CN116276965A - Fixed time track tracking control method for mechanical arm based on nonsingular terminal sliding mode - Google Patents
Fixed time track tracking control method for mechanical arm based on nonsingular terminal sliding mode Download PDFInfo
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Abstract
The application is applicable to the technical field of track tracking, and provides a fixed time track tracking control method of a mechanical arm based on a nonsingular terminal sliding mode, which comprises the following steps: establishing a dynamic model of the mechanical arm with uncertainty based on data of an expected track of a joint of the mechanical arm designed in advance; acquiring real-time track data of joints of the mechanical arm based on a dynamics model; determining a sliding mode signal based on the data of the expected track and the real-time track data; based on a dynamics model, constructing a radial basis function neural network, and determining a weight update law of a weight vector of the radial basis function neural network by using a projection method; and applying the self-adaptive updating law of the sliding mode signal and the weight vector of the radial basis function neural network to a controller of the mechanical arm to obtain a tracking expected track of the joint of the mechanical arm at fixed time. According to the method, the uncertainty of the model parameters of the estimated mechanical arm and the accuracy of external interference can be improved under various complex scenes.
Description
Technical Field
The application belongs to the technical field of track tracking, and particularly relates to a fixed time track tracking control method of a mechanical arm based on a nonsingular terminal sliding mode.
Background
The robot arm can assist or replace people to perform tasks accurately and effectively in extreme situations, particularly in semiconductor devices, where the robot arm plays an important role. Because the steps of the semiconductor equipment are complicated in the production process, the requirement on precision is high, and the mechanical arm can accurately move according to the joint track set in advance, so that the key for realizing the complex tasks is realized. However, as the physical parameters of the mechanical arm can be changed along with the changes of the load, the external disturbance and the motion characteristics, uncertainty exists, the model parameter uncertainty and the external disturbance of the mechanical arm can be accurately estimated through an advanced control method, and the mechanical arm can quickly and accurately track the expected track, so that the mechanical arm has very important practical significance.
In recent years, many control strategies for nonlinear systems have been proposed, and most of these methods can take a mechanical arm as a controlled object, including PID control, robust control, fuzzy control, feedback linearization, neural network control, sliding mode control, and the like, but the above control strategies are still inaccurate for estimating model parameter uncertainty and external interference of the mechanical arm when dealing with various complex scenarios.
Disclosure of Invention
In order to overcome the problems in the related art, the embodiment of the application provides a fixed time track tracking control method of a mechanical arm based on a nonsingular terminal sliding mode, which can improve the accuracy of estimating the uncertainty of model parameters and external interference of the mechanical arm under various complex scenes.
The application is realized by the following technical scheme:
in a first aspect, an embodiment of the present application provides a method for controlling tracking of a fixed time track of a mechanical arm based on a nonsingular terminal sliding mode, including:
establishing a dynamic model of the mechanical arm with uncertainty based on data of a preset expected track of a joint of the mechanical arm;
acquiring real-time track data of joints of the mechanical arm based on a dynamics model;
determining a sliding mode signal based on the data of the expected track and the real-time track data;
based on a dynamics model, constructing a radial basis function neural network, and determining a weight update law of a weight vector of the radial basis function neural network by using a projection method;
and applying the self-adaptive updating law of the sliding mode signal and the weight vector of the radial basis function neural network to a controller of the mechanical arm to obtain a tracking expected track of the joint of the mechanical arm at fixed time.
In one possible implementation manner of the first aspect, the mechanical arm dynamics model is expressed as:
wherein q is an acceleration signal of a joint of the mechanical arm,
a second derivative of q; m is an inertia matrix of the mechanical arm; τ is the control moment; />
Is a model uncertainty composed of parameter uncertainty of the mechanical arm and external disturbance, wherein +.>
M(q)＝M 0 (q)+M Δ (q)∈R n×n ；g(q)＝g 0 (q)+g Δ (q)∈R n Is a gravity vector; />
Is a centrifugal coriolis force matrix; d E R n Is a bounded external disturbance moment.
In a possible implementation manner of the first aspect, determining the sliding mode signal based on the data of the desired trajectory and the real-time trajectory data includes:
the real-time track data of the joints of the mechanical arm and the data of the pre-designed expected track are used for obtaining an error signal;
reconstructing a dynamic model of the mechanical arm with uncertainty into a second-order system based on the error signal;
and designing a nonsingular rapid terminal sliding mode surface based on a second-order system, and constructing a sliding mode signal.
