CN111399500A - Centralized formation control method for two-wheeled self-balancing vehicle - Google Patents

Centralized formation control method for two-wheeled self-balancing vehicle Download PDF

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CN111399500A
CN111399500A CN202010060834.7A CN202010060834A CN111399500A CN 111399500 A CN111399500 A CN 111399500A CN 202010060834 A CN202010060834 A CN 202010060834A CN 111399500 A CN111399500 A CN 111399500A
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balance car
following
ideal
error
linear velocity
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CN111399500B (en
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董辉
袁登鹏
董浩
吴祥
吴宇航
田叮
童涛
钱学成
夏启剑
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Zhejiang University of Technology ZJUT
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • 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
    • G05D1/0287—Control of position or course in two dimensions specially adapted to land vehicles involving a plurality of land vehicles, e.g. fleet or convoy travelling
    • G05D1/0291—Fleet control
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • 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
    • G05D1/0223—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving speed control of the vehicle
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • 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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
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Abstract

The invention discloses a centralized formation control method for two-wheeled self-balancing vehicles, which comprises the following steps: calculating ideal position information of the following balance car; calculating the position error of the following balance car according to the current actual position information and the ideal position information of the following balance car; a kinematic controller is adopted to output and control an ideal linear velocity and an ideal angular velocity of the following robot according to the position error; if the rotation angle of the ideal angular velocity is the same as the actual rotation angle of the following balance car, outputting the ideal angular velocity to the following balance car; otherwise, constructing an incremental PD controller, and outputting the actual angular speed to the following balance car according to the angular error rotating in the sampling time; if the coordinate running according to the ideal linear velocity is the same as the coordinate actually running by the following balance car, outputting the ideal linear velocity to the following balance car; and outputting the actual linear speed to the following balance car according to the coordinate error running in the sampling time. The balance vehicle can stably run while keeping the formation.

Description

Centralized formation control method for two-wheeled self-balancing vehicle
Technical Field
The application belongs to the field of formation control of mobile robots, and particularly relates to a two-wheeled self-balancing vehicle centralized formation control method.
Background
With the development of mechanical structures and industrial designs, two-wheeled self-balancing agents have attracted great attention from researchers. The two-wheeled self-balancing intelligent body occupies a small space, is flexible in movement and low in manufacturing cost, and is suitable for various fields of modern social life, industrial production and scientific research and exploration. With the increasing complexity of application functions, all workflows cannot be completed through a single intelligent agent, such as unmanned aerial vehicle formation flight, multi-satellite cooperative operation, formation transportation of intelligent vehicles and the like, and a plurality of intelligent agents are required to cooperate to complete tasks. In the cooperative control research of the multi-agent, the method is divided into a multi-agent bee-space control research, an agent formation control research, a multi-agent consistency research and the like, wherein the multi-agent formation control is the research focus of the scheme.
The intelligent agent formation control is a control method which can not only form a target formation but also adapt to specific environmental constraints when a plurality of intelligent agents reach the target formation. There are many mature control methods for multi-agent formation control, such as methods based on the pilot-follower method, the virtual structure method, the behavior-based method, the graph theory, and the potential energy method. Although the current control method can accurately control formation of the intelligent bodies, the intelligent bodies with relatively stable structures are mostly adopted, such as four-wheel car models, two-wheel differential speed and additionally one supporting wheel model, three-wheel all-wheel drive models and other intelligent body formation control. The two-wheeled balance car is influenced by the stability factor of the two-wheeled balance car, and the content of the formation control research of the two-wheeled balance car is less. In the process of movement of the self-balancing vehicle, the self-balancing vehicle needs to maintain self-balancing, so the linear acceleration and the angular acceleration for controlling the self-balancing vehicle cannot be too large. When the track route is too complicated, the situation of sudden and too fast acceleration can occur in order to track the track and keep the formation of the formation along with the balance car, and under the condition of such large acceleration, the balance car can be impacted greatly in self balance.
