CN106125728B - A kind of 4 wheel driven wheeled mobile robot trace tracking and controlling method - Google Patents
A kind of 4 wheel driven wheeled mobile robot trace tracking and controlling method Download PDFInfo
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Abstract
The present invention provides a kind of 4 wheel driven wheeled mobile robot trace tracking and controlling methods, initially set up the kinematics model, kinetic model, driving motor model of system；Then kinematic controller is designed, for adjusting the speed of system according to the state of given reference locus on the basis of kinematics model；Dynamics Controller, for obtaining the expectation torque of motor according to the speed of required adjustment system on the basis of kinetic model；Drive motor controller, for for the expectation torque for meeting motor, designing system suitable driving voltage on the basis of driving motor model；Trajectory Tracking Control is finally carried out to 4 wheel driven wheeled mobile robot using the robust trajectory tracking control method of Backstepping.Method provided by the invention realizes the purpose that the stability of 4 wheel driven Control of Wheeled Mobile Robots system is improved under complicated uncertain environment, improves the validity controlled containing system under the conditions of uncertain factor.
Description
Technical field
The present invention relates to robotic tracking control methods, more particularly to a kind of 4 wheel driven wheeled mobile robot trace
Tracking and controlling method.
Background technique
One important point as mobile robot of wheeled mobile robot (Wheeled Mobile Robot, WMR)
Branch, compared to traditional industrial robot, with work efficiency is high, driving and control are simple, load-carrying is big, flexible operation facilitates
Advantage, therefore had a wide range of applications in each field.With wheeled mobile robot service ability, to the adaptation of varying environment
Ability etc. is greatly improved, and wheeled mobile robot has become essential helper in human production life.Wherein exist
Civil field, wheeled mobile robot can replace human work person and be engaged in various heavy tasks, such as substation equipment
The occasions such as inspection, the tour of market Security Personnel, earthquake relief work.In military field, various unmanned combat aerial vehicles, bomb disposal blasting-proof machine
The application of device people etc. is also increasingly extensive.In addition, with increasingly mature, the service robot, all kinds of inspection machines of intellectualized technology
People etc. will have and more be widely applied.
It, can be so that wheeled mobile robot be completed pair by various sensor applications to wheel type mobile robot platform
Tour, study and decision of uncertain complex environment etc., such wheeled mobile robot can complete various high-risk
Business, such as the inspection of high voltage substation, the detection of nuclear power station.In addition, wheeled mobile robot is widely used but also the mankind
Life it is more convenient, such as play in the carrying of large cargo, household services occasion wheeled mobile robot very important
Effect.Wheeled mobile robot generally all works in unknown complex environment, this will bring more to robot system
Uncertain and complexity, kinetic control system will have stronger anti-interference ability, therefore study under complicated circumstances not known
The motion control of wheeled mobile robot theory and practice meaning with higher.
Currently, to the research of wheeled mobile robot motion control being carried out under conditions of external environment is constant
, but when robot is run in various complex environments, the parameter of wheeled mobile robot system will change,
This will just will affect the stability of kinetic control system.
Summary of the invention
The technical problem to be solved by the present invention is to how 4 wheel driven wheeled mobile robot be improved under complicated uncertain environment
The stability of control system.
In order to solve the above-mentioned technical problem, the technical solution of the present invention is to provide a kind of 4 wheel driven wheeled mobile robot traces
Tracking and controlling method, it is characterised in that: this method is made of following 3 steps:
Step 1: establishing the kinematics model, kinetic model, driving motor model of system；
Step 2: design
Kinematic controller, for adjusting system according to the state of given reference locus on the basis of kinematics model
The speed of system；
Dynamics Controller, for obtaining motor according to the speed of required adjustment system on the basis of kinetic model
Expectation torque；
Drive motor controller, for for the expectation torque for meeting motor, designing on the basis of driving motor model
The suitable driving voltage of system；
Step 3: using Backstepping robust trajectory tracking control method to 4 wheel driven wheeled mobile robot carry out track with
Track control, detailed process is as follows:
Step 3.1: according to given reference locus, the machine under corresponding coordinate system being obtained by the foundation to system model
People's position and attitude error；
Step 3.2: determining whether the position and attitude error is zero, if zero, then complete corresponding track following；Conversely, adjusting
The desired speed of whole kinematics model input；
Step 3.3: under conditions of meeting the desired speed of kinematics model, suitable Torque Control rule is set；
Step 3.4: the voltage of driving motor is set, voltage control law appropriate is obtained, the phase for obtaining system
Speed and torque condition is hoped to meet simultaneously.
