CN113459160A - Robot collision detection method based on second-order generalized momentum observer - Google Patents

Robot collision detection method based on second-order generalized momentum observer Download PDF

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CN113459160A
CN113459160A CN202110699021.7A CN202110699021A CN113459160A CN 113459160 A CN113459160 A CN 113459160A CN 202110699021 A CN202110699021 A CN 202110699021A CN 113459160 A CN113459160 A CN 113459160A
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collision detection
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CN113459160B (en
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张岳翔
黄石峰
高萌
陈思敏
周星
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Foshan Institute Of Intelligent Equipment Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J19/00—Accessories fitted to manipulators, e.g. for monitoring, for viewing; Safety devices combined with or specially adapted for use in connection with manipulators
    • B25J19/0095—Means or methods for testing manipulators

Abstract

The invention discloses a robot collision detection method based on a second-order generalized momentum observer. Then, a generalized momentum observer is established, a gain coefficient is determined, a friction model is established in a targeted mode, and model parameters are identified. And then, establishing a second-order generalized momentum observer by using a second-order damping model, connecting a PD regulator in series on the basis of the second-order damping model, and setting a threshold value. According to the robot collision detection method based on the second-order generalized momentum observer, the adjustable parameters are increased, the controllability of the system is increased, shorter transition time is easier to obtain, the collision detection delay of the system is reduced, and the application value is high. The invention can be applied to the collision detection technology.

Description

Robot collision detection method based on second-order generalized momentum observer
Technical Field
The invention relates to the technical field of collision detection, in particular to a robot collision detection method based on a second-order generalized momentum observer.
Background
Robot collaboration is widely used in various production fields. The robot may collide with a person or an environment due to an erroneous operation or a machine failure, and collision detection is an indispensable functional module of the cooperative robot to ensure safety of the person and the machine.
The collision detection method can be mainly divided into external moment monitoring based on a dynamic model and external moment monitoring without the dynamic model, and the external moment monitoring based on the dynamic model is the mainstream research direction at the present stage.
In the prior art, an energy-based observer is firstly proposed, which reflects the change of the external moment through the change of the system energy. However, the method cannot detect external force when the robot is static or external force perpendicular to the moving direction of the robot, and the monitoring signals directly reflect energy rather than external moment information. And then, an external moment observer based on the speed is provided, the method solves the problem that the specific external force of the energy observer cannot be detected, but due to the inverse operation of an inertia matrix, the nonlinear coupling relation between the monitoring signal and the external moment exists. And then, an external moment observer based on generalized momentum is provided, the method successfully realizes decoupling, the output of the observer directly reflects the external moment change of each joint, the calculation is simple, inversion is not needed, and the delay in detection exists.
Disclosure of Invention
The invention aims to provide a robot collision detection method based on a second-order generalized momentum observer, which aims to solve one or more technical problems in the prior art and at least provides a beneficial selection or creation condition.
The technical scheme adopted for solving the technical problems is as follows:
a robot collision detection method based on a second-order generalized momentum observer is characterized by comprising the following steps: the method comprises the following steps:
step S1: constructing a robot dynamics model and identifying dynamics parameters;
step S2: establishing a generalized momentum observer;
step S3: determining a gain factor;
step S4: establishing a friction model in a targeted manner, and identifying model parameters;
step S5: establishing a second-order generalized momentum observer by using a second-order damping model;
step S6: a threshold value is set.
The robot collision detection method based on the second-order generalized momentum observer provided by the invention at least has the following beneficial effects: replacing a first-order inertia link with a second-order transfer function model, and rebuilding a second-order observer on the basis of the generalized momentum observer; compared with a first-order model, the adjustable parameters of a second-order model are increased, shorter transition time is obtained more easily, controllability of a system is increased, system collision detection delay is reduced, and better collision detection is realized. And need not to use external sensor can realize the detection of collision power, reduction in production cost. Compared with the traditional generalized momentum observer, the robot collision detection method based on the second-order generalized momentum observer has the advantages that adjustable parameters are increased, the collision detection sensitivity is improved, and meanwhile, the detection delay is reduced.
