CN107479556B - Double-wheel self-balancing car owner moves collision free trajectory and tenacious tracking control method - Google Patents
Double-wheel self-balancing car owner moves collision free trajectory and tenacious tracking control method Download PDFInfo
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
- G05D1/02—Control of position or course in two dimensions
- G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
- G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
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- G—PHYSICS
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- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
- G05D1/02—Control of position or course in two dimensions
- G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
- G05D1/0276—Control of position or course in two dimensions specially adapted to land vehicles using signals provided by a source external to the vehicle
Abstract
The present invention relates to a kind of double-wheel self-balancing car owners to move collision free trajectory and tenacious tracking control method, including based on circular arc and easement curve collision free trajectory method with based on non-singular terminal sliding formwork and the nested tenacious tracking control method for being saturated algorithm.The track that the local path planing method is planned includes lane-change track, surmounts track and simultaneously road track.The complete driving of non-singular terminal sliding Mode Algorithm control double-wheel self-balancing vehicle turns to subsystem, and the nested algorithm that is saturated controls before the drive lacking of double-wheel self-balancing vehicle to subsystem.The characteristics of avoidance track that the present invention is planned has trajectory tortuosity variation gentle, is convenient for drive lacking double-wheel self-balancing vehicle tenacious tracking；The tenacious tracking control algolithm proposed can make double-wheel self-balancing vehicle under larger car body obliqueness initial value, the avoidance track that tenacious tracking is planned, while vehicle body being kept to stablize, to realize the automatic obstacle avoidance of double-wheel self-balancing vehicle.
Description
Technical field
The invention belongs to double-wheel self-balancing vehicle control field, specifically a kind of double-wheel self-balancing vehicle automatic obstacle avoidance track
Planning and tenacious tracking control method.
Background technique
Extension of the double-wheel self-balancing vehicle as single inverted pendulum system is not only the gedanken experiment of verifying relevant control theory
Platform, and it is all many-sided with important practical application value in amusement and recreation, medical instrument, space exploration etc..It can lead
It is dynamic to evade the barrier encountered in traveling process, it is the one of the important signs that of double-wheel self-balancing vehicle intelligence degree height.
Currently, the research about avoidance obstacle drives robot mainly for complete, and for drive lacking double-wheel self-balancing vehicle
Research in terms of automatic obstacle avoidance is rarely reported.For example, proposing one kind application No. is 201610118977.2 Chinese patent
" self-balancing two-wheeled balance car and control method ", the balance car mainly include left and right wheels, crossbeam and mobile platform, pass through balance
Driving motor automatically adjusts mobile platform, makes Self-Balancing vehicle adjust automatically center of gravity, keeps balance, is not directed to double-wheel self-balancing vehicle
Avoidance obstacle.Application No. is 201610573390.0 Chinese patent, a kind of " mobile robot path planning and keep away is proposed
Hinder method and system ", two-dimensional grid map is established according to obstacle information, shortest path is obtained using jump point searching algorithm, from
And realize the independent navigation of mobile robot.But this method, mainly for full driving robot, drive lacking double-wheel self-balancing vehicle is difficult
The track cooked up with tenacious tracking the method.Application No. is the Chinese patents of 201410448977.X to propose a kind of " be based on
The double-wheel self-balancing robot obstacle avoidance system and control method of fuzzy control ", system include attitude detection module, motion control
Module and Motor execution module, by remote controller key to double-wheel self-balancing robot send control instruction, realize its advance, after
It moves back, spin, pinpointing balance.Robot is according to obstacle distance information and fuzzy rule, and to make corresponding steering, realization is kept away
Barrier.The implementation of the patent needs to cannot achieve the automatic obstacle avoidance of double-wheel self-balancing robot by remote controler.
To sum up, existing control method is difficult to realize the automatic obstacle avoidance control of double-wheel self-balancing vehicle.
Summary of the invention
In view of the above-mentioned problems, the object of the present invention is to provide a kind of double-wheel self-balancing car owners to move collision free trajectory and stabilization
Tracking and controlling method, when so that double-wheel self-balancing vehicle encountering barrier during traveling, can collisionless active avoid hindering
Hinder object, and return on set travel route, while vehicle body being kept to stablize.
