CN108153309A - For the control method and caterpillar robot of caterpillar robot - Google Patents
For the control method and caterpillar robot of caterpillar robot Download PDFInfo
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- 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
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- 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
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Abstract
The present invention relates to moveable robot movement control fields, disclose a kind of control method and caterpillar robot for caterpillar robot.Caterpillar robot is considered as the cascade system being made of motor driven systems and body movement system by the present invention, structure becomes the Adaptive Integral sliding formwork switching function of tilt parameters, and the adaptive sliding mode tracing control based on equivalent control and switching control is proposed according to Adaptive Integral sliding formwork switching function, with the speed of robot, driving motor time-varying uncertain parameter obtained by on-line identification, and that is asked in kinematics model feeds back to the error of object pose in the controller of drive system, then according to kinematic relation, decompose the desired speed of each motor, and then realize the stable motion control of robot.
Description
Technical field
The present invention relates to moveable robot movement controls, and in particular, to a kind of control method for caterpillar robot
And caterpillar robot.
Background technology
With the extensive use of agricultural caterpillar robot (Agricultural Tracked Robot, ATR), to robot
Adaptivity, the accuracy of control and the stationarity of movement of system made higher requirement.However farmland is with a varied topography,
Environment is changeable, in addition ATR systems existing close coupling and the uncertain characteristic of model in itself so that the design of ATR control systems
With difficulty is used to increase.
For this purpose, domestic and foreign scholars have made intensive studies it, some scholars propose various Trajectory Tracking Controls, mainly
It is the model combined using kinematics model or kinematics or dynamics, some scholars propose linear feedback scheme, PID controls
Preparation method, computed-torque approach, Backstepping, sliding formwork control, ANN Control method and fuzzy control etc..Wherein linear feedback scheme
It is a kind of common control method, since ATR models are nonlinear, control accuracy is relatively low；Pid control law, due to it
Control parameter is fixed, poor for non-linear and structure uncertain system control effect；Computed-torque approach is dependent on controlled pair
The kinetic model of elephant, and Dynamic Modeling is inherently sufficiently complex, and builds difficulty, therefore the theory and practice meaning of this method
It is adopted little；Although neural network can overcome the uncertainty and unknown disturbance of system, control algolithm is complicated；Fuzzy control
It does not need to establish accurate mathematical model, is suitble to the control of nonlinear time-varying, delay system, but the selection of fuzzy rule lacks system
System property, it is difficult to on-line tuning；Virtual controlling amount has been used in Backstepping, has been carried out at the same time iteration derivation so that controller architecture ten
Divide complexity, Project Realization difficulty is larger.
The complexity of farm environment causes there is many uncertainties in ATR motion processes, such as：Parameter Perturbation and load
Disturbance and the measurement error of sensor, can all cause ATR running orbits to deviate reference path.Conventional control method is difficult to full
Sufficient high-precision Trajectory Tracking Control requirement.Moding structure control has the robustness of fast transient response, does not depend on controlled device
Accurate mathematical model, the advantages of and Project Realization insensitive to parameter and environmental change is simple, therefore suitable for farm environment
Robot control.
Invention content
The object of the present invention is to provide a kind of control methods for caterpillar robot, and this method is by establishing adaptive sliding
Control of the mould tracing control model realization to the movement locus of caterpillar robot, improves control accuracy.
To achieve these goals, the present invention provides a kind of control method for caterpillar robot, includes the following steps：
Obtain the pose under the current state of caterpillar robot；The reference locus of caterpillar robot is set, reference locus refers to including pose
Order and speed command；Establish the kinematics of the restriction relation between the pose of description caterpillar robot and the speed of caterpillar robot
Model, speed include angular speed and linear velocity；According to the pose under current state and the reference locus of setting, track machines are established
The position and attitude error model of people is according to kinematics model and the position and attitude error Differential Model of position and attitude error model foundation caterpillar robot；
The left motor for being used to drive left driving wheel of caterpillar robot and the driving model for driving the right motor of right driving wheel are established,
Driving model includes torque driving model and electric potential balancing model；Left electricity is obtained according to torque driving model and electric potential balancing model
The dynamic model of machine and right motor；Establish the adaptive sliding mode switching model changed with parameter adjustment；It is micro- according to position and attitude error
Sub-model and adaptive sliding mode switching model obtain the desired speed of caterpillar robot, and desired speed includes it is expected linear velocity and phase
Hope angular speed；The expectation angular speed of left motor and right motor is obtained according to the desired speed of caterpillar robot.
Preferably, control method further includes：Establish for correct caterpillar robot desired speed switching control model；
Using the desired speed of switching control Modifying model caterpillar robot and the revised desired speed of acquisition caterpillar robot；
The expectation angular speed of left motor and right motor is obtained according to revised desired speed；According to the expectation angle of left motor and right motor
Speed and the dynamic model of left motor and right motor calculate the driving voltage of left motor and right motor.
Preferably, the kinematics mould of the restriction relation between the pose of caterpillar robot and the speed of caterpillar robot is described
Type is represented using formula (1)：
Wherein, x, y are respectively position coordinates of the barycenter of caterpillar robot in XOY coordinate systems, and θ is caterpillar robot
The angle of the direction of motion and X-axis, v, ω are respectively the linear velocity and angular speed of caterpillar robot, and d is the barycenter of caterpillar robot
The distance between geometric center,WithRespectively x, y and θ are to the derivative of time；
According to the pose under the current state of caterpillar robot and the reference locus of setting, the position of the caterpillar robot of foundation
Appearance error model is represented using formula (2)：
Wherein, (x, y, θ)TFor the pose under caterpillar robot current state, x, y are respectively the barycenter of caterpillar robot
The coordinate of current location, θ be caterpillar robot angle of its direction of motion and X-axis under current state, (xr,yr,θr)TFor position
Appearance instructs, xr、yrThe respectively coordinate of the target location of the barycenter of caterpillar robot, θrTarget location is reached for caterpillar robot
When its direction of motion and X-axis angle, xeThe current location and target location of barycenter for caterpillar robot are along its current kinetic
The error amount in direction, yeThe current location and target location of barycenter for caterpillar robot with its current kinetic direction Vertical Square
To error amount, θeFor θ and θrBetween error amount；
According to kinematics model and the position and attitude error Differential Model of the caterpillar robot of position and attitude error model foundation：
Wherein, xeError of the current location and target location of barycenter for caterpillar robot along its current kinetic direction
Value, yeThe current location and target location of barycenter for caterpillar robot are in the error with its current kinetic direction vertical direction
Value, θeFor caterpillar robot under current state the angle of its direction of motion and X-axis and its direction of motion when reaching target location
Error amount between the angle of X-axis,Respectively xe、yeAnd θeTo the derivative of time, v and ω are respectively crawler belt
Linear velocity and angular speed of the robot under current state, (vr,ωr)TFor speed command, vrAnd ωrRespectively caterpillar robot
Linear velocity and angular speed during arrival target location, d are the distance between barycenter and geometric center of caterpillar robot.
