CN108563227A - A kind of motion control method of the 2D wheeled robots based on movable castor - Google Patents
A kind of motion control method of the 2D wheeled robots based on movable castor Download PDFInfo
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- CN108563227A CN108563227A CN201810360530.5A CN201810360530A CN108563227A CN 108563227 A CN108563227 A CN 108563227A CN 201810360530 A CN201810360530 A CN 201810360530A CN 108563227 A CN108563227 A CN 108563227A
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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
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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
- G05D1/08—Control of attitude, i.e. control of roll, pitch, or yaw
- G05D1/0891—Control of attitude, i.e. control of roll, pitch, or yaw specially adapted for land vehicles
Abstract
The present invention discloses a kind of motion control method of the 2D wheeled robots based on movable castor, including constantly updates control robot motion state according to following below scheme：Step S1 determines the dbjective state of current time robot according to mission requirements；The movement for the particle that the movement representation of robot entirety is robot chassis geometric center P points is calculated motion vector of the current time robot under global coordinate system by step S2 according to dbjective state；Step S3 calculates the rotating speed n of each wheel with the principle that wheel does not stress laterallyiWith wheel towards the angle ψ of the X-axis with robot local coordinate systemi；Step S4, by the rotating speed n of each wheeliWith angle ψiThe state of wheel is adjusted, realizes control robot motion.The present invention supports robot to realize the motion modes such as forward, traversing, diagonal, rotation and combinations thereof, can be used for 2 and with the motion control of the 2D wheeled robots of first-class multiple Casters, the sliding of wheel is small, stability, the flexibility higher of movement.
Description
Technical field
The invention belongs to motion planning and robot control technical fields, and in particular to a kind of 2D wheel type machines based on movable castor
The Motion Controlling Model and method of people.
Background technology
With the continuous development of industrial automation, the application in daily life such as intelligent carriage, mobile robot
Also more and more extensive, 2D wheeled robots are one of most widely used robots, therefore people are for 2D wheeled robots
Kinematic dexterity and sport efficiency have increasingly higher demands.
Wheel applied to wheeled robot have omni-directional wheel (Omni wheel), Mecanum wheel (Mecanum wheel),
Traditional movable castor, that is, universal wheel etc..
Wheeled robot field can meet the flexible fortune of robot omnibearing using wide Mecanum wheel at present
It is dynamic, robot is provided and is carried out at the same time the efficient Move Mode such as translation and rotation, but the robot of application activity castor at present
In, the Controlling models such as spider gear pattern or front-wheel steer are mostly used greatly, this greatly reduces the robot based on movable castor
The flexibility of movement does not give full play to the movement advantage of movable castor.For the robot based on movable castor, it is badly in need of
More efficient, the flexible Motion Controlling Model of one kind and method.
Invention content
Of the existing technology in order to solve the problems, such as, the present invention provides a kind of 2D wheeled robots based on movable castor
Motion Controlling Model and method, the movements sides such as which makes robot may be implemented to move ahead, traversing, diagonal, rotation and combinations thereof
Formula, and the invention can be used for 2 and with the motion control of the 2D wheeled robots of first-class multiple movable castors, the cunning of wheel
Small, stability, the flexibility higher of movement are moved, there is prodigious advantage in practical applications.
The technical solution adopted in the present invention is a kind of motion control method of the 2D wheeled robots based on movable castor,
The movable castor has controllability at two aspects, includes the rotating speed of control wheel, and control wheel connects around wheel and ground
360 degree of rotations of axis where contact and wheel barycenter；The robot support changes any one movable castor at any time
Rotating speed niWith wheel towards in the plane with the angle ψ of robot positive directioni, 0≤i≤m, movable castor quantity m >=2；According to
Following below scheme constantly updates control robot motion state,
Step S1 determines the dbjective state of current time robot according to mission requirements；
The movement representation of robot entirety is the movement of the particle of robot chassis geometric center P points by step S2, according to
Dbjective state calculates motion vector T={ V of the current time robot under global coordinate systemx Vy ωz, wherein VxFor machine
The velocity component of people's X-axis under global coordinate system, VyFor the velocity component of robot Y-axis under global coordinate system, ωzFor machine
The angular speed of people's Z axis under global coordinate system；
Step S3 calculates the rotating speed n of each wheel with the principle that wheel does not stress laterallyiWith wheel direction and office of robot
The angle ψ of the X-axis of portion's coordinate systemi；
Step S4, according to the rotating speed n of each wheel obtained by step S3iWith wheel towards the X with robot local coordinate system
The angle ψ of axisiThe state of wheel is adjusted, realizes control robot motion.
