CN110155236A - Pulling type bicycle based on ZMP topples over boolean's evaluation method in orientation - Google Patents
Pulling type bicycle based on ZMP topples over boolean's evaluation method in orientation Download PDFInfo
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- CN110155236A CN110155236A CN201910430131.6A CN201910430131A CN110155236A CN 110155236 A CN110155236 A CN 110155236A CN 201910430131 A CN201910430131 A CN 201910430131A CN 110155236 A CN110155236 A CN 110155236A
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Classifications
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B62—LAND VEHICLES FOR TRAVELLING OTHERWISE THAN ON RAILS
- B62K—CYCLES; CYCLE FRAMES; CYCLE STEERING DEVICES; RIDER-OPERATED TERMINAL CONTROLS SPECIALLY ADAPTED FOR CYCLES; CYCLE AXLE SUSPENSIONS; CYCLE SIDE-CARS, FORECARS, OR THE LIKE
- B62K13/00—Cycles convertible to, or transformable into, other types of cycles or land vehicle
- B62K13/02—Cycles convertible to, or transformable into, other types of cycles or land vehicle to a tandem
- B62K13/025—Cycles convertible to, or transformable into, other types of cycles or land vehicle to a tandem from two or more cycles
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B62—LAND VEHICLES FOR TRAVELLING OTHERWISE THAN ON RAILS
- B62K—CYCLES; CYCLE FRAMES; CYCLE STEERING DEVICES; RIDER-OPERATED TERMINAL CONTROLS SPECIALLY ADAPTED FOR CYCLES; CYCLE AXLE SUSPENSIONS; CYCLE SIDE-CARS, FORECARS, OR THE LIKE
- B62K27/00—Sidecars; Forecars; Trailers or the like specially adapted to be attached to cycles
- B62K27/10—Other component parts or accessories
- B62K27/12—Coupling parts for attaching cars or the like to cycle; Arrangements thereof
Abstract
The present invention discloses boolean's evaluation method that the pulling type bicycle based on ZMP topples over orientation, in conjunction with each corner of pulling type bicycle, angular speed, dimensional parameters etc. calculate the coordinate of ZMP coordinate and three grounding points, vector triangle is constructed by three grounding points, and inner product operation is carried out to direction vector sum characteristic vector, it is used as the judge on dangerous side with corresponding sign function, orientation is toppled over the quantity confirmation on dangerous side again, the boolean's evaluation method provided by the invention for toppling over orientation, ZMP is fully considered, the mechanical structure of pulling type bicycle itself, real-time kinematic parameter, also consider the direction vector and characteristic vector of vector triangle each edge, it can be accurately, it judges out in real time and topples over orientation.
Description
Technical field
The present invention relates to self-balancing technical field of bicycles, and in particular to the pulling type bicycle based on ZMP topples over orientation
Boolean's evaluation method.
Background technique
Pulling type bicycle is the novel self-balanced bicycle path walking being made of two-wheel tractor and single-wheel towed vehicle
Mechanism, rigid structure mainly include tractor chassis, handlebar, tractor front-wheel, draw back wheels of vehicle, pull vehicle carriage and pull
Vehicle wheel.The configuration of pulling type bicycle is three ground wheels, is a kind of mechanically moving system of three grounding points.
For dicycly self-balancing bicycle, the balance of bicycle usually is realized by reducing vehicle body tendency inclination angle,
That is, measuring the degree that bicycle deviates balance to be inclined to inclination angle.The study found that the balancing method is applied to pulling type bicycle
When, error is larger.Pulling type bicycle mainly includes two-wheel tractor and single-wheel towed vehicle, when orientation is toppled in judge, neither
It can only be to judge object with the lateral inclination angle of two-wheel tractor or single-wheel mounting vehicle, it can not be simply with the simple algebra of the two
With for judge object.Therefore, a kind of evaluation method that can accurately reflect pulling type bicycle and topple over orientation need to be proposed, after ensureing
The accuracy of continuous data analysis and balance control.
Summary of the invention
The present invention provides boolean's evaluation method that the pulling type bicycle based on ZMP topples over orientation, solves the prior art and deposits
The not accurate enough problem of judge for toppling over orientation.
