CN109816687A - The concurrent depth identification of wheeled mobile robot visual servo track following - Google Patents
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Abstract
A kind of concurrent depth discrimination method of wheeled mobile robot visual servo track following.The wheeled mobile robot that the present invention is directed under nonholonomic devises a kind of vision tracking and controlling method, and the depth information of scene can be picked out while servo track tracks.Firstly, recording one section of image/video to coplanar characteristic point to represent desired trajectory to be tracked.Then, by comparing the characteristic point in static reference image, the characteristic point in realtime graphic and the image/video prerecorded, the homography matrix under European coordinate system is established in conjunction with perspective geometry relationship.Then it by decomposing obtained homography matrix, devises motion control rule and the adaptive updates about unknown depth parameter is restrained.By the way that concurrent learning algorithm is added in adaptive updates rate, restore unknown depth information using history and current system data.It is restrained simultaneously finally by Lyapunov method and extension Barbara theorem proving track following error and depth Identification Errors, thus this method can effectively pick out depth information of scene.
Description
Technical field
The invention belongs to the technical fields of computer vision and mobile robot, same more particularly to a kind of mobile robot
When the concurrent adaptive depth discrimination method of visual servo track following, desired time-varying track can be tracked and believe its scene depth
Breath identifies.
Background technique
Wheeled mobile robot often works in dangerous environment, many due to the uncertain factor in working environment
Researcher has developed a variety of different solutions to improve the autonomous control ability of system.Recently, due to image procossing
The development of the raising of technology and control algolithm theory, many scientific research personnel use the autonomous control technology of view-based access control model sensor,
And then to realize independent navigation and the control of system.
For mobile-robot system, its intelligence, flexibility and environment can be greatly enhanced by introducing visual sensor
Sensing capability is controlled the movement of mobile robot, i.e. visual servo technology using realtime graphic feedback, can be widely used in
Various fields, if intelligent transportation and environment are explored, for these reasons, this technology is especially paid close attention to and becomes robot
The research hotspot in field.For visual sensor, by being imaged thus according to perspective projection model, the missing of depth information is main
Defect is wanted, therefore, for monocular-camera vision system, it is difficult to completely recover exterior three dimensional scene information and mobile robot
Displacement information；In addition, because there is nonholonomic in mobile robot, so that the design of Pose Control device
Very challenging, therefore, the missing of depth information and the limitation of nonholonomic constraint make mobile robot visual control task
Become abnormal arduous；However, existing method is mostly that unknown scene information is set on the basis of original Visual servoing control device
Count compensating module.In the sense that, it is still unable to get model of place after the completion of visual servo task, since working space is believed
Breath can not obtain completely, therefore limit further applying and popularization for robot system.In conclusion how in visual servo
Depth information identification is carried out while control, is a difficult but very valuable problem in robot control field.
Summary of the invention
A kind of concurrent depth discrimination method of wheeled mobile robot visual servo track following.The present invention is directed to incomplete fortune
Wheeled mobile robot under moving constraint devises a kind of vision tracking and controlling method, and can be in the same of visual servo track following
When recognize appearance scape depth information.Firstly, recording one section of image/video to coplanar characteristic point to represent expectation rail to be tracked
Mark.Then, by comparing the characteristic point in static reference image, characteristic point in current realtime graphic and the image prerecorded
Video establishes the homography matrix under European coordinate system in conjunction with perspective geometry relationship.Then by decomposing obtained homography square
Battle array devises the adaptive updates rule of motion control rule and depth identified parameters.In addition, being used by extending concurrent learning method
History and current system data go to establish an adaptive updates rate to restore unknown depth information.Finally by Lyapunov
Method restrains simultaneously with extension Barbara theorem proving system tracking error and depth Identification Errors, system Existence of Global Stable, energy
It is enough effectively to pick out the depth information of scene.
