CN110514567B - Gas source searching method based on information entropy - Google Patents

Gas source searching method based on information entropy Download PDF

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CN110514567B
CN110514567B CN201910802556.5A CN201910802556A CN110514567B CN 110514567 B CN110514567 B CN 110514567B CN 201910802556 A CN201910802556 A CN 201910802556A CN 110514567 B CN110514567 B CN 110514567B
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王伟东
杜志江
王艺博
朱洪彪
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Harbin Institute of Technology
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Abstract

A gas source searching method based on information entropy relates to the field of gas source searching. The method aims to solve the problem that existing research for carrying out gas source positioning search by utilizing information retrieval or information entropy theory does not consider the existence of obstacles and the influence of the obstacles on the source searching effect. Firstly, initializing coordinates, and finding smoke plume information through Z-shaped search by a robot; sampling multidimensional particles according to the initialization parameters, calculating and distributing the weight of the particles according to gas concentration data measured by a gas sensor, and then resampling; and judging the convergence condition of the particles, if the convergence condition is reached, estimating the position information of the gas source according to the convergence result, otherwise, calculating the next target pose of the robot according to the improved entropy scoring target function and the search area edge target point planning algorithm, updating the particle state after new sensor measurement data is obtained, and resampling the particles. The method is mainly used for gas source searching.

Description

Gas source searching method based on information entropy
Technical Field
The invention relates to a gas source searching method. Belongs to the field of gas source searching.
Background
Aiming at the problem of gas source searching, the existing research is mainly divided into a gas source positioning method based on biological inspiration and a gas source positioning method based on Bayes, and the two source searching methods are simply summarized and compared in table 1.
TABLE 1 comparison of the biological inspiration method with the Bayesian method
Figure BDA0002182739300000011
Gas source localization methods based on biological inspiration appear earlier than gas source localization methods based on bayesian. The chemical concentration distribution of the detected space gas is required to be higher by a single chemical tendency algorithm or a wind tendency algorithm: when the gas is weak, the concentration gradient is small and has certain randomness, so that the failure of a source searching algorithm is easily caused; when the detected gas is greatly influenced by medium-high intensity turbulence, the wind direction and the concentration of the airflow are unstable, and the probability of misjudgment of the source searching direction is increased. The method for positioning the biological inspiration gas source is improved by combining chemical tendency and wind tendency for use, plays a certain improvement role in effect, even if the effect is improved, the method cannot be well adapted to the conditions of strong turbulence and variable wind direction, and is easy to lose targets.
The Bayesian-based source search algorithm is more complex than the biological inspiration-based gas source positioning algorithm, has a certain adaptive effect on turbulence, intermittent and discontinuous gas flow due to the introduction of the probability theory, further improves the source searching robustness due to the appearance of the gas source information retrieval theory, is expensive to calculate, is complex in algorithm design and implementation, and is not ideal in implementation effect compared with a simple reactivity strategy (a traditional biological inspiration-based gas source positioning method) in a simple scene with small turbulence effect, stable concentration distribution and obvious concentration gradient, and the source search algorithm is mainly applied to a complex environment in order to fully exert the advantages of information theories such as information retrieval and the like.
The existing research for carrying out gas source positioning search by utilizing information retrieval or information entropy theory does not consider the existence of obstacles, but the obstacles generally exist in a source searching scene and the influence of the obstacles on the source searching effect cannot be ignored.
Disclosure of Invention
The invention aims to solve the problem that the existing research for positioning and searching the gas source by utilizing the information retrieval or information entropy theory does not consider the existence of obstacles and the influence of the obstacles on the source searching effect.
The gas source searching method based on the information entropy comprises the following steps:
setting the initial coordinate system of the robot to coincide with the coordinate system of the map and the coordinate system of the milemeter;
the robot finds the smoke plume information through Z-shaped search;
sampling multidimensional particles according to the initialization parameters, calculating and distributing the weight of the particles according to gas concentration data measured by a gas sensor, and then resampling;
judging the convergence condition of the particles, if the convergence condition is reached, estimating the position information of the gas source according to the convergence result, and otherwise, calculating the next target pose of the robot according to the improved entropy scoring target function and the search area edge target point planning algorithm;
the robot moves again according to the calculated target pose, the particle state is updated after new sensor measurement data are obtained, and the particles are resampled;
alternately iterating the particle filter algorithm and the information entropy algorithm to drive the robot to move, and estimating the state parameters of the gas source while searching the gas source;
in the process that the robot obtains new sensor measurement data according to the calculated target pose and then updates the particle state, the observation result generated by the current estimation state needs to be calculated according to a measurement model, wherein the measurement model of the sensor is as follows:
Figure BDA0002182739300000021
Figure BDA0002182739300000022
Figure BDA0002182739300000023
in the formula (I), the compound is shown in the specification,
Figure BDA0002182739300000024
representing the state vector, p, of the gas sourcekIs the position of the robot, i.e. the sensor coordinate, psIs the gas source position, C (p)k|Γs) Representing a known state vector ΓsIn case of (2) pkAverage concentration of gas at a location, λ and β being intermediate amounts; (x)s,ys) Representing gas source coordinates, (x)k,yk) Denotes the robot coordinate, rsIn order to be the rate of release of the gas,Dsindicates the effective diffusion rate, vsWhich is indicative of the wind speed,
Figure BDA0002182739300000025
indicating the wind direction, τsThe output concentration of the gas sensor is expressed by mass concentration for the lifetime of the gas particles.