Step 3.5: according to the design philosophy of Backstepping, a feedback system is formed, so that in t → ∞, when t is indicated
Between, position and attitude error 0, to realize tracking of the actual mobile robot to reference locus.
Preferably, the feedback system structure are as follows: kinematic controller, Dynamics Controller, drive motor controller, drive
Dynamic motor model, kinetic model, kinematics model are sequentially connected, and driving motor model output result feeds back to driving motor control
Device processed, kinetic model output result feed back to Dynamics Controller and drive motor controller, and kinematics model exports result
Dynamics Controller, the position and attitude error input of actual path and reference locus are fed back to by forming actual path after integral element
Kinematic controller, reference locus are used as feed-forward signal input motion controller simultaneously.
Preferably, the method for building up of the kinematics model is as follows:
Kinematics model is in order to describe the relationship between system speed and its pose；
The nonholonomic constraint of Pfaffian form, such as formula (1):
Wherein, θ is the angle between trolley horizontal axis and the X-axis of inertial coodinate system, it can indicate the pose angle of robot,
A (q)=[sin θ-cos θ 0],It is the pose of system；
Then mutual conversion such as formula (2) of the system pose between local coordinate system xoy and inertial coodinate system XoY:
Wherein,For pose of the robot under local coordinate system, vxThe component for being robot speed in x-axis,
vyFor the component of robot speed on the y axis, ω is the angular speed of robot；
The kinematics of system can be released on the basis of the nonholonomic constraint of Pfaffian form and system model
Model, such as formula (3):
Wherein, v is the linear velocity of robot wheel, and ω is the angular speed of robot.
Preferably, the method for building up of the kinetic model is as follows:
The kinetic model of general wheeled mobile robot, such as formula (4):
Wherein, M (q) is the symmetrical inertial matrix of positive definite；For related and speed and position Ge Shi torque battle array；For frictional force；G (q) is gravity item；τdBeing includes unstructured Unmarried pregnancy bounded unknown disturbance vector；B (q) is defeated
Enter transformation matrix；τ=[τL τR]TIt is in some cases, equal with the torque of driving motor for torque input vector；λ is constraint
Force vector isSpecial built-in variable；
By the way that it is as follows that formula (5) can be obtained to formula (3) derivation:
Assuming that the uncertainty of system dynamics model is bounded, and meet
|τvd|≤ρv(τ)
|τωd|≤ρω(τ)
τvdFor the uncertain parameter of linear velocity, τωdFor the uncertain parameter of angular speed, ρv(τ)、ρω(τ) is that bounded is normal
Numerical value；
In the case where ignoring gravity and other factors are interfered, using formula (4) and (5) it can be concluded that wheeled mobile robot
The kinetic model formula (6) of people is as follows:
Wherein,
And then it follows that
Wherein,
B is the half of left and right wheels spacing, and r is radius of wheel, and m is the quality of car body, and g is gravity constant.