Preferably, formula (4) is respectively adopted in the equalising torque model of left motor and right motor and formula (5) represents：
Wherein, Jr(t)、Jl(t) be respectively left motor and right motor shaft rotary inertia, F be left motor and right motor
Output shaft on viscosity friction coefficient, ktFor left motor and the electric torque coefficient of right motor, Tdr(t)、Tdl(t) it is respectively a left side
The disturbance torque that motor and right motor are subject to, ωr(t)、ωl(t) be respectively left motor and right motor shaft rotation angle speed
Degree,WithRespectively ωr(t) and ωl(t) to the derivative of time, ir(t)、il(t) it is respectively left motor and right electricity
The armature supply of machine；
Formula (6) is respectively adopted in the electric potential balancing model of left motor and right motor and formula (7) represents：
Wherein, L is the armature inductance of left motor and right motor, and R is the armature resistance of left motor and right motor, keFor left electricity
The back EMF coefficient of machine and right motor, and ke=0.10472kt, ktFor left motor and the electric torque coefficient of right motor, ωr
(t)、ωl(t) be respectively left motor and right motor shaft rotation angular speed, ir(t)、il(t) it is respectively left motor and right electricity
The armature supply of machine,WithRespectively ir(t) and il(t) to the derivative of time, ur(t) and ul(t) it is respectively right motor
Driving voltage and left motor driving voltage；
The left motor and the dynamic model of right motor obtained according to torque driving model and electric potential balancing model uses formula (8)
It is represented with formula (9)：
Wherein, Tl(t)=RJl(t)/(RF+kTke), Tr(t)=RJr(t)/(RF+kTke),
k1=kt/(RF+kTke), k2=R/ (RF+kTke), R is the armature resistance of left motor and right motor, Jr(t)、Jl(t)
The rotary inertia of the shaft of respectively left motor and right motor, F are the viscous friction system on the output shaft of left motor and right motor
Number, ktFor left motor and the electric torque coefficient of right motor, keFor left motor and the back EMF coefficient of right motor, and ke=
0.10472kt, Tdr(t)、Tdl(t) it is respectively disturbance torque that left motor and right motor are subject to, ωr(t)、ωl(t) it is respectively a left side
The angular speed of the shaft of motor and right motor rotation,WithRespectively ωr(t) and ωl(t) to the derivative of time, ur
(t) and ul(t) be respectively right motor driving voltage and left motor driving voltage.
Preferably, the adaptive sliding mode switching model changed with parameter adjustment of foundation is represented using formula (10)：
Wherein, α1And α2For tilt parameters,xeFor caterpillar robot
Barycenter error amount along its current kinetic direction of current location and target location, yeBarycenter for caterpillar robot it is current
Position and target location are in the error amount with its current kinetic direction vertical direction, θeFor caterpillar robot under current state its
The error amount when direction of motion and the angle of X-axis and arrival target location between its direction of motion and the angle of X-axis, vrFor crawler belt
Robot reaches linear velocity during target location, c1、c2、c3、c4、kk1、kk2It is normal number, s1And s2Respectively about xeAnd θe
Switching function；
Preferably, the expectation of caterpillar robot obtained according to position and attitude error Differential Model and adaptive sliding mode switching model
Speed is represented using formula (11)：
Wherein, vdAnd ωdRespectively the expectation linear velocity of caterpillar robot and expectation angular speed, α1And α2For tilt parameters,ω be angular speed of the caterpillar robot under current state, vrAnd ωrPoint
Not Wei caterpillar robot reach target location when linear velocity and angular speed,For vrTo the derivative of time, xeFor caterpillar robot
Barycenter error amount along its current kinetic direction of current location and target location, yeBarycenter for caterpillar robot it is current
Position and target location are in the error amount with its current kinetic direction vertical direction, θeFor caterpillar robot under current state its
The error amount when direction of motion and the angle of X-axis and arrival target location between its direction of motion and the angle of X-axis, d is crawler belt
The distance between the barycenter of robot and geometric center, c1、c2、c3、c4、kk1、kk2It is normal number.
Preferably, switching control model is represented using formula (12)：
Wherein, β1、β2To be more than zero handoff gain, β1、β2、Δ1And Δ2It is empirical value, sat is saturation function；
The revised desired speed of caterpillar robot is represented using formula (13)：
Wherein, v 'dWith ω 'dThe respectively revised expectation linear velocity of caterpillar robot and revised expectation angle speed
Degree, α1And α2For tilt parameters,ω is caterpillar robot in current state
Under angular speed, vrAnd ωrRespectively caterpillar robot reach target location when linear velocity and angular speed,For vrTo the time
Derivative, xeError amount of the current location and target location of barycenter for caterpillar robot along its current kinetic direction, yeTo carry out
The current location and target location of the barycenter of carrying machine people are in the error amount with its current kinetic direction vertical direction, θeFor crawler belt
The robot angle of its direction of motion and X-axis and angle of its direction of motion and X-axis when reaching target location under current state
Between error amount, d is the barycenter of caterpillar robot and the distance between geometric center, c1、c2、c3、c4、kk1、kk2It is normal
Number, β1、β2To be more than zero handoff gain, β1、β2、Δ1And Δ2It is empirical value, sat is saturation function, s1And s2Respectively it is
About xeAnd θeSwitching function；
Formula (14) is respectively adopted in the expectation angular speed of left motor and right motor and formula (15) represents：
ωrd=(v 'd+ω′dA)r-1Formula (14)
ωld=(v 'd-ω′dA)r-1Formula (15)
Wherein, ωrdAnd ωldThe expectation angular speed for it is expected angular speed and left motor of respectively right motor, v 'dWith ω 'dPoint
Not Wei caterpillar robot revised expectation linear velocity and revised expectation angular speed, A be left driving wheel and right driving wheel
Between spacing half, r is the radius of left driving wheel and right driving wheel.
