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CN117086865B - Mechanical arm tracking control method, system, equipment and medium based on input limitation - Google Patents

Mechanical arm tracking control method, system, equipment and medium based on input limitation

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Publication number
CN117086865B
CN117086865B CN202310968835.5A CN202310968835A CN117086865B CN 117086865 B CN117086865 B CN 117086865B CN 202310968835 A CN202310968835 A CN 202310968835A CN 117086865 B CN117086865 B CN 117086865B
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robotic arm
mechanical arm
system model
optimal
input
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CN117086865A (en
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周琪
张兴怡
郭子杰
马慧
李鸿一
鲁仁全
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Guangdong University of Technology
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Guangdong University of Technology
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    • BPERFORMING OPERATIONS; TRANSPORTING
    • B25HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25JMANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00Programme-controlled manipulators
    • B25J9/16Programme controls
    • B25J9/1628Programme controls characterised by the control loop
    • B25J9/163Programme controls characterised by the control loop learning, adaptive, model based, rule based expert control

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  • Engineering & Computer Science (AREA)
  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Feedback Control In General (AREA)

Abstract

The invention discloses a mechanical arm tracking control method, a mechanical arm tracking control system, mechanical arm tracking control equipment and a mechanical arm tracking control medium based on input limitation, and relates to the technical field of intelligent control. The method comprises the steps of obtaining physical characteristic data and preset performance indexes of the mechanical arm, constructing a constrained system model of the mechanical arm according to the physical characteristic data and the preset performance indexes, carrying out equivalent system conversion on the constrained system model to obtain an unconstrained system model, constructing a Hamiltonian-Jacobian-Belman equation according to the unconstrained system model and an optimal control strategy of the mechanical arm, and solving the Hamiltonian-Jacobian-Belman equation through a self-adaptive dynamic programming method to obtain an optimal control law so as to control the mechanical arm according to the optimal control law. The invention solves the technical problem that the existing mechanical arm control method can not realize optimal control while meeting the constraint of preset performance indexes and overcoming the asymmetric input limit.

Description

Mechanical arm tracking control method, system, equipment and medium based on input limitation
Technical Field
The invention relates to the technical field of intelligent control, in particular to a mechanical arm tracking control method, system, equipment and medium based on input limitation.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
Along with the continuous progress of science and technology, intelligent control research on the mechanical arm is mature, so that higher standard is also provided for the control precision of the mechanical arm. In order to improve the control accuracy of the mechanical arm, a requirement on performance indexes is generally required, so that the control by combining the preset performance indexes in the design process of the controller has important significance. The optimal control is a control strategy considering the control performance and the energy-saving effect of the system, and the motion process of the mechanical arm belongs to a highly-coupled nonlinear system, so that a great challenge is brought to the traditional optimal control method. In industrial production, due to the influence of many practical factors such as voltage, weather, temperature and the like, the input is often not symmetrical, and asymmetric input limitation has to be considered in order to improve the safety of the application of the mechanical arm system.
Therefore, how to meet the preset performance index constraint and consider the asymmetric input limitation to realize the optimal control in the mechanical arm control process becomes a problem to be solved.
Disclosure of Invention
Aiming at the defects existing in the prior art, the invention aims to provide a mechanical arm tracking control method, a system, equipment and a medium based on input limitation, and aims to solve the technical problem that the existing mechanical arm control method cannot realize optimal control while meeting preset performance index constraint and overcoming asymmetric input limitation.
In order to achieve the above object, the present invention is realized by the following technical scheme:
The invention provides a mechanical arm tracking control method based on input limitation, which comprises the following steps:
acquiring physical characteristic data and preset performance indexes of the mechanical arm;
constructing a constrained system model of the mechanical arm according to the physical characteristic data and the preset performance index;
performing equivalent system conversion on the constrained system model to obtain an unconstrained system model;
Constructing a Hamiltonian-Jacobian-Bellman equation according to an unconstrained system model and an optimal control strategy of the mechanical arm, wherein the optimal control strategy is the optimal control strategy of the mechanical arm limited by asymmetric input;
And solving the Hamiltonian-Jacobian-Bellman equation by a self-adaptive dynamic programming method to obtain an optimal control law, so as to control the mechanical arm according to the optimal control law.
Further, the specific steps of constructing the constrained system model of the mechanical arm according to the physical characteristic data and the preset performance index are as follows:
establishing a state space equation of the mechanical arm according to the physical characteristic data;
defining a preset performance function according to a preset performance index;
And constructing a constrained system model according to the state space equation and a preset performance function.
