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CN112632803A - Tracking control method and device, electronic equipment and storage medium - Google Patents

Tracking control method and device, electronic equipment and storage medium Download PDF

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CN112632803A
CN112632803A CN202110035049.0A CN202110035049A CN112632803A CN 112632803 A CN112632803 A CN 112632803A CN 202110035049 A CN202110035049 A CN 202110035049A CN 112632803 A CN112632803 A CN 112632803A
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mobile robot
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赵涛
邹雪根
佃松宜
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Sichuan University
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Abstract

The embodiment of the application provides a tracking control method and device, an electronic device and a storage medium, and relates to the technical field of tracking control. The tracking control method comprises the following steps: firstly, acquiring motion parameters of a mobile robot to be processed; secondly, obtaining a state space motion model of the mobile robot to be processed according to the motion parameters; and then, performing control analysis processing on the state space motion model to obtain controller parameters of the mobile robot to be processed, and controlling the mobile robot to be processed to track a preset reference track according to the controller parameters. By the method, control analysis can be directly performed according to the motion parameters of the robot, and the problem of low tracking control efficiency caused by the fact that a tracking control method in the prior art needs a large number of model parameters which are difficult to obtain is solved.

Description

Tracking control method and device, electronic equipment and storage medium
Technical Field
The present application relates to the field of tracking control technologies, and in particular, to a tracking control method and apparatus, an electronic device, and a storage medium.
Background
The inventor researches and finds that in the prior art, a tracking control method based on a Mecanum wheel mobile robot needs a large amount of model parameters which are difficult to obtain, so that the tracking control efficiency is low.
Disclosure of Invention
In view of the above, an object of the present application is to provide a tracking control method and apparatus, an electronic device, and a storage medium, so as to solve the problems in the prior art.
In order to achieve the above purpose, the embodiment of the present application adopts the following technical solutions:
in a first aspect, the present invention provides a tracking control method, including:
acquiring motion parameters of a mobile robot to be processed;
obtaining a state space motion model of the mobile robot to be processed according to the motion parameters;
and performing control analysis processing on the state space motion model to obtain controller parameters of the mobile robot to be processed, and controlling the mobile robot to be processed to track a preset reference track according to the controller parameters.
In an optional embodiment, the motion parameters include a first motion parameter and a second motion parameter, and the step of obtaining a state space motion model of the mobile robot to be processed according to the motion parameters includes:
obtaining a kinematic model of the mobile robot to be processed according to the first motion parameter;
obtaining a dynamic model of the mobile robot to be processed according to the second motion parameter;
and carrying out fusion processing on the kinematic model and the dynamic model to obtain a state space motion model of the mobile robot to be processed.
In an alternative embodiment, the formula of the kinematic model comprises:
Figure BDA0002893883180000021
Figure BDA0002893883180000022
Figure BDA0002893883180000023
wherein,
Figure BDA0002893883180000024
representing the speed of the mobile robot to be processed under a robot coordinate system, J representing a transformation matrix,
Figure BDA0002893883180000025
representing the angular velocity of the mobile robot to be processed, r representing the radius of the wheels of the mobile robot to be processed, L1Represents the distance from the center of the mobile robot to be processed to the center of the wheel in a first direction, L2Indicating the distance from the center of the mobile robot to be processed to the center of the wheel in a second direction,
Figure BDA0002893883180000026
respectively representing the angular speeds of four wheels of the mobile robot to be processed.
In an alternative embodiment, the formula of the dynamical model comprises:
Figure BDA0002893883180000027
Figure BDA0002893883180000028
Figure BDA0002893883180000029
Figure BDA00028938831800000210
Figure BDA00028938831800000211
wherein M represents an inertia matrix of the mobile robot,
Figure BDA00028938831800000212
represents an angular acceleration of the mobile robot,
Figure BDA00028938831800000213
a friction matrix representing the mobile robot,
Figure BDA00028938831800000214
representing the angular velocity of the mobile robot to be processed, d representing an external disturbance, τ representing the torque input of the inertial matrix of the mobile robot, IMRepresenting the moment of inertia of the wheels of the mobile robot, IzRepresenting the moment of inertia of the mobile robot, r representing the radius of the wheels of the mobile robot to be processed, L1Represents the distance from the center of the mobile robot to be processed to the center of the wheel in a first direction, L2Represents the distance from the center of the mobile robot to be processed to the center of the wheel in a second direction, m represents the mass of the mobile robot, mu1、μ2、μ3、μ4Respectively representing the sliding friction coefficients between the four wheels of the mobile robot to be processed and the ground.
In an optional embodiment, the state space motion model includes at least one sub model, and the step of performing control analysis processing on the state space motion model to obtain the controller parameters of the mobile robot to be processed includes:
and aiming at each submodel, performing control analysis processing on the submodel to obtain controller parameters corresponding to the submodel.
In an optional embodiment, the tracking control method further includes:
acquiring a reference track;
and controlling the mobile robot to be processed to track the reference track according to the controller parameters to obtain a tracking track.
In a second aspect, the present invention provides a tracking control apparatus, including:
the parameter acquisition module is used for acquiring the motion parameters of the mobile robot to be processed;
the model acquisition module is used for acquiring a state space motion model of the mobile robot to be processed according to the motion parameters;
and the analysis processing module is used for controlling, analyzing and processing the state space motion model to obtain controller parameters of the mobile robot to be processed, so as to control the mobile robot to be processed to track a preset reference track according to the controller parameters.
In an optional embodiment, the motion parameters include a first motion parameter and a second motion parameter, and the model obtaining module is specifically configured to:
obtaining a kinematic model of the mobile robot to be processed according to the first motion parameter;
obtaining a dynamic model of the mobile robot to be processed according to the second motion parameter;
and carrying out fusion processing on the kinematic model and the dynamic model to obtain a state space motion model of the mobile robot to be processed.
