CN115328168A - Mobile robot synchronous positioning and mapping method and system based on adaptive strong tracking - Google Patents
Mobile robot synchronous positioning and mapping method and system based on adaptive strong tracking Download PDFInfo
- Publication number
- CN115328168A CN115328168A CN202211137399.9A CN202211137399A CN115328168A CN 115328168 A CN115328168 A CN 115328168A CN 202211137399 A CN202211137399 A CN 202211137399A CN 115328168 A CN115328168 A CN 115328168A
- Authority
- CN
- China
- Prior art keywords
- mobile robot
- time
- pose
- estimation
- covariance
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000000034 method Methods 0.000 title claims abstract description 101
- 230000003044 adaptive effect Effects 0.000 title claims abstract description 34
- 238000013507 mapping Methods 0.000 title claims abstract description 33
- 230000001360 synchronised effect Effects 0.000 title claims abstract description 32
- 238000001914 filtration Methods 0.000 claims abstract description 53
- 230000008569 process Effects 0.000 claims abstract description 49
- 238000010276 construction Methods 0.000 claims abstract description 11
- 239000000654 additive Substances 0.000 claims abstract description 7
- 230000000996 additive effect Effects 0.000 claims abstract description 7
- 238000004422 calculation algorithm Methods 0.000 claims description 49
- 238000005259 measurement Methods 0.000 claims description 38
- 239000011159 matrix material Substances 0.000 claims description 22
- 230000002596 correlated effect Effects 0.000 claims description 14
- 150000001875 compounds Chemical class 0.000 claims description 10
- 238000012546 transfer Methods 0.000 claims description 10
- 238000004364 calculation method Methods 0.000 claims description 9
- 238000012937 correction Methods 0.000 claims description 6
- 230000007613 environmental effect Effects 0.000 claims description 5
- 230000003313 weakening effect Effects 0.000 claims description 5
- 238000009826 distribution Methods 0.000 claims description 4
- 230000008859 change Effects 0.000 abstract description 6
- 238000012544 monitoring process Methods 0.000 abstract description 2
- 230000006870 function Effects 0.000 description 16
- 238000010586 diagram Methods 0.000 description 10
- 238000004590 computer program Methods 0.000 description 7
- 238000002474 experimental method Methods 0.000 description 5
- 238000012545 processing Methods 0.000 description 5
- 230000006872 improvement Effects 0.000 description 4
- 230000035772 mutation Effects 0.000 description 4
- 238000004088 simulation Methods 0.000 description 4
- 238000005457 optimization Methods 0.000 description 3
- 238000003860 storage Methods 0.000 description 3
- 230000009286 beneficial effect Effects 0.000 description 2
- 238000011161 development Methods 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
- 238000005562 fading Methods 0.000 description 2
- 238000005070 sampling Methods 0.000 description 2
- 230000002159 abnormal effect Effects 0.000 description 1
- 230000003321 amplification Effects 0.000 description 1
- 230000003416 augmentation Effects 0.000 description 1
- 238000005094 computer simulation Methods 0.000 description 1
- 238000009795 derivation Methods 0.000 description 1
- 238000001514 detection method Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 229910052739 hydrogen Inorganic materials 0.000 description 1
- 239000001257 hydrogen Substances 0.000 description 1
- 125000004435 hydrogen atom Chemical class [H]* 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000003199 nucleic acid amplification method Methods 0.000 description 1
- 230000003287 optical effect Effects 0.000 description 1
- 230000010355 oscillation Effects 0.000 description 1
- 239000011541 reaction mixture Substances 0.000 description 1
- 238000012827 research and development Methods 0.000 description 1
- 230000026676 system process Effects 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- G05D1/02—Control of position or course in two dimensions
- G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
- G05D1/0231—Control of position or course in two dimensions specially adapted to land vehicles using optical position detecting means
- G05D1/0238—Control of position or course in two dimensions specially adapted to land vehicles using optical position detecting means using obstacle or wall sensors
- G05D1/024—Control of position or course in two dimensions specially adapted to land vehicles using optical position detecting means using obstacle or wall sensors in combination with a laser
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- G05D1/02—Control of position or course in two dimensions
- G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
- G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
- G05D1/0221—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving a learning process
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- G05D1/02—Control of position or course in two dimensions
- G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
- G05D1/0276—Control of position or course in two dimensions specially adapted to land vehicles using signals provided by a source external to the vehicle
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Aviation & Aerospace Engineering (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Optics & Photonics (AREA)
- Electromagnetism (AREA)
- Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)
Abstract
The invention discloses a mobile robot synchronous positioning and mapping method and a system based on self-adaptive strong tracking, wherein the method comprises the following steps: on the premise that noise in the synchronous positioning and map building process is additive Gaussian noise, a kinematic model and an observation model of the mobile robot are built according to the chassis style of the mobile robot and the characteristics of a sensor, and the initial pose and the initial estimation error covariance of the mobile robot under a global coordinate system are obtained through initialization; iterative estimation is carried out on the pose of the mobile robot based on the adaptive strong tracking extended Kalman filtering method, and real-time pose estimation and map construction of the mobile robot are achieved. The method provided by the invention can carry out self-adaptive estimation on the process noise by monitoring the change of innovation when the mobile robot generates a sudden change of a motion state or a mismatch of model parameters, so that the mobile robot keeps stronger pose tracking capability and good landmark estimation accuracy.
Description
Technical Field
The invention belongs to the technical field of synchronous positioning, mapping and autonomous navigation of mobile robots, and particularly relates to a synchronous positioning and mapping method and system of a mobile robot based on adaptive strong tracking.