In a possible implementation manner of the first aspect, the error signal is expressed as:
wherein e 1 And e 2 As error signal x 1 (t)＝q(t)，
x d (t)＝q d (t)，/>
Is x d Q (t) is the position signal of the joints of the manipulator, +.>
Is the derivative of q (t), q d (t) a position signal taking into account external disturbance moment for a joint of the robotic arm.
In one possible implementation manner of the first aspect, the sliding mode signal is expressed as:
wherein,,
is the coefficient of the sliding mode variable, which is the sum error e 1 Related time-varying coefficients, using diagonal matrix
Indicating (I)>
Wherein i=1, 2, …, n, α, β, p, g, k is a constant, and α>0，β>0，k>1，v 1 >1, and p, g satisfies gk>1，1/v 1 <pk<1。
In a possible implementation manner of the first aspect, based on the dynamics model, constructing a radial basis function neural network, and designing an adaptive update law of a weight vector of the radial basis function neural network according to a projection method, including:
constructing a radial basis function, namely a radial basis neural network according to an approximation principle;
according to the radial basis function, determining an optimal approximation equation of the radial basis function to the nonlinear function;
selecting a Gaussian function as an activation function of the radial basis function neural network;
determining an output vector of the radial basis function after uncertainty approximation of the radial basis function to the dynamic model based on an optimal approximation equation and an activation function of the radial basis neural network;
defining an approximation error of the radial basis function on the basis of an output vector after the uncertainty of the radial basis function on the dynamic model approximates;
and determining a weight update law of a weight vector of the radial basis neural network by using a projection method based on the output vector of the radial basis function after the uncertainty of the radial basis function on the dynamic model is approximated and an approximation error of the radial basis neural network.
In a possible implementation manner of the first aspect, the output vector after the uncertainty approximation of the radial basis function to the dynamics model is expressed as:
wherein w is i ＝[w i1 ,w i2 ,…,w im ] T Is a weight vector, z i ＝[e 1i ,e 2i ] T Is an input to the neural network; sigma (sigma) i ＝[σ i1 ,σ i2 ,…,σ im ] T ∈R m Representing an activation function;
the approximation error of the radial basis neural network is expressed as:
wherein,,
representing the optimal weight vector.
In a possible implementation manner of the first aspect, determining a weight update law of a weight vector of the radial basis function neural network by using a projection method includes:
designing an update law of a weight vector of the radial basis function neural network;
correcting the update law of the weight vector of the radial basis function neural network;
the method comprises the steps of ensuring the bouncy of weight vectors by using a projection method, and determining a weight update law of the weight vectors of a final radial basis neural network; the final weight update law of the weight vector of the radial basis function neural network is expressed as:
wherein,,
ρ i and xi i Is bounded; delta is the learning rate of the neural network, delta>0; normal vector->
Satisfy->
In a possible implementation manner of the first aspect, the control moment of the controller of the mechanical arm is expressed as:
wherein M is 0 An inertial matrix of the mechanical arm; v 1 、v 2 、v 3 、v 4 Is a constant;
as coefficients of the sliding mode variable,
is two diagonal matrices; k (K) s Is a controller parameter; />
Is x d Is a second derivative of (c).
In a second aspect, the present application provides a terminal device, including a memory and a processor, where the memory stores a computer program that can run on the processor, where the processor implements the fixed time track tracking control method for a mechanical arm based on a nonsingular terminal sliding mode according to any one of the first aspects when the processor executes the computer program.
Compared with the prior art, the embodiment of the application has the beneficial effects that:
according to the embodiment of the application, the sliding mode signal and the weight updating law of the weight vector of the radial basis function neural network are combined, so that the joint motion can rapidly track the expected track under the condition that the dynamic model of the mechanical arm is uncertain, the bounty of the weight vector can be ensured, various complex scenes controlled by the mechanical arm can be dealt with, and the accuracy of estimating the model parameter uncertainty and external interference of the mechanical arm is improved.
It will be appreciated that the advantages of the second aspect may be found in the relevant description of the first aspect, and will not be described in detail herein.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure.
