller generation
Number, for compensating the disturbance torque τ that parallel robot is subject in motion processδ, design principle is as follows：
U=τ Gf(s)Gk(s)+τδ (12)
U is the output of the system under thermal compensation signal and disturbance torque collective effect, G in formulaf(s) it is dynamics feedforward compensation
Controller, Gk(s) it is the transmission function of compensation point to output, its expression formula is as follows：
τGf(s)Gk(s) it is thermal compensation signal, τ=τ is thought in the design processδ, make u=0, you can allow thermal compensation signal to disappear
Except the influence of disturbance torque, it can be obtained by formula (12), (13)：
L is armature inductance, K in formulatIt is motor electromagnetic moment coefficient, KpiIt is the proportional gain system of driver current ring
Number, TiiIt is the time of integration coefficient of driver current ring, R is armature resistance, NcFor a small arithmetic number；
6) foregoing obtained motion control amount e, is passed through into designed fractional order PDμController is sent to driver drives electricity
Machine is moved；Obtained thermal compensation signal τ G will be calculated simultaneouslyf(s)Gk(s) it is sent to driver and compensates parallel robot in motion process
In suffered disturbance torque, it is ensured that kinematic accuracy, final control parallel robot movement locus, meet duty requirements.
Embodiment
A kind of parallel robot motion control method with quick response and robust performance proposed is applied to one
Platform space two-freedom parallel robot, the parallel robot are as shown in figure 1, the robot is slided by the first sliding block 1 and second
The motion of block 2 drives the motion of terminal moving platform 3, and the first sliding block 1 is driven with the second sliding block 2 by corresponding motor, moving platform 3 and the
It is attached, is attached between the sliding block 2 of moving platform 3 and second by the second rod member 5 by the first rod member 4 between one sliding block 1, moves flat
Also it is attached between platform 3 and silent flatform 6 by the 3rd rod member 7.The present embodiment control method implementation steps are as follows：1), each driving
The desired displacement of axle is solved：
The parallel robot working space that the present embodiment is controlled is α ∈ (- 45 ° 45 °), β ∈ (- 45 ° 45 °), here α, β
For traditional Eulerian angles, the rotation posture for describing parallel robot.The theoretical length of rod member 4,5 is 2m, and the theory of rod member 6 is long
Spend for 3m.The pose track of moving platform is that α, β move to 45 ° from -45 ° in working space.It is anti-with position using geometrical relationship
The desired motion displacement for calculating and obtaining each drive shaft sliding block corresponding with the pose track of moving platform is solved equation, its result is sliding block
1 moves to 1.43m positions by 0.58m positions, and right sliding block 2 moves to 1.37m positions, guide screw lead p by 0.77m positionsh=
0.01m.According to formula (1) and then the preferable corner instruction θ of corresponding motor can be calculateddIt is as follows：
2), fractional order PDμController design：
Selection control system cut-off frequency ωc=550rad/s, control system phase margin φM=120 °.According to equation
(7)-(9) can solve one group of corresponding parameter [Kp Kdμ] all design conditions are met, bringing parameters obtained into formula (2) can score
Number rank PDμController expression formula is as follows：
Gp(s)=344.02 (1+0.0016s1.11) (16)
3) actual slide block movement state, is obtained by grating scale feedback, and resolving obtains corner displacement θc, and then missed
Poor e：
E=θd-θc (17)
4) the present embodiment parallel robot kinetics equation, is set up as follows：
Wherein τ=[τ1 τ2]TFor the driving moment for the motor for driving sliding block 1,2, phFor guide screw lead, JmFor rotor
Inertia matrix, MsFor sliding block mass matrix, g is acceleration of gravity；QpFor moving platform institute's stress and torque, GaFor matrix J-1Before
Two row, J is parallel robot Jacobian matrix here；QiFor rod member i barycenter institute's stress and torque (i=4,5,6), JivωFor bar
Part i Jacobian matrix；The respectively acceleration of sliding block 1,2；
5), dynamics feedforward compensation controller is designed：
First according to selected drive parameter, the transmission function G a little to output is compensatedk(s) it is as follows：
And then dynamics feedforward compensation controller is realized according to formula (14), realize that result is as follows：
6) foregoing obtained motion control amount e, is passed through into designed fractional order PDμController is sent to driver drives electricity
Machine is moved；Obtained thermal compensation signal τ G will be calculated simultaneouslyf(s)Gk(s) it is sent to the perturbed force during driver compensation campaign
Square, final control parallel robot is desirably moved track.