Moreover, in step S1, the dbjective state that current time robot is selected according to mission requirements includes the position of target point
Set B, reach moving target when directional velocity α, reach moving target when posture rot B and reach target when speed
VB, the wherein position (Bx, By, Bz) of moving target is any position in robot motion's plane under global coordinate system, is reached
When moving target the directional velocity α of robot be under global coordinate system in robot motion's plane any direction α ∈ (- π, π],
Posture rot B when reaching target point are robot positive direction and world coordinates when robot reaches target point when reaching target point
Be X-axis arbitrary angle rot B ∈ (- π, π], the speed for reaching target point is the arbitrary speed under the limitation of robot maximum speed
Spend 0≤VB≤Vmax。
Moreover, step S3, the rotating speed n of each wheel is calculated with the principle that wheel does not stress laterallyiWith wheel direction and machine
The angle ψ of the X-axis of device people's local coordinate systemi, realization method is as follows,
ni×2×π×r×cos(ψi+ rotA)=Vx-ωz×di×sin(λi)
ni×2×π×r×sin(ψi+ rotA)=Vy+ωz×di×cos(λi)
Wherein, radius of wheel r, wheel i and the straight line and local coordinate where ground contact points and the line of wheel subcenter
It is the intersection point M and robot local coordinate system point of origin P distance d of X/Y planei, the directions PM and vehicle body local coordinate system X-axis folder
Angle λiFor known fixed, Vx、Vy、ωzIt being calculated by step S2, rotA is posture of the robot in A points, is given value,
It is resolved to obtain the rotating speed n of wheel i according to above formulaiWith wheel towards the angle ψ of the X-axis with robot local coordinate systemi,0≤i≤
M, movable castor quantity m >=2.
Moreover, support following motor pattern,
(1) robot moves in a straight line and does not change the posture of its own in the plane, that is, move along a straight line pattern；
(2) robot is rotated around local coordinate system Z axis in the plane, i.e., from rotary-die type；
(3) robot makes curvilinear motion and does not change itself posture in the plane, i.e. curvilinear motion pattern；
(4) robot is moved in a straight line and is rotated around local coordinate system Z axis in the plane, i.e., the fortune kept straight on simultaneously with rotation
Dynamic model formula；
(5) robot does curvilinear motion and is rotated around local coordinate system Z axis in the plane, i.e. curve translation simultaneously and rotation
Motor pattern；
(6) it stops, terminates all motion states.
Advantages of the present invention is：
(1) movable castor that the present invention supports, installation cost is low, and packaging efficiency is high；
(2) present invention provides a kind of Motion Controlling Model unrelated with installation activity castor quantity, for install 2 and its
The wheeled robot of movable castor described above can use motion model provided by the invention；
(3) present invention make robot may be implemented to move ahead, traversing, diagonal, the motion modes such as rotation and combinations thereof, improve
The flexibility of robot in a limited space, and robot can be the arbitrary intelligent platform for installing the movable castor, packet
Intelligent carriage, mobile robot etc. are included but are not limited to, market value is high；
The present invention when angle of the rotating speed and wheel direction and robot forward direction that calculate wheel with wheel laterally not
Stress is principle, and without lateral sliding in wheel motion process, the friction of movement is small, and stability is high.
Description of the drawings
Fig. 1 is the relation schematic diagram of the global coordinate system and local coordinate system of the embodiment of the present invention.
Fig. 2 is the calculating center location schematic diagram of the embodiment of the present invention.
Fig. 3 is motion vector of the robot in A points of the embodiment of the present invention.
Fig. 4 is the relational graph of the motion state and robot motion's state of the wheel of the embodiment of the present invention.
Fig. 5 is the motion control flow diagram of the embodiment of the present invention.