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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 for the embodiments or the description of the prior art will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present application, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a schematic flow chart of a fixed time track tracking control method of a mechanical arm based on a nonsingular terminal sliding mode according to an embodiment of the present application;
fig. 2 is a schematic diagram of an operation process of a fixed time track tracking control method of a mechanical arm based on a nonsingular terminal sliding mode in a system according to an embodiment of the present application;
fig. 3 is a schematic diagram of the position and speed tracking of a joint 1 of a mechanical arm of a robot according to an embodiment of the present disclosure;
fig. 4 is a schematic diagram of the position and speed tracking of the joint 2 of the mechanical arm of the robot according to an embodiment of the present disclosure;
fig. 5 is a tracking error of a joint 1 of a robot arm of a robot according to an embodiment of the present application;
fig. 6 is a tracking error of a joint 2 of a robot arm of a robot according to an embodiment of the present application;
FIG. 7 is a schematic diagram of a controller input torque provided in an embodiment of the present application;
FIG. 8 is a weight vector norm of a radial basis function neural network according to one embodiment of the present application;
fig. 9 is a schematic structural diagram of a terminal device according to an embodiment of the present application.
Detailed Description
In the following description, for purposes of explanation and not limitation, specific details are set forth, such as particular system configurations, techniques, etc. in order to provide a thorough understanding of the embodiments of the present application. It will be apparent, however, to one skilled in the art that the present application may be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present application with unnecessary detail.
It should be understood that the terms "comprises" and/or "comprising," when used in this specification and the appended claims, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
It should also be understood that the term "and/or" as used in this specification and the appended claims refers to any and all possible combinations of one or more of the associated listed items, and includes such combinations.
As used in this specification and the appended claims, the term "if" may be interpreted as "when..once" or "in response to a determination" or "in response to detection" depending on the context. Similarly, the phrase "if a determination" or "if a [ described condition or event ] is detected" may be interpreted in the context of meaning "upon determination" or "in response to determination" or "upon detection of a [ described condition or event ]" or "in response to detection of a [ described condition or event ]".
In addition, in the description of the present application and the appended claims, the terms "first," "second," "third," and the like are used merely to distinguish between descriptions and are not to be construed as indicating or implying relative importance.
The appearances of the phrases "in one embodiment," "in some embodiments," "in other embodiments," and the like in various places throughout this specification are not necessarily all referring to the same embodiment, but mean "one or more, but not all, embodiments" unless expressly specified otherwise. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless expressly specified otherwise.
In order to make the technical solution of the present invention better understood by those skilled in the art, the technical solution in the examples of the present application will be clearly and completely described below with reference to the accompanying drawings and the detailed description.
Fig. 1 is a flow chart of a fixed time track tracking control method of a mechanical arm based on a nonsingular terminal sliding mode according to an embodiment of the present application, and referring to fig. 1 and 2, the fixed time track tracking control method of the mechanical arm based on the nonsingular terminal sliding mode includes the following detailed procedures:
in step 101, a kinetic model of the mechanical arm is established based on data of a preset desired trajectory of joints of the mechanical arm.
Specifically, according to the data of the preset expected track of the joint of the mechanical arm, a dynamic model of the mechanical arm is established based on the Euler-Lagrange method, and the dynamic model of the mechanical arm is expressed as follows:
wherein,,
acceleration signals of joints of the mechanical arm; t (t) ε R n To control the moment; d (t) ∈R n Is a bounded external disturbance moment; m (q) =m 0 (q)+M Δ (q)∈R n×n Is an inertial matrix of the mechanical arm;
is a centrifugal coriolis force matrix; m is M 0 (q),/>
g 0 (q) is known, M Δ (q),/>
g Δ (q) is unknown but bounded; g (q) =g 0 (q)+g Δ (q)∈R n And (5) a gravity vector.
According to an inertia matrix M 0 (q) non-singularity, M 0 (q) is reversible, so the mechanical arm dynamics model can be expressed as:
wherein,,
for the model uncertainty composed of the parameter uncertainty of the mechanical arm and the external disturbance, +.>
The mechanical arm dynamics model uncertainty term κ generally satisfies the following conditions, including: all items of kappa are bounded and for all kappa i (i=1, 2, …, n) all satisfy
Wherein, kappa id (i=1, 2, …, n) is an unknown positive constant.
In step 102, real-time trajectory data of joints of the robotic arm is acquired based on the kinetic model.
The method includes the steps of inputting a preset expected track of a joint of the mechanical arm under the dynamic model to a controller of the mechanical arm, and acquiring real-time track data when the joint of the mechanical arm moves according to the preset expected track.
In step 103, a sliding mode signal is determined based on the data of the desired trajectory and the real-time trajectory data.