Further, the specific steps of establishing the state space equation of the mechanical arm according to the physical characteristic data are as follows:
modeling the physical characteristic data to obtain a dynamic model of the mechanical arm;
And converting the dynamic model according to the physical characteristics of the mechanical arm to obtain a state space equation of the mechanical arm. Further, the specific steps of constructing the hamilton-jacobian-bellman equation according to the unconstrained system model and the optimal control strategy of the mechanical arm are as follows:
defining a cost function according to an unconstrained system model and an optimal control strategy of the mechanical arm limited by the asymmetric input;
and constructing a Hamiltonian-Jacobian-Belman equation according to the cost function.
Further, the specific steps of defining the cost function according to the unconstrained system model and the optimal control strategy of the mechanical arm limited by the asymmetric input are as follows:
defining a position tracking error according to an unconstrained system model to obtain an augmentation state and a positive term designed by asymmetric input;
And defining a cost function by combining the augmentation state, the positive term designed due to asymmetric input and the optimal control strategy of the mechanical arm.
Further, the specific steps of constructing the hamilton-jacobian-bellman equation according to the cost function are as follows:
defining a Hamiltonian function and an optimal cost function according to the cost function;
Solving the optimal cost function by utilizing a Belman optimal principle to obtain an optimal solution of the optimal cost function;
Substituting the optimal solution into the Hamiltonian to obtain a Hamiltonian-Jacobian-Belman equation.
Furthermore, the Hamiltonian-Jacobian-Bellman equation is solved by adopting a self-adaptive dynamic programming method based on a neural network architecture, so that an optimal control law is obtained.
The second aspect of the present invention provides a robot arm tracking control system based on input limitation, comprising:
the data acquisition module is used for acquiring physical characteristic data and preset performance indexes of the mechanical arm;
the model construction module is used for constructing a constrained system model of the mechanical arm according to the physical characteristic data and the preset performance index;
The system conversion module is used for carrying out equivalent system conversion on the constrained system model to obtain an unconstrained system model;
The equation construction module is used for constructing a Hamiltonian-Jacobian-Bellman equation according to the unconstrained system model and an optimal control strategy of the mechanical arm, wherein the optimal control strategy is the optimal control strategy of the mechanical arm limited by asymmetric input;
And the optimal control module is used for solving the Hamiltonian-Jacobian-Bellman equation through a self-adaptive dynamic programming method to obtain an optimal control law so as to control the mechanical arm according to the optimal control law.
A third aspect of the present invention provides an apparatus comprising a memory, a processor and a program stored on the memory and executable on the processor, the processor implementing the steps in the input-limitation-based robotic arm tracking control method according to the first aspect of the present invention when the program is executed.
A fourth aspect of the present invention provides a medium having stored thereon a program which, when executed by a processor, implements the steps of the input-limitation-based robotic arm tracking control method according to the first aspect of the present invention.
The one or more of the above technical solutions have the following beneficial effects:
The invention discloses a mechanical arm tracking control method, a system, equipment and a medium based on input limitation, which fully analyze constraint conditions of preset performance indexes, consider asymmetric input limitation in the control process, perform optimal control on the basis of ensuring the preset performance indexes and realize high-precision control of mechanical arms. The method can lead the system of the mechanical arm to output an effective tracking reference signal, lead tracking errors and the like to meet preset requirements, improve control precision, overcome the problem of limited asymmetrical input which is possibly faced by the actual scene of the mechanical arm, and have energy-saving effect.
Additional aspects of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention.
FIG. 1 is a schematic flow chart of a method for controlling tracking of a mechanical arm according to a first embodiment of the invention;
FIG. 2 is a convergence graph for evaluating network weights according to a first embodiment of the present invention;
FIG. 3 is a diagram showing tracking effects of the reference signal x d and the system state x according to the first embodiment of the present invention;
FIG. 4 is a graph showing the tracking error e 1 and the predetermined performance boundary according to the first embodiment of the present invention;
FIG. 5 is a graph showing the tracking error e 2 and the predetermined performance boundary according to the first embodiment of the present invention;
FIG. 6 is a graph of a controller in an asymmetric limit input in accordance with a first embodiment of the present invention;
fig. 7 is a schematic diagram of a functional module of a mechanical arm control device in a second embodiment of the present invention;
fig. 8 is a schematic hardware structure of a mechanical arm control device in the third embodiment of the present invention.
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the invention. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present invention. As used herein, the singular is also intended to include the plural unless the context clearly indicates otherwise, and furthermore, it is to be understood that the terms "comprises" and/or "comprising" when used in this specification are taken to specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof;
embodiment one:
Analysis of the prior art finds that quick response and high-precision position tracking control are research hot spots of the mechanical arm all the time, most of the tracking control methods of the mechanical arm stay at the stage of ensuring gradual convergence of tracking errors at present, and the problems of low response speed, excessive overshoot and the like exist, so that the control precision of the mechanical arm is further improved, and the requirements on performance indexes such as convergence rate, maximum overshoot, steady-state errors and the like are generally required. Therefore, the method has important significance in combination with the preset performance index for control in the design process of the controller. At the same time, but in industrial production, asymmetric input restrictions have to be taken into account, due to the influence of many realistic factors, in between the safety of the system applications.