On the other hand, embodiments of the present invention additionally provide a kind of caterpillar robot, which includes：It is left
Driving wheel, for driving left crawler belt；Right driving wheel, for driving right-hand track chiain；Left motor, for driving left driving wheel；Right motor,
For driving right driving wheel；Sensor, for detecting the pose under the current state of caterpillar robot, which includes tracked machine
Position and angle of inclination of the device people in specified coordinate system；And controller, it is above-mentioned for caterpillar robot for performing
Control method.
Through the above technical solutions, caterpillar robot is considered as by motor driven systems and body movement system group by the present invention
Into cascade system, structure become tilt parameters Adaptive Integral sliding formwork switching function, and according to Adaptive Integral sliding formwork switch
Function proposes the adaptive sliding mode tracing control based on equivalent control and switching control, with the speed of robot, on-line identification institute
Driving motor time-varying uncertain parameter and that is asked in kinematics model feed back to driving with the error of object pose
In the controller of system, then according to kinematic relation, the desired speed of each motor is decomposed, and then realize the stabilization of robot
Motion control.
Other features and advantages of the present invention will be described in detail in subsequent specific embodiment part.
Description of the drawings
Attached drawing is to be used to provide further understanding of the present invention, and a part for constitution instruction, with following tool
Body embodiment is used to explain the present invention, but be not construed as limiting the invention together.In the accompanying drawings：
Fig. 1 is the flow chart of the control method for caterpillar robot according to an embodiment of the present invention；
Fig. 2 is the flow chart of the control method for caterpillar robot according to an embodiment of the present invention；
Fig. 3 shows the illustraton of model of the caterpillar robot of one embodiment of the present invention；
Fig. 4 shows the position and attitude error illustraton of model of the caterpillar robot of one embodiment of the present invention；
Fig. 5 shows the response curve of the angular speed of left motor；
Fig. 6 shows the tracking error curve of the angular speed of left motor；
Fig. 7 shows the voltage output curve of left motor；
Fig. 8 shows the broken line movement locus of caterpillar robot；
Fig. 9 shows the tracking error curve of the broken line movement locus of caterpillar robot；
Figure 10 shows the angular speed response curve of left motor and right motor；
Figure 11 shows the circular motion track of caterpillar robot；
Figure 12 shows the tracking error curve of the circular motion track of caterpillar robot；
Figure 13 shows the angular speed response curve of left motor and right motor；
Figure 14 shows movement locus of caterpillar robot when using ASMTC control methods；And
Figure 15 shows the position and attitude error curve of movement locus of caterpillar robot when using ASMTC control methods.
Specific embodiment
The specific embodiment of the present invention is described in detail below in conjunction with attached drawing.It should be understood that this place is retouched
The specific embodiment stated is merely to illustrate and explain the present invention, and is not intended to restrict the invention.
Fig. 1 is the flow chart of the control method for caterpillar robot according to an embodiment of the present invention.Such as Fig. 1 institutes
Show, one embodiment of the present invention provides a kind of control method for caterpillar robot, the control method can include with
Lower step：
In step S101, the pose under the current state of caterpillar robot is obtained；
In step s 102, the reference locus of caterpillar robot is set, reference locus includes pose instruction and speed command；
In step s 103, the restriction relation between the pose of description caterpillar robot and the speed of caterpillar robot is established
Kinematics model, speed include angular speed and linear velocity；
In step S104, according to the pose under current state and the reference locus of setting, the position of caterpillar robot is established
Appearance error model；
In step S105, according to kinematics model and the position and attitude error differential of position and attitude error model foundation caterpillar robot
Model；
In step s 106, establish caterpillar robot for driving the left motor of left driving wheel and for driving right driving
The driving model of the right motor of wheel, driving model include torque driving model and electric potential balancing model；
In step s 107, the dynamic analog of left motor and right motor is obtained according to torque driving model and electric potential balancing model
Type；
In step S108, the adaptive sliding mode switching model establishing with parameter adjustment and change；
In step S109, caterpillar robot is obtained according to position and attitude error Differential Model and adaptive sliding mode switching model
Desired speed, desired speed include it is expected linear velocity and it is expected angular speed.
In step s 110, the expectation angular speed of left motor and right motor is obtained according to the desired speed of caterpillar robot.
Fig. 3 shows the illustraton of model of the caterpillar robot of one embodiment of the present invention.As shown in figure 3, caterpillar robot
Pose refer to position and posture (inclined degree) of the caterpillar robot in XOY coordinate systems, in the present invention using p=(x,
y,θ)TRepresent the pose of caterpillar robot.
The reference locus of caterpillar robot refers to the designated position that caterpillar robot to be reached and reaches designated position
When caterpillar robot angle of inclination, operation linear velocity and angular speed.
As shown in figure 3, point m is the barycenter of caterpillar robot, point OaFor the geometric center of caterpillar robot, tracked machine is described
Formula (1) expression for example may be used in the kinematics model of restriction relation between the pose of device people and the speed of caterpillar robot：
Wherein, x, y are respectively position coordinates of the barycenter of caterpillar robot in XOY coordinate systems, and θ is caterpillar robot
The angle of the direction of motion and X-axis, v, ω are respectively the linear velocity and angular speed of caterpillar robot, and d is the barycenter of caterpillar robot
The distance between geometric center,WithRespectively x, y and θ are to the derivative of time.