The present invention solves technical problem by the following technical programs:
Pulling type bicycle based on ZMP topples over boolean's evaluation method in orientation, includes the following steps:
(1) coordinate for three grounding points that ZMP coordinate and the pulling type bicycle are contacted with the earth 7 is calculated, with institute
State three grounding point building vector triangles；The vector triangle contains three directed edges, and three articles of directed edges are respectively the
One directed edge, the second directed edge and third directed edge；
(2) in the vector triangle, any two adjacent directed edges is chosen and do cross product operation, obtain the vector
The direction vector of triangle；
(3) starting point and the ZMP for connecting first directed edge, obtain the first vector, the direction of first vector is
It is directed toward ZMP in starting point；It connects the ZMP and first directed edge ends end, obtain the second vector, the side of second vector
Cut-off end is directed toward to for ZMP；First vector sum, second vector carries out cross product operation, obtains fisrt feature vector；The side
Inner product operation is executed to vector and the fisrt feature vector, obtains sign function, institute is judged with the result of the sign function
Stating the first directed edge is danger while still not dangerous；
(4) method that second directed edge and third directed edge press step (3) carries out the judge on dangerous side；
(5) total quantity on dangerous side is obtained according to step (3) and (4), it is described to topple over if the total quantity on dangerous side is 1
Orientation is the normal orientation on the dangerous side of this, if the total quantity on dangerous side is 2, described to topple over orientation be this 2 dangerous sides
The compound direction of normal orientation.
Further, in step (1), coordinate of the ZMP under 7 coordinate systems of the earth meets formula:
In formula: M is the gross mass of the pulling type bicycle；G is acceleration of gravity；xc、ycFor the pulling type bicycle
Mass center the earth 7 coordinate systems under coordinate；Px、Py、PzFor the pulling type bicycle linear momentum respectively the earth 7 coordinates
Component on the x, y, z axis of system,For PxSingle order lead,For PySingle order lead,For PzSingle order lead；Lx、LyFor around the earth
The angular momentum of 7 coordinate system centers of circle rotation in x, the component of y-axis,For LxSingle order lead,For LySingle order lead；xzmp、yzmp、
zzmpFor coordinate of the ZMP under 7 coordinate systems of the earth, pulling type bicycle z in flat overground locomotionzmp=0.
Further, in step (1), three grounding points are respectively that the first grounding point, the second grounding point and third connect
Place, the coordinate calculating process of first grounding point, the second grounding point and third grounding point under 7 coordinate systems of the earth are as follows:
1) the tractor vehicle is calculated by three Euler angle rates of the tractor chassis 1 of the pulling type bicycle
Angular speed of the frame 1 under 7 coordinate systems of the earth；
2) the traction back wheels of vehicle 4 of the pulling type bicycle is calculated big by the angular speed of the tractor chassis 1
Angular speed under 7 coordinate system of ground；
3) origin of traction 4 place coordinate system of back wheels of vehicle is calculated in the earth 4 by the angular speed of the traction back wheels of vehicle 4
Linear velocity under coordinate system；
4) integral operation is carried out to the linear velocity, obtains the origin of the traction 4 place coordinate system of back wheels of vehicle in the earth 7
Coordinate under coordinate system；
5) become by coordinate and coordinate of the origin of the traction 4 place coordinate system of back wheels of vehicle under 7 coordinate systems of the earth
It changes, calculate first grounding point, the second grounding point and the pulling type bicycle pulls 5 place coordinate system of vehicle carriage
Origin the earth 7 coordinate systems under coordinate；
6) third ground connection is calculated by pulling coordinate of the origin of 5 place coordinate system of vehicle carriage under 7 coordinate systems of the earth
Coordinate of the point under 7 coordinate systems of the earth.
Further, in step (3), first grounding point is P1, the second grounding point is P2, third grounding point is P3,
The direction vector expression formula are as follows:
Further, in step (3), the ZMP is A point；First directed edge isFirst vector isSecond vector isThe fisrt feature vector expression isThe fisrt feature vector is
0, or it is identical as the direction of the direction vector or contrary with the direction vector.
Further, in step (3), the direction vector and the fisrt feature vector execute inner product operation, expression formula
ForThe sign function expression formula isThe sign1(x1)=1 or when 0, described
One directed edge isFor dangerous side,When, first directed edge isFor not dangerous side.
