CN109960145A - Mobile robot mixes vision track following strategy - Google Patents
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Abstract
The present invention discloses a kind of mobile robot mixing vision track following strategy.Vision Trajectory Tracking Control method is proposed for the wheeled mobile robot equipped with vehicle-mounted vision system, wherein being readily maintained at visual signature within the scope of camera coverage using 2.5 dimension visual servo frames, and then improves the effect of vision track following.Firstly, designing the systematic error of mixed form by characteristics of image and robot direction according to present image, reference picture and desired image sequence.New systematic error is introduced later, is derived open cycle system error equation after doing corresponding transformation.Based on this, a kind of adaptive controller is devised to realize visual servo track following task, wherein passing through parameter update mechanism complementary characteristics point depth.According to Lyapunov method and Barbalat lemma, it was demonstrated that go out mentioned method can make systematic error under depth unknown situation asymptotic convergence to zero.Contrast simulation results showed that mentioned method performance.
Description
Technical field
The invention belongs to the technical fields of computer vision and mobile robot, mixed more particularly to a kind of mobile robot
Close vision track following strategy.
Background technique
With the fast development of robot technology, mobile robot is played an increasingly important role.Nowadays, it has
Move the advantages that flexible, easily operated and working space is big.In addition, visual sensor is widely used in respective intelligent body, this
Class sensor has abundant information, non-cpntact measurement, high reliability.Mobile robot and visual sensor are combined
Come, the ability of robot system perception external environment can be enhanced, and then complicated task can be easily accomplished.View-based access control model feedback
Control, the also referred to as visual servo of mobile robot guides mobile robot using the feedback of realtime graphic, make robot with
The given tracking of track is calmed to expected pose.Therefore, this technology can be applied hands in many fields, such as intelligence
It is logical, home services, automatic material flow etc..This technology is a research hotspot of robot and automatic field.
Compared with the control of the posture stabilization of mobile robot, track following strategy can mutually be tied with other motion measurements
It closes, therefore is more suitable for completing complicated task.For the mobile-robot system of view-based access control model, wherein main challenge is a lack of
The depth information of environment makes mobile robot pose be difficult to be restored completely, and brings uncertainty for Closed dynamitic system.
On the other hand, mobile robot is the typical under-actuated systems with nonholonomic motion, therefore existing robot control strategy,
Including track following, it is not directly applicable mobile-robot system.It is machine in view of uncertain factors such as nonholonomic constraints
People designs a high performance hybrid vision track following strategy and is challenging.
Up to the present, certain methods have been devised to realize the track following target of mobile robot.Blazic is mentioned
A kind of frame constructing various contrail trackers out can obtain different tracking performances by changing time-varying function.Base
In polar expression, Chwa designs a sliding mode controller to track given track, can obtain efficient motion path.Li
Et al. combine quadratic programming and predictive control model to solve track following problem, wherein considering mobile robot speed
Constraint of saturation.Zambelli et al. combines tracking error with decreasing function, designs controller in order to adjust transitory
It can be with track following effect.But tracking above is effective when mobile robot total state can be surveyed.Due to
It carries out lacking depth information when track following when using visual sensor, so bringing difficulty to track following.
When using visual sensor, it should be readily maintained at visual signature within the scope of camera coverage.The benefits such as Fang
Active vision is formed with holder result, tracking sensation target is accordingly rotated.Mariottini etc. is in order in mobile robot
Visible feature is kept when mobile, omnidirectional's camera is then used in visual servo task.In addition, in order to handle unknown depth
Information is spent, the adaptive controller that Zhang et al. devises a kind of visual servo compensates depths of features.Simultaneously to expectation
Track tracked, Wang et al. propose identification algorithm can be with the depths of features of On-line Estimation and robot global position.
