CN111189454A - Unmanned vehicle SLAM navigation method based on rank Kalman filtering - Google Patents

Unmanned vehicle SLAM navigation method based on rank Kalman filtering Download PDF

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CN111189454A
CN111189454A CN202010020887.6A CN202010020887A CN111189454A CN 111189454 A CN111189454 A CN 111189454A CN 202010020887 A CN202010020887 A CN 202010020887A CN 111189454 A CN111189454 A CN 111189454A
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unmanned vehicle
state
prediction
rank
formula
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娄泰山
班鸿业
赵素娜
贺振东
丁国强
焦玉召
王晓雷
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Zhengzhou University of Light Industry
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    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20—Instruments for performing navigational calculations

Abstract

The invention provides an unmanned vehicle SLAM navigation method based on rank Kalman filtering to solve the technical problems of low positioning precision and insufficient stability of the conventional SLAM navigation. The invention comprises the following steps: 1. modeling the mobile robot, establishing a dynamic model and an observation model of the mobile robot, and initializing; 2. prediction and update of SLAM; 3. and updating and outputting the pose information of the mobile robot by adopting rank Kalman filtering. The invention has the beneficial effects that: the method has no requirement on whether the dynamic model meets Gaussian distribution or not, has small error and has higher positioning and mapping accuracy in unknown environment.

Description

Unmanned vehicle SLAM navigation method based on rank Kalman filtering
Technical Field
The invention relates to the field of unmanned vehicle autonomous navigation, in particular to an unmanned vehicle SLAM navigation method based on rank Kalman filtering.
Background
SLAM is a technique that solves the problem of navigation of unmanned vehicles in unknown environments. The technology is that the unmanned vehicle uses a sensor carried by the unmanned vehicle to obtain data, calculates and determines the environment information of the unmanned vehicle, and updates the position of the unmanned vehicle by using the environment information obtained by the unmanned vehicle. And meanwhile, the method also becomes a hot algorithm in a robot navigation algorithm.
SLAM algorithms have been studied with a focus on using filter theory, typically using odometer inputs as the prediction inputs for the filter and lidar or vision sensor outputs as the inputs for the filter update phase. The most traditional method is to introduce Extended Kalman Filtering (EKF) into SLAM, which is actually to process the nonlinear model by using extended kalman filtering. The EKF expands the nonlinear function into Taylor series and omits second-order and above terms, can solve a part of nonlinear problems, but when the system nonlinearity is serious, the truncation error generated by the approximate linearization can reduce the filtering precision and stability, so in the actual engineering, the EKF can only carry out local linearization processing on a weak nonlinear system.
Disclosure of Invention
The invention provides an unmanned vehicle SLAM navigation method based on rank Kalman filtering to solve the technical problems of low positioning precision and insufficient stability of the conventional SLAM navigation.
In order to solve the technical problems, the invention adopts the following technical scheme:
an unmanned vehicle SLAM navigation method based on rank Kalman filtering is designed, and comprises the following steps:
the method comprises the following steps: the dynamic model and the observation model of the unmanned vehicle are established as follows:
Figure BDA0002360696990000011
wherein the content of the first and second substances,
Figure BDA0002360696990000012
for the pose information of the mobile robot at time k, ukIs nuDimension control vector, zkIs nzObservation vector of dimension, wkAnd vkRespectively a system noise vector and a measurement noise vector;
step two: establishing a SLAM model, predicting and updating, wherein the SLAM model is as follows:
Figure BDA0002360696990000021
in the formula
Figure BDA0002360696990000022
A feature map at time k;
the prediction is through a model of the unmanned vehicle's state
Figure BDA0002360696990000023
And the posterior probability distribution of the k-1 moment to obtain the prior probability distribution of the k moment:
Figure BDA0002360696990000024
this probability distribution corresponds to the kinetic model of the unmanned vehicle
Figure BDA0002360696990000025
The updating is that the measurement equation obtains the measured value z at the moment kkThen, a posterior probability distribution is obtained:
Figure BDA0002360696990000026
this probability distribution corresponds to the observation model z of the above-mentioned unmanned vehiclek＝h(xk)+vk. Therefore, the whole unmanned vehicle SLAM navigation method can be solved by Kalman filtering.