Furthermore, control puts higher demands on its energy consumption. The control cost of the mechanical arm is reduced, the energy consumption is reduced, and the control method is particularly important to the current technology. Optimal control is a class of control strategies that takes into account system control performance and energy-saving effects. Research shows that the motion process of the mechanical arm in the system belongs to a highly-coupled nonlinear system, which brings great challenges to the traditional optimal control method.
The solution to the optimal control problem of a strong nonlinear system is an adaptive dynamic programming method. Based on the self-adaptive dynamic programming design technology, the obtained optimal controller can ensure the stability of a controlled system and simultaneously can ensure the optimal performance of the system. However, at present, for the problem of high-precision tracking control of the mechanical arm, overcoming the asymmetric input limitation, designing an optimal controller meeting the constraint of the preset performance index is still a problem to be solved.
In view of the technical problem that the mechanical arm tracking control method in the prior art cannot realize optimal control while meeting the constraint of preset performance indexes and overcoming the asymmetric input limitation, the first embodiment of the invention provides a mechanical arm tracking control method based on input limitation, as shown in fig. 1, comprising the following steps:
s100, acquiring physical characteristic data and preset performance indexes of the mechanical arm.
In a specific embodiment, the characteristics of the mechanical arm are the relationship between displacement control and force control, and in order to simplify the study, the embodiment is controlled by a design controller, and the mechanical arm is equivalent to one mechanical arm.
The physical characteristic data refers to mechanical characteristics corresponding to a hardware structure of the mechanical arm, for example, the quality, damping, spring coefficient, control input and other parameter characteristics of the mechanical arm in the mechanical arm. The preset performance index refers to a parameter index of the mechanical arm for realizing preset performance control, for example, the tracking error requirement of the mechanical arm, wherein the tracking error is the difference value between an output signal of the mechanical arm and an input signal to be tracked, and the tracking error index can be a range value.
S200, constructing a constrained system model of the mechanical arm according to the physical characteristic data and the preset performance index.
And S210, establishing a state space equation of the mechanical arm according to the physical characteristic data. When the state space equation is built according to the physical characteristic data of the mechanical arm, a dynamic model can be built first and then converted into a state space equation form, or the corresponding state space equation can be obtained after the physical characteristic data is directly input through a set program or method, such as some existing modeling software.
In a specific embodiment, the model is reconverted into the form of a state space equation by creating a kinetic model:
and S211, modeling the physical characteristic data to obtain the mechanical arm dynamics model.
In this embodiment, to obtain the physical characteristics of the mechanical arm, including the total mass Mg of the mechanical arm itself of the mechanical arm, the damping coefficient B of the mechanical arm, the total rotational inertia of the motor is J, and the control device inputs u (t) to the mechanical arm. Modeling the physical characteristics of the mechanical arm, and obtaining a dynamic model which is as follows:
wherein Mg represents the total mass of the mechanical arm, q represents the rotation angle of the mechanical arm, Representing the angular velocity of the mechanical arm,The angular acceleration is represented by B, the damping of the mechanical arm is represented by B, the total rotational inertia of the motor is J, u (t) represents the control input, and t represents time.
S212, converting the dynamic model according to physical characteristics of the mechanical arm to obtain a state space equation of the mechanical arm.
In this embodiment, according to the physical characteristics of the mechanical arm, the equation of the kinetic model obtained by modeling can be converted into a state space equation. Specifically, after the control device obtains the physical characteristic data of the mechanical arm, a constrained system model of the mechanical arm can be constructed. The model may be a kinetic model or a model of a state equation. When the state space equation is built according to the physical characteristic data of the mechanical arm, a dynamic model can be built first and then converted into a state space equation form, or the corresponding state space equation can be obtained after the physical characteristic data is directly input through a set program or method, such as some existing modeling software.
In one specific embodiment, let x 1 = q,The state space equation of the mechanical arm is obtained as follows:
assuming that the input signal to be tracked of the mechanical arm is x d, the first derivative thereof Second derivativeAll the two systems exist, then the compact structure of the state space equation of the mechanical arm can be further obtained, namely, the formula of the constrained system model is expressed as follows:
wherein, the
S220, defining a preset performance function according to the preset performance index.
The preset performance control is a practical technology capable of predetermining dynamic performance indexes such as convergence speed, control precision and the like, and can enable tracking errors of the mechanical arm to be kept in a limited range formed by two specified performance functions, so that high dynamic performance of the mechanical arm is guaranteed.
In this embodiment, the tracking error of the mechanical arm is the difference between the output signal x and the input signal to be tracked, which is defined as:
e(t)=[e1,e2,…,en]T
=[x1-xd1,x2-xd2,…,xn-xdn]T
Where e i (t) denotes a difference between the tracking signal and the tracked signal, i.e. a tracking error.