Background
In recent years, with the development of related technologies in the field of mobile robots, people pay more and more attention to the research and development of mobile robots which have autonomous navigation capability and can autonomously complete set tasks; robots with autonomous navigation capability are increasingly applied to scenes such as forest fire detection, express delivery logistics transportation, food delivery in restaurants and the like, and the basis for realizing path planning and autonomous navigation of mobile robots is high-precision robot position and posture estimation and accurate environment maps.
The synchronous positioning and Mapping (SLAM) technology refers to a process in which a mobile robot simultaneously performs self positioning, landmark estimation and environment map construction in an unknown environment. According to different back-end optimization strategies, SLAM can be divided into two types of frames based on Bayesian filtering and nonlinear optimization; compared with a nonlinear optimization algorithm, the Bayesian filtering algorithm is simple and easy to implement, and the development is relatively mature.
The existing Extended Kalman Filter (EKF) algorithm is implemented simply by performing taylor expansion on a nonlinear system and taking a first-order approximation, and has been widely applied to the nonlinear system; however, the EKF algorithm abandons high-order information of the system, so that the accuracy of the pose estimation of the robot is low, and the EKF algorithm has no self-adaptive capability on inaccurate parameters in the model; the Strong Tracking Filter (STF) algorithm proposed on the basis of the EKF improves the robot pose estimation accuracy to a certain extent, but fails to realize adaptive estimation on noise, has no good adaptive capability on sudden changes of the robot motion state and mismatch of parameters, and is easy to generate a filtering divergence phenomenon when being actually applied to the SLAM problem. In summary, a method for synchronously positioning and mapping a mobile robot based on adaptive strong tracking is needed.
Disclosure of Invention
The invention aims to provide a mobile robot synchronous positioning and mapping method and system based on adaptive strong tracking to solve the existing technical problems. The method provided by the invention can perform self-adaptive estimation on the process noise by monitoring the change of innovation when the mobile robot generates a sudden change of a motion state or a mismatch of model parameters, so that the mobile robot keeps stronger pose tracking capability and good landmark estimation precision, and the robustness of the SLAM algorithm of the mobile robot can be improved.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides a mobile robot synchronous positioning and mapping method based on self-adaptive strong tracking, which comprises the following steps:
on the premise that noise in the synchronous positioning and map building process is additive Gaussian noise, a kinematics model and an observation model of the mobile robot are built according to the chassis pattern of the mobile robot and the characteristics of a sensor; initializing a kinematic model and an observation model of the mobile robot, and acquiring an initial pose and an initial estimation error covariance of the mobile robot under a global coordinate system;
iterative estimation is carried out on the pose of the mobile robot based on a self-adaptive strong tracking extended Kalman filtering method, so that real-time pose estimation and map construction of the mobile robot are realized;
wherein in the process of carrying out iterative estimation on the pose of the mobile robot based on the adaptive strong tracking extended Kalman filtering method, the step of iterative estimation at the k moment comprises the following steps of,
based on the pose of the mobile robot at the time k-1 and the covariance of the estimated errors at the time k-1, obtaining a predicted value of the pose of the mobile robot at the time k by using an extended Kalman filtering method and a kinematic model of the mobile robot;
acquiring observation information of a sensor at the time k on an environmental landmark, and performing landmark data association to obtain landmark association results at the time k and the time k-1; acquiring correlated k-time sensor observation information based on the landmark correlation result;
judging whether the iteration result of the mobile robot synchronous positioning and mapping method diverges or not to obtain a judgment result; based on the judgment result, updating the time of the k moment estimation error covariance by using the pose of the mobile robot at the k-1 moment, the k-1 moment estimation error covariance, a kinematic model of the mobile robot and an observation model to obtain a k moment estimation error covariance predicted value;
and obtaining the pose of the mobile robot at the time k and the estimation error covariance at the time k through measurement updating based on the correlated observation information of the sensor at the time k, the predicted value of the pose of the mobile robot at the time k and the predicted value of the estimation error covariance at the time k.
The invention is further improved in that the obtained kinematic model and observation model of the mobile robot are constructed as,
in the formula, z k As observed information of the sensor at time k, u k For the input of the robot at the time k, f (-) is a state transfer function, h (-) is a measurement function, w k-1 And v k For uncorrelated process noise and measurement noise, the mean value is 0 and the covariance is R k And Q k Gaussian distribution;
for the state information of the mobile robot at time k,
to move the robot's coordinate position in two-dimensional space,
the orientation of the mobile robot is deviated from the global coordinate system by an angle.
The invention has the further improvement that the process of judging whether the iteration result of the mobile robot synchronous positioning and mapping method diverges or not and obtaining the judgment result comprises the following steps:
the criterion expression of whether to diverge is as follows,
in the formula (I), the compound is shown in the specification,
for the sequence of innovation at time k,
for a mobile robot at time k a measurement function is provided
Taylor expansion is performed and the result of the first order approximation is taken, and
kappa is more than or equal to 1 and is an adjustable coefficient, tr [. Cndot.)]Tracing operators for matrices, P k/k-1 Estimating a predicted value of the error covariance for the time k;
when the criterion expression is satisfied, a strong tracking algorithm is required to be introduced to inhibit filtering divergence.
In the process of utilizing the pose of the mobile robot at the moment k-1, the estimation error covariance at the moment k-1, the kinematic model of the mobile robot and the observation model to update the estimation error covariance at the moment k to obtain the estimation value of the estimation error covariance at the moment k based on the judgment result,
when the filtering is already dispersed, introducing a self-adaptive strong tracking algorithm, calculating parameters of a self-adaptive strong tracking filter, and carrying out time updating on the covariance of the estimation error, wherein the time updating comprises the following steps:
calculating an innovation sequence covariance matrix V k The expression is as follows,
in the formula, rho is more than 0 and less than or equal to 1, and is a forgetting factor;
obtaining a parameter matrix M k And N k The expression is as follows,
in the formula, the parameter beta is more than or equal to 1 and is a weakening factor;
to moveThe state transfer function of the robot at the moment k-1 is
Taylor expansion is performed and the result of the first order approximation is taken,
moving the pose of the robot at the moment k-1;
λ k the computational expression of (a) is as follows,
in the formula (I), the compound is shown in the specification,
after introducing the self-adaptive strong tracking filtering algorithm, the time updating formula of the estimation error covariance is as follows,
in the formula, P k-1|k-1 Is the covariance of the estimation error at time k-1, lambda k Q k-1 The term can be considered as a correction term for noise when the noise parameters mismatch.