Step three: the pose information of the unmanned vehicle is sampled, and a rank sampling point set is obtained as follows:
Figure BDA0002360696990000027
in the formula, xk-1，iIs composed of
Figure BDA0002360696990000028
4n sample points in total; n is
Figure BDA0002360696990000029
Dimension (d) of (a).
Figure BDA00023606969900000210
Is represented by Pk-1The ith column vector of square roots; u. ofpIs a standard normal offset;
Figure BDA00023606969900000211
the state of the unmanned vehicle at the k-1 moment is shown;
step four: obtaining the state one-step prediction of the k step of the unmanned vehicle:
xk/k-1，i＝f(χk-1，i)，i＝1，2，…，4n (3)
Figure BDA00023606969900000212
in the formula xk/k-1，iThe state prediction value of the ith sampling point is shown;
Figure BDA00023606969900000213
the state prediction value of the mobile robot is shown;
step five: obtaining a one-step prediction of covariance:
Figure BDA00023606969900000214
in the formula, Pk/k-1Representing the one-step prediction error covariance of the state of the mobile robot; qk-1Represents the covariance of the process noise;
step six: covariance Q due to process noise in one-step prediction of covariance obtained in step fivek-1Thus, one step prediction of the state will be re-rank sampled:
Figure BDA0002360696990000031
in the formula, xk/k-1，iIs composed of
Figure BDA0002360696990000032
The ith sample point of (a);
Figure BDA0002360696990000033
is a one-step prediction of state; pk/k-1A one-step prediction of covariance;
step seven: obtaining a measurement prediction value zk/k-1，i：
zk/k-1，i＝h(χk/k-1，i)，i＝1，2，…，4n (7)
Figure BDA0002360696990000034
In the formula, zk/k-1，iThe measured predicted value of the ith sampling point is shown;
Figure BDA0002360696990000035
the measurement predicted value of the mobile robot is shown;
step eight: obtaining a filter gain matrix Kk：
Figure BDA0002360696990000036
Figure BDA0002360696990000037
In the formula, PzzRepresenting the covariance of the measurement prediction value of the mobile robot; pxzRepresenting the cross covariance of the state predicted value and the measurement predicted value; kkRepresenting the gain of rank Kalman filtering;
step nine: and (3) acquiring state updating:
Figure BDA0002360696990000038
step ten: obtaining a state estimation error variance Pk：
Figure BDA0002360696990000039
Step eleven: circularly iterating the steps from three to ten to obtain the state estimation value of the unmanned vehicle
Figure BDA0002360696990000041
Further, w in step 1kAnd vkAre respectively QkAnd RkAnd satisfies:
Figure BDA0002360696990000042
further, QkAnd RkRespectively as follows:
Figure BDA0002360696990000043
and
Figure BDA0002360696990000044
further, the initial state of the unmanned vehicle in step 1 is as follows:
Figure BDA0002360696990000045
Figure BDA0002360696990000046
further, the initial state value of the unmanned vehicle is
Figure BDA0002360696990000047
Initial error variance matrix
Figure BDA0002360696990000048
Compared with the prior art, the invention has the beneficial technical effects that:
the SLAM navigation method based on the rank Kalman filtering has no requirement on whether a dynamics model of the unmanned vehicle is in Gaussian distribution or not, and the method based on the rank filtering has the advantages of smaller error, better effect, higher positioning and mapping accuracy of the unmanned vehicle in an unknown environment and stronger adaptability to the unknown environment.
Drawings
FIG. 1 is a graph of the results of a simulation experiment of the present invention;
FIG. 2 is a plot of x-axis root mean square error versus EKF-SLAM and RKF-SLAM algorithms used in the present invention during unmanned vehicle navigation;
FIG. 3 is a plot of the root mean square error of the y-axis of the invention using EKF-SLAM and RKF-SLAM algorithms while the drone is navigating.
