CN111859297A - Retort loading track extraction method based on Gaussian mixture model - Google Patents

Retort loading track extraction method based on Gaussian mixture model Download PDF

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CN111859297A
CN111859297A CN202010698351.XA CN202010698351A CN111859297A CN 111859297 A CN111859297 A CN 111859297A CN 202010698351 A CN202010698351 A CN 202010698351A CN 111859297 A CN111859297 A CN 111859297A
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gaussian mixture
mixture model
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retort loading
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刘超
张栗寅
杨艺
张建华
盛鑫军
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Shanghai Jiaotong University
Hebei University of Technology
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Hebei University of Technology
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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
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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
    • B25J9/1628—Programme controls characterised by the control loop
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning

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Abstract

The invention discloses a retort loading track extraction method based on a Gaussian mixture model, which comprises the following steps of: the method comprises the following steps: denoising the acquired position signal original data by using a Butterworth filter, and calculating the speed of each moment by using front and rear sampling points of each moment; step two: fitting a Gaussian mixture model by using a maximum expectation algorithm; step three: according to the method, the noise tolerance of the method is improved through multiple retort loading action teaching, the problems of action deformation, action acceleration and deceleration and the like in the manual retort loading process are high in robustness, and the extraction of the retort loading track is finally realized and a good effect is achieved.

