CN110068330B - Autonomous positioning method of robot based on ARMA model - Google Patents

Abstract

The invention provides a method for autonomous positioning of a robot based on an ARMA model, which uses an autoregressive moving average model (ARMA) to estimate parameters for data and states in a long-term changing environment of a map, and finally establishes the change and probability of the environment. A map model in the form of a grid; follow-up predictions are performed in the grid time domain of the established map model, and the prediction confidence is evaluated to obtain a predicted grid map with a prediction confidence label; finally, the Bayesian The rule fuses the real-time observation information into the predicted grid map, and obtains an updated environment map available for the robot. Under the map, the robot realizes autonomous long-term positioning in the changing environment in combination with the particle filter algorithm. Thus, the effect of high positioning accuracy and positioning robustness in the long-term changing environment of the robot is achieved.

Description

Autonomous positioning method of robot based on ARMA model

technical field

The invention relates to the field of robot technology, in particular to an autonomous positioning method of a robot in a long-term changing environment based on an ARMA model.

Background technique

The positioning problem has always been the core content of research in the field of autonomous mobile robots, and the performance at the positioning level will also greatly affect the performance of robot path planning, autonomous navigation and other tasks. In a static environment, the classical particle filter algorithm can be used to establish a static probability grid map, and on this basis, lidar and odometer can be used as sensors for autonomous positioning. However, in many practical scenarios in reality, the environment is often not static, but is affected by human daily actions and changes with certain rules. At this time, the classical particle filter algorithm is based on a static map, and often fails due to inaccurate prior map information due to changes in the environment. For example, the cars entering and leaving the parking lot, the people coming and going, the goods being picked and transported in the industrial workshop, etc., will affect the positioning effect of the particle filter through changes in the environment.

There is a positioning algorithm based on the dynamic positioning capability matrix in foreign countries, and it has been tested in a dynamic environment with large traffic such as subway stations and campus restaurants, which verifies the effectiveness of the algorithm. However, the above methods are still based on the assumption that the environment in which the robot is located is static, which makes such methods no longer applicable when the environment changes for a long time.

For the existence of positioning by combining the temporary map and the static map, when the environmental information does not match the map information, a temporary map will be created according to the current observation information and used as the basis for positioning matching; and when the environmental information matches the map information , the temporary map will be released, and the static map will be used for positioning and matching. Although this modeling method takes into account the impact of environmental changes on positioning and corrects it through temporary maps, when the environment undergoes structural and large-scale changes, the static map will completely fail, and long-term reliance on temporary map positioning cannot guarantee positioning. Long-term robustness of the algorithm.

For models using dynamic probability grid maps, the matching score is calculated by scan-matching, and real-time map updates are performed on the basis of static maps. When the matching score is greater than the set threshold and the environment change is detected, the map is updated to obtain a map that is more consistent with the current real environment and improve the robustness of positioning. This algorithm also has the same problem. When the environmental change is quite different from the static map in advance, the matching degree between the observation information and the map information is too poor, so that the current positioning information feedback of the robot cannot be obtained, resulting in the failure of the update of the static map.

Foreign scholars believe that many daily activities of human beings are periodic, and there are certain rules to follow. They define the unknown environmental change process as a periodic function, and use the frequency spectrum to model the spatial and temporal changes of the environment. At the same time, the time domain is converted into the frequency domain, which can efficiently identify, analyze and save the regular environmental change process. In this way, the robot can predict the state of the environment after the model is established, thereby helping the robot to achieve long-term positioning. The disadvantage of this method is that from the method level, it needs to assume that the environmental characteristics have strong periodicity, and the modeling process is relatively complicated.

Based on the work of the predecessors, the present invention innovatively proposes an algorithm that can predict and update the map by modeling the environment in a long-term changing environment, thereby realizing the long-term positioning of the robot.

SUMMARY OF THE INVENTION

In view of the defects in the prior art, the purpose of the present invention is to provide an autonomous positioning method of a robot based on an ARMA model.

A kind of autonomous positioning method of robot based on ARMA model implementation provided according to the present invention, comprises the following steps:

Step 1: Environment modeling step: use the sensors carried by the robot to collect map data, and perform parameter estimation and modeling on the map data through the autoregressive moving average model ARMA to obtain a map model.

Step 2: Map prediction step: use the map model to predict the grid in the time domain, evaluate the prediction confidence, and obtain a grid map with a prediction confidence label.