Disclosure of Invention
The application aims to provide a two-wheeled self-balancing vehicle centralized formation control method, which can realize stable operation of a balance vehicle while maintaining formation.
In order to achieve the purpose, the technical scheme adopted by the application is as follows:
a two-wheel self-balancing vehicle centralized formation control method comprises the following steps:
step S1, calculating ideal position information of the following balance car according to the position information of the piloting balance car and the target formation structure, wherein the position information comprises coordinates and an azimuth angle;
step S2, calculating the position error of the following balance car according to the current actual position information and the ideal position information of the following balance car, wherein the position error comprises a coordinate error and an azimuth error;
step S3, constructing a kinematics controller, and controlling the ideal linear velocity and the ideal angular velocity of the following robot by adopting the kinematics controller according to the position error output;
step S4, judging whether the angle of rotation according to the ideal angular speed in the sampling time is the same as the actual angle of rotation of the following balance car, and if so, outputting the ideal angular speed to the following balance car; otherwise, constructing an incremental PD controller, and outputting the actual angular speed to the following balance car according to the angular error rotating in the sampling time;
step S5, judging whether the coordinate calculated according to the ideal linear velocity in the sampling time is the same as the coordinate of the actual running of the following balance car, and if so, outputting the ideal linear velocity to the following balance car; otherwise, a prediction controller is constructed, and the actual linear speed is output to the following balance car according to the coordinate error running in the sampling time.
Preferably, the calculating the ideal position information of the following balance car according to the position information of the piloting balance car and the target formation structure comprises:
step S1.1, define (x y θ)TFor the abscissa, the ordinate and the azimuth of the first-order non-integral wheel type balance vehicle in a world coordinate system, the kinematic equation of the balance vehicle is as follows:
Figure BDA0002374413070000021
wherein v is the current actual linear velocity of the balance car, and omega is the current actual angular velocity of the balance car;
step S1.2, obtaining a piloting balance car RiIs Pi＝[xiyiθi]TFollowing balance car RjThe current actual position information is Pj＝[xjyjθj]TThen according to
Figure BDA0002374413070000023
Control method for calculating following balance car RjIdeal position information P ofj dComprises the following steps:
Figure BDA0002374413070000022
wherein, follow the balance car RjThe current actual position information is PjThe following relation is satisfied:
Figure BDA0002374413070000031
wherein ,Lij dAnd
Figure BDA0002374413070000032
respectively showing following balance cars RjAnd piloting balance car RiDesired distance and desired relative angle of rotation, LijAnd
Figure BDA0002374413070000033
respectively showing following balance cars RjAnd piloting balance car RiAnd the actual relative rotation angle.
Preferably, the calculating the position error of the following balance car according to the current actual position information and the ideal position information of the following balance car includes:
s2.1, obtaining the following balance car R according to the current actual position information and the ideal position information of the following balance carjThe position error under the world coordinate system is:
Figure BDA0002374413070000034
Figure BDA0002374413070000035
Figure BDA0002374413070000036
wherein ,
Figure BDA0002374413070000037
is the error of coordinate x direction under the world coordinate system,
Figure BDA0002374413070000038
is the error of coordinate y direction under the world coordinate system,
Figure BDA0002374413070000039
the azimuth angle error under the world coordinate system;
s2.2, converting the position error under the world coordinate system into a balance car coordinate system to obtain the position error of a following balance car under the balance car coordinate system as follows:
Figure BDA00023744130700000310
wherein ,ej1Error in x direction of coordinate in coordinate system of balance car, ej2Error in the y-direction of the coordinate in the coordinate system of the balance car, ej3Representing the azimuth angle error of the balance car coordinate system;
s2.3, carrying out derivation on the position error of the following balance car under the balance car coordinate system to obtain:
Figure BDA00023744130700000311
wherein ,
Figure BDA00023744130700000312
is ej1The derivative of (a) of (b),
Figure BDA00023744130700000313
is ej2The derivative of (a) of (b),
Figure BDA00023744130700000314
is ej3Derivative of vjFor following balance car RjCurrent actual linear velocity, viFor piloting balance car RiCurrent actual linear velocity, ωjFor following balance car RjCurrent actual angular velocity, ωiFor piloting balance car RiCurrent actual angular velocity, djIndicating following balance car RjTo the center of the axle.