As a further improvement of the above technical solution, the step S2 specifically includes: setting observer output r as joint external moment tauextListing the relational expression according to the monitoring value of (1); deriving generalized momentums p and τextThe theoretical relationship of (1); using p as intermediate quantity, and combining theoretical relation to deduce r and tauextAnd (4) in a relation form on a time domain, so as to construct the observer model.
As a further improvement of the above technical solution, the step S3 specifically includes: set different K1Collecting the output value of the generalized momentum observer when the robot repeatedly runs along a given track under the condition of no external force, comprehensively considering detection delay and sensitivity, and selecting proper K1While substantially determining the high frequency noise frequency wNAnd a low frequency error frequency wEAnd the second-order model gain coefficient is used as a setting basis of the second-order model gain coefficient. K1The method represents the corner frequency of a first-order inertia link adopted by the observer, and the selection of the value is related to the frequency range of high-frequency noise in the experimental process. The invention comprehensively considers the time delay and the error, thereby selecting the gain coefficient value.
As a further improvement of the above technical solution, the step S4 specifically includes: acquiring an observer output value, a motor driving torque and a joint position during actual running under the condition of no external force, and calculating a friction torque corresponding to each point position through a dynamic model or directly using the observer output value; and observing a relation curve of the friction torque and the joint speed, establishing a proper friction model, and identifying parameters of the friction model by using a least square method. Through the technical scheme, the sampling value is substituted into the dynamic model to extract the friction torque, and the friction model is established in a pertinence manner according to the relation between the friction torque and the joint angular velocity, so that the identification effect is improved.
As a further improvement of the above technical solution, the step S5 specifically includes: replacing an inertia element with a second-order damping model according to the high-frequency noise frequency w in the step 3NThe system cutoff frequency is set, the damping ratio is set, and the second order observer model is constructed with reference to step S2. According to the technical scheme, the first-order inertia link is replaced by the second-order transfer function model, the observer is built again, and lower detection delay and higher detection precision are easy to obtain.
Further, on the basis of the technical scheme, a PD regulator is connected in series on the basis of a second-order damping model and is used for regulating the frequency w according to the low-frequency errorESetting the corner frequency of the PD regulator; and 2, constructing an observer model by referring to the step 2, and realizing the amplification of the collision signal and the reduction of the attenuation rate of the high-frequency signal. Through the technical scheme, after the second-order damping model is connected with the PD regulator in series, the controllability of the system is further enhanced, the overshoot can be conveniently adjusted, the response rapidity can be further improved, the side effect influence of the high-frequency signal caused by the damping model, which is caused by the too fast attenuation rate, can be reduced, and the collision detection effect is improved.
As a further improvement of the above technical solution, the step S6 specifically includes: and acquiring output values of the running observer in the [0, T ] time under the condition of no external force, and setting a threshold value according to the maximum value and the minimum value.
As a further improvement of the above technical solution, the robot collision detection method further includes step S7: comparing collision detection results; and (3) configuring the algorithms of the first-order generalized momentum observer, the second-order damping model observer and the damping PD adjusting observer to the same program, collecting the output values of the observers during actual running, and comparing the detection effects when the collision force is applied. In the comparison experiment process, the detection results need to be compared to determine the quality of the detection effect of each observer algorithm on the collision force.
