CN114131600A - Method and system for generating robot source search scheme based on Gaussian mixture model - Google Patents

Method and system for generating robot source search scheme based on Gaussian mixture model Download PDF

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CN114131600A
CN114131600A CN202111457525.4A CN202111457525A CN114131600A CN 114131600 A CN114131600 A CN 114131600A CN 202111457525 A CN202111457525 A CN 202111457525A CN 114131600 A CN114131600 A CN 114131600A
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陈彬
季雅泰
王翔汉
徐珂
杨妹
程光权
黄金才
胡星辰
吕欣
唐文杰
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National University of Defense Technology
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Abstract

The invention discloses a method and a system for generating a robot source search scheme based on a Gaussian mixture model, wherein the method for generating the robot source search scheme based on the Gaussian mixture model comprises the following steps: establishing a source searching process model and determining an estimation representation of a source item parameter; aiming at a source search process model, representing probability estimation of source item parameters by using a particle filtering method; reconstructing probability estimation of the particles by using a Gaussian mixture model; determining an action scheme for searching autonomous sources of the control robot according to parameters of Gaussian distribution in the Gaussian mixture model; and (5) carrying out numerical experiments and adjusting the optimal parameters of the Gaussian mixture model. According to the method, the Gaussian mixture model is used for fitting the parameters obtained by the distribution fitting of the particles in the particle filter to control the action of the robot and generate the source search action scheme, so that the source search efficiency is greatly improved, and the calculation cost of the source search is reduced.

Description

Method and system for generating robot source search scheme based on Gaussian mixture model
Technical Field
The invention relates to the field of robot control, in particular to a method and a system for generating a robot source searching scheme based on a Gaussian mixture model, which are suitable for various gas signal source searching scenes, such as harmful gas leakage in chemical industrial parks, ocean oil spill pollution events and the like.
Background
In nature, it is particularly important to find weak, intermittent or noisy sources of gaseous signal emissions. Animals are hunted and searched for spouses by tracking odor signals, human beings provide an emergency decision scheme for the events such as chemical plant leakage, ocean oil spill pollution and the like by utilizing a signal source searching algorithm, and the perception robot can search for the sources of gas and radiation by an autonomous searching method. For an autonomous searcher, an efficient autonomous search action scheme is of great help in performing search tasks.
Biologically inspired algorithms have investigated the way animals find sources of odors and perform path planning. Random search is a search mode ubiquitous in nature. For example, ants in deserts follow an archimedes spiral path while foraging. Predatory fish in open sea areas follow the Levy pattern when predating in areas with rare prey, which can be demonstrated by a large number of motion data sets. When a priori knowledge or sensory cues can be perceived, the searcher will use some search strategies to obtain more additional useful information. Some organisms (e.g. e.coli, lobster) tend to move in the direction of the concentration gradient, which is defined as the Chemotaxis strategy. In addition, many work locates odor sources by mimicking the behavior of moths and proposes the silk algorithm. The biologically inspired search algorithm has high computational efficiency but relies on significant concentration gradients and concentration boundaries. However, in a real-world environment, turbulence can break the stable plume into disconnected blobs, disrupting the process of source search.
Most of the previously mentioned bio-inspired search strategies can be considered reactive. In addition, methods based on the principles of information theory have also been developed, i.e. cognitive search strategies. Vergasola et al proposed the earliest cognitive search strategy, known as the Infotaxis algorithm, which uses a grid-based approach to maintain information state. Ristic refines the Infotaxi algorithm by using sparse sensing cues in the form of sporadic non-zero sensor measurements. Hutchinson et al propose another cognitive search algorithm, Entrotaxi, which designs a reward function based on maximum entropy sampling. These search strategies express the source search problem as a particle filter-based Partially Observable Markov Decision Process (POMDP), replacing the grid-based approach. The proposal of the cognitive search strategy greatly improves the source search performance under the turbulent flow condition. However, the huge computational burden of cognitive strategies results in lengthy search times, which limits their application in practical search tasks. Therefore, it is important and challenging to improve the efficiency of cognitive strategies.
In summary, in the conventional solution process, for the source search problem based on the cognitive search strategy, the source item estimation is represented by a particle filtering method, and then a reward function is calculated to control the action of the robot. However, the calculation of the reward function is too complex, so that the efficiency of source search is influenced, and the calculation cost is increased.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: aiming at the problems in the prior art, the invention provides a method and a system for generating a robot source search scheme based on a Gaussian mixture model.
