CN112947442A - Finite time convergence vehicle formation controller and design method - Google Patents
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Abstract
The invention discloses a finite time convergence vehicle formation controller and a design method, wherein the current pose of a leading vehicle and the reference pose of a virtual target vehicle to be tracked by a following vehicle are given, an error system is obtained through a control problem conversion module to obtain an error pose, the converted error system is combined with a backstepping recursion technology to obtain an intermediate control law with fractional power parameters, the converted error system is combined with the intermediate control law to obtain a finite time actual control law with fractional power, and finally the actual control law is returned to the converted error system, so that the error system is stable in finite time, the following vehicle and the leading vehicle synchronously move, and the effective control of a vehicle formation system is realized.
Description
Technical Field
The invention relates to the technical field of vehicle formation control, in particular to a limited time convergence vehicle formation controller and a design method.
Background
Vehicle formation control can improve the efficiency of vehicle travel on the road by improving the flexibility and agility of the vehicle formation. Meanwhile, the vehicle formation can also increase the capacity of the road by improving the density of the vehicles on the road, so that the traffic safety and the road smoothness are improved to a certain extent. In addition, from the energy consumption perspective, the vehicle passing through the formation can reduce the resistance of the air encountered during the driving process, so that the oil consumption of the vehicle is effectively reduced.
Currently, there are several common approaches to the study of vehicle formation control: a following navigator method, a behavior-based method, a virtual structure method, an artificial potential field method, and the like. The behavior-based formation method is simple to implement and suitable for uncertain environments, but the formation precision is poor and accurate mathematical analysis is difficult to perform; the virtual structure method and the piloting following method both need the full state information of the virtual structure and the piloting robot respectively; the artificial potential field method is a method for converting complex environment information into a repulsive field model and a gravitational field model and finding a path from an initial point to a target point through the models. The following navigator method has the following problems:
firstly, the problem of convergence speed of a system is not basically considered in the conventional vehicle formation control method. From a practical point of view, people hope to reach the control target as soon as possible, but due to the limitation of technologies and the like, the conventional vehicle formation control scheme can not realize the desired formation effect within the expected time.
And secondly, although the existing formation control method can realize the control of the vehicle, the safety and the reliability of the vehicle system in a large speed range can not be ensured when the vehicle system is in a complex road condition, such as the condition of limiting the driving time and the like.
Disclosure of Invention
The invention provides a limited time convergence vehicle formation controller and a design method thereof, which aim to overcome the technical problems.
The invention relates to a design method of a limited time convergence vehicle formation controller, which comprises the following steps:
establishing a formation vehicle motion model; obtaining vehicle pose information through the formation vehicle motion model; the vehicle pose information includes: position and attitude information of a pilot vehicle, a following vehicle and a virtual target vehicle;
obtaining the pose of the virtual target vehicle according to the pose information of the virtual target vehicle and the pilot vehicle; calculating errors of the virtual target vehicle pose and the pilot vehicle pose, and combining a coordinate system of the following vehicle to obtain a converted error system;
designing a virtual error surface according to the pose of the virtual target vehicle; calculating an intermediate control variable by the error system and a virtual error surface;
obtaining a control law of finite time convergence according to the virtual target vehicle pose and the intermediate control quantity;
substituting the control law into the error system to enable the error system to be stable within a limited time, and therefore enabling the following vehicle and the pilot vehicle to move synchronously.
Further, establishing a formation vehicle motion model, comprising:
the motion model of any vehicle in the formation is expressed as:
setting the gravity center of any vehicle as x, y, and the gravity center x of the rear wheel of the vehicle1,y1Distance to center of gravity of vehicle and center of gravity x of front wheel of vehicle2,y2Equal distances to the center of gravity of the vehicle, each half of the inter-axle distance of the vehicle, are expressed as:
X＝b1x+b2y+c1 cosθ-c2 sinθ (2)
wherein X is ═ X1,x2,y1,y2]T，b1＝[1,1,0,0]T，b2＝[0,0,1,1]T，c1＝[-l/2,l/2,0,0]T，c2＝[0,0,l/2,l/2]T；
And (3) calculating the formula (2) to obtain a vehicle constraint relation:
in the formula, the pose of the vehicle is represented by a vector
In which x and y represent the position coordinates of the vehicle in the coordinate system, theta is the inclination angle of the vehicle body to the x-axis,
the steering angle of the front wheel to the vehicle body; v. of1Is the forward speed, v, of the rear wheel of the vehicle2Is the side steering angular velocity of the front wheel, and l represents the interaxial distance between the front wheel and the rear wheel.