Specific implementation mode
Below in conjunction with the drawings and examples technical solution that the present invention will be described in detail.
The present invention proposes that a kind of motion control method of the 2D wheeled robots based on movable castor, the movable castor exist
Two aspects have controllability, can control the rotating speed of wheel first, secondly can control wheel around wheel and ground contact points
With 360 degree of rotations of axis where wheel barycenter.The robot can change turning for any one movable castor at any time
Fast niAnd wheel towards in the plane with the angle ψ of robot positive directioni, 0≤i≤m, movable castor quantity m >=2.This base
Prior art existing procucts can be used in the 2D wheeled robots of movable castor, the present invention is carried out for the motion control of the device
Research.
It may be implemented with the 2D wheeled robots based on movable castor of the present invention but be not limited to following motor pattern：
(1) robot moves in a straight line and does not change the posture of its own in the plane, that is, move along a straight line pattern；
(2) robot is rotated around local coordinate system Z axis in the plane, i.e., from rotary-die type；
(3) robot makes curvilinear motion and does not change itself posture in the plane, i.e. curvilinear motion pattern；
(4) robot is moved in a straight line and is rotated around local coordinate system Z axis in the plane, i.e., the fortune kept straight on simultaneously with rotation
Dynamic model formula；
(5) robot does curvilinear motion and is rotated around local coordinate system Z axis in the plane, i.e. curve translation simultaneously and rotation
Motor pattern；
(6) it stops, terminates all motion states.
Wherein, it is one in robot motion's plane under global coordinate system that linear motion, which refers to the motion track of robot,
Straight line, the rectilinear direction can not be the positive direction of robot comprising robot moving ahead, retreating on plane of movement,
Traversing, diagonal etc..Curvilinear motion refers to that the motion track of robot is one in robot motion's plane under global coordinate system
Curve, the curve can have different curvature radius in different location.
The technical solution adopted in the present invention comprises the steps of：
S1 determines the dbjective state of current time robot according to mission requirements；
S2 is by the movement for the particle that the movement representation of robot entirety is robot chassis geometric center P points, according to target
Motion vector T={ V of the state computation current time robot under global coordinate systemx Vy ωz, wherein VxExist for robot
The velocity component of X-axis, V under global coordinate systemyFor the velocity component of robot Y-axis under global coordinate system, ωzExist for robot
The angular speed of Z axis under global coordinate system, under this motion model, this three amounts can all be not zero in synchronization；
S3 calculates the rotating speed n of each wheel with the principle that wheel does not stress laterallyiIt is locally sat towards with robot with wheel
Mark the angle ψ of the X-axis of systemi, it is motion model proposed by the present invention；
S4, according to the rotating speed n of each wheel of calculatingiWith wheel towards the angle ψ of the X-axis with robot local coordinate systemi
The state of wheel is adjusted to achieve the purpose that control robot motion.
Since the movement of robot is continuous process, S1-S4 controls robot and updates a motion state, therefore,
It needs to repeat the above S1-S4 with stable turnover rate when practical operation so that robot steadily reaches dbjective state.
As shown in Figure 1, defining two coordinate systems that this motion model is related to first：
(1) local coordinate system：Using the chassis geometric center P of robot as coordinate origin, with the robot of definition just before
Side is X-axis, and using the front-left of robot as Y direction, Z axis forms right-handed coordinate system perpendicular to the plane where XY, in machine
In the motion process of people, which changes with the movement and steering of robot.
(2) global coordinate system：Using a point Q in space as coordinate origin, horizontal direction is X-axis, and vertical direction is Y-axis, Z axis
Right-handed coordinate system is formed perpendicular to the plane where XY, in the motion process of robot, which does not occur to translate and revolve
Turn.
(3) in the present embodiment, it calculates for convenience, the Z axis of global coordinate system is taken to be parallel to local coordinate system Z axis and side
To identical.
It will be appreciated by those skilled in the art that the position of above-mentioned global coordinate system is not that whenever can get
, but know that target point can also be calculated relative to the relative coordinate of current location using following steps, at this time complete
The origin of office's coordinate system is current location, and the world coordinates of target point is relative coordinate.