Yang et al. proposes one kind in the case where mobile robot does not demarcate visual parameters under uncertain robot dynamics
Contrail tracker based on adaptive torque.In a sense, challenge is related to by visual sensor bring
Visual field constraint and unknown depths of features.In visual servo tracing task, it should handle with great care.
Many solutions are that mobile robot visual servo tracking design is with ceiling camera.For example, beam etc.
It proposes and proposes a kind of contrail tracker based on not calibrated camera image, camera plane does not need in this scheme
It is parallel with robot motion's plane.However, the application potential frame of eyes opponent is limited, because mobile robot is limited
Within small range.On the other hand, mobile robot visual servo track task is completed, recent years, various methods are
It is developed for Airborne camera configuration.
Chen et al. proposes a kind of controller that there is vision track following characteristic point depth adaptive to update rule, i.e.,
Required motion profile is determined by the image sequence prerecorded.The track given by the tracking of a series of key images,
Jia et al. devises the adaptive tracking control unit of one kind to handle the camera substantially installed.Cherubini et al. utilizes pass
Key image sequence defines the desired motion path of mobile robot, and devises one kind by image mistake and Obstacle Position
Contrail tracker.
Becerra et al. has used pole and trifocal tensor to design the angular speed of mobile robot, wherein according to compared with
The image obtained in big working space defines track to be tracked.Regrettably, existing method seldom considers visual field problem
Or the effect of track following is discussed.
Summary of the invention
The present invention discloses a kind of mobile robot mixing vision track following strategy.For equipped with vehicle-mounted vision system
Wheeled mobile robot proposes vision Trajectory Tracking Control method, wherein making visual signature using 2.5 dimension visual servo frames
It is readily maintained within the scope of camera coverage, and then improves the effect of vision track following.Firstly, according to present image, reference
Image and desired image sequence are designed the systematic error of mixed form by characteristics of image and robot direction.It introduces later
New systematic error is derived open cycle system error equation after doing corresponding transformation.Based on this, a kind of adaptive controller is devised
To realize visual servo track following task, wherein passing through parameter update mechanism complementary characteristics point depth.According to the side Lyapunov
Method and Barbalat lemma, it was demonstrated that go out mentioned method can make systematic error under depth unknown situation asymptotic convergence to zero.It is right
Than the performance that simulation result shows proposed method.
The mixing vision track strategy of mobile robot provided by the invention includes:
1st, the design of visual servo Trajectory Tracking System
The description of 1.1st scheme
In the present invention, we design a kind of mobile robot mixing visual servo track following strategy；Utilize 2.5 dimensions
Visual servo frame is so that visual signature is readily maintained within the scope of camera coverage, and then improves the effect of track following；It is first
First, according to present image, reference picture and desired image sequence, 2-1/2-D view is defined by characteristics of image and robot rotation amount
Feel servo tracking errors；Adaptive controller is devised later, wherein passing through parameter update mechanism complementary characteristics point depth information；
According to Lyapunov method and Barbalat lemma, it was demonstrated that go out in the case where scene depth is unknown, the vision track that is mentioned with
Track control method is able to achieve Asymptotic Stability as a result, comparing simulation result, compared with our pervious work, tracks in visual servo
With set point it is constant in the case where, mentioned method need to only adjust less control parameter and complete track following task, relatively be suitble to
Actual use；
2nd, construct system model
The description of 2.1st problem
In-vehicle camera coordinate system FcIt is overlapped with the coordinate system of mobile robot with nonholonomic constraints；Coordinate system FcZcAxis is along camera
Optical axis direction, and with mobile robot towards unanimously；xcAxis is parallel with wheel axis direction, ycAxis is perpendicular to robot motion's plane
zcxc；In addition, with FdIndicate the coordinate system on desired trajectory, wherein desired trajectory is defined by the image sequence prerecorded；It is quiet
Only coordinate system F*Indicate robot/video camera reference pose, be set to reference frame, can make desired image sequence with