Further, the pose of the virtual target vehicle is obtained according to the pose information of the virtual target vehicle and the pilot vehicle; calculating the error between the virtual target vehicle pose and the pilot vehicle pose, and combining the coordinate system of the following vehicle to obtain a converted error system, wherein the error system comprises:
establishing a vehicle formation pose error equation as follows:
wherein the current pose of the lead vehicle is
Control input is [ u ]1,u2]ΤThe reference pose of the virtual target vehicle to be followed by the following vehicle is
Control input is [ u ]v1,uv2]ΤPose error of
The transformed error system is described as:
in the formula uv1Is the forward speed, u, of the rear wheel of the virtual target vehiclev2Is the side steering angular velocity of the front wheels of the virtual target vehicle,
for the steering angle of the front wheels of the lead vehicle to the vehicle body,
steering angle, u, of virtual target vehicle front wheel to vehicle body1，u2Is the control rate.
Further, the designing a virtual error surface according to the virtual target vehicle pose comprises:
according to the position and posture error coordinate x of the rear wheel of the vehicle in the coordinate systemeAnd yePose error inclination angle theta of vehicle body to x-axis coordinateeSteering angle of front wheel to vehicle body
The virtual error surface is designed as follows:
wherein alpha is an introduced intermediate control variable;
said calculating intermediate control variables by said error system and virtual error plane comprising:
and (3) solving the derivative of the virtual error surface through a quadratic Lyapunov equation, wherein the form of the intermediate control variable alpha is as follows:
in the formula, k2，k3Is a positive design parameter, ρ is a positive fractional power parameter, and 1/2 < ρ < 1;
obtaining a derivative of a virtual error surface from the error system and the virtual error surface, expressed as:
in the formula (I), the compound is shown in the specification,
g1(·)＝uv1cosζ3+αζ2-u1，g2(·)＝uv1 sinζ3-αζ1，
h1(·)＝ζ2，h2(·)＝-ζ1，h3(·)＝-1；
order to
For the intermediate control variable, the intermediate control variable β is designed according to the lyapunov stability theory, and is expressed as:
wherein k is4Is a positive design parameter.
Further, the obtaining of the control law of finite time convergence according to the virtual target vehicle pose and the intermediate control quantity includes:
obtaining a control law u that the error system converges in a limited time according to the formula (5), the formula (7) and the formula (9)1And u2Expressed as:
in the formula, k1Is a positive design parameter, sgn (·) is a sign function.
A limited time convergence vehicle formation controller comprising: the control problem conversion module, the virtual control input solving module and the actual control input solving module;
the control problem conversion module is used for obtaining the pose of the virtual target vehicle according to the pose information of the virtual target vehicle and the pilot vehicle; calculating errors of the virtual target vehicle pose and the pilot vehicle pose, and combining a coordinate system of the following vehicle to obtain a converted error system;
the virtual control input solving module is used for designing a virtual error surface according to the pose of the virtual target vehicle; calculating an intermediate control variable by the error system and a virtual error surface;
the actual control input solving module is used for obtaining a control law of finite time convergence according to the virtual target vehicle pose and the intermediate control quantity; substituting the control law into the error system to enable the error system to be stable within a limited time, and therefore enabling the following vehicle and the pilot vehicle to move synchronously.
According to the invention, the formation control problem is converted into the problem of track tracking of the following vehicle to the leading vehicle by combining with the limited time control, so that the dynamic vehicle formation control method under the complex road condition can be realized, and the reliability and the anti-interference performance of the vehicle formation control are effectively improved. Meanwhile, under the condition of considering the convergence rate, the system can still be controlled by introducing control input based on the fractional power parameter to the control law, and the method has better robustness and faster convergence.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a flow chart of a method of designing a limited time convergence vehicle formation controller;
FIG. 2 is a schematic diagram of a finite time convergence vehicle formation controller;
FIG. 3 is a diagram showing the effect of controlling the forward speed of the rear wheels of the vehicle in a simulation experiment according to the present invention;
FIG. 4 is a diagram showing the effect of controlling the steering angular velocity of the front wheels of the vehicle in a simulation experiment according to the present invention;
fig. 5 is a diagram showing the steering angle control effect of the front wheels of the vehicle on the vehicle body in the simulation experiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. 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 invention.