Step 3: Map update step: According to the deviation between the grid map and the actual map, the Bayesian rule is used to integrate the real-time observation information into the prediction information, and perform real-time map update to obtain an updated map.

Step 4: Autonomous positioning step: Based on the updated map, particle filtering is used to realize the autonomous long-term positioning of the robot.

Preferably, the environment modeling step includes:

Model order determination step: determine the first parameter p and the second parameter q of the ARMA model according to the environmental characteristics, the first parameter p represents the state correlation of the physical environment feature state in time, and the second parameter q represents the map prediction The serial correlation of the state error term on the time series;

Parameter estimation step: Based on the first parameter p and the second parameter q of the ARMA model, the third parameter (α, β) is estimated, and the third parameter (α, β) represents the grid state before and after in the time domain State relationship, where ^α∈Rp and ^β∈Rq .

Preferably, the environment modeling step further includes:

迭代求出σ²的最小二乘估计，即

将

代入

得到A(0,0),A(0,1),A(1,1),……A(P,P)，则有

其中i表示地图数据中栅格的第i行，j表示地图数据中栅格的第j列，下标T表示样本个数，

表示在第i行第j列的第T个样本，σ²表示最小二乘估计的值，k表示地图数据中栅格的第k行，

表示第k行第j列的栅格样本的最小二乘估计值，

表示栅格样本的均值，

表示栅格样本最小二乘估计的回归系数a，

表示栅格样本最小二乘估计的回归系数b，n表示时间序列的总数，

表示第k行第j列的栅格样本的AIC准则值，A(p,q)表示模型定阶确定的p和q的值所对应的AIC准则值。Modeling step: Select the common upper bound P value of the first parameter p and the second parameter q, that is, 0≤p≤P and 0≤q≤P;

Iteratively find the least squares estimate of ^σ2 , that is

Will

substitute

Get A(0,0), A(0,1), A(1,1),...A(P,P), then we have

where i represents the ith row of the grid in the map data, j represents the jth column of the grid in the map data, and the subscript T represents the number of samples,

represents the T-th sample at the i-th row and the j-th column, σ ² represents the least squares estimated value, k represents the k-th row of the raster in the map data,

represents the least squares estimate of the raster sample at row k and column j,

represents the mean of the raster samples,

represents the regression coefficient a of the raster sample least squares estimate,

represents the regression coefficient b of the raster sample least squares estimate, n represents the total number of time series,

Represents the AIC criterion value of the grid sample in the kth row and the jth column, and A(p,q) indicates the AIC criterion value corresponding to the values of p and q determined by the model order.

Preferably, the parameter estimation step includes:

作高阶自回归滑动模型AR(p)的拟合；Fitting Step: Using the Number of Raster Samples

Fit the high-order autoregressive sliding model AR(p);

即Recursive step: recursively calculate the residual sequence

which is

t=P+1,P+2,…T

作为独立序列，利用线性回归模型：Regression step: convert the residual sequence

As independent series, use a linear regression model:

The third parameter representation is obtained as follows:

表示状态误差；

表示p时刻栅格在ARMA模型下的回归参数；α_i表示ARMA模型的回归参数；β_j表示ARMA模型的误差滑动参数；Z′表示Z的转置，

表示

的转置，

表示概率栅格地图的状态值；The subscript t represents the sampling time series, t=P+1, P+2,...T;

Indicates state error;

Represents the regression parameter of the grid at time p under the ARMA model; α _i represents the regression parameter of the ARMA model; β _j represents the error sliding parameter of the ARMA model; Z′ represents the transposition of Z,

express

transpose of ,

Represents the state value of the probability raster map;

Model replacement step: set the model parameter detection, when the parameter change is greater than the set threshold, the model is replaced, that is

S=|p ₁ -p ₂ |+|q ₁ -q ₂ |>S _th

其中下标为1和2分别代表计算的两组参数模型；当其阶数差值或者参数大于设定值后认为模型发生改变，用当前模型参数替换前模型参数。

The subscripts 1 and 2 respectively represent the two groups of parameter models calculated; when the order difference or the parameter is greater than the set value, the model is considered to have changed, and the current model parameters are used to replace the previous model parameters.

Preferably, the map prediction step includes:

State prediction step: use the existing map data to predict the grid in the time domain, obtain the grid state of each grid at time t, and obtain the entire predicted grid map.