Detailed Description
The following examples are intended to illustrate the present invention in detail and should not be construed as limiting the scope of the present invention in any way.
The programs referred to or relied on in the following embodiments are all conventional programs or simple programs in the art, and those skilled in the art can make routine selection or adaptation according to specific application scenarios.
Example 1: an unmanned vehicle SLAM navigation method based on rank Kalman filtering comprises the following steps:
the method comprises the following steps: modeling the unmanned vehicle, establishing a dynamic model and an observation model of the unmanned vehicle, and initializing;
selecting the state information vector of the system as
Figure BDA0002360696990000051
The dynamics and observation models of the system are then:
Figure BDA0002360696990000052
wherein the content of the first and second substances,
Figure BDA0002360696990000053
the pose information of the unmanned vehicle at the moment k,
Figure BDA0002360696990000054
characteristic map of time k, ukIs nuDimension control vector, zkIs nzObservation vector of dimension, wkAnd vkRespectively, the system noise vector and the measured noise vector, and the variance matrix is QkAnd RkAnd satisfy
Figure BDA0002360696990000055
Wherein the content of the first and second substances,
Figure BDA0002360696990000056
Figure BDA0002360696990000057
initializing a state model of the system
Figure BDA0002360696990000058
Figure BDA0002360696990000059
Wherein, the initial state
Figure BDA00023606969900000510
Initial error variance matrix
Figure BDA00023606969900000511
P0、QkAnd RkAre all unrelated;
step two: SLAM prediction and update
The SLAM model was:
Figure BDA0002360696990000061
wherein z isk，ukCan be formed by zk＝h(xk)+vk，uk(v, γ) (including forward velocity and angular velocity) is calculated. The Bayes filtering principle is adopted to calculate the posterior probability distribution, so that the optimal state estimation can be obtained, namely after the path is planned, the unmanned vehicle can drive along the track closest to the planned path in the navigation process through calculation. The whole calculation step is divided into two steps:
the first step of prediction is through a model of the state of the vehicle
Figure BDA0002360696990000062
And the posterior probability distribution of the k-1 moment to obtain the prior probability distribution of the k moment:
Figure BDA0002360696990000063
this probability distribution corresponds to the kinetic model of the unmanned vehicle
Figure BDA0002360696990000064
The second step of updating is to obtain the measured value z at the time k from the measurement equationkThen, a posterior probability distribution is calculated:
Figure BDA0002360696990000065
this probability distribution corresponds to the observation model z of the above-mentioned unmanned vehiclek＝h(xk)+vk. Therefore, the whole unmanned vehicle SLAM navigation method can be solved by Kalman filtering.
Step three: updating pose information of the unmanned vehicle by adopting Rank Kalman (RKF) filtering and outputting the pose information
1. Calculating rank sampling points:
rank sample point set { χ for m-2 sampling strategy and symmetric distribution casek-1，iIs as
Figure BDA0002360696990000066
In the formula, xk-1，iIs composed of
Figure BDA0002360696990000067
4n sample points in total; n is
Figure BDA0002360696990000068
Dimension (d) of (a).
Figure BDA0002360696990000069
Is represented by Pk-1The ith column vector of square roots;
Figure BDA00023606969900000610
the state of the unmanned vehicle at the k-1 moment is shown; u. ofpFor standard normal bias, p is calculated using the median rankj＝(j+2.7)/5.4，p1＝0.6852，
Figure BDA00023606969900000612
p2＝0.8704，
Figure BDA00023606969900000613
ω denotes a covariance weight coefficient, and
Figure BDA00023606969900000611
2. calculating a state one-step prediction:
state estimation at time k-1
Figure BDA0002360696990000071
And its error variance matrix Pk-1And predicting the state of the k step as follows:
xk/k-1，i＝f(χk-1，i)，i＝1，2，…，4n (11)
Figure BDA0002360696990000072
in the formula xk/k-1，iThe state prediction value of the ith sampling point is shown;
Figure BDA0002360696990000073
the predicted value of the state of the unmanned vehicle is shown.