Further, the process of finding the smoke plume information through the zigzag search by the robot is as follows:
the robot reads the information of the wind speed and wind direction sensor and carries out Z-shaped search in the upwind direction at a certain angle with the wind direction, when the output data of the gas sensor is higher than a set data threshold value, smoke plume is considered to be found, and the pose of the robot at the moment is recorded as XRnORnYRnAnd establishing a search coordinate system X by taking the pose as a centerSOSYSThe search area is set to be square, the side length is set manually, and the search area is required to contain a gas source;
the relationship between the search coordinate system and the world coordinate system can be expressed as the following formula:
Figure BDA0002182739300000031
Figure BDA0002182739300000032
in the formula, the first step is that,Rnp andSp respectively represents the pose of the robot under the searching coordinate system when the robot finds the smoke plume and after the robot finds the smoke plume,
Figure BDA0002182739300000033
and
Figure BDA0002182739300000034
respectively representing pose transformation matrixes between a search coordinate system and a world coordinate system when the robot finds the smoke plume and after the robot finds the smoke plume,
Figure BDA0002182739300000035
andWp respectively represents the pose of the robot in a world coordinate system when the smoke plume is found and after the smoke plume is found; and the pose under the world coordinate system is used for providing a target for the navigation module and guiding the robot to move.
Furthermore, the process of sampling the multidimensional particles according to the initialization parameters, calculating and distributing the weight of the particles according to the gas concentration data measured by the gas sensor and then resampling comprises the following steps:
the gas source searching algorithm is implemented in a searching area, multidimensional particles are sampled according to initialization parameters, the particles are resampled after the weights of the particles are calculated and distributed according to gas concentration data measured by a gas sensor, and regular particle filtering is used for passing
Figure BDA0002182739300000036
Updating the particles;
Figure BDA0002182739300000037
a source parameter vector representing an estimate from the ith particle at time k; a. thekA transformation matrix at time k; h isoptTo an optimal kernel width; e is a natural constant;
and determining whether to accept the transfer of the particles by M-H sampling, sampling U-U [0,1], and judging whether to accept or reject the transfer by the following formula:
Figure BDA0002182739300000038
where α is the probability of acceptance, U is a random variable, and U is subject to a uniform distribution, i.e., U-U [0,1]]；Γs,kA source parameter vector representing the estimate at time k,
Figure BDA0002182739300000039
a source parameter vector representing an estimate from the ith particle at time k; z is a radical of1:k＝{z1,…,zkIs an observed value in particle filtering, zkIs the observed value at the time k; i tableShows the ith particle, i ∈ {1, …, N };
if u is less than or equal to alpha, then accept the move, let
Figure BDA00021827393000000310
If not, the mobile is refused to move,
Figure BDA00021827393000000311
Figure BDA00021827393000000312
k-1 in the subscript refers to the corresponding parameter from 0 to k-1;
Figure BDA00021827393000000313
the subscript 0: k refers to the parameters corresponding to time 0 to k.
Further, the process of determining the convergence condition of the particle includes the following steps:
judging the convergence condition of the particles, and setting the convergence condition of the particles as max (sigma)x,σy) Smaller than the set value, that is, the standard deviation of the particles in the x and y directions is required to be smaller than the set value;
if the gas source position information is converged, estimating a posterior probability density curve of the gas source position information according to the following two formulas to obtain the most probable position of the gas source, and finishing the gas source searching; otherwise, calculating the next target pose of the robot according to the improved entropy scoring target function and the search area edge target point planning algorithm;
Figure BDA0002182739300000041
Figure BDA0002182739300000042
in the formula (I), the compound is shown in the specification,
Figure BDA0002182739300000043
normalized weight carried by ith particle at time kWeighing; kh(x ') is a new kernel density function resulting from rescaling the kernel density K (·), x' representing the argument in the function; h denotes kernel bandwidth, n denotes dimension of state vector, S ═ AATRepresenting the covariance matrix of the particle system, A being the transformation matrix, ATIs the transpose of A.
Further, the process of calculating the next target pose of the robot according to the improved entropy scoring target function and the search area edge target point planning algorithm comprises the following steps:
improved entropy scoring objective function
Figure BDA0002182739300000044
Optimal movement direction corresponding to highest score
Figure BDA0002182739300000045
Respectively as follows:
Figure BDA0002182739300000046
Figure BDA0002182739300000047
wherein H (·) is the fragrance information entropy; alpha '> 0 and beta' > 0 respectively represent the weight of the two terms; j is a number of bits of 1,2,3,4,
Figure BDA0002182739300000048
4 movement directions which represent robot selectable; lambda [ alpha ]mRepresenting the step of movement, p representing the step multiple, p λmDenotes the search range, (ρ λ)m)-1Denotes ρ λmThe score of each of the repeated trajectory planning points within the range,
Figure BDA0002182739300000049
representing alternative planning points
Figure BDA00021827393000000410
NearbyRho lambda ofmThe number of repeat points within the range;
a calculation formula for obtaining the trajectory planning point of the robot which moves in the next step and falls in the search area based on the search area edge target point planning algorithm is shown as the following formula.
Figure BDA00021827393000000411
Wherein, [ x ]k yk θk]TAnd [ x ]k+1 yk+1 θk+1]TRespectively representing the pose of the robot before and after recursion, thetakRepresenting the current pose.