In the present embodiment, the realization process of the technical solution adopted in the present invention will be described in detail.Specific packet
Include following steps：
S1 determines the dbjective state of current time robot according to mission requirements：
The dbjective state of robot may include：The position B of target point, it directional velocity α when reaching moving target, reaches
Posture rot B when moving target, speed V when reaching targetB.The position (Bx, By, Bz) of wherein moving target can be complete
Any position under office's coordinate system in robot motion's plane, the directional velocity α of robot can be full when reaching moving target
Under office's coordinate system in robot motion's plane any direction α ∈ (- π, π], posture rot B when reaching target point can be to
When reaching target point up to robot when target point robot positive direction and global coordinate system X-axis arbitrary angle rot B ∈ (- π,
π], the speed for reaching target point is that can reach 0≤V of arbitrary speed under maximum speed limitation in robotB≤Vmax。
Such as Fig. 2, according to the mobile mission requirements of robot, the target location of current time robot is B points, and B points are complete
Coordinate under office's coordinate system is (Bx, By, Bz).The current location of robot is A points, can be according to the sensor of robot itself
It is (Ax, Ay, Az) to obtain coordinate of the A points (being overlapped with Platform center P) under global coordinate system, because of the plane of movement of robot
It is parallel with global coordinate system X/Y plane, therefore Az=Bz.
S2 determines the motion vector T={ V of robot under current state according to the moving target of robotx Vy ωz,
Middle VxFor the velocity component of robot X-axis under global coordinate system, VyFor the velocity component of robot Y-axis under global coordinate system,
ωzFor the angular speed of robot Z axis under global coordinate system, under this motion model, this three amounts can be complete in synchronization
Portion is not zero：
The center of circle O of S2.1 Calculation Planes movement revolution：
When A points are overlapped with B points, robot requires to reach the speed of B Dian Shi robots without plane motion or dbjective state
Direction α is consistent with AB rectilinear directions or does not require to reach the directional velocity of B Dian Shi robots, robot straight along AB in the plane
Line direction moves in a straight line, and without the position of Calculation Plane revolution center of circle O, skips the step and executes S2.2.
When A points and B points are misaligned, the directional velocity that dbjective state requires to reach B Dian Shi robots is the directions α, and α is straight with AB
Line direction is inconsistent, therefore the translation of robot is curvilinear motion, in the present embodiment, for convenience of explanation, it is assumed herein that bent
The radius of curvature of each point is equal on line, that is, robot is one section of circular arc from A points to the plane motion track of B points.It needs at this time
According to the position of 2 points of A, B, reach B points when the center of circle O of planar circumferential movement that is calculated of directional velocity.As shown in Fig. 2,
Computational methods are as follows：
(1) straight line where the line of center of circle O and B points is perpendicular to the directional velocity of B points, VBWith the X-axis of global coordinate system
Angle α it is known that the angle β of BO straight lines and X-axis under global coordinate system therefore can be obtained, since vertical relation is known：
In conjunction with the coordinate (Bx, By, Bz) of the point B on BO straight lines, it is flat that BO straight lines XY under global coordinate system can be obtained
Linear equation on face：
If the point slope form equation of BO straight lines：Y=kx+b
Wherein parameter：
K=tan (β)
B=By-k × Bx
Therefore the linear equation of BO can be obtained：
Y=tan (β) × x+ (By-tan (β) × Bx)
(2) coordinate according to A points and B points under global coordinate system calculates AB perpendicular bisectors DO under global coordinate system
Linear equation：
D point coordinates (Dx, Dy, Dz)：
AB rectilinear directions and global coordinate system X-axis angle
By DO straight lines perpendicular to AB straight lines, therefore DO rectilinear directions γ：
In conjunction with coordinate and DO rectilinear direction of the D points under global coordinate system, DO linear equations can be obtained：
If the point slope form equation of DO straight lines is y=k2x+b2
Wherein parameter:
k2=tan (γ)
b2=Dy-k2×Dx
Therefore the linear equation of DO can be obtained：
Y=tan (γ) × x+ (Dy-tan (γ) × Dx)
(3) because robot moves in the plane for being parallel to global coordinate system X/Y plane, therefore Az=Bz=Dz=Oz,
Therefore two linear equation of simultaneous or more is only needed to can be obtained coordinates of the center of circle O under global coordinate system：
Therefore coordinate (Ox, Oy, Oz) of the O points under global coordinate system can be obtained：
Wherein parameter：
K=tan (β)
k2=tan (γ)
B=By-k × Bx
b2=Dy-k2×Dx
S2.2 determines directional velocity of the robot in A points：
1. when A points are overlapped with B points, robot is skipped without plane motion without calculating robot in the directional velocity of A points
This step executes S2.3.