Compared with prior art, it has a characteristic that
Each corner, angular speed, dimensional parameters in conjunction with pulling type bicycle etc. calculate ZMP coordinate and three grounding points
Coordinate, vector triangles are constructed by three grounding points, and inner product operation is carried out to direction vector sum characteristic vector, with corresponding
Sign function be used as the judge on dangerous side, then orientation is toppled over the quantity confirmation on dangerous side, it is provided by the invention to topple over orientation
Boolean's evaluation method, fully considered the mechanical structure of ZMP, pulling type bicycle itself, real-time kinematic parameter, it is also contemplated that
The direction vector and characteristic vector of vector triangle each edge, can accurately, judge out topple over orientation in real time.
Detailed description of the invention
Fig. 1 be ZMP of the present invention in vector triangle when for judge directed edgeIt whether is dangerous side and the feature constructed
Schematic vector diagram.
Fig. 2 be ZMP of the present invention in vector triangle when for judge directed edgeIt whether is dangerous side and the feature constructed
Schematic vector diagram.
Fig. 3 be ZMP of the present invention in vector triangle when for judge directed edgeIt whether is dangerous side and the feature constructed
Schematic vector diagram.
Fig. 4 be ZMP of the present invention outside vector triangle when for judge directed edgeIt whether is dangerous side and the feature constructed
Schematic vector diagram.
Fig. 5 be ZMP of the present invention outside vector triangle when for judge directed edgeIt whether is dangerous side and the feature constructed
Schematic vector diagram.
Fig. 6 be ZMP of the present invention outside vector triangle when for judge directed edgeIt whether is dangerous side and the feature constructed
Schematic vector diagram.
Fig. 7 is the mechanical construction drawing of prior art pulling type bicycle.
Figure label are as follows: 1, tractor chassis；2, handlebar, 3, tractor front-wheel；4, back wheels of vehicle is drawn；5, towed vehicle vehicle
Frame；6, towed vehicle wheel；7, the earth.
Fig. 8 is coordinate mapping calculation chain type figure.
Specific embodiment
The invention will be further described with reference to embodiments, but the invention is not limited to these embodiments.
Pulling type bicycle includes following rigid body: tractor chassis 1, tractor front-wheel 3, traction back wheels of vehicle 4, is dragged handlebar 2
Trailer type frame for use in vehicle 5 and towed vehicle wheel 6.Motor is installed on handlebar 2, motor passes through gear drive and tractor front-wheel 3
It matches, driving tractor front-wheel 3 rotates；Motor is installed in tractor chassis 1, the motor by gear drive with
Handlebar 2 matches, and driving handlebar 2 rotates.Tractor chassis 1 with vehicle carriage 5 is pulled is connected by cross shaft assembly, towed vehicle
Vehicle frame 5 can be rotated upwardly and downwardly around tractor chassis 1 and left-right rotation.The mechanical construction drawing of pulling type bicycle is as shown in Figure 7.
Gyroscope is installed in tractor chassis 1, detects three Euler angles of tractor chassis 1 and three corresponding
Euler angle rate；Incremental encoder and absolute encoder are installed in tractor chassis 1, detect handlebar 2 around tractor chassis 1
Corner and angular speed；Incremental encoder, angular speed of the detection tractor front-wheel 3 around handlebar 2 are installed on handlebar 2；In tractor
Incremental encoder, angular speed of the detection traction back wheels of vehicle 4 around tractor chassis 1 are set on vehicle frame 1；Pacify in tractor chassis 1
2 incremental encoders and 2 absolute encoders are filled, corner and angle of the vehicle carriage 5 around 1 left-right rotation of tractor chassis are pulled in detection
Speed, and pull corner and angular speed that vehicle carriage 5 is rotated upwardly and downwardly around tractor chassis 1；It installs and increases on pulling vehicle carriage 5
Encoder is measured, detection towed vehicle wheel 6 is around the angular speed for pulling the rotation of vehicle carriage 5.