To achieve the above object, the present invention takes following technical scheme: double-wheel self-balancing car owner move collision free trajectory with
Tenacious tracking control method, comprising: collision free trajectory method based on circular arc and easement curve is based on non-singular terminal sliding formwork
With the tenacious tracking control method of nested saturation algorithm；The track that the collision free trajectory method is cooked up includes lane-change, surpasses
The road Yue Hebing three parts；The tenacious tracking control method, first by double-wheel self-balancing vehicle attained pose for avoidance track institute
The tracking of determining reference pose is converted into actual forward speed and steering angular velocity in the case where considering nonholonomic constraint
It is then that full driving turns to by entire double-wheel self-balancing vehicle system decoupling for it is expected the tracking of forward speed and steering angular velocity
It is respectively controlled before subsystem and drive lacking to subsystem.
Further, lane-change track, including the 1st transition track, the 1st arc track, the 2nd transition track, the 2nd circular arc rail
Mark, the 3rd transition track；The 1st transition track start respectively with avoidance before straight-line travelling track and the 1st arc track connect
It connects, expression formula is x (t)=v0T,Using avoidance starting point position as geodetic coordinates origin, started with avoidance
Moment is zero moment, wherein v0For the forward speed of double-wheel self-balancing vehicle, 0≤t≤t1,R is the 1st arc track
Radius of curvature, J are the permitted maximum transversal acceleration of double-wheel self-balancing vehicle；2nd arc track and the 1st arc track
Radius of curvature R and corresponding central angle ψ it is equal in magnitude, the 2nd arc track and the 1st arc track concave towards on the contrary,
Its track expression formula is determined according to the parametric equation of uniform circular motion；The 2nd transition track respectively with the 1st arc track and
The connection of 2nd arc track, expression formula are
t1+t2< t≤t1+t2+t3
Wherein, t1、t2、t3The respectively time used in the 1st transition track, the 1st arc track and the 2nd transition track, ψ according toIt determines,δ is safe clearance, WbAnd LvIt is respectively two
Take turns the dimensional parameters of Self-Balancing vehicle and barrier；
The 3rd transition track respectively with the 2nd arc track and surmount track and connect, track expression formula is
X (t)=L+2Rsin ψ+2Lcos ψ+v0(t-t1-t2-t3-t4)
t1+t2+t3+t4< t≤t1+t2+t3+t4+t5
Wherein, t4、t5Time used in respectively the 2nd arc track and the 3rd transition track；
Surmounting track is a straight line, and track expression formula is determined according to linear uniform motion equation；
And road track and lane-change track are symmetrical about the perpendicular bisector for surmounting track.
Further, the tenacious tracking control method, first by double-wheel self-balancing vehicle attained poseIt is right
Pose is referred to determined by the avoidance track cooked upTracking, consider nonholonomic constraintIn the case where, actual forward speed v and steering angular speed omega are converted into for it is expected forward speed vd
And steering angular speed omegadTracking；Wherein, x, y are coordinate of the double-wheel self-balancing vehicle under earth coordinates,For steering angle,It is led for the single order of x,It is led for the single order of y,
vd=vr cos e3+λ1tanh e1
Wherein, xr、yrFor coordinate of the avoidance track under earth coordinates,For reference steering angle determined by avoidance track,For xrSingle order lead,For yrSingle order lead,λ1、λ2And λ3What is be positive sets
Count parameter；Work as e3When=0,
Further, the full driving of non-singular terminal sliding Mode Algorithm control double-wheel self-balancing vehicle turns to subsystem, control
Rule byIt determines；Wherein WithRespectively it is expected angular velocity omegadIntegral, ωdAnd ωdSingle order lead, β > 0, η > 0, p, q
It is positive odd number, andmwFor wheel mass, r is radius of wheel, and d is wheelspan, I1It is wheel around the rotation of its diameter
Inertia, I2It is wheel around the rotary inertia of its wheel shaft, I3It is chassis around the rotary inertia of the vertical line of its mass center, I5For vehicle body
Around the rotary inertia of the vertical line of its mass center, τL、τRThe respectively output torque of left and right motor；Function sat (x) meets as follows
Definition: whenWhen,WhenWhen, sat (x)=1；WhenWhen, sat (x)=- 1, φ is normal
Number.