Preferably, the method for building up of the driving motor model is as follows:
The output torque τ of driving motor and the relationship such as formula (7) of electric current:
τ=[τL τR]T=[2kniL 2kniR]T (7)
Wherein, k is constant coefficient, and n is the reduction ratio of motor, iL,iRThe respectively electric current of left and right sides motor；
Consider under system parameter uncertainty and disturbed condition shown in the voltage equation such as formula (8) of direct current generator:
Wherein, U is armature voltage, and L is armature inductance, and R is armature resistance, keFor motor torque constant, Δ expression parameter
Uncertainty, d (t) indicates uncertain interference；
Using formula (7) and (8), it can show that the mathematical modeling formula (9) of driving motor is as follows:
Wherein,U=[UL UR]T
D=[DL DR]T=Δ LU- Δ R τ-Δ K η+d (t) is the total uncertainty of system.
Preferably, specific step is as follows for Trajectory Tracking Control:
Step A sets the reference locus of system first
Wherein, qr=[xr yr θr]TFor reference locus, ηr=[vr ωr]T, vrFor with reference to linear velocity, ωrFor reference angle speed
Degree；
The error e of pose under local coordinate is obtained using formula (2)q, such as formula (10):
The system parameter for comprehensively considering the 4 wheel driven wheeled mobile robot carries out data processing to position and attitude error；By anti-
The design philosophy of footwork designs liapunov function for the kinematics model subsystem, it is assumed that the Li Ya of kinematics control law
Pu Nuofu function is
Pass through the data processing to formula (11), it can be deduced that so that in the case where t → ∞ (t is the time), eqWhen=0
The velocity control law of design is
Wherein, k1,k2For constant coefficient, k1>0,k2>0；
Using the determination of stability condition of liapunov function, have
Step B regard formula (12) output in Motion Controlling Model as desired speed, is denoted as [vr ωr]T, then move
Mechanics tracking error is eη=[ev ew]T=[vr-v wr-w]T, it is assumed that the liapunov function for defining Dynamics Controller is
By the data processing to formula (12), setting Torque Control rule is
Wherein, k3,k4For constant coefficient, k3>0,k4>0；
Using the determination of stability condition of liapunov function, have
Step C assumes initially that the uncertain of driving motor is bounded, and do it is slowly varying, i.e.,
ρDIt (t) is bounded constant value；
Expectation torque by the output formula (14) of Dynamics Controller as system, is denoted as [τLr τRr]T, driving torque
Error is
eτ=[eτL eτR]T
=[τLr-τL τRr-τR]T (16)
Define electric machine controller liapunov function be
By the data processing to formula (17), set control law as
Wherein, k5,k6For constant coefficient, k5>0,k6>0；
Using the determination of stability condition of liapunov function, have
Further, and if only if ep=eη=eτWhen=0,Formula (18) can known to Lyapunov theorem
So that system is gradually stable.
Preferably, it needs to make the following assumptions when the kinematics model is established:
1) four driving wheels are symmetrically distributed in same plane；
2) it is point contact between driving wheel and ground, ignores thickness；
3) radius when car body turns to is greater than wheel radius；
4) four driving wheels and ground will not generate longitudinal sliding in relative motion；
5) robot body regards the rigid body moved on wheel as, and only moves in the plane.
Preferably, when the kinematics model, need to provide system model between local coordinate system and global coordinate system
Mutually convert relationship.
Preferably, when the kinematics model, since the lateral velocity of the wheeled mobile robot four wheels is usually
Zero, when robot turns to, mechanical structure determines that its outer side slip is necessary.Therefore in order to complete the movement of the design
Model is learned, the nonholonomic constraint of Pfaffian form is introduced.
Preferably, when the kinetic model is established, the interference of gravity and extraneous factor is had ignored.
Preferably, when the driving motor model foundation, in order to simplify theory analysis, it is assumed that the driving motor of four-wheel is adopted
With the direct current generator and motor driver of identical parameters, and reduction ratio having the same.
Preferably, using the robust trajectory tracking control method of Backstepping to 4 wheel driven wheeled mobile robot carry out track with
Track control.
Preferably, it before the robust trajectory tracking control strategy design control law using Backstepping, needs to assume system
The gain of the unknown dynamic process of uncertain disturbance be bounded, the mathematical model of the bound function and controlled device that then will assume
Combine construction one liapunov function, the function can make system for the either element in uncertain disturbance set all
With robustness.