In the further improvement of the invention, in the process of obtaining the pose of the mobile robot at the time k and the covariance of the estimation error at the time k by measurement and updating based on the correlated observation information of the sensor at the time k, the predicted value of the pose of the mobile robot at the time k and the predicted value of the covariance of the estimation error at the time k,
the measurement updating step comprises the following steps:
calculating Kalman filter gain K at moment K k The calculation expression is
Calculate pose of k moment robot
Is calculated as
Updating an estimation error covariance matrix P k|k Updating expression as P k|k ＝(I-K k H k )P k|k-1 ；
In the formula, I is an identity matrix.
The invention provides a mobile robot synchronous positioning and mapping system based on self-adaptive strong tracking, which comprises:
the model acquisition and initialization module is used for constructing a kinematic model and an observation model of the mobile robot according to the chassis style of the mobile robot and the characteristics of the sensor on the premise of assuming that the noises in the synchronous positioning and map construction process are additive Gaussian noises; initializing a kinematic model and an observation model of the mobile robot, and acquiring an initial pose and an initial estimation error covariance of the mobile robot under a global coordinate system;
the iterative estimation module is used for carrying out iterative estimation on the pose of the mobile robot based on the adaptive strong tracking extended Kalman filtering method so as to realize real-time pose estimation and map construction of the mobile robot;
wherein in the process of carrying out iterative estimation on the pose of the mobile robot based on the adaptive strong tracking extended Kalman filtering method, the step of iterative estimation at the moment k comprises the steps of,
based on the pose of the mobile robot at the time k-1 and the covariance of the estimated errors at the time k-1, obtaining a predicted value of the pose of the mobile robot at the time k by using an extended Kalman filtering method and a kinematic model of the mobile robot;
acquiring observation information of a sensor at the time k on an environmental landmark, and performing landmark data association to obtain landmark association results at the time k and the time k-1; acquiring correlated k-time sensor observation information based on the road sign correlation result;
judging whether the iteration result of the mobile robot synchronous positioning and mapping method diverges or not to obtain a judgment result; based on the judgment result, updating the time of the k moment estimation error covariance by using the pose of the mobile robot at the k-1 moment, the k-1 moment estimation error covariance, a kinematic model of the mobile robot and an observation model to obtain a k moment estimation error covariance predicted value;
and obtaining the pose of the mobile robot at the time k and the estimation error covariance at the time k through measurement updating based on the correlated observation information of the sensor at the time k, the predicted value of the pose of the mobile robot at the time k and the predicted value of the estimation error covariance at the time k.
In a further improvement of the present invention, in the model acquisition and initialization module, the kinematic model and the observation model of the mobile robot are constructed and obtained as,
in the formula, z k As observed information of the sensor at time k, u k For the input of the robot at the time k, f (-) is a state transfer function, h (-) is a measurement function, w k-1 And v k For uncorrelated process noise and measurement noise, the mean value of the signals is 0, and the covariance is R k And Q k A Gaussian distribution;
for the state information of the mobile robot at time k,
to move the robot's coordinate position in two-dimensional space,
the orientation of the mobile robot is deviated from the global coordinate system by an angle.
The further improvement of the present invention lies in that, in the iterative estimation module, the determination of whether the iterative result of the mobile robot synchronous positioning and mapping method diverges is implemented, and in the process of obtaining the determination result:
the criterion expression of whether to diverge is as follows,
in the formula (I), the compound is shown in the specification,
is an innovation sequence at the time of k,
for a mobile robot at time k a measurement function is provided
Taylor expansion is performed and the result of the first order approximation is taken, and
kappa is more than or equal to 1 and is an adjustable coefficient, tr [ · [ ]]Tracing the operator for the matrix, P k/k-1 Estimating a predicted value of the error covariance for the time k;
when the criterion expression is satisfied, a strong tracking algorithm is required to be introduced to inhibit filtering divergence.
The invention is further improved in that, in the iterative estimation module, in the process of utilizing the pose of the mobile robot at the time k-1, the estimation error covariance at the time k-1, the kinematic model of the mobile robot and the observation model to update the estimation error covariance at the time k to obtain the estimation value of the estimation error covariance at the time k based on the judgment result,
when the filtering is already dispersed, introducing a self-adaptive strong tracking algorithm, calculating parameters of a self-adaptive strong tracking filter, and carrying out time updating on the covariance of the estimation error, wherein the time updating comprises the following steps:
calculating an innovation sequence covariance matrix V k The expression is as follows,
in the formula, rho is more than 0 and less than or equal to 1 and is a forgetting factor;
obtaining a parameter matrix M k And N k The expression is as follows,
wherein the parameter beta is more than or equal to 1 and is a weakening factor;
for the mobile robot at the moment k-1, the state transfer function is
Taylor expansion is performed and the result of the first order approximation is taken,
moving the pose of the robot at the moment k-1;
λ k the computational expression of (a) is as follows,
in the formula (I), the compound is shown in the specification,
after introducing the self-adaptive strong tracking filtering algorithm, the time updating formula of the estimation error covariance is as follows,
in the formula, P k-1|k-1 Is the covariance of the estimation error at time k-1, lambda k Q k-1 The term can be considered as a correction term for noise when the noise parameters mismatch.