Effect using the effect of the present embodiment control method and existing conventional motion control method is contrasted, tied
Fruit is as shown in Figure 4 to 7.
Fig. 4 represent under existing control method moving platform α directions motion tracking error, Fig. 5 represent controlling
Motion tracking error of the moving platform in β directions under method；Fig. 6 is represented proposed by the present invention a kind of with quick response and robust
Moving platform is in the motion tracking error in α directions under the parallel robot motion control method of performance, and Fig. 7 is represented to be proposed in the present invention
A kind of parallel robot motion control method with quick response and robust performance under moving platform β directions motion tracking
Error.The abscissa of all images represents run duration, and Fig. 4 and Fig. 6 ordinate represent α directions tracking error, Fig. 5 and figure
7 ordinate represents β directions tracking error.It will be evident that proposed by the present invention a kind of with quick sound from Comparative result
Answer and the parallel robot motion control method of robust performance compares conventional motion control method, eliminate static error, reduce
Fluctuating error during tracking, is greatly improved the exercise performance of parallel robot.
Claims (3)
1. a kind of parallel robot motion control method with quick response and robust performance, it is characterised in that this method includes
Following steps：
1) parallel robot desired trajectory is planned according to duty requirements, the ideal of each drive shaft sliding block is obtained by Inverse Kinematics Solution
Displacement commands, and the preferable corner instruction of respective drive motor is calculated, corner instruction will be used to obtaining parallel robot each
The control instruction of motor；
2) using fractional order PDμController is handled the control instruction of motor, and its expression is：
Gp(s)=Kp(1+Kdsμ)
G in formulap(s) it is controller transfer function, KpFor controller proportional gain factor, KdFor controller differential gain coefficient, s
It is differential operator, μ is a positive non-integer；Preferable ω is selected firstcWith φM, ω herecFor control system cut-off frequency,
φMFor control system phase margin；To make control system that there is quick response and robust performance, while utilizing three Domain Designs
Constraints：
(a) cut-off frequency design constraint：
|G(jωc)|dB=| Gp(jωc)P(jωc)|dB=0
ω in formulacFor control system cut-off frequency, cut-off frequency directly determines control system responding ability, passes through design ideal
Cut-off frequency, it is ensured that system has fast-response energy；G (j ω) is open-loop transfer function, | | it is modulus computing, j is unit
Imaginary number, ω is frequency；P (j ω) is control object, including driver and motor model, and its expression is：
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A=K in formulatKpiKpvTiiTiv, b=KtKpiKpv(Tii+Tiv), c=KtKpiKpv, A=JLTiiTiv, B=J (R+Kpi)
TiiTiv, C=JKpiTiv+KtKeTiiTiv+KtKpiKpvTiiTiv, D=KtKpiKpv(Tii+Tiv), E=KtKpiKpv, L is armature
Inductance, R is armature resistance, and J is motor inertia, KtIt is motor electromagnetic moment coefficient, KeIt is back emf coefficient, KpiIt is driving
The proportional gain factor of device electric current loop, KpvIt is the proportional gain factor of drivers velocity ring, TiiIt is the integration of driver current ring
Time coefficient, TivIt is the time of integration coefficient of drivers velocity ring；
(b) phase margin design constraint：
Arg[G(jωc)]=Arg [Gp(jωc)P(jωc)]=φM-π
φ in formulaMFor control system phase margin, phase margin directly determines the stability and robustness of control system；Arg[]
For phase operation, represent to solve the phase of respective transfer functions；
(c) Robustness Design constraints：
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D () is derivative operation in formula, by phase margin to frequencies omega derivation；
3) the actual motion state of each drive shaft sliding block is detected and fed back by grating scale, and resolves the reality for obtaining motor
Moving corner state；
4) parallel manipulator human occupant dynamic model is set up, for obtaining corresponding driving moment instruction；
5) dynamics feedforward compensation controller is used, for the disturbance torque during compensation campaign；
6) the preferable corner instruction of each motor is made the difference with actual motion corner value and obtains motion control amount, this motion is controlled
Amount processed passes through the fractional order PDμController is sent to the motion of motor driver drive motor；Kinetic model will be passed through simultaneously
Calculate obtained driving moment instruction and be compensated controlled quentity controlled variable by dynamics feedforward compensation controller, by this compensation controlled quentity controlled variable hair
The disturbance torque during driver compensation campaign is given, final control parallel robot movement locus meets duty requirements.