A kind of wheeled mobile robot concurrent adaptive depth discrimination method of visual servo simultaneously, it is characterised in that include following
Step:
1, a kind of wheeled mobile robot concurrent adaptive depth discrimination method of vision track following simultaneously, it is characterised in that
The following steps are included:
1st, define system coordinate system, comprising:
1.1st, establish system model
The coordinate system for defining wheeled mobile robot is as follows: withIndicate that video camera is sat relative to the reference of static feature point
Mark system, withIndicate the current pose coordinate system of wheeled mobile robot, withIndicate that corresponding to wheeled mobile robot it is expected position
The rectangular coordinate system of appearance, by coplanar characteristic point PiDetermining plane is reference planes π, and the unit normal vector for defining plane π is n*,
3-D Euclidean coordinate Pi?It is lower to use P respectivelyi(t), Pi d(t),To indicate:
Assuming that distance perseverance of the origin of each coordinate system to characteristic point along optical axis direction is positive, fromIt arrivesSpin matrix
ForFromIt arrivesTranslation vector beWhereincT*(t) forMiddle expression, equally
Indicate expectation fromIt arrivesTime-varying it is expected spin matrix, fromIt arrivesExpectation translation vector beWhereindT*(t)
?Middle expression,cT*(t) anddT*(t) it is defined as follows:
WithIt is defined as follows:
It is defined as follows:
In addition indicate fromIt arrivesSpin matrix the right hand rotate angle, θdIt indicatesIt arrivesSpin matrix the right hand
Rotate angle, it will thus be seen that
WhereinThe expectation angular speed for representing WMR existsIn expression, fromTo the unit normal vector along π of π
Distance be set asThen
WhereinIndicate the unit normal vector of π.
1.2nd, European reconstruction
Reconstruction features point firstWithThe European coordinate P of normalizationi?WithUnder expression:
Euclidean coordinate in order to obtain, each characteristic point byUnder vi(t), Under vdi(t), Under The projected pixel coordinate shown, Ta Menshi(i.e. practical time varying image point),(it is expected
Trajectory diagram picture point),The normalization Euclidean coordinate of the element of (i.e. constant reference picture point), characteristic point passes through pinhole lens
Model and picture point establish following relationship:
WhereinIt is known constant camera intrinsic parameter calibration matrix, spin matrix and translation between coordinate system
Vector can be as follows by normalization Euclidean coordinate representation:
Wherein H (t),Indicate Euclidean homography matrix,cT*h(t),For the flat of the content ratio factor
The amount of shifting to:
Then pass through Euclid's reconstruction technique decomposing H and Hd, obtain cT*h(t),dT*h(t), θ (t), θd
(t).
3rd, construct adaptive controller
According to the open loop dynamical equation of system, for the mobile-robot system design controller equipped with video camera and adaptively
The purpose of more new law, control is to ensure that coordinate systemIn trackingTime-varying track, with e (t)=[e1, e2, e3]TIndicate translation
With rotation tracking error, it is defined as follows:
WhereincT*h1(t),cT*h2(t),dT*h1(t) anddT*h2Definition, θ (t), θ in (12)d(t) definition in (13), separately
Outer auxiliary variableIt is defined as follows:
Open loop error equation are as follows:
Depth estimation errorIt is defined as follows:
WhereinIt is depth identification, whenUnknown depth information will be identified effectively when being intended to zero, wheel
The linear velocity and angular speed of formula mobile robot design are as follows:
According to concurrent learning method, recognized for depthAdaptive updates rule is designed, form is as follows:
WhereinFor more new gain,For normal number, tk∈ [0, t] be initial time and current time it
Between time point.Projection function Proj (χ) is defined as:
WhereinIt is positive valueLower bound, thus haveAvailable following formula:
According to derivation before, closed-loop error system is as follows:
When following formula is set up:
So far, completing mobile robot, visual servo track following and concurrent adaptive depth recognize simultaneously.