In the iterative estimation module, in the process of obtaining the pose of the mobile robot at the time k and the estimated error covariance at the time k by measurement and update based on the correlated observation information of the sensor at the time k, the predicted value of the pose of the mobile robot at the time k and the predicted value of the estimated error covariance at the time k,
the measurement updating step comprises the following steps:
calculating Kalman filter gain K at moment K k The calculation expression is
Calculate pose of k moment robot
Is calculated as
Updating an estimation error covariance matrix P k|k Updating expression as P k|k ＝(I-K k H k )P k|k-1 ；
In the formula, I is an identity matrix.
Compared with the prior art, the invention has the following beneficial effects:
the mobile robot synchronous positioning and mapping method provided by the invention is based on a self-adaptive strong tracking algorithm and combined with a robot system model and the measurement data of a laser radar, can carry out high-precision estimation on the pose of the robot and the position of a road sign under the conditions of sudden change of the motion state of the mobile robot, inaccurate modeling of system parameters, parameter mismatch and the like, and is beneficial to improving the positioning and mapping precision of the mobile robot in an unknown environment. Compared with traditional SLAM methods such as EKF and STF, the mobile robot synchronous positioning and mapping method based on self-adaptive strong tracking provided by the invention can obtain accurate robot pose and landmark estimation results, can realize online identification of unknown environment, and the constructed high-precision global environment map can be used for path planning and autonomous navigation of the mobile robot. On the basis of an STF algorithm frame, the invention directly acts the fading factor on the process noise covariance matrix in the time updating step, thereby realizing the self-adaptive estimation of the system process noise and the real-time correction of the filter gain. The method establishes the introduction condition of strong tracking filtering based on the idea of covariance matching, solves the filtering divergence phenomenon caused by abnormal fading factor calculation in the STF algorithm, and improves the position tracking capability and the landmark estimation precision of the robot under the scenes of model uncertainty and state mutation.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art are briefly introduced below; it is obvious that the drawings in the following description are some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort.
Fig. 1 is a schematic flowchart of a mobile robot synchronous positioning and mapping method based on adaptive strong tracking according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a system modeling by taking a differential chassis mobile robot as an example according to an embodiment of the present invention;
FIG. 3 is a schematic view of a scenario for performing a simulation experiment in an embodiment of the present invention;
FIG. 4 shows the result of performing robot SLAM experiments using EKF algorithm in accordance with an embodiment of the present invention;
FIG. 5 shows the result of an experiment of performing robot SLAM using STF algorithm according to an embodiment of the present invention;
FIG. 6 shows the result of the robot SLAM experiment using the adaptive strong tracking filtering algorithm according to the embodiment of the present invention;
fig. 7 is a schematic diagram of a mean square error variation curve of a pose estimation result of the robot obtained by using two algorithms, namely EKF and adaptive strong tracking filtering, in the embodiment of the present invention.
Detailed Description
In order to make those skilled in the art better understand the technical solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, shall fall within the protection scope of the present invention.
It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
The invention is described in further detail below with reference to the accompanying drawings:
referring to fig. 1, a method for synchronously positioning and mapping a mobile robot based on adaptive strong tracking according to an embodiment of the present invention includes the following steps:
step S1: a mobile robot is modeled. Assuming that the noises in the SLAM process of the mobile robot are additive noises, and constructing a kinematic model and an observation model of the mobile robot according to the chassis model of the mobile robot and the characteristics of the sensor.
The specific modeling process of step S1 of the embodiment of the present invention is as follows:
aiming at a certain mobile robot, selecting a certain point in a working scene of the mobile robot as a coordinate origin to construct a global coordinate system, and simultaneously selecting a geometric center of the mobile robot as the coordinate origin to construct a local coordinate system;
definition of
For the state information of the mobile robot at time k,
to move the robot's coordinate position in two-dimensional space,
deviating the orientation of the mobile robot from the included angle of the global coordinate system; definition of
Characteristic information of the road sign at the moment k; the state vector for the SLAM problem can be described as:
according to the motion modes of different chassis of the mobile robot and the measurement principle of the sensor, an abstract mobile robot kinematics equation and an observation equation can be constructed, and are expressed as follows:
in the formula, z k Is measurement information at time k, u k For the input of the robot at the time k, f (-) is a state transfer function, h (-) is a measurement function, w k-1 And v k The noise covariance is Q k And R k 。
Referring to fig. 2, in the embodiment of the present invention, a differential chassis mobile robot is taken as an example to model a mobile robot; in FIG. 2, point O g As the origin of a global coordinate system, with the geometric center O of the mobile robot r Establishing a dynamic equation and an observation equation of the mobile robot for the origin of the local coordinate system as follows:
in the formula (x) r,k ,y r,k ,θ k ) Is the pose, epsilon, of the robot at the moment k in a global coordinate system k And ω k Respectively linear velocity and angular velocity of the robot at the moment k, T is a sampling period, w k-1 Is process noise. r is a radical of hydrogen k And
respectively the distance from the ith road sign to the geometric center of the robot at the moment k and the included angle between the ith road sign and the running direction of the robot, (x) i,k ,y i,k ) For the i-th landmark, v, coordinates in the global coordinate system k Is the measurement noise of the sensor.
Step S2: and initializing parameters. Initializing the maximum distance measurement, resolution and other information of the sensor, and acquiring the initial pose of the mobile robot in the global coordinate system
And initial estimation error covariance P 0 The specific calculation method comprises the following steps:
in the formula (I), the compound is shown in the specification,
is the real pose of the robot at the initial moment,
operators are desired for mathematics.