In a third aspect, the present invention provides an electronic device comprising: a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the tracking control method according to any of the preceding embodiments when executing the program.
In a fourth aspect, the present invention provides a storage medium, where the storage medium includes a computer program, and the computer program controls, when running, an electronic device in which the storage medium is located to execute the tracking control method according to any of the foregoing embodiments.
According to the tracking control method and device, the electronic equipment and the storage medium, the state space motion model is obtained according to the motion parameters of the mobile robot to be processed, the state space motion model is analyzed to obtain the controller parameters, the mobile robot to be processed is subjected to tracking control according to the controller parameters, control analysis is directly carried out according to the motion parameters of the robot, and the problem that the tracking control efficiency is low due to the fact that a large number of model parameters which are difficult to obtain are needed in the tracking control method in the prior art is solved.
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In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are required to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained from the drawings without inventive effort.
Fig. 1 shows a block diagram of a tracking control system according to an embodiment of the present application.
Fig. 2 shows a block diagram of an electronic device according to an embodiment of the present application.
Fig. 3 shows a flowchart of a tracking control method provided in an embodiment of the present application.
Fig. 4 is a schematic coordinate diagram of a mobile robot to be processed according to an embodiment of the present application.
Fig. 5 shows another schematic flow chart of a tracking control method provided in an embodiment of the present application.
Fig. 6 shows a block diagram of a tracking control apparatus according to an embodiment of the present application.
Icon: 10-a tracking control system; 100-an electronic device; 110-a memory; 120-a processor; 130-a communication module; 200-a mobile robot to be processed; 600-a tracking control device; 610-parameter obtaining module; 620-model acquisition module; 630-analysis processing module.
Detailed Description
In recent years, an omnidirectional mobile robot has received a wide attention and application because of its high flexibility in being able to move in any direction. In order for a mobile robot to perform a predetermined task according to a given trajectory under unknown circumstances and in the presence of external disturbances, a highly accurate robust controller is critical. In other words, for the mobile robot, the rotation speed and direction of each drive motor need to be specified by the controller.
The controllers designed in the prior art all consider the physical parameters of the robot to be known, but in general, the physical parameters of the robot are unknown, which brings difficulty to the application of the controller on the robot. In fact, the unknown physical parameters become an obstacle in the initial modeling phase.
It is very necessary to model the mobile robot before designing the controller. When modeling, there can be two difficulties. Firstly, model data such as rotational inertia and motor armature resistance are difficult to obtain, and the data are often changed in the motion process of the robot; secondly, the external disturbance is mainly the friction force reflected on the robot, and at present, a sufficiently accurate expression model is lacked. Fortunately, learning models such as neural networks and fuzzy systems can effectively solve the problem of such unknown models. The difference between the two is that the fuzzy system has an explicit rule-based reasoning mechanism and can incorporate the knowledge and experience of human experts. On a complete fuzzy set, the fuzzy system has the capability of approximating any nonlinear model with any precision, so that the fuzzy system is feasible for expressing real-time changing models and models which cannot be accurately modeled, and the problem that the controller excessively depends on the physical parameters of the mobile robot can be solved. Fuzzy systems are also used to express complex known functions in addition to unknown functions to simplify the analysis and computation of the system.
In a type of fuzzy system, the degree of membership of an input to a fuzzy set is deterministic, but the input may be noisy, meaning that the degree of membership of an input to a fuzzy set should be an interval rather than an exact number. Therefore, in order to deal with uncertainty of membership and achieve higher approximation accuracy, an interval type two fuzzy system is developed. Accordingly, it requires a larger amount of computation and a reduction algorithm as a cost.
None of the prior art controllers take into account the time required to reach steady state during control. The most interesting issue in analyzing and designing algorithms is still the stability of the controller. The most common method of analyzing control system stability is the lyapunov second method. However, the lyapunov second method can only guarantee that the system is stable when the time t approaches infinity. In fact, a concern with control systems is stability over a limited time. At present, for the Mecanum wheel mobile robot, a related scheme capable of theoretically guaranteeing the tracking performance within a limited time is also lacked, and the dependence on hard-to-obtain physical parameters is still a problem.
In the application, in order to solve the problem of tracking control of a finite-time Mecanum wheel mobile robot, an adaptive interval type two fuzzy control strategy based on an inversion method is used, a finite-time stable tracking controller is designed, and parameters depended on by the controller are only the radius of a wheel of the mobile robot and the transverse and longitudinal spacing between the wheels, and the main contributions of the application can be summarized as follows:
1. in a Mecanum wheel type mobile robot system, an interval two-type fuzzy system is adopted to approximate an unknown function. Compared with a one-section fuzzy system, the interval two-section fuzzy system can process input noise and approximate an unknown function with higher precision, so that the requirement of higher tracking precision is met;
2. by taking the existing BMM model reduction algorithm and the improved BMM algorithm as reference, a new improved BMM model reduction algorithm is adopted to calculate the output of the interval type II fuzzy system;
3. based on an inversion method and a fractional exponent power Lyapunov function, the designed controller can theoretically ensure that the mobile robot reaches a stable state within a limited time;
4. compared with the existing controller, the controller provided by the application only needs three physical parameters of the mobile robot platform, which are easy to measure and are not changed in time, and the problem that the controller needs a large number of model parameters is solved.
Considering non-linear systems
Figure BDA0002893883180000071
If the initial state is set for all the systems
Figure BDA0002893883180000072
Presence of epsilon>0 and a determined time
Figure BDA0002893883180000073
So that for all t>t0+T，
Figure BDA0002893883180000074
All are true, then the balance point of the system
Figure BDA0002893883180000075
Is semi-global positive time stable (SGPFS).