In order to solve the technical problems, the invention adopts the technical scheme that:
a method for generating a robot source search scheme based on a Gaussian mixture model comprises the following steps:
1) establishing a source searching process model and determining an estimation representation of a source item parameter;
2) aiming at a source search process model, representing probability estimation of source item parameters by using a particle filtering method;
3) reconstructing probability estimation of the particles by using a Gaussian mixture model;
4) determining an action scheme for searching autonomous sources of the control robot according to parameters of Gaussian distribution in the Gaussian mixture model;
5) and (5) carrying out numerical experiments and adjusting the optimal parameters of the Gaussian mixture model.
Optionally, the source search process model established in step 1) is a partial observable markov decision process modeled as a source search process, and a functional expression of the source search process model is obtained as follows:
Figure BDA0003387059080000021
in the above formula, R (R | θ)0) Is the gas concentration at an arbitrary position r ═ { x, y } position, θ0＝{r0Q represents the source term parameter of the source, r0＝{x0,y0The position of the source in the two-dimensional search domain Ω, Q the diffusion intensity, a the spherical sensor radius, V the mean wind speed, D the effective diffusion coefficient of the gas, λ the intermediate variable, τ the lifetime of the gas molecules.
Optionally, the determining of the estimated representation of the source item parameters in step 1) refers to an information state in a partial observable markov decision process, and a bayesian framework shown in the following formula is adopted to estimate and update the posterior probability density function PDF of any k-th step:
Figure BDA0003387059080000022
in the above formula, θkRepresenting the source term parameters of step k, D1:k＝{d1(r1),d2(r2),…,dk(rk) Is the accumulated information of the time step k, d1(r1),d2(r2),…,dk(rk) Are respectively at an arbitrary position r1～rkInformation obtained, P (theta)k-1|D1:k-1) As a posterior probability density function PDF, P (d) of step k-1k(rk)|θk) For the probability of induction measurement, P (d)k(rk)|D1:k-1) Is a weight of probability density, and P (d)k(rk)|D1:k-1) The formula of the calculation function is:
P(dk(rk)|D1:k-1)＝∫P(θk-1|D1:k-1)P(dk(rk)|θk)dθk，(3)
probability of induction measurement P (d)k(rk)|θk) The formula of the calculation function is:
Figure BDA0003387059080000031
in the above formula, P (d | θ)0) Is the probability of contacting a gas molecule d times per unit time.
Optionally, the step 2) of representing the probability estimation of the source parameter by using the particle filtering method specifically means that the probability estimation of the source parameter is implemented by using a sequential monte carlo framework and the particle filtering method, and the specific steps include: generating PDF with a posterior probability density function by sampling any k-th step
Figure BDA0003387059080000032
N random samples of the weights, wherein,
Figure BDA0003387059080000033
represents an estimate of the parameters of the source item,
Figure BDA0003387059080000034
is the associated weight, and the sum of the weights of the N random samples is 1, thereby expressing the posterior probability density function PDF of any k-th step as:
Figure BDA0003387059080000035
in the above equation, θ is the source term estimate,
Figure BDA0003387059080000036
is a dirac function;
sampling from the proposed distribution to approximate the a posteriori probability density function PDF of any k-th step using a sequential importance sampling method using a sequential monte carlo framework, whereby the update of the a posteriori probability density function PDF of any k-th step is converted to an update of the associated weights as shown by:
Figure BDA0003387059080000037
in the above formula, the first and second carbon atoms are,
Figure BDA0003387059080000038
is the non-normalized weight of the particle,
Figure BDA0003387059080000039
in order to be the probability of a state transition,
Figure BDA00033870590800000310
can be obtained from the formula (4) below,
Figure BDA00033870590800000311
an importance function in the importance sampling principle;
presume q (θ) assuming that the source term parameters remain unchanged during the source search processk)＝P(θk-1|D1:k-1) Thereby obtaining an updated simplified expression of the correlation weights as shown in the following equation:
Figure BDA00033870590800000312
and for the updated simplified expression of the correlation weights, an effective sampling proportion ESS shown by the following formula is adopted to define the degradation degree of the particle filter adopted in the particle filtering method:
Figure BDA00033870590800000313
when effective sampling ratio ESS is lower than threshold NTAnd a resampling method is adopted to solve the problem of particle degradation.