Current image is compared by reference to image；The angle, θ calculated by the method for homographyc(t) and θd(t) the two angles
Degree is illustrated respectively in F under reference framecAnd FdRotation angle；According to the definition of these coordinate systems, the present invention designs a kind of view
Feel Trajectory Tracking Control method, makes in-vehicle camera coordinate system FcWith desired trajectory coordinate system FdIt coincides；
2.2nd can survey signal
Consider static nature point P in the scenei(i=1；2；...；N), in F*, FdAnd FcUnder coordinate use respectivelyCarry out F*, FdAnd FcDescription:
The corresponding homogeneous image pixel coordinates of above three coordinate are respectively
Normalized image coordinate is measurable:
Wherein K ∈ R3×3It is calibrated camera intrinsic parameter matrix；
For the ease of subsequent analysis, depth ratio is defined as follows:
Since mobile robot is usually maintained a certain distance with target object, thus variableWithIt is positive
Know γi1(t) and γi2(t) singular problem, Ke Yiyong will not occurTo estimate；
Angular speed w on desired trajectoryd(t) and scale meaning under expectation linear velocityIt can be by following
The form of calculus of finite differences calculates
Wherein θd(k) θ at current time is indicatedd(t) value, θd(k-1) θ of previous moment is indicatedd(t) value,WithDefinition it is similar therewith, Δ tkIt is the time interval between two moment；
3rd, controller design
Analysis robot kinematics first, then planned course tracking control unit is with Active Compensation unknown characteristics point depth,
Prove that proposed controller can make tracking error asymptotic convergence to zero using Lyapunov method.
3.1st, robot kinematics
FcAnd FdBetween translation error ez(t), exIt (t) can be by arbitrary characteristics point PiIt obtains, is defined as follows:
It considersKnow that above-mentioned definition mode does not have singularity problem furthermore FcAnd FdBetween rotation error eθ
(t) is defined as:
eθ:=θc-θd. (7)
By (6) (7) it is found that the track following error constructed is made of characteristics of image and the rotation angle estimated
's；The thus invention is built upon under 2.5 dimension visual servo frames, and visual signature can be made to be easily held in camera coverage model
Within enclosing；
For the ease of the controller design of next part, the present invention constructs a new error vector:
To ρ1, ρ2And ρ3After time derivation, available following chain type kinematical equation:
WhereinIndicate unknown characteristics point depth information；In addition, using the pose algorithm for estimating based on homography, it can
To obtain error signal ez(t), ex(t), eθ(t)；
For the ease of the controller design of next part, the present invention makes following hypothesis:
Assuming that 1: the speed v on desired trajectoryd(t), wdIt (t) is bounded, and
3.2nd controller design
In the open loop error system-based of formula (9), the present invention devises shifting on the basis of the depth of characteristic point is unknown
The hybrid visual servo contrail tracker of mobile robot；
Based on Lyapunov method for analyzing stability, the mobile robot linear velocity and angular speed control of following form are devised
System rule:
Wherein kv, kwThe control gain being positive.It is the estimated value of unknown constant α related with characteristic point depth, and leads to
Following manner is crossed to be updated:
Wherein Γ ∈ R+It is more new gain；
After controller is substituted into open loop kinetics equation (9), it is as follows that closed-loop error equation can be obtained:
WhereinIt is the definition of parameter estimating error:
Theorem 1: control law (10) and parameter more new law (11) can make the error asymptotic convergence in system dynamical equation (9) extremely
Zero:
It proves: choosing following non-negative Lyapunov function V (t):
To (14) both sides about time derivation, then bring into known to closed loop kinematic equation (12):
After formula (11) are substituted into (15), it can obtain
According to formula (14) and (16), it is apparent from ρ1(t), ρ2(t), ρ3(t),And then v can be obtained according to formula (10)c
(t), wc(t)∈L∞；As it is assumed that vd(t), wd(t) it is bounded, thus can be obtained according to (9) and (11)Cause
This, system mode is all bounded；
In turn, from ρ known to (16)1, ρ2∈L2；Therefore, it can directly be obtained using Barbalat lemma
Then, to ρ in formula (12)1(t) corresponding sin ρ1/ρ1Partial derivative is as follows:
It is set up in addition, being apparent from following relationship:
Due toIt is continuous in section (0, ∞), therefore it can be concluded that knot
It can be seen that sin ρ1/ρ1It is congruous continuity；
In addition, being easy to getIt is also congruous continuity.We also haveWith
Therefore, to ρ1(t) closed-loop error system can be obtained using extension Barbalat lemma
From (6) and (7) it is found that when formula (13) are set up, it can be achieved that vision track following task.