In the embodiment of the invention, the initial pose (x) of the mobile robot is set r,0 ,y r,0 ,θ 0 ) = (0 m, -3m, 0rad), initial estimation error covariance
Referring to fig. 3, in this embodiment, a simulation field with a length and a width of 20m is built in the MATLAB, and three circles of landmark points are uniformly arranged at intervals of 30 ° by taking the center of the field as the center of a circle and taking 3m, 5m, and 8m as the radius, respectively, as shown in fig. 3. And setting the maximum measurement distance of the laser radar carried by the robot to be 5m. In order to simulate the phenomena of model parameter mismatch and state mutation of the robot in the operation process, three sections of different process noises Q are uniformly arranged in the simulation process k And linear velocity ε k Please refer to table 1 for detailed parameter setting.
TABLE 1 Process noise and line speed parameters
In addition, the signpost state vector needs to be initialized
Usually, the state vector of the signpost is managed in an incremental mode, and no signpost information exists at the initial moment, so that
Is a null vector.
And step S3: and predicting the pose of the mobile robot. According to the idea of extended Kalman filtering, the pose of the robot is estimated by the posterior of k-1 moment
Predicting the pose of the robot at the k moment by combining a dynamic model of the robot
The calculation formula is as follows:
and step S4: and acquiring observation information of the sensor and performing landmark data association. Before the landmark data is merged into the global map, data association must exist between the newly observed landmark and the landmark already existing in the map. In order to ensure the convergence of the algorithm, after the sensor finishes sampling the landmark information at each moment, the landmark information at the moment k needs to be subjected to data association with the landmark information at the moment k-1. The processing of landmarks observed by sensors can be divided into two categories, including:
(1) If the landmark has already been observed. The state of the landmark only needs to be updated in the subsequent measurement update, and the latest landmark state is obtained.
(2) If the landmark has not been observed. Then, according to the observation model of the sensor, the state of the new observed landmark needs to be obtained by inverse operation and added to the landmark state vector
In the middle, the augmentation of the road sign state vector is realized; at the same time, the covariance matrix after the amplification needs to be calculated.
Step S5: it is determined whether the filter is diverging. In this embodiment, an error divergence criterion is constructed based on the covariance matching idea, a strong tracking algorithm is introduced only when a filter diverges due to system model parameter mismatch or state mutation, and a detailed derivation process is as follows:
when the system state is not mutated or the system model is accurate, the following formula is satisfied:
in the formula, gamma k Is an innovation sequence at time k, an
For a mobile robot at time k a measurement function is provided
Taylor expansion is performed and the result of the first order approximation is taken.
The mutation of the system state or the mismatch of the model parameters can cause innovation increase, the orthogonality principle is no longer satisfied, and according to the characteristics of the innovation sequence, the criterion of filter divergence can be constructed:
in the formula, kappa is more than or equal to 1 and is an adjustable coefficient, can be selected according to needs, and is the strictest judgment condition when kappa = 1; tr [ · ] is a matrix tracing operator; when the filter satisfies the above formula, it is proved that parameter mismatch may occur in the prediction model, or the measurement information is seriously interfered, and at this time, a strong tracking algorithm needs to be introduced to suppress filtering divergence.
Step S6: the estimation error covariance is updated temporally. According to the judgment result of whether the filtering is divergent in step S5, the updating of the error covariance can be classified into the following two cases:
(1) The filtering has not diverged. At the moment, a self-adaptive strong tracking algorithm is not required to be introduced, and only time updating is required to be carried out according to a calculation formula of estimation error covariance in the traditional EKF algorithm:
in the formula (I), the compound is shown in the specification,
for a mobile robot, k time state transfer functions are
Taylor expansion is performed and the result of the first order approximation is taken.
(2) The filtering has already diverged. At this time, an adaptive strong tracking algorithm needs to be introduced, parameters of the adaptive strong tracking filter are calculated, and time updating is carried out on the estimation error covariance. The key of the self-adaptive strong tracking algorithm lies in that the attenuation factor lambda is changed when the solution is carried out k Usually find the optimum lambda k Complex solving process is needed, which is not suitable for on-line calculation, so that the engineering generally uses approximate suboptimal formula, and the calculating process is as follows:
step S6.1: firstly, an innovation sequence covariance matrix V is calculated k ：
In the formula (11), ρ is more than 0 and less than or equal to 1, which is a forgetting factor.
Step S6.2: calculating two parameter matrices M k And N k ：
In the formula (13), the parameter β ≧ 1 is a weakening factor, which can enhance the smoothness of the state estimation.
Step S6.3: lambda k Can be derived by the following formula:
in the formula (14), the reaction mixture is,
after introducing the adaptive strong tracking filtering algorithm, the time updating formula of the estimation error covariance is changed into:
in formula (15), λ k Q k-1 The term can be considered as a correction term for noise when the noise parameters mismatch.
Step S7: and (6) updating the measurement. The step of measurement updating is mainly to correct the state according to the measurement information of the sensor in the step S4 and obtain the posterior estimation x of the state k|k And updating the estimation error covariance P k|k 。
In the embodiment of the invention, the detailed steps of the measurement updating link are as follows:
step S7.1: calculating Kalman filter gain K k ：
Step S7.2: a posteriori estimation of a computational state
Step S7.3: updating an estimation error covariance matrix P k|k ：
P k|k ＝(I-K k H k )P k|k-1 (18)
Step S8: and circularly iterating the step S1 to the step S7, so as to realize the pose estimation and map construction process of the mobile robot.
Referring to fig. 4 to 7, the experimental results of synchronous positioning and mapping of the simulated mobile robot using three algorithms of extended kalman filtering, strong tracking filtering and adaptive strong tracking filtering in this embodiment are shown, and the deviation degree between the estimated trajectory and the actual motion trajectory of the mobile robot and the variation of the mean square error of the estimated robot position during the whole mapping process are observed.