The present invention is realized by the design to the robust trajectory tracking control method of Backstepping in master controller in complexity
Under uncertain environment improve 4 wheel driven Control of Wheeled Mobile Robots system stability purpose, improve containing uncertainty because
The validity that system controls under the conditions of element.
Detailed description of the invention
Fig. 1 is 4 wheel driven wheeled mobile robot trace tracking control system structural block diagram provided in this embodiment；
Fig. 2 is 4 wheel driven wheeled mobile robot trace tracking and controlling method flow chart provided in this embodiment；
Fig. 3 is PID control track following result figure；
Fig. 4 is the track following result figure of Trajectory Tracking Control method of the present invention；
Fig. 5 is PID control pose angle tracking error figure；
Fig. 6 is the pose angle tracking error figure of Trajectory Tracking Control method of the present invention；
Fig. 7 is PID control linear velocity tracking error figure；
Fig. 8 is the linear velocity tracking error figure of Trajectory Tracking Control method of the present invention.
Specific embodiment
Present invention will be further explained below with reference to specific examples.It should be understood that these embodiments are merely to illustrate the present invention
Rather than it limits the scope of the invention.In addition, it should also be understood that, after reading the content taught by the present invention, those skilled in the art
Member can make various changes or modifications the present invention, and such equivalent forms equally fall within the application the appended claims and limited
Range.
Fig. 1 is 4 wheel driven wheeled mobile robot trace tracking control system structural block diagram provided in this embodiment, described
4 wheel driven wheeled mobile robot trace tracking control system includes:
Kinematic controller 103, on the basis of system kinematics model 108, according to the shape of given reference locus 101
The speed of state adjustment system；
Dynamics Controller 104 obtains on the basis of system dynamics model 107 according to the speed of required adjustment system
The expectation torque of motor out；
Drive motor controller 105, on the basis of system drive motor model 106, for the expectation torque for meeting motor,
Design the suitable driving voltage of system.
According to assumed condition, the longitudinal sliding motion between car body and ground be can be ignored, and have vix=r ωi, wherein vix
For i-th of wheel general speed vector viLongitudinal component.Comprehensively consider the operating status of four wheels, it is mutual between each wheel
Relationship is
Wherein, vLFor the longitudinal velocity of left side wheels, vRFor the longitudinal velocity of right-hand wheel, vFFor the lateral velocity of front side wheel, vB
For the lateral velocity of rear side wheel.v1xFor the general speed vector v of first wheelxLongitudinal component, v2xFor the total of second wheel
Velocity vector vxLongitudinal component, v3xFor the general speed vector v of third wheelxLongitudinal component, v4xFor four wheels
General speed vector vxLongitudinal component, v1yFor the general speed vector v of first wheelyCross stream component, v2yFor second wheel
General speed vector vyCross stream component, v3yFor the general speed vector v of third wheelyCross stream component, v4yIt is taken turns for the 4th
The general speed vector v of sonyCross stream component.
So the component of two wheels, two, right side wheel in x-axis distinguishes phase on the left of the 4 wheel driven wheeled mobile robot
Together, the wheel of front side two, the component of two wheels of rear side on the y axis are also identical respectively.The wheeled mobile robot four wheels
Lateral velocity be usually zero, when robot turn to when, mechanical structure determines that its outer side slip is necessary.It introduces
The nonholonomic constraint of Pfaffian form, can go out system kinematics modelIn this way by changing the big of η
Urine can be realized to 4 wheel driven wheeled mobile robot poseControl.