Fig. 4 shows the position and attitude error illustraton of model of the caterpillar robot of one embodiment of the present invention.As shown in figure 4, root
According to the pose under the current state of caterpillar robot and the reference locus of setting, the position and attitude error model of the caterpillar robot of foundation
Such as formula (2) expression may be used：
Wherein, (x, y, θ)TFor the pose under caterpillar robot current state, x, y are respectively the barycenter of caterpillar robot
The coordinate of current location, θ be caterpillar robot angle of its direction of motion and X-axis under current state, (xr,yr,θr)TFor position
Appearance instructs, xr、yrThe respectively coordinate of the target location of the barycenter of caterpillar robot, θrTarget location is reached for caterpillar robot
When its direction of motion and X-axis angle, xeThe current location and target location of barycenter for caterpillar robot are along its current kinetic
The error amount in direction, yeThe current location and target location of barycenter for caterpillar robot with its current kinetic direction Vertical Square
To error amount, θeFor θ and θrBetween error amount.
By formula (2) differential, convolution (1) obtains the position and attitude error Differential Model of caterpillar robot, the position and attitude error differential
Formula (3) expression for example may be used in model：
Wherein, xeError of the current location and target location of barycenter for caterpillar robot along its current kinetic direction
Value, yeThe current location and target location of barycenter for caterpillar robot are in the error with its current kinetic direction vertical direction
Value, θeFor caterpillar robot under current state the angle of its direction of motion and X-axis and its direction of motion when reaching target location
Error amount between the angle of X-axis,Respectively xe、yeAnd θeTo the derivative of time, v and ω are respectively crawler belt
Linear velocity and angular speed of the robot under current state, (vr,ωr)TFor speed command, vrAnd ωrRespectively caterpillar robot
Linear velocity and angular speed during arrival target location, d are the distance between barycenter and geometric center of caterpillar robot.
The driving actuator of caterpillar robot is left motor for driving left driving wheel and for driving right driving wheel
Right motor, left motor and right motor for example can be direct current generators.It is left according to different control targes under different road conditions
Motor and the rotation of right motor coordination, driving caterpillar robot movement, therefore the motion control of caterpillar robot is left motor and the right side
The coordination control of motor.
Formula (4) can be for example respectively adopted in the equalising torque model of left motor and right motor and formula (5) represents：
Wherein, Jr(t)、Jl(t) be respectively left motor and right motor shaft rotary inertia, F be left motor and right motor
Output shaft on viscosity friction coefficient, ktFor left motor and the electric torque coefficient of right motor, Tdr(t)、Tdl(t) it is respectively a left side
The disturbance torque that motor and right motor are subject to, ωr(t)、ωl(t) be respectively left motor and right motor shaft rotation angle speed
Degree,WithRespectively ωr(t) and ωl(t) to the derivative of time, ir(t)、il(t) it is respectively left motor and right motor
Armature supply.
Formula (6) can be for example respectively adopted in the electric potential balancing model of left motor and right motor and formula (7) represents：
Wherein, L is the armature inductance of left motor and right motor, and R is the armature resistance of left motor and right motor, keFor left electricity
The back EMF coefficient of machine and right motor, and ke=0.10472kt, ktFor left motor and the electric torque coefficient of right motor, ωr
(t)、ωl(t) be respectively left motor and right motor shaft rotation angular speed, ir(t)、il(t) it is respectively left motor and right electricity
The armature supply of machine,WithRespectively ir(t) and il(t) to the derivative of time, ur(t) and ul(t) it is respectively right motor
Driving voltage and left motor driving voltage.
Due to the executing agency of left motor and right motor for caterpillar robot, fast response time, in the armature for ignoring motor
In the case of inductance, formula (8) for example may be used for the dynamic model of left motor and right motor and formula (9) represents：
Wherein, Tl(t)=RJl(t)/(RF+ktke), Tr(t)=RJr(t)/(RF+ktke),
k1=kt/(RF+ktke), k2=R/ (RF+ktke), R is the armature resistance of left motor and right motor, Jr(t)、Jl(t)
The rotary inertia of the shaft of respectively left motor and right motor, F are the viscous friction system on the output shaft of left motor and right motor
Number, ktFor left motor and the electric torque coefficient of right motor, keFor left motor and the back EMF coefficient of right motor, and ke=
0.10472kt, Tdr(t)、Tdl(t) it is respectively disturbance torque that left motor and right motor are subject to, ωr(t)、ωl(t) it is respectively a left side
The angular speed of the shaft of motor and right motor rotation,WithRespectively ωr(t) and ωl(t) to the derivative of time, ur
(t) and ul(t) be respectively right motor driving voltage and left motor driving voltage.
Due to the multi input of position and attitude error Differential Model, nonlinear feature, in one embodiment of the present invention, establish
The adaptive sliding mode switching model changed with parameter adjustment so that in the case where position and attitude error is larger, limit can be played
The effect of integral term processed, it is smaller in position and attitude error, there is certain amplification, improve control accuracy.
Formula (10) expression for example may be used in the adaptive sliding mode switching model changed with parameter adjustment：
Wherein, α1And α2For tilt parameters,xeFor caterpillar robot
Barycenter error amount along its current kinetic direction of current location and target location, yeBarycenter for caterpillar robot it is current
Position and target location are in the error amount with its current kinetic direction vertical direction, θeFor caterpillar robot under current state its
The error amount when direction of motion and the angle of X-axis and arrival target location between its direction of motion and the angle of X-axis, vrFor crawler belt
Robot reaches linear velocity during target location, c1、c2、c3、c4、kk1、kk2It is normal number, s1And s2Respectively about xeAnd θe
Switching function；
Formula (11) can be obtained to the derivative of formula (10) seeking time：
Wherein, α1And α2For tilt parameters,xeFor caterpillar robot
Barycenter error amount along its current kinetic direction of current location and target location, yeBarycenter for caterpillar robot it is current
Position and target location are in the error amount with its current kinetic direction vertical direction, θeFor caterpillar robot under current state its
The error amount when direction of motion and the angle of X-axis and arrival target location between its direction of motion and the angle of X-axis, vrFor crawler belt
Robot reaches linear velocity during target location,WithRespectively xeAnd θeTo the derivative of time, c1、c2、c3、c4、kk1、kk2
It is normal number, s1And s2Respectively about xeAnd θeSwitching function；WithRespectively s1And s2To the derivative of time.