In order to achieve the specified transient performance and steady state performance of the tracking error, the tracking error is constrained to a specified rangeThe preset performance function determined according to the preset performance index of the mechanical arm is as follows:
Wherein, delta i,mini,maxii,0 and eta i,∞ are positive design parameters, which can be set according to actual needs.
The function of the preset performance function is to limit the tracking error to a settable range, wherein the limit range can be adjusted by adjusting the design parameters in the function.
S230, constructing a constrained system model according to the state space equation and a preset performance function.
And S300, performing equivalent system conversion on the constrained system model to obtain an unconstrained system model.
In this embodiment, in order to achieve the goal of high-precision control, a system conversion technique based on a preset performance function is adopted. For the output signal of the mechanical arm, a smooth, strictly increasing function is introduced:
wherein z i represents the unconstrained tracking error after conversion;
And has the following steps:
ei(t)=ηi(t)ki(zi),
the constrained tracking error may be converted to an unconstrained tracking error according to the following conversion scheme:
the converted unconstrained error derivatives are:
wherein the method comprises the steps of Representing an original system by using converted unconstrained errors
Where u is the control input and x d is the ideal signal.
To facilitate the design of the tracking controller, this embodiment designs an augmented state matrix:
the converted amplification system is in the form of a compact set:
wherein the method comprises the steps of
The system transformation technology is utilized to process the problem of preset performance constraint, and the constrained system model can be converted into an unconstrained equivalent system model by defining a nonlinear mapping function based on the preset performance index. The control strategy designed for the converted unconstrained system model can enable the tracking error of the mechanical arm to be kept within a limited range formed by a preset performance function, so that the control precision is effectively improved.
S400, constructing a Hamiltonian-Jacobian-Bellman equation according to the unconstrained system model and an optimal control strategy of the mechanical arm, wherein the optimal control strategy is the optimal control strategy of the mechanical arm limited by asymmetric input.
S410, defining a cost function for balancing the control precision and the energy consumed by the control input so as to realize the aim of optimal control. Specifically, the cost function is defined according to an unconstrained system model and an optimal control strategy of the mechanical arm limited by the asymmetric input.
S411, defining a position tracking error according to the unconstrained system model to obtain an augmentation state and a positive term of the asymmetric input design.
In this embodiment, a new augmentation matrix is defined for the unconstrained system model after transformation. The input control of the input controlled object is u min<u<umax and u min||≠||umax, where u min represents the minimum value of the input limit and u max represents the maximum value of the input limit.
And define positive definite terms due to asymmetric input designThe method comprises the following steps:
wherein, the M is the number of control inputs u, s is the integral variable, and tanh is the hyperbolic tangent function.
S412, defining a cost function by combining the augmentation state, the positive term designed by asymmetric input and the optimal control strategy of the mechanical arm.
In this embodiment, the optimal control strategy of the mechanical arm refers to a control method that enables the system to achieve optimal performance within a certain time range under given system models, performance indexes and constraint conditions. The goal of optimal control is typically to maximize or minimize a particular performance metric, such as minimizing energy consumption, maximizing system stability, or transitioning the system from an initial state to a target state in a limited time. In this embodiment, an optimal control strategy is determined according to an actual control task, and then the following cost function is obtained.
To ensure the stability of the system, a discount coefficient ρ is introduced, and a cost function V (X (t)) is defined as:
wherein, the Is a positive definite matrix, which can be set according to actual needs, t is a time variable, and τ is an integral variable.
S420 the optimal control problem may be converted into solving the hamilton-jacobian-bellman equation by deriving the hamilton-jacobian-bellman equation based on the cost function defined by the optimal control strategy. Specifically, a hamilton-jacobian-bellman equation is constructed from the cost function.
S421, defining a Hamiltonian and an optimal cost function according to the cost function.
The cost function defines the hamiltonian as:
wherein, the
In the optimal control, the cost function needs to be minimum so as to obtain the desired control precision through the minimum control input. In this embodiment, an optimal cost function is defined as follows:
Where Ω denotes a set of allowed control strategies for the robotic arm, V * (X) satisfies V * (0) =0.
And S422, solving the optimal cost function by utilizing a Bellman optimal principle to obtain an optimal solution of the optimal cost function.
According to the Belman optimal principle, the following steps are obtained:
wherein, the
From the following componentsThe optimal solution for the optimal cost function can be obtained as:
s423, substituting the optimal solution into the Hamiltonian to obtain a Hamiltonian-Jacobian-Belman equation.
In this embodiment, the optimal solution u * (t) is substituted into the hamilton function, so that the hamilton-jacobian-bellman equation can be obtained as follows:
And S500, solving the Hamiltonian-Jacobian-Bellman equation by a self-adaptive dynamic programming method to obtain an optimal control law, so as to control the mechanical arm according to the optimal control law.