2. when A points and B points are misaligned, dbjective state requires to reach the directional velocity α of B Dian Shi robots and AB rectilinear directions
Directional velocity that is consistent or not requiring to reach B Dian Shi robots, robot are moved in a straight line along AB rectilinear directions in the plane,
It is AB rectilinear directions in the directional velocity of A points.Speed V of the robot in A pointsA, by itself and global coordinate system X-axis forward direction
Angle is denoted as θ, value range (- π, π]：
Therefore VASize with the angle theta of global coordinate system X-axis is：
3. when A points and B points are misaligned, dbjective state requires to reach the directional velocity α of B Dian Shi robots and AB rectilinear directions
When inconsistent, such as Fig. 4, according to speed V of the location determination robot of center of circle O in A pointsA, just with global coordinate system X-axis by it
To angle be denoted as θ, value range (- π, π]：
The direction of AO straight lines in the plane is determined by the coordinate and O point coordinates of A points
Due to VAIt is vertical with AO straight lines, therefore：
The determination principle of plus-minus symbol in above formula is：Because A, 2 points of B is in same section of circular arc, therefore VAWith the directions AO
Angle and VBIt is equal with the angle in the directions BO, because of V at this timeBWith the directions BO it is known that thus may determine that robot is in A points
Directional velocity.
S2.3, in the posture of the posture of A points and arrival B points, calculates its spin velocity according to robot：
1. when A points are overlapped with B points, robot according to posture rot A of the robot in A points and reaches B without plane motion
Known to posture rot B when point in the moving process from A points to B points, the variation of posture is Δ rot=rot B-rot A, if
Δ rot=0, the variation of robot without motion state in space, i.e. current time robot plane movement velocity VA=0 and machine
Device people is around angular velocity omega=0 that local coordinate system Z axis rotates；
2. when A points are overlapped with B points, robot according to posture rot A of the robot in A points and reaches B without plane motion
Posture rot B known in the moving process from A points to B points, the variation of posture is Δ rot=rot B-rot A, if Δ
Rot ≠ 0, robot rotation about the z axis, the angular velocity omega that robot is rotated around local coordinate system Z axis at this time are provided by dbjective state,
Value is arbitrary value (0 ＜ ω≤ω under maximum spin velocity limitationmax)。
3. when A points and B points are misaligned, dbjective state requires to reach the directional velocity α of B Dian Shi robots and AB rectilinear directions
Directional velocity that is consistent or not requiring to reach B Dian Shi robots, robot are moved in a straight line along AB rectilinear directions in the plane,
It is AB rectilinear directions in the directional velocity of A points.Speed of the robot in A points is VA：
(1) according to the speed V of linear motionACalculate that robot is moved to the time t needed for B points from A points：
Air line distance between AB：
According to VACalculate that the time t that robot is moved to from A points needed for B points is：
(2) the posture rot A according to robot in A points and posture rot B when reaching B points are from A points to B points
Moving process in, the variation of posture is Δ rot=rot B-rot A；
(3) angular speed that robot is rotated around local coordinate system Z axis in from A points to B point motion processes is：
4. when A points and B points are misaligned, dbjective state requires to reach the directional velocity α of B Dian Shi robots and AB rectilinear directions
When inconsistent：
(1) center of circle O being calculated according to S2.2, calculating robot pass by the length L of circular arc from A points to B points：
Under known global coordinate system under BO straight lines and the angle β and global coordinate system of X-axis AO straight lines in the plane with X-axis
AngleThen known by the calculated relationship of arc length and central angle：
Wherein R is the radius size of global coordinate system lower plane revolution circular arc, can use A points under global coordinate system and O points
Coordinate is calculated：
By the movement velocity V of arc length L and robot at this timeASize, robot is calculated and is moved to B from A points
Time needed for point