2. a kind of parallel robot motion control method with quick response and robust performance according to claim 1,
Characterized in that, step 4) described in parallel manipulator human occupant dynamic model use following expression：
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τ represents the driving moment of parallel robot each motor in motion process in formula, and M is inertia matrix, and C is Coriolis
Power/centrifugal force matrix, G is gravity,For the nominal speed of each drive shaft slide block movement,For the name of each drive shaft slide block movement
Adopted acceleration.
3. a kind of parallel robot motion control method with quick response and robust performance according to claim 1,
Characterized in that, step 5) described in dynamics feedforward compensation controller use following expression：
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G in formulaf(s) it is dynamics feedforward compensation controller transmission function, NcFor a small arithmetic number.
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| CN105974797B (en) * | 2016-07-01 | 2018-07-17 | 厦门大学 | Consider the wire saws parallel robot motion control method of elasticity effect and compensation |
| CN106338913A (en) * | 2016-11-04 | 2017-01-18 | 河北省科学院应用数学研究所 | Fractional-order PID control design method based on phase margin and cutoff frequency |
| CN106527152B (en) * | 2017-01-09 | 2019-05-07 | 山东大学 | Closed loop fractional order PDɑThe design method and system of type iterative learning robot controller |
| CN107263541B (en) * | 2017-06-19 | 2019-08-20 | 中山长峰智能自动化装备研究院有限公司 | Robot and control method and system for force tracking error of robot |
| CN107390525B (en) * | 2017-07-27 | 2020-07-10 | 清华大学 | Control system parameter setting method applied to series-parallel mechanism |
| CN107457785B (en) * | 2017-09-26 | 2020-08-18 | 南京航空航天大学 | Robot position compensation method based on joint feedback |
| CN107831669B (en) * | 2017-11-24 | 2020-08-28 | 江苏大学 | Feedforward compensation optimization fractional order PID control method of series-parallel automobile electrophoretic coating conveying mechanism |
| CN108724195B (en) * | 2018-07-04 | 2021-10-19 | 天津大学 | Coupling feedforward control method for robot |
| CN108983703B (en) * | 2018-07-06 | 2020-03-31 | 清华大学 | Parameter setting method for feedforward controller of ultra-precise motion system |
| CN109986558A (en) * | 2019-02-26 | 2019-07-09 | 浙江树人学院（浙江树人大学） | Industrial robot motion control method based on error compensation |
| CN111216131B (en) * | 2020-01-21 | 2023-03-24 | 重庆邮电大学 | Robot cascade anti-interference control method and system based on flexible actuator driving |
| CN112666822B (en) * | 2020-12-17 | 2023-01-24 | 上海应用技术大学 | Fractional order-based heavy-load AGV speed control method |
| CN113199481B (en) * | 2021-05-14 | 2022-11-11 | 广东拓斯达科技股份有限公司 | Robot motion control method, device, electronic apparatus, and medium |
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