The advantages of the present invention
The invention proposes a kind of wheeled mobile robot while visual servos and adaptive depth discrimination method.The present invention
Mainly be made that following several respects work: 1. successfully recognize the depth information in the visual field, are obtained by vision system to external environment
Excellent perception；2. the homography matrix established under European coordinate system is used, later the homography matrix as obtained by decomposing, by robot
Effectively expected pose is arrived in driving；3. combined controller and depth identification module solve system Existence of Global Stable because error restrains simultaneously
Problem.
Detailed description of the invention:
Fig. 1 is to define coordinate system relationship；
Fig. 2 is simulation result: the desired current kinetic path of wheeled mobile robot；
Fig. 3 is simulation result: the image path [dotted line: required track of characteristic point；Solid line: current track]；
Fig. 4 is simulation result: systematic error converges to zero [dotted line: desired value；Solid line: true value]；
Fig. 5 is simulation result: the angular speed and linear velocity of wheeled mobile robot；
Fig. 6 indicates experimental result: being obtained by parameter adaptive more new lawVariation [solid line:Value；Dotted line: d*'s
True value].
Specific embodiment:
Embodiment 1
1, a kind of wheeled mobile robot concurrent adaptive depth discrimination method of vision track following simultaneously, it is characterised in that
The following steps are included:
1st, define system coordinate system, comprising:
The coordinate system for defining wheeled mobile robot is as follows: withIndicate that video camera is sat relative to the reference of static feature point
Mark system, withIndicate the current pose coordinate system of wheeled mobile robot, withIndicate that corresponding to wheeled mobile robot it is expected position
The rectangular coordinate system of appearance, by coplanar characteristic point PiDetermining plane is reference planes π, and the unit normal vector for defining plane π is n*,
3-D Euclidean coordinate Pi?It is lower to use respectivelyTo indicate:
Assuming that distance perseverance of the origin of each coordinate system to characteristic point along optical axis direction is positive, fromIt arrivesSpin matrix
ForFromIt arrivesTranslation vector beWhereincT*(t) forMiddle expression, equally
Indicate expectation fromIt arrivesTime-varying it is expected spin matrix, fromIt arrivesExpectation translation vector beWhereindT*
(t) existMiddle expression,cT*(t) anddT*(t) it is defined as follows:
WithIt is defined as follows:
It is defined as follows:
In addition indicate fromIt arrivesSpin matrix the right hand rotate angle, θdIt indicatesIt arrivesSpin matrix the right hand
Rotate angle, it will thus be seen that
WhereinThe expectation angular speed for representing WMR existsIn expression, fromTo the unit normal vector along π of π
Distance be set asThen
WhereinIndicate the unit normal vector of π.
1.2nd, European reconstruction
Reconstruction features point firstWithThe European coordinate P of normalizationi?WithUnder expression:
Euclidean coordinate in order to obtain, each characteristic point byUnderUnder Under
'sThe projected pixel coordinate shown, Ta Menshi(i.e. practical time varying image point),(i.e. desired trajectory
Picture point),The normalization Euclidean coordinate of the element of (i.e. constant reference picture point), characteristic point passes through pinhole lens model
Following relationship is established with picture point:
WhereinIt is known constant camera intrinsic parameter calibration matrix, spin matrix and translation between coordinate system
Vector can be as follows by normalization Euclidean coordinate representation:
Wherein H (t),Indicate Euclidean homography matrix,For the translation of the content ratio factor
Vector:
Then pass through Euclid's reconstruction technique decomposing H and Hd, obtain cT*h(t),dT*h(t), θ (t), θd
(t).