The detection data of above-mentioned gyroscope, incremental encoder and absolute encoder, specifically includes: the pulling type is voluntarily
Three Euler angle q of the tractor chassis 1 of vehicle1、q2、q3, corresponding three Euler angle ratesIt is described to pull
Corner and angular speed of the handlebar 2 of formula bicycle around tractor chassis 1The tractor front-wheel 3 of the pulling type bicycle around
The angular speed of handlebar 2Angular speed of the traction back wheels of vehicle 4 of the pulling type bicycle around tractor chassis 1It is described to pull
Formula bicycle pulls vehicle carriage 5 around the corner and angular speed of 1 left-right rotation of tractor chassisThe pulling type bicycle
Pull corner and angular speed that vehicle carriage 5 is rotated upwardly and downwardly around tractor chassis 1The towed vehicle wheel of the pulling type bicycle
6 around the angular speed for pulling the rotation of vehicle carriage 5
Pulling type bicycle provided by the invention based on ZMP topples over boolean's evaluation method in orientation, includes the following steps:
(1) coordinate for three grounding points that ZMP coordinate and the pulling type bicycle are contacted with the earth 7 is calculated, with institute
State three grounding point building vector triangles；The vector triangle contains three directed edges, and three articles of directed edges are respectively the
One directed edge, the second directed edge and third directed edge；
(2) in the vector triangle, any two adjacent directed edges is chosen and do cross product operation, obtain the vector
The direction vector of triangle；
(3) starting point and the ZMP for connecting first directed edge, obtain the first vector, the direction of first vector is
It is directed toward ZMP in starting point；It connects the ZMP and first directed edge ends end, obtain the second vector, the side of second vector
Cut-off end is directed toward to for ZMP；First vector sum, second vector carries out cross product operation, obtains fisrt feature vector；The side
Inner product operation is executed to vector and the fisrt feature vector, obtains sign function, institute is judged with the result of the sign function
Stating the first directed edge is danger while still not dangerous；
(4) method that second directed edge and third directed edge press step (3) carries out the judge on dangerous side；
(5) total quantity on dangerous side is obtained according to step (3) and (4), it is described to topple over if the total quantity on dangerous side is 1
Orientation is the normal orientation on the dangerous side of this, if the total quantity on dangerous side is 2, described to topple over orientation be this 2 dangerous sides
The compound direction of normal orientation.
In step (1), coordinate of the ZMP under 7 coordinate systems of the earth meets formula:
In formula: M is the gross mass of the pulling type bicycle；G is acceleration of gravity；xc、ycFor the pulling type bicycle
Coordinate of the mass center under earth coordinates；Px、Py、PzFor the pulling type bicycle linear momentum respectively in earth coordinates
X, y, z axis on component, Px、Py、PzFor the function about each rigid body linear velocity, and each rigid body linear velocity is by corresponding
The angular speed detected is calculated and is obtained；For PxSingle order lead,For PySingle order lead,For PzSingle order lead；Lx、LyFor around
The angular momentum of earth coordinates center of circle rotation is in x, the component of y-axis, Lx、LyIt is the letter about each Rigid-body Angular Velocity for angular momentum
Number,For LxSingle order lead,For LySingle order lead；xzmp、yzmp、zzmpIt is described to drag for coordinate of the ZMP under earth coordinates
Hanging bicycle z in flat overground locomotionzmp=0.
Coordinate system of the present invention has 7: the global coordinate system being fixed on the earth 7, i.e. 7 coordinate system greatly, coordinate
Origin is O0；The coordinate system of tractor chassis 1, and coordinate origin is at the geometric center of tractor front-wheel 3, coordinate origin O1；
The coordinate system of handlebar 2, and coordinate origin is in the point of intersection of tractor chassis 1 and 2 axis of handlebar, coordinate origin O2；Tractor
The coordinate system of front-wheel 3, and coordinate origin is at tractor front-wheel, 3 geometric center；Coordinate origin is O3；Draw back wheels of vehicle 4
Coordinate system, and coordinate origin traction back wheels of vehicle 4 geometric center at, coordinate origin O4；The coordinate system of vehicle carriage 5 is pulled,
And coordinate origin is at the geometric center of cross axle, coordinate origin O5；The coordinate system of towed vehicle wheel 6, and coordinate origin exists,
At the geometric center of towed vehicle wheel 6, coordinate origin O6。
Each angular speed detected is the detection carried out under the coordinate system where its installation site, uses angular speed
When data, coordinate conversion is carried out, the angular speed being scaled under 7 coordinate systems of the earth.Therefore, detection handlebar 2 is around tractor
The corner of vehicle frame 1 pulls vehicle carriage 5 around the corner of 1 left-right rotation of tractor chassis and pulls vehicle carriage 5 around tractor chassis
1 corner rotated upwardly and downwardly utilizes rotation for the spin matrix between 7 coordinate systems of the coordinate system where obtaining each corner and the earth
Corresponding angular speed is converted to the angular speed under 7 coordinate systems of the earth by torque battle array, in order to obtain the linear speed under 7 coordinate systems of the earth
Degree, and then obtain Px、Py、Pz、Lx、LyValue, and then seek ZMP the earth 7 coordinate systems under coordinate.