Formula (12) can be obtained by bringing formula (3) into formula (11)：
Wherein, α1And α2For tilt parameters,V and ω is respectively crawler belt
Linear velocity and angular speed of the robot under current state, vrAnd ωrRespectively caterpillar robot reach target location when linear speed
Degree and angular speed,For vrTo the derivative of time, xeThe current location and target location of barycenter for caterpillar robot are current along it
The error amount of the direction of motion, yeThe current location and target location of barycenter for caterpillar robot are hung down with its current kinetic direction
Nogata to error amount, θeFor caterpillar robot the angle of its direction of motion and X-axis and target location is reached under current state
When its direction of motion and X-axis angle between error amount, d is the barycenter of caterpillar robot and the distance between geometric center,
c1、c2、c3、c4、kk1、kk2It is normal number, s1And s2Respectively about xeAnd θeSwitching function,WithRespectively s1And s2
To the derivative of time.
Enable formula (12) that the desired speed of caterpillar robot can be obtained equal to zero, the desired speed of caterpillar robot for example may be used
To be represented using formula (13)：
Wherein, vdAnd ωdRespectively the expectation linear velocity of caterpillar robot and expectation angular speed, α1And α2For tilt parameters,ω be angular speed of the caterpillar robot under current state, vrAnd ωrPoint
Not Wei caterpillar robot reach target location when linear velocity and angular speed,For vrTo the derivative of time, xeFor caterpillar robot
Barycenter error amount along its current kinetic direction of current location and target location, yeBarycenter for caterpillar robot it is current
Position and target location are in the error amount with its current kinetic direction vertical direction, θeFor caterpillar robot under current state its
The error amount when direction of motion and the angle of X-axis and arrival target location between its direction of motion and the angle of X-axis, d is crawler belt
The distance between the barycenter of robot and geometric center, c1、c2、c3、c4、kk1、kk2It is normal number.
Fig. 2 is the flow chart of the control method for caterpillar robot according to an embodiment of the present invention.Such as Fig. 2 institutes
Show, provide a kind of control method for caterpillar robot, control method shown in Fig. 2 in one embodiment of the present invention
It can also include the following steps compared with control method shown in FIG. 1：
In step S210, establish for correct caterpillar robot desired speed switching control model；
In step S211, using the desired speed of switching control Modifying model caterpillar robot and acquisition track machines
The revised desired speed of people；
In step S212, the expectation angular speed of left motor and the right motor is obtained according to revised desired speed；
In step S213, according to left motor and the expectation angular speed and the dynamic analog of left motor and right motor of right motor
Type calculates the driving voltage of left motor and right motor.
In one embodiment of the present invention, for correcting the switching control model of the desired speed of caterpillar robot for example
Formula (12) expression may be used：
Wherein, β1、β2To be more than zero handoff gain, β1、β2、Δ1And Δ2It is empirical value, sat is saturation function, s1
And s2Respectively about xeAnd θeSwitching function；
The revised desired speed of convolution (13) caterpillar robot is represented using formula (15)：
Wherein, v 'dWith ω 'dThe respectively revised expectation linear velocity of caterpillar robot and revised expectation angle speed
Degree, α1And α2For tilt parameters,ω is caterpillar robot in current state
Under angular speed, vrAnd ωrRespectively caterpillar robot reach target location when linear velocity and angular speed,For vrTo the time
Derivative, xeError amount of the current location and target location of barycenter for caterpillar robot along its current kinetic direction, yeTo carry out
The current location and target location of the barycenter of carrying machine people are in the error amount with its current kinetic direction vertical direction, θeFor crawler belt
The robot angle of its direction of motion and X-axis and angle of its direction of motion and X-axis when reaching target location under current state
Between error amount, d is the barycenter of caterpillar robot and the distance between geometric center, c1、c2、c3、c4、kk1、kk2It is normal
Number, β1、β2To be more than zero handoff gain, β1、β2、Δ1And Δ2It is empirical value, sat is saturation function, s1And s2Respectively close
In xeAnd θeSwitching function；
Formula (14) is respectively adopted in the expectation angular speed of left motor and right motor and formula (15) represents：
ωrd=(v 'd+ω′dA)r-1Formula (14)
ωld=(v 'd-ω′dA)r-1Formula (15)
Wherein, ωrdAnd ωldThe expectation angular speed for it is expected angular speed and left motor of respectively right motor, v 'dWith ω 'dPoint
Not Wei caterpillar robot revised expectation linear velocity and revised expectation angular speed, A be left driving wheel and right driving wheel
Between spacing half, r is the radius of left driving wheel and the right driving wheel.
β1And β2Value can be taken as 0.01%, Δ1Value can be taken as ± 0.01%, Δ2Value can be taken as ±
0.01%.
By the expectation angular velocity omega of right motorrdWith the expectation angular velocity omega of left motorldBring left motor dynamics model into respectively
The dynamic analog pattern (9) of formula (8) and right motor, can be calculated the driving voltage u that should be applied to right motorrIt (t) and should
As the driving voltage u for being applied to left motorl(t)。
Although show the specific step of the control method for caterpillar robot in a particular order in fig. 1 and 2
Suddenly, it will be recognized to those skilled in the art that unless logically there must be precedence relationship, otherwise control method need not must
It must be performed according to the step of being shown in figure.
One embodiment of the present invention also provides a kind of caterpillar robot, which can include：
Left driving wheel, for driving left crawler belt；Right driving wheel, for driving right-hand track chiain；
Left motor, for driving the left driving wheel；Right motor, for driving the right driving wheel；
Sensor, for detecting the pose under the current state of caterpillar robot, which is referring to including caterpillar robot
Position and angle of inclination in position fixing system；And
Controller, for performing the control method for caterpillar robot in above-mentioned arbitrary embodiment.
In order to verify the validity of the control method for caterpillar robot of embodiments of the present invention, the present invention provides
Following embodiment.