Further, to subsystem, control law before the drive lacking of the nested saturation algorithm control double-wheel self-balancing vehicle
By vz=-σ4(y4+σ3(y3+σ2(y2+σ1(y1)))) determine, wherein
ξ1=θ,z3=tan ξ1, z4=(1+tan2ξ1)ξ2, xvd、WithRespectively vdIntegral, vdAnd vd
Single order lead；θ is car body obliqueness, θd、Respectively θ,Desired value, be zero；mcFor chassis quality, mbFor body quality, L is vehicle
Distance of the body mass center to wheel axis center, I4It is chassis around the rotary inertia of wheel shaft, I6It is vehicle body around the rotary inertia of wheel shaft；Linearly
Saturation function σ (x): R → R is continuous nondecreasing function, and meets following condition: when | x | when < A, σ (x)=x；As x >=A, σ
(x)=A；As x≤- A, σ (x)=- A；A is known as the amplitude of σ.
Further, time t used in the 2nd transition track3=2t1, time t used in the 3rd transition track5=t1；2nd circle
Time t used in arc track4With time t used in the 1st arc track2It is equal, and
Further, work as Lb≤2(xE-S0) when, surmounting path length is zero；Otherwise, surmounting path length is Lb-2
(xE-S0)；Wherein, xEThe horizontal displacement of double-wheel self-balancing vehicle at the end of for lane-change, LbFor barrier dimensional parameters, S0For avoidance
Double-wheel self-balancing vehicle is at a distance from barrier when beginning.
Further, during avoidance, under bodywork reference frame, the transverse acceleration of double-wheel self-balancing vehicle becomes at any time
Positive inverse taper is turned to, forward acceleration is approximately zero.
As further, the minimum range of avoidance starting point and barrierWherein, xcFor
For double-wheel self-balancing vehicle just with horizontal displacement when bar contact, α is the angle of orbit tangent and horizontal direction at this time, LvFor
Double-wheel self-balancing vehicle dimensional parameters.
The beneficial effects of the present invention are:: 1, the collision free trajectory method based on circular arc and easement curve proposed,
Under bodywork reference frame, the transverse acceleration of double-wheel self-balancing vehicle changes over time the inverse taper that is positive, it is ensured that trajectory tortuosity
Consecutive variations；And forward acceleration is approximately zero, the realization that this feature keeps drive lacking double-wheel self-balancing vehicle relatively easy
To the tenacious tracking of institute's planned trajectory.2, a kind of two-wheeled based on non-singular terminal sliding mode technology with nested saturation process is proposed
Self-Balancing vehicle stable trajectory Tracking Control Scheme can be realized double-wheel self-balancing vehicle the larger car body obliqueness initial value the case where
Under, avoidance track that stable tracking is cooked up.
Detailed description of the invention
The present invention shares 9 width of attached drawing:
Fig. 1 is the structure chart of involved double-wheel self-balancing vehicle in the present invention；
Fig. 2 is the location diagram of double-wheel self-balancing vehicle and barrier before avoidance；
Fig. 3 is the avoidance track that the present invention is cooked up；
Fig. 4 is the relationship of transverse acceleration and time of the double-wheel self-balancing vehicle under bodywork reference frame during avoidance；
Fig. 5 be during avoidance double-wheel self-balancing vehicle just with positional relationship when bar contact；
Fig. 6 is control principle block diagram of the invention；
Fig. 7 be vehicle body initial tilt be 0.1 when embodiment simulation result；
Fig. 8 be vehicle body initial tilt be 0.2 when embodiment simulation result；
Fig. 9 be vehicle body initial tilt be 0.3 when embodiment simulation result；
Specific embodiment
To make the objectives, technical solutions, and advantages of the present invention clearer, right in the following with reference to the drawings and specific embodiments
The present invention is described in detail.
The present invention is described in detail below with reference to the accompanying drawings and embodiments.
As shown in Figure 1, double-wheel self-balancing car owner according to the present invention will include the components such as wheel 1, chassis 2 and vehicle body 3.