Optionally, when reconstructing a probability estimation of a particle using a gaussian mixture model in step 3), a function expression that a posterior probability density function PDF for an arbitrary k-th step is approximated by a density of the gaussian mixture model is:
Figure BDA0003387059080000041
in the above formula, PG(theta) represents an approximate Gaussian mixture model probability density function, K represents the number of Gaussian distributions, and coefficient piiSatisfy sigma pii＝1，N(θ|μi,Σi) Representing covariance arrays sigma with a gaussian distributioniGaussian distribution of (u)iIs mean value, ΣiIs a Gaussian distribution covariance array; assuming that the distribution of the sampled particles is approximately PG(θ), introducing a hidden variable γ, which is a binary random variable of K dimensions, wherein among K values of the hidden variable γ, only one specific element γ (K) is 1, and the other elements are 0, so as to determine which gaussian model hidden variable in the gaussian mixture model is sampled by the sample, and the corresponding log-likelihood function functional expression is:
Figure BDA0003387059080000042
in the above formula, L (pi)i,μi,Σi) As a maximum likelihood function, gammaiFor hiding the ith dimension, π, of the variable γkIs a Gaussian distribution coefficient, N (θ | μk,Σk) Representing covariance arrays sigma with a gaussian distributionk(ii) a gaussian distribution of; and finally, solving the estimation of the weighted log-likelihood function of the Gaussian mixture model by adopting a maximum expectation algorithm EM.
Optionally, the solving of the estimate of the weighted log-likelihood function of the gaussian mixture model using the maximum expectation algorithm EM includes:
s1) setting initial parameters including random sample number N, gaussian distribution covariance array ΣkDistribution mean μkAnd the number of iterations mloop(ii) a Setting an initial cycle variable k and a cycle variable i to be 1;
s2) judging that the loop variable k is equal to the iteration number mloopIf the result is not true, skipping to the next step; if not, then,
s3) traverse the cyclic variable i from 1 to the random number of samples N and calculate a reference probability η (i, k) for each component:
Figure BDA0003387059080000043
in the above formula, N (θ (i) |. mu.)k,Σk) Representing covariance arrays sigma with a gaussian distributionk(ii) a gaussian distribution of; k represents the number of Gaussian distributions,. pikAnd pijAre all Gaussian distribution coefficients;
s4) calculating a mean value μ from the reference probability η (i, k) of each component based on the following equationkGaussian distribution covariance array sigmakGaussian coefficient of distribution pikAnd the value of the log-likelihood function lk；
Figure BDA0003387059080000051
Figure BDA0003387059080000052
Figure BDA0003387059080000053
lk＝lnL(πi,μi,Σi)，(15)
In the above formula, γ (i) represents a local weight;
s5) judging condition lk-lk-1Whether epsilon is less than or equal to epsilon or not is true, if not, jumping to execute the step S2); otherwise, the parameter mean value mu of the finally obtained Gaussian mixture modelkGaussian distribution covariance array sigmakGaussian coefficient of distribution pikAnd outputting as a result.
Optionally, step 4) comprises: firstly, searching a region where the maximum Gaussian distribution is located, defining the average central position of particle samples owned by the maximum Gaussian distribution as the center of the region, and after determining the center, firstly controlling the robot to go to the center of the region for searching: and (3) searching the whole area by using the area center as a search starting point and applying a square search strategy, and terminating the square search mode when the collected information updates the Gaussian mixture model to generate a new maximum Gaussian distribution area, so that a searcher moves to the new area center to search.
Optionally, the adjusting of the optimal parameters of the gaussian mixture model in step 5) specifically means adjusting the optimal number K of gaussian distributions.
In addition, the invention also provides a device for generating the robot source searching scheme based on the Gaussian mixture model, which comprises a microprocessor and a memory which are connected with each other, wherein the microprocessor is programmed or configured to execute the steps of the method for generating the robot source searching scheme based on the Gaussian mixture model.
Furthermore, the present invention also provides a computer-readable storage medium having stored therein a computer program programmed or configured to execute the method for generating the gaussian mixture model-based robot source search scheme.
Compared with the prior art, the invention has the following advantages: modeling a source searching process based on a cognitive search strategy, and representing source item parameters as information states; converting the information state into probability estimation by using a particle filtering method; extracting spatial information of particle distribution, and expressing the particle filter estimation into a plurality of Gaussian distributions by using a Gaussian mixture model; determining a robot autonomous source searching action scheme based on a Gaussian mixture model according to the parameters of Gaussian distribution; the optimal Gaussian mixture model parameters are determined through Monte Carlo simulation experiments, the Gaussian mixture model is used for fitting the distribution of particles in the particle filter, the action of the robot is controlled according to the parameters obtained through fitting, and a source searching action scheme is generated.
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FIG. 1 is a schematic diagram of a basic flow of a method according to an embodiment of the present invention.
Fig. 2 is a schematic diagram of a maximum gaussian distribution region searching method in the embodiment of the present invention.
Fig. 3 is a schematic diagram of a robot autonomous source search scheme based on a gaussian mixture model in an embodiment of the present invention.
FIG. 4 is a diagram illustrating experimental results of Gaussian mixture model parameters in an embodiment of the present invention.