And S510, solving the Hamiltonian-Jacobian-Bellman equation by adopting a self-adaptive dynamic programming method based on a neural network architecture to obtain an optimal control law.
In this embodiment, an evaluation network of a single network is established based on a neural network architecture, and the optimal cost function V * (X) can be approximated by the evaluation network as:
wherein, the As an ideal weight vector for the system,As a vector of the basis functions,Is an approximation error, m represents the number of neural network nodes, and
Order theRepresenting an estimate of the ideal weight, the optimal cost function may be estimated as:
then an approximate optimal control law can be obtained as:
Therefore, the control equipment can correspondingly control the mechanical arm according to the optimal control law, optimal control is performed on the basis of guaranteeing preset performance indexes, and high-precision control of the system is realized.
The optimal control law is approximately obtained through a single-network self-adaptive dynamic programming method, the control of the mechanical arm is realized, and a single evaluation network is adopted to approximate an optimal cost function.
Alternatively, the weight update law of the designed evaluation network may be:
wherein, the Is a positive design parameter, can be set according to actual needs,
In order to verify the effectiveness of the mechanical arm tracking control method provided by the embodiment, the following simulation experiment is performed:
In the simulation experiment, the control target is set to enable the output signal of the mechanical arm to track the upper reference signal in an optimal manner According to the actual system of the mechanical arm, the total mass mg=10 of the mechanical arm itself, the damping b=2 of the spring in the mechanical arm, and the total rotational inertia of the motor is j=1. The preset performance errors are finally converged to-0.7 < e 1 <0.7 and-2<e 2 <2 respectively, the state initial value of the mechanical arm is x 1(0)=0.1,x2 (0) =0.1, and the tracking signal is x d1(0)=0.4,xd2 (0) =0.4. Setting the function of the evaluation network asThe initial weight value is w c(0)=[0,3000,300,0,0,0]T and finally converges to
[1.1993,2995.9,304.5066,0.0651, -4.8015,5.0840] T. In addition, the asymmetric input is set as u min=-4,umax =5, ρ=0.6,
Selecting a Liapunov functionThe time derivative is analyzed based on parameters designed in the practical situation in the simulation experiment, which are not exemplified here, and the analysis results are obtainedFrom the Liapunov stability theorem, it can be known that the tracking error z and the positive term due to the asymmetric input designEvaluating weight estimation errors of a networkIs consistent and ultimately bounded, i.e., the output signal of the robotic arm system can track the reference signal, the weight of the evaluation network can converge to a near-ideal value, as shown in fig. 2, which is a graph of convergence of the evaluation network weights, where the horizontal axis represents time in seconds(s) and the vertical axis represents the value of the evaluation network weights. From this figure it can be seen that the evaluation network can accurately approximate the cost function, so that the resulting control input u (t) can then be seen as optimal.
Fig. 3 shows a graph of the reference signal x d and the system state x in the present embodiment, in which the horizontal axis represents time in seconds(s) and the vertical axis represents values corresponding to respective curves, fig. 4 shows a graph of the tracking error e 1 and the preset performance limit in the present embodiment, in which the horizontal axis represents time in seconds(s) and the vertical axis represents values corresponding to respective curves, fig. 5 shows a graph of the tracking error e 2 and the preset performance limit in the present embodiment,
In the figure, the horizontal axis represents time in seconds(s), and the vertical axis represents values corresponding to respective curves, wherein the preset performance boundary line is a curve corresponding to a preset performance index value. As can be seen from fig. 3 to fig. 5, the system state of the mechanical arm corresponding to the output signal is consistent with the reference signal, the tracking effect of the control method is good, the tracking error meets the requirement of the preset performance index, and the high-precision control of the mechanical arm can be realized. Fig. 6 shows the control input under the asymmetric input limit in this embodiment, in which the horizontal axis represents time in seconds(s), the vertical axis represents the corresponding value of each curve, where u min represents the minimum value in the control input limit and u max represents the maximum value in the control input limit. As can be seen from fig. 6, in the present embodiment, the control input is effectively limited to the maximum minimum interval.
According to the mechanical arm tracking control method, the constrained system model of the mechanical arm is built according to the physical characteristic data and the preset performance index of the mechanical arm, equivalent system conversion is carried out on the constrained system model to obtain an unconstrained system model, then a Hamiltonian-Jacobian-Belman equation is built according to the unconstrained system model and the optimal control strategy of the mechanical arm limited by asymmetric input, the Hamiltonian-Jacobian-Belman equation is solved through a self-adaptive dynamic programming method to obtain an optimal control law, the mechanical arm is controlled according to the optimal control law, optimal control is carried out on the basis of guaranteeing the preset performance index, and high-precision control of the mechanical arm is achieved.