Preferably, the constructing a kinematic controller, which controls an ideal linear velocity and an ideal angular velocity of the following robot according to the position error output by using the kinematic controller, includes:
the kinematic controller was constructed as follows:
Figure BDA0002374413070000041
wherein ,kx、ky、kθPositive vector constants representing x, y, and theta, respectively;
control of kinematic controller output following robot theoryDesired linear velocity vjcIdeal angular velocity of omegajc。
Preferably, judging whether the angle of rotation according to the ideal angular speed in the sampling time is the same as the actual angle of rotation of the following balance car, and if so, outputting the ideal angular speed to the following balance car; otherwise, designing an incremental PD controller, and outputting the actual angular speed to the following balance car according to the angular error rotating in the sampling time, wherein the incremental PD controller comprises:
s4.1, setting the sampling time to be delta T;
step S4.2, following the balance vehicle in the sampling time according to the ideal angular speed omegajcThe angle of rotation is: theta1＝ωjc*ΔT；
S4.3, acquiring the actual rotation angle theta of the following balance car in the sampling time2Then the angular error of rotation within the sampling time is eθ＝θ1-θ2；
Step S4.4, if eθWhen the angular velocity is 0, the ideal angular velocity omega is output to the following balance carjcAnd finishing the angle regulation and control; otherwise, executing the next step;
step S4.5, constructing an incremental PD controller as follows:
Δθ＝λeθ(k)+βeθ(k-2)
Figure BDA0002374413070000042
Figure BDA0002374413070000043
where Δ θ is the actual angular velocity output by the incremental PD controller, eθ(k) Angle error at time k, eθ(k-2) is the angle error at time k-2, kpIs a proportionality coefficient, TdIs a differential coefficient, and T is a sampling period; and sends the actual angular velocity delta theta output by the incremental PD controller to the following balance car.
Preferably, judging whether the coordinate calculated according to the ideal linear velocity in the sampling time is the same as the coordinate of the actual running of the following balance car, and if so, outputting the ideal linear velocity to the following balance car; otherwise, constructing a prediction controller, and outputting the actual linear speed to the following balance car according to the coordinate error running in the sampling time, wherein the method comprises the following steps:
s5.1, setting the sampling time to be delta T;
s5.2, following the balance car in sampling time according to the ideal linear velocity vjcThe calculated coordinate corresponding to the time is (x)d,yd)；
S5.3, acquiring the actual coordinate (x) of the corresponding moment running along the balance car in the sampling timer,yr) Then the running coordinate error in sample time is as follows:
Figure BDA0002374413070000051
wherein ,xe,yeErrors in the x and y directions, respectively;
step S5.4, if xe0 and yeWhen the linear velocity is 0, the ideal linear velocity v is takenjcAs the linear velocity to be sent, and step S5.7 is executed; otherwise, executing step S5.5;
step S5.5, calculating the differential value of the coordinate error running in the sampling time as follows:
Figure BDA0002374413070000052
wherein v is the current actual linear speed of the following balance car, and theta is the current actual azimuth angle of the following balance car;
setting a middle virtual control rule to obtain virtual linear speeds in x and y directions as follows:
Figure BDA0002374413070000053
wherein ,u1Is a virtual linear velocity in the y direction, u2Is a virtual linear velocity in the y direction, k1Is a constantNumber, k2Is a constant;
step S5.6, considering only the position error in the x-direction, i.e. setting yeWhen 0, construct the predictive controller as:
Figure BDA0002374413070000054
actual linear velocity v to be output by a predictive controllerrAs the linear velocity to be sent;
step S5.7, taking the linear velocity to be sent as the linear velocity v (k) at the current k moment, and judging whether the linear velocity v (k) meets the amplitude limiting requirement according to the following formula:
Figure BDA0002374413070000055
wherein v (k-1) is the linear velocity at the moment of k-1, Δ t is the time interval between two previous and subsequent velocity calculations, atvIs a preset speed change rate threshold value, vtvIs a preset speed threshold;
if the linear velocity v (k) meets the amplitude limiting requirement, outputting the linear velocity v (k) to a following balance car; otherwise, outputting a speed threshold value v to the following balance cartv。
The application provides a two-wheeled self-balancing vehicle centralized formation control method, linear velocity and angular velocity of the following balancing vehicle are obtained according to position information of a piloting balancing vehicle and a target formation structure, in order to avoid damage to stable running of the following balancing vehicle caused by the calculated linear velocity and angular velocity, an incremental PD controller and a prediction controller are adopted to correct the linear velocity and the angular velocity according to actual conditions of the balancing vehicle, the vehicle body can run stably, and normal running of all the balancing vehicles in formation is guaranteed.