Has the advantages that:
1. the invention gives play to the advantages of information theories such as information retrieval and the like, and can adapt to complex environments with higher turbulence degree.
2. The invention adopts the fragrance concentration information entropy, improves the calculation speed, and can play a role in both the barrier environment and the barrier-free environment, thereby ensuring that the invention can obtain good source searching effect in both the barrier environment and the barrier-free environment.
3. The iterative position search algorithm based on the octree further improves the entropy scoring target function, and is beneficial to improving the efficiency of gas source searching.
4. The invention designs the planning algorithm of the target point at the edge of the search area based on the idea of the zigzag search algorithm, and improves the robustness of the source searching algorithm.
Drawings
FIG. 1 is a gas source search strategy flow diagram;
FIG. 2 is a schematic diagram of a repetitive planning point search;
FIG. 3 is a schematic diagram of the folding angle selection of the target point at the edge of the search area;
fig. 4 is a smoke plume information tracking simulation experiment track, where fig. 4(a) is a smoke plume tracking experiment track in an obstacle-free scene, and fig. 4(b) is a smoke plume tracking experiment track in an obstacle-containing scene.
Detailed Description
The first embodiment is as follows: the present embodiment is described in detail with reference to figure 1,
the invention relates to a gas source searching method based on information entropy, which can enable a mobile robot to automatically complete a gas source positioning searching task in an environment without obstacles and in an environment with obstacles.
The invention discloses a gas source searching method based on information entropy, which comprises the following steps:
coordinate initialization: setting the initial coordinate system of the robot to coincide with the coordinate system of the map and the coordinate system of the milemeter;
the robot finds the smoke plume information through Z-shaped search; sampling multidimensional particles according to the initialization parameters, calculating and distributing the weight of the particles according to gas concentration data measured by a gas sensor, and then resampling; judging the convergence condition of the particles, if the convergence condition is reached, estimating the position information of the gas source according to the convergence result, and otherwise, calculating the next target pose of the robot according to the improved entropy scoring target function and the search area edge target point planning algorithm; and the robot moves again according to the calculated target pose, and the state of the particles is updated after new sensor measurement data is obtained, so that the particles are resampled. And (3) alternately iterating the particle filter algorithm and the information entropy algorithm to drive the robot to move, and estimating the state parameters of the gas source while searching the gas source.
The design and implementation of the gas source positioning search algorithm need to derive the analytical solution of the diffusion equation on the basis of a fluid mechanics model with high complexity, and the gas source positioning search algorithm has the characteristic of high computational complexity. The simplified equation based on the atmospheric statistics is used, the gas distribution data can be calculated on line and efficiently, and the real gas distribution can be fitted more correctly under the short-range turbulence condition. The model can be represented as follows:
Figure BDA0002182739300000051
Figure BDA0002182739300000061
Figure BDA0002182739300000062
in the formula (I), the compound is shown in the specification,
Figure BDA0002182739300000063
representing the state vector, p, of the gas sourcekIs the position of the robot, i.e. the sensor coordinate, psIs the gas source position, C (p)k|Γs) Representing a known state vector ΓsIn case of (2) pkThe average concentration of the gas at the position, λ and β being intermediate amounts, as shown in equations (2) and (3), (x)s,ys) Representing gas source coordinates, (x)k,yk) Denotes the robot coordinate, rsTo the rate of gas release, DsIndicates the effective diffusion rate, vsWhich is indicative of the wind speed,
Figure BDA0002182739300000064
indicating the wind direction, τsThe output concentration of the gas sensor is expressed by mass concentration for the lifetime of the gas particles.
The gas source searching based on the information entropy is realized through the process. In order to more clearly express the process of the invention, the specific process of the gas source searching method based on the information entropy is as follows:
step 1, carrying out coordinate initialization:
and setting the initial coordinate system of the robot to be superposed with the map coordinate system and the odometer coordinate system.
Step 2, the robot finds the smoke plume information through Z-shaped search:
the robot reads the information of the wind speed and wind direction sensor and carries out Z-shaped search in the upwind direction at a certain angle with the wind direction, when the output data of the gas sensor is higher than a set data threshold value, smoke plume is considered to be found, and the pose of the robot at the moment is recorded as XRnORnYRnAnd establishing a search coordinate system X by taking the pose as a centerSOSYSThe search area is set to be square, the side length is set manually, andlarge enough so that the search area contains the gas source.
When the smoke plume is found, the relation between the search coordinate system and the world coordinate system can be expressed as formula (4); after the smoke plume is found, the relation between the coordinate system and the world coordinate system is searched and can be expressed as formula (5);
Figure BDA0002182739300000065
Figure BDA0002182739300000066
in the formula, the first step is that,Rnp andSp respectively represents the pose of the robot under the searching coordinate system when the robot finds the smoke plume and after the robot finds the smoke plume,
Figure BDA0002182739300000067
and
Figure BDA0002182739300000068
respectively representing pose transformation matrixes between a search coordinate system and a world coordinate system when the robot finds the smoke plume and after the robot finds the smoke plume,
Figure BDA0002182739300000069
andWp represents the pose of the robot in the world coordinate system when the smoke plume is found and after the smoke plume is found, respectively (when p is in the form of parameters, it represents the parameters related to the pose). And the pose under the world coordinate system is used for providing a target for the navigation module and guiding the robot to move.