As shown in fig. 1, the present embodiment provides a method for designing a limited-time convergence vehicle formation controller, including:
101. establishing a formation vehicle motion model; obtaining vehicle pose information through a formation vehicle motion model; vehicle pose information, including: position and attitude information of a pilot vehicle, a following vehicle and a virtual target vehicle;
specifically, the motion model of any vehicle in formation is represented as:
setting the gravity center of any vehicle as x, y, and the gravity center x of the rear wheel of the vehicle1,y1Distance to center of gravity of vehicle and center of gravity x of front wheel of vehicle2,y2Go to the carThe vehicle center of gravity distances are equal and are half of the axle distance of the vehicle, and are expressed as:
X＝b1x+b2y+c1 cosθ-c2 sinθ (2)
wherein X is ═ X1,x2,y1,y2]T，b1＝[1,1,0,0]T，b2＝[0,0,1,1]T，c1＝[-l/2,l/2,0,0]T，c2＝[0,0,l/2,l/2]T；
And (3) calculating the formula (2) to obtain a vehicle constraint relation:
in the formula, the pose of the vehicle is represented by a vector
In which x and y represent the position coordinates of the vehicle in the coordinate system, theta is the inclination angle of the vehicle body to the x-axis,
the steering angle of the front wheel to the vehicle body; v. of1Is the forward speed, v, of the rear wheel of the vehicle2Is the side steering angular velocity of the front wheel, and l represents the interaxial distance between the front wheel and the rear wheel.
102. Obtaining the pose of the virtual target vehicle according to the pose information of the virtual target vehicle and the pilot vehicle; calculating errors of the positions of the virtual target vehicle and the position of the pilot vehicle, and combining a coordinate system of the following vehicle to obtain a converted error system;
specifically, an error equation of the vehicle formation pose is established as follows:
in the formula, the current pose of the lead vehicle is
Control input is [ u ]1,u2]ΤThe reference pose of the virtual target vehicle to be followed by the following vehicle is
Control input is [ u ]v1,uv2]ΤPose error of
For a pilot following formation system, the primary trajectory of the formation is typically determined by the pilot vehicle occupant, and the reference trajectory of the following vehicle is determined by the virtual vehicle trajectory generated by the pilot vehicle and the structural parameters.
The transformed error system is described as:
in the formula uv1Is the forward speed, u, of the rear wheel of the virtual target vehiclev2Is the side steering angular velocity of the front wheels of the virtual target vehicle,
for the steering angle of the front wheels of the lead vehicle to the vehicle body,
steering angle, u, of virtual target vehicle front wheel to vehicle body1，u2Is the control rate.
The method mainly comprises the steps of firstly determining the distance and the angle between a virtual target vehicle and the expected position and attitude of a pilot vehicle so as to obtain the reference position and attitude of the virtual target vehicle
Secondly, the position and pose of the pilot vehicle are subtracted from the position and pose of the virtual target vehicle to obtain position and pose errors
Through coordinate transformation, a pose error equation (4) of the pose error in a coordinate system of the following vehicle can be obtained; and finally, obtaining an error system of the converted formula (5) by deriving the formula (4) and combining the vehicle formation motion model. The converted error system completes the problem of changing the formation control problem into the problem of tracking the track of the leading vehicle by the following vehicle, and the proper control law u is searched1And u2The converted error system can be stabilized in a limited time.