3rd, construct adaptive controller
According to the open loop dynamical equation of system, for the mobile-robot system design controller equipped with video camera and adaptively
The purpose of more new law, control is to ensure that coordinate systemIn trackingTime-varying track, with e (t)=[e1, e2, e3]TIndicate translation
With rotation tracking error, it is defined as follows:
WhereincT*h1(t),cT*h2(t),dT*h1(t) anddT*h2Definition, θ (t), θ in (10)d(t) definition in (4), separately
Outer auxiliary variableIt is defined as follows:
Open loop error equation are as follows:
Depth estimation errorIt is defined as follows:
It is depth identification, whenUnknown depth information will be identified effectively when being intended to zero, wheeled shifting
The linear velocity and angular speed of mobile robot design are as follows:
According to concurrent learning method, recognized for depthAdaptive updates rule is designed, form is as follows:
WhereinFor more new gain,For normal number, tk∈ [0, t] be initial time and current time it
Between time point.WhereinFor more new gain,For normal number, tk∈ [0, t] is initial time and current time
Between time point, it can be seen that used in the concurrent learning method of adaptive updates rate and to have been recorded in N sampling period
Data, it is therefore desirable to which optimal smoother is estimatedwc(tk),cT*h2(tk), vc(tk) exact value, in this journey
For degree, it can be seen that have in parameter Estimation and be significantly improved.
Projection function Proj (χ) is defined as:
WhereinIt is positive valueLower bound, thus haveAvailable following formula:
In fact, control parameter kv, kwMainly to the control of robot and more new gain Γ1, Γ2Have an impact to change
The depth recognition of robot, but since parameter is fairly small, this makes it be easy to correct adjusting parameter, so as to for actually answering
With.According to derivation before, closed-loop error system is as follows:
When following formula is set up:
So far, completing mobile robot, visual servo track following and concurrent adaptive depth recognize simultaneously.
4th, stability analysis
Theorem 1: control law and parameter more new law ensure that the tracking error of wheeled mobile robot is progressive and go to zero, and will move
Mobile robot calms and tracks desired path while having carried out depth identification, i.e., following formula is set up:
It is assumed that the time-derivative of expectation path meets following condition:
It proves:
Define non-negative Lyapunov function are as follows:
It can be obtained to Lyapunov function derivation, and by the substitution of open loop error equation:
(16) are substituted into above formula (24), obtain following expression:
It can be seen that
From e known to (23) and (26)1(t),e3(t),And e1(t),Find out from (14)d*It is constant, according to what is constructeddT*h1(t),dT*h2(t), θd(t),For bounded function andProperty, utilize (11) (12) and (16) in the provable e of expression formula2(t),cT*h1(t),cT*h2(t), θd
(t),Development based on front passes through (13) (15) (16) available vc(t),Therefore all system state variables all keep boundedness.In addition, defining Ф is all makePoint set:
The maximum invariant set that M is Ф is defined, the point in M is set up from following relationship known to (25):
Therefore:
Then (28) and (29) are substituted intoClosed-loop dynamic equation in (19), obtains as follows:
Therefore according to aboveIt is assumed that obtaining in set ME can be proved from (12) and (29)2
=0, due to using projection function (17) to makePiecewise smooth, but it is continuously, from (14) (16) for given primary condition
(28) it can be seen that
Therefrom obtainPositive boundaryBe it is constant, maximum invariant set M only includes equalization point, and form is as follows:
According to Russell's principle of invariance, mobile robot tracking error and depth Identification Errors asymptotic convergence to zero, i.e.,
5th, system emulation
In in this section, the performance of proposed method is verified the present invention provides simulation result, is singly answered in order to obtain
Property matrix, randomly selects 4 plane characteristic points, then the intrinsic parameter of video camera is provided that
The stability and feature height that the picture noise test controller that standard deviation is σ=0.15 is added recognize anti-interference
Ability, selection control parameter are simultaneously set as kv=0.605, kω=0.100, Γ1=Γ2=0.900.N is selected as 100, record
Data in preceding 100 sampling periods.
After emulation, from the path of wheeled mobile robot shown in Fig. 2, it can be seen that robot successfully tracks the phase
The track of prestige；It can find out in Fig. 3, current signature point image track effectively tracks the image path of desired character point；From Fig. 4
As can be seen that systematic error converges to zero；Fig. 5 shows the v of wheeled mobile robotc(t) and ωc(t)；Fig. 6 shows that depth is estimated
Meter rapidly and efficiently converges on its true value, it means that unknown depth information of scene can identify completely；As can be seen that
Robot has small steady-state error with trajectory path needed for high efficiency tracking.