(4) the posture rot A according to robot in A points and posture rot B when reaching B points are from A points to B points
Moving process in, the variation of posture is Δ rot=rot B-rot A；
(5) angular speed that robot is rotated around local coordinate system Z axis in from A points to B point motion processes is：
S2.4 calculates the motion vector of current time robot according to robot in the speed and spin velocity of A points：
As shown in figure 3, the movement of the movement representation robot entirety with robot chassis geometric center P in space,
The barycenter of middle P not necessarily robots.So robot can be expressed as in the motion vector of A points：
(1) by robot A points speed VAIt is decomposed into the velocity component V of X-direction under global coordinate systemx, world coordinates
The velocity component V of the lower Y-axis of systemx：
Vx=VA×cos(θ)
Vy=VA×sin(θ)
(2) ω is calculated by S2.3 in robot angular speed of Z axis under global coordinate systemz=ω；
(3) this three variables determine the motion state of robot at this time, are denoted as motion vector T={ Vx Vy
ωz}。
S3 calculates the rotating speed n of each wheel with the principle that wheel does not stress laterallyiIt is locally sat towards with robot with wheel
Mark the angle ψ of the X-axis of systemi：
In the shared m wheel of the present embodiment one, m >=2.For i-th of wheel, the rotating speed n for calculating wheel at this time is neededi(0
≤ i≤m, movable castor quantity m >=2) and wheel towards the X-axis with robot local coordinate system angle ψi(0≤i≤m, it is living
Dynamic castor quantity m >=2)；
By taking i-th of wheel of robot as an example, wheel and the line of ground contact points and wheel subcenter are parallel to local seat
Mark system Z axis, by the intersection point of straight line and local coordinate system X/Y plane where wheel and ground contact points and the line of wheel subcenter
It is denoted as M points.M and robot local coordinate system point of origin P distance diFor fixed value, measured according to the installation site of robot
It arrives, and the included angle X in the directions PM and vehicle body local coordinate system X-axisiIt is also known quantity related with installation site, the radius r of wheel
It is also known quantity, the above spatial relation respectively measured is as shown in Figure 4.
Since the rotation of robot causes M points in space perpendicular to the linear velocity in the directions MP, the actual speed V of M pointsMIt is
The synthesis of the plane motion speed and this linear velocity of robot chassis geometric center P, be by the Kinematic Decomposition of M points in space
The velocity component V of X-direction under global coordinate systemMxWith the velocity component V of Y direction under global coordinate systemMy, then itself and machine
Motion vector T={ the V of device people's center chassis Px Vy ωzMeet following relationship：
VMx=Vx-ωz×di×sin(λi)
VMy=Vy+ωz×di×cos(λi)
Radius r, the wheel rotor speed n of wheeliThe velocity magnitude v being a little translatable in space with wheel outermostiMeet：
vi=ni×2×π×r
Because wheel and its shaft are rigid connection, M be in its shaft a bit, do not stressed laterally principle with wheel, this
When wheel direction and global coordinate system X-axis angle and VMDirection is identical, and wheel outermost is a little translatable in space
Velocity magnitude viWith VMSize it is identical.Therefore the velocity magnitude v that wheel outermost is a little translatable in spacei, wheel at this time with
The angle ψ of the X-axis of robot local coordinate systemiMeet with component motion of the M points under global coordinate system：
vi×cos(ψi+ rotA)=VMx
vi×sin(ψi+ rotA)=VMy
It is various above to merge into：
ni×2×π×r×cos(ψi+ rotA)=Vx-ωz×di×sin(λi)
ni×2×π×r×sin(ψi+ rotA)=Vy+ωz×di×cos(λi)
Radius of wheel r, wheel i and the straight line and local coordinate where ground contact points and the line of wheel subcenter in above formula
It is the intersection point M and robot local coordinate system point of origin P distance d of X/Y planei, the directions PM and vehicle body local coordinate system X-axis folder
Angle λiFor known fixed, Vx、Vy、ωzMotion vector is calculated by S2, and rot A are posture of the robot in A points, for
Know value, therefore can be resolved to obtain the rotating speed n of each wheel according to above formulaiWith wheel towards the X with robot local coordinate system
The angle ψ of axisi, 0≤i≤m, movable castor quantity m >=2.