Step 3, sampling and resampling the particles based on particle filtering:
initializing multidimensional particles, sampling according to initialization parameters, calculating and distributing particle weights according to gas concentration data measured by a gas sensor, and then resampling:
estimating the posterior probability distribution of the source parameter vector based on particle filtering can be expressed as:
Figure BDA0002182739300000071
in the formula, gammas,kA source parameter vector representing the estimate at time k,
Figure BDA0002182739300000072
a source parameter vector, z, representing the estimate from the ith particle at time k1:k＝{z1,…,zkIs observed value. Using i to represent the ith particle and i e {1, …, N },
Figure BDA0002182739300000073
normalized weight carried by the ith particle at time k, i.e.
Figure BDA0002182739300000074
δ (·) is the Dirac delta function. p (-) represents the probability.
To obtain
Figure BDA0002182739300000075
Using the Sequential Importance Sampling (Sequential Importance Sampling) algorithm, expressed as:
Figure BDA0002182739300000076
algorithm first samples
Figure BDA0002182739300000077
Figure BDA0002182739300000078
I.e. a series of new samples at time k,
Figure BDA0002182739300000079
can be distributed from importance
Figure BDA00021827393000000710
Is obtained, then the non-normalized particle weight is obtained
Figure BDA00021827393000000711
Is represented as follows:
Figure BDA00021827393000000712
the invention assumes a fixed gas source position to be estimated and a constant gas release rate, for any particle i e {1, …, N }, there is
Figure BDA00021827393000000713
The normalized particle weight can be reduced to:
Figure BDA00021827393000000714
the particle weight at the k moment depends on likelihood probability according to the above formula
Figure BDA00021827393000000715
And the weight of the particle at the last moment
Figure BDA00021827393000000716
To solve likelihood probability
Figure BDA00021827393000000717
The method includes the steps that a Poisson probability model is introduced, the model can represent the matching degree of expected counting rate and real measurement data of a sensor in unit time, the expected counting rate is obtained based on a sensor measurement model, and an observation result generated by calculating the current estimation state according to the measurement model is needed. The poisson probability model is as follows:
Figure BDA00021827393000000718
in the formula, λkFor desired count rates, characteriseThe average number of random events that a gas particle encounters a sensor per unit time,
Figure BDA0002182739300000081
t is the unit sampling time, R is the average frequency of the sensor encountering the gas particles, pkFor the position of the sensor, gammasIs a gas source state parameter. h iskIndicating that the sensor is at pkThe number of particles meeting at the position is the real measured value of the sensor.
The output of the used sensor is concentration value and has lambdak∝Ck，CkRepresents pkThe expected observed concentration of the position, in order to ensure uniform Poisson probability distribution dimension, lambda in the formula (10)kAnd hkAll using concentration units, and because of hk∈Z+Let us order
Figure BDA0002182739300000082
Figure BDA0002182739300000083
To round down, zkAn untrimmed concentration value output by the sensor. The likelihood probability calculation formula can be expressed as follows:
Figure BDA0002182739300000084
in the formula (I), the compound is shown in the specification,
Figure BDA0002182739300000085
indicating that the state particle i is at p at time kkThe expected value of the observed concentration at the site is calculated from equation (1).
The above-mentioned general particle filter algorithm may generate a particle degradation phenomenon, that is, after continuous iteration, part of the particle weights become so small that their roles in the posterior probability estimation are negligible. Meanwhile, the particles occupy a large amount of computing resources, greatly influence the estimated performance, and the effective particle number N is generally usedeffCharacterizing the degree of particle degradation:
Figure BDA0002182739300000086
when N is presenteffWhen the total number of the particles is smaller than the set threshold value, the sampled particles need to be resampled, and the basic idea is to keep the total number N of the particles unchanged, copy the particles with large weight, and discard the particles with low weight.
In order to reduce the influence of particle dissipation caused by resampling, a mode of combining regular particle filtering and M-H (Metropolis-Hastings) sampling is adopted. The regular particle filter introduces new samples through a Gaussian kernel, an M-H sampling algorithm compares the likelihood values of the new samples with the original likelihood values, and then the samples are accepted or rejected with a certain probability according to the comparison result, and the sampling efficiency is improved by the method.
The regular particle filter converts discrete approximate probability distribution obtained by the particle filter into continuous approximate probability distribution by performing nuclear density sampling on each particle, and the posterior probability distribution can be expressed as:
Figure BDA0002182739300000087
Figure BDA0002182739300000088
in the formula, Kh(x ') is a new kernel density function resulting from rescaling the kernel density K (·), x' representing the argument in the function; h represents the kernel bandwidth, and n represents the dimension of the state vector; s ═ AATRepresenting the covariance matrix of the particle system, A being the transformation matrix, ATIs the transpose of A. The kernel density function should be a symmetric probability density function, | K (x ') dx ═ 1 and | | | x' | | purple light2K (x ') dx' < ∞. Selecting a Gaussian kernel density function K (x ') -phi (x '), and phi (x ') as a standard normal probability density function, wherein the optimal kernel width is as follows:
Figure BDA0002182739300000091
wherein N is the number of particles.