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Fig. 1 is a flowchart of a two-wheeled self-balancing vehicle centralized formation control method according to the present application.
Detailed Description
The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used in the description of the present application herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.
In one embodiment, as shown in fig. 1, a centralized formation control method for two-wheeled self-balancing vehicles is provided, which is capable of maintaining self-balancing of the two-wheeled self-balancing vehicles while keeping the two-wheeled self-balancing vehicles moving in a preset formation.
Specifically, the centralized formation control method for the two-wheeled self-balancing vehicle of the embodiment includes the following steps:
and step S1, calculating ideal position information of the following balance car according to the position information of the piloting balance car and the target formation structure, wherein the position information comprises coordinates and an azimuth angle. Q in FIG. 1rRepresenting the actual formation structure, qdRepresenting the target formation structure.
Step S1.1, define (x y θ)TFor the abscissa, the ordinate and the azimuth of the first-order non-integral wheel type balance vehicle in a world coordinate system, the kinematic equation of the balance vehicle is as follows:
Figure BDA0002374413070000061
wherein v is the current actual linear velocity of the balance car, and ω is the current actual angular velocity of the balance car.
Step S1.2, obtaining a piloting balance car RiIs Pi＝[xiyiθi]T, wherein xiFor piloting balance car RiActual position in x-direction of (a), yiFor piloting balance car RiActual position in the y direction of (e), thetaiFor piloting balance car RiActual azimuth of, following balance car RjThe current actual position information is Pj＝[xjyjθj]T, wherein xjFor following balance car RjActual position in x-direction of (a), yjFor following balance car RjActual position in the y direction of (e), thetajFor following balance car RjThe actual azimuth angle of (c).
Then according to
Figure BDA00023744130700000712
Control method for calculating following balance car RjIdeal position information P ofj dComprises the following steps:
Figure BDA0002374413070000071
wherein follows balance car RjThe current actual position information is PjThe following relation is satisfied:
Figure BDA0002374413070000072
wherein ,Lij dAnd
Figure BDA0002374413070000073
respectively showing following balance cars RjAnd piloting balance car RiDesired distance and desired relative angle of rotation, LijAnd
Figure BDA0002374413070000074
respectively showing following balance cars RjAnd piloting balance car RiAnd the actual relative rotation angle. In this embodiment, it is assumed that the following balance car and the piloting balance car have the same azimuth angle, so θ existsi＝θj。
And step S2, calculating the position error of the following balance car according to the current actual position information and the ideal position information of the following balance car, wherein the position error comprises a coordinate error and an azimuth angle error.