Detailed Description
The following will take the gas leakage source search problem as an example, and further describe the generation method and system of the robot source search scheme based on the gaussian mixture model in detail.
As shown in fig. 1, the method for generating the robot source search scheme based on the gaussian mixture model in this embodiment includes:
1) establishing a source searching process model and determining an estimation representation of a source item parameter;
2) aiming at a source search process model, representing probability estimation of source item parameters by using a particle filtering method;
3) reconstructing probability estimation of the particles by using a Gaussian mixture model;
4) determining an action scheme for searching autonomous sources of the control robot according to parameters of Gaussian distribution in the Gaussian mixture model;
5) and (5) carrying out numerical experiments and adjusting the optimal parameters of the Gaussian mixture model.
As known by cognitive search strategies, the source search process can be modeled as a partially observable Markov decision process, the source term estimation can be expressed as a posterior probability density function, and the position with the highest probability is the position of the estimated source. According to the cognitive search strategy, the source item estimation is expressed as an information state in a partial observable Markov decision process, and the subsequent utilization of the source item estimation is facilitated. In this embodiment, the source search process model established in step 1) refers to modeling a source search process as a partially observable markov decision process, and a function expression of the source search process model is obtained as follows:
Figure BDA0003387059080000061
in the above formula, R (R | θ)0) Is the gas concentration at an arbitrary position r ═ { x, y } position, θ0＝{r0Q represents the source term parameter of the source, r0＝{x0,y0The position of the source in the two-dimensional search domain Ω, Q the diffusion intensity, a the spherical sensor radius, V the mean wind speed, D the effective diffusion coefficient of the gas, λ the intermediate variable, τ the lifetime of the gas molecules.
In this embodiment, the determination of the estimation representation of the source item parameter in step 1) refers to an information state in a partial observable markov decision process, and a bayesian framework shown in the following formula is adopted to estimate and update the posterior probability density function PDF of any k-th step:
Figure BDA0003387059080000062
in the above formula, θkRepresenting the source term parameters of step k, D1:k＝{d1(r1),d2(r2),…,dk(rk) Is the time stepCumulative information of length k, d1(r1),d2(r2),…,dk(rk) Are respectively at an arbitrary position r1～rkInformation obtained, P (theta)k-1|D1:k-1) As a posterior probability density function PDF, P (d) of step k-1k(rk)|θk) For the probability of induction measurement, P (d)k(rk)|D1:k-1) Is a weight of probability density, and P (d)k(rk)|D1:k-1) The formula of the calculation function is:
P(dk(rk)|D1:k-1)＝∫P(θk-1|D1:k-1)P(dk(rk)|θk)dθk，(3)
probability of induction measurement P (d)k(rk)|θk) The formula of the calculation function is:
Figure BDA0003387059080000071
in the above formula, P (d | θ)0) Is the probability of contacting a gas molecule d times per unit time. At the beginning of the source search, since there is no source item information of the history, it is assumed that the estimation range of the parameters is determined using a priori knowledge and the initial posterior probability density function PDF is represented using a uniform distribution.
Because the direct calculation of the source item estimation parameters in the source search process is too complex, the bayesian estimation of the source item parameters is realized by adopting a sequential monte carlo frame and a particle filtering method, degraded particles are screened by utilizing a resampling step, and newly sampled particles are added to obtain the particle filtering estimation of the source item parameters. Firstly, obtaining random samples through sampling, then updating a posterior probability density function according to a sequential importance sampling method, screening degraded particles after a resampling step, and adding new sampling particles to obtain particle filter estimation of source item parameters. In this embodiment, the probability estimation of the source parameter by using the particle filtering method in step 2) specifically refers to using a sequential monte carlo framework and the particle filtering methodThe probability estimation of the source item parameters is realized, and the specific steps comprise: generating PDF with a posterior probability density function by sampling any k-th step
Figure BDA0003387059080000072
N random samples of the weights, wherein,
Figure BDA0003387059080000073
represents an estimate of the parameters of the source item,
Figure BDA0003387059080000074
is the associated weight, and the sum of the weights of the N random samples is 1, i.e.:
Figure BDA0003387059080000075
the posterior probability density function PDF of any kth step is thus expressed as:
Figure BDA0003387059080000076
in the above equation, θ is the source term estimate,
Figure BDA0003387059080000077
is a dirac function;
posterior probability density function PDFP (theta) from step kk|D1:k) Intermediate sampling is difficult and therefore sequential importance sampling methods are utilized. At each step, samples are taken from the proposed distribution to approximate P (θ)k|D1:k). The update of the PDF is then converted into an update of the associated weight. In this embodiment, a sequential monte carlo framework is adopted to sample the proposed distribution to approximate the a posteriori probability density function PDF of any k-th step using a sequential importance sampling method, so that the update of the a posteriori probability density function PDF of any k-th step is converted into an update of the correlation weight shown by the following formula:
Figure BDA0003387059080000081
in the above formula, the first and second carbon atoms are,
Figure BDA0003387059080000082
is the non-normalized weight of the particle,
Figure BDA0003387059080000083
in order to be the probability of a state transition,
Figure BDA0003387059080000084
can be obtained from the formula (4) below,
Figure BDA0003387059080000085
an importance function in the importance sampling principle;
presume q (θ) assuming that the source term parameters remain unchanged during the source search processk)＝P(θk-1|D1:k-1) Thereby obtaining an updated simplified expression of the correlation weights as shown in the following equation:
Figure BDA0003387059080000086
and for the updated simplified expression of the correlation weights, an effective sampling proportion ESS shown by the following formula is adopted to define the degradation degree of the particle filter adopted in the particle filtering method:
Figure BDA0003387059080000087
when effective sampling ratio ESS is lower than threshold NTAnd a resampling method is adopted to solve the problem of particle degradation.
