CN113296401B - Direct obstacle avoidance tracking control method based on switching strategy and storage medium - Google Patents

Direct obstacle avoidance tracking control method based on switching strategy and storage medium Download PDF

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CN113296401B
CN113296401B CN202110534276.8A CN202110534276A CN113296401B CN 113296401 B CN113296401 B CN 113296401B CN 202110534276 A CN202110534276 A CN 202110534276A CN 113296401 B CN113296401 B CN 113296401B
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obstacle avoidance
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郑晓龙
杨学博
李湛
高会军
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Harbin Institute of Technology
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Abstract

A direct obstacle avoidance tracking control method based on a switching strategy and a storage medium belong to the field of nonlinear system obstacle avoidance tracking control. The invention solves the problem that the existing indirect obstacle avoidance tracking control method is unreliable. The method comprises the steps of establishing a nonlinear system state space model for a robot, and giving a system target signal and an obstacle coordinate; designing a Lyapunov function by utilizing a tracking error variable, and designing a virtual tracking control function and a target tracking control strategy according to a first-order derivative of the Lyapunov function to time; designing a Lyapunov function by using an obstacle avoidance error variable, and designing a virtual obstacle avoidance control function and an obstacle avoidance control strategy according to a first-order derivative of the Lyapunov function on time; and designing a direct obstacle avoidance tracking control strategy based on a switching strategy by utilizing a target tracking control strategy and an obstacle avoidance control strategy to realize the control of the robot. The invention is used for the obstacle avoidance tracking control of the nonlinear system on the robot.

Description

Direct obstacle avoidance tracking control method based on switching strategy and storage medium
Technical Field
The invention belongs to the field of non-linear system obstacle avoidance tracking control.
Background
Obstacle avoidance tracking control is always a research hotspot in the field of nonlinear system control, and the obstacle avoidance tracking control means that a system avoids obstacles through a self-measuring technology and a control means on the premise of no manual control, and finally safely reaches a target point. Common non-linear systems with obstacle avoidance tracking control requirements include autonomous driving systems, robot systems, flight control systems, and the like. The current popular obstacle avoidance tracking methods include a visual graph method, a grid method, a potential field method, and the like, and reference may be made to chinese patent CN110609547A, chinese patent CN109263639A, and chinese patent CN112577491A for these methods. It is worth pointing out that these obstacle avoidance tracking methods all belong to indirect obstacle avoidance tracking control methods, they only plan the obstacle avoidance tracking path of the system, and subsequently, it is necessary to apply control action to the system by the path following control strategy, so that the system finally completes the obstacle avoidance tracking task. If the path planning time of the system is too long or the path planning of the system fails, the path following of the system is limited or fails, and finally the task execution efficiency is reduced or the task fails. Therefore, how to directly design an obstacle avoidance tracking control strategy for a system without depending on path planning is a key problem.
Disclosure of Invention
The invention aims to solve the problem that the existing indirect obstacle avoidance tracking control method is unreliable, and provides a direct obstacle avoidance tracking control method based on a switching strategy.
A direct obstacle avoidance tracking control method based on a switching strategy is used for establishing a two-degree-of-freedom nonlinear system state space model aiming at a controlled object and controlling a direct obstacle avoidance tracking control strategy based on the switching strategy, wherein the direct obstacle avoidance tracking control strategy based on the switching strategy is as follows
Figure GDA0003511000850000011
Figure GDA0003511000850000012
Figure GDA0003511000850000013
Figure GDA0003511000850000014
Wherein x is1And x2Respectively representing the system x-axis position and velocity, x3And x4Respectively representing the y-axis position and the speed of the system; u. of1、u2Respectively as control functions in the directions of an x axis and a y axis; z is a radical of1＝x1-xd、z2＝x2-α1、z3＝x3-yd、z4＝x4-α2To track error variables, (x)d,yd) For a given system target signal, α1,α2Representing a virtual tracking control function; s1,i＝x1-pi、s2,i＝x2-β1,i、s3,i＝x3-qi、s4,i＝x4-β2,iTo avoid the barrier error variable, (p)i,qi) Is the coordinate of the obstacle, i is 1,2, …, m, beta1,iAnd beta2,iRepresenting a virtual obstacle avoidance control function; b1,b2Is a constant number, k1,k2,k3,k4Is a normal number;
the system is an established two-degree-of-freedom nonlinear system.