3. One-step prediction for covariance calculationk/k-1；
One-step prediction based on the state of the k-th step
Figure BDA0002360696990000074
Obtaining a state estimation error variance matrix one-step prediction:
Figure BDA0002360696990000075
in the formula, Pk/k-1The method comprises the steps of representing the one-step prediction error covariance of the state of the unmanned vehicle; qk-1The covariance of the process noise is shown.
4. Covariance Q due to process noise in one-step prediction of covariance obtained in step fivek-1So that a re-rank sampling of the state one-step prediction will be performed;
Figure BDA0002360696990000076
in the formula, xk/k-1，iIs composed of
Figure BDA0002360696990000077
The ith sample point of (a);
Figure BDA0002360696990000078
is a one-step prediction of state; pk/k-1Is a one-step prediction of covariance.
5. Calculating a measurement prediction value zk/k-1，i
zk/k-1，i＝h(χk/k-1，i)，i＝1，2，…，4n (15)
Figure BDA0002360696990000079
In the formula, zk/k-1，iThe measured predicted value of the ith sampling point is shown;
Figure BDA00023606969900000710
the measured predicted value of the unmanned vehicle is shown.
6. Calculating a filter gain matrix Kk；
Figure BDA0002360696990000081
Figure BDA0002360696990000082
Figure BDA0002360696990000083
In the formula, PzzRepresenting the covariance of the unmanned vehicle measurement predicted value; pxzRepresenting the cross covariance of the state predicted value and the measurement predicted value; kkRepresenting the gain of the rank kalman filter.
7. Computing state updates
Figure BDA0002360696990000084
In the formula (I), the compound is shown in the specification,
Figure BDA0002360696990000085
the estimated value of the state of the unmanned vehicle at the time k is shown.
8. Calculating a state estimation error variance Pk；
Figure BDA0002360696990000086
In the formula, PkRepresenting the covariance estimation value of the unmanned vehicle at the time k;
9. the above steps are iterated circularly to obtain the state estimation value of the unmanned vehicle
Figure BDA0002360696990000087
In this embodiment, the sampling time interval h is 0.025[ s ], the car speed v is 3[ m/s ], the angular speed γ is pi/6 [ rad/s ] and the car axle distance d is 4[ m ], and the landmark detection time interval t is 0.3[ s ]; as shown in fig. 2 and 3, when the proposed rank kalman filtering SLAM navigation method is adopted, the root mean square error of the position is small, and the errors in the x direction and the y direction are both within the range of 0.12m, that is, the rank kalman filtering SLAM navigation method has small error, good estimation effect, higher positioning and mapping accuracy for unmanned vehicles in an unknown environment, and stronger adaptability to the unknown environment.
While the present invention has been described in detail with reference to the drawings and the embodiments, those skilled in the art will understand that various specific parameters in the above embodiments can be changed without departing from the spirit of the present invention, and a plurality of specific embodiments are formed, which are common variation ranges of the present invention, and will not be described in detail herein.