The particle filter estimation of the source item parameters actually converts source item information into a point estimation of particles, and on one hand, the point estimation can be used for carrying out calculation based on a cognitive search strategy and calculation of a reward function from the perspective of data information, and also can be used for extracting information from the perspective of space. The Gaussian mixture model is a model capable of representing the overall distribution of particles in space, and source item information is fully acquired by fitting point estimation into a probability model with a plurality of Gaussian distributions to obtain definite parameters of source item estimation. Any posterior probability density function PDF can be approximated by the density of the gaussian mixture model, so when reconstructing a probability estimation of a particle by using the gaussian mixture model in step 3) of this embodiment, the function expression of the posterior probability density function PDF of any k-th step approximated by the density of the gaussian mixture model is:
Figure BDA0003387059080000088
in the above formula, PG(theta) represents an approximate Gaussian mixture model probability density function, K represents the number of Gaussian distributions, and coefficient piiSatisfy sigma pii＝1，N(θ|μi,Σi) Representing covariance arrays sigma with a gaussian distributioniGaussian distribution of (u)iIs mean value, ΣiIs a Gaussian distribution covariance array; assuming that the distribution of the sampled particles is approximately PG(θ), introducing a hidden variable γ, which is a binary random variable of K dimensions, wherein among K values of the hidden variable γ, only one specific element γ (K) is 1, and the other elements are 0, so as to determine which gaussian model hidden variable in the gaussian mixture model is sampled by the sample, and the corresponding log-likelihood function functional expression is:
Figure BDA0003387059080000091
in the above formula, L (pi)i,μi,Σi) As a maximum likelihood function, gammaiFor hiding the ith dimension, π, of the variable γkIs a Gaussian distribution coefficient, N (θ | μk,Σk) Representing covariance arrays sigma with a gaussian distributionk(ii) a gaussian distribution of; finally adopting maximum expectation algorithm EM to solve Gaussian mixtureEstimation of a weighted log-likelihood function of the model.
In this embodiment, the estimation of the weighted log-likelihood function of the gaussian mixture model by using the maximum expectation algorithm EM includes:
s1) setting initial parameters including random sample number N, gaussian distribution covariance array ΣkDistribution mean μkAnd the number of iterations mloop(ii) a Setting an initial cycle variable k and a cycle variable i to be 1;
s2) judging that the loop variable k is equal to the iteration number mloopIf the result is not true, skipping to the next step; if not, then,
s3) traverse the cyclic variable i from 1 to the random number of samples N and calculate a reference probability η (i, k) for each component:
Figure BDA0003387059080000092
in the above formula, N (θ (i) |. mu.)k,Σk) Representing covariance arrays sigma with a gaussian distributionk(ii) a gaussian distribution of; k represents the number of Gaussian distributions,. pikAnd pijAre all Gaussian distribution coefficients;
s4) calculating a mean value μ from the reference probability η (i, k) of each component based on the following equationkGaussian distribution covariance array sigmakGaussian coefficient of distribution pikAnd the value of the log-likelihood function lk；
Figure BDA0003387059080000093
Figure BDA0003387059080000094
Figure BDA0003387059080000095
lk＝lnL(πi,μi,Σi)，(15)
In the above formula, γ (i) represents a local weight;
s5) judging condition lk-lk-1Whether epsilon is less than or equal to epsilon or not is true, if not, jumping to execute the step S2); otherwise, the parameter mean value mu of the finally obtained Gaussian mixture modelkGaussian distribution covariance array sigmakGaussian coefficient of distribution pikAnd outputting as a result.