Further, the design process of the direct obstacle avoidance tracking control strategy based on the switching strategy comprises the following steps:
step one, aiming at a controlled object, establishing a two-degree-of-freedom nonlinear system state space model, simplifying the two-degree-of-freedom nonlinear system as a system, and respectively using x as four state variables in the system1,x2,x3,x4Is represented by the formula (I) in which x1And x2Respectively representing the system x-axis position and velocity, x3And x4Respectively representing the y-axis position and the speed of the system; at the same time, a system target signal (x) is givend,yd) And m obstacle coordinates (p)i,qi),i＝1,2,…,m；
Step two, defining a tracking error variable z1＝x1-xd，z2＝x2-α1，z3＝x3-ydAnd z4＝x4-α2(ii) a Wherein alpha is1,α2Representing a virtual tracking control function to be designed;
step three, designing a Lyapunov function V by using the tracking error variable defined in the step two, and solving a first derivative of the Lyapunov function V to obtain a first derivative
Figure GDA0003511000850000021
According to
Figure GDA0003511000850000022
Designing a virtual tracking control function alpha1,α2And a target tracking control strategy;
step four, defining an obstacle avoidance error variable s1,i＝x1-pi，s2,i＝x2-β1,i，s3,i＝x3-qiAnd s4,i＝x4-β2,iWherein, β1,iAnd beta2,iRepresenting a virtual obstacle avoidance control function to be designed;
step five, designing the Lyapunov function V by using the obstacle avoidance error variable defined in the step fouri(ii) a To lyapunov function ViObtaining the first derivative
Figure GDA0003511000850000023
According to
Figure GDA0003511000850000024
Designing a virtual obstacle avoidance control function beta1,i，β2,iAnd an obstacle avoidance control strategy;
and step six, designing a direct obstacle avoidance tracking control strategy based on a switching strategy according to the target tracking control strategy in the step three and the obstacle avoidance control strategy in the step five.
Further, the state space model of the two-degree-of-freedom nonlinear system in the step one is as follows:
Figure GDA0003511000850000025
wherein the content of the first and second substances,
Figure GDA0003511000850000026
represents a state variable x1,x2,x3,x4First derivative of b1,b2Is a known constant, b1,b2Is not zero; f. of1(x1,x2),f2(x3,x4) For a known non-linear continuous function, u1,u2Representing control input signals of a non-linear system, the control being aimed at designing the system control input u1,u2Make the system status (x)1,x3) To the target point (x)d,yd) Simultaneously avoid m obstacles (p)i,qi)。
Further, the lyapunov function V described in step three is as follows:
Figure GDA0003511000850000031
wherein z is1＝x1-xd，z2＝x2-α1，z3＝x3-yd，z4＝x4-α2；α1,α2Representing the virtual tracking control function to be designed.
Further, the first derivative of the lyapunov function V with respect to time in step three is as follows:
Figure GDA0003511000850000032
wherein the content of the first and second substances,
Figure GDA0003511000850000033
and
Figure GDA0003511000850000034
representing a virtual tracking control function alpha1And alpha2The first derivative of (a).
Further, step three according to
Figure GDA0003511000850000035
Designed virtual tracking control function alpha1,α2And the target tracking control strategy is as follows:
α1＝-k1z1 (4)
Figure GDA0003511000850000036
α2＝-k3z3 (6)
Figure GDA0003511000850000037
wherein k is1,k2,k3,k4Is a normal number, and is,
Figure GDA0003511000850000038
and
Figure GDA0003511000850000039
representing a virtual tracking control function alpha1And alpha2The first derivative of (a).
Further, the Lyapunov function V in the fifth stepiThe following were used:
Figure GDA00035110008500000310
wherein i is 1,2, …, m, s1,i＝x1-pi，s2,i＝x2-β1,i，s3,i＝x3-qi，s4,i＝x4-β2,i，riThe system and the obstacle (p) are represented as normal numbersi,qi) A safety distance of beta1,iAnd beta2,iAnd representing a virtual obstacle avoidance control function to be designed.