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The invention is further described with reference to the accompanying drawings and examples;
fig. 1 is a collision detection method of a robot based on a second-order generalized momentum observer according to an embodiment of the present invention, which is a collision detection flowchart;
fig. 2 is a generalized momentum observer model diagram of an embodiment of a robot collision detection method based on a second-order generalized momentum observer provided by the invention;
fig. 3 is a diagram illustrating a comparison of monitoring errors when different gain coefficients are selected according to an embodiment of a robot collision detection method based on a second-order generalized momentum observer provided by the present invention;
fig. 4 is a diagram illustrating a comparison of monitoring errors when different gain coefficients are selected according to an embodiment of a robot collision detection method based on a second-order generalized momentum observer provided by the present invention;
FIG. 5 is a comparison graph of monitoring effects of a collision process according to an embodiment of the robot collision detection method based on the second-order generalized momentum observer provided by the present invention;
FIG. 6 is a comparison graph of monitoring effects of a collision process according to an embodiment of the robot collision detection method based on the second-order generalized momentum observer provided by the present invention;
FIG. 7 is a diagram of a friction torque and joint angular velocity curve of an embodiment of a robot collision detection method based on a second-order generalized momentum observer according to the present invention;
FIG. 8 is a second-order damping observer model diagram of an embodiment of a robot collision detection method based on a second-order generalized momentum observer provided by the invention;
fig. 9 is a schematic diagram of an amplitude-frequency characteristic curve of an embodiment of a robot collision detection method based on a second-order generalized momentum observer according to the present invention;
FIG. 10 is a schematic diagram of a damping PD adjustment observer model according to an embodiment of the robot collision detection method based on the second-order generalized momentum observer provided by the invention;
fig. 11 is a monitoring error curve diagram of a first-order generalized momentum observer to three front axes of a robot according to an embodiment of the method for detecting robot collision based on a second-order generalized momentum observer provided by the present invention;
FIG. 12 is a diagram of a monitoring error curve of a second-order damping model to the front three axes of a robot according to an embodiment of the method for detecting robot collision based on a second-order generalized momentum observer provided by the present invention;
fig. 13 is a graph of monitoring error of a damped PD model to three front axes of a robot according to an embodiment of the method for detecting robot collision based on a second-order generalized momentum observer provided by the present invention;
FIG. 14 is a comparison graph of detection effects of an embodiment of the robot collision detection method based on the second-order generalized momentum observer provided by the invention;
fig. 15 is a comparison diagram of detection effects of an embodiment of the robot collision detection method based on the second-order generalized momentum observer provided by the invention.
Detailed Description
Reference will now be made in detail to the present preferred embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to like elements throughout.
In the description of the present invention, it should be understood that the orientation or positional relationship referred to in the description of the orientation, such as the upper, lower, front, rear, left, right, etc., is based on the orientation or positional relationship shown in the drawings, and is only for convenience of description and simplification of description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus, should not be construed as limiting the present invention.
In the description of the present invention, if words such as "a plurality" are described, the meaning is one or more, the meaning of a plurality is two or more, more than, less than, more than, etc. are understood as excluding the present number, and more than, less than, etc. are understood as including the present number.
In the description of the present invention, unless otherwise explicitly limited, terms such as arrangement, installation, connection and the like should be understood in a broad sense, and those skilled in the art can reasonably determine the specific meanings of the above terms in the present invention in combination with the specific contents of the technical solutions.
Referring to fig. 1 to 15, the robot collision detection method based on the second-order generalized momentum observer of the present invention makes the following embodiments:
a robot collision detection method based on a second-order generalized momentum observer is disclosed, an algorithm flow chart of the robot collision detection method is shown in figure 1, and the robot collision detection method comprises the following steps:
step S1: and constructing a robot dynamics model and identifying dynamics parameters.
Specifically, the method comprises the following steps: firstly, a robot dynamic model is constructed by utilizing a Newton Lagrange method; and (5) carrying out model linearization, and establishing a regression equation to obtain a minimum parameter set. And then, designing an excitation track by using Fourier series to obtain a track point position, issuing the track point position by a controller, and collecting current parameter values of the encoder and the motor. And then, the data are converted and filtered to obtain joint position, speed, acceleration parameters and motor driving torque. And finally, substituting the sampling data into the linear regression array based on a weighted least square method, and identifying kinetic parameters.
Based on a Lagrange dynamics formula, a robot dynamics model is established as follows:
Figure BDA0003129016140000061
in the above formula, q represents a joint position parameter, M is an inertia matrix, C is a centrifugal force and Coriolis force matrix, and G is a gravity term，τfFor friction torque, τmIs the joint drive torque.
Step S2: and establishing a generalized momentum observer.
Specifically, the method comprises the following steps: firstly, the output r of the observer is set as the external joint torque tauextList the relationship:
the generalized momentum observer adopts an inertia link as a transfer function model, and outputs a signal r and an external moment tauextThe relationship is as follows:
Figure BDA0003129016140000071
in the above formula, r is the observer output, K1As a gain factor, τextThe moment outside the joint.