Confidence evaluation step: Determine the prediction confidence of each grid state by comparing the predicted state with the actual observation state, assign the initial confidence before each confidence evaluation, and then compare the real map state obtained through the database update. Get the final prediction confidence. The final output is a raster map with prediction confidence labels.

Preferably, the map updating step includes:

Introducing steps: Introducing a positioning capability matrix to measure the reliability at different locations;

Normalization step: find the determinant of the positioning capability matrix and normalize it to obtain m ₂ , where m ₂ reflects the reliability of the data corresponding to different positions on the map; the corrected matching degree is used as the judgment of valid observation data standard, namely:

m=λm ₁ +(1-λ)m ₂

Among them, λ is the observation weight item, which indicates the feasibility of the observation matching. The larger the value of λ, the larger the proportion of the observation matching in the calculation weight of the entire matching degree; m indicates the matching between the revised map and the observation data. m ₁ represents the matching degree between the map and the observed data, and m ₂ represents the reliability of the data corresponding to different positions on the map; when m is greater than the set threshold, that is, m > m _th , the observed data is defined as valid , so that m is regarded as reliable data.

Preferably, the map updating step includes:

Data fusion steps: apply Bayesian rule for data fusion, integrate long-term prediction information and short-term observation information, and obtain real-time and accurate maps; use dynamic probability grid maps as the form of map data storage, use HMMs as the basic model, and integrate The confidence in the long-term information is used as a weight item to update the state to obtain the state vector at time t+1. The fusion formula is as follows:

是预测状态，B_z是观测信息，η是归一化因子,I是单位矩阵；下标t表示时间序列t，下标k表示地图栅格的第k行，下标c表示矩阵，下标z表示观测where Q _t is the map grid state output after fusing the data, A _c is the state transition matrix, G is the prediction confidence,

is the prediction state, B _z is the observation information, η is the normalization factor, and I is the identity matrix; the subscript t represents the time series t, the subscript k represents the kth row of the map grid, the subscript c represents the matrix, and the subscript z stands for observation

In the autonomous positioning step, after obtaining the dynamic map updated in real time, combined with the dynamic positioning capability, the dynamic attributes in the environment that have not been updated to the map are evaluated, and the particle filtering algorithm based on the positioning capability is used to realize the autonomous long-term positioning of the robot.

Preferably, the environment modeling step is in an offline form, and the map prediction step and the map updating step are in an online form.

Preferably, the model order determination step adopts AIC criterion to determine, and the parameter estimation step adopts autoregressive approximation.

Compared with the prior art, the present invention has the following beneficial effects:

It can make the robot have good positioning accuracy and positioning robustness in the long-term changing environment.

Description of drawings

Other features, objects and advantages of the present invention will become more apparent by reading the detailed description of non-limiting embodiments with reference to the following drawings:

FIG. 1 is a flow chart of the method of the present invention.

Detailed ways

The present invention will be described in detail below with reference to specific embodiments. The following examples will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that, for those skilled in the art, several changes and improvements can be made without departing from the inventive concept. These all belong to the protection scope of the present invention.

Aiming at the shortcomings of the original technology, this paper innovatively proposes an autonomous positioning method for robots based on the ARMA model, which is suitable for the autonomous positioning of robots in long-term changing environments.

The autonomous positioning method of the robot in the long-term changing environment based on the ARMA model proposed by the present invention mainly includes the following steps:

Step 1: Modeling, use the sensors carried by the robot to collect map data, and perform parameter estimation and modeling on the map data through an autoregressive moving average model (ARMA).

Step 2: Predict, use the established model to predict the grid in the time domain, evaluate the prediction confidence, and finally output a grid map with the prediction confidence label.

Step 3: Update, in view of the deviation between the predicted map and the actual map caused by some uncertain factors, the Bayesian rule is used to integrate the real-time observation information into the predicted information, and the real-time map update is performed as a priori for particle filter positioning. Map basis. Autonomous long-term localization of robots using particle filter algorithm.

Specifically, the modeling process of step 1 mainly includes the following steps:

Step 1.1: Determine the order of the model. Before the ARMA model is established, the parameters p and q of the model should be determined. The parameter p represents the state correlation of the physical environment feature state in time, and the parameter q represents the correlation of the map prediction state error term in the time series. For the i-th row, j-th column of the raster in the map, the modeling process is as follows:

Step 1.1.1 Select the common upper bound P value of order p and q, that is, 0≤p, q≤P

迭代求出σ²的最小二乘估计，即Step 1.1.2 by the number of samples

Iteratively find the least squares estimate of ^σ2 , that is

代入

得到A(0,0),A(0,1),A(1,1),……A(P,P)，则有Step 1.1.3 will

substitute

Get A(0,0), A(0,1), A(1,1),...A(P,P), then we have

Then p and q are the required model order at this time.