103. Designing a virtual error surface according to the pose of the virtual target vehicle; calculating an intermediate control variable through the error system and the virtual error surface;
specifically, the position and orientation error coordinate x of the rear wheel of the vehicle in the coordinate systemeAnd yePose error inclination angle theta of vehicle body to x-axis coordinateeSteering angle of front wheel to vehicle body
The virtual error surface is designed as follows:
wherein alpha is an introduced intermediate control variable;
and (3) solving the derivative of the virtual error surface through a quadratic Lyapunov equation, wherein the form of the intermediate control variable alpha is as follows:
in the formula, k2，k3Is a positive design parameter, ρ is a positive fractional power parameter, and 1/2 < ρ < 1;
obtaining a derivative of the virtual error surface by the error system and the virtual error surface, expressed as:
in the formula (I), the compound is shown in the specification,
g1(·)＝uv1cosζ3+αζ2-u1，g2(·)＝uv1 sinζ3-αζ1，
h1(·)＝ζ2，h2(·)＝-ζ1，h3(·)＝-1；
order to
For the intermediate control variable, the intermediate control variable β is designed according to the lyapunov stability theory, and is expressed as:
wherein k is4Is a positive design parameter.
104. Obtaining a control law of finite time convergence according to the virtual target vehicle pose and the intermediate control quantity;
specifically, a control law u in which the error system converges in a finite time is obtained from equations (5), (7) and (9)1And u2Expressed as:
in the formula, k1Is a positive design parameter, sgn (·) is a sign function.
105. Substituting the control law into the error system to stabilize the error system within a limited time, so that the following vehicle and the pilot vehicle synchronously move.
Specifically, the control law is substituted into the error system, so that the error system is stable in limited time, the stability of the error system in limited time indicates that the converted error system is stable, the stability of the error system indicates that the vehicle follows a pilot vehicle, and the formation of the vehicle formation can be kept after the vehicle follows the pilot vehicle.
As shown in fig. 2, the present embodiment provides a limited-time convergence vehicle formation controller, including: the control problem conversion module, the virtual control input solving module and the actual control input solving module;
the control problem conversion module is used for obtaining the pose of the virtual target vehicle according to the pose information of the virtual target vehicle and the pilot vehicle; calculating errors of the positions of the virtual target vehicle and the position of the pilot vehicle, and combining a coordinate system of the following vehicle to obtain a converted error system; the input end of the control problem conversion module is connected with the vehicle pose information (pose information of the lead vehicle, the following vehicle and the virtual target vehicle) and the output end of the actual control solving module.
The virtual control input solving module is used for designing a virtual error surface according to the pose of the virtual target vehicle; calculating an intermediate control variable through the error system and the virtual error surface; the input end of the virtual control input solving module is connected with the output end of the control problem conversion module and the virtual target vehicle pose calculated and output by the vehicle motion model.
The actual control input solving module is used for obtaining a control law of finite time convergence according to the virtual target vehicle pose and the intermediate control quantity; substituting the control law into the error system to stabilize the error system within a limited time, so that the following vehicle and the pilot vehicle synchronously move. The input end of the actual control input solving module is connected with the output end of the virtual control input solving module and the virtual target vehicle pose calculated and output by the vehicle motion model.
In the simulation experiment, through fig. 3, 4 and 5, it can be seen that the following vehicle can track the piloting vehicle in a limited time.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (6)
1. A method of designing a limited time convergence vehicle formation controller, comprising:
establishing a formation vehicle motion model; obtaining vehicle pose information through the formation vehicle motion model; the vehicle pose information includes: position and attitude information of a pilot vehicle, a following vehicle and a virtual target vehicle;
obtaining the pose of the virtual target vehicle according to the pose information of the virtual target vehicle and the pilot vehicle; calculating errors of the virtual target vehicle pose and the pilot vehicle pose, and combining a coordinate system of the following vehicle to obtain a converted error system;
designing a virtual error surface according to the pose of the virtual target vehicle; calculating an intermediate control variable by the error system and a virtual error surface;
obtaining a control law of finite time convergence according to the virtual target vehicle pose and the intermediate control quantity;
substituting the control law into the error system to enable the error system to be stable within a limited time, and therefore enabling the following vehicle and the pilot vehicle to move synchronously.
