CN113885317A - Path tracking control method, system and computer readable storage medium - Google Patents

Path tracking control method, system and computer readable storage medium Download PDF

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CN113885317A
CN113885317A CN202010637988.8A CN202010637988A CN113885317A CN 113885317 A CN113885317 A CN 113885317A CN 202010637988 A CN202010637988 A CN 202010637988A CN 113885317 A CN113885317 A CN 113885317A
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function
control
state
control method
path tracking
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刘胜明
杨松岩
司秀芬
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Suzhou Agv Robot Co ltd
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators

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Abstract

The invention provides a path tracking control method, a system and a computer readable storage medium, wherein the path tracking control method is characterized by comprising the following steps: s1, establishing a kinematic model and a state space equation of the mobile robot; s2, calculating matrix coefficients according to the system state variables and control inputs; s3, establishing a Cost-Function target Function, and acquiring a state feedback controller under the condition that the target Function is minimum in a prediction period; s4, obtaining the optimal control input in the next prediction period and executing S3. The path tracking control method, the path tracking control system and the computer readable storage medium can accurately control the mobile robot.

Description

Path tracking control method, system and computer readable storage medium
Technical Field
The present invention relates to the field of technologies, and in particular, to a method and a system for path tracking control and a computer-readable storage medium.
Background
Path tracking is a key technology in the direction of unmanned vehicle research. The path tracking control method is a control method which can enable the unmanned vehicle to safely and stably run according to a preset path.
Proportional-integral-derivative control, PID control for short, is one of the earliest developed control strategies, and because of its simple algorithm, good robustness and high reliability, it is widely used in industrial process control, and so far, about 90% of control loops have PID structures.
In brief, a control deviation is formed according to a given value and an actual output value, the deviation is combined in proportion, integral and differential through linearity to form a control quantity, and a controlled object is controlled. A conventional PID controller acts as a linear controller.
When the mobile robot is controlled, the PID control is not accurate enough.
Disclosure of Invention
In view of the above, the technical problem to be solved by the present invention is to provide a method, a system and a computer readable storage medium for path tracking control, which can perform precise control on a mobile robot.
The technical scheme of the invention is realized as follows:
a path tracking control method, comprising the steps of:
s1, establishing a kinematic model and a state space equation of the mobile robot;
s2, calculating matrix coefficients according to the system state variables and control inputs;
s3, establishing a Cost-Function target Function, and acquiring a state feedback controller under the condition that the target Function is minimum in a prediction period;
s4, obtaining the optimal control input in the next prediction period and executing S3.
Preferably, in S1, the state equation of the controlled system is:
Figure RE-GDA0002922068510000021
u(t)＝K(t)x(t)
wherein x (t) represents the real-time pose of the robot, which can be represented by coordinates and angles
Figure RE-GDA0002922068510000022
u (t) represents the control amount of the robot, which is represented by the speed and angle of the steering wheel
Figure RE-GDA0002922068510000023
K (t) is a state feedback controller;
the control state equation for the system is then expressed as:
Figure RE-GDA0002922068510000024
the input quantity is
Figure RE-GDA0002922068510000025
The observed value is
Figure RE-GDA0002922068510000026
Preferably, the mobile robot steering wheel speed VwheelSteering wheel angle alphawheelThe distance L from the motion center to the steering wheel; angular velocity of vehicle body: w ═ Vwheel*sin(αwheel)/L
Vehicle body movement center speed: vcar＝w*L/tanθ＝Vwheel*cos(αwheel)
Then:
Figure RE-GDA0002922068510000027
Figure RE-GDA0002922068510000028
Figure RE-GDA0002922068510000029
to obtain
Figure RE-GDA00029220685100000210
Linearization is performed for a nonlinear system.
Will be provided with
Figure RE-GDA0002922068510000031
Are respectively paired
Figure RE-GDA0002922068510000032
And
Figure RE-GDA0002922068510000033
and performing first-order Taylor expansion to obtain matrix coefficients A and B.
Establishing a Cost-Function target Function, and solving a state feedback controller K (t) under the condition that the target Function is minimum in a prediction period; establishing a Cost-Function objective Function, and finding an optimal control Function u (t) to enable the system to be in a given state x0Transition from departure to target control end state xtfMake the system index optimal