The probability distribution of the source term parameters is fitted to a plurality of gaussian distributions using a gaussian mixture model algorithm. However, it is necessary to consider how to use multiple gaussian distributed parameters to obtain an efficient search algorithm. After obtaining a plurality of probability models of gaussian distribution of the overall distribution, we can control the action of the robot according to the parameters of the mixed distribution. Each of the plurality of gaussian distributions has its own gaussian distribution parameter, and each gaussian distribution has its scaling factor in the overall distribution, and based on the parameters of the gaussian distributions and their scaling factors, we can determine that there is a higher probability that a source exists in a particular region. Exploring these areas requires the use of some commonly used search algorithms, while the robot updates the source item estimates in time based on the detected results, thus generating a new robot source search action scheme.
After obtaining multiple gaussian distributed parameters, we can use these parameters to determine a robot source search action scheme based on gaussian mixture distribution. In the gaussian mixture model, the gaussian distribution with the largest ratio of the dominant samples among all samples is defined as the largest effective gaussian distribution, i.e., the gaussian distribution with the largest ratio coefficient. We first search for the region where the maximum gaussian distribution is located, since the probability that this region is the region where the source location is located is the greatest. The average center position of the particle samples possessed by the maximum gaussian distribution is defined as the center of the region. After the center is determined, the robot is controlled to go to the center of the area to search. The center of the area is used as a search starting point, and a square search strategy is applied to search the whole area, as shown in fig. 2. When the collected information updates the Gaussian mixture model to generate a new maximum Gaussian distribution area, the square search mode is terminated, and a searcher goes to the center of the new area to search. Therefore, in this embodiment, step 4) includes: firstly, searching a region where the maximum Gaussian distribution is located, defining the average central position of particle samples owned by the maximum Gaussian distribution as the center of the region, and after determining the center, firstly controlling the robot to go to the center of the region for searching: and (3) searching the whole area by using the area center as a search starting point and applying a square search strategy, and terminating the square search mode when the collected information updates the Gaussian mixture model to generate a new maximum Gaussian distribution area, so that a searcher moves to the new area center to search.
Some parameters in the gaussian mixture model need to be preset in advance, and the number of the parameters such as gaussian distribution has an important influence on the generation of an action scheme, so that a monte carlo simulation experiment needs to be carried out to find the influence of the parameters of the gaussian mixture model on the robot source searching efficiency. In this embodiment, the adjusting of the optimal parameter of the gaussian mixture model in step 5) specifically means adjusting the optimal gaussian distribution number K. The initial parameter settings of the gaussian mixture model have an important influence on the result of the fitting. The number of gaussian distributions is particularly important, so that a large number of monte carlo experiments are performed to test parameters in the embodiment to select the optimal number K of gaussian distributions.
As shown in fig. 4, in this embodiment, 100 simulation experiments were performed under different gaussian distribution numbers K and source intensities Q, and the simulation parameters of the experiments are as follows: the value range Y of the coordinate Y is 10, the value range X of the coordinate X is 10, r0＝{6,6.5},r＝{0.5,0.5}，Q＝1,V＝1,a＝1τ＝250,D＝1,N＝3000,mloop1000. When the distance between the position of the autonomous searching robot and the source position is less than a certain value, namely Dis<0.5, indicating that the robot successfully found the source, the search terminates. Similarly, if the source location is not searched after 500 steps of searching, the searching fails. Experiments evaluate the effectiveness of the robot autonomous source search action scheme based on the Gaussian mixture model under different conditions. It was found that the performance of the course of action under all conditions is best when the number of gaussian distributions K has a value of 3.
In summary, the method of the present embodiment can provide an autonomous source search action scheme for various gas source search problems, and the method of the present embodiment models a source search process based on a cognitive search strategy and re-represents source item parameters by using a particle filtering method. In order to improve the operation efficiency, a Gaussian mixture model is introduced to process the result of the particle filter estimation, and the point estimation of the particles is fitted into a plurality of Gaussian distributions. According to the parameters of the Gaussian distribution, the scheme of robot autonomous source searching action based on the Gaussian mixture model is designed. Compared with the existing autonomous source searching scheme, the method greatly improves the algorithm efficiency and the source searching success rate, and has the advantages of wide applicable scenes, high searching efficiency and success rate and strong robustness under various source searching conditions.
In addition, the present embodiment also provides a device for generating a robot source search solution based on a gaussian mixture model, which includes a microprocessor and a memory connected to each other, where the microprocessor is programmed or configured to execute the steps of the method for generating a robot source search solution based on a gaussian mixture model.