Further, the Lyapunov function V in the fifth stepiThe first derivative with respect to time is as follows:
Figure GDA00035110008500000311
wherein the content of the first and second substances,
Figure GDA00035110008500000312
and
Figure GDA00035110008500000313
representing a virtual obstacle avoidance control function beta1,iAnd beta2,iThe first derivative of (a).
Further, the virtual obstacle avoidance control function β in step five1,iAnd beta2,iAnd the obstacle avoidance control strategy is as follows:
β1,i＝c1,is1,i (10)
Figure GDA0003511000850000041
β2,i＝c3,is3,i (12)
Figure GDA0003511000850000042
wherein i is 1,2, …, m, c1,i,c2,i,c3,i,c4,iIs a normal number.
A storage medium stores at least one instruction, and the at least one instruction is loaded and executed by a processor to implement a direct obstacle avoidance tracking control method based on a switching strategy.
Has the advantages that:
the invention provides a direct obstacle avoidance tracking control method based on a switching strategy, which is designed by utilizing the switching strategy, and a system does not need to directly complete the avoidance of obstacles and the tracking of a target point on the premise of path planning. Compared with the traditional indirect obstacle avoidance tracking control method, the method has the advantages that the obstacle avoidance tracking controller is directly designed on the control layer, so that the problem that the task fails due to unreliable path planning in the indirect obstacle avoidance tracking control method can be solved.
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FIG. 1 is a flow chart of the present invention;
FIG. 2 is a graph of system x, y plane position response;
FIG. 3 is a graph of system x-axis position response;
FIG. 4 is a y-axis position response plot of the system;
FIG. 5 is a graph of system x, y plane position response;
FIG. 6 is a graph of system x-axis position response;
FIG. 7 is a graph of the y-axis position response of the system.
Detailed Description
The first embodiment is as follows: the present embodiment is described in connection with figure 1,
the embodiment is a direct obstacle avoidance tracking control method based on a switching strategy, which comprises the following steps:
step one, aiming at a controlled object, establishing a state space model of a two-degree-of-freedom nonlinear system, and shorthand the two-degree-of-freedom nonlinear system as a system, wherein four state variables in the system respectively use x1,x2,x3,x4Is represented by the formula (I) in which x1And x2Respectively representing the system x-axis position and velocity, x3And x4Respectively representing the y-axis position and velocity of the system. At the same time, a system target signal (x) is givend,yd) And m obstacle coordinates (p)i,qi) I is 1,2, …, m. The controlled object comprising a robot or a robotA motor-driven vehicle, etc.
Step two, defining a tracking error variable z1＝x1-xd，z2＝x2-α1，z3＝x3-ydAnd z4＝x4-α2. Wherein alpha is1,α2Representing a virtual tracking control function to be designed;
step three, designing a Lyapunov function V by using the tracking error variable defined in the step two, and solving a first derivative of the Lyapunov function V to obtain a first derivative
Figure GDA0003511000850000051
According to
Figure GDA0003511000850000052
Designing a virtual tracking control function alpha1,α2And a target tracking control strategy;
step four, defining an obstacle avoidance error variable s1,i＝x1-pi，s2,i＝x2-β1,i，s3,i＝x3-qiAnd s4,i＝x4-β2,iWherein i is 1,2, …, m, beta1,iAnd beta2,iRepresenting a virtual obstacle avoidance control function to be designed;
step five, designing the Lyapunov function V by using the obstacle avoidance error variable defined in the step fouriWhere i is 1,2, …, m. To lyapunov function ViObtaining the first derivative
Figure GDA0003511000850000053
According to
Figure GDA0003511000850000054
Designing a virtual obstacle avoidance control function beta1,i，β2,iAnd an obstacle avoidance control strategy;
and step six, designing a direct obstacle avoidance tracking control strategy based on a switching strategy according to the target tracking control strategy in the step three and the obstacle avoidance control strategy in the step five.
And seventhly, controlling the robot by using a direct obstacle avoidance tracking control strategy based on a switching strategy.