Claims (5)

1. An unmanned vehicle SLAM navigation method based on rank Kalman filtering is characterized by comprising the following steps:
the method comprises the following steps: the dynamic model and the observation model of the unmanned vehicle are established as follows:
Figure FDA0002360696980000011
wherein the content of the first and second substances,
Figure FDA0002360696980000012
for the pose information of the mobile robot at time k, ukIs nuDimension control vector, zkIs nzObservation vector of dimension, wkAnd vkRespectively a system noise vector and a measurement noise vector;
step two: establishing a SLAM model, predicting and updating, wherein the SLAM model is as follows:
Figure FDA0002360696980000013
in the formula
Figure FDA0002360696980000014
A feature map at time k;
the prediction is through a model of the unmanned vehicle's state
Figure FDA0002360696980000015
And the posterior probability distribution of the k-1 moment to obtain the prior probability distribution of the k moment:
Figure FDA0002360696980000016
this probability distribution corresponds to the kinetic model of the unmanned vehicle
Figure FDA0002360696980000017
The updating is that the measurement equation obtains the measured value z at the moment kkThen, a posterior probability distribution is obtained:
Figure FDA0002360696980000018
this probability distribution corresponds to the observation model z of the above-mentioned unmanned vehiclek＝h(xk)+vk；
Step three: the pose information of the unmanned vehicle is sampled, and a rank sampling point set is obtained as follows:
Figure FDA0002360696980000019
in the formula, xk-1，iIs composed of
Figure FDA00023606969800000110
I th of (1)4n sampling points in total; n is
Figure FDA00023606969800000111
Dimension (d) of (a).
Figure FDA00023606969800000112
Is represented by Pk-1The ith column vector of square roots; u. ofpIs a standard normal offset;
Figure FDA00023606969800000113
the state of the unmanned vehicle at the k-1 moment is shown;
step four: obtaining the state one-step prediction of the k step of the unmanned vehicle:
xk/k-1，i＝f(χk-1，i)，i＝1，2，…，4n (3)
Figure FDA00023606969800000114
in the formula xk/k-1，iThe state prediction value of the ith sampling point is shown;
Figure FDA0002360696980000021
the state prediction value of the mobile robot is shown;
step five: obtaining a one-step prediction of covariance:
Figure FDA0002360696980000022
in the formula, Pk/k-1Representing the one-step prediction error covariance of the state of the mobile robot; qk-1Represents the covariance of the process noise;
step six: re-rank sampling the state one-step prediction:
Figure FDA0002360696980000023
in the formula, xk/k-1，iIs composed of
Figure FDA0002360696980000024
The ith sample point of (a);
Figure FDA0002360696980000025
is a one-step prediction of state; pk/k-1A one-step prediction of covariance;
step seven: obtaining a measurement prediction value zk/k-1，i：
zk/k-1，i＝h(χk/k-1，i)，i＝1，2，…，4n (7)
Figure FDA0002360696980000026
In the formula, zk/k-1，iThe measured predicted value of the ith sampling point is shown;
Figure FDA0002360696980000027
the measurement predicted value of the mobile robot is shown;
step eight: obtaining a filter gain matrix Kk：
Figure FDA0002360696980000028
Figure FDA0002360696980000029
In the formula, PzzRepresenting the covariance of the measurement prediction value of the mobile robot; pxzRepresenting the cross covariance of the state predicted value and the measurement predicted value; kkRepresenting the gain of rank Kalman filtering;
step nine: and (3) acquiring state updating:
Figure FDA0002360696980000031
step ten: obtaining a state estimation error squareDifference Pk：
Figure FDA0002360696980000032
Step eleven: circularly iterating the steps from three to ten to obtain the state estimation value of the unmanned vehicle
Figure FDA00023606969800000310
2. The rank kalman filter-based unmanned vehicle SLAM navigation method of claim 1, wherein: w in said step 1kAnd vkAre respectively QkAnd RkAnd satisfies:
Figure FDA0002360696980000033
3. the rank kalman filter-based unmanned vehicle SLAM navigation method of claim 2, characterized in that: said QkAnd RkRespectively as follows:
Figure FDA0002360696980000034
and
Figure FDA0002360696980000035
4. the rank kalman filter-based unmanned vehicle SLAM navigation method of claim 1, wherein:
the initial state of the unmanned vehicle in the step 1 is as follows:
Figure FDA0002360696980000036
Figure FDA0002360696980000037
5. the rank Kalman filtering based unmanned vehicle SLAM navigation method of claim 4, characterized in that: the initial state has a value of
Figure FDA0002360696980000038
Initial error variance matrix
Figure FDA0002360696980000039
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