Then, the relationship of the generalized momentum and the moment outside the joint is deduced:
Figure BDA0003129016140000072
order to
Figure BDA0003129016140000073
The above formula is rewritten as:
Figure BDA0003129016140000074
the above formula shows
Figure BDA0003129016140000075
And τextIn a linear relationship.
By means of the following effect of a first-order inertia link, an expression of an observer output signal r can be obtained:
Figure BDA0003129016140000076
under observer model, considerErrors of the dynamic and friction models, order
Figure BDA0003129016140000077
The robot dynamics model becomes:
Figure BDA0003129016140000078
combining a robot dynamic model and a relation between generalized momentum and the moment outside the joint, and assuming
Figure BDA0003129016140000079
Figure BDA00031290161400000710
Figure BDA00031290161400000711
The two sides of the equation are integrated simultaneously, and the observer is constructed in the following form:
Figure BDA00031290161400000712
building an observer model as shown in FIG. 2 by referring to a robot dynamics model; from the above derivation and observer model, r and τextThe deviation of (a) will cause a momentum observation
Figure BDA00031290161400000713
And the actual value
Figure BDA00031290161400000714
Will continuously feed back the adjustment monitor value r so as to follow tauextChange, finally satisfy r ≈ tauext。
Step S3: determining a gain factor K1。
Gain factor K1The method represents the corner frequency of a first-order inertia link adopted by the observer, and the selection of the value is related to the frequency range of high-frequency noise in the experimental process. At present, no effective means is available to obtain the frequency distribution of high-frequency noise in the experimental process, so different K is set1And (3) carrying out a plurality of groups of experiments, comparing with a direct method, and selecting a gain coefficient value by comprehensively considering two aspects of time delay and error.
Selecting different K by taking the joint 2 as an object1The pair of monitoring errors in value is shown in FIGS. 3 and 4 (K in FIG. 3)1Taking the monitoring errors at 0.5, 5 and 10 hours; FIG. 4 is K1Taking the monitoring error at 15 or 20), the comparison yields: k1The smaller the value is, the smaller the error is; k1When the values are 10 and 15, the error is basically unchanged; k1The larger the value, the larger the noise. K1At 20, the error curve covers K substantially completely1As the error curve of 15, the noise influence is larger and the detection effect is reduced. On the other hand, this also indicates the lower cut-off frequency w of the high-frequency noiseNIs approximately located in the frequency range of 10-20 Hz.
Select K1Values of 0.5 and 15, artificially applied collision force, compared to the direct method; the comparison results are shown in fig. 5 and 6; the specific test results of the Generalized Momentum Observer (GMO) and direct method are shown in the following table:
Figure BDA0003129016140000081
K1in the case of 15, the GMO collision detection time precedes that of the direct method, and K1The opposite is true in the case of 0.5. K1When the value of the maximum amplitude of the GMO output signal is 15, the ratio of the maximum amplitude of the GMO output signal to the upper limit of the threshold value is 3.5, the direct method is 2, and when the gain coefficient is set to be 15 under the same environment, the detection sensitivity of the GMO is 1.75 times that of the direct method; k1When the value is 0.5, the ratio of the maximum amplitude of the GMO output signal to the upper limit of the threshold is 1.8, the direct method is 1.6, and the detection sensitivity of the GMO is 1.125 times that of the direct method. Setting K by comprehensively considering detection sensitivity and detection delay1The GMO detection performance was better when 15.
Combining the above factors, setting K 115, preliminarily setting the upper limit frequency w of the low-frequency errorEIs 5Hz, the lower limit frequency w of high frequency errorNIs 15 Hz. The error is not processed in the experimental process, and the method is only used for determining the approximate distribution of the gain coefficient and the high-frequency error, so that the parameters can be conveniently set in the subsequent experiment.
Step S4: a friction model is established in a targeted manner, and model parameters are identified.