Kinetic model 107 describes the relationship between its speed and corresponding motor output driving torque, passes through one
As wheeled mobile robot kinetic model
In conjunction with system kinematics modelAnd to its derivation, the case where ignoring gravity and other factors are interfered
The kinetic model of 4 wheel driven wheeled mobile robot can be obtained down
Driving motor model 106 describes the relationship between the torque being output on driving wheel and motor electric signal.System
Controller is built upon on the basis of the mathematical model comprising driving motor, in order to simplify theory analysis, it is assumed that the drive of four-wheel
Dynamic motor is all made of the direct current generator and motor driver of identical parameters, and reduction ratio n having the same.In order to keep car body left
The driving wheel of right two sides velocity of rotation having the same, it is necessary to so that being input to the torque phase on two driving wheels of left and right sides
Together, therefore it can be concluded that the output torque of driving motor and relationship τ=[τ of electric currentL τR]T=[2kniL
2kniR]T, in conjunction with the voltage equation of direct current generator, can obtain the driving motor model of robot
Fig. 2 is the flow chart of Trajectory Tracking Control strategy implement example of the present invention, according to the robust track following control of Backstepping
System strategy, comprising the following steps:
Step 1: 201 obtain given reference locusIt is obtained by the foundation to system model corresponding
Robot pose error e under coordinate systemq202；
Step 2: determining whether the position and attitude error is 0 203, if zero, then completes corresponding track following 207；Instead
It, then need to adjust the input desired speed 204 of kinematics model under the control of the law of progression；
Step 3: suitable Torque Control rule [τ is arranged in the desired velocity conditions in meeting kinematics modelLr τRr]T205；
Step 4: it to enable a system to tracking of the stable realization to setting track, needs to meet simultaneously system and obtains the phase
The speed and torque of prestige.Therefore it in order to meet the two conditions simultaneously, needs to set the voltage of driving motor, obtain suitable
When voltage control law.
Step 5: according to the design philosophy of Backstepping, forming a feedback system and make in t → ∞, eq=0, with reality
Existing tracking of the actual mobile robot to reference locus.
According to the parameter designing of above controller, from original state (0,0), tracking one section of track is Y=sin (0.2 π X)
Sine wave, pose angle θ (0)=0rad, the reference value 1m/s of linear velocity, the emulation ginseng of 4 wheel driven wheeled mobile robot and controller
Number setting is as shown in table 1.
In order to show the validity of the control strategy, by robust trajectory tracking control strategy and PID based on Backstepping
Control compares, PID controller parameter kp=3.2, ki=0.6, kd=0.36, wherein kpFor proportionality coefficient, kiFor integral
Coefficient, kiFor differential coefficient, comparison result such as Fig. 3 to Fig. 8.
The setting of the simulation parameter of 14 wheel driven wheeled mobile robot of table and controller
By regulatory PID control and the robust control simulation comparison based on Backstepping, can be seen that from Fig. 3 and Fig. 4 to same
One track is tracked, and the worst error of the robust control tracking based on Backstepping is much smaller compared to regulatory PID control；Comparison
Fig. 5 and Fig. 6, Fig. 7 and Fig. 8 based on the robust control of Backstepping than PID control pose angle tracking worst error it is found that reduced
0.18rad, linear velocity tracks worst error and reduces 0.2m/s, and convergence time reduces 60%.By analysis above it is found that right
It is more preferable than traditional PID control effect based on the robust control of Backstepping in same pursuit path.