The second embodiment is as follows:
the embodiment is a direct obstacle avoidance tracking control method based on a switching strategy, and in the step one, the specific form of establishing a state space model of a two-degree-of-freedom nonlinear system is as follows:
Figure GDA0003511000850000055
solutions for the state space model of two-degree-of-freedom nonlinear systems exist and are unique, where x1,x2,x3,x4Representing the state variable of the system, x1And x2Respectively representing the system x-axis position and velocity, x3And x4Respectively representing the y-axis position and velocity of the system,
Figure GDA0003511000850000056
represents a state variable x1,x2,x3,x4First derivative of b1,b2Is a known constant, b1,b2Is not zero; f. of1(x1,x2),f2(x3,x4) For a known non-linear continuous function, u1,u2Representing control input signals of a non-linear system, the control being aimed at designing the system control input u1,u2Make the system status (x)1,x3) To the target point (x)d,yd) Simultaneously avoid m obstacles (p)i,qi),i＝1,2,…,m。
Other steps and parameters are the same as in the first embodiment.
The third concrete implementation mode:
the embodiment is a direct obstacle avoidance tracking control method based on a switching strategy, and a lyapunov function V in the third step is designed as follows:
Figure GDA0003511000850000061
wherein z is1＝x1-xd，z2＝x2-α1，z3＝x3-yd，z4＝x4-α2。α1,α2Representing the virtual tracking control function to be designed.
Other steps and parameters are the same as in one of the first to second embodiments.
The fourth concrete implementation mode:
the embodiment is a direct obstacle avoidance tracking control method based on a switching strategy, and a first derivative of a lyapunov function V in the third step is obtained by solving the time:
Figure GDA0003511000850000062
wherein the content of the first and second substances,
Figure GDA0003511000850000063
and
Figure GDA0003511000850000064
representing a virtual tracking control function alpha1And alpha2The first derivative of (a).
Other steps and parameters are the same as in one of the first to third embodiments.
Detailed description of the invention
The embodiment is a direct obstacle avoidance tracking control method based on a switching strategy, and a virtual tracking control function alpha in the step three1And alpha2And the target tracking control strategy is designed according to the formula (3) as follows:
α1＝-k1z1 (4)
Figure GDA0003511000850000065
α2＝-k3z3 (6)
Figure GDA0003511000850000066
wherein k is1,k2,k3,k4Is a normal number, and is,
Figure GDA0003511000850000067
and
Figure GDA0003511000850000068
representing a virtual tracking control function alpha1And alpha2The first derivative of (a).
Other steps and parameters are the same as in one of the first to fourth embodiments.
The sixth specific implementation mode:
the embodiment is a direct obstacle avoidance tracking control method based on a switching strategy, and in the fifth step, a Lyapunov function V is adoptediThe design is as follows:
Figure GDA0003511000850000069
wherein i is 1,2, …, m, s1,i＝x1-pi，s2,i＝x2-β1,i，s3,i＝x3-qi，s4,i＝x4-β2,i，riThe system and the obstacle (p) are represented as normal numbersi,qi) A safety distance of beta1,iAnd beta2,iAnd representing a virtual obstacle avoidance control function to be designed.
Other steps and parameters are the same as in one of the first to fifth embodiments.
The seventh embodiment:
the present embodiment is a direct obstacle avoidance tracking control method based on a switching strategy, and the lyapunov function V in the fifth stepiThe first derivative over time can be found:
Figure GDA0003511000850000071
wherein the content of the first and second substances,
Figure GDA0003511000850000072
and
Figure GDA0003511000850000073
representing a virtual obstacle avoidance control function beta1,iAnd beta2,iThe first derivative of (a).
Other steps and parameters are the same as in one of the first to sixth embodiments.
The specific implementation mode is eight:
the embodiment is a direct obstacle avoidance tracking control method based on a switching strategy, and a virtual obstacle avoidance control function beta is adopted in the fifth step1,iAnd beta2,iAnd the obstacle avoidance control strategy is designed according to the formula (9) as follows:
β1,i＝c1,is1,i (10)
Figure GDA0003511000850000074
β2,i＝c3,is3,i (12)
Figure GDA0003511000850000075
wherein i is 1,2, …, m, c1,i,c2,i,c3,i,c4,iIs a normal number, g1,iAnd g2,iComprises the following steps:
Figure GDA0003511000850000076
Figure GDA0003511000850000077
other steps and parameters are the same as in one of the first to seventh embodiments.