S2.1, obtaining the following balance car R according to the current actual position information and the ideal position information of the following balance carjThe position error under the world coordinate system is:
Figure BDA0002374413070000075
Figure BDA0002374413070000076
Figure BDA0002374413070000077
wherein ,
Figure BDA0002374413070000078
is the error of coordinate x direction under the world coordinate system,
Figure BDA0002374413070000079
is the error of coordinate y direction under the world coordinate system,
Figure BDA00023744130700000710
the azimuth angle error under the world coordinate system;
s2.2, converting the position error under the world coordinate system into a balance car coordinate system to obtain the position error of a following balance car under the balance car coordinate system as follows:
Figure BDA00023744130700000711
wherein ,ej1Error in x direction of coordinate in coordinate system of balance car, ej2Error in the y-direction of the coordinate in the coordinate system of the balance car, ej3And indicating the azimuth angle error of the balance car coordinate system.
S2.3, carrying out derivation on the position error of the following balance car under the balance car coordinate system to obtain:
Figure BDA0002374413070000081
wherein ,
Figure BDA0002374413070000082
is ej1The derivative of (a) of (b),
Figure BDA0002374413070000083
is ej2The derivative of (a) of (b),
Figure BDA0002374413070000084
is ej3Derivative of vjFor following balance car RjCurrent actual linear velocity, viFor piloting balance car RiCurrent actual linear velocity, ωjFor following balance car RjCurrent actual angular velocity, ωiFor piloting balance car RiCurrent actual angular velocity, djIndicating following balance car RjThe center of gravity of the following balance car coincides with the center of the wheel axle, namely dj＝0。
And step S3, constructing a kinematic controller, and controlling the ideal linear velocity and the ideal angular velocity of the following robot by adopting the kinematic controller according to the position error output.
The kinematic controller constructed according to the backstepping method is as follows:
Figure BDA0002374413070000085
wherein ,kx、ky、kθPositive vector constants representing x, y, and theta, respectively;
the ideal linear velocity of the following robot is output by the kinematic controllerjcIdeal angular velocity of omegajc。
Step S4, judging whether the angle of rotation according to the ideal angular speed in the sampling time is the same as the actual angle of rotation of the following balance car, and if so, outputting the ideal angular speed to the following balance car; otherwise, an incremental PD controller is constructed, and the actual angular speed is output to the following balance car according to the angular error rotating in the sampling time.
And S4.1, setting the sampling time to be delta T.
Step S4.2, following the balance vehicle in the sampling time according to the ideal angular speed omegajcThe angle of rotation is: theta1＝ωjc*ΔT。
S4.3, acquiring the actual rotation angle theta of the following balance car in the sampling time2Then the angular error of rotation within the sampling time is eθ＝θ1-θ2。
Step S4.4, if eθWhen the angular velocity is 0, the ideal angular velocity omega is output to the following balance carjcAnd finishing the angle regulation and control; otherwise, executing the next step.
Step S4.5, constructing an incremental PD controller as follows:
Δθ＝λeθ(k)+βeθ(k-2)
Figure BDA0002374413070000091
Figure BDA0002374413070000092
where Δ θ is the actual angular velocity output by the incremental PD controller, eθ(k) Angle error at time k, eθ(k-2) is the angle error at time k-2, kpIs a proportionality coefficient, TdIs a differential coefficient, and T is a sampling period; and sends the actual angular velocity delta theta output by the incremental PD controller to the following balance car.
The embodiment selects the angular speed sent to the balance car by judging the ideal rotating angle and the actual rotating angle, namely, when the angle is regulated and controlled, the actual vehicle condition of the two-wheel self-balancing car is actually combined for regulation and control, the regulation and control accuracy is high, and the self stability of the two-wheel self-balancing car can be ensured.
Step S5, judging whether the coordinate calculated according to the ideal linear velocity in the sampling time is the same as the coordinate of the actual running of the following balance car, and if so, outputting the ideal linear velocity to the following balance car; otherwise, a prediction controller is constructed, and the actual linear speed is output to the following balance car according to the coordinate error running in the sampling time.