Embodiment two:
the second embodiment of the present invention provides a mechanical arm tracking control system based on input limitation, as shown in fig. 7, including:
the data acquisition module is used for acquiring physical characteristic data and preset performance indexes of the mechanical arm;
the model construction module is used for constructing a constrained system model of the mechanical arm according to the physical characteristic data and the preset performance index;
The system conversion module is used for carrying out equivalent system conversion on the constrained system model to obtain an unconstrained system model;
The equation construction module is used for constructing a Hamiltonian-Jacobian-Bellman equation according to the unconstrained system model and an optimal control strategy of the mechanical arm, wherein the optimal control strategy is the optimal control strategy of the mechanical arm limited by asymmetric input;
And the optimal control module is used for solving the Hamiltonian-Jacobian-Bellman equation through a self-adaptive dynamic programming method to obtain an optimal control law so as to control the mechanical arm according to the optimal control law.
Embodiment III:
The third embodiment of the invention provides a device, which comprises a memory, a processor and a program stored on the memory and capable of running on the processor, wherein the processor realizes the steps in the mechanical arm tracking control method based on input limitation according to the first embodiment of the invention when executing the program.
In a specific embodiment, the mechanical arm control device refers to a terminal device or a control device capable of realizing data transmission, and may be a terminal device such as a mobile phone, a computer, an embedded industrial personal computer, or a control device such as a controller, a processor, etc. located in a system.
As shown in fig. 8, a hardware configuration of the robot arm control device is schematically shown. The robotic arm control device may include a processor 1001, such as a CPU (Central Processing Unit ), a communication bus 1002, a user interface 1003, a network interface 1004, a memory 1005. Those skilled in the art will appreciate that the hardware configuration shown in fig. 8 is not limiting of the robotic arm control device of the present invention, and may include more or fewer components than shown, or may combine certain components, or a different arrangement of components.
In particular, the communication bus 1002 is used for enabling connection communication between these components, the user interface 1003 is used for connecting a client and communicating data with the client, the user interface 1003 may include an output unit, such as a display screen, an input unit, such as a keyboard, the network interface 1004 is used for connecting a background server and communicating data with the background server, the network interface 1004 may include an input/output interface, such as a standard wired interface, a wireless interface, such as a Wi-Fi interface, the memory 1005 is used for storing various types of data, such as instructions of any application program or method in the mechanical arm control device, and data related to the application program, the memory 1005 may be a high-speed RAM memory or a stable memory, such as a disk memory, the memory 1005 may optionally be a storage device independent of the processor 1001, the memory 1005 may include an operating system, a network communication module, a user interface module, and a mechanical arm control program, and the processor 1001 is used for calling the mechanical arm control program stored in the memory 1005.
The memory is used to store various types of data, which may include, for example, instructions of any application or method in the robotic arm control device, as well as application-related data. The Memory may be implemented by any type of volatile or non-volatile Memory device or combination thereof, such as static random access Memory (Static Random Access Memory, SRAM for short), random access Memory (Random Access Memory, RAM for short), electrically erasable programmable Read-Only Memory (ELECTRICALLY ERASABLE PROGRAMMABLE READ-Only Memory, EPROM for short), programmable Read-Only Memory (Programmable Read-Only Memory, PROM for short), read-Only Memory (ROM for short), magnetic Memory, flash Memory, magnetic or optical disk, optionally, the Memory may also be a processor-independent Memory device.
The Processor is used to call the mechanical arm control program stored in the memory and execute the mechanical arm tracking control method as described above, and the Processor may be an Application SPECIFIC INTEGRATED Circuit (ASIC), a digital signal Processor (DIGITAL SIGNAL Processor, DSP), a digital signal processing device (DIGITAL SIGNAL Processing Device, DSPD), a programmable logic device (Programmable Logic Device, PLD), a field programmable gate array (Field Programmable GateArray, FPGA), a controller, a microcontroller, a microprocessor, or other electronic components for executing all or part of the steps of the various embodiments of the mechanical arm tracking control method as described above.
Embodiment four:
A fourth embodiment of the present invention provides a medium having a program stored thereon, which when executed by a processor, implements the steps in the method for controlling tracking of a robot arm based on input limitation according to the first embodiment of the present invention.
The steps involved in the second, third and fourth embodiments correspond to the first embodiment of the method, and the detailed description of the second embodiment refers to the relevant description of the first embodiment. The term "computer-readable storage medium" shall be taken to include a single medium or multiple media that includes one or more sets of instructions, and shall also be taken to include any medium that is capable of storing, encoding or carrying a set of instructions for execution by the processor and that cause the processor to perform any one of the methodologies of the present invention.
It will be appreciated by those skilled in the art that the modules or steps of the invention described above may be implemented by general-purpose computer means, alternatively they may be implemented by program code executable by computing means, whereby they may be stored in storage means for execution by computing means, or they may be made into individual integrated circuit modules separately, or a plurality of modules or steps in them may be made into a single integrated circuit module. The present invention is not limited to any specific combination of hardware and software.