Furthermore, the present embodiment also provides a computer-readable storage medium, in which a computer program programmed or configured to execute the aforementioned generation method of the robot source search scheme based on the gaussian mixture model is stored.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-readable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein. The present application is directed to methods, apparatus (systems), and computer program products according to embodiments of the application, wherein the instructions that execute via the flowcharts and/or processor of the computer program product create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks. These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may occur to those skilled in the art without departing from the principle of the invention, and are considered to be within the scope of the invention.

Claims (10)

1. A method for generating a robot source search scheme based on a Gaussian mixture model is characterized by comprising the following steps:
1) establishing a source searching process model and determining an estimation representation of a source item parameter;
2) aiming at a source search process model, representing probability estimation of source item parameters by using a particle filtering method;
3) reconstructing probability estimation of the particles by using a Gaussian mixture model;
4) determining an action scheme for searching autonomous sources of the control robot according to parameters of Gaussian distribution in the Gaussian mixture model;
5) and (5) carrying out numerical experiments and adjusting the optimal parameters of the Gaussian mixture model.
2. The method for generating the robot source search scheme based on the gaussian mixture model according to claim 1, wherein the source search process model established in step 1) is a partial observable markov decision process modeled as a source search process, and the functional expression of the source search process model is obtained as follows:
Figure FDA0003387059070000011
in the above formula, R (R | θ)0) Is the gas concentration at an arbitrary position r ═ { x, y } position, θ0＝{r0Q represents the source term parameter of the source, r0＝{x0,y0The position of the source in the two-dimensional search domain Ω, Q the diffusion intensity, a the spherical sensor radius, V the mean wind speed, D the effective diffusion coefficient of the gas, λ the intermediate variable, τ the lifetime of the gas molecules.
3. The method for generating the robot source search scheme based on the gaussian mixture model according to claim 2, wherein the estimation representation of the source item parameters determined in step 1) is an information state in a partial observable markov decision process, and a bayesian framework shown in the following formula is adopted to estimate and update the posterior probability density function PDF of any k step:
Figure FDA0003387059070000012
in the above formula, θkRepresenting the source term parameters of step k, D1:k＝{d1(r1),d2(r2),…,dk(rk) Is the accumulated information of the time step k, d1(r1),d2(r2),…,dk(rk) Are respectively at an arbitrary position r1～rkInformation obtained, P (theta)k-1|D1:k-1) As a posterior probability density function PDF, P (d) of step k-1k(rk)|θk) For the probability of induction measurement, P (d)k(rk)|D1:k-1) Is a weight of probability density, and P (d)k(rk)|D1:k-1) The formula of the calculation function is:
P(dk(rk)|D1:k-1)＝∫P(θk-1|D1:k-1)P(dk(rk)|θk)dθk， (3)
probability of induction measurement P (d)k(rk)|θk) The formula of the calculation function is:
Figure FDA0003387059070000013
in the above formula, P (d | θ)0) Is the probability of contacting a gas molecule d times per unit time.
4. The method for generating the robot source search scheme based on the gaussian mixture model according to claim 3, wherein the step 2) of representing the probability estimation of the source parameter by using the particle filtering method specifically means that the probability estimation of the source parameter is realized by using a sequential monte carlo framework and the particle filtering method, and the specific steps include: generating PDF with a posterior probability density function by sampling any k-th step
Figure FDA0003387059070000021
N random samples of the weights, wherein,
Figure FDA0003387059070000022
represents an estimate of the parameters of the source item,
Figure FDA0003387059070000023
is the associated weight, and the sum of the weights of the N random samples is 1, thereby expressing the posterior probability density function PDF of any k-th step as:
Figure FDA0003387059070000024
in the above equation, θ is the source term estimate,
Figure FDA0003387059070000025
is a dirac function;
sampling from the proposed distribution to approximate the a posteriori probability density function PDF of any k-th step using a sequential importance sampling method using a sequential monte carlo framework, whereby the update of the a posteriori probability density function PDF of any k-th step is converted to an update of the associated weights as shown by:
Figure FDA0003387059070000026
in the above formula, the first and second carbon atoms are,
Figure FDA0003387059070000027
is the non-normalized weight of the particle,
Figure FDA0003387059070000028
in order to be the probability of a state transition,
Figure FDA0003387059070000029
can be obtained from the formula (4) below,
Figure FDA00033870590700000210
an importance function in the importance sampling principle;
presume q (θ) assuming that the source term parameters remain unchanged during the source search processk)＝P(θk-1|D1:k-1) Thereby obtaining an updated simplified expression of the correlation weights as shown in the following equation:
Figure FDA00033870590700000211
and for the updated simplified expression of the correlation weights, an effective sampling proportion ESS shown by the following formula is adopted to define the degradation degree of the particle filter adopted in the particle filtering method:
Figure FDA00033870590700000212
when effective sampling ratio ESS is lower than threshold NTAnd a resampling method is adopted to solve the problem of particle degradation.