Illustratively, the modeling uncertainty κ (t) is a state-related function. In particular, the complex disturbance κ (t) in the present application is dependent on the joints of the robot's armPosition q, speed
And a torque input τ. Since the input power of the robot arm is limited by the electrical energy and the movement space of the robot is limited and continuous, the modeling uncertainty κ (t) is assumed to be bounded.
Specifically, step 103 may include: the real-time track data of the joints of the mechanical arm and the data of the pre-designed expected track are used for obtaining an error signal; reconstructing a dynamic model of the mechanical arm with uncertainty into a second-order system based on the error signal; and designing a nonsingular rapid terminal sliding mode surface based on a second-order system, and constructing a sliding mode signal.
Illustratively, the real-time state trajectory of the robot arm joint is differenced from a pre-designed desired trajectory to obtain an error signal.
Definition x 1 (t)＝q(t)，
x d (t)＝q d (t) reconstructing the mechanical arm dynamics model into a second order system:
further defining an error signal:
substituting equation (3) into (4) yields a second order system with the error signal as the state variable:
the nonsingular rapid terminal sliding mode surface is designed based on an error signal, and the sliding mode signal is expressed as:
wherein,,
is a diagonal matrix; />
Expressed as:
wherein alpha is>0，β>0，k>1，v 1 >1, and p, g satisfies gk>1，1/v 1 <pk<1。
Coefficient of sliding mode variable
Is with error e 1 Compared with the traditional nonsingular terminal sliding mode, the sliding mode variable can be quickly pulled back to the sliding mode surface s=0 when the system state error is large, so that the convergence performance of the sliding mode variable is enhanced, and the derivative of the sliding mode signal s is as follows in the formula (6):
wherein,,
is two diagonal matrices>
Expressed as:
the implementation principle of the sliding mode variable structure control in the application mainly refers to the fact that in the dynamic response process of a system, the motion trail of the system state is forcedly changed, so that the system state moves on a sliding mode surface until reaching an equilibrium point. The method is characterized by insensitivity to parameter uncertainty and external interference, strong robustness and suitability for nonlinear mechanical arm systems with high tracking precision requirements. However, the system state is easy to jump back and forth on the sliding mode surface, shake phenomenon is generated, and hardware equipment is easy to damage, so that the sliding mode variable structure control is usually combined with other technologies to restrain shake, such as a neural network, adaptive control and the like.
Compared with the traditional nonsingular terminal sliding mode, the sliding mode variable can be quickly pulled back to the sliding mode surface s=0 when the system state error is large, so that the convergence performance of the sliding mode variable is enhanced, and the picture variable meets the fixed time convergence. The fixed time stability can be easily demonstrated by a lyapunov function.
Illustratively, when
In the time-course of which the first and second contact surfaces,
the expression defining the lyapunov function is:
according to the relevant theorem that the controller design depends on the following fixed time stability theory, see formulas (27) - (29), the sliding mode variable satisfies the fixed time stability, and the error signal contained in the sliding mode variable will converge to the origin within the fixed time T, where the expression of the fixed time T is:
in step 104, a radial basis neural network is constructed based on the dynamics model, and a weight update law of a weight vector of the radial basis neural network is determined by using a projection method.
Specifically, step 104 may include:
step 1041: according to the approximation principle, a radial basis function, i.e. a radial basis neural network, is constructed.
Illustratively, in step 1041, if f (x): r is R n R is a continuous function defined on the compact set Ω, f (w, x): r is R m ×R n R is a continuous and dependent approximation function of w and x, then the key to approximation is to determine the optimal parameter w * So that the distance function d * The method meets the following conditions:
d * (f(w * ,x),f(x))≤∈ (14)
where e is an acceptably small value.
The approximation of a radial basis function to a nonlinear function can be expressed by the following equation:
wherein z is i ＝[z i1 ,z i2 ,…,z iq ] T ∈R q Representing the input vector, w i ＝[w i1 ,w i2 ,…,w im ] T ∈R m Represents weight vector, m is greater than or equal to 2 represents hidden node number, sigma i ＝[σ i1 ,σ i2 ,…,σ im ] T ∈R m Representing an activation function, f i ∈R。
Step 1042: and determining an optimal approximation equation of the radial basis function to the nonlinear function according to the radial basis function.
Illustratively, by adjusting the size of m,
can accurately approximate the nonlinear continuous function f i The optimal approximation equation can be expressed as:
wherein ε i Is an approximation function error, satisfies
Is a very small positive constant, +.>
Is the optimal weight vector.