In one embodiment of this invention, the left motor of caterpillar robot and the parameters of right motor for example can be：
Jr=Jl=0.155kgm2, L=0.4510-3H, ke=0.265V/rad, kt=2.52nm/A, R=3.68 Ω, F=
0.001, k1=2, k2=2, the control voltage u of left motor and right motor meets | u |≤15V.The parameters example of caterpillar robot
Such as can be：The radius r=of the length l=0.555m of caterpillar robot, width w=0.4m, left driving wheel and right driving wheel
0.1m, the spacing 2A=0.36m between left driving wheel and right driving wheel, white noise acoustic jamming d (t)=50 × randn (1,1).Control
The parameters of device processed for example can be：kk1=kk2=2, c1=c2=2, c3=c4=4, kω1=kω2=1000, the sampling time
For 50ms.Verification to the control of left motor and motor
The control method (following and attached drawing in abbreviation ASMTC control methods) of embodiments of the present invention and normal is respectively adopted
The sliding formwork control (Sliding Mode Control, abbreviation SMC control methods below and in attached drawing) of exponentially approaching rule is advised to carrying out
Carrying machine people carries out simulation calculation, and control caterpillar robot is transported with linear velocity v=2m/s and the velocity linear of angular velocity omega=0
Row.
Fig. 5 shows the response curve of the angular speed of left motor, and Fig. 6 shows that the tracking error of the angular speed of left motor is bent
Line, Fig. 7 show the voltage output curve of left motor.Due to the simulation calculation condition of left driving wheel and right driving wheel, parameter and
Model is identical, in the case of caterpillar robot linear running, the complete phase of simulation result and left driving wheel of right driving wheel
Together.As shown in Figure 5, Figure 6, it is left when the control method of embodiment using the present invention controls left motor and right motor
The angular speed response curve of motor is smooth, and reaches stable state in 0.375s, the stop value of the angular speed of left motor output
For 20rad/s, angular speed tracking error converges to zero；And when being controlled using SMC methods, caterpillar robot needs 0.75s
Stable state is can be only achieved, and has chattering phenomenon.As shown in Figure 7, it is of the invention to obtain what ASMTC methods exported compared with SMC methods
Voltage curve is more smooth, buffets amplitude and is not more than 0.01V.Since the saturation for becoming tilt parameters integral term in sliding formwork switching function is special
Property, when the situation of large error occurs in caterpillar robot, integral term effect can be limited, system is made not occur excessive surpass
It adjusts；There is amplification to improve control accuracy in the case where not causing buffeting when error is smaller.
Different tracks sliding mode tracking control simulation calculation
The present invention provides the embodiment of the following simulation calculation that broken line and Circular test tracking are carried out to caterpillar robot.
(a) dog-leg path sliding mode tracking control
In one embodiment of this invention, using dog leg path as simulation calculation path, the pose instruction of caterpillar robot is
[0,0,pi/4]T, the initial pose of caterpillar robot is [- 2, -2, pi/4]T, constant linear velocity 2m/s, simulation calculation when
Between be 0 ＜ t ＜ 12s.
Fig. 8 shows the broken line movement locus of caterpillar robot, and Fig. 9 shows the broken line movement locus of caterpillar robot
Tracking error curve, Figure 10 show the angular speed response curve of left motor and right motor.By Fig. 8 and Fig. 9 as it can be seen that track machines
People starts from initial position, and the position and attitude error of machine crawler belt device people can converge to 0 in a relatively short period of time, 8 ＜ t ＜ 10s'
In period, although the Curvature varying of reference path is larger, controller remains able to track reference path quickly, stablizes
Position and attitude error afterwards is：xeIn (- 0.08,0.04) section, yeIn (- 0.07,0.07) section, θeAt (- 0.02,0.045)
In section.As shown in Figure 10, left motor/right motor has faster response speed, reaches energy held stationary after expectation angular speed.
(b) Circular test sliding mode tracking control
In one embodiment of this invention, the circular path using radius as 10m is simulation calculation path, with the constant of 2m/s
Linear velocity at the uniform velocity tracks circular path, and reference locus is：X=10cos θ, y=10sin θ.
The initial pose of caterpillar robot is [10,0, pi/2]T, pose instruction is [7,0, pi/2]T, left driving wheel and the right side
The angular speed of driving wheel is respectively 10rad/s, 30rad/s, constant linear velocity 2m/s, is counterclockwise run, simulation calculation
Time is 0 ＜ t ＜ 32s.
Figure 11 shows the circular motion track of caterpillar robot, and Figure 12 shows the circular motion track of caterpillar robot
Tracking error curve, Figure 13 shows the angular speed response curve of left motor and right motor.As shown in Figure 11 to Figure 13, it uses
The control method of embodiments of the present invention enables to the angular speed quick response of left motor and right motor, reaches expectation speed
Held stationary after degree.Caterpillar robot can preferably track designed circular path, and position and attitude error tends to 0.Particularly with
During track circular path, the variation of path curvatures moment can adjust output control, the left electricity of output in time using ASMTC control methods
The angular speed curve of machine and right motor is relatively smooth, ensures that tracking does not depart from reference locus, control accuracy is high.Sliding mode tracking control
Experiment
In one embodiment of this invention, field control is carried out in fact with the caterpillar robot of embodiments of the present invention
It tests, using controller of the microcontroller of model S3C2440 as caterpillar robot, experiment surface condition is mushy water-melon pulp soil and miscellaneous
The farmland that grass mixes.Using integrated navigation and location system SPAN-CPT as the receiving device of the status information of caterpillar robot,
SPAN-CPT is mounted on caterpillar robot, and information turnover rate is 10hz, velocity accuracy 0.01m/s, and angle precision is
0.02rad, positional accuracy measurement 0.01m, the pursuit path path of caterpillar robot are：
The operation linear velocity of caterpillar robot be 2m/s, initial pose [x (0) y (0) θ (0)]T=[0 20 pi/12]T,
Pose instructs：[xr(0) yr(0) θr(0)]T=[10 40 pi/4]T, initial position and attitude error is：[xe(0) ye(0) θe
(0)]T=[10 20 pi/6]T。
Figure 14 shows movement locus of caterpillar robot when using ASMTC control methods, except initial position and tracking
The region that trajectory tortuosity changes greatly, the movement locus are more smooth.Figure 15 shows that caterpillar robot is controlled using ASMTC
The position and attitude error curve of movement locus during method.As can be seen from Figure 15, the starting stage moved in caterpillar robot, by
It is inconsistent in the initial pose of caterpillar robot and pose instruction so that initial pose deviation is larger, in 39-50s and 79-90s
Period in, since path curvatures change greatly, mechanical steering amplitude is larger, the sideslip and centrifugation that caterpillar robot is subject to
Power influence is also more serious, generates more serious Parameter Perturbation and external interference, causes larger position and attitude error, generated
Pose parameter error range is respectively：-0.03≤xe≤ 0.04m, -0.08≤ye≤ 0.06m, -0.03≤ye≤0.05rad.It carries out
When carrying machine people operates in Curvature varying smaller region, pursuit path is very smooth, and the deviation between reference curve approaches
Zero.