Figure RE-GDA0002922068510000034
Wherein Q (t), R (t) are the control weights of x (t), u (t), respectively, Q (t) is a semi-positive definite matrix, and R (t) is a positive definite matrix. Substituting the formula (2) into the formula (6) to obtain
Figure RE-GDA0002922068510000035
According to the Riccati method
K(t)＝R-1(t)BT(t)P(t) (8)
AT(t)P(t)+P(t)A(t)+Q(t)-P(t)B(t)R-1(t)BT(t)P(t)＝0 (9)
The value of K (t) is related to P (t), which is an assumed quantity, and P (t) is only required to satisfy equation (9).
After P (t) is obtained, the feedback matrix K (t) for minimizing the Cost-Function objective Function can be obtained according to the formula (8). The optimal control input u (t) in the next prediction cycle is obtained by obtaining the final control amount, that is, the speed and angle of the steering wheel in the next cycle, based on the formula (2) u (t) ═ k (t) · x (t), and the procedure goes to step 3.
The invention also provides a path tracking control system, comprising:
the building unit is used for building a kinematic model and a state space equation of the mobile robot;
a calculation unit for calculating matrix coefficients from system state variables and control inputs;
the acquisition unit is used for establishing a Cost-Function target Function and acquiring the state feedback controller under the condition that the target Function is minimum in the prediction period;
and the execution unit is used for obtaining the optimal control input in the next prediction period and starting the acquisition unit.
The invention also provides a path tracking control device, which comprises a memory and a processor; the memory for storing a computer program; the processor is configured to implement the path tracking control method when executing the computer program.
The present invention also provides a computer-readable storage medium, wherein the storage medium stores a computer program, and when the computer program is executed by a processor, the computer program implements the path tracking control method.
Compared with the traditional PID control, the path tracking control method, the system and the computer readable storage medium provided by the invention adopt the idea of the optimal LQR control, so that the control is more accurate.
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Fig. 1 is a flowchart of a path tracking control method according to an embodiment of the present invention;
fig. 2 is a block diagram of a path tracking control system according to an embodiment of the present invention;
fig. 3 is a vehicle model diagram of a path tracking control method according to an embodiment of the present invention.
Detailed Description
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 only a part of the embodiments of the present invention, 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 invention.
As shown in fig. 1, an embodiment of the present invention provides a path tracking control method, including the following steps:
s101, establishing a kinematic model and a state space equation of the mobile robot;
s102, calculating matrix coefficients according to system state variables and control input;
s103, establishing a Cost-Function target Function, and acquiring a state feedback controller under the condition that the target Function is minimum in a prediction period;
and S104, obtaining the optimal control input in the next prediction period and executing S103.
Therefore, compared with the traditional PID control, the path tracking control method, the system and the computer readable storage medium provided by the embodiment of the invention adopt the idea of the optimal LQR control, so that the control is more accurate.
The embodiment of the invention comprises the following specific steps:
establishing a kinematic model of the mobile robot and a state space equation;
the state equation of the known controlled system is:
Figure RE-GDA0002922068510000051
u(t)＝K(t)x(t) (2)
wherein x (t) represents the real-time pose of the robot, which can be represented by coordinates and angles
Figure RE-GDA0002922068510000052
u (t) represents the control amount of the robot, which is represented by the speed and angle of the steering wheel
Figure RE-GDA0002922068510000053
K (t) is a state feedback controller.
The control state equation for the system can be expressed as:
Figure RE-GDA0002922068510000054
the input quantity is
Figure RE-GDA0002922068510000055
The observed value is
Figure RE-GDA0002922068510000056
Calculating matrix coefficients A (t) and B (t) from system state variables and control inputs
A known vehicle model is shown in FIG. 3; speed V of steering wheel of mobile robotwheelSteering wheel angle alphawheelThe distance L from the motion center to the steering wheel; angular velocity of vehicle body: w ═ Vwheel*sin(αwheel)/L
Vehicle body movement center speed: vcar＝w*L/tanθ＝Vwheel*cos(αwheel)
Then:
Figure RE-GDA0002922068510000061
substituting the formula (4) into the formula (1) to obtain:
Figure RE-GDA0002922068510000062
linearization of non-linear systems is required.
Will be provided with
Figure RE-GDA0002922068510000063
Are respectively paired
Figure RE-GDA0002922068510000064
And
Figure RE-GDA0002922068510000065
matrix coefficients a and B in equation (1) can be obtained by performing first-order taylor expansion.