The specific implementation method nine:
the embodiment is a direct obstacle avoidance tracking control method based on a switching strategy, wherein in the sixth step, according to the target tracking control strategy in the third step and the obstacle avoidance control strategy in the fifth step, the direct obstacle avoidance tracking control strategy based on the switching strategy is designed as follows:
Figure GDA0003511000850000078
Figure GDA0003511000850000081
direct obstacle avoidance tracking control strategies (16) and (17) based on switching strategies will be demonstrated below to enable the system to reach the target point and avoid all obstacle points. The demonstration process is as follows:
substituting the formulas (4) - (7) into the formula (3) to obtain the final product
Figure GDA0003511000850000082
Wherein, a1＝min1≤i≤4{2ki}. Equation (18) indicates the system state (x)1,x3) With obstacles (p)i,qi) Distance is greater than or equal to riTime will exponentially converge to the target point (x)d,yd)。
Substituting the formulas (10) - (13) into the formula (9) to obtain the final product
Figure GDA0003511000850000083
An acid series of the formula (19)System State (x)1,x3) With obstacles (p)i,qi) Distance less than riAnd is available when not zero
Figure GDA0003511000850000084
Thus, it is possible to provide
Figure GDA0003511000850000085
Will converge progressively to zero, indicating that the system will move progressively away from the obstacle until it reaches the obstacle (p)i,qi) A distance ri. When the system is in contact with an obstacle (p)i,qi) A distance riAnd when the target tracking controller is used, the controller is switched to the target tracking controller, so that the system continues to move to the target point. After the syndrome is confirmed.
Other steps and parameters are the same as in one of the first to eighth embodiments.
The detailed implementation mode is ten:
the embodiment is a storage medium, where at least one instruction is stored, and the at least one instruction is loaded and executed by a processor to implement a direct obstacle avoidance tracking control method based on a switching policy.
The embodiment includes, but is not limited to, a storage medium itself, and may also be an apparatus, where the apparatus includes the storage medium and a processor, and the storage medium stores at least one instruction, and the at least one instruction is loaded and executed by the processor to implement a direct obstacle avoidance tracking control method based on a switching policy.
Example one
Taking the initial value of the system (1) as x1(0)＝2m，x2(0)＝0m/s，x3(0)＝-1.2m，x3(0) 0m/s, constant b1＝0.24，b20.15, function f1(x1,x2)＝-x2，f2(x3,x4)＝-x4. The system target point is set to (x)d,yd) (0,0) and the obstacle coordinate is (p)1,q1) The system is at a safe distance r from the obstacle (0.6, -0.8)1＝0.5m。
Parameters in the virtual tracking control functions (4) and (6) and the target tracking control strategies (5) and (7) are taken as k1＝3.5，k2＝3.5，k3＝2.5，k42.5. The parameters in the virtual obstacle avoidance control functions (10) and (12) and the obstacle avoidance control strategies (11) and (13) are taken as c1,1＝0.5，c2,1＝300，c3,1＝0.6，c4,1200. The system sampling interval time is 0.001 seconds.
FIG. 2 is a graph showing the x, y plane position response of the system under the method of the present invention, wherein the solid line represents the trajectory of the system, the dashed line represents the range of obstacle avoidance, and the asterisks represent the coordinate position of the obstacle; FIG. 3 is a graph showing the evolution of the x-axis position of the system over time in accordance with the method of the present invention; FIG. 4 is a graph showing the evolution of the y-axis position of the system over time in accordance with the method of the present invention.
Example two
Taking the initial value of the system (1) as x1(0)＝8m，x2(0)＝0m/s，x3(0)＝-8m，x3(0) 0m/s, constant b1＝0.24，b20.15, function f1(x1,x2)＝-x2，f2(x3,x4)＝-x4. The system target point is set to (x)d,yd) (0,0) and the obstacle coordinate is (p)1,q1)＝(6,-7)，(p2,q2)＝(6,-3)，(p3,q3)＝(1,-4)，(p4,q4) The system is at a safe distance r from the obstacle (0.6, -0.8)1＝1m，r2＝2.8m，r3＝1.5m，r4＝0.5m。
Parameters in the virtual tracking control functions (4) and (6) and the target tracking control strategies (5) and (7) are taken as k1＝3.5，k2＝3.5，k3＝2.5，k42.5. The parameters in the virtual obstacle avoidance control functions (10) and (12) and the obstacle avoidance control strategies (11) and (13) are taken as c1,1＝0.5，c2,1＝300，c3,1＝0.6，c4,1200. The system sampling interval time is 0.001 seconds.