In step (1), three grounding points of the pulling type bicycle and ground face contact are respectively the first grounding point, second
Grounding point and third grounding point, i.e. P1, P2, P3 in Fig. 7, first grounding point, the second grounding point and third grounding point exist
The greatly coordinate calculating process under 7 coordinate systems are as follows:
1) tractor chassis 1 is calculated in 7 coordinates of the earth by three Euler angle rates of the tractor chassis 1
It is O0Under angular speed；
2) traction back wheels of vehicle 4 is calculated in 7 coordinate system O of the earth by the angular speed of the tractor chassis 10Under angle speed
Degree；
3) the origin O of traction 4 place coordinate system of back wheels of vehicle is calculated by the angular speed of the traction back wheels of vehicle 44Big
Linear velocity under 7 coordinate system of ground；
4) integral operation is carried out to the linear velocity, obtains the origin O of the traction 4 place coordinate system of back wheels of vehicle4Big
Coordinate under 7 coordinate system of ground；
5) pass through the origin O of the traction 4 place coordinate system of back wheels of vehicle4Coordinate and coordinate under 7 coordinate systems of the earth
Transformation, calculates first grounding point, the second grounding point and the origin O for pulling 5 place coordinate system of vehicle carriage5In the earth 7
Coordinate under coordinate system；
6) by pulling the origin O of 5 place coordinate system of vehicle carriage5Coordinate under 7 coordinate systems of the earth calculates third and connects
Coordinate of the place under 7 coordinate systems of the earth.
In step 1), the expression formula of angular speed of the tractor chassis 1 under 7 coordinate systems of the earth are as follows:
In formula, ωB1For
Angular speed of the tractor chassis 1 under 7 coordinate systems of the earth, s1=sin (q1), s2=sin (q2), c1=cos (q1), c2=cos
(q2), c3=cos (q3)。
In step 2), angular speed expression formula of the traction back wheels of vehicle 4 under 7 coordinate systems of the earth are as follows:
In formula, ωB4For angular speed of the traction back wheels of vehicle 4 under 7 coordinate systems of the earth, s1=sin (q1), s2=sin (q2),
c1=cos (q1), c2=cos (q2)。
In step 3), the origin O of 4 place coordinate system of back wheels of vehicle is drawn4The expression formula of linear velocity under 7 coordinate systems of the earth
Are as follows:
Formula
In, vB4Indicate the origin O of traction 4 place coordinate system of back wheels of vehicle4Linear velocity under 7 coordinate systems of the earth, s1=sin (q1), s2=
sin(q2), c1=cos (q1), c2=cos (q2), r is the radius for drawing back wheels of vehicle 4.
In step 4), the origin O of 4 place coordinate system of back wheels of vehicle is drawn4Coordinate expressions under 7 coordinate systems of the earth are as follows:
In formula, s1=sin (q1), s2=sin (q2), c1=cos (q1), c2=cos (q2), r is draw back wheels of vehicle 4 half
Diameter.
In step 5), the first grounding point P1 is calculated in the coordinate under 7 coordinate systems of the earth: under 7 coordinate systems of the earthIt can
By the vector for drawing 4 place coordinate system of back wheels of vehicleThat is [0 0-l1]TRotation transformation obtains, wherein l1For O4To O3's
Distance.Under 7 coordinate systems of the earthThe vector of 3 place coordinate system of tractor front-wheel can be passed throughThat is [0 0-r]TRotation
Transformation obtains, under 7 coordinate systems of the earthThe first grounding point P1 can be found out to sit in the earth 7
Coordinate under mark system.