While the foregoing description of the embodiments of the present invention has been presented in conjunction with the drawings, it should be understood that it is not intended to limit the scope of the invention, but rather, it is intended to cover all modifications or variations within the scope of the invention as defined by the claims of the present invention.

Claims (7)

1.一种基于输入受限的机械臂跟踪控制方法,其特征在于,包括以下步骤:1. A tracking control method for a robotic arm based on input constraints, characterized by comprising the following steps: 获取机械臂的物理特性数据和预设性能指标;Acquire the physical characteristics data and preset performance indicators of the robotic arm; 根据物理特性数据和预设性能指标,构建机械臂的受约束系统模型;Based on physical property data and preset performance indicators, a constrained system model of the robotic arm is constructed. 对受约束系统模型进行等价系统转换,得到无约束系统模型;The constrained system model is transformed into an equivalent system model to obtain an unconstrained system model. 根据无约束系统模型和机械臂的最优控制策略,构建哈密顿-雅克比-贝尔曼方程;其中,最优控制策略为受非对称输入限制的机械臂的最优控制策略,所述根据无约束系统模型和机械臂的最优控制策略,构建哈密顿-雅克比-贝尔曼方程的具体步骤为:Based on the unconstrained system model and the optimal control strategy of the robotic arm, the Hamilton-Jacobi-Bellman equations are constructed; wherein, the optimal control strategy is the optimal control strategy of the robotic arm constrained by asymmetric input. The specific steps for constructing the Hamilton-Jacobi-Bellman equations based on the unconstrained system model and the optimal control strategy of the robotic arm are as follows: 根据无约束系统模型和所述受非对称输入限制的机械臂的最优控制策略定义代价函数;所述根据无约束系统模型和所述受非对称输入限制的机械臂的最优控制策略定义代价函数的具体步骤为:The cost function is defined based on the unconstrained system model and the optimal control strategy of the robotic arm constrained by asymmetric input. The specific steps for defining the cost function based on the unconstrained system model and the optimal control strategy of the robotic arm constrained by asymmetric input are as follows: 根据无约束系统模型定义位置跟踪误差,得到增广状态和因非对称输入设计的正定项;针对转化后无约束系统模型,定义新的增广矩阵;所谓受非对称输入限制,即输入被控对象的控制为,其中代表输入限制的最小值,代表输入限制的最大值;Based on the position tracking error defined in the unconstrained system model, the augmented state and the positive definite term due to asymmetric input design are obtained. For the transformed unconstrained system model, a new augmented matrix is defined. The so-called asymmetric input constraint refers to the control of the controlled object being... and ,in This represents the minimum value of the input limit. Represents the maximum value of the input limit; 并定义因非对称输入设计的正定项为:And define the positive definite terms for the asymmetric input design. for: 其中,,m为控制输入u的个数,s为积分变量,tanh是双曲正切函数;in, m is the number of control inputs u, s is the integration variable, and tanh is the hyperbolic tangent function; 结合增广状态、因非对称输入设计的正定项和机械臂的最优控制策略,定义代价函数,所述代价函数为:Combining the augmented state, the positive definite term designed due to asymmetric input, and the optimal control strategy of the robotic arm, a cost function is defined as follows: 其中,是正定矩阵,可根据实际需要设定,t是时间变量,是积分变量;in, It is a positive definite matrix, which can be set according to actual needs, and t is a time variable. It is an integral variable; 根据代价函数构建哈密顿-雅克比-贝尔曼方程;所述根据代价函数构建哈密顿-雅克比-贝尔曼方程的具体步骤为:The Hamilton-Jacobi-Bellman equation is constructed based on the cost function; the specific steps for constructing the Hamilton-Jacobi-Bellman equation based on the cost function are as follows: 根据代价函数定义哈密顿函数和最优代价函数,所述代价函数定义哈密顿函数为:Based on the cost function, the Hamiltonian function and the optimal cost function are defined. The cost function defines the Hamiltonian function as follows: 其中, in, ; 所述最优代价函数为:The optimal cost function is: 其中,表示针对机械臂的允许的控制策略的集合,满足in, This represents the set of permitted control strategies for a robotic arm. satisfy ; 利用贝尔曼最优原则求解所述最优代价函数,得到最优代价函数的最优解为:Using the Bellman optimality principle, the optimal solution to the optimal cost function is obtained as follows: ; 将最优解代入哈密顿函数,得到哈密顿-雅克比-贝尔曼方程为:Substituting the optimal solution into the Hamiltonian function, we obtain the Hamilton-Jacobi-Bellman equation: ; 通过自适应动态规划方法求解所述哈密顿-雅克比-贝尔曼方程,得到最优控制律,以根据所述最优控制律对所述机械臂进行控制;所述最优控制律为:The Hamilton-Jacobi-Bellman equations are solved using an adaptive dynamic programming method to obtain the optimal control law, which is then used to control the robotic arm. The optimal control law is as follows: . 