Consider a system
Figure BDA0002893883180000076
If there is a smooth positive definite function
Figure BDA0002893883180000077
And c>0，0<β<1，ρ>0, this system is semi-global finite time stable (SGPFS) if the following holds:
Figure BDA0002893883180000078
bernoulli inequality: for real numbers 0 ≦ r ≦ 1, x ≧ 1, the following holds:
(1+r)r≤1+rx； (2)
for any z and xi, positive numbers μ, θ, iota, there is always the following:
Figure BDA0002893883180000079
one type of pasting system consists of three parts: fuzzy rules, fuzzy and fuzzy. The fuzzy rule consists of a plurality of the following basic fuzzy rules:
Figure BDA00028938831800000710
then y isyi；
wherein,
Figure BDA00028938831800000711
is a fuzzy set, yiIs a single value, xiAre fuzzy system input variables. Selecting a fuzzy system with a product inference engine, a single-value fuzzifier and a center average solution fuzzy, wherein the output of the designed fuzzy system is as follows:
Figure BDA00028938831800000712
wherein:
θ＝[y1，y2，…，yr]T；
η(x)＝[η1(x)，η2(x)，…，ηr(x)]T；
Figure BDA0002893883180000081
universal approximation theorem of fuzzy system: let f (x) be a continuous function defined over the complete blur set Ω, for any constant ε >0, then there is a blur system (4) that can approximate the continuous function f (x) with any small precision, i.e., such that the following holds:
supx∈Ω|f(x)-θTη(x)|≤ε； (5)
the zone-two type fuzzy system is an extension of the one type fuzzy system. The degree of membership of the input variable to the fuzzy set is no longer a certain value but an interval. The membership function of a fuzzy system of one type is a gaussian function, which has two parameters: center and variance. The membership function of the two-type fuzzy system is divided into a left Gaussian function and a right Gaussian function and has three parameters of a center, a width and a variance. The area enclosed by the left function, the right function and the coordinate axes is an uncertainty Footprint (FOU), the upper boundary of the area is an Upper Membership Function (UMF), and the lower boundary of the area is a Lower Membership Function (LMF).
The output of the interval two-type fuzzy system needs a type reduction algorithm. Referring to the BMM reduction type algorithm, another improved BMM algorithm is adopted to calculate the output of the interval type two fuzzy system, which can be expressed as:
Figure BDA0002893883180000082
wherein,
Figure BDA0002893883180000083
calculated according to the formula (4) by using the upper membership function,
Figure BDA0002893883180000084
calculated according to the formula (4) by using the lower membership function,
Figure BDA0002893883180000085
αis an adaptive parameter.
BMM method requirements
Figure BDA0002893883180000086
And
Figure BDA0002893883180000087
improve BMM method and let go
Figure BDA0002893883180000088
Must be andθare equally restricted such that
Figure BDA0002893883180000089
Further, the improved BMM method of the present application releases
Figure BDA00028938831800000810
Andαa limit where the sum is 1, that is,
Figure BDA00028938831800000811
andαthe sum is no longer limited to 1. In fact, the improved BMM method is simulated on the mobile robot, and the result shows that
Figure BDA00028938831800000812
Andαeither of which always converges to 0, i.e., the interval two-type fuzzy system using the improved BMM method is effectively equivalent to a one-type fuzzy system, so that pairs can be released
Figure BDA00028938831800000813
Andαthe limit of (2).
The defects existing in the above solutions are the results obtained after the inventor has practiced and studied carefully, so the discovery process of the above problems and the solutions proposed by the embodiments of the present application in the following description to the above problems should be the contributions made by the inventor in the invention process.
In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, 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 some embodiments of the present application, but not all embodiments. The components of the embodiments of the present application, generally described and illustrated in the figures herein, can be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present application, presented in the accompanying drawings, is not intended to limit the scope of the claimed application, but is merely representative of selected embodiments of the application. 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.
It is to be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.
It should be noted that the features of the embodiments of the present application may be combined with each other without conflict.
FIG. 1 is a schematic diagram of exemplary hardware and software components of a tracking control system 10 that may implement the concepts of the present application, according to some embodiments of the present application. The tracking control system 10 may include an electronic device 100 and a mobile robot 200 to be processed, which are communicatively connected.
The electronic device 100 may obtain a motion parameter of the mobile robot 200 to be processed, and obtain a controller parameter of the mobile robot 200 to be processed according to the motion parameter, so as to control the mobile robot 200 to be processed to track a preset reference trajectory according to the controller parameter.
Optionally, the electronic device 100 may be a part of the mobile robot 200 to be processed, or may be a control terminal of the mobile robot 200 to be processed, and specifically may be any one or more of a remote controller, a smart phone, a tablet computer, a laptop computer, a ground station, and a wearable device (watch, bracelet). The mobile robot 200 to be processed may be a four-wheeled mecanum wheel type omnidirectional mobile robot.
Referring to fig. 2, which is a block diagram of an electronic device 100 according to an embodiment of the present disclosure, the electronic device 100 includes a memory 110, a processor 120, and a communication module 130. The memory 110, the processor 120, and the communication module 130 are electrically connected to each other directly or indirectly to enable data transmission or interaction. For example, the components may be electrically connected to each other via one or more communication buses or signal lines.
The memory 110 is used to store programs or data. The Memory 110 may be, but is not limited to, a Random Access Memory (RAM), a Read Only Memory (ROM), a Programmable Read-Only Memory (PROM), an Erasable Read-Only Memory (EPROM), an electrically Erasable Read-Only Memory (EEPROM), and the like.
The processor 120 is used to read/write data or programs stored in the memory 110 and perform corresponding functions. The communication module 130 is used for establishing a communication connection between the electronic device 100 and another communication terminal through a network, and for transceiving data through the network.