As it is assumed thatIt is readily seenTherefore, it is understood that the systematic error constructed
Equal asymptotic convergence is to 0, it may be assumed that
In addition, according to the ρ in (8)1(t), ρ2(t), ρ3(t) and ez(t), ex(t), eθ(t) relationship, it is known that track following
Error asymptotic convergence is to zero, it may be assumed that
Detailed description of the invention:
Fig. 1 is the coordinate system in this visual servo tracing task；
Fig. 2 is the block diagram of entire control system；
Fig. 3 is the scheme that is proposed: moveable robot movement track is marked with desired and current motion profile；
Fig. 4 is the scheme that is proposed: the differentiation [dotted line: desired value (zero)] of mobile robot tracking error；
Fig. 5 is the scheme proposed: the speed [solid line: rate of current of mobile robot；Dotted line: the speed of target trajectory]；
Fig. 6 is the scheme proposed: the two-dimentional track [solid line: current signature track of characteristics of image；Dotted line: desired feature
Track]；
Fig. 7 is to indicate experimental result: the motion profile of mobile robot is marked with desired and current motion profile；
Fig. 8 is to indicate experimental result: the differentiation [dotted line: desired value (zero)] of mobile robot tracking error；
Fig. 9 indicates experimental result: the speed [solid line: present speed of mobile robot；Dotted line: the speed on required track
Degree]；
Figure 10 indicates experimental result: the two-dimentional track [solid line: present image track of the characteristic point in image space；Dotted line:
Required image path]；
Figure 11 indicates experimental result: the differentiation of the position and direction error of mobile robot forms [dotted line: desired value
(zero)]；
Figure 12 indicates experimental result: the linear and angular speed [solid line: rate of current of mobile robot；Dotted line: required track
On speed].
Specific embodiment:
Embodiment 1
1st, the design of visual servo Trajectory Tracking System
The description of 1.1st scheme
In the present invention, we design a kind of mobile robot mixing visual servo track following strategy；Utilize 2.5 dimensions
Visual servo frame is so that visual signature is readily maintained within the scope of camera coverage, and then improves the effect of track following；It is first
First, according to present image, reference picture and desired image sequence, 2-1/2-D view is defined by characteristics of image and robot rotation amount
Feel servo tracking errors；Adaptive controller is devised later, wherein passing through parameter update mechanism complementary characteristics point depth information；
According to Lyapunov method and Barbalat lemma, it was demonstrated that go out in the case where scene depth is unknown, the vision track that is mentioned with
Track control method is able to achieve Asymptotic Stability as a result, comparing simulation result, compared with our pervious work, tracks in visual servo
With set point it is constant in the case where, mentioned method need to only adjust less control parameter and complete track following task, relatively be suitble to
Actual use；
2nd, construct system model
The description of 2.1st problem
In-vehicle camera coordinate system FcIt is overlapped with the coordinate system of mobile robot with nonholonomic constraints；Coordinate system FcZcAxis is along camera
Optical axis direction, and with mobile robot towards unanimously；xcAxis is parallel with wheel axis direction, ycAxis is perpendicular to robot motion's plane
zcxc；In addition, with FdIndicate the coordinate system on desired trajectory, wherein desired trajectory is defined by the image sequence prerecorded；It is quiet
Only coordinate system F*Indicate robot/video camera reference pose, be set to reference frame, can make desired image sequence with
Current image is compared by reference to image；The angle, θ calculated by the method for homographyc(t) and θd(t) the two angles
Degree is illustrated respectively in F under reference framecAnd FdRotation angle；According to the definition of these coordinate systems, the present invention designs a kind of view
Feel Trajectory Tracking Control method, makes in-vehicle camera coordinate system FcWith desired trajectory coordinate system FdIt coincides；
2.2nd can survey signal
Consider static nature point P in the scenei(i=1；2；...；N), in F*, FdAnd FcUnder coordinate use respectivelyCarry out F*, FdAnd FcDescription:
The corresponding homogeneous image pixel coordinates of above three coordinate are respectively
Normalized image coordinate is measurable:
Wherein K ∈ R3×3It is calibrated camera intrinsic parameter matrix；
For the ease of subsequent analysis, depth ratio is defined as follows:
Since mobile robot is usually maintained a certain distance with target object, thus variableWithIt is positive
Know γi1(t) and γi2(t) singular problem, Ke Yiyong will not occurTo estimate；
Angular speed w on desired trajectoryd(t) and scale meaning under expectation linear velocityIt can be by following
The form of calculus of finite differences calculates
Wherein θd(k) θ at current time is indicatedd(t) value, θd(k-1) θ of previous moment is indicatedd(t) value,WithDefinition it is similar therewith, Δ tkIt is the time interval between two moment；
3rd, controller design
Analysis robot kinematics first, then planned course tracking control unit is with Active Compensation unknown characteristics point depth,
Prove that proposed controller can make tracking error asymptotic convergence to zero using Lyapunov method.
3.1st, robot kinematics
FcAnd FdBetween translation error ez(t), exIt (t) can be by arbitrary characteristics point PiIt obtains, is defined as follows:
It considersKnow that above-mentioned definition mode does not have singularity problem furthermore FcAnd FdBetween rotation error eθ
(t) is defined as:
eθ:=θc-θd. (7)
By (6) (7) it is found that the track following error constructed is made of characteristics of image and the rotation angle estimated
's；The thus invention is built upon under 2.5 dimension visual servo frames, and visual signature can be made to be easily held in camera coverage model
Within enclosing；
For the ease of the controller design of next part, the present invention constructs a new error vector:
To ρ1, ρ2And ρ3After time derivation, available following chain type kinematical equation:
WhereinIndicate unknown characteristics point depth information；In addition, using the pose algorithm for estimating based on homography, it can
To obtain error signal ez(t), ex(t), eθ(t)；
For the ease of the controller design of next part, the present invention makes following hypothesis:
Assuming that 1: the speed v on desired trajectoryd(t), wdIt (t) is bounded, and
3.2nd controller design
In the open loop error system-based of formula (9), the present invention devises shifting on the basis of the depth of characteristic point is unknown
The hybrid visual servo contrail tracker of mobile robot；
Based on Lyapunov method for analyzing stability, the mobile robot linear velocity and angular speed control of following form are devised
System rule:
Wherein kv, kwThe control gain being positive.It is the estimated value of unknown constant α related with characteristic point depth, and leads to
Following manner is crossed to be updated:
Wherein Γ ∈ R+It is more new gain；
After controller is substituted into open loop kinetics equation (9), it is as follows that closed-loop error equation can be obtained:
WhereinIt is the definition of parameter estimating error:
Theorem 1: control law (10) and parameter more new law (11) can make the error asymptotic convergence in system dynamical equation (9) extremely
Zero:
It proves: choosing following non-negative Lyapunov function V (t):
To (14) both sides about time derivation, then bring into known to closed loop kinematic equation (12):
After formula (11) are substituted into (15), it can obtain
According to formula (14) and (16), it is apparent from ρ1(t), ρ2(t), ρ3(t),And then v can be obtained according to formula (10)c
(t), wc(t)∈L∞；As it is assumed that vd(t), wd(t) it is bounded, thus can be obtained according to (9) and (11)Cause
This, system mode is all bounded；
In turn, from ρ known to (16)1, ρ2∈L2；Therefore, it can directly be obtained using Barbalat lemmaThen, to ρ in formula (12)1(t) corresponding sin ρ1/ρ1Partial derivative is as follows:
It is set up in addition, being apparent from following relationship:
Due toIt is continuous in section (0, ∞), therefore it can be concluded that knot
It can be seen that sin ρ1/ρ1It is congruous continuity；
In addition, being easy to getIt is also congruous continuity.We also haveWith
Therefore, to ρ1(t) closed-loop error system can be obtained using extension Barbalat lemma
From (6) and (7) it is found that when formula (13) are set up, it can be achieved that vision track following task.