Establishing a Cost-Function target Function, and solving a state feedback controller K (t) under the condition of minimizing the target Function in a prediction period
Establishing a Cost-Function objective Function, and finding an optimal control Function u (t) to enable the system to be in a given state x0Transition from departure to target control end state xtfMake the system index optimal
Figure RE-GDA0002922068510000066
Wherein Q (t), R (t) are the control weights of x (t), u (t), respectively, Q (t) is a semi-positive definite matrix, and R (t) is a positive definite matrix. Substituting the formula (2) into the formula (6) to obtain
Figure RE-GDA0002922068510000071
According to the Riccati method:
K(t)＝R-1(t)BT(t)P(t) (8)
AT(t)P(t)+P(t)A(t)+Q(t)-P(t)B(t)R-1(t)BT(t)P(t)＝0 (9)
the value of K (t) is related to P (t), which is an assumed quantity, and P (t) is only required to satisfy equation (9). After P (t) is obtained, the feedback matrix K (t) for minimizing the Cost-Function objective Function can be obtained according to the formula (8). The optimal control input u (t) in the next prediction cycle is obtained by obtaining the final control amount, that is, the speed and angle of the steering wheel in the next cycle, based on the formula (2) u (t) ═ k (t) · x (t), and the procedure goes to step 3.
As shown in fig. 2, the present invention further provides a path tracking control system, including:
the establishing unit 21 is used for establishing a kinematic model and a state space equation of the mobile robot;
a calculation unit 22 for calculating matrix coefficients from system state variables and control inputs;
an obtaining unit 23, configured to establish a Cost-Function target Function, and obtain a state feedback controller under a condition that the target Function is minimized within a prediction period;
and the execution unit 24 is used for obtaining the optimal control input in the next prediction period and starting the acquisition unit.
The embodiment of the invention also provides a path tracking control device, which comprises a memory and a processor; the memory for storing a computer program; the processor is configured to implement the above-mentioned path tracking control method when executing the computer program.
An embodiment of the present invention further provides a computer-readable storage medium, where a computer program is stored on the storage medium, and when the computer program is executed by a processor, the path tracking control method is implemented.
Through the above description of the embodiments, those skilled in the art will clearly understand that the present application can be implemented by software plus necessary general-purpose hardware, and certainly can also be implemented by special-purpose hardware including special-purpose integrated circuits, special-purpose CPUs, special-purpose memories, special-purpose components and the like. Generally, functions performed by computer programs can be easily implemented by corresponding hardware, and specific hardware structures for implementing the same functions may be various, such as analog circuits, digital circuits, or dedicated circuits. However, for the present application, the implementation of a software program is more preferable. Based on such understanding, the technical solutions of the present application may be substantially embodied in the form of a software product, which is stored in a readable storage medium, such as a floppy disk, a usb disk, a removable hard disk, a ROM, a RAM, a magnetic disk, or an optical disk of a computer, and includes several instructions for enabling a computer device (which may be a personal computer, a server, or a network device) to execute the method of the embodiments of the present application.
In the above embodiments, the implementation may be wholly or partially realized by software, hardware, firmware, or any combination thereof. When implemented in software, may be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. The procedures or functions according to the embodiments of the present application are all or partially generated when the computer program instructions are loaded and executed on a computer. The computer may be a general purpose computer, a special purpose computer, a network of computers, or other programmable device. The computer instructions may be stored in a computer readable storage medium or transmitted from one computer readable storage medium to another, e.g., the computer instructions may be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, Digital Subscriber Line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. A computer-readable storage medium may be any available medium that a computer can store or a data storage device, such as a server, a data center, etc., that is integrated with one or more available media. The usable medium may be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., Solid State Disk (SSD)), among others.
Finally, it is to be noted that: the above description is only a preferred embodiment of the present invention, and is only used to illustrate the technical solutions of the present invention, and not to limit the protection scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention shall fall within the protection scope of the present invention.