It should be understood that the configuration shown in fig. 2 is merely a schematic diagram of the configuration of the electronic device 100, and that the electronic device 100 may include more or fewer components than shown in fig. 2, or have a different configuration than shown in fig. 2. The components shown in fig. 2 may be implemented in hardware, software, or a combination thereof.
Referring to fig. 3, a flowchart of a tracking control method according to an embodiment of the present application may be executed by the electronic device 100 in fig. 2, for example, may be executed by the processor 120 in the electronic device 100. It should be understood that, in other embodiments, the order of some steps in the tracking control method of the present embodiment may be interchanged according to actual needs, or some steps may be omitted or deleted. The following describes in detail the flow of the tracking control method shown in fig. 3.
In step S310, the motion parameters of the mobile robot 200 to be processed are acquired.
Step S320, obtaining a state space motion model of the mobile robot 200 to be processed according to the motion parameters.
Step S330, performing control analysis processing on the state space motion model to obtain a controller parameter of the mobile robot 200 to be processed, so as to control the mobile robot 200 to be processed to track a preset reference trajectory according to the controller parameter.
According to the method, the state space motion model is obtained according to the motion parameters of the mobile robot to be processed, the state space motion model is analyzed to obtain the controller parameters, and the mobile robot to be processed is subjected to tracking control according to the controller parameters, so that the control analysis is directly carried out according to the motion parameters of the robot, and the problem of low tracking control efficiency caused by the fact that a large amount of model parameters which are difficult to obtain are needed in a tracking control method in the prior art is solved.
In step S310, the four-wheel mecanum wheel mobile robot has two wheel mounting methods, i.e., X-type and O-type. The two installation modes are in a mathematical motion model, have the same numerical value and different positive and negative values, and the embodiment of the application takes X type as an example for analysis.
The relation between the mobile robot coordinate system and the global coordinate system is shown in figure 4,
Figure BDA0002893883180000111
respectively representing the rotation speeds of four wheels of the robot, theta represents a robot coordinate system xroryrThe included angle between the coordinate system xoy and the world coordinate system xoy is expressed by a mathematical formula as follows:
Figure BDA0002893883180000112
Figure BDA0002893883180000113
wherein,
Figure BDA0002893883180000114
represents the velocity of the mobile robot 200 to be processed under the robot coordinate system, R (theta) represents the rotation matrix of the robot coordinate system and the global coordinate system,
Figure BDA0002893883180000115
represents the velocity of the mobile robot 200 to be processed in the global coordinate system.
For step S320, it should be noted that the specific manner of obtaining the state space motion model is not limited, and may be set according to the actual application requirement. For example, in an alternative example, the motion parameters include a first motion parameter and a second motion parameter, and the step S320 may include a step of obtaining a state space motion model through a fusion process. Therefore, on the basis of fig. 3, fig. 5 is a schematic flowchart of another data processing method provided in the embodiment of the present application, and referring to fig. 5, step S320 may include:
step S321, a kinematic model of the mobile robot 200 to be processed is obtained according to the first motion parameter.
In detail, the first motion parameters may include a radius of the wheel of the mobile robot 200 to be processed, a distance from the center of the mobile robot 200 to be processed to the center of the wheel in a first direction, a distance from the center of the mobile robot 200 to be processed to the center of the wheel in a second direction, and angular velocities of four wheels of the mobile robot 200 to be processed.
Figure BDA0002893883180000121
The speed of the robot in the x, y, theta directions in the global coordinate system can be represented, i.e. the linear speed in the x direction, the linear speed in the y direction, and the angular speed of the robot rotating around the origin o of the global coordinate system. From fig. 4, a kinematic model of the mobile robot in a global coordinate system can be obtained:
Figure BDA0002893883180000122
wherein,
Figure BDA0002893883180000123
denotes x in the robot coordinate systemr，yr，θrSpeed of the robot in the direction, i.e. xrSpeed in the direction, yrSpeed in direction and robot around its center orThe angular speed of the rotation is such that,
Figure BDA0002893883180000124
a vector representing the angular velocity of the four wheels of the robot.
Figure BDA0002893883180000125
J represents xroryrRobot under coordinate system
Figure BDA0002893883180000126
To
Figure BDA0002893883180000127
R denotes the radius of the wheel, L1And L2Respectively, the center of the robot system to the center of the wheel at xrAnd yrThe distance in the direction.
Step S322, a dynamic model of the mobile robot 200 to be processed is obtained according to the second motion parameter.
In detail, the second motion parameters may include an angular velocity of the mobile robot 200 to be processed, a moment of inertia of wheels of the mobile robot, a moment of inertia of the mobile robot, a mass of the mobile robot, and a coefficient of sliding friction between four wheels of the mobile robot 200 to be processed and the ground.
The kinetic model of the robot can be obtained by lagrangian kinetic equations:
Figure BDA0002893883180000131
Figure BDA0002893883180000132
Figure BDA0002893883180000133
Figure BDA0002893883180000134
Figure BDA0002893883180000135
wherein M represents an inertia matrix of the mobile robot,
Figure BDA0002893883180000136
represents the angular acceleration of the mobile robot,
Figure BDA0002893883180000137
a friction matrix representing the mobile robot,
Figure BDA0002893883180000138
denotes an angular velocity of the mobile robot 200 to be processed, d denotes an external disturbance, and τ ═ τ1，τ2，τ3，τ4]TRepresenting the torque input of four wheels of the robot, IzRepresents the moment of inertia of the robot, IMRepresenting the moment of inertia of the wheels, m representing the mass of the robot,
Figure BDA0002893883180000139
representing the friction matrix, mu, of the mobile robot1、μ2、μ3、μ4Respectively, the coefficients of sliding friction between the four wheels and the ground.