As it is assumed thatIt is readily seenTherefore, it is understood that the systematic error constructed
Equal asymptotic convergence is to 0, it may be assumed that
In addition, according to the ρ in (8)1(t), ρ2(t), ρ3(t) and ez(t), ex(t), eθ(t) relationship, it is known that track following
Error asymptotic convergence is to zero, it may be assumed that
4th, simulation result
In in this section, the performance of proposed method is verified the present invention provides simulation result.It is randomly selected total
Region feature point is taken as sensation target, and reference picture is in F*Place obtains.In order to obtain required image sequence, needed for it is defined
Robot motion track, virtual robot camera system is manipulated by the speed of sinusoid.Further it is provided that scheme and warp
The visual servo tracking strategy of allusion quotation and unified visual servo method are compared.Required track is from posture (- 4.2m；1.2m；
3 °) it starts setting up, then with snakelike movement.Motion profile is from (- 5.2m at present；1.7m；5 °) it starts setting up.Gaussian noise is added
It is added on required image sequence and the pixel of standard deviation δ=0.2 of present image.
For the scheme proposed, control parameter such as k is selectedv=0.3, kw=0.3, Γ=80.In addition, after filtering use
Desired value speed is calculated to difference algorithmwd(t).Attached drawing 3 shows the track of current and desired robot.Fig. 4 is aobvious
Track of the robot of tracking mistake between expectation and current kinetic is shown, wherein * Tdz(t), * Tdx(t) Z, X-coordinate are indicated
In coordinate system F*Under coordinate system FdOrigin, * Tcz(t), * Tcx(t) Z is indicated, X-coordinate is in coordinate system F*Under coordinate system FcOrigin.
According to Fig. 3 and Fig. 4, it is understood that by initial error quickly to reach desired motion profile bigger for mobile robot.Fig. 5
Show the linear and angular speed of robot, it is seen that when mobile robot is mobile with current speed and desired speed
Degree is consistent.Image path shown in attached drawing 6, we see that current feature is consistent with required image sequence there.
Control parameter kv, kw, γ1Be chosen as k by comparingv=0.3, kw=0.1, γ1It conscientiously adjusts, ties after=8
Fruit is shown in attached drawing 7 to 10.Motion profile and attitude error are shown in attached drawing 7 and attached drawing 8.Attached drawing 9 and 10 respectively illustrates machine
The speed and image path of device people.For locus configurations, vertical and horizontal tracking error is 1.0m and 0.6m, difference when being initial
It is tracked.But, tracking mistake is reduced rapidly after target controller works 10 seconds, and mistake is suppressed sufficiently small, control
At 22 seconds.Method for being compared, lateral error is sufficiently small after about 35 seconds, and anisotropy is received after 50 seconds
It holds back.Accordingly, it has been known that tracking error is slowly restrained by comparing controller.It is arrived by comparing attached drawing 3 to attached drawing 6 and attached drawing 7
Attached drawing 10, it is known that desired motion profile having the same and target signature, the reaction of the method proposed is better than other
Method, in the case, track following mistake quickly converge to zero.