As illustrated in fig. 2, it is assumed that double-wheel self-balancing vehicle 4 is along straight way side at the uniform velocity v0To right travel, there are a barrier 5, road in front
It is sufficiently wide.The size Expressing of its boundary rectangle projected in horizontal plane of the size of barrier, upside and double-wheel self-balancing vehicle
The distance of initial straight track is Wb, length Lb.Rectangle, a length of L are also regarded in the projection of two wheeler in the horizontal plane asv, width is
Wv。
One, nonholonomic constraint, kinematics model and kinetic model suffered by double-wheel self-balancing vehicle are derived, as follows respectively:
Wherein, x, y are coordinate of the double-wheel self-balancing vehicle in earth coordinates,For steering angle, θ is car body obliqueness, mwFor
Wheel mass, mcFor chassis quality, mbFor body quality, r is radius of wheel, and d is wheelspan, and L is vehicle body mass center to wheel axis center
Distance, I1It is wheel around the rotary inertia of its diameter, I2It is wheel around the rotary inertia of its wheel shaft, I3Its mass center is bypassed for chassis
Vertical line rotary inertia, I4It is chassis around the rotary inertia of wheel shaft, I5It is used around the rotation of the vertical line of its mass center for vehicle body
Amount, I6It is vehicle body around the rotary inertia of wheel shaft, τL、τRThe respectively output torque of left and right motor.
Two, the barrier morpheme information measured according to sensor plans avoidance track.To start the position of lane-change as origin
Earth coordinates xOy is established, as zero moment at the time of to start lane-change, as shown in figure 3, the avoidance track mainly includes three
Point: lane-change track O E, surmount track EF and simultaneously road track FK.
The lane-change track mainly includes the 1st transition track OA, the 1st arc track AB, the 2nd transition track BC, the 2nd circle
Arc track CD, the 3rd transition track DE.Central angle corresponding to 1st arc track and the 2nd arc track is ψ, and radius of curvature is equal
For R.W is the maximum transversal displacement during avoidance, can be determined by following formula:
Wherein, δ is safe clearance.
OA sections of track expression formula is
Wherein,J is the permitted maximum transversal acceleration of double-wheel self-balancing vehicle.
Acquiring forward speed according to (5) formula isTransverse acceleration isIf taking R=
1000, v0=2, J=2 (are all made of international unit, similarly hereinafter), can obtain t1=0.002, yr(t) ∈ [0,0.0000000027] ≈ 0,
vr(t)∈[2,2.000000000004]≈v0,
Obviously, double-wheel self-balancing vehicle does linear uniform motion approximately along x-axis on this easement curve；Meanwhile passing through this mistake
Curve is crossed, transverse acceleration can be made to be smoothly transitted into from zeroTrajectory tortuosity is smoothly transitted into 1/R from zero.
BC sections of track expression formula is
t1+t2< t≤t1+t2+t3；Wherein, t1、t2、t3The respectively time used in OA, AB and BC,t3=
2t1, ψ according toIt determines.
Similar to the analysis to OA sections of track expression formulas, it is found that double-wheel self-balancing vehicle is approximate on this easement curve
Common tangent along two circular arcs does linear uniform motion；Meanwhile by this easement curve, can make transverse acceleration fromIt is flat
Cunning is transitioned intoCorresponding trajectory tortuosity is smoothly transitted into -1/R from 1/R.
DE sections of track expression formulas can OA sections of track expression formulas of analogy determine, time t used in DE sections5=t1, AB sections and CD sections
Track expression formula can be determining according to the parametric equation of uniform circular motion, time t used in CD sections4=t2.To entire lane-change rail
Mark expression formula is all determined.
If start avoidance, double-wheel self-balancing vehicle is S at a distance from barrier left margin0.If the length L of barrierbMeet
Lb≤2(xE-S0), surmounting path length is zero；Otherwise, surmount track to be not zero, i.e., double-wheel self-balancing vehicle along straight horizontal to the right
A distance is at the uniform velocity moved, if this process finish time is tF, then corresponding track expression formula be
Wherein,xEHorizontal displacement at the end of for lane-change, tEFor entire lane-change process institute
Use the time.
And road track and lane-change track are symmetrical about the perpendicular bisector for surmounting track, track expression formula analogy lane-change track table
It is determined up to formula.
During entire avoidance, under bodywork reference frame, the transverse acceleration a of double-wheel self-balancing vehiclenChange over time for
Positive inverse taper, as shown in Figure 4；And forward acceleration is approximately zero.
Three, minimum safe distance S is determinedminNamely avoidance when starting with the minimum range of barrier left margin.