In step 5), calculate the second grounding point P2 the earth 7 coordinate systems under coordinate: the earth 7 coordinate systems under obtain to
AmountUnder 7 coordinate systems of the earthThe vector of traction 4 place coordinate system of back wheels of vehicle can be passed throughThat is [0 0-r]T
Rotation transformation obtains, under 7 coordinate systems of the earth,The second grounding point can be found out, i.e. in Fig. 8
Coordinate of the two grounding point P2 under 7 coordinate systems of the earth；
In step 5), the second grounding point O is calculated5Coordinate under 7 coordinate systems of the earth: by being sat where traction back wheels of vehicle 4
Mark the vector of systemThat is [- lx1 0 lz1]TRotation transformation obtains, wherein lx1For O4To O5Edge traction back wheels of vehicle 4 where sit
The distance of mark system x-axis direction, lzFor O4To O5Edge traction 4 place coordinate system z-axis direction of back wheels of vehicle distance, the earth 7 coordinates
Under system, O can be found out5Coordinate of the point under 7 coordinate systems of the earth.
In step 6), by the vector for pulling 5 place coordinate system of vehicle carriageThat is [- lx2 0 -lz2]TRotation transformation obtains
It arrives, wherein lx2For O5To O6Edge pull the distance of 5 place coordinate system x-axis direction of vehicle carriage, lzFor O5To O6Along towed vehicle vehicle
The distance in 5 place coordinate system z-axis direction of frame；Under 7 coordinate systems of the earthCan by towed vehicle wheel 6 place coordinate system to
AmountThat is [0 0-r]TRotation transformation obtains, under 7 coordinate systems of the earth,It can ask
Coordinate of the third grounding point under 7 coordinate systems of the earth out.
Above-mentioned steps 5) and step 6) to be related to relevant coordinate mapping calculation chain type figure as shown in Figure 8.Above-mentioned ZMP, three
The calculation method of grounding point coordinate is the prior art.
Pulling type bicycle by three grounding points P1, P2, P3 concurrent force and reach balance, these three grounding points building
Vector triangle Δ P1P2P3 real-time change, and vector arrows are end to end, constitute the triangle of closure.Vector triangle Δ
The first directed edge of P1P2P3 isSecond directed edge isThird directed edge isAccording to vector arrows direction, appoint
Two adjacent directed edges of meaning do cross product operation, obtain direction vectorPass through direction
Vector may determine that whether three grounding points are conllinear, if direction vector is 0, then show three grounding points point-blank, this
When three, if direction vector is not 0, show that three grounding points are not conllinear when being dangerous, be only only capable of judging pulling type from
Whether driving balances, but cannot judge it is specific which while to be dangerous, so as to cause imbalance, it is seen then that sweared only by direction
Amount topples over orientation to judge, and accuracy is lower.The present invention then topples over orientation, energy using the relationship of ZMP and direction vector to judge
It effectively improves dangerous side and topples over the accuracy of orientation judge.In Fig. 1 into Fig. 6,Indicate direction perpendicular to paper inwards,
⊙ indicates outside perpendicular to paper.
It is judge directed edge when Fig. 1-3 gives ZMP in vector triangleIt whether is dangerous side
And the characteristic vector schematic diagram constructed.The first directed edge is judged when the ZMP of Fig. 1 is in vector triangleIt whether is dangerous
Side: ZMP A constructs the first vectorConstruct the second vectorObtain fisrt feature vectorDescribed
One characteristic vector is 0, or identical as the direction of the direction vector or contrary with the direction vector；Direction vector
Inner product operation is executed with fisrt feature vector, that is,Obtain following sign functionIf
sign1(x1)=1 illustrates that fisrt feature vector is identical as direction vector direction, the first directed edgeFor dangerous side, if sign1
(x1)=0 illustrates ZMP in the first directed edgeOn, the first directed edgeFor dangerous side, if sign1(x1)=- 1, explanation
Fisrt feature direction vector and direction vector are on the contrary, the first directed edgeFor not dangerous side.