Step S323, a fusion process is performed on the kinematic model and the dynamic model to obtain a state space motion model of the mobile robot 200 to be processed.
In detail, in order to unify the kinematic equation and the kinetic equation, the transformation matrix J needs to be inverted. However, J is not a square matrix, and there is no inverse in a general form, and only a generalized inverse of J can be used. Obviously, the full rank of J rows can obtain the right inverse matrix of J through generalized inverse operation:
J·J+＝I； (11)
Figure BDA0002893883180000141
thus, there are:
Figure BDA0002893883180000142
combining equations (7) to (12), it is possible to obtain:
Figure BDA0002893883180000143
wherein,
Figure BDA0002893883180000144
to represent
Figure BDA0002893883180000145
The derivative of (a), i.e. the second derivative of q,
Figure BDA0002893883180000146
represents linear accelerations of the mobile robot 200 to be processed in the x, y directions. If the physical parameters of all the electric machines are considered to be the same, the relationship between the torque input to the wheels and the voltage input to the electric machines can be expressed as:
Figure BDA0002893883180000147
wherein, JmRepresenting the moment of inertia, k, of the motor shaftaRepresenting the motor torque constant, kbRepresenting the back-emf constant, R, of the motoraRepresenting armature resistance, kvRepresenting the viscous friction coefficient, r, of the machineeRepresents the motor reduction ratio, and u represents the armature voltage. Bringing (14) into (13) can result in:
Figure BDA0002893883180000148
wherein, I4×4Representing an identity matrix of size 4 x 4, it can be seen that (13) and (15) are formally consistent in potential. For better simulation, a relatively simple equation (13) will be analyzed below.
Computer simulation of control systems is usually performed using a fourth-order longge-kutta method. Therefore, the simulation needs to satisfy the convergence condition of the Runge-Kutta method, i.e. there is a maximum limit condition for the simulation step size. If the step size is too large, the calculation results of the Runge-Kutta method diverge. If (15) is applied to the simulation, the step size needs to be set to 0.001s, which makes the simulation very time consuming. If (13) is used, the step size need only be 0.01 s. On the other hand, accurate parameters of the driving motor of the mobile robot are difficult to obtain and difficult to simulate. Since (13) and (15) are consistent in form, it is possible to analyze (13) which is relatively simple.
First, the torque input tau of the four wheat wheels can be converted into the torque input in the x, y and theta directions under the global coordinate system
Figure BDA0002893883180000151
And multiplying R on both sides of the equation of equation (13)-1(θ)JM-1Here, it can be known through simple analysis that the matrices M and R (θ) are invertible, and equation (13) can be rewritten as:
Figure BDA0002893883180000152
Figure BDA0002893883180000153
G(θ)＝R(θ)-1JM-1J+R(θ)；
Figure BDA0002893883180000154
Figure BDA0002893883180000155
it can be calculated that:
Figure BDA0002893883180000156
Figure BDA0002893883180000157
Figure BDA0002893883180000158
Figure BDA0002893883180000159
Figure BDA00028938831800001510
Figure BDA00028938831800001511
Figure BDA00028938831800001512
Figure BDA00028938831800001513
Figure BDA00028938831800001514
Figure BDA00028938831800001515
let x be according to equations (16) and (17)1＝x，x2＝y，x3＝θ，
Figure BDA00028938831800001516
The state space model can be written:
Figure BDA0002893883180000161
Figure BDA0002893883180000162
Figure BDA0002893883180000163
for step S330, it should be noted that the specific way of performing the control analysis processing is not limited, and may be set according to the actual application requirement. For example, in an alternative example, where the state space motion model includes at least one sub-model, step S330 may include the sub-steps of:
and aiming at each submodel, performing control analysis processing on the submodel to obtain controller parameters corresponding to the submodel.
In detail, observing the state space model (18), it can be known that the state space motion model comprises at least one sub-model, that is, the robot system can be divided into 3 sub-systems,
Figure BDA0002893883180000164
and
Figure BDA0002893883180000165
the system is formed into a subsystem,
Figure BDA0002893883180000166
and
Figure BDA0002893883180000167
Figure BDA0002893883180000168
and
Figure BDA0002893883180000169
two other subsystems are formed. Here only to
Figure BDA00028938831800001610
And
Figure BDA00028938831800001611
the composed subsystem (19) is used for control analysis, a fuzzy self-adaptive controller based on an inversion method is designed, and the other two subsystems are analyzed similarly.
Figure BDA00028938831800001612
For the subsystem (19), a reference trajectory x is given1dDesign control rate
Figure BDA00028938831800001613
So as to be treatedTracking trajectory x of mobile robot 2001Is able to track x with as little error as possible1d。
For an omnidirectional mobile robotic system (19), the controller (28) and adaptive laws (32) may ensure that all signals in the closed loop system (19) are bounded and that the tracking error may converge near the origin.
Let z1＝x1-x1d，z4＝x4-v4，v4Is a first step of virtual control input, x1dIs x1I.e. the reference trajectory in the x-direction in the global coordinate system.
The first step is as follows: design the following Lyapunov function V1(0<r1<1)：
Figure BDA0002893883180000171
To V1And (5) derivation to obtain:
Figure BDA0002893883180000172
the virtual input is designed as follows:
Figure BDA0002893883180000173
wherein, c1And r1Representing a controller parameter.
