CN109366488A - A kind of superimposed oscillation power Cartesian impedance control method of object manipulator assembly - Google Patents
A kind of superimposed oscillation power Cartesian impedance control method of object manipulator assembly Download PDFInfo
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- CN109366488A CN109366488A CN201811494757.5A CN201811494757A CN109366488A CN 109366488 A CN109366488 A CN 109366488A CN 201811494757 A CN201811494757 A CN 201811494757A CN 109366488 A CN109366488 A CN 109366488A
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- mechanical arm
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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
- B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
Abstract
The invention proposes a kind of superimposed oscillation power Cartesian impedance control methods of object manipulator assembly, the described method comprises the following steps: Step 1: being directed to the insertion stage of assembling assembly, combined impedance control principle carries out Dynamic Modeling；Step 2: establishing location-based impedance controller model in component assembly system of the cartesian space to mechanical arm；Step 3: increasing superimposed oscillation power to location-based impedance controller model, and analyze superimposed oscillation power effect；Step 4: establishing the Cartesian impedance control device model with superimposed oscillation power.The pose deviation that the method for the present invention can be inserted into the stage to assembling assembly is adjusted, it is obviously reduced since fit-up gap is small and the brings assembly resistance such as outer bound pair tip turbulence, avoid blocking, make to assemble it is more compliant, solve the problems, such as mechanical arm small―gap suture plug assembly flexibility.It the composite can be widely applied in a variety of robotic asssembly tasks, process is simple, it is easy to accomplish.
Description
Technical field
The invention belongs to robot control fields, more particularly to a kind of superimposed oscillation Li Dika of object manipulator assembly
That impedance adjustment.
Background technique
With the rapid development of robot technology, autonomous assembly is carried out increasingly by the weight of scientific research personnel using mechanical arm
Depending on.For the fittage under some particular surroundings, mechanical arm can greatly mitigate human work's pressure and efficiently complete
Fittage, it is particularly possible to the danger for avoiding people from working in extreme circumstances.Therefore, robot autonomous mounting technology becomes current
One of hot spot of research.
Especially for the small―gap suture high-precision fittage under particular surroundings such as space-orbit assembly, used by robot
Assembly control method is just particularly important.General fittage, which can be substantially divided into, to be approached and is inserted into two stages, in difference
Stage it is different to the control method demand of mechanical arm.It is generally being used close to the stage for the high accuracy positioning for guaranteeing mechanical arm
Position control method；In the insertion stage, mechanical arm is in contact with rigid environment, and mechanical arm is needed to have certain flexibility,
Generally use Shared control method.Mechanical arm, which carries during operational instrument is contacted with external environment, can generate interaction
Power can comply with external force using the mechanical arm of Shared control, to protect the safety of mechanical arm and target well.Therefore
It is with important application prospects that research assembly control method is especially inserted into the Shared control method in stage.
The method for realizing the submissive performance of mechanical arm mainly has passive compliance and two kinds of active compliance.The core of passive compliance is thought
Think be energy conversion, extraneous work done is absorbed or stored using the mechanical structures such as such as spring, damper, mechanical arm is made to exist
Passive movement can be generated under force when contacting with extraneous rigid environment, to show certain flexibility.But by
In the limitation of itself, it is difficult to realize the control of degree of precision.Active Compliance Control is a pass in emerging intelligence manufacture
Key technology is generally divided into power/position mixing control and impedance control.Although power/position mixing control is theoretical clear, in Practical Project
In it is relatively difficult to achieve.Impedance control can be divided into location-based impedance control and the impedance control based on power.Location-based impedance
Control strategy is suitable for middle high rigidity occasion；And the impedance control based on power needs the accurate kinetic model of mechanical arm and impedance
Model, robustness and reliability are also not so good as location-based impedance control.And variation nothing unknown additionally, due to external environment rigidity
Method precognition, the accurate more difficult searching of impedance control parameter, when facing the plugging in fitting task of precision components, lesser assembly
Gap, the small range error being difficult to avoid that and tip turbulence etc. make assembling process be easy to block, to reduce autonomous
The success rate of assembly.Therefore, the present invention proposes a kind of object manipulator on the basis of location-based Cartesian impedance control
The superimposed oscillation power Cartesian impedance control method of assembly.