The second directed edge is judged when the ZMP of Fig. 2 is in vector triangleIt whether is dangerous side: ZMP A, building the
Three vectorsConstruct the four-vectorObtain second feature vectorThe second feature vector is 0, or
It is identical as the direction of the direction vector or contrary with the direction vector；Direction vector is held with second feature vector
Row inner product operation, that is,Obtain following sign functionIf sign2(x2)=1, says
Bright second feature vector is identical as direction vector direction, the second directed edgeFor dangerous side, if sign2(x2)=0, illustrates ZMP
In the second directed edgeOn, the second directed edgeFor dangerous side, if sign2(x2)=- 1 illustrates second feature vector and side
To direction vector on the contrary, the second directed edgeFor not dangerous side.
Third directed edge is judged when the ZMP of Fig. 3 is in vector triangleIt whether is dangerous side: ZMP A, building the 5th
VectorConstruct the 6th vectorObtain third feature vectorThe third feature vector is 0, or with
The direction of the direction vector is identical, or contrary with the direction vector；Direction vector and third feature vector execute
Inner product operation, that is,Obtain following sign functionIf sign3(x3)=1 illustrates
Three characteristic vectors are identical as direction vector direction, third directed edgeFor dangerous side, if sign3(x3)=0 illustrates ZMP
Three directed edgesOn, third directed edgeDangerous side, if sign3(x3)=- 1 illustrates third feature vector and direction vector
It is contrary, third directed edgeFor not dangerous side.
Fig. 4-6 are to judge directed edge when giving ZMP outside vector triangleIt whether is dangerous
Side and the characteristic vector schematic diagram constructed, no matter ZMP is in vector triangle or outer, and the evaluation method for toppling over orientation is homogeneous
Together, here, the Appraisal process to Fig. 4-6 repeats no more.
In conjunction with the dangerous side evaluation result of step (3) and (4), the sum on dangerous side can be obtained, if the sum on dangerous side
Amount is 1, then described to topple over the normal orientation that orientation is the dangerous side of this, described to topple over orientation if the total quantity on dangerous side is 2
For the compound direction of the normal orientation on this 2 dangerous sides.
Claims (6)
1. boolean's evaluation method that the pulling type bicycle based on ZMP topples over orientation, which comprises the steps of:
(1) coordinate for three grounding points that ZMP coordinate and the pulling type bicycle are contacted with the earth (7) is calculated, with described
Three grounding points construct vector triangle；The vector triangle contains three directed edges, and three directed edges are respectively first
Directed edge, the second directed edge and third directed edge；
(2) in the vector triangle, any two adjacent directed edges is chosen and do cross product operation, obtain the triangle of vectors
The direction vector of shape；
(3) starting point and the ZMP for connecting first directed edge, obtain the first vector, and the direction of first vector is starting
It is directed toward ZMP in end；It connects the ZMP and first directed edge ends end, obtain the second vector, the direction of second vector is
ZMP is directed toward cut-off end；First vector sum, second vector carries out cross product operation, obtains fisrt feature vector；The direction arrow
Amount executes inner product operation with the fisrt feature vector, obtains sign function, judges described the with the result of the sign function
One directed edge is dangerous while still not dangerous；
(4) method that second directed edge and third directed edge press step (3) carries out the judge on dangerous side；
(5) total quantity on dangerous side is obtained according to step (3) and (4), it is described to topple over orientation if the total quantity on dangerous side is 1
It is described to topple over the normal direction that orientation is this 2 dangerous sides if the total quantity on dangerous side is 2 for the normal orientation on the dangerous side of this
The compound direction in direction.
2. the pulling type bicycle according to claim 1 based on ZMP topples over boolean's evaluation method in orientation, feature exists
In:
In step (1), coordinate of the ZMP under the earth (7) coordinate system meets formula:
In formula: M is the gross mass of the pulling type bicycle；G is acceleration of gravity；xc、ycFor the matter of the pulling type bicycle
Coordinate of the heart under the earth (7) coordinate system；Px、Py、PzFor the pulling type bicycle linear momentum respectively the earth (7) coordinate
Component on the x, y, z axis of system,For PxSingle order lead,For PySingle order lead,For PzSingle order lead；Lx、LyFor around big
The angular momentum of ground (7) coordinate system center of circle rotation in x, the component of y-axis,For LxSingle order lead,For LySingle order lead；xzmp、
yzmp、zzmpFor coordinate of the ZMP under the earth (7) coordinate system, pulling type bicycle z in flat overground locomotionzmp=0.