Fig. 4 to 6 are the results of synchronous positioning and mapping experiments of the mobile robot using three algorithms of extended kalman filtering, strong tracking filtering and adaptive strong tracking filtering, respectively. As can be seen by combining the three pictures in fig. 4 to 6, when the process noise is small and the noise prior is the same as the true value, the estimated trajectories of the three algorithms are substantially the same as the true trajectory; with the increase of noise and the sudden change of the robot state, the error of the EKF algorithm in the estimation of the robot pose is gradually increased, the estimation result of the STF algorithm is rapidly dispersed after a period of oscillation, and the adaptive strong tracking filtering algorithm can still realize better estimation effect. In the whole simulation process, the estimated track of the self-adaptive strong tracking filtering algorithm is basically overlapped with the real track. In addition, the comparison experiment result is easy to see that the self-adaptive strong tracking filtering algorithm is obviously superior to the other two algorithms in the estimation of the landmark position.
Fig. 7 is a mean square error variation curve of robot pose estimation in the whole SLAM process by the EKF algorithm and the adaptive strong tracking filtering, and it can be seen that, compared with the EKF algorithm, the mean square error curve of the adaptive strong tracking filtering algorithm is relatively flat, and the absolute value of the mean square error is obviously smaller than that of the EKF algorithm, which indicates that the adaptive strong tracking filtering algorithm is superior to the EKF algorithm in pose estimation of the robot SLAM.
The following are embodiments of the apparatus of the present invention that may be used to perform embodiments of the method of the present invention. For details of non-careless mistakes in the embodiment of the apparatus, please refer to the embodiment of the method of the present invention.
In another embodiment of the present invention, a system for synchronously positioning and mapping a mobile robot based on adaptive strong tracking is provided, which includes:
the model acquisition and initialization module is used for constructing a kinematic model and an observation model of the mobile robot according to the chassis pattern of the mobile robot and the characteristics of the sensor on the premise of assuming that the noise in the synchronous positioning and map construction process is additive Gaussian noise; initializing a kinematic model and an observation model of the mobile robot, and acquiring an initial pose and an initial estimation error covariance of the mobile robot under a global coordinate system;
the iterative estimation module is used for carrying out iterative estimation on the pose of the mobile robot based on a self-adaptive strong tracking extended Kalman filtering method so as to realize real-time pose estimation and map construction of the mobile robot;
wherein in the process of carrying out iterative estimation on the pose of the mobile robot based on the adaptive strong tracking extended Kalman filtering method, the step of iterative estimation at the k moment comprises the following steps of,
based on the pose of the mobile robot at the time k-1 and the covariance of the estimated errors at the time k-1, obtaining a predicted value of the pose of the mobile robot at the time k by using an extended Kalman filtering method and a kinematic model of the mobile robot;
acquiring observation information of a sensor at the time k on an environmental landmark, and performing landmark data association to obtain landmark association results at the time k and the time k-1; acquiring correlated k-time sensor observation information based on the road sign correlation result;
judging whether the iteration result of the mobile robot synchronous positioning and mapping method diverges to obtain a judgment result; based on the judgment result, updating the time of the k moment estimation error covariance by using the pose of the mobile robot at the k-1 moment, the k-1 moment estimation error covariance, a kinematic model of the mobile robot and an observation model to obtain a k moment estimation error covariance predicted value;
and obtaining the pose of the mobile robot at the time k and the estimation error covariance at the time k through measurement updating based on the correlated observation information of the sensor at the time k, the predicted value of the pose of the mobile robot at the time k and the predicted value of the estimation error covariance at the time k.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.
Claims (10)
1. A mobile robot synchronous positioning and mapping method based on adaptive strong tracking is characterized by comprising the following steps:
on the premise that noise in the synchronous positioning and map building process is additive Gaussian noise, a kinematic model and an observation model of the mobile robot are built according to the chassis style of the mobile robot and the characteristics of the sensor; initializing a kinematic model and an observation model of the mobile robot, and acquiring an initial pose and an initial estimation error covariance of the mobile robot under a global coordinate system;
iterative estimation is carried out on the pose of the mobile robot based on a self-adaptive strong tracking extended Kalman filtering method, so that real-time pose estimation and map construction of the mobile robot are realized;
wherein in the process of carrying out iterative estimation on the pose of the mobile robot based on the adaptive strong tracking extended Kalman filtering method, the step of iterative estimation at the k moment comprises the following steps of,
based on the pose of the mobile robot at the time k-1 and the covariance of the estimated errors at the time k-1, obtaining a predicted value of the pose of the mobile robot at the time k by using an extended Kalman filtering method and a kinematic model of the mobile robot;
acquiring observation information of a sensor at the time k on an environmental landmark, and performing landmark data association to obtain landmark association results at the time k and the time k-1; acquiring correlated k-time sensor observation information based on the road sign correlation result;
judging whether the iteration result of the mobile robot synchronous positioning and mapping method diverges or not to obtain a judgment result; based on the judgment result, updating the time of the k moment estimation error covariance by using the pose of the mobile robot at the k-1 moment, the k-1 moment estimation error covariance, a kinematic model of the mobile robot and an observation model to obtain a k moment estimation error covariance predicted value;
and obtaining the pose of the mobile robot at the time k and the estimation error covariance at the time k through measurement updating based on the correlated observation information of the sensor at the time k, the predicted value of the pose of the mobile robot at the time k and the predicted value of the estimation error covariance at the time k.
2. The mobile robot synchronous positioning and mapping method based on the adaptive strong tracking as claimed in claim 1, wherein the obtained kinematic model and observation model of the mobile robot are constructed and expressed as,
in the formula, z k As observed information of the sensor at time k, u k For the input of the robot at the time k, f (-) is a state transfer function, h (-) is a measurement function, w k-1 And v k For uncorrelated process noise and measurement noise, the mean value is 0 and the covariance is R k And Q k Gaussian distribution;
for the state information of the mobile robot at time k,
to move the robot's coordinate position in two-dimensional space,
the orientation of the mobile robot is deviated from the global coordinate system by an included angle.