Method by being compared, control parameter are adjusted to γ1=2, γ2=0.5, γ3=0.1, k1=0.4, k2=
5, Γ1=100, Γ2=100, as a result attached drawing 12 is arrived in attached drawing 11.We have seen that tracking error was in 15 seconds or so fast convergences.So
And jitter phenomenon occurs because the tracking error of angular speed is very big, although angular speed is filtered.With other methods phase
Than the method proposed can obtain comparable tracking performance using medium linear and angular speed.In addition, in the method
7 control parameters should be adjusted carefully to obtain satisfied tracking performance, and proposed method only needs to adjust 3 parameters.Cause
This, this method is more suitably applied to actual tracking task.
It should be noted that in simulating scenes, vd(t) and wd(t) sinusoidal finally it is arranged to desired
Zero velocity.Although theory analysis is to set up, as long as vd(t) it just not should be equal to zero in Infinite Time.It can be seen that the control proposed
Device processed is with good performance, illustrates that this method can be applied in practice.
Claims (1)
1. the 1st, the design of visual servo Trajectory Tracking System
The description of 1.1st scheme
In the present invention, we design a kind of mobile robot mixing visual servo track following strategy；Utilize 2.5 dimension visions
Servo frame is so that visual signature is readily maintained within the scope of camera coverage, and then improves the effect of track following；Firstly, root
According to present image, reference picture and desired image sequence, 2-1/2-D visual servo is defined by characteristics of image and robot rotation amount
Tracking error；Adaptive controller is devised later, wherein passing through parameter update mechanism complementary characteristics point depth information；According to
Lyapunov method and Barbalat lemma, it was demonstrated that go out in the case where scene depth is unknown, the vision track following control mentioned
Method processed is able to achieve Asymptotic Stability as a result, comparing simulation result, compared with our pervious work, tracks and sets in visual servo
Pinpoint it is constant in the case where, mentioned method need to only adjust less control parameter and complete track following task, relatively be suitble to practical
It uses；
2nd, construct system model
The description of 2.1st problem
In-vehicle camera coordinate system FcIt is overlapped with the coordinate system of mobile robot with nonholonomic constraints；Coordinate system FcZcAxis is along camera optical axis
Direction, and with mobile robot towards unanimously；xcAxis is parallel with wheel axis direction, ycAxis is perpendicular to robot motion's plane zcxc；This
Outside, with FdIndicate the coordinate system on desired trajectory, wherein desired trajectory is defined by the image sequence prerecorded；Static coordinate
It is F*Indicate robot/video camera reference pose, be set to reference frame, can make desired image sequence and currently
Image is compared by reference to image；The angle, θ calculated by the method for homographyc(t) and θd(t), the two angles are distinguished
Indicate the F under reference framecAnd FdRotation angle；According to the definition of these coordinate systems, the present invention designs a kind of vision track
Tracking and controlling method makes in-vehicle camera coordinate system FcWith desired trajectory coordinate system FdIt coincides；
2.2nd can survey signal
Consider static nature point P in the scenei(i=1；2；...；N), in F*, FdAnd FcUnder coordinate use P respectivelyi *, Pi d, Pi c
∈R3Carry out F*, FdAnd FcDescription:
The corresponding homogeneous image pixel coordinates of above three coordinate are respectively
Normalized image coordinate is measurable:
Wherein K ∈ R3×3It is calibrated camera intrinsic parameter matrix；
For the ease of subsequent analysis, depth ratio is defined as follows:
Since mobile robot is usually maintained a certain distance with target object, thus variableWithIt is known to positive
γi1(t) and γi2(t) singular problem, Ke Yiyong will not occurTo estimate；
Angular speed w on desired trajectoryd(t) and scale meaning under expectation linear velocityFollowing difference can be passed through
The form of method calculates
Wherein θd(k) θ at current time is indicatedd(t) value, θd(k-1) θ of previous moment is indicatedd(t) value,With's
Define similar therewith, Δ tkIt is the time interval between two moment；
3rd, controller design
Analysis robot kinematics first, then planned course tracking control unit is utilized with Active Compensation unknown characteristics point depth
Lyapunov method proves that proposed controller can make tracking error asymptotic convergence to zero.