Summary of the invention
The present invention in order to solve the problems in the prior art, provides a kind of superimposed oscillation Li Dika of object manipulator assembly
That impedance adjustment.The present invention introduces the oscillating force of superposition on the basis of location-based Descartes controls, and makes small―gap suture
Assembly is not susceptible to block, and realizes the flexibility of mechanical arm plugging in fitting middle and later periods, mechanical arm is enable to go on smoothly assembly
The accurate plugging in fitting of component changes task.
The purpose of the present invention is achieved through the following technical solutions: a kind of superimposed oscillation power Descartes of object manipulator assembly
Impedance adjustment the described method comprises the following steps:
Step 1: being directed to the insertion stage of assembling assembly, combined impedance control principle carries out Dynamic Modeling；
Step 2: establishing location-based impedance controller mould in component assembly system of the cartesian space to mechanical arm
Type；
Step 3: increasing superimposed oscillation power to location-based impedance controller model, and analyze superimposed oscillation power effect；
Step 4: establishing the Cartesian impedance control device model with superimposed oscillation power.
Further, the step 1 specifically:
Impedance control principle is described using " mass-spring-damper " model, as shown in formula (1), mathematical model is indicated
For following second order differential equation:
Wherein: Md、Bd、KdRespectively represent inertia, damping and the stiffness matrix of desired impedance model；Fe、FrRespectively indicate machine
The practical contact force in tool arm end and expected force；X,Respectively indicate physical location, the velocity and acceleration of mechanical arm；Xr、It respectively indicates and generates expected force FrDesired locations, velocity and acceleration；EfIndicate the practical contact force of mechanical arm and phase
Hope the deviation of power；
Laplace transformation is carried out to formula (1), collated to obtain, transmission function, that is, desired impedance between power deviation and position deviation
Characteristic are as follows:
By desired impedance parameter Md、BdAnd KdIt is set as positive semidefinite matrix, impedance point is carried out to any freedom degree therein
Analysis, Selecting All Parameters Md、Bd、Kd、X、XrAnd EfIn element md、bd、kd、x、xrAnd ef, therefore formula (1) can be described below:
When considering that mechanical arm is in the ambient condition of free space, end contact force feIt is 0, it can thus be concluded that:
If expected force f at this timerValue be also 0, then when the system is stable, x → xr, therefore can realize expected motion trajectory with
Track control；If mechanical arm is in constraint space, end can generate contact force at this time, and can be due to power deviation efGenerate position
Change of error amount Δ x, modifies to the motion profile of target, to realize the adjustment of mechanical arm tail end contact force；
When ignoring the damping factor of environment, kinetic model are as follows:
Fe=Ke(X-Xe) (5)
Wherein, X, XeAnd FeIt is 6*1 dimensional vector, respectively represents mechanical arm tail end physical location, environment contact surface reference bit
It sets and to the active force of environment；KeThe diagonal environment rigidity matrix of positive definite is tieed up for 6*6.
Further, the step 2 specifically: the entire control structure in system is divided into two layers: internal position control
Preparative layer and external impedance control layer；In external impedance control ring, measured by the sextuple torque sensor of mechanical arm tail end
The stress F of mechanical arme, then location-based impedance controller model is obtained by desired impedance relationship:
Wherein xrFor position desired under cartesian space, xdFor the input value of control system positioner part.
Further, described that superimposed oscillation power is increased to location-based impedance controller model specifically: in mechanical arm
Each Cartesian degree of freedom of work increases separately superimposed oscillation power to make mechanical arm generate corresponding movement, the superposition vibration
Corresponding oscillation action can be generated in oscillation by swinging power, and the superimposed oscillation power is superposition pure oscillation power, and the superposition is sinusoidal
Oscillating force can make the displacement of end generation pure oscillation；The superposition pure oscillation power refers to a kind of with certain amplitude and frequency
The size and Orientation of output is a kind of oscillating force of special shape in the form of periodically variable power.
Further, described to establish the Cartesian impedance control device model with superimposed oscillation power specifically: superimposed oscillation
Power makes an addition to the place of outer ring input expected force, i.e. the expected force of impedance control becomes former expected force and the vector of oscillating force is folded
Add, is denoted as Fr', so that the mechanical arm of impedance control is exported the contact force with duration ranges fluctuation under impedance relationship characteristic,
To make mechanical arm tail end position generate with oscillation displacement x '.