FIG. 5 is a graph showing the x, y plane position response of the system under the method of the present invention, wherein the solid line represents the trajectory of the system, the dashed line represents the range of obstacle avoidance, and the asterisks represent the coordinate position of the obstacle; FIG. 6 is a graph showing the evolution of the x-axis position of the system over time in accordance with the method of the present invention; FIG. 7 is a graph showing the evolution of the y-axis position of the system over time in accordance with the method of the present invention.
And conclusion one: from fig. 2 and fig. 5, it can be derived that the system can effectively avoid single and multiple obstacles and can safely reach the target position under the method of the present invention.
And a second conclusion: the first embodiment and the second embodiment show that the method does not need to plan the path of the system in advance, and the direct obstacle avoidance tracking control method based on the switching strategy can ensure that the system can complete the obstacle avoidance tracking task.
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.

Claims (9)

1. A direct obstacle avoidance tracking control method based on a switching strategy is characterized in that a two-degree-of-freedom nonlinear system state space model is established for a controlled object, and the direct obstacle avoidance tracking control method based on the switching strategy is used for controlling,
the state space model of the two-degree-of-freedom nonlinear system is as follows:
Figure FDA0003511000840000011
wherein the content of the first and second substances,
Figure FDA0003511000840000012
represents a state variable x1,x2,x3,x4First derivative of b1,b2Is a known constant, b1,b2Is not zero; f. of1(x1,x2),f2(x3,x4) For a known non-linear continuous function, u1,u2Representing control input signals of a non-linear system, the control being aimed at designing the system control input u1,u2Make the system status (x)1,x3) To the target point (x)d,yd) Simultaneously avoid m obstacles (p)i,qi)；
The direct obstacle avoidance tracking control strategy based on the switching strategy is as follows
Figure FDA0003511000840000013
Figure FDA0003511000840000014
Figure FDA0003511000840000015
Figure FDA0003511000840000016
Wherein x is1And x2Respectively representing the system x-axis position and velocity, x3And x4Respectively representing the y-axis position and the speed of the system; u. of1、u2Respectively as control functions in the directions of an x axis and a y axis; z is a radical of1＝x1-xd、z2＝x2-α1、z3＝x3-yd、z4＝x4-α2To track error variables, (x)d,yd) For a given system target signal, α1,α2Representing a virtual tracking control function; s1,i＝x1-pi、s2,i＝x2-β1,i、s3,i＝x3-qi、s4,i＝x4-β2,iTo avoid the barrier error variable, (p)i,qi) Is the coordinate of the obstacle, i is 1,2, …, m, beta1,iAnd beta2,iRepresenting a virtual obstacle avoidance control function; b1,b2Is a constant number, k2,k4Is a normal number; r isiIndicating a safe distance of the system from the obstacle; c. C2,i,c4,iIs a normal number;
the system is an established two-degree-of-freedom nonlinear system.