Claims (8)
1. a kind of 4 wheel driven wheeled mobile robot trace tracking and controlling method, it is characterised in that: this method is by following 3 step groups
At:
Step 1: establishing the kinematics model, kinetic model, driving motor model of system；
Step 2: design
Kinematic controller, for adjusting system according to the state of given reference locus on the basis of kinematics model
Speed；
Dynamics Controller, for obtaining the phase of motor according to the speed of required adjustment system on the basis of kinetic model
Hope torque；
Drive motor controller, for for the expectation torque for meeting motor, designing system on the basis of driving motor model
Suitable driving voltage；
Step 3: track following control is carried out to 4 wheel driven wheeled mobile robot using the robust trajectory tracking control method of Backstepping
System, detailed process is as follows:
Step 3.1: according to given reference locus, being obtained by the foundation to system model in corresponding coordinate Xi Xia robot position
Appearance error；
Step 3.2: determining whether the position and attitude error is zero, if zero, then complete corresponding track following；Conversely, adjustment fortune
The dynamic desired speed for learning mode input；
Step 3.3: under conditions of meeting the desired speed of kinematics model, suitable Torque Control rule is set；
Step 3.4: the voltage of driving motor is set, voltage control law appropriate is obtained, the expectation speed for obtaining system
Degree and torque condition meet simultaneously；
Step 3.5: according to the design philosophy of Backstepping, a feedback system is formed, so that in t → ∞, position and attitude error 0,
To realize tracking of the actual mobile robot to reference locus；Wherein, t indicates the time；
The method for building up of the kinematics model is as follows:
Kinematics model is in order to describe the relationship between system speed and its pose；
The nonholonomic constraint of Pfaffian form, such as formula (1):
Wherein, θ is the angle between trolley horizontal axis and the X-axis of inertial coodinate system, it can indicate the pose angle of robot, A (q)
=[sin θ-cos θ 0],It is the pose of system；
Then mutual conversion such as formula (2) of the system pose between local coordinate system xoy and inertial coodinate system XoY:
Wherein,For pose of the robot under local coordinate system, vxThe component for being robot speed in x-axis, vyFor machine
The component of device people speed on the y axis, ω are the angular speed of robot；
The kinematics model of system can be released on the basis of the nonholonomic constraint of Pfaffian form and system model,
Such as formula (3):
Wherein, v is the linear velocity of robot wheel, and ω is the angular speed of robot；
The method for building up of the kinetic model is as follows:
The kinetic model of wheeled mobile robot, such as formula (4):
Wherein, M (q) is the symmetrical inertial matrix of positive definite；For coriolis force matrix relevant to speed and position；For
Frictional force；G (q) is gravity item；τdBeing includes unstructured Unmarried pregnancy bounded unknown disturbance vector；B (q) is Input transformation
Matrix；τ=[τL τR]TIt is in some cases, equal with the torque of driving motor for torque input vector；λ be restraining force to
It measures, isSpecial built-in variable；
By the way that it is as follows that formula (5) can be obtained to formula (3) derivation:
Assuming that the uncertainty of system dynamics model is bounded, and meet
|τvd|≤ρv(τ)
|τωd|≤ρω(τ)
τvdFor the uncertain parameter of linear velocity, τωdFor the uncertain parameter of angular speed, ρv(τ)、ρω(τ) is bounded constant value；
In the case where ignoring gravity and other factors and interfere, using formula (4) and (5) it can be concluded that wheeled mobile robot
Kinetic model formula (6) is as follows:
Wherein,
And then it follows that
Wherein,
B is the half of left and right wheels spacing, and r is radius of wheel, and m is the quality of car body, and g is gravity constant.
2. a kind of 4 wheel driven wheeled mobile robot trace tracking and controlling method as described in claim 1, it is characterised in that: described
Feedback system structure are as follows: kinematic controller, Dynamics Controller, drive motor controller, driving motor model, kinetic simulation
Type, kinematics model are sequentially connected, and driving motor model output result feeds back to drive motor controller, kinetic model output
As a result Dynamics Controller and drive motor controller are fed back to, it is real by being formed after integral element that kinematics model exports result
Border track feeds back to Dynamics Controller, the position and attitude error input motion controller of actual path and reference locus, with reference to rail
Mark is used as feed-forward signal input motion controller simultaneously.
3. a kind of 4 wheel driven wheeled mobile robot trace tracking and controlling method as described in claim 1, it is characterised in that: described
The method for building up of driving motor model is as follows:
The output torque τ of driving motor and the relationship such as formula (7) of electric current:
τ=[τL τR]T=[2kniL 2kniR]T (7)
Wherein, k is constant coefficient, and n is the reduction ratio of motor, iL,iRThe respectively electric current of left and right sides motor；
Consider under system parameter uncertainty and disturbed condition shown in the voltage equation such as formula (8) of direct current generator:
Wherein, U is armature voltage, and L is armature inductance, and R is armature resistance, keFor motor torque constant, Δ expression parameter not really
Qualitative, d (t) indicates uncertain interference；
Using formula (7) and (8), it can show that the mathematical modeling formula (9) of driving motor is as follows:
Wherein,U=[UL UR]T
D=[DL DR]T=Δ LU- Δ R τ-Δ K η+d (t) is the total uncertainty of system.