Step 1043: a gaussian function is selected as the activation function of the radial basis neural network.
Illustratively, a radial basis function is a classical neural network activation function whose kernel function generally selects a gaussian function, expressed as:
wherein k=1, 2, …, m.mu. ik ＝[μ ik1 ,μ ik2 ,…,μ ikq ] T Is the center of receptive field, eta ik Is the width of the gaussian kernel.
Step 1044: and determining an output vector after the uncertainty of the radial basis function to the dynamic model approximates based on the optimal approximation equation and the activation function of the radial basis function neural network.
Illustratively, the output vector of the radial basis function after model uncertainty approximation is expressed as:
wherein w is i ＝[w i1 ,w i2 ,…,w im ] T Is a weight vector, z i ＝[e 1i ,e 2i ] T Is an input to the neural network.
Step 1045: and defining an approximation error of the radial basis function neural network based on an output vector after the uncertainty of the radial basis function on the dynamic model is approximated.
Defining the neural network approximation error as:
wherein,,
representing the optimal weight vector.
Step 1046: and determining a weight update law of a weight vector of the radial basis neural network by using a projection method based on the output vector of the radial basis function after the uncertainty of the radial basis function on the dynamic model is approximated and an approximation error of the radial basis neural network.
Specifically, in step 1046, determining a weight update law of a weight vector of the radial basis function neural network by using a projection method includes: designing an update law of a weight vector of the radial basis function neural network; correcting the update law of the weight vector of the radial basis function neural network; and (5) ensuring the bouncy of the weight vectors by using a projection method, and determining the weight update law of the weight vectors of the final radial basis neural network.
The final weight update law of the weight vector of the radial basis function neural network is expressed as:
wherein,,
ρ i and xi i Is bounded; delta is the learning rate of the neural network, delta>0; normal vector->
Satisfy->
Definition of the definition
The weight update law of the neural network is designed as follows:
here, δ >0 is the learning rate of the neural network, and since μ is an unknown variable, the update law is modified as:
the method of parameter projection self-adaption is adopted to ensure the bouncy of weight vectors, and a constant vector is defined
Satisfy->
The update law of the neural network weight vector is designed based on projection as follows:
wherein,,
ρ i and xi i Is bounded.
The radial basis function neural network can map the relation between the known input and output data, and has good function approximation capability. The method based on the radial basis function neural network can accurately approximate the nonlinear function by adjusting the node number of the hidden layer theoretically. For an uncertain system which cannot acquire a specific mathematical model of the system, data can be effectively provided for a construction controller, and the self-adaptive regulation rule of the weight is generally obtained by using Lyapunov stability criteria.
The self-adaptive updating law is designed by adopting a projection method for the weight vector of the neural network, so that the weight vector is ensured to be always kept in a bounded range in the learning process of the neural network.
To prove the weight vector
Is selected from the lyapunov function:
according to the projection adaptive update law (23), there are two cases that need to be considered.
Case 1: if it is
Or->
The method can obtain:
case 2: if it is
The method can obtain:
from the above, it can be seen that the following is satisfied
Projection update law (23) always ensures
In step 105, the adaptive update law of the sliding mode signal and the weight vector of the radial basis function neural network is applied to the controller of the mechanical arm, so as to obtain the tracking expected track of the joint of the mechanical arm at a fixed time.
The controller design depends on the following relevant arguments to the fixed time stability theory:
lemma 1: for nonlinear systems
f(0)＝0，x(t)∈R n Time T for the system to reach equilibrium point r The agreement is bounded and independent of the state initial value, i.e.:
the system is stable for a fixed time.