Step 1.2: Parameter estimation, when the parameters p and q of the autoregressive moving average model are available, the parameters of the model need to be estimated. The parameters to be determined here are α and β, where α∈R ^p , β∈R ^q , and the physical meaning of the representation is the relationship between the state before and after the grid state in the time domain. The parameter estimation adopts the method of autoregressive approximation, and the specific steps are as follows:

作高阶自回归滑动模型AR(p)的拟合Step 1.2.1 First utilize raster raw data

Fitting the higher-order autoregressive sliding model AR(p)

即Step 1.2.2 Calculate the residual sequence recursively from the above estimated AR(p) model

which is

t=P+1,P+2,…T

为独立序列，利用线性回归模型：Step 1.2.3 put the residual column

For independent series, use a linear regression model:

where t=P+1,P+2,…T

As a result, the estimated parameter representation is as follows:

in,

Considering the change of the environmental model, it is necessary to set the model parameter detection. When the parameter change is greater than a certain threshold, the model is replaced, that is,

S=|p ₁ -p ₂ |+|q ₁ -q ₂ |>S _th

其中下标为1和2分别代表计算的两组参数模型。当其阶数差值或者参数大于设定值后都认为模型发生改变，用当前模型参数替换前模型参数。

The subscripts 1 and 2 represent the calculated two sets of parameter models, respectively. When the order difference or the parameter is greater than the set value, it is considered that the model has changed, and the previous model parameters are replaced with the current model parameters.

Specifically, the prediction process of step 2 mainly includes the following steps:

Step 2.1: State prediction, use the existing map data to predict the grid in the time domain, so that the grid state of each grid at time t can be obtained, so that the entire predicted grid map can be obtained.

Step 2.2: Confidence evaluation. After the grid state is predicted, the prediction confidence needs to be evaluated to measure the accuracy of each grid prediction. The prediction confidence of each grid state is determined by comparing the predicted state with the actual observation state. Before each confidence evaluation, it will be given an initial confidence, and then compared with the real map state obtained through the database update. Get the final prediction confidence. The final output is a raster map with prediction confidence labels.

Specifically, the update process of step 3 mainly includes the following steps:

Step 3.1: Introduce a positioning capability matrix to measure the credibility of different locations

Step 3.2: Calculate the determinant of the positioning capability matrix and normalize it to obtain m ₂ , which reflects the reliability of the data corresponding to different positions on the map. The corrected matching degree is used as the criterion for valid observation data, namely:

m=λm ₁ +(1-λ)m ₂

Among them, λ is the observation weight item, and its value represents the feasibility of the observation matching. The larger the value, the larger the proportion of the observation matching in the calculation weight of the entire matching degree. Only when m is equal to the set threshold, that is, m>m _th , the observed data is considered to be valid, and thus it is regarded as reliable data.

Step 3.3 Apply Bayesian rule for data fusion, fuse long-term prediction information with short-term observation information, and obtain real-time and accurate maps. Use dynamic probabilistic raster maps as the form of map data storage, and use HMMs as its basic model. At the same time, the confidence in the long-term information is used as a weight item to update the state to obtain the state vector at time t+1. The fusion formula is as follows:

是预测状态，B_z是观测信息，η是归一化因子,I是单位矩阵。where Q _t is the map grid state output after fusing the data, A _c is the state transition matrix, G is the prediction confidence,

is the predicted state, B _z is the observation information, η is the normalization factor, and I is the identity matrix.

After obtaining the dynamic map updated in real time, combined with the dynamic positioning ability to evaluate the dynamic attributes in the environment that have not been updated to the map, the particle filter algorithm based on the positioning ability is used to realize the autonomous long-term positioning of the robot.

Specifically, the modeling process in step 1 adopts an offline form, the prediction process in step 2 and the updating process in step 3 adopt an online form, the sensor is a lidar, and the environmental feature data is stored in a map database.