Beneficial effects of the present invention: the present invention is that the high-precision small―gap suture fittage of mechanical arm proposes one kind with folded
Add the Cartesian impedance control method of oscillating force.The control can be inserted into the pose deviation in stage to assembling assembly and carry out fine motion tune
It is whole, hence it is evident that reduce since the brings such as the small and outer bound pair tip turbulence in fit-up gap assemble resistance, avoid blocking, make assembly more
It is submissive, solve the problems, such as the flexibility of mechanical arm small―gap suture plug assembly.It the composite can be widely applied to a variety of robotic asssemblies
In task, process is simple, it is easy to accomplish.
Detailed description of the invention
Fig. 1 is the superimposed oscillation power Cartesian impedance control method flow diagram of object manipulator of the present invention assembly；
Fig. 2 is impedance control schematic diagram；
Fig. 3 is the kinetic model figure of mechanical arm and environment；
Fig. 4 is the location-based impedance controller schematic diagram of cartesian space；
Fig. 5 is that Lisa eats curvilinear path figure；
Fig. 6 is the Cartesian impedance control device schematic diagram with superimposed oscillation power；
Fig. 7 is the control of superimposed oscillation mechanical impedance and general position impedance control end stress comparison diagram.
Specific embodiment
Technical solution in the embodiment of the present invention that following will be combined with the drawings in the embodiments of the present invention carries out clear, complete
Ground description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.Based on this
Embodiment in invention, every other reality obtained by those of ordinary skill in the art without making creative efforts
Example is applied, shall fall within the protection scope of the present invention.
Present implementation is illustrated in conjunction with Fig. 1.It is to be filled for mechanical arm small―gap suture high-precision described in the method for the present invention
A kind of superimposed oscillation power Cartesian impedance control method of object manipulator assembly with the task insertion stage, including walk as follows
It is rapid:
Step 1: being directed to the insertion stage of assembling assembly, combined impedance control principle carries out Dynamic Modeling；
The target of impedance control is not directly using the contact force of mechanical arm tail end as control object, but based on end
Kinematics and kinetic parameter, such as the feedback of position, speed, acceleration and power, to construct a kind of desired impedance relationship mould
Type (target impedance), therefore the control of end contact force can be realized indirectly by changing target impedance parameter.With " quality-spring-
Damping " model (such as Fig. 2) describes impedance control principle, and as shown in formula (1), it is micro- that mathematical model can be expressed as second order
Divide equation:
Wherein: Md、Bd、KdRespectively represent inertia, damping and the stiffness matrix of desired impedance model；Fe、FrRespectively indicate machine
The practical contact force in tool arm end and expected force；X,Respectively indicate physical location, the velocity and acceleration of mechanical arm；Xr、It respectively indicates and generates expected force FrDesired locations, velocity and acceleration；EfIndicate the practical contact force of mechanical arm and phase
Hope the deviation of power；
Formula (1) carries out Laplace transformation, collated to obtain, and transmission function, that is, desired impedance between power deviation and position deviation is special
Property are as follows:
The essence of impedance control is that a kind of desired dynamic relationship is created between mechanical arm tail end position is in contact with it power, fortune
Mechanical arm movement is constantly adjusted by motion controller during dynamic, to maintain this ideal dynamic model.To protect
Card mechanical arm in cartesian coordinate system decouples the control of each freedom degree, usually by desired impedance parameter (Md、
Bd、Kd) it is set as positive semidefinite matrix, and when carrying out impedance analysis to any freedom degree therein, Selecting All Parameters Md、Bd、Kd、X、XrWith
EfIn element md、bd、kd、x、xrAnd ef, therefore formula (1) can be described below:
When considering that mechanical arm is in the ambient condition of free space, end contact force feIt is 0, it can thus be concluded that:
If expected force f at this timeeValue be also 0, then when the system is stable, x → xr, therefore can realize expected motion trajectory with
Track control；If mechanical arm is in constraint space, end can generate contact force at this time, and can be due to power deviation efGenerate position
Change of error amount Δ x, modifies to the motion profile of target, to realize the adjustment of mechanical arm tail end contact force.