And (4) lemma 2: for nonlinear systems
f(0)＝0，x(t)∈R n Assuming that there is a lyapunov function V (x (t)), the following holds:
wherein α, β, p, g, k are normal numbers satisfying pk<1,gk>1,
Is a bounded normal number, then the state of the system may be at a fixed time T r Inner convergence to region Ω, where
According to the fixed time stability basis, a controller is designed to ensure that the mechanical arm can track the expected track quickly and accurately in the fixed time, and the controller is designed as follows:
in one embodiment of the invention, the validity of the proposed controller is verified by means of a double-link rigid mechanical arm. Definition x 1 ＝[x 11 ,x 12 ] T As the joint angle of the robotic arm, a correlation matrix in a two-bar robot mathematical model is then given:
wherein,,
p 3 ＝m 2 l 1 l c2 ,p 4 ＝m 1 l c2 +m 2 l 1 ,p 5 ＝m 2 l c2 ；m i and l i The mass and length of the connecting rod i, m 1 ＝2.00(kg),m 2 ＝0.85(kg)，l 1 ＝0.35(m),l 2 ＝0.31(m)；I i Is the moment of inertia of the connecting rod i, +.>
l ci Is the centroid of the ith link; g=9.8 (m/s) 2 )。
The initial position and speed of the robot are:
x 11 (0)＝x 12 (0)＝1.5(rad)，x 21 (0)＝x 22 (0)＝0(rad/s) (32)
the set expected track is:
x d ＝[0.1sin(0.5t)+cos(0.5t)，0.1cos(t)+cos(t)] T (33)
wherein t is [0, t ] m ]，t m ＝10(s)。
The disturbance torque is:
d(t)＝[0.1sin(0.5t)+0.25cos(0.5t),0.25sin(0.5t)+0.1sin(0.5t)] T (34)
the controller parameters are set as follows: α=2.5, β=2.5, p=0.5,
v 1 ＝2，/>
v 4 ＝2，K s ＝10，δ a ＝0.001。
the simulation results are shown in fig. 2-7, wherein fig. 3 shows that the angular position of the two-link rigid mechanical arm joint 1 and the angular speed of the joint 1 can quickly and stably track the desired joint angular track with high precision; fig. 4 shows that the angular position of the two-bar rigid mechanical arm joint 2 and the angular velocity of the joint 2 can track the desired joint angular trajectory quickly and stably with high accuracy. Fig. 5 shows that the angular position and angular velocity tracking error of the joint 1 can converge rapidly to zero; fig. 6 shows that the angular position and angular velocity tracking error of the joint 2 can converge rapidly to zero. Fig. 7 shows that the control signals of the proposed controller are continuous and bounded; fig. 8 shows that the radial basis function neural network always has a bounded weight vector during learning. Simulation results indicate that the proposed control method is feasible and efficient.
The invention provides a fixed time track tracking control method of a mechanical arm based on a nonsingular terminal sliding mode, which considers the model uncertainty of the mechanical arm, designs a nonsingular terminal sliding mode surface with simple calculation, can enable track tracking errors to quickly converge in fixed time, the convergence time does not depend on an initial state, and the upper limit of the convergence time of the errors is independent of the initial state of a system and is only determined by parameters of a controller; the model uncertainty of the mechanical arm is approximated by adopting a radial basis function neural network, the mechanical arm model uncertainty is estimated and compensated, the self-adaptive update law of the weight vector is designed based on a projection method in consideration of the limitation of the weight, and the limitation of the weight vector is ensured; therefore, various complex scenes of mechanical arm control are dealt with, and the uncertainty of model parameters and the accuracy of external interference of the estimated mechanical arm are improved.
It should be understood that the sequence number of each step does not mean the sequence of execution, and the execution sequence of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.
Corresponding to the method for controlling fixed time track of mechanical arm based on nonsingular terminal sliding mode in the above embodiment, the embodiment of the present application further provides a terminal device, referring to fig. 9, the terminal device 300 may include: at least one processor 310 and a memory 320, said memory 320 having stored therein a computer program 321 executable on said at least one processor 310, said processor 310 implementing steps in any of the various method embodiments described above, such as steps 101 to 105 in the embodiment shown in fig. 1, when said computer program is executed.
By way of example, a computer program may be partitioned into one or more modules/units that are stored in memory 320 and executed by processor 310 to complete the present application. The one or more modules/units may be a series of computer program segments capable of performing specific functions for describing the execution of the computer program in the terminal device 300.
It will be appreciated by those skilled in the art that fig. 9 is merely an example of a terminal device and is not limiting of the terminal device, and may include more or fewer components than shown, or may combine certain components, or different components, such as input-output devices, network access devices, buses, etc.
The processor 310 may be a central processing unit (Central Processing Unit, CPU), but may also be other general purpose processors, digital signal processors (Digital Signal Processor, DSP), application specific integrated circuits (Application Specific Integrated Circuit, ASIC), off-the-shelf programmable gate arrays (Field-Programmable Gate Array, FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The memory 320 may be an internal storage unit of the terminal device, or may be an external storage device of the terminal device, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash Card (Flash Card), or the like. The memory 320 is used for storing the computer program and other programs and data required by the terminal device. The memory 320 may also be used to temporarily store data that has been output or is to be output.