The order determination process is determined by the AIC criterion, the parameter estimation is by the method of autoregressive approximation, and the prediction expression used in the state prediction is as follows

Specifically, only when the matching degree between the laser data and the map reaches a certain threshold, the observed laser data obtained under the current positioning is considered valid, and the observed data is fused into the prediction information.

Specifically, a positioning capability matrix is introduced to measure the reliability of different locations, as shown in the following formula:

是在LRF模型中的

激光束中的期望距离。N₀是LRF模型激光束的总数量。而对于

表示机器人移动Δx后LRF模型的激光束返回值的改变。Among them, p=(x, y, θ) is the pose of the robot.

is in the LRF model

Desired distance in the laser beam. _N0 is the total number of LRF model laser beams. And for

Represents the change in the return value of the laser beam of the LRF model after the robot moves by Δx.

Specifically, the map information fusion formula is as follows:

where Q _t is the map grid state output after the fusion data, A _c is the state transition matrix, G is the prediction confidence, X _(t) is the predicted state, B _z is the observation information, η is the normalization factor, and I is the identity matrix.

Specifically, the coordinates of the final robot can be expressed as the following formula

In the specific implementation process, as shown in Figure 1, the present invention is divided into three parts (1) modeling (2) prediction (3) updating, mainly including the following steps:

Step 1: Collect environmental data through sensors carried by the robot itself, and establish an environmental feature database in the time dimension. Parameter estimation and modeling are carried out through the autoregressive moving average model (ARMA) to evaluate the correlation of the environmental feature states in the time dimension, and then predict the future changes and trends of the environmental state.

Step 1.1: Model ordering. Before establishing the ARMA model, the first thing to determine is the parameters p and q of the model. The parameter p represents the state correlation of the physical environment feature state in time, and the parameter q represents the correlation of the map prediction state error term in the time series. The order determination process is determined by the AIC criterion. For the grid in the i-th row and the j-th column in the map, the modeling process is as follows:

Step 1.1.1 Select the common upper bound P value of order p and q, that is, 0≤p, q≤P

迭代求出σ²的最小二乘估计，即Step 1.1.2 by the number of samples

Iteratively find the least squares estimate of ^σ2 , that is

代入

得到A(0,0),A(0,1),A(1,1),……A(P,P)，则有Step 1.1.3 will

substitute

Get A(0,0), A(0,1), A(1,1),...A(P,P), then we have

Then p and q are the required model order at this time.

Step 1.2: Parameter estimation, when the parameters p and q of the autoregressive moving average model are available, the parameters of the model need to be estimated. The parameters to be determined here are α and β, where α∈R ^p , β∈R ^q , and the physical meaning of the representation is the relationship between the state before and after the grid state in the time domain. The parameter estimation adopts the method of autoregressive approximation, and the specific steps are as follows:

作高阶自回归滑动模型AR(p)的拟合Step 1.2.1 First utilize raster raw data

Fitting the higher-order autoregressive sliding model AR(p)

即Step 1.2.2 Calculate the residual sequence recursively from the above estimated AR(p) model

which is

t=P+1, P+2,...T (3)

为独立序列，利用线性回归模型：Step 1.2.3 put the residual column

For independent series, use a linear regression model:

where t=P+1,P+2,…T

As a result, the estimated parameter representation is as follows:

in,

Considering the change of the environmental model, it is necessary to set the model parameter detection. When the parameter change is greater than a certain threshold, the model is replaced, that is,

S=|p ₁ -p ₂ |+|q ₁ -q ₂ |>S _th

The subscripts 1 and 2 represent the calculated two sets of parameter models, respectively. When the order difference or the parameter is greater than the set value, it is considered that the model has changed, and the previous model parameters are replaced with the current model parameters.

Step 2: Use the established model to predict the grid in the time domain, evaluate the prediction confidence, and finally output a grid map with the prediction confidence label.