Figure BDA0002182739300000092
The covariance matrix of (2) is as shown in equation (16):
Figure BDA0002182739300000093
in the formula, mukRepresenting the expected value of the source parameter at the k moment; a. thekIs the transformation matrix at time k. The formula for updating the particles using the regular particle filter is
Figure BDA0002182739300000094
In the formula ei～N(0,In) Where e is a natural constant, i refers to the ith particle; e.g. of the typei～N(0,In) Denotes eiObeying a normal distribution, InIs a random variable eiThe variance of (a);
M-H sampling uses regular particle filtering to update particles and not update state particles to compare likelihood probability value, and decides whether to accept particle transfer. Samples U through U [0,1], acceptance or rejection of a transfer is determined by the following equation:
Figure BDA0002182739300000095
in the formula, alpha is the acceptance probability, U is the random variable, and U obeys the uniform distribution, i.e. U-U0, 1;
if u is less than or equal to alpha, then accept the move, let
Figure BDA0002182739300000096
If not, the mobile is refused to move,
Figure BDA0002182739300000097
Figure BDA0002182739300000098
k-1 in the subscript refers to the corresponding parameter from 0 to k-1;
Figure BDA0002182739300000099
the subscript 0: k refers to the parameters corresponding to time 0 to k.
Step 4, judging the convergence condition of the particles, if the convergence condition exists, estimating the position information of the gas source according to the convergence result, finishing the gas source searching, otherwise, executing the step 5:
set the particle convergence condition to max (σ)x,σy) Less than the set value, i.e. the standard deviation of the particles in both x and y directions is required to be less than the set value. Since the particles can represent an estimate of the gas source state vector, the state vector posterior probability density distribution of the gas source can be estimated from equation (13) and equation (14) based on the particle convergence results, resulting in the most likely location of the gas source.
And 5, calculating the next target pose of the robot according to the improved entropy scoring target function and the search area edge target point planning algorithm:
the information entropy is used for describing the uncertainty of the information source, the larger the information entropy is, the larger the uncertainty of the information is, the more quickly the uncertainty of the information can be reduced by moving towards the maximum direction of the information entropy, the information gain is increased to the maximum extent, the posterior estimation becomes more definite, and the purpose of searching the source is achieved. The information entropy selects the aroma information entropy, and is favorable for improving the calculation speed of the algorithm compared with the traditional information divergence formula, namely the relative entropy.
Motion control set M under robot coordinate system is setk{ ↓, ←, ° } respectively represent the robot moves towards the front, back, left and right direction on the basis of the current pose, then the track recurrence formula is as follows:
Figure BDA0002182739300000101
in the formula (I), the compound is shown in the specification,[xkykθk]Tand [ x ]k+1yk+1θk+1]TRespectively representing the pose of the robot before and after recursion, using [ dxk+1dyk+ 1dθk+1]TIndicates the increment of robot motion generated by the new motion control command, theta epsilon [0 DEG, 360 deg ].
The motion increment corresponding to the motion control set may be expressed as follows:
Figure BDA0002182739300000102
in the formula (d)f、db、dl、drRepresents the increment of movement, λ, in forward, backward, left, and right movements, respectivelymRepresenting the motion step.
The basic formula of the entropy of the fragrance information can be expressed as:
Figure BDA0002182739300000103
in the formula, p (x)i) Denotes a random event X as XiThe probability of (c).
Finding the optimal motion direction corresponding to the maximum information entropy based on the information entropy algorithm can be expressed as:
Figure BDA0002182739300000104
Figure BDA0002182739300000105
in the formula, mk∈Mk，
Figure BDA0002182739300000106
Expressing the optimal moving direction, and after calculating and finding the optimal moving direction, generating a search coordinate system according to formula (18) and formula (19)The invention names the point as a track planning point
Figure BDA0002182739300000107
The position points needing to be calculated before the optimal motion direction is not obtained are named as alternative planning points
Figure BDA0002182739300000111
Z1:k＝{z1(p1),…,zk(pk) Denotes the robot from the trajectory planning point p at time 1 to k1Move to the trajectory planning point pkThe set of sensor measurement data in the process,
Figure BDA0002182739300000112
representing the hypothesis warp mkPosition of next step after movement
Figure BDA0002182739300000113
To estimate the measured sensor data
Figure BDA0002182739300000114
The data is unknown before the robot reaches the designated position, but the unknown data can be approximately presumed by using the current existing posterior probability distribution information obtained by particle filtering, and the derivation based on the total probability formula is represented as follows:
Figure BDA0002182739300000115
posterior probability distribution usage
Figure BDA0002182739300000116
Is approximately characterized, therefore
Figure BDA0002182739300000117
Corresponding to the likelihood probability in equation (11), p (Γ)s,k|Z1:k) Corresponding to the normalized particle weight, so one can obtain:
Figure BDA0002182739300000118
so far, H (m) in the formula (22)k) Can be calculated, and then the moving direction of the robot can be determined
Figure BDA0002182739300000119
The gas transmission is characterized by intermittence and discontinuity, so that a strong turbulent flow effect is easily generated in the transmission process, when the transmission distance is long, gas is sparse, the concentration gradient is small, gas accumulation and gas cavities can occur under the influence of obstacles, and the influence factors cause the robot to have an obvious repeated search phenomenon and seriously influence the source searching efficiency. Aiming at the problem, the invention provides an octree-based repeated position searching algorithm which is used for searching repeated points, and then an entropy scoring target function is further improved based on a repeated point searching quantity grading idea.
The time complexity of the octree algorithm is O (1), and the time complexity of simple cycle detection is O (n), so that the detection speed of repeated position points can be obviously improved based on the octree algorithm, and the effect is obviously improved when the number of motion steps of the robot is large. And setting octree nodes to represent the position data of the stored track planning points, wherein the position resolution depends on the tree structure resolution, the position points falling in the resolution small area are regarded as the same position point, and the times of repeated planning of the position in the existing track are mounted under the leaf nodes so as to realize repeated point detection.