The bus may be an industry standard architecture (Industry Standard Architecture, ISA) bus, an external device interconnect (Peripheral Component, PCI) bus, or an extended industry standard architecture (Extended Industry Standard Architecture, EISA) bus, among others. The buses may be divided into address buses, data buses, control buses, etc. For ease of illustration, the buses in the drawings of the present application are not limited to only one bus or one type of bus.
The fixed time track tracking control method of the mechanical arm based on the nonsingular terminal sliding mode can be applied to terminal equipment such as computers, tablet computers, notebook computers, netbooks, personal digital assistants (personal digital assistant, PDA) and the like, and the specific type of the terminal equipment is not limited.
The embodiment of the application also provides a computer readable storage medium, wherein the computer readable storage medium stores a computer program, and the computer program realizes the steps in each embodiment of the fixed time track tracking control method of the mechanical arm based on the nonsingular terminal sliding mode when being executed by a processor.
The embodiment of the application provides a computer program product, which can realize the steps in each embodiment of the fixed time track tracking control method of the mechanical arm based on the nonsingular terminal sliding mode when being executed on a mobile terminal.
The integrated units, if implemented in the form of software functional units and sold or used as stand-alone products, may be stored in a computer readable storage medium. Based on such understanding, the present application implements all or part of the flow of the method of the above embodiments, and may be implemented by a computer program to instruct related hardware, where the computer program may be stored in a computer readable storage medium, where the computer program, when executed by a processor, may implement the steps of each of the method embodiments described above. Wherein the computer program comprises computer program code which may be in source code form, object code form, executable file or some intermediate form etc. The computer readable medium may include at least: any entity or device capable of carrying computer program code to a photographing device/terminal apparatus, recording medium, computer Memory, read-Only Memory (ROM), random access Memory (RAM, random Access Memory), electrical carrier signals, telecommunications signals, and software distribution media. Such as a U-disk, removable hard disk, magnetic or optical disk, etc. In some jurisdictions, computer readable media may not be electrical carrier signals and telecommunications signals in accordance with legislation and patent practice.
In the foregoing embodiments, the descriptions of the embodiments are emphasized, and in part, not described or illustrated in any particular embodiment, reference is made to the related descriptions of other embodiments.
Those of ordinary skill in the art will appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, or combinations of computer software and electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present application.
In the embodiments provided in the present application, it should be understood that the disclosed apparatus/network device and method may be implemented in other manners. For example, the apparatus/network device embodiments described above are merely illustrative, e.g., the division of the modules or units is merely a logical functional division, and there may be additional divisions in actual implementation, e.g., multiple units or components may be combined or integrated into another system, or some features may be omitted, or not performed. Alternatively, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection via interfaces, devices or units, which may be in electrical, mechanical or other forms.
The units described as separate units may or may not be physically separate, and units shown as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.
The above embodiments are only for illustrating the technical solution of the present application, and are not limiting; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present application, and are intended to be included in the scope of the present application.
Claims (10)
1. The fixed time track tracking control method of the mechanical arm based on the nonsingular terminal sliding mode is characterized by comprising the following steps:
establishing a dynamic model of the mechanical arm with uncertainty based on data of a preset expected track of a joint of the mechanical arm;
acquiring real-time track data of joints of the mechanical arm based on the dynamic model;
determining a sliding mode signal based on the data of the expected track and the real-time track data;
based on the dynamics model, constructing a radial basis function neural network, and determining a weight update law of a weight vector of the radial basis function neural network by using a projection method;
and applying the self-adaptive update law of the sliding mode signal and the weight vector of the radial basis function neural network to a controller of the mechanical arm to obtain a tracking expected track of a joint of the mechanical arm at fixed time.
2. The fixed time track tracking control method of the mechanical arm based on the nonsingular terminal sliding mode according to claim 1, wherein the mechanical arm dynamics model is expressed as:
wherein,,
acceleration signals of joints of the mechanical arm; m is an inertia matrix of the mechanical arm; τ is the control moment;
is a model uncertainty composed of the parameter uncertainty of the mechanical arm and external disturbance, wherein +.>
M(q)＝M 0 (q)+M Δ (q)∈R n×n ；g(q)＝g 0 (q)+g Δ (q)∈R n Is a gravity vector; />
Is a centrifugal coriolis force matrix; d E R n Is a bounded external disturbance moment.