After the angular velocity is corrected by adopting the incremental PD controller, the vehicle body of the following balance vehicle rotates to an expected position, and the linear velocity of the balance vehicle is limited by the following factors: the method comprises the steps that the maximum speed of a balance car body for keeping balance and the maximum speed of a balance car for keeping the balance car stable in a complex path are taken into consideration, meanwhile, the difference value between the distance between the following balance car and the piloting balance car and the ideal distance of the formation and the time required for the following balance car to reach the complex path are also considered, and the linear speed of the balance car is pre-judged according to the influence factors.
The line speed correction process provided in one embodiment is as follows:
and S5.1, setting the sampling time to be delta T.
S5.2, following the balance car in sampling time according to the ideal linear velocity vjcThe calculated coordinate corresponding to the time is (x)d,yd)。
S5.3, acquiring the actual coordinate (x) of the corresponding moment running along the balance car in the sampling timer,yr) Then the running coordinate error in sample time is as follows:
Figure BDA0002374413070000093
wherein ,xe,yeError in x and y directions, respectively.
Step S5.4, if xe0 and yeWhen the linear velocity is 0, the ideal linear velocity v is takenjcAs the linear velocity to be sent, and step S5.7 is executed; otherwise step S5.5 is performed.
Step S5.5, calculating the differential value of the coordinate error running in the sampling time as follows:
Figure BDA0002374413070000101
and v is the current actual linear speed of the following balance car, and theta is the current actual azimuth angle of the following balance car.
Setting a middle virtual control rule to obtain virtual linear speeds in x and y directions as follows:
Figure BDA0002374413070000102
wherein ,u1Is a virtual linear velocity in the y direction, u2Is a virtual linear velocity in the y direction, k1Is a constant number, k2Is a constant.
Step S5.6, since the incremental PD controller corrects the angular velocity and then the angle of the following balance car is accurate, it is not necessary to consider the angular deviation again here, and only the position error in the x direction is considered, i.e. y is seteWhen 0, construct the predictive controller as:
Figure BDA0002374413070000103
actual linear velocity v to be output by a predictive controllerrThe onset is the linear velocity to be sent.
Step S5.7, taking the linear velocity to be sent as the linear velocity v (k) at the current k moment, and judging whether the linear velocity v (k) meets the amplitude limiting requirement according to the following formula:
Figure BDA0002374413070000104
wherein v (k-1) is the linear velocity at the moment of k-1, Δ t is the time interval between two previous and subsequent velocity calculations, atvIs a preset speed change rate threshold value, vtvIs a preset speed threshold.
If the linear velocity v (k) meets the amplitude limiting requirement, outputting the linear velocity v (k) to a following balance car; otherwise, outputting a speed threshold value v to the following balance cartv。
In order to avoid unbalance of the following balance car due to sudden speed change, the calculated speed needs to be filtered through amplitude limiting judgment, so that the following balance car can stably run under the condition that the following balance car follows the piloting balance car.
In one embodiment, vtvIs taken to be 1m/s and atvIs taken to be 2m/s2And when the balance car is actually applied, the balance car can be adjusted according to the actual structural characteristics of the balance car.
The technical features of the embodiments described above may be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the embodiments described above are not described, but should be considered as being within the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (6)

1. A two-wheel self-balancing vehicle centralized formation control method is characterized by comprising the following steps:
step S1, calculating ideal position information of the following balance car according to the position information of the piloting balance car and the target formation structure, wherein the position information comprises coordinates and an azimuth angle;
step S2, calculating the position error of the following balance car according to the current actual position information and the ideal position information of the following balance car, wherein the position error comprises a coordinate error and an azimuth error;
step S3, constructing a kinematics controller, and controlling the ideal linear velocity and the ideal angular velocity of the following robot by adopting the kinematics controller according to the position error output;
step S4, judging whether the angle of rotation according to the ideal angular speed in the sampling time is the same as the actual angle of rotation of the following balance car, and if so, outputting the ideal angular speed to the following balance car; otherwise, constructing an incremental PD controller, and outputting the actual angular speed to the following balance car according to the angular error rotating in the sampling time;
step S5, judging whether the coordinate calculated according to the ideal linear velocity in the sampling time is the same as the coordinate of the actual running of the following balance car, and if so, outputting the ideal linear velocity to the following balance car; otherwise, a prediction controller is constructed, and the actual linear speed is output to the following balance car according to the coordinate error running in the sampling time.