3. The mobile robot synchronous positioning and mapping method based on adaptive strong tracking according to claim 2, wherein the determining whether the iteration result of the mobile robot synchronous positioning and mapping method diverges, and in the process of obtaining the determining result:
the criterion expression of whether to diverge is as follows,
in the formula (I), the compound is shown in the specification,
is an innovation sequence at the time of k,
measuring a function for a mobile robot at time k
Taylor expansion is performed and the result of the first order approximation is taken, and
kappa is more than or equal to 1 and is an adjustable coefficient, tr [. Cndot.)]Tracing operators for matrices, P k/k-1 Estimating a predicted value of the error covariance for the time k;
when the criterion expression is satisfied, a strong tracking algorithm is required to be introduced to inhibit filtering divergence.
4. The method as claimed in claim 3, wherein in the process of obtaining the predicted value of the covariance of the estimated error at the time k by using the pose of the mobile robot at the time k-1, the covariance of the estimated error at the time k-1, the kinematic model of the mobile robot and the observation model to update the covariance of the estimated error at the time k based on the judgment result,
when the filtering is already dispersed, introducing a self-adaptive strong tracking algorithm, calculating parameters of a self-adaptive strong tracking filter, and carrying out time updating on the covariance of the estimation error, wherein the time updating comprises the following steps:
calculating an innovation sequence covariance matrix V k The expression is as follows,
in the formula, rho is more than 0 and less than or equal to 1, and is a forgetting factor;
obtaining a parameter matrix M k And N k The expression is as follows,
wherein the parameter beta is more than or equal to 1 and is a weakening factor;
for the mobile robot at the moment k-1, the state transfer function is
Taylor expansion is performed and the result of the first order approximation is taken,
moving the pose of the robot at the moment k-1;
λ k the computational expression of (a) is as follows,
in the formula (I), the compound is shown in the specification,
after introducing the self-adaptive strong tracking filtering algorithm, the time updating formula for estimating the error covariance is as follows,
in the formula, P k-1|k-1 Is the covariance of the estimation error at time k-1, lambda k Q k-1 The term can be considered as a correction term for noise when the noise parameters mismatch.
5. The method according to claim 4, wherein in the process of obtaining the pose of the mobile robot at the time k and the estimated error covariance at the time k through measurement update based on the correlated observation information of the sensor at the time k, the predicted pose of the mobile robot at the time k and the predicted error covariance at the time k,
the measurement updating step comprises the following steps:
calculating Kalman filter gain K at moment K k The calculation expression is
Calculating pose of robot at k moment
Is calculated as
Updating an estimation error covariance matrix P k|k Updating expression as P k|k ＝[I-K k H k )P k|k-1 ；
In the formula, I is an identity matrix.
6. A mobile robot synchronous positioning and mapping system based on adaptive strong tracking is characterized by comprising:
the model acquisition and initialization module is used for constructing a kinematic model and an observation model of the mobile robot according to the chassis style of the mobile robot and the characteristics of the sensor on the premise of assuming that the noises in the synchronous positioning and map construction process are additive Gaussian noises; initializing a kinematic model and an observation model of the mobile robot, and acquiring an initial pose and an initial estimation error covariance of the mobile robot under a global coordinate system;
the iterative estimation module is used for carrying out iterative estimation on the pose of the mobile robot based on the adaptive strong tracking extended Kalman filtering method so as to realize real-time pose estimation and map construction of the mobile robot;
wherein in the process of carrying out iterative estimation on the pose of the mobile robot based on the adaptive strong tracking extended Kalman filtering method, the step of iterative estimation at the k moment comprises the following steps of,
based on the pose of the mobile robot at the time k-1 and the covariance of the estimated errors at the time k-1, obtaining a predicted value of the pose of the mobile robot at the time k by using an extended Kalman filtering method and a kinematic model of the mobile robot;
acquiring observation information of a sensor at the time k on an environmental landmark, and performing landmark data association to obtain landmark association results at the time k and the time k-1; acquiring correlated k-time sensor observation information based on the road sign correlation result;
judging whether the iteration result of the mobile robot synchronous positioning and mapping method diverges or not to obtain a judgment result; based on the judgment result, updating the time of the k moment estimation error covariance by using the pose of the mobile robot at the k-1 moment, the k-1 moment estimation error covariance, a kinematic model of the mobile robot and an observation model to obtain a k moment estimation error covariance predicted value;
and obtaining the pose of the mobile robot at the time k and the estimation error covariance at the time k through measurement updating based on the correlated observation information of the sensor at the time k, the predicted value of the pose of the mobile robot at the time k and the predicted value of the estimation error covariance at the time k.
7. The system for synchronously positioning and mapping the mobile robot based on the adaptive strong tracking as claimed in claim 6, wherein the model obtaining and initializing module is used for constructing a kinematic model and an observation model of the obtained mobile robot,
in the formula，z k As observed information of the sensor at time k, u k For the input of the robot at the time k, f (-) is a state transfer function, h (-) is a measurement function, w k-1 And v k For uncorrelated process noise and measurement noise, the mean value is 0 and the covariance is R k And Q k Gaussian distribution;
for the state information of the mobile robot at time k,
to move the robot's coordinate position in two-dimensional space,
the orientation of the mobile robot is deviated from the global coordinate system by an angle.
8. The system according to claim 7, wherein said iterative estimation module is configured to determine whether an iteration result of said method for synchronously positioning and mapping a mobile robot diverges, and in the process of obtaining the determination result:
the criterion expression of whether to diverge is as follows,
in the formula (I), the compound is shown in the specification,
for the sequence of innovation at time k,
for a mobile robot at time k a measurement function is provided
Taylor expansion is performed and the result of the first order approximation is taken, an
Kappa is more than or equal to 1 and is an adjustable coefficient, tr [ · [ ]]Tracing operators for matrices, P k/k-1 Estimating a predicted value of the error covariance for the time k;
when the criterion expression is satisfied, a strong tracking algorithm is required to be introduced to inhibit filtering divergence.