The robot runs along an excitation track, friction torque is extracted through a robot dynamic model, and the following friction model is established by taking the joint 1 as an object:
Figure BDA0003129016140000091
wherein tau iscThe driving moment is constant, and the direction of the driving moment is opposite to that of the friction force on the transmission chain; tau issThe maximum static friction force which needs to be overcome when the robot is started; tau isvFor the viscous friction term, the following is set:
Figure BDA0003129016140000092
parameter to be identified theta ═ tauc τs β1 β2 β3]TThe regression equation can be obtained by combining the above formula with the generalized momentum observer model as follows:
Figure BDA0003129016140000093
wherein:
Figure BDA0003129016140000094
Figure BDA0003129016140000095
Figure BDA0003129016140000096
the extracted friction torque and the recognition result are shown in fig. 7.
The friction model adopted by the GMO increases the maximum static friction force which needs to be overcome by the joint when starting, and is more in line with the actual running condition of the robot. Since the viscous friction force in fig. 7 does not strictly increase linearly with the velocity, the identification result can be closer to the actual sampling data by increasing the joint angular velocity order of the viscous friction term, and the identification effect is improved.
In addition, under the condition of no external force action, the friction torque extracted by the robot dynamic model comprises the following dynamic model errors:
Figure BDA0003129016140000101
and replacing the re-identified friction torque to the original dynamic model, so that the elimination of part of model errors can be realized.
Step S5: and establishing a second-order generalized momentum observer, and connecting a PD regulator in series on the basis of the second-order generalized momentum observer.
Specifically, the method comprises the following steps: taking a second-order damping system as a transfer function model of the generalized momentum observer:
Figure BDA0003129016140000102
let K1＝wn 2,K1K2＝2ξwn：
Figure BDA0003129016140000103
Both sides of the equation integrate simultaneously:
r(t)＝K1∫[∫(τext-r)dt-K2r]dt
combining the above equation and the observer output signal r and the external torque τ obtained in step S2extAnd (3) obtaining a time domain relational expression by using the expression and a robot kinematics model expression:
Figure BDA0003129016140000104
the second-order damping observer model is shown in fig. 8, and it can be known that the adjustable parameters of the second-order damping observer model are increased, and the system controllability is higher. When the damping xi is 0.707, the amplitude-frequency characteristic curve is approximate to a straight line in a low frequency band, and the system response rapidity and the oscillation stability performance are balanced and optimal. Compared with a first-order generalized momentum observer, the system is easy to obtain lower detection delay and higher detection accuracy, but simultaneously the high-frequency attenuation rate is increased, so that the high-frequency signal detection effect is reduced, and the amplitude-frequency characteristic of the system is shown in fig. 9.
The PD regulator is connected in series on the basis of a second-order damping model, the 20dB/dec slope of the PD regulator is utilized, the corner frequency is set according to the upper limit frequency of the low-frequency error, the high-frequency attenuation rate is reduced, meanwhile, the amplification of a collision signal can be realized, the amplitude-frequency characteristic is shown in figure 9, and a system transfer function model is as follows:
Figure BDA0003129016140000111
and combining the derivation process to obtain a time domain relational expression:
Figure BDA0003129016140000112
the damped PD tuning observer model is shown in fig. 10.
Step S6: setting an observer threshold value:
reference low frequency error upper limit frequency wEIs 5Hz, the lower limit frequency w of high frequency errorNFor 15Hz, observer coefficients are set such asThe following table shows:
type (B) K1 K2 K3
First-order generalized momentum observer 15
Second order damping model 225 0.0943
Damping system PD adjustment 74.3343 0.1640 0.1429
The detection errors of the observer on the front three axes are shown in FIGS. 11 to 13 (FIG. 11 is the monitoring error of the first-order generalized momentum observer; FIG. 12 is the monitoring error of the second-order damping model; FIG. 13 is the monitoring error of the damping PD model; wherein the solid line is the monitoring value, and the dotted line is the threshold);
the observer threshold settings are shown in the following table:
Figure BDA0003129016140000113
Figure BDA0003129016140000121
step S7: and respectively applying collision force to the shaft 2 and the shaft 3, and comparing the detection effects of the second order observer and the first order observer.