2. The two-wheeled self-balancing vehicle centralized formation control method of claim 1, wherein the calculating of the ideal position information of the following balance vehicle according to the position information of the piloting balance vehicle and the target formation structure comprises:
step S1.1, define (x y θ)TFor the abscissa, the ordinate and the azimuth of the first-order non-integral wheel type balance vehicle in a world coordinate system, the kinematic equation of the balance vehicle is as follows:
Figure FDA0002374413060000011
wherein v is the current actual linear velocity of the balance car, and omega is the current actual angular velocity of the balance car;
step S1.2, obtaining a piloting balance car RiIs Pi＝[xiyiθi]TFollowing balance car RjThe current actual position information is Pj＝[xjyjθj]TThen according to
Figure FDA0002374413060000012
Control method for calculating following balance car RjIdeal position information P ofj dComprises the following steps:
Figure FDA0002374413060000013
wherein, follow the balance car RjThe current actual position information is PjThe following relation is satisfied:
Figure FDA0002374413060000021
wherein ,Lij dAnd
Figure FDA0002374413060000022
respectively showing following balance cars RjAnd piloting balance car RiDesired distance and desired relative angle of rotation, LijAnd
Figure FDA0002374413060000023
respectively showing following balance cars RjAnd piloting balance car RiAnd the actual relative rotation angle.
3. The two-wheeled self-balancing vehicle centralized formation control method of claim 2, wherein calculating the position error of the following balancing vehicle from the current actual position information and the ideal position information of the following balancing vehicle comprises:
s2.1, obtaining the following balance car R according to the current actual position information and the ideal position information of the following balance carjThe position error under the world coordinate system is:
Figure FDA0002374413060000024
Figure FDA0002374413060000025
Figure FDA0002374413060000026
wherein ,
Figure FDA0002374413060000027
is the error of coordinate x direction under the world coordinate system,
Figure FDA0002374413060000028
is the error of coordinate y direction under the world coordinate system,
Figure FDA0002374413060000029
the azimuth angle error under the world coordinate system;
s2.2, converting the position error under the world coordinate system into a balance car coordinate system to obtain the position error of a following balance car under the balance car coordinate system as follows:
Figure FDA00023744130600000210
wherein ,ej1Error in x direction of coordinate in coordinate system of balance car, ej2Error in the y-direction of the coordinate in the coordinate system of the balance car, ej3Representing the azimuth angle error of the balance car coordinate system;
s2.3, carrying out derivation on the position error of the following balance car under the balance car coordinate system to obtain:
Figure FDA00023744130600000211
wherein ,
Figure FDA00023744130600000212
is ej1The derivative of (a) of (b),
Figure FDA00023744130600000213
is ej2The derivative of (a) of (b),
Figure FDA00023744130600000214
is ej3Derivative of vjFor following balance car RjCurrent actual linear velocity, viFor piloting balance car RiCurrent actual linear velocity, ωjFor following balance car RjCurrent actual angular velocity, ωiFor piloting balance car RiCurrent actual angular velocity, djIndicating following balance car RjTo the center of the axle.