When the impedance control to mechanical arm conducts a research, the kinetic model of practical contact environment need to be established.When ignoring
When the damping factor of environment, kinetic model are as follows:
Fe=Ke(X-Xe) (5)
Wherein, X, XeAnd FeIt is 6*1 dimensional vector, respectively represents mechanical arm tail end physical location, environment contact surface reference bit
It sets and to the active force of environment.KeEnvironment rigidity matrix is tieed up for 6*6, to realize the solution under cartesian coordinate system under each freedom degree
Coupling is generally set to positive definite diagonal matrix.If the case where only considering certain single-degree-of-freedom in cartesian coordinate system, with corresponding small
Lowercase alphabet shows the element in matrix, and the kinetic model that mechanical arm is contacted with environment in the freedom degree at this time is as shown in Figure 3.
Step 2: establishing location-based impedance controller mould in component assembly system of the cartesian space to mechanical arm
Type；
Fittage to arrangement requires mechanical arm to have stronger robustness and reliability, and should ensure that mechanical arm exists
Flexibility in certain freedom degree directions, location-based impedance control principle is as shown in Figure 4 on cartesian space.In system
Controller is designed under operating space, and entire control structure can be divided into two layers: internal position control layer and outer
The impedance control layer in portion.The high-gain positioner of inside in Fig. 4 can be calculated using the control of general mechanical arm position
Method, such as PD control and computed moment control.In external impedance control ring, by the sextuple torque sensor of mechanical arm tail end Lai
Measure the stress F of mechanical arme, then location-based impedance controller model is obtained by desired impedance relationship:
Wherein xrFor position desired under cartesian space, xdFor the input value of control system positioner part.It can be with
Regard the formula as a second-order low-pass filter.
The tracking error of power in each freedom degree of mechanical arm is analyzed below, sees formula (7):
E=fr-fe=fr-ke(x-xe)=fr+kexe-ke[xr+h(s)ef] (7)
Wherein,The steady-state error of force tracking can further be obtained:
Then the practical contact force of mechanical arm and environment components is shown in formula (9).
In practice, contact surface position xeIt is unknown, environment rigidity keIt is very big and unknown, even if contact surface position deviation very little,
The tracking error of the power of generation is still very big, will produce a very large impact to the control precision of mechanical arm, fills especially for small―gap suture
Match, is also easy to block and cause independently to assemble failure.
Step 3: increasing superimposed oscillation power to location-based impedance controller model, and analyze superimposed oscillation power effect；
Construct the model of common location-based Cartesian impedance control in step 2, it is basic under the control mode
The flexibility of common fittage may be implemented, but small―gap suture high-precision is assembled, be still easy to happen obstruction, cannot reach
Satisfactory effect.Consider that small―gap suture easily blocks, this method imitates the skill of mankind's precision assembly, after assembling assembly contact
It is superimposed lesser oscillating force in a plurality of directions.
Superimposed oscillation power can be increased respectively in each Cartesian degree of freedom of mechanical arm work to make mechanical arm
Corresponding movement is generated, superimposed oscillation power can generate corresponding oscillation action in oscillation, and superposition pure oscillation power can make end
Generate the displacement of pure oscillation.Superposition pure oscillation power refers to that a kind of size and Orientation with certain amplitude and rate-adaptive pacemaker is in
The form of periodically variable power is a kind of oscillating force of special shape.The torque of same frequency can be generated around the forced oscillation of axis
Oscillation, superposition torque oscillation can lead to the generation of rotational oscillation.Superposition constant force or sinusoidal force can make robot mobile.?
The appropriately combined of oscillating force can be used to generate different motor patterns in each freedom degree.
The power that superposition additional force applies robot motion and robot can have a great impact.For example, Low rigidity and height
Superposed force will lead to robot and accelerate suddenly.Therefore, if using superposed force, it is necessary to the size of careful selective stacking power.Generally
Lesser power should be applied and be stepped up and approach suitable value.