Table 1 shows that caterpillar robot is to same track following in identical experiment condition, the linear velocity difference of operation
When the position and attitude error that generates.As shown in Table 1, it is respectively 1m/s, 3m/s and 4m/s when caterpillar robot runs linear velocity at it
Under the conditions of, along when providing curve motion, position and attitude error can quickly reduce, and close to zero, meet the requirement of control accuracy.
Track following position and attitude error under 1 low-speed conditions of table
By the above embodiment, caterpillar robot is considered as by motor driven systems and body movement system group by the present invention
Into cascade system, structure become tilt parameters Adaptive Integral sliding formwork switching function, and according to Adaptive Integral sliding formwork switch
Function proposes the adaptive sliding mode tracing control based on equivalent control and switching control, with the speed of robot, distinguishes online
Know the driving motor time-varying uncertain parameter of gained and that is asked in kinematics model feeds back to the error of object pose
In the controller of drive system, then according to kinematic relation, the desired speed of each motor is decomposed, and then realize robot
Stable motion controls.
The preferred embodiment of the present invention is described in detail above in association with attached drawing, still, the present invention is not limited to above-mentioned realities
Mode is applied, within the scope of the technical concept of the present invention, a variety of modifications can be carried out to technical scheme of the present invention, these simple changes
Type all belongs to the scope of protection of the present invention.
Claims (8)
1. for the control method of caterpillar robot, which is characterized in that include the following steps：
Obtain the pose under the current state of caterpillar robot；
The reference locus of the caterpillar robot is set, the reference locus includes pose instruction and speed command；
Establish the kinematics of the restriction relation between the speed of pose and the caterpillar robot for describing the caterpillar robot
Model, the speed include linear velocity and angular speed；
According to the pose under the current state and the reference locus of setting, the position and attitude error mould of the caterpillar robot is established
Type；
According to the position and attitude error Differential Model of caterpillar robot described in the kinematics model and the position and attitude error model foundation；
Establish the caterpillar robot for driving the left motor of left driving wheel and for driving the right motor of right driving wheel
Driving model, the driving model include torque driving model and electric potential balancing model；
The dynamic model of the left motor and the right motor is obtained according to the torque driving model and electric potential balancing model；
Establish the adaptive sliding mode switching model changed with parameter adjustment；
The expectation of the caterpillar robot is obtained according to the position and attitude error Differential Model and the adaptive sliding mode switching model
Speed.
2. control method according to claim 1, which is characterized in that the control method further includes：
Establish for correct the caterpillar robot desired speed switching control model；
Using the desired speed of caterpillar robot described in the switching control Modifying model and obtain the caterpillar robot
Revised desired speed；
The expectation angular speed of the left motor and the right motor is obtained according to the revised desired speed；
According to the left motor and the expectation angular speed and the dynamic analog of the left motor and the right motor of the right motor
Type calculates the driving voltage of the left motor and the right motor.
3. control method according to claim 2, which is characterized in that describe the pose of caterpillar robot and the tracked machine
The kinematics model of restriction relation between the speed of device people is represented using formula (1)：
Wherein, x, y are respectively position coordinates of the barycenter of the caterpillar robot in XOY coordinate systems, and θ is the track machines
The direction of motion of people and the angle of X-axis, v, ω are respectively the linear velocity and angular speed of the caterpillar robot, and d is the crawler belt
The distance between the barycenter of robot and geometric center, WithRespectively x, y and θ are to the derivative of time；
According to the pose under the current state of the caterpillar robot and the reference locus of setting, the caterpillar robot of foundation
Position and attitude error model using formula (2) represent：
Wherein, (x, y, θ)TFor the pose under the caterpillar robot current state, x, y are respectively the matter of the caterpillar robot
The coordinate of the current location of the heart, θ be caterpillar robot angle of its direction of motion and X-axis under current state, (xr,yr,
θr)TIt is instructed for the pose, xr、yrThe coordinate of the target location of the barycenter of respectively described caterpillar robot, θrFor the crawler belt
The angle of its direction of motion and X-axis when robot reaches target location, xeThe current location of barycenter for the caterpillar robot
With error amount of the target location along its current kinetic direction, yeThe current location of barycenter for the caterpillar robot and target position
It puts in the error amount with its current kinetic direction vertical direction, θeFor θ and θrBetween error amount；
According to the kinematics model and the position and attitude error Differential Model of the caterpillar robot of position and attitude error model foundation：
Wherein, xeError amount of the current location and target location of barycenter for the caterpillar robot along its current kinetic direction,
yeThe current location and target location of barycenter for the caterpillar robot are in the error with its current kinetic direction vertical direction
Value, θeFor the caterpillar robot under current state the angle of its direction of motion and X-axis and it is moved when reaching target location
Error amount between direction and the angle of X-axis,Respectively xe、yeAnd θeTo the derivative of time, v and ω are respectively
Linear velocity and angular speed of the caterpillar robot under current state, (vr,ωr)TFor the speed command, vrAnd ωrRespectively
Linear velocity and angular speed, d during for caterpillar robot arrival target location are the barycenter and geometry of the caterpillar robot
The distance between center.