3. The fixed time track following control method for a robot arm based on a nonsingular terminal sliding mode according to claim 1, wherein the determining a sliding mode signal based on the data of the desired track and the real-time track data comprises:
the real-time track data of the joints of the mechanical arm and the data of the pre-designed expected track are used for obtaining an error signal;
reconstructing a kinetic model of the mechanical arm of uncertainty into a second-order system based on the error signal;
and designing a nonsingular rapid terminal sliding mode surface based on the second-order system, and constructing the sliding mode signal.
4. The fixed time trace tracking control method for a mechanical arm based on a nonsingular terminal sliding mode according to claim 3, wherein the error signal is expressed as:
wherein e 1 And e 2 For the error signal x 1 (t)＝q(t)，
x d (t)＝q d (t)，/>
Is x d Q (t) is the position signal of the joints of the manipulator, +.>
Is the derivative of q (t), q d (t) is theThe joints of the mechanical arm take into account the position signal of the external disturbance moment.
5. The fixed time track tracking control method for a mechanical arm based on a nonsingular terminal sliding mode according to claim 4, wherein the sliding mode signal is represented as:
wherein,,
is the coefficient of the sliding mode variable, which is the sum error e 1 Related time-varying coefficients, using diagonal matrix
Indicating (I)>
Wherein i=1, 2, …, n, α, β, p, g, k is a constant, and α>0，β>0，k>1，v 1 >1, and p, g satisfies gk>1，1/v 1 <pk<1。
6. The fixed time track tracking control method of a mechanical arm based on a nonsingular terminal sliding mode according to claim 1, wherein the constructing a radial basis neural network based on the dynamics model and designing an adaptive update law of a weight vector of the radial basis neural network according to a projection method comprises the following steps:
constructing a radial basis function, namely a radial basis neural network according to an approximation principle;
determining an optimal approximation equation of the radial basis function to a nonlinear function according to the radial basis function;
selecting a gaussian function as an activation function of the radial basis function network;
determining an output vector of the radial basis function after uncertainty approximation of the radial basis function to the dynamic model based on the optimal approximation equation and an activation function of the radial basis function;
defining an approximation error of the radial basis function based on an output vector of the radial basis function after the uncertainty of the radial basis function on the dynamic model approximates;
and determining a weight update law of the weight vector of the radial basis neural network by using a projection method based on the output vector of the radial basis function after the uncertainty of the radial basis function on the dynamic model is approximated and an approximation error of the radial basis neural network.
7. The fixed time track tracking control method for a mechanical arm based on a nonsingular terminal sliding mode according to claim 5 or 6, wherein an output vector after uncertainty approximation of a radial basis function to the dynamic model is expressed as:
wherein w is i ＝[w i1 ,w i2 ,…,w im ] T Is a weight vector, z i ＝[e 1i ,e 2i ] T Is an input to the neural network; sigma (sigma) i ＝[σ i1 ,σ i2 ,…,σ im ] T ∈R m Representing an activation function;
the approximation error of the radial basis function network is expressed as:
wherein,,
representing the mostAnd (5) an optimal weight vector.
8. The fixed time track tracking control method of a mechanical arm based on a nonsingular terminal sliding mode according to claim 7, wherein determining a weight update law of a weight vector of the radial basis function neural network by using a projection method comprises:
designing an update law of a weight vector of the radial basis function neural network;
correcting the update law of the weight vector of the radial basis function neural network;
ensuring the bouncy of the weight vector by using a projection method, and determining a weight update law of the weight vector of the final radial basis function neural network; the weight update law of the weight vector of the final radial basis function neural network is expressed as:
wherein,,
ρ i and xi i Is bounded; delta is the learning rate of the neural network, delta>0; normal vector->
Satisfy->
9. The fixed time track tracking control method of the mechanical arm based on the nonsingular terminal sliding mode according to claim 8, wherein the control moment of the controller of the mechanical arm is expressed as:
wherein M is 0 An inertial matrix of the mechanical arm; v 1 、v 2 、v 3 、v 4 Is a constant;
as coefficients of the sliding mode variable,
is two diagonal matrices; k (K) s Is a controller parameter; />
Is x d Is a second derivative of (c).
10. A terminal device comprising a memory and a processor, wherein the memory stores a computer program executable on the processor, and wherein the processor implements the non-singular terminal sliding mode based robot arm fixed time trace tracking control method according to any one of claims 1 to 9 when executing the computer program.
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