When pure oscillation power is superimposed upon 2 different Descartes directions, Lisa eats force curve generation.Two oscillations it is folded
Very different form can be created for path by adding.Exact path depends on multiple parameters.It is superimposed upon in each freedom degree
Pure oscillation power can all make mechanical arm tail end operating point deviate intended path, as sinuous path is moved to terminal from starting point.Often
When the forced oscillation being superimposed on a Descartes direction, robot end can be while executing relative motion on superposed force direction
Generate the displacement of oscillation.Maximum position offset Δ is the deviation for deviateing initial path in the positive negative direction of oscillation, is by the flute card
What the rigidity c and amplitude f that the impedance controller on your direction defines were determined, according to Hooke law:
Δ=f/c (10)
Wavelength may be used to determine how many oscillation will be executed between the starting point and terminal of movement for robot.Wavelength be by
The frequency that impedance controller with superimposed oscillation power defines, and robot speed by programming determine.Wavelength calculates such as
Under:
L=C/F (11)
In formula, C is speed, and F is frequency.
It is superimposed the sinusoidal forced oscillation of two different frequencies, in application to generate oscillation in tool coordinates system TCP.It is such
Oscillation can eliminate the tension occurred in assembling process and interference.Pure oscillation power is superimposed upon the X and Y of TCP tool coordinates system
On direction.Peak excursion Δ x and Δ y are determined that this is by the impedance controller institute in Descartes X and Y-direction by rigidity and amplitude
Definition.Other than the parameter of known impedance controller, the phase offset between two oscillations plays important in the paths
Effect.
As shown in figure 5, the form in path depends primarily on the phase offset between the ratio of two frequencies and two oscillations.?
The curve arrived is always axisymmetric and point symmetry.The setting amplitude and rigidity of orientation of oscillation determine the size of its position amplitude,
Ratio between two position amplitudes determines the ratio between width and height of curve.
Step 4: establishing the Cartesian impedance control device model with superimposed oscillation power.
According to the effect of superposed force, the Cartesian impedance control device with superimposed oscillation power is devised, it belongs to Descartes
A kind of special shape of impedance controller, as shown in Figure 6: the power of oscillation makes an addition to the place of outer ring input expected force, i.e. impedance
The expected force of control becomes former expected force and is superimposed with the vector of oscillating force, is denoted as Fr', make the mechanical arm of impedance control certain
Output is with the contact force for continuing small range fluctuation under impedance relationship characteristic, to make mechanical arm tail end position in all directions
Displacement x of the generation with small oscillatory '.The oscillating force of addition can be the multidimensional superposed force under cartesian space.Multidimensional superposition
Sinusoidal force oscillation action on the small―gap suture component easily blocked, so that component is made smooth advances under the auxiliary of small oscillatory, thus
Complete the fittage inserted or pull out.
The oscillating force of superposition sine has optimal effectiveness, so general should be noted that using sinusoidal oscillating force, and when implementation
Superposed force amplitude should not be too large.According to the form of input expected force, this Descartes with superimposed oscillation power can also be claimed to hinder
Anti- control method is Descartes's sine impedance adjustment.As shown in fig. 7, using the impedance of superposition multiple directions pure oscillation power
Terminal contact points maximum weighted is in 15N or so when control method is assembled, hence it is evident that than the end of general Cartesian position impedance control
50~250N of stress is much smaller, this is neither easy damage assembling assembly, but also blockage percentage reduces.
Above to a kind of superimposed oscillation power Cartesian impedance control method of object manipulator assembly provided by the present invention,
It is described in detail, used herein a specific example illustrates the principle and implementation of the invention, the above reality
The explanation for applying example is merely used to help understand method and its core concept of the invention；Meanwhile for the general technology of this field
Personnel, according to the thought of the present invention, there will be changes in the specific implementation manner and application range, in conclusion this theory
Bright book content should not be construed as limiting the invention.
Claims (5)
1. a kind of superimposed oscillation power Cartesian impedance control method of object manipulator assembly, which is characterized in that the method packet
Include following steps:
Step 1: being directed to the insertion stage of assembling assembly, combined impedance control principle carries out Dynamic Modeling；
Step 2: establishing location-based impedance controller model in component assembly system of the cartesian space to mechanical arm；
Step 3: increasing superimposed oscillation power to location-based impedance controller model, and analyze superimposed oscillation power effect；
Step 4: establishing the Cartesian impedance control device model with superimposed oscillation power.