As shown in figure 5, being located at during lane-change, tcIt is contacted just with barrier upper left corner on the right side of moment two wheeler, this
When orbit tangent and the angle of horizontal direction be α, double-wheel self-balancing vehicle is respectively x along the displacement of x-axis and y-axiscAnd yc。
According to the geometrical relationship in Fig. 5, can obtain:
WhenWhen, contact point is on the first segment circular arc of avoidance track, at this time
WhenWhen, transition of the contact point between two sections of circular arcs
On curve, at this time
α=ψ (10)
WhenWhen, contact point according to formula (8), (9) and (10) and is kept away on second segment circular arc
Hinder track expression formula, x can be acquiredcWith the value of α.
May finally obtain minimum safe distance is
Four, tenacious tracking controls.
The avoidance track cooked up has determined the reference pose p of double-wheel self-balancing vehicler=[xr,yr,φr]TIf two wheeler
Current pose be p=[x, y, φ]T, the error with reference pose is pe=[e1,e2,e3]T, wherein
If forward speed reference value determined by avoidance track is vr, steering angular velocity reference value is ωr.Utilize Li Yapu
Promise husband's direct method is easy proof, takes (13) formula to determine if the forward speed v and steering angular speed omega of double-wheel self-balancing vehicle are corresponding
vdAnd ωd, then for arbitrary initial position and attitude error pe, have
Wherein, λ1、λ2And λ3The design parameter being positive；Work as e3When=0,
1. turning to subsystem controls
According to kinetic model (3), can obtain second order steering subsystem equation is
Wherein, τω=τR-τL。
IfWithIt is the ω determined by (13) formula respectivelydIntegral, ωdAnd ωdSingle order lead, defineNegated unusual terminal sliding mode face and control law are respectively
Wherein, β > 0, η > 0, p, q are positive odd number, andFunction sat (x) satisfaction is such as given a definition: whenWhen,WhenWhen, sat (x)=1；WhenWhen, sat (x)=- 1.φ is normal number.
Using Lyapunov direct method and phase plane analysis is combined, is easy to prove, using control law (16), can make
WithIn Finite-time convergence to zero.
To subsystem controls before 2.
It can be obtained before drive lacking according to kinetic model (3) and be to subsystem equation
Wherein, xvFor the forward direction displacement of double-wheel self-balancing vehicle under bodywork reference frame, g is acceleration of gravity.
It enables
z3=tan ξ1, z4=(1+tan2ξ1)ξ2.Wherein xvd、WithIt is the v determined by (13) formula respectivelydIntegral,
vdAnd vdSingle order lead；θ,Desired value θd、It is zero；
Then define deviation variables ez1=z1-z1d, ez2=z2-z2d, ez3=z3, ez4=z4, by deriving, deviation system can be obtained
System
Wherein,
Due to the v on the avoidance track cooked uprFor definite value, and non-singular terminal sliding formwork control can be such that steering angle misses
Poor e3Quickly converge on zero, tanhe1∈ (- 1,1), therefore work as λ1When being taken as small value, from (13), formula can be seen that vd≈vr, in turn
HaveFormula (19) becomes following feedforward system:
It is easy to show that there are linear transformation y using Lyapunov direct methodi:R4→ R and amplitude are Ai(AiIt is sufficiently small)
Linear saturation function σi, wherein i=1,2,3,4, Using following nested saturation
Control law
vz=-σ4(y4+σ3(y3+σ2(y2+σ1(y1)))) (21)
System (20) asymptotically stable in the large can be made to origin.
Wherein,y4=
ez4。
Linear σ: R → R of saturation function is continuous nondecreasing function, and meets following condition: when | x | when < A, σ (x)=x；When
When x >=A, σ (x)=A；As x≤- A, σ (x)=- A.A is known as the amplitude of σ.
To sum up, described that double-wheel self-balancing vehicle can be made with the control method of nested saturation algorithm based on non-singular terminal sliding formwork
The avoidance track that tenacious tracking is cooked up, the control block diagram of whole system are as shown in Figure 7.