2. The method of claim 1, wherein the establishing a formation vehicle motion model comprises:
the motion model of any vehicle in the formation is expressed as:
setting the center of gravity of any vehicleX, y, the center of gravity x of the rear wheel of the vehicle1,y1Distance to center of gravity of vehicle and center of gravity x of front wheel of vehicle2,y2Equal distances to the center of gravity of the vehicle, each half of the inter-axle distance of the vehicle, are expressed as:
X＝b1x+b2y+c1cosθ-c2sinθ (2)
wherein X is ═ X1,x2,y1,y2]T，b1＝[1,1,0,0]T，b2＝[0,0,1,1]T，c1＝[-l/2,l/2,0,0]T，c2＝[0,0,l/2,l/2]T；
And (3) calculating the formula (2) to obtain a vehicle constraint relation:
in the formula, the pose of the vehicle is represented by a vector
In which x and y represent the position coordinates of the vehicle in the coordinate system, theta is the inclination angle of the vehicle body to the x-axis,
the steering angle of the front wheel to the vehicle body; v. of1Is the forward speed, v, of the rear wheel of the vehicle2Is the side steering angular velocity of the front wheel, and l represents the interaxial distance between the front wheel and the rear wheel.
3. The method of claim 2, wherein the virtual target vehicle pose is obtained according to pose information of the virtual target vehicle and the pilot vehicle; calculating the error between the virtual target vehicle pose and the pilot vehicle pose, and combining the coordinate system of the following vehicle to obtain a converted error system, wherein the error system comprises:
establishing a vehicle formation pose error equation as follows:
wherein the current pose of the lead vehicle is
Control input is [ u ]1,u2]ΤThe reference pose of the virtual target vehicle to be followed by the following vehicle is
Control input is [ u ]v1,uv2]ΤPose error of
The transformed error system is described as:
in the formula uv1Is the forward speed, u, of the rear wheel of the virtual target vehiclev2Is the side steering angular velocity of the front wheels of the virtual target vehicle,
for the steering angle of the front wheels of the lead vehicle to the vehicle body,
steering angle, u, of virtual target vehicle front wheel to vehicle body1，u2Is the control rate.
4. The method for designing a limited-time convergence vehicle formation controller according to claim 3, wherein the designing a virtual error surface according to the virtual target vehicle pose comprises:
according to the position and posture error coordinate x of the rear wheel of the vehicle in the coordinate systemeAnd yePose error inclination angle theta of vehicle body to x-axis coordinateeSteering angle of front wheel to vehicle body
The virtual error surface is designed as follows:
wherein alpha is an introduced intermediate control variable;
said calculating intermediate control variables by said error system and virtual error plane comprising:
and (3) solving the derivative of the virtual error surface through a quadratic Lyapunov equation, wherein the form of the intermediate control variable alpha is as follows:
in the formula, k2，k3Is a positive design parameter, ρ is a positive fractional power parameter, and 1/2 < ρ < 1;
obtaining a derivative of a virtual error surface from the error system and the virtual error surface, expressed as:
in the formula (I), the compound is shown in the specification,
g1(·)＝uv1cosζ3+αζ2-u1，g2(·)＝uv1sinζ3-αζ1，
h1(·)＝ζ2，h2(·)＝-ζ1，h3(·)＝-1；
order to
For the intermediate control variable, the intermediate control variable β is designed according to the lyapunov stability theory, and is expressed as:
wherein k is4Is a positive design parameter.
5. The method for designing the limited-time convergence vehicle formation controller according to claim 4, wherein the obtaining of the control law of the limited-time convergence according to the virtual target vehicle pose and the intermediate control quantity comprises:
obtaining a control law u that the error system converges in a limited time according to the formula (5), the formula (7) and the formula (9)1And u2Expressed as:
in the formula, k1Is a positive design parameter, sgn (·) is a sign function.
6. A limited time convergence vehicle formation controller, comprising:
the control problem conversion module, the virtual control input solving module and the actual control input solving module;
the control problem conversion module is used for obtaining the pose of the virtual target vehicle according to the pose information of the virtual target vehicle and the pilot vehicle; calculating errors of the virtual target vehicle pose and the pilot vehicle pose, and combining a coordinate system of the following vehicle to obtain a converted error system;
the virtual control input solving module is used for designing a virtual error surface according to the pose of the virtual target vehicle; calculating an intermediate control variable by the error system and a virtual error surface;
the actual control input solving module is used for obtaining a control law of finite time convergence according to the virtual target vehicle pose and the intermediate control quantity; substituting the control law into the error system to enable the error system to be stable within a limited time, and therefore enabling the following vehicle and the pilot vehicle to move synchronously.
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