Claims (7)

1. A path tracking control method, comprising the steps of:
s1, establishing a kinematic model and a state space equation of the mobile robot;
s2, calculating matrix coefficients according to the system state variables and control inputs;
s3, establishing a Cost-Function target Function, and acquiring a state feedback controller under the condition that the target Function is minimum in a prediction period;
s4, obtaining the optimal control input in the next prediction period and executing S3.
2. The path-tracing control method according to claim 1, wherein in S1, the state equation of the controlled system is:
Figure FDA0002567188100000011
u(t)＝K(t)x(t)
wherein x (t) represents the real-time pose of the robot, which can be represented by coordinates and angles
Figure FDA0002567188100000012
u (t) represents the control amount of the robot, which is represented by the speed and angle of the steering wheel
Figure FDA0002567188100000013
K (t) is a state feedback controller;
the control state equation for the system is then expressed as:
Figure FDA0002567188100000014
the input quantity is
Figure FDA0002567188100000015
The observed value is
Figure FDA0002567188100000016
3. The path-tracing control method of claim 2, whereinSpeed V of steering wheel of mobile robotwheelSteering wheel angle alphawheelThe distance L from the motion center to the steering wheel; angular velocity of vehicle body: w ═ Vwheel*sin[αwheel)/L
Vehicle body movement center speed: vcar＝w*L/tanθ＝Vwheel*cos(αwheel)
Then:
Figure FDA0002567188100000021
Figure FDA0002567188100000022
Figure FDA0002567188100000023
to obtain
Figure FDA0002567188100000024
Linearizing the nonlinear system;
will be provided with
Figure FDA0002567188100000025
Are respectively paired
Figure FDA0002567188100000026
And
Figure FDA0002567188100000027
and performing first-order Taylor expansion to obtain matrix coefficients A and B.
4. The path tracking control method according to claim 2, wherein the S3 specifically includes:
establishingThe Cost-Function objective Function finds an optimal control Function u (t) to make the system from a given state x0Transition from departure to target control end state xtfThe system index is optimized;
Figure FDA0002567188100000028
wherein Q (t), R (t) are the control weights of x (t), u (t), respectively, Q (t) is a semi-positive definite matrix, R (t) is a positive definite matrix;
and calculating to obtain:
Figure FDA0002567188100000029
according to the Riccati method:
K(t)＝R-1(t)BT(t)P(t)
AT(t)P(t)+P(t)A(t)+Q(t)-P(t)B(t)R-1(t)BT(t)P(t)＝0
the feedback matrix k (t) that minimizes the Cost-Function objective Function is calculated.
5. A path tracking control system, comprising:
the building unit is used for building a kinematic model and a state space equation of the mobile robot;
a calculation unit for calculating matrix coefficients from system state variables and control inputs;
the acquisition unit is used for establishing a Cost-Function target Function and acquiring the state feedback controller under the condition that the target Function is minimum in the prediction period;
and the execution unit is used for obtaining the optimal control input in the next prediction period and starting the acquisition unit.
6. A path tracking control apparatus, comprising a memory and a processor; the memory for storing a computer program; the processor, when executing the computer program, is configured to implement the path-tracing control method according to any of claims 1-4.
7. Computer-readable storage medium, characterized in that the storage medium has stored thereon a computer program which, when being executed by a processor, carries out a path-tracing control method according to any one of claims 1-4.
CN202010637988.8A 2020-07-02 2020-07-02 Path tracking control method, system and computer readable storage medium Pending CN113885317A (en)

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