Claims (1)
1. a kind of wheeled mobile robot concurrent adaptive depth discrimination method of vision track following simultaneously, it is characterised in that including
Following steps:
1st, define system coordinate system, comprising:
1.1st, establish system model
The coordinate system for defining wheeled mobile robot is as follows: withIndicate reference frame of the video camera relative to static feature point,
WithIndicate the current pose coordinate system of wheeled mobile robot, withIt indicates to correspond to the straight of wheeled mobile robot expected pose
Angular coordinate system, by coplanar characteristic point PiDetermining plane is reference planes π, and the unit normal vector for defining plane π is n*, 3-D Euclidean
Coordinate Pi?It is lower to use respectivelyTo indicate:
Assuming that distance perseverance of the origin of each coordinate system to characteristic point along optical axis direction is positive, fromIt arrivesSpin matrix beFromIt arrivesTranslation vector beWhereincT*(t) forMiddle expression.EquallyTable
Show expectation fromIt arrivesTime-varying it is expected spin matrix, fromIt arrivesExpectation translation vector beWhereindT*(t)
?Middle expression,cT*(t) anddT*(t) it is defined as follows:
cT*(t)=[cT*x, 0,cT*z]T,dT*(t)=[dT*x, 0,dT*z]T. (2)
KindIt is defined as follows:
It is defined as follows:
In addition indicate fromIt arrivesSpin matrix the right hand rotate angle, θdIt indicatesIt arrivesSpin matrix the right hand rotation
Angle, it will thus be seen that
WhereinThe expectation angular speed for representing WMR existsIn expression, fromTo the distance of the unit normal vector along π of π
It is set asThen
d*=n*TPi * (6)
WhereinIndicate the unit normal vector of π.
1.2nd, European reconstruction
Reconstruction features point firstWithThe European coordinate P of normalizationi?WithUnder expression:
Euclidean coordinate in order to obtain, each characteristic point byUnderUnder UnderThe projected pixel coordinate shown, Ta Menshi(i.e. practical time varying image point),(i.e. expectation trajectory diagram
Picture point),The element of (i.e. constant reference picture point), the normalization Euclidean coordinate of characteristic point by pinhole lens model with
Picture point establishes following relationship:
WhereinIt is known constant camera intrinsic parameter calibration matrix, spin matrix and translation vector between coordinate system
It can be as follows by normalization Euclidean coordinate representation:
Wherein H (t),Indicate Euclidean homography matrix,For the translation vector of the content ratio factor:
Then pass through Euclid's reconstruction technique decomposing H and Hd, obtain
3rd, construct adaptive controller
According to the open loop dynamical equation of system, controller and adaptive updates are designed for the mobile-robot system equipped with video camera
Rule, the purpose of control are to ensure that coordinate systemIn trackingTime-varying track, with e (t)=[e1, e2, e3]TIndicate translation and rotation
Turn tracking error, be defined as follows:
WhereincT*h1(t),cT*h2(t),dT*h1(t) anddT*h2Definition, θ (t), θ in (10)d(t) definition in (4).In addition auxiliary
Help variableIt is defined as follows:
Open loop error equation are as follows:
Depth estimation errorIt is defined as follows:
It is depth identification, whenUnknown depth information will be identified effectively when being intended to zero, wheel type mobile machine
The linear velocity and angular speed of device people design are as follows:
According to concurrent learning method, recognized for depthAdaptive updates rule is designed, form is as follows:
WhereinFor more new gain,For normal number, tk∈ [0, t] is between initial time and current time
Time point.Projection function Proj (χ) is defined as:
WhereinIt is positive valueLower bound, thus haveAvailable following formula:
According to derivation before, closed-loop error system is as follows:
When following formula is set up:
So far, completing mobile robot, visual servo track following and concurrent adaptive depth recognize simultaneously.
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