2. The direct obstacle avoidance tracking control method based on the switching strategy as claimed in claim 1, wherein the design process of the direct obstacle avoidance tracking control strategy based on the switching strategy comprises the following steps:
step one, aiming at a controlled object, establishing a two-degree-of-freedom nonlinear system state space model, simplifying the two-degree-of-freedom nonlinear system as a system, and respectively using x as four state variables in the system1,x2,x3,x4Is represented by the formula (I) in which x1And x2Respectively representing the system x-axis position and velocity, x3And x4Respectively representing the y-axis position and the speed of the system; at the same time, a system target signal (x) is givend,yd) And m obstacle coordinates (p)i,qi),i＝1,2,…,m；
Step two, defining a tracking error variable z1＝x1-xd，z2＝x2-α1，z3＝x3-ydAnd z4＝x4-α2(ii) a Wherein alpha is1,α2Representing a virtual tracking control function to be designed;
step three, designing a Lyapunov function V by using the tracking error variable defined in the step two, and solving a first derivative of the Lyapunov function V to obtain a first derivative
Figure FDA0003511000840000026
According to
Figure FDA0003511000840000027
Designing a virtual tracking control function alpha1,α2And a target tracking control strategy;
step four, defining an obstacle avoidance error variable s1,i＝x1-pi，s2,i＝x2-β1,i，s3,i＝x3-qiAnd s4,i＝x4-β2,iWherein, β1,iAnd beta2,iRepresenting a virtual obstacle avoidance control function to be designed;
step five, designing the Lyapunov function V by using the obstacle avoidance error variable defined in the step fouri(ii) a To lyapunov function ViObtaining the first derivative
Figure FDA0003511000840000028
According to
Figure FDA0003511000840000029
Designing a virtual obstacle avoidance control function beta1,i，β2,iAnd an obstacle avoidance control strategy;
and step six, designing a direct obstacle avoidance tracking control strategy based on a switching strategy according to the target tracking control strategy in the step three and the obstacle avoidance control strategy in the step five.
3. The direct obstacle avoidance tracking control method based on the switching strategy according to claim 2, wherein the lyapunov function V in step three is as follows:
Figure FDA0003511000840000021
wherein z is1＝x1-xd，z2＝x2-α1，z3＝x3-yd，z4＝x4-α2；α1,α2Representing the virtual tracking control function to be designed.
4. The direct obstacle avoidance tracking control method based on the switching strategy as claimed in claim 3, wherein the first derivative of the Lyapunov function V in step III with respect to time is as follows:
Figure FDA0003511000840000022
wherein the content of the first and second substances,
Figure FDA0003511000840000023
and
Figure FDA0003511000840000024
representing a virtual tracking control function alpha1And alpha2The first derivative of (a).
5. The direct obstacle avoidance tracking control method based on switching strategy as claimed in claim 4, wherein the method in step three is based on
Figure FDA0003511000840000025
Designed virtual tracking control function alpha1,α2And the target tracking control strategy is as follows:
α1＝-k1z1 (4)
Figure FDA0003511000840000031
α2＝-k3z3 (6)
Figure FDA0003511000840000032
wherein k is1,k2,k3,k4Is a normal number, and is,
Figure FDA0003511000840000033
and
Figure FDA0003511000840000034
representing a virtual tracking control function alpha1And alpha2The first derivative of (a).
6. The direct obstacle avoidance tracking control method based on switching strategy as claimed in claim 5, wherein the Lyapunov function V of step fiveiThe following were used:
Figure FDA0003511000840000035
wherein i is 1,2, …, m, s1,i＝x1-pi，s2,i＝x2-β1,i，s3,i＝x3-qi，s4,i＝x4-β2,i，riThe system and the obstacle (p) are represented as normal numbersi,qi) A safety distance of beta1,iAnd beta2,iAnd representing a virtual obstacle avoidance control function to be designed.
7. The direct obstacle avoidance tracking control method based on switching strategy as claimed in claim 6, wherein the Lyapunov function V of step fiveiThe first derivative with respect to time is as follows:
Figure FDA0003511000840000036
wherein the content of the first and second substances,
Figure FDA0003511000840000037
and
Figure FDA0003511000840000038
representing a virtual obstacle avoidance control function beta1,iAnd beta2,iThe first derivative of (a).
8. The direct obstacle avoidance tracking control method based on switching strategy as claimed in claim 7, wherein the virtual obstacle avoidance control function β of step five1,iAnd beta2,iAnd the obstacle avoidance control strategy is as follows:
β1,i＝c1,is1,i (10)
Figure FDA0003511000840000039
β2,i＝c3,is3,i (12)
Figure FDA00035110008400000310
wherein i is 1,2, …, m, c1,i,c2,i,c3,i,c4,iIs a normal number.
9. A storage medium, wherein at least one instruction is stored in the storage medium, and the at least one instruction is loaded and executed by a processor to implement a direct obstacle avoidance tracking control method based on a switching policy according to one of claims 1 to 8.
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