Thus:
Figure BDA0002893883180000174
the second step is that: consider the following Lyapunov function V4(0<r4<1)：
Figure BDA0002893883180000175
Figure BDA0002893883180000176
Figure BDA0002893883180000177
Figure BDA0002893883180000178
Figure BDA0002893883180000179
Wherein,
Figure BDA00028938831800001710
is that
Figure BDA00028938831800001711
Is determined by the estimated value of (c),
Figure BDA00028938831800001712
is that
Figure BDA00028938831800001713
Is determined by the estimated value of (c),
Figure BDA00028938831800001714
is that
Figure BDA00028938831800001715
Is determined by the estimated value of (c),
Figure BDA00028938831800001716
is that
Figure BDA00028938831800001717
Is determined by the estimated value of (c),
Figure BDA00028938831800001718
and
Figure BDA00028938831800001719
the specific meaning of (c) will be explained in equation (26).
To V4And (5) derivation to obtain:
Figure BDA00028938831800001720
Figure BDA0002893883180000181
wherein,
Figure BDA0002893883180000182
to represent
Figure BDA0002893883180000183
The adaptive rate parameter of (a) is,λto represent
Figure BDA0002893883180000184
The adaptive rate parameter of (a) is,
Figure BDA0002893883180000185
to represent
Figure BDA0002893883180000186
The adaptive rate parameter of (a) is,λ αto represent
Figure BDA0002893883180000187
The adaptive rate parameter of (2).
Approximated by a zone two-type fuzzy system (26):
Figure BDA0002893883180000188
obtaining:
Figure BDA0002893883180000189
wherein,
Figure BDA00028938831800001810
denotes x1，x4The membership function of the two-type fuzzy system in the subsystem corresponds to the activation strength of the fuzzy rule,
Figure BDA00028938831800001811
denotes x1，x4The activation strength of the membership function corresponding to the fuzzy rule under the two-type fuzzy system in the subsystem,
Figure BDA00028938831800001812
denotes x1，x4The membership function of the two-type fuzzy system in the subsystem corresponds to the output fuzzy set center of the fuzzy rule,
Figure BDA00028938831800001813
denotes x1，x4In the subsystem, the membership function under the two-type interval fuzzy system corresponds to the output fuzzy set center of the fuzzy rule,
Figure BDA00028938831800001814
denotes x1，x4The membership function of the two-type fuzzy system in the subsystem corresponds to the output weighting parameter of the fuzzy system,
Figure BDA00028938831800001815
denotes x1，x4And the membership function in the two-type fuzzy system in the subsystem corresponds to the output weighting parameter of the fuzzy system.
Then (25) can be written as:
Figure BDA00028938831800001816
approximation error of interval two-type fuzzy system
Figure BDA00028938831800001817
And estimation error
Figure BDA00028938831800001818
And external disturbances
Figure BDA00028938831800001819
Are bounded. The controller can be designed as follows:
Figure BDA0002893883180000191
then:
Figure BDA0002893883180000192
wherein, c4And r4Representing a controller parameter.
The estimation error of the interval type two fuzzy system in brackets of formula (29) can be written as:
Figure BDA0002893883180000193
then, it is possible to obtain:
Figure BDA0002893883180000194
Figure BDA0002893883180000201
designing an adaptive rate:
Figure BDA0002893883180000202
wherein,
Figure BDA0002893883180000203
to represent
Figure BDA0002893883180000204
The adaptive rate parameter of (a) is,γto represent
Figure BDA0002893883180000205
The adaptive rate parameter of (a) is,
Figure BDA0002893883180000206
to represent
Figure BDA0002893883180000207
The adaptive rate parameter of (a) is,γ αto represent
Figure BDA0002893883180000208
The adaptive rate parameter of (2).
Further, consider two more subsystems in (18). The virtual inputs of the other two subsystems can be written directly according to equation (22):
Figure BDA0002893883180000209
z2＝x2-x2d；
z3＝x3-x3d；
wherein x is2d，x3dAre each x2，x3The expected value of (a) is the reference trajectory.
According to the formula (26), an expression of approximating an unknown function by an interval two-type fuzzy system in the other two subsystems can be obtained:
Figure BDA00028938831800002010
according to the controller (28), the controllers of the other two subsystems can be written directly:
Figure BDA0002893883180000211
z5＝x5-v5；
z6＝x6-v6；
from the adaptation rate (32), the adaptation rates of the other two subsystems can be written:
Figure BDA0002893883180000212
it is noted that all three subsystems in the system (18) share a group
Figure BDA0002893883180000213
And (4) parameters. The resulting torque inputs for the four wheels of the robot are:
Figure BDA0002893883180000214
wherein e isf，4，
Figure BDA0002893883180000215
Are bounded, i.e. there is a constant s>0, such that:
Figure BDA0002893883180000216
according to the Yang inequality:
Figure BDA0002893883180000221
substituting (32), (38) to (31), applying (39) to (31), can result in:
Figure BDA0002893883180000222
according to the bernoulli inequality:
Figure BDA0002893883180000223
order to
Figure BDA0002893883180000224
Applying (41) to (40), then (40) can be written as:
Figure BDA0002893883180000225
order to
Figure BDA0002893883180000226
Obtaining:
Figure BDA0002893883180000227
at 0< β <1, the following formula can be obtained:
Figure BDA0002893883180000228
order to
Figure BDA0002893883180000231
Can be written as
Figure BDA0002893883180000232
Bringing (46) into (44):
Figure BDA0002893883180000233
order to
Figure BDA0002893883180000234
Obtaining:
Figure BDA0002893883180000235
(48) it can be shown that the system (19) can be stabilized for a limited time by the controller (28) and the adaptation law (32). From the derivation procedures of (44) to (48), we can always follow; (44) thus, a result (48) was obtained. In other words, (44) can also be considered as a criterion of finite time stability. A system; (18) the other two of x2，x5And x3，x6The stability of the constituent subsystems can be demonstrated with reference to the above methods.
For an omnidirectional mobile robotic system (18), the controllers (28) and (35) and the adaptive laws (32) and (36) may ensure that all signals in the closed loop system (18) are bounded and that the tracking error may converge near the origin.