2. the method according to claim 1, wherein the step 1 specifically:
Impedance control principle is described using " mass-spring-damper " model, as shown in formula (1), mathematical model be expressed as
Lower second order differential equation:
Wherein: Md、Bd、KdRespectively represent inertia, damping and the stiffness matrix of desired impedance model；Fe、FrRespectively indicate mechanical arm
The practical contact force in end and expected force；X,Respectively indicate physical location, the velocity and acceleration of mechanical arm；Xr、It respectively indicates and generates expected force FrDesired locations, velocity and acceleration；EfIndicate the practical contact force of mechanical arm and phase
Hope the deviation of power；
Laplace transformation is carried out to formula (1), collated to obtain, transmission function, that is, desired impedance operator between power deviation and position deviation
Are as follows:
By desired impedance parameter Md、BdAnd KdIt is set as positive semidefinite matrix, impedance analysis is carried out to any freedom degree therein,
Selecting All Parameters Md、Bd、Kd、X、XrAnd EfIn element md、bd、kd、x、xrAnd ef, therefore formula (1) can be described below:
When considering that mechanical arm is in the ambient condition of free space, end contact force feIt is 0, it can thus be concluded that:
If expected force f at this timerValue be also 0, then when the system is stable, x → xr, therefore can realize the tracking control of expected motion trajectory
System；If mechanical arm is in constraint space, end can generate contact force at this time, and can be due to power deviation efGenerate position deviation
Variation delta x modifies to the motion profile of target, to realize the adjustment of mechanical arm tail end contact force；
When ignoring the damping factor of environment, kinetic model are as follows:
Fe=Ke(X-Xe) (5)
Wherein, X, XeAnd FeBe 6*1 dimensional vector, respectively represent mechanical arm tail end physical location, environment contact surface reference position and
To the active force of environment；KeThe diagonal environment rigidity matrix of positive definite is tieed up for 6*6.
3. according to the method described in claim 2, it is characterized by: the step 2 specifically: the entire control knot in system
Structure is divided into two layers: internal position control layer and external impedance control layer；In external impedance control ring, by mechanical arm end
The sextuple torque sensor at end measures the stress F of mechanical arme, then location-based impedance is obtained by desired impedance relationship
Controller model:
Wherein xrFor position desired under cartesian space, xdFor the input value of control system positioner part.
4. according to the method described in claim 3, it is characterized by: described increase location-based impedance controller model is folded
Add oscillating force specifically: increase separately superimposed oscillation power in each Cartesian degree of freedom of mechanical arm work to make mechanical arm produce
Raw corresponding movement, the superimposed oscillation power can generate corresponding oscillation action in oscillation, and the superimposed oscillation power is superposition
Pure oscillation power, the superposition pure oscillation power can make the displacement of end generation pure oscillation；The superposition pure oscillation power is
Refer to it is a kind of by the size and Orientation of certain amplitude and rate-adaptive pacemaker in the form of periodically variable power, be a kind of special shape
Oscillating force.
5. according to the method described in claim 4, it is characterized by: described establish the Cartesian impedance control with superimposed oscillation power
Device model processed specifically: superimposed oscillation power makes an addition to the place of outer ring input expected force, i.e. the expected force of impedance control becomes former
Expected force is superimposed with the vector of oscillating force, is denoted as Fr', export the mechanical arm of impedance control under impedance relationship characteristic with holding
The contact force of continuous range fluctuation, thus make mechanical arm tail end position generate the displacement x with oscillation '.
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| CN111037571A (en) * | 2019-12-31 | 2020-04-21 | 广东工业大学 | Robot self-adaptive variable damping impedance control method |
| CN111319042A (en) * | 2020-02-06 | 2020-06-23 | 北京凡川智能机器人科技有限公司 | Robot flexible assembly control method based on forgetting factor dynamic parameters |
| CN111640495A (en) * | 2020-05-29 | 2020-09-08 | 北京机械设备研究所 | Variable force tracking control method and device based on impedance control |
| CN112171673A (en) * | 2020-09-24 | 2021-01-05 | 哈尔滨工业大学（深圳） | Robot arm operation control method, control apparatus, and computer-readable storage medium |
| CN112936291A (en) * | 2021-03-26 | 2021-06-11 | 中国科学院宁波材料技术与工程研究所 | Force control end effector vibration suppression method based on impedance control |
| CN113892848A (en) * | 2021-10-08 | 2022-01-07 | 上海景吾智能科技有限公司 | Overturning following track planning method, device and system for overturning object |
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