Description

Retort loading track extraction method based on Gaussian mixture model
Technical Field
The invention relates to the technical field of white spirit production, in particular to a retort loading track extraction method based on a Gaussian mixture model.
Background
Chinese liquor has a long history, and liquor brewing technology is continuously developed and innovated along with the progress of times. Wherein, the steamer is an important part in the white spirit brewing process. The quality of the operation of the retort loading operation can directly determine the quality of the wine. Particularly, the steamer loading operation requires that the raw materials are uniformly and loosely spread into a steamer pot layer by layer in the brewing process, and the uniformity and the looseness of the raw materials ensure that the raw materials do not leak steam and do not press steam. Because the retort pot is in a circular truncated cone shape, the general charging equipment is difficult to realize the retort loading operation, so the traditional manual retort loading mode is generally adopted in the wine making industry at present, and wine making raw materials are manually spread.
However, the traditional manual retort loading method has the problems of high labor intensity, poor working environment, different wine quality and wine yield among people and the like. To improve this production situation, attempts have been made in the market to perform retort loading operations using robots. Compared with a common loading device, the robot has the advantages of large movement space, excellent dynamic performance and the like, and therefore, an improved technology is urgently needed to solve the problem existing in the prior art.
Disclosure of Invention
In order to enable a robot to finish retort loading operation, namely the robot needs to simulate the traditional manual retort loading method, the invention provides a retort loading process library established by utilizing a manual retort loading track so as to achieve the goals of wine quality improvement, traditional process inheritance and the like based on a Gaussian mixture model.
The invention aims to provide a retort loading track extraction method based on a Gaussian mixture model, which introduces track matching into the process of retort loading action learning of a robot, fits the Gaussian mixture model through a maximum expectation algorithm to establish repeated teaching track matching characteristics, obtains fitting data under a limiting condition through Gaussian mixture regression, and finally realizes retort loading action track fitting.
In order to achieve the purpose, the invention provides the following technical scheme: a retort loading track extraction method based on a Gaussian mixture model comprises the following steps:
the method comprises the following steps: denoising the acquired position signal original data by using a Butterworth filter, and calculating the speed of each moment by using front and rear sampling points of each moment;
step two: fitting a Gaussian mixture model by using a maximum expectation algorithm;
step three: and generating a fitting track by using Gaussian mixed regression.
Preferably, the gaussian mixture model in the second step is a clustering model.
Preferably, the gaussian mixture model in the second step uses a combination of multiple gaussian distributions to describe the data distribution, and the expression of the gaussian distribution is as follows:
Figure BDA0002592102650000021
preferably, the maximization expectation algorithm in the second step includes a first part and a second part, the first part is described by a likelihood function of obtaining complete data according to an existing model, and the second part is used for maximizing the likelihood function of the first part.
Preferably, the joint probability density distribution function of the gaussian mixture model in the second step is as follows:
Figure BDA0002592102650000031
preferably, the joint probability density distribution function of the gaussian mixture model in the second step is as follows:
Figure BDA0002592102650000032
preferably, the gaussian mixture model in the second step introduces a maximization expectation algorithm.
Preferably, the trajectory fitted in step three is an expectation of a gaussian mixture model distribution to obtain generalized data points.
Compared with the prior art, the invention has the beneficial effects that:
according to the method, the trajectory matching is introduced into the retort loading action learning process of the robot, the repeated teaching trajectory matching characteristic is established by fitting a Gaussian mixture model through a maximum expectation algorithm, fitting data under the limiting condition is obtained through Gaussian mixture regression, and finally retort loading action trajectory fitting is realized.
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FIG. 1 is a schematic flow chart of the present invention.
Fig. 2 is a schematic diagram of a two-dimensional gaussian distribution.
FIG. 3 is a schematic diagram of a Gaussian mixture model distribution.
FIG. 4 is a schematic diagram of the fitting of the EM algorithm to a two-dimensional variable double Gaussian mixture model.
Fig. 5 is a schematic diagram of sampled data.
FIG. 6 is a schematic representation of the projection of sampled data onto the t-z plane and processing using 8 Gaussian models.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a technical scheme that: a retort loading track extraction method based on a Gaussian mixture model comprises the following steps:
the method comprises the following steps: and denoising the acquired position signal original data by using a Butterworth filter, and calculating the speed of each moment by using front and rear sampling points of each moment.
Raw data obtained by passive optical motion capture systems, Inertial Measurement Units (IMUs), or video keypoint capture, etc., usually have serious noise and singularity problems. The invention uses Butterworth Filter to reduce noise of the collected position signal, and uses the sampling points before and after each time to calculate the speed of the time;
Using speed as a feature is a great advantage over using position as a feature. Because human motion deformation is large, the assumption that the closest points of the position features correspond to each other is not true; for the speed characteristics, the points with similar speeds are generally the same functional point in the action, and the corresponding relation is established, so in practice, the effect of fitting the track can be obviously improved by using the speed characteristics.
Step two: a gaussian mixture model is fitted using a maximum expectation algorithm.
The gaussian mixture model is a widely used clustering model. The model assumes that the experimental data satisfies a multi-kernel gaussian distribution, and generally fits the experimental data with sufficient gaussian distributions in superposition.
Gaussian distribution:
gaussian Distribution (Gaussian Distribution), also known as normal Distribution (NormalDistribution), is the most common form of Distribution in nature. The expression of the gaussian distribution is as follows:
Figure BDA0002592102650000051
the expression comprises two parameters, wherein the parameter mu represents a mean value, the parameter sigma represents a standard deviation, the mean value corresponds to the middle position of normal distribution, and the standard deviation measures the degree of data dispersion around the mean value. The gaussian distribution has a strong information characterization capability because the limit of the plurality of remaining distributions is the gaussian distribution, such as binomial distribution, super-geometric distribution, etc.
Meanwhile, for the multidimensional model, a multidimensional Gaussian distribution model is used, and the joint probability density distribution function of the multidimensional model is as follows:
Figure BDA0002592102650000052
wherein d represents a variable dimension; μ is an n-dimensional vector representing the mean of the variables of each dimension; and Σ is a covariance matrix describing the correlation between variables of each dimension. A schematic diagram of a two-dimensional gaussian distribution is shown in fig. 2.
Mixed gaussian distribution:
the gaussian mixture model is a simple extension of the gaussian model, i.e. a combination of multiple gaussian distributions is used to characterize the data distribution, in which one gaussian distribution is called a gaussian kernel and the number of gaussian distributions is called the number of gaussian kernels. The joint probability density distribution function of the gaussian mixture model is:
Figure BDA0002592102650000061
wherein p (x | k) ═ N (x | μ ═ Nk，∑k) Is the probability density function of the kth gaussian model, i.e. the probability that the model produces x after the data is determined to be the kth model; p (k) ═ pikIs the weight of the kth Gaussian model, i.e. the prior probability, π, of selecting the kth modelkShould satisfy sigma pik＝1。
Gaussian mixture models can produce more complex models than gaussian models. Theoretically, if the number of gaussian models provided to the mixture gaussian model is sufficiently large, the mixture model can fit arbitrarily distributed samples.
A schematic diagram of the distribution of the gaussian mixture model is shown in fig. 3. The lower curve represents the probability density function of a single gaussian model, and the highest curve represents the approximate probability density function of a weighted gaussian mixture model. Note that the highest curve also needs to be normalized to be gaussian mixture model distribution.
The Gaussian mixture model fitting method comprises the following steps:
the fitting method of the Gaussian mixture model is a method for obtaining parameters of the fitted Gaussian mixture model when the experimental data are supposed to accord with the Gaussian mixture model.
For a simple multidimensional gaussian model, a common fitting method is Maximum Likelihood Estimation (MLE). The essence is to find a set of parameters that maximize the likelihood of the multidimensional gaussian model appearing in the data set. However, because the Gaussian mixture model is fitted with an implicit variable πkThe information of the Gaussian mixture model cannot be directly obtained from the data, summation is introduced into the log-likelihood function, and the likelihood function has strong non-convexity so that the likelihood function cannot be solved by an optimization method.
Therefore, for Gaussian mixture models, the maximization-Expectation algorithm (EM) is introduced. The EM algorithm can be divided into two parts. The first part (part E) gets a likelihood function description of the full data from the current model. Note that the decision of the gaussian mixture model to which the individual belongs in the complete data is obtained by the current model, and is considered as a constant value when the second part is found to be descending later. And a second part (M part) for maximizing the likelihood function and updating the current model by using the model for maximizing the function. The EM algorithm performs the two parts in turn until the result converges.
Compared with the maximum likelihood estimation method, the EN algorithm can avoid the non-convexity of the likelihood function, and can also converge on the global optimal solution while improving the convergence speed. The fitting of the EM algorithm to the two-dimensional variable double gaussian mixture model is shown in fig. 4.
Step three: and generating a fitting track by using Gaussian mixed regression.
After the Gaussian mixture model is obtained according to the method, fitting data of the region of interest are obtained by using Gaussian mixture regression. Gaussian mixture model regression is to obtain the expectation of the distribution of the Gaussian mixture model under the specified limiting conditions, thereby obtaining the generalization data points.
Specifically, if desired, X is required1＝x1The generalized data value of time. P (x | k) is known to satisfy the following gaussian distribution:
Figure BDA0002592102650000071
then at fixed x(1，k)When x2：n，kAlso satisfies a Gaussian distribution as follows:
Figure BDA0002592102650000072
the mean and variance of the kth gaussian kernel under this constraint can be found. From the weight parameters of the gaussian mixture model, the generalized data values under this constraint can be obtained as follows:
Figure BDA0002592102650000073
at this point, the gaussian mixture model method completes the output of the fitting data. It should be noted that the gaussian mixture model method is a method for learning the internal features of data, so that the gaussian mixture model method can still complete fitting data output even if the required generalized data limiting conditions are not included in the teaching data.
The tests were carried out as follows:
the experiment uses real sampled retort loading data for track fitting, the sampled data is shown in figure 5, the sampled data has large fluctuation, and the action consistency is poor. In addition, the interval of a plurality of groups of sampling data is large, and the rule among the data is difficult to find in a manual mode.
For convenience of presentation, the sampled data were projected onto the t-z plane and processed using 8 gaussian models, with the final result shown in fig. 6. Thin lines in the graph are original data, thick lines are fitting data, gray area ellipses are Gaussian mixture distribution graphs, and the Gaussian mixture distribution graphs can be observed from the graph 6.
According to the method, the trajectory matching is introduced into the retort loading action learning process of the robot, the repeated teaching trajectory matching characteristic is established by fitting a Gaussian mixture model through a maximum expectation algorithm, fitting data under the limiting condition is obtained through Gaussian mixture regression, and finally retort loading action trajectory fitting is realized.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (8)