Setting up
Figure BDA00021827393000001110
Showing 4 directions of motion that the robot can select,
Figure BDA00021827393000001111
for alternative planning points, the hypothetical warp is represented
Figure BDA00021827393000001112
Post-motion robot predictionLocation. Lambda [ alpha ]mRepresenting the step of movement, p representing the step multiple, p λmThe method and the device represent the search range, simultaneously select a plurality of search range indexes to jointly represent the repetition degree of the planning points near the candidate planning points, and the more the number of the repetition of the trajectory planning points in the close range is, the more the repetition degree is. Let rho be an Sρ，SρThe method is a set formed by a plurality of step-size multiples and used for representing a plurality of search ranges, and track planning points which are counted in a small range are not counted repeatedly in a larger range. The improved objective function is represented as follows:
Figure BDA0002182739300000121
object function characterization candidate planning points
Figure BDA0002182739300000122
The score of (2) is obtained by weighting two indexes of information entropy and repeated planning point number, alpha '> 0 and beta' > 0 respectively represent the weights of the two items, and because the two items of index scale degrees are inconsistent, each item is respectively normalized. In the second term, (ρ λ)m)-1Denotes ρ λmThe score of each of the repeated trajectory planning points within the range,
Figure BDA0002182739300000123
representing alternative planning points
Figure BDA0002182739300000124
Nearby ρ λmThe number of repeat points within the range,
Figure BDA0002182739300000125
is composed of
Figure BDA0002182739300000126
Nearby ρ λmThe total score of the repeating plan points within the range,
Figure BDA0002182739300000127
is composed of
Figure BDA0002182739300000128
The repeat plan point score of (1) contains all the selectable search scopes. A schematic diagram of the robot repeated planning point search obtained according to the improved objective function is shown in fig. 2, and the step length multiples are 0.4,2.0 and 4.0, respectively.
At this time, instead of the scoring function represented by the information entropy alone, the improved objective function (25) is used to find the optimal motion direction corresponding to the highest score, which can be represented as:
Figure BDA0002182739300000129
in the invention, after the robot finds the gas, a square search area is established by taking the pose of the robot at the moment as the center, the search area is large enough to contain the gas source, and a necessary assumption that the gas source is in the search area is established. Due to the badness of external conditions in the smoke plume information tracking process, in addition to repeated search of the region, the situation that the robot crosses the boundary of the search region can also occur, and the situation is mainly caused by the loss of smoke plumes. In order to deal with the loss condition of the smoke plume and improve the robustness of tracking the information of the smoke plume, the invention designs a planning algorithm of target points at the edge of a search area based on the idea of a zigzag search algorithm.
Setting search area
Figure BDA00021827393000001210
Current position point pk(x, y), next step trajectory planning point
Figure BDA00021827393000001211
Control instruction
Figure BDA00021827393000001212
Current attitude θkAngle of turn-back
Figure BDA00021827393000001213
Alternative set of reentrant angles
Figure BDA00021827393000001214
When in use
Figure BDA00021827393000001215
When the next step track planning point of the robot is judged to cross the boundary of the search area, the edge target point planning algorithm of the search area is operated to replace the next step track planning point
Figure BDA00021827393000001216
A schematic diagram of the edge target point folding angle selection is shown in fig. 3.
In order to ensure that the robot turns back correctly at the edge of the search area, the calculation process needs to be carried out
Figure BDA00021827393000001217
Make it
Figure BDA00021827393000001218
When the algorithm knows that the next track planning point can cross the boundary of the search area, firstly, the algorithm controls an instruction according to the motion of the robot
Figure BDA00021827393000001219
Judging the boundary crossing caused by the robot moving to any direction, and calculating to obtain
Figure BDA00021827393000001220
The positive direction of the X-axis of the robot is made to face the boundary, and different judgment standards are set according to which boundary the robot crosses to obtain
Figure BDA0002182739300000131
Optimum angle psi in*And the next movement direction of the robot is better towards the inside of the search area. At the output psi*On the basis, according to a track recursion formula, a track planning point of the next step of movement falling in a search area can be obtained, and a command is given
Figure BDA0002182739300000132
The calculation formula is as follows:
Figure BDA0002182739300000133
and 6, the robot moves again according to the calculated target pose, the particle state is updated after new sensor measurement data are obtained, the particles are resampled, and the step 3 is executed again.
The invention can enable the robot to gradually approach the gas source, thereby achieving the purpose of searching the gas source. The most important invention points are as follows:
1. the invention adopts the alternating iteration of the particle filter algorithm and the information entropy algorithm to drive the robot to approach the gas source, thereby exerting the advantages of the information theory.
2. Aiming at the problem of repeated search of the region, based on the classification concept of repeated point search quantity, the entropy scoring target function is further improved, and the efficiency of gas source searching is improved.
3. Aiming at the problem of smoke plume loss, the invention provides a target point planning algorithm for searching the edge of the area, and the robustness of the source searching algorithm is improved.
The invention has the following beneficial effects:
1. the invention gives play to the advantages of information theories such as information retrieval and the like, and can adapt to complex environments with higher turbulence degree.
2. The invention adopts the fragrance concentration information entropy, improves the calculation speed, and can play a role in both the barrier environment and the barrier-free environment, thereby ensuring that the invention can obtain good source searching effect in both the barrier environment and the barrier-free environment.