3. the pulling type bicycle according to claim 1 based on ZMP topples over boolean's evaluation method in orientation, feature exists
In:
In step (1), three grounding points are respectively the first grounding point, the second grounding point and third grounding point, and described first
The coordinate calculating process of grounding point, the second grounding point and third grounding point under the earth (7) coordinate system are as follows:
1) tractor chassis is calculated by three Euler angle rates of the tractor chassis (1) of the pulling type bicycle
(1) angular speed under the earth (7) coordinate system；
2) the traction back wheels of vehicle (4) of the pulling type bicycle is calculated big by the angular speed of the tractor chassis (1)
Angular speed under ground (7) coordinate system；
3) origin of coordinate system is in the earth where calculating traction back wheels of vehicle (4) by the angular speed of traction back wheels of vehicle (4)
(7) linear velocity under coordinate system；
4) integral operation is carried out to the linear velocity, the origin of coordinate system is in the earth (7) where obtaining traction back wheels of vehicle (4)
Coordinate under coordinate system；
5) become by coordinate and coordinate of the origin of coordinate system where traction back wheels of vehicle (4) under the earth (7) coordinate system
It changes, calculates the coordinate where pulling vehicle carriage (5) of first grounding point, the second grounding point and the pulling type bicycle
Coordinate of the origin of system under the earth (7) coordinate system；
6) third ground connection is calculated by coordinate of the origin of coordinate system where pulling vehicle carriage (5) under the earth (7) coordinate system
Coordinate of the point under the earth (7) coordinate system.
4. the pulling type bicycle according to claim 3 based on ZMP topples over boolean's evaluation method in orientation, feature exists
In:
In step (3), first grounding point is P1, the second grounding point is P2, third grounding point is P3, the direction vector table
Up to formula are as follows:
5. the pulling type bicycle according to claim 4 based on ZMP topples over boolean's evaluation method in orientation, feature exists
In:
In step (3), the ZMP is A point；First directed edge isFirst vector isSecond arrow
Amount isThe fisrt feature vector expression isThe fisrt feature vector be 0, or with the direction
The direction of vector is identical, or contrary with the direction vector.
6. the pulling type bicycle according to claim 5 based on ZMP topples over boolean's evaluation method in orientation, feature exists
In:
In step (3), the direction vector and the fisrt feature vector execute inner product operation, and expression formula isInstitute
Stating sign function expression formula isThe sign1(x1)=1 or when 0, first directed edge isFor dangerous side, sign1(x1When)=- 1, first directed edge isFor not dangerous side.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN2315027Y (en) * | 1998-01-12 | 1999-04-21 | 深圳保安自行车有限公司 | Foldable tailer for bicycle |
| EP1288116A2 (en) * | 2001-08-10 | 2003-03-05 | Riccardo Borelli | Device for pulling a stroller by means of a bicycle |
| US20060186634A1 (en) * | 2003-03-24 | 2006-08-24 | Curtis Frederick Giese | Bicycle towing device |
| CN201021085Y (en) * | 2007-02-09 | 2008-02-13 | 北京凯鼎国际科贸有限责任公司 | Tow truck coupler |
| CN205737928U (en) * | 2016-01-04 | 2016-11-30 | 代运波 | A kind of Foldable light two-wheeled towed vehicle |
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2019
- 2019-05-22 CN CN201910430131.6A patent/CN110155236B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN2315027Y (en) * | 1998-01-12 | 1999-04-21 | 深圳保安自行车有限公司 | Foldable tailer for bicycle |
| EP1288116A2 (en) * | 2001-08-10 | 2003-03-05 | Riccardo Borelli | Device for pulling a stroller by means of a bicycle |
| US20060186634A1 (en) * | 2003-03-24 | 2006-08-24 | Curtis Frederick Giese | Bicycle towing device |
| CN201021085Y (en) * | 2007-02-09 | 2008-02-13 | 北京凯鼎国际科贸有限责任公司 | Tow truck coupler |
| CN205737928U (en) * | 2016-01-04 | 2016-11-30 | 代运波 | A kind of Foldable light two-wheeled towed vehicle |
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