Fig. 14 shows an example of the detection effect of the joint 2 when an impact force is applied to the shaft 2, and fig. 15 shows an example of the detection effect of the joint 3 when an impact force is applied to the shaft 3. The two subgraphs respectively represent the damping model and the PD adjustment of the damping system. In the figure, a dotted curve is output of a first-order generalized momentum observer, and a real curve is output of a second-order observer; the dotted line represents the threshold of a first-order generalized momentum observer, the dashed straight line represents the threshold of a second-order observer, and the local amplification at the peak position of detection enables the result to be clearer.
Comparison of the detection results of the collision force of the first-order observer and the second-order observer is shown in the following table (wherein GMO represents a first-order generalized momentum observer, Damp represents a second-order damping model, and PD represents a damping system PD adjustment observer):
Figure BDA0003129016140000122
according to the comparison result, the designed observer algorithm can respond to the change of the external moment, and the output of the observer can generate a peak exceeding a threshold value when the collision occurs, so that the algorithm can be used for realizing the collision detection function. If the ratio of the maximum amplitude of the output signal of the observer to the upper limit of the threshold value is taken as the standard for measuring the collision detection sensitivity of the observer, the detection sensitivity of the collision force of the second-order observer is better than that of GMO (Gaussian mixture model) as can be known from the table above, wherein the detection sensitivity of the damping model observer is the highest. If the point where the output signal of the observer initially exceeds the threshold is used as the collision detection point, the second-order observer detects the collision before the GMO, as can be seen from the above table. In summary, the second-order algorithm has an improved impact force detection effect compared to the first-order algorithm.
While the preferred embodiments of the present invention have been illustrated and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (8)

1. A robot collision detection method based on a second-order generalized momentum observer is characterized by comprising the following steps: the method comprises the following steps:
step S1: constructing a robot dynamics model and identifying dynamics parameters;
step S2: establishing a generalized momentum observer;
step S3: determining a gain factor;
step S4: establishing a friction model in a targeted manner, and identifying model parameters;
step S5: establishing a second-order generalized momentum observer by using a second-order damping model;
step S6: a threshold value is set.
2. The robot collision detection method based on the second-order generalized momentum observer according to claim 1, wherein: the step S2 specifically: setting observer output r as joint external moment tauextListing the relational expression according to the monitoring value of (1); deriving generalized momentums p and τextThe theoretical relationship of (1); using p as intermediate quantity, and combining theoretical relation to deduce r and tauextRelational form in the time domain.
3. The robot collision detection method based on the second-order generalized momentum observer according to claim 2, wherein: the step S3 specifically: set different K1Collecting the output value of the generalized momentum observer when the robot repeatedly runs along a set track under the condition of no external force; the appropriate K is selected by comprehensively considering the detection delay and the sensitivity1While substantially determining high frequency noiseFrequency wNAnd a low frequency error frequency wE。
4. The robot collision detection method based on the second-order generalized momentum observer according to claim 3, wherein: the step S4 specifically: acquiring an observer output value, a motor driving torque and a joint position during actual running under the condition of no external force, and calculating a friction torque corresponding to each point position through a dynamic model or directly using the observer output value; and observing a relation curve of the friction torque and the joint speed, establishing a proper friction model, and identifying parameters of the friction model.
5. The robot collision detection method based on the second-order generalized momentum observer according to claim 4, wherein: the step S5 specifically: replacing the inertia element with a second-order damping model according to the high-frequency noise frequency w in step S3NSetting a system cut-off frequency; the damping ratio is set, and a second order observer model is constructed with reference to step S2.
6. The robot collision detection method based on the second-order generalized momentum observer according to claim 5, wherein: the step S5 specifically: and (4) connecting a PD regulator in series on the basis of the second-order damping model, and building the observer model again.
7. The robot collision detection method based on the second-order generalized momentum observer according to claim 1, wherein: the step S6 specifically: and acquiring output values of the running observer in the [0, T ] time under the condition of no external force, and setting a threshold value according to the maximum value and the minimum value.
8. The robot collision detection method based on the second-order generalized momentum observer according to claim 1, wherein: the robot collision detection method further includes step S7: comparing collision detection results; and (3) configuring the algorithms of the first-order generalized momentum observer, the second-order damping model observer and the damping PD adjusting observer to the same program, collecting the output values of the observers during actual running, and comparing the detection effects when the collision force is applied.
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