S4 according to each wheel of calculating ni, ψiThe state of wheel is adjusted to achieve the purpose that control robot motion：
Utilize obtained each wheel rotor speed n calculated aboveiWith the wheel folder with the X-axis of robot local coordinate system at this time
Angle ψi, the state of wheel is adjusted in conjunction with the speed of current wheel and direction, and then reach adjustment robot motion's state
Purpose.
Since the movement of robot is continuous process, the state of each wheel is also required to constantly be adjusted, with
Fixed time interval executes the above S1-S4, realizes continuous detection and update to robot motion's state, is detecting and is updating
During, if target point does not change, constantly to detect whether to reach target；If target point is sent out during the motion
Changing can adjust motion state, efficiently execute movement instruction at any time, to reach accurate to robot motion, flexible, high
Imitate the purpose of control.When it is implemented, the automatic running of software technology implementation process can be used.
The achievable 6 kinds of motor patterns of the robot under this motion model are the macroscopic views that robot moves in space
Performance, in this motion model of practical application, this motion model can according under current time robot global coordinate system position,
Directional velocity, velocity magnitude etc. when posture, target location, posture, arrival target are dynamically determined the current movement mould of robot
Formula, since target point may be to change constantly, the aggregate performance form of the movement of robot in space is described 6
One or more combinations of kind motor pattern：
When A points and B points are misaligned, dbjective state requires to reach the directional velocity α of B Dian Shi robots and AB rectilinear directions one
The directional velocity of B Dian Shi robots is caused or does not require to reach, robot does straight line fortune along AB rectilinear directions in the plane at this time
Dynamic, the posture direction of initial machine people is the angle of local coordinate system X-axis and global coordinate system X-axis positive direction, is expressed as rot
A, the angle of local coordinate system X-axis and global coordinate system X-axis positive direction, is expressed as when reaching the posture of B Dian Shi robots thus
Rot B, if rot B=rot A, therefore robot, in doing plane curve movement and reaching B point process, the posture of robot is not sent out
Changing, without rotation during linear motion, robot at this time enters linear motion pattern for robot；
When A points are overlapped with B points, i.e., robot is in the plane without translation, but rot B ≠ rot A, the posture of robot occur
There are rotation in variation, robot around itself center chassis P.The athletic performance of robot in space is around local coordinate system Z axis
Rotation, robot at this time enter from rotary-die type；
When A points and B points are misaligned, and the directional velocity that dbjective state requires to reach B Dian Shi robots is the directions α, α and AB
Rectilinear direction is inconsistent, therefore the translation of robot is curvilinear motion, if rot B=rot A, robot is doing plane curve fortune
Dynamic to reach in B point process, the posture of robot does not change, robot during curvilinear motion without rotation, at this time
Robot arrival curve motor pattern；
When A points and B points are misaligned, dbjective state requires to reach the directional velocity α of B Dian Shi robots and AB rectilinear directions one
The directional velocity of B Dian Shi robots is caused or does not require to reach, robot does straight line fortune along AB rectilinear directions in the plane at this time
It is dynamic.If rot B ≠ rot A, robot is in moving in a straight line arrival B point process, and the posture of robot changes, robot
Rotation is carried out at the same time during linear motion, robot at this time enters straight line and the motor pattern of rotation；
When A points and B points are misaligned, and the directional velocity that dbjective state requires to reach B Dian Shi robots is the directions α, α and AB
Rectilinear direction is inconsistent, therefore the translation of robot is curvilinear motion, if rot B ≠ rot A, therefore robot is doing straight line fortune
Dynamic to reach in B point process, the posture of robot changes, and robot is carried out at the same time rotation during curvilinear motion, this
When robot arrival curve and rotation motor pattern；
When A points overlap and when rot B=rot A, i.e., robot reaches dbjective state, at this time robot without motion with B points,
All motion states are terminated, are stopped.
It should be understood that the above-mentioned description for preferred embodiment is more detailed, can not therefore be considered to this
The limitation of invention patent protection range, those skilled in the art under the inspiration of the present invention, are not departing from power of the present invention
Profit requires in the case of protecting, and can also make replacement or deformation, each fall within protection scope of the present invention, of the invention
Range, which is claimed, to be determined by the appended claims.