After step S330, it should be noted that, the embodiment of the present application may further include a step of controlling the mobile robot 200 to be processed according to the controller parameter, and therefore, the tracking control method may further include the following sub-steps:
acquiring a reference track;
and controlling the mobile robot 200 to be processed to track the reference track according to the controller parameters to obtain a tracking track.
In detail, for an actual robot system, one robot is placed at an initial location, and a target location may be specified within a program or in the ROS operating system rviz interface on the electronic device 100. The initial position of the robot defaults to 0, i.e., the origin of coordinates, and if the initial position is not at the origin of coordinates, initial position correction is required.
After the target point is set, the robot calls a path planning algorithm to plan a reference path, which can be an expected coordinate point of the next control cycle or an expected coordinate point of several control cycles in the future. The robot calculates the deviation z according to the coordinate point where the robot is located and the expected coordinate point of the next control period1，z2，z3，z4，z5，z6And virtual input v4，v5，v6The output of the tracking controller is calculated according to equations (28) and (35). The output is sent to the robot, and the robot generates action according to the output and moves to the target point until the path planning part considers that the robot reaches the target point. That is, after the target point is set, a planned path process may be performed to obtain a reference trajectory, a deviation between the current position and the reference trajectory may be calculated, an output of the tracking controller may be calculated according to the deviation, and the robot may be controlled to move to the target point according to the output.
The model data and controller parameters used in the tracking are shown in table 1, and the interval two-type fuzzy and the interval one-type fuzzy can be respectively tested.
TABLE 1 model parameters and controller parameters
Figure BDA0002893883180000241
The experimental result shows that the designed controller can enable the mobile robot to track the reference track, and the track tracking precision designed based on the interval two-type fuzzy system can reach 10-3An order of magnitude. From the view of track tracking error, the precision of the interval two-type fuzzy system is superior to that of the interval one-type fuzzy system, and the requirement of higher precision can be met. It is worth mentioning that a one-type blurring system is more gradual during the transition. Perturbation sin (5t) is added according to the experimental results, in the x, y, theta directions. According to the experimental result, the designed controller can well restrain the disturbance and well complete the track tracking task.
By the method, the interval two-mode fuzzy adaptive controller with stable limited time is designed for the X-type four-Mecanum wheel mobile robot. The particular lyapunov function is chosen, as shown at (20), to avoid singularities with its derivative near the origin. The results obtained using the modified BMM reduction algorithm do not differ much from the results obtained using the one-type fuzzy, so another modified BMM reduction algorithm is used to calculate the output of the interval two-type fuzzy system.
The effectiveness of the type reduction algorithm is verified through experimental results. The controller is designed to use only three easily measurable parameters, namely the length, width and wheel radius of the robot, without other parameters that need to be obtained through complicated experimentation or special equipment, and thus has wide applicability. Further, a disturbance observer can be designed to compensate for the disturbance d, which will help to further improve the tracking accuracy.
That is to say, in the embodiment of the application, for the problem of trajectory tracking of a four-wheel mecanum wheel type omnidirectional mobile robot, a fractional exponential power lyapunov function is selected, and a finite time interval binary fuzzy adaptive controller is designed through an inversion method. An interval two-type fuzzy approximator is used for approximating a dynamic model of the mobile robot, and a reduction algorithm is an improved BMM algorithm. The proposed controller relies only on easily measured and time-invariant parameters: the spacing and radius of the four wheels, and thus the wide applicability, demonstrates the stability of the designed controller over a limited time using semi-global finite time stability theory.
With reference to fig. 6, an embodiment of the present application further provides a tracking control apparatus 600, where the functions implemented by the tracking control apparatus 600 correspond to the steps executed by the foregoing method. The tracking control apparatus 600 may be understood as the processor 120 of the electronic device 100, or may be understood as a component that is independent of the electronic device 100 or the processor 120 and implements the functions of the present application under the control of the electronic device 100. The tracking control apparatus 600 may include a parameter obtaining module 610, a model obtaining module 620, and an analysis processing module 630, among others.
A parameter obtaining module 610, configured to obtain motion parameters of the mobile robot 200 to be processed. In the embodiment of the present application, the parameter obtaining module 610 may be configured to perform step S310 shown in fig. 3, and for the relevant content of the parameter obtaining module 610, reference may be made to the foregoing detailed description of step S310.
And a model obtaining module 620, configured to obtain a state space motion model of the mobile robot 200 to be processed according to the motion parameters. In this embodiment of the application, the model obtaining module 620 may be configured to perform step S320 shown in fig. 3, and reference may be made to the foregoing detailed description of step S320 for relevant contents of the model obtaining module 620.
The analysis processing module 630 is configured to perform control analysis processing on the state space motion model to obtain a controller parameter of the mobile robot 200 to be processed, so as to control the mobile robot 200 to be processed to track a preset reference trajectory according to the controller parameter. In the embodiment of the present application, the analysis processing module 630 may be configured to execute step S330 shown in fig. 3, and for the relevant content of the analysis processing module 630, reference may be made to the foregoing detailed description of step S330.
Further, when the motion parameters include a first motion parameter and a second motion parameter, the model obtaining module is specifically configured to:
obtaining a kinematic model of the mobile robot to be processed according to the first motion parameter;
obtaining a dynamic model of the mobile robot to be processed according to the second motion parameter;
and carrying out fusion processing on the kinematic model and the dynamic model to obtain a state space motion model of the mobile robot to be processed.
Furthermore, an embodiment of the present application further provides a computer-readable storage medium, where a computer program is stored on the computer-readable storage medium, and the computer program is executed by the processor 120 to perform the steps of the tracking control method.