3. The iterative position search algorithm based on the octree further improves the entropy scoring target function, and is beneficial to improving the efficiency of gas source searching.
4. The invention designs the planning algorithm of the target point at the edge of the search area based on the idea of the zigzag search algorithm, and improves the robustness of the source searching algorithm.
Examples
The gas source searching strategy based on the information entropy takes a mobile robot as a carrier, the mobile robot has the functions of positioning, navigation and drawing, and carries a wind speed and wind direction integrated sensor, a gas sensor and a laser radar sensor, which are basic functions required by source searching. The source searching process can be summarized as a cyclic reciprocating process of algorithm calculation and robot movement, wherein the robot reads sensor data in each step of movement, then the robot moves again after the target pose of the next movement is calculated through the source searching algorithm, the robot gradually approaches to the gas source in the circulation until the particles converge, and the searching is finished after the most possible position of the gas source is obtained.
The experiment comprises the following specific steps:
step 1, carrying out coordinate initialization: and setting the initial coordinate system of the robot to be superposed with the map coordinate system and the odometer coordinate system.
And 2, finding the smoke plume information through Z-shaped search by the robot.
And 3, implementing a gas source searching algorithm in a searching area, sampling the multidimensional particles according to the initialization parameters, calculating and distributing the weight of the particles according to gas concentration data measured by the gas sensor, then resampling, and updating the particles by using regular particle filtering.
Step 4, judging the particle convergence condition, and setting the particle convergence condition as max (sigma)x,σy) Less than the set value, i.e. the standard deviation of the particles in both x and y directions is required to be less than the set value. And if the gas source is converged, estimating a posterior probability density curve of the gas source position information to obtain the most likely position of the gas source, and ending the gas source searching. Otherwise, step 5 is executed.
And 5, calculating the next target pose of the robot according to the improved entropy scoring target function and the search area edge target point planning algorithm.
And 6, the robot moves again according to the calculated target pose, the particle state is updated after new sensor measurement data are obtained, the particles are resampled, and the step 3 is executed again.
According to the above steps, a smoke plume information tracking simulation experiment is performed, and the trajectory of the robot is shown in fig. 4, wherein fig. 4(a) is a smoke plume tracking experiment trajectory in an obstacle-free scene, and fig. 4(b) is a smoke plume tracking experiment trajectory in an obstacle-containing scene. In the experiment, the robot coordinate is obtained by track recursion, the measured value of the robot sensor is obtained by gas field distribution calculation, the initial state of the particles is obtained by sampling in uniform distribution, then the particles in the state are regressed by a particle filter algorithm, and the robot is guided by an information entropy algorithm to move towards the direction with the highest entropy value score. The particle filter algorithm and the information entropy algorithm alternately drive the robot to move in an iterative mode, and the gas source state parameters are estimated while the gas source is positioned.

Claims (6)

1. The gas source searching method based on the information entropy is characterized by comprising the following steps of:
setting the initial coordinate system of the robot to coincide with the coordinate system of the map and the coordinate system of the milemeter;
the robot finds the smoke plume information through Z-shaped search;
sampling multidimensional particles according to the initialization parameters, calculating and distributing the weight of the particles according to gas concentration data measured by a gas sensor, and then resampling;
judging the convergence condition of the particles, if the convergence condition is reached, estimating the position information of the gas source according to the convergence result, and otherwise, calculating the next target pose of the robot according to the improved entropy scoring target function and the search area edge target point planning algorithm;
the robot moves again according to the calculated target pose, the particle state is updated after new sensor measurement data are obtained, and the particles are resampled;
alternately iterating the particle filter algorithm and the information entropy algorithm to drive the robot to move, and estimating the state parameters of the gas source while searching the gas source;
in the process that the robot obtains new sensor measurement data according to the calculated target pose and then updates the particle state, the observation result generated by the current estimation state needs to be calculated according to a measurement model, wherein the measurement model of the sensor is as follows:
Figure FDA0003247255300000011
Figure FDA0003247255300000012
Figure FDA0003247255300000013
in the formula (I), the compound is shown in the specification,
Figure FDA0003247255300000014
representing the state vector, p, of the gas sourcekIs the position of the robot, i.e. the sensor coordinate, psIs the gas source position, C (p)k|Γs) Representing a known state vector ΓsIn case of (2) pkAverage concentration of gas at a location, λ and β being intermediate amounts; (x)s,ys) Representing gas source coordinates, (x)k,yk) Denotes the robot coordinate, rsTo the rate of gas release, DsIndicates the effective diffusion rate, vsWhich is indicative of the wind speed,
Figure FDA0003247255300000015
indicating the wind direction, τsThe output concentration of the gas sensor is expressed by mass concentration for the lifetime of the gas particles.
2. An information entropy based gas source searching method according to claim 1, wherein the process of finding the smoke plume information through zigzag search by the robot is as follows:
the robot reads the information of the wind speed and wind direction sensor and carries out Z-shaped search in the upwind direction at a certain angle with the wind direction, when the output data of the gas sensor is higher than a set data threshold value, smoke plume is considered to be found, and the pose of the robot at the moment is recorded as XRnORnYRnAnd build with the pose as the centerVertical search coordinate system XSOSYSThe search area is set to be square, the side length is set manually, and the search area is required to contain a gas source;
the relationship between the search coordinate system and the world coordinate system can be expressed as the following formula:
Figure FDA0003247255300000021
Figure FDA0003247255300000022
in the formula, the first step is that,Rnp andSp respectively represents the pose of the robot under the searching coordinate system when the robot finds the smoke plume and after the robot finds the smoke plume,
Figure FDA0003247255300000023
and
Figure FDA0003247255300000024
respectively representing pose transformation matrixes between a search coordinate system and a world coordinate system when the robot finds the smoke plume and after the robot finds the smoke plume,
Figure FDA0003247255300000025
andWp respectively represents the pose of the robot in a world coordinate system when the smoke plume is found and after the smoke plume is found; and the pose under the world coordinate system is used for providing a target for the navigation module and guiding the robot to move.