Five, it emulates
Choose following simulation parameter: R=1000, Lb=40, Wb=3, Lv=0.7, Wv=0.3, δ=0.2, J=2, v0=
2, mw=1, mc=5, mb=3, d=0.6, L=1, r=0.15, I1=1, I2=1.5, I3=1, I4=4, I5=0.5, I6=1,
G=9.8；Consider that the output saturation of driving motor, the peak torque of the driving motor of two wheels are taken as 35, namely | τv|≤
70, | τω|≤70；The position and attitude error initial value e of double-wheel self-balancing vehicle1=0, e2=0, e3=0.1, car body obliqueness angular speed initial valueAccording to the above parameter, ψ=0.0596, x are acquiredE=119.216Smin=99.119, consider certain safe clearance,
When sensor detect two wheeler apart from barrier be S0Start to execute avoidance when=105.L againb2 (x of=40 >E-S0)=
28.432, therefore surmount path length and be not zero.Emulation knot when car body obliqueness initial value is respectively θ=0.1, θ=0.2 and θ=0.3
Fruit is as shown in Figure 7, Figure 8 and Figure 9.As can be seen that the avoidance track (x cooked upr,yr) curvature is smooth, it is capable of avoiding for safety
Barrier, and return on set travel route；Used tenacious tracking control method can make double-wheel self-balancing vehicle larger
In the case where car body obliqueness, avoidance track (x that actual path (x, y) tenacious tracking is cooked upr,yr), each state variable with
Track error ex,ey,θ,Zero can be converged in a short time.To demonstrate, proposed double-wheel self-balancing car owner is dynamic to be kept away
Hinder the validity of trajectory planning and tenacious tracking control method.
The avoidance track that the present invention is planned, under bodywork reference frame, transverse acceleration changes over time the inverse taper that is positive,
The characteristics of forward acceleration is zero, has trajectory tortuosity variation gentle, is convenient for drive lacking double-wheel self-balancing vehicle tenacious tracking；It is mentioned
Tenacious tracking control algolithm out can make double-wheel self-balancing vehicle under larger car body obliqueness initial value, what tenacious tracking was planned
Avoidance track, while vehicle body being kept to stablize, to realize the automatic obstacle avoidance of double-wheel self-balancing vehicle.
The foregoing is only a preferred embodiment of the present invention, but scope of protection of the present invention is not limited thereto,
Anyone skilled in the art within the technical scope of the present disclosure, according to the technique and scheme of the present invention and its
Inventive concept is subject to equivalent substitution or change, should be covered by the protection scope of the present invention.
Claims (7)
1. double-wheel self-balancing car owner moves collision free trajectory and tenacious tracking control method, comprising: be based on circular arc and easement curve
Collision free trajectory method, based on non-singular terminal sliding formwork and it is nested saturation algorithm tenacious tracking control method；Its feature
It is, the track that the collision free trajectory method is cooked up includes lane-change, is surmounted and simultaneously road three parts；The tenacious tracking control
Method processed:
First by double-wheel self-balancing vehicle attained poseFor determined by the avoidance track cooked up with reference to poseTracking, consider nonholonomic constraintIn the case where, it is converted into actual forward
Speed v and steering angular speed omega are for it is expected forward speed vdAnd steering angular speed omegadTracking；Wherein, x, y are that two-wheeled is certainly flat
Weigh coordinate of the vehicle under earth coordinates,For steering angle, It is led for the single order of x,For the single order of y
It leads,
Then by entire double-wheel self-balancing vehicle system decoupling be full driving turn to before subsystem and drive lacking to subsystem respectively into
Row control；
Lane-change track, including the 1st transition track, the 1st arc track, the 2nd transition track, the 2nd arc track, the 3rd transition track；
The 1st transition track start respectively with avoidance before straight-line travelling track and the 1st arc track connect, expression formula be x (t)
=v0T,Using avoidance starting point position as geodetic coordinates origin, using avoidance start time as zero moment,
In, v0For the forward speed of double-wheel self-balancing vehicle, 0≤t≤t1,R is the radius of curvature of the 1st arc track, J two
Take turns the permitted maximum transversal acceleration of Self-Balancing vehicle；The radius of curvature R of 2nd arc track and the 1st arc track and
Corresponding central angle ψ is equal in magnitude, and the 2nd arc track and the 1st arc track concave towards on the contrary, its track expression formula root
It is determined according to the parametric equation of uniform circular motion；The 2nd transition track connects with the 1st arc track and the 2nd arc track respectively