4. The two-wheeled self-balancing vehicle centralized formation control method of claim 3, wherein the building of the kinematic controller, the controlling of the ideal linear velocity and the ideal angular velocity of the following robot according to the position error output by the kinematic controller, comprises:
the kinematic controller was constructed as follows:
Figure FDA0002374413060000031
wherein ,kx、ky、kθPositive vector constants representing x, y, and theta, respectively;
the ideal linear velocity of the following robot is output by the kinematic controllerjcIdeal angular velocity of omegajc。
5. The two-wheeled self-balancing vehicle centralized formation control method of claim 4, wherein the determination is made as to whether the angle of rotation at the ideal angular velocity within the sampling time is the same as the actual angle of rotation of the following balance vehicle, and if so, the ideal angular velocity is output to the following balance vehicle; otherwise, designing an incremental PD controller, and outputting the actual angular speed to the following balance car according to the angular error rotating in the sampling time, wherein the incremental PD controller comprises:
s4.1, setting the sampling time to be delta T;
step S4.2, following the balance vehicle in the sampling time according to the ideal angular speed omegajcThe angle of rotation is: theta1＝ωjc*ΔT；
Step S4.3, obtaining the miningThe actual rotation angle of the following balance car in the sample time is theta2Then the angular error of rotation within the sampling time is eθ＝θ1-θ2；
Step S4.4, if eθWhen the angular velocity is 0, the ideal angular velocity omega is output to the following balance carjcAnd finishing the angle regulation and control; otherwise, executing the next step;
step S4.5, constructing an incremental PD controller as follows:
Δθ＝λeθ(k)+βeθ(k-2)
Figure FDA0002374413060000032
Figure FDA0002374413060000033
where Δ θ is the actual angular velocity output by the incremental PD controller, eθ(k) Angle error at time k, eθ(k-2) is the angle error at time k-2, kpIs a proportionality coefficient, TdIs a differential coefficient, and T is a sampling period; and sends the actual angular velocity delta theta output by the incremental PD controller to the following balance car.
6. The two-wheeled self-balancing vehicle centralized formation control method of claim 5, wherein it is determined whether the coordinates calculated according to the ideal linear velocity within the sampling time are the same as the coordinates of the actual operation of the following balance vehicle, and if so, the ideal linear velocity is output to the following balance vehicle; otherwise, constructing a prediction controller, and outputting the actual linear speed to the following balance car according to the coordinate error running in the sampling time, wherein the method comprises the following steps:
s5.1, setting the sampling time to be delta T;
s5.2, following the balance car in sampling time according to the ideal linear velocity vjcThe calculated coordinate corresponding to the time is (x)d,yd)；
S5.3, acquiring running of the balance car in the sampling timeThe actual coordinate of the corresponding time is (x)r,yr) Then the running coordinate error in sample time is as follows:
Figure FDA0002374413060000041
wherein ,xe,yeErrors in the x and y directions, respectively;
step S5.4, if xe0 and yeWhen the linear velocity is 0, the ideal linear velocity v is takenjcAs the linear velocity to be sent, and step S5.7 is executed; otherwise, executing step S5.5;
step S5.5, calculating the differential value of the coordinate error running in the sampling time as follows:
Figure FDA0002374413060000042
wherein v is the current actual linear speed of the following balance car, and theta is the current actual azimuth angle of the following balance car;
setting a middle virtual control rule to obtain virtual linear speeds in x and y directions as follows:
Figure FDA0002374413060000043
wherein ,u1Is a virtual linear velocity in the y direction, u2Is a virtual linear velocity in the y direction, k1Is a constant number, k2Is a constant;
step S5.6, considering only the position error in the x-direction, i.e. setting yeWhen 0, construct the predictive controller as:
Figure FDA0002374413060000044
actual linear velocity v to be output by a predictive controllerrAs the linear velocity to be sent;
step S5.7, taking the linear velocity to be sent as the linear velocity v (k) at the current k moment, and judging whether the linear velocity v (k) meets the amplitude limiting requirement according to the following formula:
Figure FDA0002374413060000045
wherein v (k-1) is the linear velocity at the moment of k-1, Δ t is the time interval between two previous and subsequent velocity calculations, atvIs a preset speed change rate threshold value, vtvIs a preset speed threshold;
if the linear velocity v (k) meets the amplitude limiting requirement, outputting the linear velocity v (k) to a following balance car; otherwise, outputting a speed threshold value v to the following balance cartv。
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