3. An information entropy based gas source searching method according to claim 2, wherein the process of sampling the multidimensional particles according to initialization parameters, calculating and assigning particle weights according to gas concentration data measured by the gas sensor, and then resampling comprises the following steps:
the gas source searching algorithm is implemented in the searching region, and the multidimensional particles are initiallySampling the parameters, calculating and distributing particle weight according to gas concentration data measured by a gas sensor, then resampling, and passing through a regular particle filter
Figure FDA0003247255300000026
Updating the particles;
Figure FDA0003247255300000027
a source parameter vector representing an estimate from the ith particle at time k; a. thekA transformation matrix at time k; h isoptTo an optimal kernel width; e is a natural constant;
and determining whether to accept the transfer of the particles by M-H sampling, sampling U-U [0,1], and judging whether to accept or reject the transfer by the following formula:
Figure FDA0003247255300000028
where α is the probability of acceptance, U is a random variable, and U is subject to a uniform distribution, i.e., U-U [0,1]]；Γs,kA source parameter vector representing the estimate at time k,
Figure FDA0003247255300000029
a source parameter vector representing an estimate from the ith particle at time k; z is a radical of1:k＝{z1,…,zkIs an observed value in particle filtering, zkIs the observed value at the time k; i represents the ith particle, i belongs to {1, …, N }, and the symbol p () is a likelihood probability function calculation formula, and the concrete form is as follows:
Figure FDA00032472553000000210
wherein
Figure FDA0003247255300000031
Indicating that the state particle i is at time kpkThe resulting observed expected concentration value for the location,
if u is less than or equal to alpha, then accept the move, let
Figure FDA0003247255300000032
If not, the mobile is refused to move,
Figure FDA0003247255300000033
Figure FDA0003247255300000034
k-1 in the subscript refers to the corresponding parameter from 0 to k-1;
Figure FDA0003247255300000035
the subscript 0: k refers to the parameters corresponding to time 0 to k.
4. An information entropy based gas source searching method according to claim 3, wherein the process for judging the convergence condition of the particles comprises the following steps:
judging the convergence condition of the particles, and setting the convergence condition of the particles as max (sigma)x,σy) Smaller than the set value, that is, the standard deviation of the particles in the x and y directions is required to be smaller than the set value;
if the gas source position information is converged, estimating a posterior probability density curve of the gas source position information according to the following two formulas to obtain the most probable position of the gas source, and finishing the gas source searching; otherwise, calculating the next target pose of the robot according to the improved entropy scoring target function and the search area edge target point planning algorithm;
Figure FDA0003247255300000036
Figure FDA0003247255300000037
in the formula (I), the compound is shown in the specification,
Figure FDA0003247255300000038
the normalized weight carried by the ith particle at the moment k; kh(x') is a new kernel density function rescaled from kernel density K (·), symbol K () is a symmetric probability density function, which is required to satisfy × (x) dx ═ 1 and | | | x | | | red pigment2K (x) dx < ∞, x' represents the argument in the function; h denotes kernel bandwidth, n denotes dimension of state vector, S ═ AATRepresenting the covariance matrix of the particle system, A being the transformation matrix, ATIs the transpose of A.
5. An information entropy based gas source searching method according to claim 4, wherein the kernel density function is a symmetric probability density function.
6. An information entropy based gas source searching method according to claim 4 or 5, wherein the process of calculating the next target pose of the robot according to the improved entropy scoring target function and the search area edge target point planning algorithm comprises the following steps:
improved entropy scoring objective function
Figure FDA0003247255300000039
Optimal movement direction corresponding to highest score
Figure FDA00032472553000000310
Respectively as follows:
Figure FDA0003247255300000041
Figure FDA0003247255300000042
wherein H(. is the entropy of aroma information; alpha '> 0 and beta' > 0 respectively represent the weight of the two terms; j is a number of bits of 1,2,3,4,
Figure FDA0003247255300000043
4 movement directions which represent robot selectable; lambda [ alpha ]mRepresenting the step of movement, p representing the step multiple, p λmDenotes the search range, (ρ λ)m)-1Denotes ρ λmThe score of each of the repeated trajectory planning points within the range,
Figure FDA0003247255300000044
representing alternative planning points
Figure FDA0003247255300000045
Nearby ρ λmThe number of repeat points within the range;
the calculation formula for obtaining the trajectory planning point of the robot which moves in the next step and falls in the searching area based on the searching area edge target point planning algorithm is shown as the following formula,
Figure FDA0003247255300000046
wherein, [ x ]kykθk]TAnd [ x ]k+1yk+1θk+1]TRespectively representing the pose of the robot before and after recursion, thetakWhich represents the current posture of the user,
Figure FDA0003247255300000047
sign of occurrence theta*The range is [0 °,360 °) for the updated pose angle.
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