4. a kind of 4 wheel driven wheeled mobile robot trace tracking and controlling method as described in claim 1, it is characterised in that: track
Specific step is as follows for tracing control:
Step A sets the reference locus of system first
Wherein, qr=[xr yr θr]TFor reference locus, ηr=[vr ωr]T, vrFor with reference to linear velocity, ωrFor reference angular velocities；
The error e of pose under local coordinate is obtained using formula (2)q, such as formula (10):
The system parameter for comprehensively considering the 4 wheel driven wheeled mobile robot carries out data processing to position and attitude error；By Backstepping
Design philosophy, for the kinematics model subsystem design liapunov function, it is assumed that the Li Yapunuo of kinematics control law
Husband's function is
Pass through the data processing to formula (11), it can be deduced that so that in the case where t → ∞, eqThe speed control designed when=0
Rule is
Wherein, k1,k2For constant coefficient, k1>0,k2>0；
Using the determination of stability condition of liapunov function, have
Step B regard formula (12) output in Motion Controlling Model as desired speed, is denoted as [vr ωr]T, then dynamics
Tracking error is eη=[ev ew]T=[vr-v wr-w]T, it is assumed that the liapunov function for defining Dynamics Controller is
By the data processing to formula (12), setting Torque Control rule is
Wherein, k3,k4For constant coefficient, k3>0,k4>0；
Using the determination of stability condition of liapunov function, have
Step C assumes initially that the uncertain of driving motor is bounded, and do it is slowly varying, i.e.,
ρDIt (t) is bounded constant value；
Expectation torque by the output formula (14) of Dynamics Controller as system, is denoted as [τLr τRr]T, driving torque error
For
eτ=[eτL eτR]T
=[τLr-τL τRr-τR]T (16)
Define electric machine controller liapunov function be
By the data processing to formula (17), set control law as
Wherein, k5,k6For constant coefficient, k5>0,k6>0；
Using the determination of stability condition of liapunov function, have
Further, and if only if ep=eη=eτWhen=0,Formula (18) can make known to Lyapunov theorem
System is gradually stable.
5. a kind of 4 wheel driven wheeled mobile robot trace tracking and controlling method as claimed in claim 2, it is characterised in that: described
When kinematics model is established, need to make the following assumptions:
1) four driving wheels are symmetrically distributed in same plane；
2) it is point contact between driving wheel and ground, ignores thickness；
3) radius when car body turns to is greater than wheel radius；
4) four driving wheels and ground will not generate longitudinal sliding in relative motion；
5) robot body regards the rigid body moved on wheel as, and only moves in the plane.
6. a kind of 4 wheel driven wheeled mobile robot trace tracking and controlling method as described in claim 1, it is characterised in that: described
When kinetic model is established, the interference of gravity and extraneous factor is had ignored.
7. a kind of 4 wheel driven wheeled mobile robot trace tracking and controlling method as described in claim 1, it is characterised in that: described
When driving motor model foundation, in order to simplify theory analysis, it is assumed that the driving motor of four-wheel is all made of the direct current of identical parameters
Machine and motor driver, and reduction ratio having the same.
8. a kind of 4 wheel driven wheeled mobile robot trace tracking and controlling method as claimed in claim 7, it is characterised in that: setting
Before counting control law, needs to assume that the gain of the unknown dynamic process of the uncertain disturbance of system is bounded, then will assume
Bound function combines one liapunov function of construction with the mathematical model of controlled device, which can make system for not
Determine that the either element in disturbance set all has robustness.
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