It connects, expression formula is
Wherein, t1、t2、t3The respectively time used in the 1st transition track, the 1st arc track and the 2nd transition track, ψ according toIt determines, L=v0t1,δ is safe clearance, WbAnd LvRespectively two-wheeled from
The dimensional parameters of balance car and barrier；
The 3rd transition track respectively with the 2nd arc track and surmount track and connect,
Its track expression formula is
Wherein, t4、t5Time used in respectively the 2nd arc track and the 3rd transition track；
Surmounting track is a straight line, and track expression formula is determined according to linear uniform motion equation；
And road track and lane-change track are symmetrical about the perpendicular bisector for surmounting track；
The expectation forward speed vdAnd steering angular speed omegadFormula be respectively as follows:
vd=vr cos e3+λ1tanh e1
Wherein, xr、
yrFor coordinate of the avoidance track under earth coordinates,For reference steering angle determined by avoidance track, For xrSingle order lead,For yrSingle order lead,λ1、λ2And λ3The design being positive
Parameter；Work as e3When=0,
2. double-wheel self-balancing car owner moves collision free trajectory and tenacious tracking control method, feature according to claim 1
Be, non-singular terminal sliding Mode Algorithm control double-wheel self-balancing vehicle full driving steering subsystem, control law byIt determines；Whereinτω=τR-τL, WithRespectively it is expected angular velocity omegadIntegral, ωdAnd ωdSingle order lead, β > 0, η > 0, p, q are positive odd number,
AndmwFor wheel mass, r is radius of wheel, and d is wheelspan, I1It is wheel around the rotary inertia of its diameter, I2For vehicle
Take turns the rotary inertia around its wheel shaft, I3It is chassis around the rotary inertia of the vertical line of its mass center, I5It is vehicle body around its mass center
The rotary inertia of vertical line, τL、τRThe respectively output torque of left and right motor；Function sat (x) satisfaction is such as given a definition: when
When,WhenWhen, sat (x)=1；WhenWhen, sat (x)=- 1, φ is normal number.
3. double-wheel self-balancing car owner moves collision free trajectory and tenacious tracking control method, feature according to claim 1
It is, to subsystem before the drive lacking of nesting saturation algorithm control double-wheel self-balancing vehicle, control law is by vz=-σ4(y4+σ3(y3+
σ2(y2+σ1(y1)))) determine, wherein
τv=τR+τL,y3=ez3+ez4, y4=ez4, ez1
=z1-z1d, ez2=z2-z2d, ez3=z3, ez4=z4, ξ1=θ,z3=tan ξ1, z4=(1+tan2ξ1)ξ2, xvd、WithRespectively vdIntegral, vdAnd vdSingle order lead；θ is vehicle
Body inclination angle, θd、Respectively θ,Desired value, be zero；mcFor chassis quality, mbFor body quality, L is vehicle body
Distance of the mass center to wheel axis center, I4It is chassis around the rotary inertia of wheel shaft, I6It is vehicle body around the rotary inertia of wheel shaft；It is linear full
It is continuous nondecreasing function with function σ (x): R → R, and meets following condition: when | x | when < A, σ (x)=x；As x >=A, σ (x)
=A；As x≤- A, σ (x)=- A；A is known as the amplitude of σ.
4. double-wheel self-balancing car owner moves collision free trajectory and tenacious tracking control method, feature according to claim 1
It is, time t used in the 2nd transition track3=2t1, time t used in the 3rd transition track5=t1；Time t used in 2nd arc track4
With time t used in the 1st arc track2It is equal, and
5. double-wheel self-balancing car owner moves collision free trajectory and tenacious tracking control method, feature according to claim 1
It is, works as Lb≤2(xE-S0) when, surmounting path length is zero；Otherwise, surmounting path length is Lb-2(xE-S0)；Wherein, xEFor
The horizontal displacement of double-wheel self-balancing vehicle at the end of lane-change, LbFor barrier dimensional parameters, S0Double-wheel self-balancing when starting for avoidance
Vehicle is at a distance from barrier.
6. double-wheel self-balancing car owner moves collision free trajectory and tenacious tracking control method, feature according to claim 1
It is, during avoidance, under bodywork reference frame, the transverse acceleration of double-wheel self-balancing vehicle changes over time the inverse taper that is positive,
Forward acceleration is approximately zero.
7. double-wheel self-balancing car owner moves collision free trajectory and tenacious tracking control method, feature according to claim 6
It is, the minimum range of avoidance starting point and barrierWherein, xcFor double-wheel self-balancing vehicle just with
Horizontal displacement when bar contact, α are the angle of orbit tangent and horizontal direction at this time, LvFor double-wheel self-balancing vehicle size ginseng
Number.
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