3.1st, robot kinematics
FcAnd FdBetween translation error ez(t), exIt (t) can be by arbitrary characteristics point PiIt obtains, is defined as follows:
It considersKnow that above-mentioned definition mode does not have singularity problem furthermore FcAnd FdBetween rotation error eθ(t) fixed
Justice are as follows:
eθ:=θc-θd. (7)
By (6) (7) it is found that the track following error constructed was made of characteristics of image and the rotation angle estimated；Cause
And the invention is built upon under 2.5 dimension visual servo frames, can make visual signature be easily held in camera coverage range it
It is interior；
For the ease of the controller design of next part, the present invention constructs a new error vector:
To ρ1, ρ2And ρ3After time derivation, available following chain type kinematical equation:
WhereinIndicate unknown characteristics point depth information；In addition, can be obtained using the pose algorithm for estimating based on homography
To error signal ez(t), ex(t), eθ(t)；
For the ease of the controller design of next part, the present invention makes following hypothesis:
Assuming that 1: the speed v on desired trajectoryd(t), wdIt (t) is bounded, and
3.2nd controller design
In the open loop error system-based of formula (9), the present invention devises moving machine on the basis of the depth of characteristic point is unknown
The hybrid visual servo contrail tracker of device people；
Based on Lyapunov method for analyzing stability, the mobile robot linear velocity and angular speed control of following form are devised
Rule:
Wherein kv, kw, the control gain that is positive.The estimated value of unknown constant α related with characteristic point depth, and by with
Under type is updated:
Wherein Γ ∈ R+It is more new gain；
After controller is substituted into open loop kinetics equation (9), it is as follows that closed-loop error equation can be obtained:
WhereinIt is the definition of parameter estimating error:
Theorem 1: control law (10) and parameter more new law (11) can make the error asymptotic convergence in system dynamical equation (9) to zero:
It proves: choosing following non-negative Lyapunov function V (t):
To (14) both sides about time derivation, then bring into known to closed loop kinematic equation (12):
After formula (11) are substituted into (15), it can obtain
According to formula (14) and (16), it is apparent from ρ1(t), ρ2(t), ρ3(t),And then v can be obtained according to formula (10)c(t), wc
(t)∈L∞；As it is assumed that vd(t), wd(t) it is bounded, thus can be obtained according to (9) and (11)Therefore, it is
System state is all bounded；
In turn, from ρ known to (16)1, ρ2∈L2；Therefore, it can directly be obtained using Barbalat lemmaSo
Afterwards, to ρ in formula (12)1(t) corresponding sin ρ1/ρ1Partial derivative is as follows:
It is set up in addition, being apparent from following relationship:
Due toIt is continuous in section (0, ∞), therefore it can be concluded that knot
It can be seen that sin ρ1/ρ1It is congruous continuity；
In addition, being easy to getIt is also congruous continuity.We also haveWith；Therefore,
To ρ1(t) closed-loop error system can be obtained using extension Barbalat lemma
From (6) and (7) it is found that when formula (13) are set up, it can be achieved that vision track following task.
As it is assumed thatIt is readily seenTherefore, it is understood that the systematic error constructed is asymptotic
Converge to 0, it may be assumed that
In addition, according to the ρ in (8)1(t), ρ2(t), ρ3(t) and ez(t), ex(t), eθ(t) relationship, it is known that track following error
Asymptotic convergence is to zero, it may be assumed that。
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