5. The method for generating a robot source search solution based on gaussian mixture model according to claim 4, wherein when reconstructing probability estimation of particles using gaussian mixture model in step 3), the function expression of the posterior probability density function PDF for any k-th step approximated by the density of gaussian mixture model is:
Figure FDA0003387059070000031
in the above formula, PG(theta) represents an approximate Gaussian mixture model probability density function, K represents the number of Gaussian distributions, and coefficient piiSatisfy sigma pii＝1，N(θ|μi,Σi) Representing covariance arrays sigma with a gaussian distributioniGaussian distribution of (u)iIs mean value, ΣiIs a Gaussian distribution covariance array; assuming that the distribution of the sampled particles is approximately PG(θ), introducing a hidden variable γ, which is a binary random variable of K dimensions, wherein among K values of the hidden variable γ, only one specific element γ (K) is 1, and the other elements are 0, so as to determine which gaussian model hidden variable in the gaussian mixture model is sampled by the sample, and the corresponding log-likelihood function functional expression is:
Figure FDA0003387059070000032
in the above formula, L (pi)i,μi,Σi) As a maximum likelihood function, gammaiFor hiding the ith dimension, π, of the variable γkIs a Gaussian distribution coefficient, N (θ | μk,Σk) Representing covariance arrays sigma with a gaussian distributionk(ii) a gaussian distribution of; and finally, solving the estimation of the weighted log-likelihood function of the Gaussian mixture model by adopting a maximum expectation algorithm EM.
6. The method for generating the Gaussian mixture model-based robot source search scheme according to claim 5, wherein the solving the estimation of the weighted log-likelihood function of the Gaussian mixture model by using the maximum expectation algorithm EM comprises:
s1) setting initial parameters including random sample number N, gaussian distribution covariance array ΣkDistribution mean μkAnd the number of iterations mloop(ii) a Setting an initial cycle variable k and a cycle variable i to be 1;
s2) judging that the loop variable k is equal to the iteration number mloopIf the result is not true, skipping to the next step; if not, then,
s3) traverse the cyclic variable i from 1 to the random number of samples N and calculate a reference probability η (i, k) for each component:
Figure FDA0003387059070000033
in the above formula, N (θ (i) |. mu.)k,Σk) Representing covariance arrays sigma with a gaussian distributionk(ii) a gaussian distribution of; k represents the number of Gaussian distributions,. pikAnd pijAre all Gaussian distribution coefficients;
s4) calculating a mean value μ from the reference probability η (i, k) of each component based on the following equationkGaussian distribution covariance array sigmakGaussian coefficient of distribution pikAnd the value of the log-likelihood function lk；
Figure FDA0003387059070000041
Figure FDA0003387059070000042
Figure FDA0003387059070000043
lk＝lnL(πi,μi,Σi)， (15)
In the above formula, γ (i) represents a local weight;
s5) judging condition lk-lk-1Whether epsilon is less than or equal to epsilon or not is true, if not, jumping to execute the step S2); otherwise, the parameter mean value mu of the finally obtained Gaussian mixture modelkGaussian distribution covariance array sigmakGaussian coefficient of distribution pikAnd outputting as a result.
7. The generation method of the robot source search scheme based on the Gaussian mixture model according to claim 6, wherein the step 4) comprises: firstly, searching a region where the maximum Gaussian distribution is located, defining the average central position of particle samples owned by the maximum Gaussian distribution as the center of the region, and after determining the center, firstly controlling the robot to go to the center of the region for searching: and (3) searching the whole area by using the area center as a search starting point and applying a square search strategy, and terminating the square search mode when the collected information updates the Gaussian mixture model to generate a new maximum Gaussian distribution area, so that a searcher moves to the new area center to search.
8. The method for generating a robot-source search solution based on gaussian mixture model as claimed in claim 7, wherein the adjusting of the optimal parameters of the gaussian mixture model in step 5) is to adjust the optimal number of gaussian distributions K.
9. An apparatus for generating a robot-derived search solution based on Gaussian mixture model, comprising a microprocessor and a memory connected to each other, wherein the microprocessor is programmed or configured to execute the steps of the method for generating a robot-derived search solution based on Gaussian mixture model according to any one of claims 1 to 8.
10. A computer-readable storage medium, wherein a computer program is stored in the computer-readable storage medium, the computer program being programmed or configured to perform the method for generating a gaussian mixture model based robot source search solution according to any one of claims 1 to 8.
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