The computer program product of the tracking control method provided in the embodiment of the present application includes a computer-readable storage medium storing a program code, where instructions included in the program code may be used to execute steps of the tracking control method in the above method embodiment, which may be referred to specifically in the above method embodiment, and details are not described here again.
In summary, the tracking control method and apparatus, the electronic device, and the storage medium provided in the embodiments of the present application obtain the state space motion model according to the motion parameters of the mobile robot to be processed, analyze the state space motion model to obtain the controller parameters, and perform tracking control on the mobile robot to be processed according to the controller parameters, so that control analysis is directly performed according to the motion parameters of the robot, and a problem of low tracking control efficiency caused by a large number of model parameters that are difficult to obtain in the tracking control method in the prior art is solved.
In the embodiments provided in the present application, it should be understood that the disclosed apparatus and method may be implemented in other ways. The apparatus embodiments described above are merely illustrative, and for example, the flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of apparatus, methods and computer program products according to embodiments of the present application. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
In addition, functional modules in the embodiments of the present application may be integrated together to form an independent part, or each module may exist separately, or two or more modules may be integrated to form an independent part.
The functions, if implemented in the form of software functional modules and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present application or portions thereof that substantially contribute to the prior art may be embodied in the form of a software product stored in a storage medium and including instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present application. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
The above description is only a preferred embodiment of the present application and is not intended to limit the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims (10)

1. A tracking control method, comprising:
acquiring motion parameters of a mobile robot to be processed;
obtaining a state space motion model of the mobile robot to be processed according to the motion parameters;
and performing control analysis processing on the state space motion model to obtain controller parameters of the mobile robot to be processed, and controlling the mobile robot to be processed to track a preset reference track according to the controller parameters.
2. The tracking control method according to claim 1, wherein the motion parameters include a first motion parameter and a second motion parameter, and the step of obtaining the state space motion model of the mobile robot to be processed based on the motion parameters includes:
obtaining a kinematic model of the mobile robot to be processed according to the first motion parameter;
obtaining a dynamic model of the mobile robot to be processed according to the second motion parameter;
and carrying out fusion processing on the kinematic model and the dynamic model to obtain a state space motion model of the mobile robot to be processed.
3. The tracking control method according to claim 2, wherein the formula of the kinematic model includes:
Figure FDA0002893883170000011
Figure FDA0002893883170000012
Figure FDA0002893883170000013
wherein,
Figure FDA0002893883170000014
representing the speed of the mobile robot to be processed under a robot coordinate system, J representing a transformation matrix,
Figure FDA0002893883170000015
representing the angular velocity of the mobile robot to be processed, r representing the radius of the wheels of the mobile robot to be processed, L1Represents the distance from the center of the mobile robot to be processed to the center of the wheel in a first direction, L2Indicating the distance from the center of the mobile robot to be processed to the center of the wheel in a second direction,
Figure FDA0002893883170000016
respectively representing the angular speeds of four wheels of the mobile robot to be processed.
4. The tracking control method according to claim 2, wherein the formula of the kinetic model includes:
Figure FDA0002893883170000021
Figure FDA0002893883170000022
Figure FDA0002893883170000023
Figure FDA0002893883170000024
Figure FDA0002893883170000025
wherein M represents an inertia matrix of the mobile robot,
Figure FDA0002893883170000026
represents an angular acceleration of the mobile robot,
Figure FDA0002893883170000027
a friction matrix representing the mobile robot,
Figure FDA0002893883170000028
representing the angular velocity of the mobile robot to be processed, d representing an external disturbance, τ representing the torque input of the inertial matrix of the mobile robot, IMRepresenting the moment of inertia of the wheels of the mobile robot, IzRepresenting the moment of inertia of the mobile robot, r representing the radius of the wheels of the mobile robot to be processed, L1Represents the distance from the center of the mobile robot to be processed to the center of the wheel in a first direction, L2Represents the distance from the center of the mobile robot to be processed to the center of the wheel in a second direction, m represents the mass of the mobile robot, mu1、μ2、μ3、μ4Respectively representing the sliding friction coefficients between the four wheels of the mobile robot to be processed and the ground.
5. The tracking control method according to claim 1, wherein the state space motion model comprises at least one sub-model, and the step of performing control analysis processing on the state space motion model to obtain the controller parameters of the mobile robot to be processed comprises:
and aiming at each submodel, performing control analysis processing on the submodel to obtain controller parameters corresponding to the submodel.
6. The tracking control method according to any one of claims 1 to 5, characterized in that the tracking control method further comprises:
acquiring a reference track;
and controlling the mobile robot to be processed to track the reference track according to the controller parameters to obtain a tracking track.
7. A tracking control apparatus, characterized by comprising:
the parameter acquisition module is used for acquiring the motion parameters of the mobile robot to be processed;
the model acquisition module is used for acquiring a state space motion model of the mobile robot to be processed according to the motion parameters;
and the analysis processing module is used for controlling, analyzing and processing the state space motion model to obtain controller parameters of the mobile robot to be processed, so as to control the mobile robot to be processed to track a preset reference track according to the controller parameters.
8. The tracking control device of claim 7, wherein the motion parameters include a first motion parameter and a second motion parameter, the model acquisition module being specifically configured to:
obtaining a kinematic model of the mobile robot to be processed according to the first motion parameter;
obtaining a dynamic model of the mobile robot to be processed according to the second motion parameter;
and carrying out fusion processing on the kinematic model and the dynamic model to obtain a state space motion model of the mobile robot to be processed.
9. An electronic device, comprising: memory, processor and computer program stored on the memory and executable on the processor, which when executed by the processor implements the tracking control method of any of claims 1 to 6.
10. A storage medium, characterized in that the storage medium comprises a computer program, which when executed controls an electronic device in which the storage medium is located to perform the tracking control method according to any one of claims 1 to 6.
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