4. control method according to claim 3, which is characterized in that the equalising torque of the left motor and the right motor
Formula (4) is respectively adopted in model and formula (5) represents：
Wherein, Jr(t)、Jl(t) be respectively the left motor and the right motor shaft rotary inertia, F be the left motor
With the viscosity friction coefficient on the output shaft of the right motor, ktElectromagnetic torque system for the left motor and the right motor
Number, Tdr(t)、Tdl(t) it is respectively disturbance torque that the left motor and the right motor are subject to, ωr(t)、ωl(t) it is respectively
The angular speed of the shaft of the left motor and right motor rotation,WithRespectively ωr(t) and ωl(t) pair when
Between derivative, ir(t)、il(t) be respectively the left motor and the right motor armature supply；
Formula (6) is respectively adopted in the electric potential balancing model of the left motor and the right motor and formula (7) represents：
Wherein, L is the armature inductance of the left motor and the right motor, and R is the armature of the left motor and the right motor
Resistance, keFor the left motor and the back EMF coefficient of the right motor, ir(t)、il(t) it is respectively left motor and right motor
Armature supply,WithRespectively ir(t) and il(t) to the derivative of time, ur(t) and ul(t) it is respectively the right electricity
The driving voltage of the driving voltage of machine and the left motor；
The left motor and the dynamic model of the right motor obtained according to the torque driving model and electric potential balancing model
It is represented using formula (8) and formula (9)：
Wherein, Tl(t)=RJl(t)/(RF+ktke), Tr(t)=RJr(t)/(RF+ktke),
k1=kt/(RF+ktke), k2=R/ (RF+ktke), R is the armature resistance of left motor and right motor, Jr(t)、Jl(t) respectively
For left motor and the rotary inertia of the shaft of right motor, F is the viscosity friction coefficient on the output shaft of left motor and right motor, kt
For left motor and the electric torque coefficient of right motor, keFor left motor and the back EMF coefficient of right motor, and ke=
0.10472kt, Tdr(t)、Tdl(t) it is respectively disturbance torque that left motor and right motor are subject to, ωr(t)、ωl(t) it is respectively a left side
The angular speed of the shaft of motor and right motor rotation,WithRespectively ωr(t) and ωl(t) to the derivative of time, ur
(t) and ul(t) be respectively the right motor driving voltage and the left motor driving voltage.
5. control method according to claim 4, which is characterized in that the adaptive sliding changed with parameter adjustment of foundation
Mould switching model is represented using formula (10)：
Wherein, α1And α2For tilt parameters,xeFor the caterpillar robot
Error amount of the current location and target location of barycenter along its current kinetic direction, yeBarycenter for the caterpillar robot is worked as
Front position and target location are in the error amount with its current kinetic direction vertical direction, θeIt is the caterpillar robot in current shape
The angle of its direction of motion and X-axis and error amount when reaching target location between its direction of motion and the angle of X-axis, v under stater
Linear velocity during target location, c are reached for the caterpillar robot1、c2、c3、c4、kk1、kk2It is normal number, s1And s2Respectively
For about xeAnd θeSwitching function.
6. control method according to claim 5, which is characterized in that according to the position and attitude error Differential Model and it is described from
The desired speed for adapting to the caterpillar robot that sliding formwork switching model obtains is represented using formula (11)：
Wherein, vdAnd ωdThe expectation linear velocity of respectively described caterpillar robot and expectation angular speed, α1And α2For tilt parameters,ω be angular speed of the caterpillar robot under current state, vrWith
ωrLinear velocity and angular speed when respectively the caterpillar robot reaches target location,For vrTo the derivative of time, xeFor
Error amount of the current location and target location of the barycenter of the caterpillar robot along its current kinetic direction, yeFor the crawler belt
The current location and target location of the barycenter of robot are in the error amount with its current kinetic direction vertical direction, θeFor the shoe
Carrying machine the people angle of its direction of motion and X-axis and folder of its direction of motion and X-axis when reaching target location under current state
Error amount between angle, d are the barycenter of the caterpillar robot and the distance between geometric center, c1、c2、c3、c4、kk1、kk2
For normal number.
7. control method according to claim 6, which is characterized in that the switching control model is represented using formula (12)：
Wherein, β1、β2To be more than zero handoff gain, β1、β2、Δ1And Δ2It is empirical value, sat is saturation function, s1And s2Point
It Wei not be about xeAnd θeSwitching function；
The revised desired speed of the caterpillar robot is represented using formula (13)：
Wherein, v 'dWith ω 'dThe revised expectation linear velocity of respectively described caterpillar robot and revised expectation angle speed
Degree, α1And α2For tilt parameters,ω is the caterpillar robot current
Angular speed under state, vrAnd ωrLinear velocity and angular speed when respectively the caterpillar robot reaches target location,For
vrTo the derivative of time, xeThe current location and target location of barycenter for the caterpillar robot are along its current kinetic direction
Error amount, yeThe current location and target location of barycenter for the caterpillar robot with its current kinetic direction vertical direction
Error amount, θeFor the caterpillar robot under current state the angle of its direction of motion and X-axis and when reaching target location
Error amount between its direction of motion and the angle of X-axis, d be the caterpillar robot barycenter and geometric center between away from
From c1、c2、c3、c4、kk1、kk2It is normal number, β1、β2To be more than zero handoff gain, β1、β2、Δ1And Δ2It is empirical value,
Sat is saturation function, s1And s2Respectively about xeAnd θeSwitching function；
Formula (14) is respectively adopted in the expectation angular speed of the left motor and the right motor and formula (15) represents：
ωrd=(v 'd+ω′dA)r-1Formula (14)
ωld=(v 'd-ω′dA)r-1Formula (15)
Wherein, ωrdAnd ωldThe expectation angular speed for it is expected angular speed and left motor of respectively described right motor, v 'dWith ω 'dPoint
Not Wei the caterpillar robot revised expectation linear velocity and revised expectation angular speed, A for the left driving wheel and
The half of spacing between right driving wheel, r are the left driving wheel and the radius of the right driving wheel.
8. a kind of caterpillar robot, which is characterized in that including：
Left driving wheel, for driving left crawler belt；
Right driving wheel, for driving right-hand track chiain；
Left motor, for driving the left driving wheel；
Right motor, for driving the right driving wheel；
Sensor, for detecting the pose under the current state of the caterpillar robot, which includes the caterpillar robot
Position and angle of inclination in specified coordinate system；And controller, for performing according to any one in claim 1 to 7
The control method for caterpillar robot.
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