2.如权利要求1所述的基于输入受限的机械臂跟踪控制方法,其特征在于,2. The robotic arm tracking control method based on input constraints as described in claim 1, characterized in that, 所述根据物理特性数据和预设性能指标,构建机械臂的受约束系统模型的具体步骤为:The specific steps for constructing the constrained system model of the robotic arm based on physical characteristic data and preset performance indicators are as follows: 根据物理特性数据建立机械臂的状态空间方程;Establish the state-space equation of the robotic arm based on physical property data; 根据预设性能指标定义预设性能函数;Define a preset performance function based on preset performance indicators; 根据状态空间方程和预设性能函数构建受约束系统模型。A constrained system model is constructed based on the state-space equations and preset performance functions. 3.如权利要求2所述的基于输入受限的机械臂跟踪控制方法,其特征在于,3. The robotic arm tracking control method based on input constraints as described in claim 2, characterized in that, 所述根据物理特性数据建立机械臂的状态空间方程的具体步骤为:The specific steps for establishing the state-space equation of the robotic arm based on physical property data are as follows: 对物理特性数据进行建模得到机械臂的动力学模型;The dynamic model of the robotic arm is obtained by modeling the physical property data; 根据机械臂的物理特性对动力学模型进行转换,得到机械臂的状态空间方程。The dynamic model is transformed based on the physical characteristics of the robotic arm to obtain the state-space equation of the robotic arm. 4.如权利要求1所述的基于输入受限的机械臂跟踪控制方法,其特征在于,4. The robotic arm tracking control method based on input constraints as described in claim 1, characterized in that, 采用基于神经网络架构的自适应动态规划方法求解所述哈密顿-雅克比-贝尔曼方程,得到最优控制律。The Hamilton-Jacobi-Bellman equations are solved using an adaptive dynamic programming method based on a neural network architecture to obtain the optimal control law. 5.一种基于输入受限的机械臂跟踪控制系统,其用于执行如权利要求1-4中任一项所述的一种基于输入受限的机械臂跟踪控制方法,其特征在于,包括:5. A robotic arm tracking control system based on input constraints, used to execute a robotic arm tracking control method based on input constraints as described in any one of claims 1-4, characterized in that it comprises: 数据获取模块,用于获取机械臂的物理特性数据和预设性能指标;The data acquisition module is used to acquire the physical characteristic data and preset performance indicators of the robotic arm; 模型构建模块,用于根据物理特性数据和预设性能指标,构建机械臂的受约束系统模型;The model building module is used to construct a constrained system model of the robotic arm based on physical property data and preset performance indicators. 系统转换模块,用于对受约束系统模型进行等价系统转换,得到无约束系统模型;The system transformation module is used to perform equivalent system transformation on the constrained system model to obtain the unconstrained system model; 方程构建模块,用于根据无约束系统模型和机械臂的最优控制策略,构建哈密顿-雅克比-贝尔曼方程;其中,最优控制策略为受非对称输入限制的机械臂的最优控制策略;The equation construction module is used to construct the Hamilton-Jacobi-Bellman equations based on the unconstrained system model and the optimal control strategy of the robotic arm; where the optimal control strategy is the optimal control strategy of the robotic arm constrained by asymmetric input. 最优控制模块,用于通过自适应动态规划方法求解所述哈密顿-雅克比-贝尔曼方程,得到最优控制律,以根据所述最优控制律对所述机械臂进行控制。The optimal control module is used to solve the Hamilton-Jacobi-Bellman equations using an adaptive dynamic programming method to obtain the optimal control law, and then control the robotic arm according to the optimal control law. 6.一种计算机可读存储介质,其特征在于,其中存储有多条指令,所述指令适于由终端设备的处理器加载并执行权利要求1-4中任一项所述的基于输入受限的机械臂跟踪控制方法。6. A computer-readable storage medium, characterized in that it stores a plurality of instructions adapted for loading and execution by a processor of a terminal device of the input-constrained robotic arm tracking control method according to any one of claims 1-4. 7.一种终端设备,其特征在于,包括处理器和计算机可读存储介质,处理器用于实现各指令;计算机可读存储介质用于存储多条指令,所述指令适于由处理器加载并执行权利要求1-4中任一项所述的基于输入受限的机械臂跟踪控制方法。7. A terminal device, characterized in that it comprises a processor and a computer-readable storage medium, the processor being configured to implement various instructions; the computer-readable storage medium being configured to store multiple instructions, the instructions being adapted to be loaded by the processor and executed by the processor according to any one of claims 1-4, based on the input-constrained robotic arm tracking control method.
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