Claims (4)
1. a kind of motion control method of the 2D wheeled robots based on movable castor, the movable castor has at two aspects
Controllability includes the rotating speed of control wheel, and control wheel around 360 degree of axis where wheel and ground contact points and wheel barycenter
Rotation；The robot supports to change the rotating speed n of any one movable castor at any timeiWith wheel towards in the plane with
The angle ψ of robot positive directioni, 0≤i≤m, movable castor quantity m >=2；It is characterized in that：It is constantly updated according to following below scheme
Robot motion state is controlled,
Step S1 determines the dbjective state of current time robot according to mission requirements；
Step S2, by the movement for the particle that the movement representation of robot entirety is robot chassis geometric center P points, according to target
Motion vector T={ V of the state computation current time robot under global coordinate systemx Vy ωz, wherein VxExist for robot
The velocity component of X-axis, V under global coordinate systemyFor the velocity component of robot Y-axis under global coordinate system, ωzExist for robot
The angular speed of Z axis under global coordinate system；
Step S3 calculates the rotating speed n of each wheel with the principle that wheel does not stress laterallyiIt is locally sat towards with robot with wheel
Mark the angle ψ of the X-axis of systemi；
Step S4, according to the rotating speed n of each wheel obtained by step S3iWith wheel towards the folder of the X-axis with robot local coordinate system
Angle ψiThe state of wheel is adjusted, realizes control robot motion.
2. the motion control method of the 2D wheeled robots based on movable castor according to claim 1, it is characterised in that：Step
In rapid S1, the dbjective state that current time robot is selected according to mission requirements includes the position B of target point, reaches moving target
When directional velocity α, reach moving target when posture rot B and reach target when speed VB, wherein moving target
Position (Bx, By, Bz) is any position in robot motion's plane under global coordinate system, robot when reaching moving target
Directional velocity α be under global coordinate system in robot motion's plane any direction α ∈ (- π, π], reach posture when target point
Rot B are the arbitrary angle rot of robot positive direction and global coordinate system X-axis when robot reaches target point when reaching target point
B ∈ (- π, π], the speed for reaching target point is 0≤V of arbitrary speed under robot maximum speed limitationB≤Vmax。
3. the motion control method of the 2D wheeled robots according to claim 1 based on movable castor, it is characterised in that：
Step S3 calculates the rotating speed n of each wheel with the principle that wheel does not stress laterallyiWith wheel direction and robot local coordinate system
X-axis angle ψi, realization method is as follows,
ni×2×π×r×cos(ψi+ rotA)=Vx-ωz×di×sin(λi)
ni×2×π×r×sin(ψi+ rotA)=Vy+ωz×di×cos(λi)
Wherein, radius of wheel r, wheel i and the straight line and local coordinate system XY where ground contact points and the line of wheel subcenter
The intersection point M of plane and robot local coordinate system point of origin P distance di, the directions PM and vehicle body local coordinate system X-axis included angle XiFor
Known fixed, Vx、Vy、ωzIt is calculated by step S2, rotA is posture of the robot in A points, is given value, according to upper
Formula resolves to obtain the rotating speed n of wheel iiWith wheel towards angle ψ i, 0≤i≤m of the X-axis with robot local coordinate system, activity
Castor quantity m >=2.
4. according to claims 1 or 2 or the motion control method of the 3 2D wheeled robots based on movable castor, feature
It is：Support following motor pattern,
(1) robot moves in a straight line and does not change the posture of its own in the plane, that is, move along a straight line pattern；
(2) robot is rotated around local coordinate system Z axis in the plane, i.e., from rotary-die type；
(3) robot makes curvilinear motion and does not change itself posture in the plane, i.e. curvilinear motion pattern；
(4) robot is moved in a straight line and is rotated around local coordinate system Z axis in the plane, i.e., the movement mould kept straight on simultaneously with rotation
Formula；
(5) robot does curvilinear motion and is rotated around local coordinate system Z axis in the plane, i.e. curve translation simultaneously and spinning motion
Pattern；
(6) it stops, terminates all motion states.
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