Step 2.1: State prediction, use the existing map data to predict the grid in the time domain, so that the grid state of each grid at time t can be obtained, so that the entire predicted grid map can be obtained. The prediction expression looks like this

Step 2.2: Confidence evaluation. After the grid state is predicted, the prediction confidence needs to be evaluated to measure the accuracy of each grid prediction. The prediction confidence of each grid state is determined by comparing the predicted state with the actual observation state. Before each confidence evaluation, it will be given an initial confidence, and then compared with the real map state obtained through the database update. Get the final prediction confidence. The final output is a raster map with prediction confidence labels. The specific implementation process is as follows:

Step 3: In view of the deviation between the predicted map and the actual map caused by some uncertain factors, the Bayesian rule is used to integrate the real-time observation information into the predicted information, and the real-time map update is performed as the prior map basis for particle filter positioning. . Specific steps are as follows

Step 3.1 introduces a positioning capability matrix to measure the reliability of different locations, as follows:

是在LRF模型中的i_th激光束中的期望距离。N₀是LRF模型激光束的总数量。而对于

表示机器人移动Δx后LRF模型的激光束返回值的改变。Among them, p=(x, y, θ) is the pose of the robot.

is the desired distance in the i _th laser beam in the LRF model. _N0 is the total number of LRF model laser beams. And for

Represents the change in the return value of the laser beam of the LRF model after the robot moves by Δx.

In step 3.2, the determinant of the positioning capability matrix is calculated and normalized to obtain m ₂ , which reflects the reliability of the data corresponding to different positions on the map. When m ₂ is large, the map information features are rich and the data reliability is high; while when m ₂ is small, the map information features are few and the data reliability is low. The corrected matching degree is used as the criterion for valid observation data, namely:

m=λm ₁ +(1-λ)m ₂ (9)

Among them, λ is the observation weight item, and its value represents the feasibility of the observation matching. The larger the value, the larger the proportion of the observation matching in the calculation weight of the entire matching degree. Only when m is equal to the set threshold, that is, m>m _th , the observed data is considered to be valid, and thus it is regarded as reliable data.

Step 3.3 Apply Bayesian rule for data fusion, fuse long-term prediction information with short-term observation information, and obtain real-time and accurate maps. Use dynamic probabilistic raster maps as the form of map data storage, and use HMMs as its basic model. At the same time, the confidence in the long-term information is used as a weight item to update the state to obtain the state vector at time t+1. The fusion formula is as follows:

是预测状态，B_z是观测信息，η是归一化因子,I是单位矩阵。where Q _t is the map grid state output after fusing the data, A _c is the state transition matrix, G is the prediction confidence,

is the predicted state, B _z is the observation information, η is the normalization factor, and I is the identity matrix.

Based on this, in a grid with a high confidence, the state of the map will be more dependent on the predicted state as the final shape of the map; while for a grid with a low confidence, it will rely more on the real-time observation data for iterative update . In this way, a map that is more in line with the real environment can be obtained.

Step 4: After obtaining the dynamic map updated in real time, combine the dynamic positioning ability to evaluate the dynamic attributes in the environment that have not been updated to the map, and use the particle filtering algorithm based on the positioning ability to realize the autonomous long-term positioning of the robot. The specific implementation is as follows:

The dynamic positioning capability matrix that reflects the positioning capability from the initial map is expressed as follows:

是观测信息方差。p＝(x,y,θ)是机器人的位姿。

是在LRF模型中的i_th激光束中的期望距离。N₀是LRF模型激光束的总数量。而对于

表示机器人移动Δx后LRF模型的激光束返回值的改变。where s _i is the probability that the laser beam sweeps to the unknown obstacle.

is the observed information variance. p=(x, y, θ) is the pose of the robot.

is the desired distance in the i _th laser beam in the LRF model. _N0 is the total number of LRF model laser beams. And for

Represents the change in the return value of the laser beam of the LRF model after the robot moves by Δx.

和里程计信息

来修正建议分布函数。之后，每个粒子的ΔO和p都会被ΔO^(k)和

替换。因此，融合过后的里程计增量将变成Fusion of observations by using classical data fusion algorithms

and odometer information

to modify the proposed distribution function. After that, the ΔO and p of each particle are divided by ΔO ^(k) and

replace. Therefore, the odometer increment after fusion will become

可通过经典的粒子滤波算法获得，而

表示在只有里程计增量

下算得的机器人坐标。where h is the scaling factor,

can be obtained by the classical particle filter algorithm, while

Indicated in odometer-only increments

The robot coordinates calculated below.

When the corrected odometer increments are obtained, the corrected sampled particles can be expressed as

Finally, the coordinates of the robot can be expressed as

Those skilled in the art know that, in addition to implementing the system, device and each module provided by the present invention in the form of pure computer readable program code, the system, device and each module provided by the present invention can be completely implemented by logically programming the method steps. The same program is implemented in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, and embedded microcontrollers, among others. Therefore, the system, device and each module provided by the present invention can be regarded as a kind of hardware component, and the modules used for realizing various programs included in it can also be regarded as the structure in the hardware component; A module for realizing various functions can be regarded as either a software program for realizing a method or a structure within a hardware component.

Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the above-mentioned specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essential content of the present invention. The embodiments of the present application and features in the embodiments may be combined with each other arbitrarily, provided that there is no conflict.

Claims (5)

1. an autonomous positioning method based on the robot realized by ARMA model, is characterized in that, comprises the following steps: Step 1: Environment modeling step: use the sensors carried by the robot to collect map data, and perform parameter estimation and modeling on the map data through the autoregressive moving average model ARMA to obtain a map model; Step 2: Map prediction step: use the map model to predict the grid in the time domain, evaluate the prediction confidence, and obtain a grid map with a prediction confidence label; Step 3: Map update step: According to the deviation between the grid map and the actual map, the Bayesian rule is used to integrate the real-time observation information into the prediction information, and the real-time map update is performed to obtain an updated map; Step 4: Autonomous positioning step: Based on the updated map, use particle filtering to realize the autonomous long-term positioning of the robot; The environment modeling steps include: Model order determination step: determine the first parameter p and the second parameter q of the ARMA model according to the environmental characteristics, the first parameter p represents the state correlation of the physical environment feature state in time, and the second parameter q represents the map prediction The serial correlation of the state error term on the time series; Parameter estimation step: Based on the first parameter p and the second parameter q of the ARMA model, the third parameter (α, β) is estimated, and the third parameter (α, β) represents the grid state before and after in the time domain state relationship, where α∈R ^p and β∈R ^q ; The environment modeling step also includes: Modeling step: Select the common upper bound P value of the first parameter p and the second parameter q, that is, 0≤p≤P and 0≤q≤P;

Iteratively find the least squares estimate of ^σ2 , that is

Will

substitute

Get A(0,0), A(0,1), A(1,1),...A(P,P), then we have

where i represents the ith row of the grid in the map data, j represents the jth column of the grid in the map data, and the subscript T represents the number of samples,

represents the T-th sample at the i-th row and the j-th column, σ ² represents the least squares estimated value, k represents the k-th row of the raster in the map data,

represents the least squares estimate of the raster sample at row k and column j,

represents the mean of the raster samples,

represents the regression coefficient a of the raster sample least squares estimate,

represents the regression coefficient b of the raster sample least squares estimate, n represents the total number of time series,

Represents the AIC criterion value of the grid sample in the kth row and the jth column, and A(p,q) indicates the AIC criterion value corresponding to the values of p and q determined by the model order. 2. the autonomous positioning method of the robot based on ARMA model realization according to claim 1, is characterized in that, described map prediction step comprises: State prediction step: use the existing map data to predict the grid in the time domain, obtain the grid state of each grid at time t, and obtain the entire predicted grid map; Confidence evaluation step: Determine the prediction confidence of each grid state by comparing the predicted state with the actual observation state, assign the initial confidence before each confidence evaluation, and then compare the real map state obtained through the database update. Get the final prediction confidence, and finally output a raster map with prediction confidence labels. 3. the autonomous positioning method of the robot based on ARMA model realization according to claim 1, is characterized in that, described map update step comprises: Introducing steps: Introducing a positioning capability matrix to measure the reliability at different locations; Normalization step: find the determinant of the positioning capability matrix and normalize it to obtain m ₂ , where m ₂ reflects the reliability of the data corresponding to different positions on the map; the corrected matching degree is used as the judgment of valid observation data standard, namely: m=λm ₁ +(1-λ)m ₂ Among them, λ is the observation weight item, which indicates the feasibility of the observation matching. The larger the value of λ, the larger the proportion of the observation matching in the calculation weight of the entire matching degree; m indicates the matching between the revised map and the observation data. m ₁ represents the matching degree between the map and the observed data, and m ₂ represents the reliability of the data corresponding to different positions on the map; when m is greater than the set threshold, that is, m > m _th , the observed data is defined as valid , so that m is regarded as reliable data. 4. The autonomous positioning method of the robot based on ARMA model realization according to claim 1, is characterized in that, the environment modeling step adopts off-line form, and the map prediction step and the map update step adopt on-line form. 5 . The autonomous positioning method of a robot based on an ARMA model according to claim 1 , wherein the model order determination step adopts AIC criterion to determine, and the parameter estimation step adopts autoregressive approximation. 6 .

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