1. A retort loading track extraction method based on a Gaussian mixture model is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps: denoising the acquired position signal original data by using a Butterworth filter, and calculating the speed of each moment by using front and rear sampling points of each moment;
step two: fitting a Gaussian mixture model by using a maximum expectation algorithm;
step three: and generating a fitting track by using Gaussian mixed regression.
2. The retort loading track extraction method based on the Gaussian mixture model as claimed in claim 1, wherein: and the Gaussian mixture model in the second step is a clustering model.
3. The retort loading track extraction method based on the Gaussian mixture model as claimed in claim 1, wherein: in the second step, the gaussian mixture model uses a combination of a plurality of gaussian distributions to describe data distribution, and the expression of the gaussian distribution is as follows:
Figure FDA0002592102640000011
4. The retort loading track extraction method based on the Gaussian mixture model as claimed in claim 1, wherein: the second step is that the maximization expectation algorithm comprises a first part and a second part, wherein the first part is described by a likelihood function of the complete data obtained according to the existing model, and the second part is used for maximizing the likelihood function of the first part.
5. The retort loading track extraction method based on the Gaussian mixture model as claimed in claim 1, wherein: the joint probability density distribution function of the Gaussian mixture model in the second step is as follows:
Figure FDA0002592102640000012
6. the retort loading track extraction method based on the Gaussian mixture model as claimed in claim 1, wherein: the joint probability density distribution function of the Gaussian mixture model in the second step is as follows:
Figure FDA0002592102640000021
7. the retort loading track extraction method based on the Gaussian mixture model as claimed in claim 1, wherein: and introducing a maximization expectation algorithm into the Gaussian mixture model in the step two.
8. The retort loading track extraction method based on the Gaussian mixture model as claimed in claim 1, wherein: and in the third step, the fitting track is the expectation of the distribution of the Gaussian mixture model so as to obtain generalized data points.
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CN105956601A (en) * 2016-04-15 2016-09-21 北京工业大学 Robot Chinese character writing learning method based on track imitation
CN110653824A (en) * 2019-07-26 2020-01-07 同济人工智能研究院(苏州)有限公司 Method for characterizing and generalizing discrete trajectory of robot based on probability model
CN111002302A (en) * 2019-09-09 2020-04-14 浙江瀚镪自动化设备股份有限公司 Mechanical arm grabbing track planning method combining Gaussian mixture model and dynamic system

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Publication number Priority date Publication date Assignee Title
CN105956601A (en) * 2016-04-15 2016-09-21 北京工业大学 Robot Chinese character writing learning method based on track imitation
CN110653824A (en) * 2019-07-26 2020-01-07 同济人工智能研究院(苏州)有限公司 Method for characterizing and generalizing discrete trajectory of robot based on probability model
CN111002302A (en) * 2019-09-09 2020-04-14 浙江瀚镪自动化设备股份有限公司 Mechanical arm grabbing track planning method combining Gaussian mixture model and dynamic system

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