9. The system of claim 8, wherein the iterative estimation module is configured to perform the process of obtaining the predicted value of the k-time estimation error covariance by performing a time update on the k-time estimation error covariance based on the pose of the mobile robot at the k-1 moment, the k-1 estimation error covariance, the kinematic model of the mobile robot, and the observation model based on the determination result,
when the filtering is already dispersed, introducing a self-adaptive strong tracking algorithm, calculating parameters of a self-adaptive strong tracking filter, and carrying out time updating on the covariance of the estimation error, wherein the time updating comprises the following steps:
calculating an innovation sequence covariance matrix V k The expression is as follows,
in the formula, rho is more than 0 and less than or equal to 1, and is a forgetting factor;
obtaining a parameter matrix M k And N k The expression is as follows,
in the formula, the parameter beta is more than or equal to 1 and is a weakening factor;
for moving the robot at k-1 moment in time the state transfer function is
Taylor expansion is performed and the result of the first order approximation is taken,
moving the pose of the robot at the moment k-1;
λ k the computational expression of (a) is as follows,
in the formula (I), the compound is shown in the specification,
after introducing the self-adaptive strong tracking filtering algorithm, the time updating formula of the estimation error covariance is as follows,
in the formula, P k-1|k-1 Is the covariance of the estimation error at time k-1, lambda k Q k-1 The term can be considered as a correction term for noise when the noise parameters mismatch.
10. The system according to claim 9, wherein in the iterative estimation module, during the process of obtaining the pose of the mobile robot at the time k and the estimated error covariance at the time k through measurement update based on the correlated observation information of the sensor at the time k, the predicted pose of the mobile robot at the time k and the predicted error covariance at the time k,
the measurement updating step comprises the following steps:
calculating Kalman filter gain K at moment K k The calculation expression is
Calculate pose of k moment robot
Is calculated as
Updating an estimation error covariance matrix P k|k Updating expression as P k|k ＝[I-K k H k )P k|k-1 ；
In the formula, I is an identity matrix.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211137399.9A CN115328168A (en) | 2022-09-19 | 2022-09-19 | Mobile robot synchronous positioning and mapping method and system based on adaptive strong tracking |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211137399.9A CN115328168A (en) | 2022-09-19 | 2022-09-19 | Mobile robot synchronous positioning and mapping method and system based on adaptive strong tracking |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN115328168A true CN115328168A (en) | 2022-11-11 |
Family
ID=83913740
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202211137399.9A Pending CN115328168A (en) | 2022-09-19 | 2022-09-19 | Mobile robot synchronous positioning and mapping method and system based on adaptive strong tracking |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115328168A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115979240A (en) * | 2022-12-05 | 2023-04-18 | 哈尔滨理工大学 | Innovation superposition synchronous positioning and mapping method based on limited augmentation |
-
2022
- 2022-09-19 CN CN202211137399.9A patent/CN115328168A/en active Pending
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115979240A (en) * | 2022-12-05 | 2023-04-18 | 哈尔滨理工大学 | Innovation superposition synchronous positioning and mapping method based on limited augmentation |
| CN115979240B (en) * | 2022-12-05 | 2023-09-29 | 哈尔滨理工大学 | Innovation superposition synchronous positioning mapping method based on limit augmentation |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN109597864B (en) | Method and system for real-time positioning and map construction of ellipsoid boundary Kalman filtering | |
| Guivant et al. | Simultaneous localization and map building using natural features and absolute information | |
| CN111207774A (en) | Method and system for laser-IMU external reference calibration | |
| CN106772524B (en) | A kind of agricultural robot integrated navigation information fusion method based on order filtering | |
| EP3159658A1 (en) | Method and device for real-time target location and map creation | |
| CN108645413A (en) | The dynamic correcting method of positioning and map building while a kind of mobile robot | |
| CN107084714A (en) | A kind of multi-robot Cooperation object localization method based on RoboCup3D | |
| CN112904358A (en) | Laser positioning method based on geometric information | |
| Demim et al. | Cooperative SLAM for multiple UGVs navigation using SVSF filter | |
| Tang et al. | Robot tracking in SLAM with Masreliez-Martin unscented Kalman filter | |
| Demim et al. | A new adaptive smooth variable structure filter SLAM algorithm for unmanned vehicle | |
| CN109520503A (en) | Adaptive Kalman filtering SLAM method for square root volume ambiguity | |
| CN108303095B (en) | Robust volume target cooperative localization method suitable for non-Gaussian filtering | |
| CN115328168A (en) | Mobile robot synchronous positioning and mapping method and system based on adaptive strong tracking | |
| CN113709662B (en) | Autonomous three-dimensional inversion positioning method based on ultra-wideband | |
| Burguera et al. | Probabilistic sonar scan matching for robust localization | |
| Garcia et al. | Portable multi-hypothesis Monte Carlo localization for mobile robots | |
| Tang et al. | An improved H-infinity unscented FastSLAM with adaptive genetic resampling | |
| Font et al. | Mobile robot localization. Revisiting the triangulation methods | |
| CN115950414A (en) | Adaptive multi-fusion SLAM method for different sensor data | |
| Fabresse et al. | Active perception for 3D range-only simultaneous localization and mapping with UAVs | |
| Goronzy et al. | Weighted online calibration for odometry of mobile robots | |
| Wang et al. | Simultaneous localization and mapping embedded with particle filter algorithm | |
| Benedettelli et al. | Multi-robot SLAM using M-Space feature representation | |
| Wei et al. | Neural network based extended kalman filter for localization of mobile robots |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |