CN116872197A - Adaptive neural network inversion control method and control system for single-rod mechanical arm - Google Patents
Adaptive neural network inversion control method and control system for single-rod mechanical arm Download PDFInfo
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Abstract
The invention relates to a inversion control method of a self-adaptive neural network of a single-rod mechanical arm and a control system thereof, wherein the method firstly establishes a dynamic model of the single-rod mechanical arm in a Cartesian coordinate system, and regards parameter disturbance, mechanical friction and coupling disturbance among joints in a dynamic nominal model as an unknown finite unmatched quantity of the system, and takes the moment of a joint servo motor as a control quantity, thereby constructing an equivalent decoupled controlled model; in order to achieve a safety performance constraint target, a Lyapunov function with constraint performance is constructed, unknown nonlinear items in a decoupled dynamics model are approximated by using two RBF neural networks, and a hyperbolic tangent function is added to each item of a control law so as to construct a novel structure inversion control law; the invention not only emphasizes the safety performance of the mechanical arm joint, but also lightens the operation load of the controller, accelerates the operation performance of the controller, enhances the robustness of the system and has better steady-state precision.
Description
Technical Field
The invention relates to the technical field of industrial mechanical arm control, in particular to an inversion control method and a control system of a self-adaptive neural network of a single-rod mechanical arm.
Background
In recent years, industrial robot arms have played an important role in manufacturing. In the age background of the trend of the China to precision, intellectualization and digitization, how to bring the traditional industrial mechanical arm control technology into play with a certain level of application of intellectualization and digitization is a technical challenge in the related field at present. Although the link joint type mechanical arm has various structures, the basic model can be summarized as a mechanical arm joint driven by a motor driving system as a power source so as to coordinate the working tasks of the end effector. The dynamics system is thus an uncertainty, strongly coupled nonlinear system.
The technology of the presently disclosed patent mainly relates to the aspects of PID control, robust self-adaptive control, sliding mode variable structure control, cross coupling optimal control and the like. But little consideration is given to safety constraint performance in the control method; therefore, in the operation process of the single-link mechanical arm, certain safety constraint performance is required for the position, the speed and the moment of the single-link mechanical arm, and the single-link mechanical arm has strong robustness on various uncertainties and comprehensive interferences and has good tracking performance on an expected track, so that the single-link mechanical arm is an advanced technical invention.
Disclosure of Invention
The invention aims to solve the technical problem of providing the self-adaptive neural network inversion control method of the single-rod mechanical arm, by the method, the robust self-adaptive neural network controller with full-state constraint of safety guarantee in the mechanical arm operation process can be obtained, so that each joint of the single-rod mechanical arm can track an expected track with high precision in a safety set constraint range, and in the track tracking process, the friction, external disturbance and inter-axis disturbance of the joint of the robot can be overcome, and the robustness is high.
In a first aspect, the present invention adopts a technical scheme that the method for controlling inversion of a self-adaptive neural network of a single-rod mechanical arm comprises the following steps:
s1, establishing a joint rigid single-link mechanical arm dynamics model of a single-link mechanical arm dynamics system in a Cartesian space coordinate system, and converting the dynamics model into a system state space model; the system state space model is as follows:wherein x is 1 Position variable signals, x, representing the joints of the single-link mechanical arm acquired in real time through a position sensor 2 Speed variable signal representing the joint of the single link mechanical arm acquired in real time by the speed sensor,/- > And->Respectively representing a system function and a control function according to the single-link mechanical arm, wherein the system function and the control function are unknown functions; d, d 1 (t) and d 2 (t) each represent a non-matching interfering signal that is bounded but unknown to the world; u represents the output signals of the mechanical arm joint speed and moment subsystem;
s2, the single-link mechanical arm dynamics system comprises a second-order subsystem, wherein the first-order subsystem of the single-link mechanical arm dynamics system is a mechanical arm joint position and speed subsystem, a double RBF neural network online approximation method is adopted to obtain the virtual control rate of the mechanical arm joint position and speed subsystem, and the specific process is as follows:
s2.01, acquiring a single-link mechanical arm joint position track tracking deviation signal in real time: z 1 ＝x 1 -y d And a speed trajectory tracking bias signal: z 2 ＝x 2 -α 1 The method comprises the steps of carrying out a first treatment on the surface of the Which is a kind ofWherein x is 1 Position variable signals, x, representing the joints of the single-link mechanical arm acquired in real time through a position sensor 2 A speed variable signal, y, representing a single-link mechanical arm joint acquired in real time through a speed sensor d A, representing a desired position track signal of a single-link mechanical arm joint 1 Output signals representing the position and speed subsystem of the mechanical arm joint, namely a virtual speed control law;
s2.02, tracking the deviation signal z of the joint position track obtained in the step S2.01 according to the system state space model 1 Conducting derivation processing to obtain a single-connecting-rod mechanical arm joint position tracking deviation signal model:
wherein (1)>A speed track signal representing a single link mechanical arm joint is represented; />Is the inverse of the control function; z 2 Representing the joint tracking speed error of the single-link mechanical arm;
s2.03, tracking an unknown uncertain function in the deviation signal model of the joint position of the single-link mechanical arm in the step S2.02And->The two first order RBF neural network controllers are used for on-line approximation respectively, and the expression is as follows: />Wherein (1)>And->Respectively representing ideal weight coefficients W of two first-order RBF neural network controllers designed in the position and speed subsystems 1 * And->Is a function of the estimated value of (2); z is Z 1 ＝[x 1 ] T ，Z 1 Input signal representing a first order RBF neural network controller network, < >>And->Neural network kernel functions respectively representing position and speed subsystems of single-link mechanical arm, c 1 Is the center point of the kernel Gaussian basis function, b 1 Width as a gaussian basis function; thereby obtaining approximation results of the two first-order RBF neural network controllers;
s2.04, according to the approximation result obtained in the step S2.03, deriving time from the position tracking deviation signal model of the single-link mechanical arm joint in the step S2.02, and obtaining the position tracking deviation signal model of the single-link mechanical arm joint: Wherein Z is 1 Representing the position variable of the joint of the single-link mechanical arm acquired in real time through a position sensor, d eq1 A neural network approximation error and an integrated uncertainty interference portion of a system dynamics model representing a mechanical arm joint position and speed subsystem; />d eq1 Is bounded and is present +.>
S2.05, designing a virtual control law of a mechanical arm joint position and speed subsystem according to an obtained position tracking deviation signal model of the single-link mechanical arm joint, wherein the virtual control law is as follows:wherein,' kappa 1 > 0 represents the speed error adjustment parameter, beta 1 ＞0,ρ 1 > 0 is the parameter to be selected, k b1 Constraint range k representing joint position deviation of single-link mechanical arm b1 ＝k c1 -A 0 ，k c1 A defined range parameter representing position tracking, A 0 Representing a positive constant;
s3, inverting the weight self-adaptive rate of the corresponding double RBF neural network according to the virtual control rate of the mechanical arm joint position and speed subsystem obtained in the step S2.05; the specific process is as follows:
s3.01, defining the weight coefficient errors of the two first-order RBF neural network controllers designed in the step S2.03, namely:wherein W is 1 * And->Ideal weight coefficients respectively representing two first-order RBF neural network controllers, +.>And->Respectively represent W 1 * And->Is a function of the estimated value of (2);
S3.02, designing a Lyapunov function V of a joint position and speed subsystem of the single-connecting-rod mechanical arm according to the weight coefficient errors of the two first-order RBF neural network controllers defined in the step S3.01 1 ：
|z 1 (0)|＜k b1 The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>And->All represent an adaptive gain coefficient matrix, |z 1 (0)|＜k b1 Representing the feasibility condition of joint position constraint, z 1 (0) Representing a position error initial value;
s3.03, deriving the Lyapunov function obtained in the step S3.12 according to the position tracking deviation signal of the single-link mechanical arm joint obtained in the step S2.04 and the control law obtained in the step S2.05 to obtain
S3.04 derivative of Lyapunov function obtained according to step S3.03Obtaining weight self-adaption rates of two first-order RBF neural network controllers of the mechanical arm joint position and speed subsystem: />Wherein sigma 11 Sum sigma 12 Representing the parameters to be designed, sigma 11 ＞0,σ 12 ＞0；/>Representing a matrix of adaptive gain coefficients,and->The weight self-adaptive coefficients of the two designed first-order RBF neural network controllers are represented;
s4, the second order subsystem of the single-link mechanical arm dynamics system is a mechanical arm joint speed and moment subsystem, the control rate of the mechanical arm joint speed and moment subsystem is obtained by adopting a double RBF neural network on-line approximation method in the same mode as the steps S2-S3, and the weight self-adaption rate of the corresponding double RBF neural network is obtained according to inversion of the control rate of the mechanical arm joint speed and moment subsystem.
The beneficial effects of the invention are as follows: by adopting the self-adaptive neural network inversion control method of the single-rod mechanical arm, the self-adaptive neural network controller with full-state constraint robustness for safety guarantee can be obtained, so that each joint of the single-rod mechanical arm can track an expected track with high precision within a safety-set constraint range, friction, external disturbance and inter-axis disturbance of a robot joint can be overcome in the track tracking process, and the self-adaptive neural network inversion control method has stronger robustness; in the method, for different subsystems, unknown factors in the two RBF neural networks are respectively adopted to approach the deviation signals on line, and the input signals of each neural network only need real-time sensor signals, so that the on-line calculated amount is greatly reduced compared with the existing method, and the operation rate is improved.
Preferably, in step S4, the specific process of obtaining the control rate of the robot joint speed and moment subsystem by using the dual RBF neural network on-line approximation method includes the following steps:
s4.01, acquiring a joint speed tracking signal in real time: z 2 ＝x 2 -α 1 Wherein z is 2 Speed tracking deviation signal, x, representing a single link mechanical arm joint 2 Representing the speed variable of the joint of the single-link mechanical arm acquired in real time through a speed sensor, alpha 1 Representing the position and velocity of a robotic arm jointVirtual control rate of the system;
s4.02, according to the system state space model, the z in the step S4.01 is calculated 2 Obtaining a speed tracking deviation signal model of the first single-link mechanical arm joint by conducting derivative processing:wherein (1)>A derivative representing the virtual control law of the position and velocity subsystem designed in step S2.05; />Representing the inverse of the second level subsystem control function; d, d 2 Representing the integrated interference of the second order subsystem, the interference being bounded but the specific threshold is unknown;
s4.03, unknown uncertainty items in the position tracking deviation signal model of the single-link mechanical arm joint in the step S4.02And->The two second order RBF neural network controllers are used for online approximation respectively, and the expression is as follows: />Wherein (1)>And->Ideal weight coefficient of RBF neural network respectively representing speed moment subsystem of single-link mechanical arm +.>And->Estimated value of ∈10->And (3) withKernel functions respectively representing neural networks of speed and moment subsystems of single-connecting-rod mechanical arms, c 2 Is the center point of the kernel Gaussian basis function, b 2 Width of Gaussian basis function, Z 2 ＝[x 1 ,x 2 ] T An input signal representing a neural network; obtaining approximation results of two second-order RBF neural network controllers in a second-order subsystem;
s4.04, constructing a speed tracking deviation signal model of the single-link mechanical arm joint obtained in the step S4.02 as a speed tracking deviation signal model of a second single-link mechanical arm joint according to the approximation result obtained in the step S4.03, wherein the speed tracking deviation signal model is as follows:wherein z is 2 D, representing the speed variable of the joint of the single-link mechanical arm acquired in real time through a speed sensor eq2 Neural network approximation errors and integration uncertainty interference of a system dynamics model of the mechanical arm joint speed and moment subsystem are represented; d, d eq2 Is bounded, i.e. there is +.>
And->Respectively represent the firstIdeal weight coefficients of two second-order RBF neural network controllers of the second-order subsystem;
s4.05, designing a control law of a mechanical arm joint speed and moment subsystem according to the speed tracking deviation signal model of the single-link mechanical arm joint, wherein the control law is as follows:wherein, kappa 2 And beta 2 Representing the parameters to be designed, beta 2 ＞0,ρ 2 ＞0，k b2 Constraint range k representing joint speed deviation of single-link mechanical arm b2 ＝k c2 -A 1 ，k c2 Representing moment constraint coefficients of a mechanical arm joint, A 1 Representing a positive constant.
Preferably, in step S4, the specific process of inverting the weight adaptive rate of the corresponding dual RBF neural network according to the control rate of the robot joint speed and moment subsystem includes the following steps:
S4.11, defining the weight coefficient errors of the two second-order RBF neural network controllers in the step S4.02, namely: and->Ideal weight coefficients respectively representing two second-order RBF neural network controllers, +.>Andrespectively indicate->And->Is a function of the estimated value of (2);
s4.12, designing a Lyapunov function V of the mechanical arm joint speed and moment subsystem according to the weight coefficient errors of the two second-order RBF neural network controllers defined in the step S4.11 2 ：
|z 2 (0)|＜k b2 The method comprises the steps of carrying out a first treatment on the surface of the Wherein Γ is 21 And Γ 22 Gain matrix representing adaptive symmetry, +.>Is an adaptive gain matrix coefficient; k (k) b2 Constraint range z representing joint speed deviation of single-link mechanical arm 2 (0) Is the initial value of the speed deviation;
s4.13, according to the speed tracking deviation signal model of the single-link mechanical arm joint obtained in the step S4.04 and the control law u obtained in the step S4.05, carrying out derivative processing on the Lyapunov function obtained in the step S4.12 to obtain the Lyapunov function of the second-order subsystem And->Ideal weight coefficient of RBF neural network of speed moment subsystem respectively representing mechanical arm joint, +.>And->Respectively indicate->And->Is a function of the estimated value of (2);
s4.14 Lyapunov function of the second order subsystem obtained according to step S4.13 The weight self-adaptive law of the two second-order RBF neural network controllers of the mechanical arm joint speed and moment subsystem is obtained as follows:
wherein Γ is 21 ,Γ 22 Representing the adaptive gain matrix coefficients to be selected, σ 21 ＞0,σ 22 > 0 represents the parameters to be designed.
Preferably, in step S1, the specific process of establishing a dynamics model of the joint rigid single-link mechanical arm of the dynamics system of the single-link mechanical arm in the cartesian space coordinate system and converting the dynamics model into a system state space model includes the following steps:
s1.1, establishing a first dynamics model of the joint rigidity single-link mechanical arm in a Cartesian space coordinate system:wherein q, & gt>Respectively representing the position, the speed and the acceleration variables of the joints of the single-link mechanical arm, < >>M(q)＝M 0 (q)+δM(q)∈R n×n M (q) represents a symmetrical positive definite inertia matrix vector, matrix vectors representing centripetal and coriolis moments, G (q) =g 0 (q)+δG(q)∈R n G (q) represents a gravity moment matrix vector, τ d Respectively representing moment vector matrix of joint servo motor and bounded external disturbance moment vector, tau and tau d ∈R n And meet the following i tau d ||≤γ；M 0 (q),/>G 0 (q) each represent an exact portion of a nominal model of a single link mechanical arm dynamics system δM 0 (q),/>δG 0 (q) each represent an uncertainty term in the first kinetic model;
S1.2, uncertainty term δM 0 (q),δG 0 (q) is equivalent to a comprehensive uncertain disturbance term, which is recorded asWherein (1)>There is an unknown upper bound, namely: />
S1.3, converting the first dynamics model into a second dynamics model of the joint rigidity single-link mechanical arm according to the comprehensive uncertain disturbance item:
s1.4, converting the dynamic model in the step S1.3 into a system state space model:
wherein x is 1 Representing the position variable, x, of a single-link mechanical arm joint acquired in real time through a position sensor 2 The speed variable of the single-link mechanical arm joint acquired in real time through the speed sensor is represented, and->The system function and the control function according to the single link mechanical arm are shown as unknown functions, respectively.
In a second aspect, the invention adopts a technical scheme that the self-adaptive neural network control system of the single-rod mechanical arm comprises a single-rod joint mechanical arm, a joint servo motor position sensor arranged on the single-rod joint mechanical arm, a joint servo motor speed sensor arranged on the single-rod joint mechanical arm, a preset joint track module, a position and speed subsystem of a robot joint, a first-order RBF neural network controller acting on the position and speed subsystem of the robot joint, a robot joint speed and moment subsystem connected with the position and speed subsystem of the robot joint and a second-order RBF neural network controller acting on the robot joint speed and moment subsystem; the joint servo motor position sensor is used for acquiring position signals of the single-link joint mechanical arm for operation in real time, the joint servo motor speed sensor is used for acquiring speed signals of the single-link joint mechanical arm for operation in real time, the preset joint track module is used for outputting set joint track signals, and the preset joint track module is used for acquiring the position signals of the single-link joint mechanical arm for operation in real time The first order RBF neural network controller is used for receiving the collected position signals and the joint track signals, controlling the position and speed subsystems of the robot joints, and outputting a control rate alpha by the position and speed subsystems of the robot joints 1 The speed and moment subsystem of the robot joint receives the control signal alpha 1 The method comprises the steps of carrying out a first treatment on the surface of the The second order RBF neural network controller is used for receiving the acquired speed signal and the control signal alpha 1 The speed and moment subsystem of the robot joint is controlled, and a control signal u is output by the speed and moment subsystem of the robot joint; the single-link joint mechanical arm receives the control signal u and performs operation.
By adopting the self-adaptive neural network control system of the single-rod mechanical arm, each joint of the single-rod mechanical arm can track an expected track with high precision in a safe constraint range, friction, external disturbance and inter-axis disturbance of the joint of the robot can be overcome in the track tracking process, and the self-adaptive neural network control system has high robustness.
Drawings
FIG. 1 is a control schematic diagram of an adaptive neural network control system for a single-lever mechanical arm according to the present invention;
FIG. 2 is a schematic diagram of a joint position trace tracking signal of an industrial robot manipulator according to the present invention;
FIG. 3 is a schematic diagram of a joint velocity trace tracking signal of an industrial robot manipulator according to the present invention;
FIG. 4 is a schematic diagram of a torque output signal of an industrial robot arm according to the present invention;
FIG. 5 is a schematic diagram of the joint position trajectory tracking error of the industrial robot arm of the present invention;
FIG. 6 is a diagram of joint velocity trajectory tracking error for an industrial robot arm according to the present invention;
FIG. 7 is a schematic diagram of a weight update law of a first order RBF neural network controller according to the present invention;
fig. 8 is a schematic diagram of a weight update law of a second order RBF neural network controller according to the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings in combination with specific embodiments to enable one skilled in the art to practice the invention by reference to the specification, the scope of the invention being limited to the specific embodiments.
It will be appreciated by those skilled in the art that in the present disclosure, the terms "longitudinal," "transverse," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," etc. refer to an orientation or positional relationship based on that shown in the drawings, which is merely for convenience of description and to simplify the description, and do not indicate or imply that the apparatus or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore the above terms should not be construed as limiting the present invention.
Furthermore, 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.
In the description of the embodiments of the present application, it should also be noted that, unless explicitly specified and limited otherwise, the terms "disposed," "mounted," "connected," and "connected" are to be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the above terms in the present application will be understood in specific cases by those of ordinary skill in the art.
The application relates to an inversion control method of a self-adaptive neural network of a single-rod mechanical arm, which comprises the following specific processes:
(1) The geometric parameters of the mechanical structure of the joint type connecting rod mechanical arm are clear and accurate, the joint is driven by a servo motor, and the mechanical friction and clearance interference of the joint are good in rigidity; first, a first dynamics model of a joint rigid single-link mechanical arm is established in a Cartesian space coordinate system:
Wherein, the liquid crystal display device comprises a liquid crystal display device,respectively representing the position, the speed and the acceleration variables of each joint of the single-link mechanical arm, M (q) =M 0 (q)+δM(q)∈R n×n M (q) represents a symmetrical positive definite inertia matrix vector; /> Matrix vectors representing centripetal and coriolis moments; g (q) =g 0 (q)+δG(q)∈R n G (q) represents a gravity moment matrix vector; τ, τ d ∈R n Respectively representing a moment vector matrix of the joint servo motor and a bounded external disturbance moment vector, and meeting the requirements of tau d ||≤γ；M 0 (q),/>G 0 (q) each represent an exact portion of the nominal model of the system, and δM 0 (q),/>δG 0 (q) each represent an uncertainty portion in the first dynamics model; equivalent said uncertainty as a comprehensive uncertainty interference term, noted as
Wherein, the liquid crystal display device comprises a liquid crystal display device,there is an unknown upper bound to be present,
according to the comprehensive uncertain disturbance item, converting the first dynamics model into a second-order subsystem dynamics model of the joint rigidity single-link mechanical arm:
let x 1 ＝q,u=τ and let ∈ ->And |d i (t)|＜D i And < -infinity, then, converting the second order subsystem dynamics model into a system state space model:
wherein, the liquid crystal display device comprises a liquid crystal display device,representing a system function, exhibiting highly nonlinear characteristics; />Representing the function of the control direction,representing state variables, corresponding to the positions, the speeds and the accelerations of the joints of the mechanical arm; in the actual single-link mechanical arm dynamics model, < - >The system function and the control function of the nominal model are obtained according to the mechanical geometrical parameters of the single-connecting-rod mechanical arm bodyIn the technology of the patent, functions of two systems are unknown;
(2) The system control aim is to design a full-state constraint robust self-adaptive neural inversion controller for safety guarantee, and the system control aim is to act on the single-connecting-rod mechanical arm dynamics system in the step (4) to achieve the following aims: (1) each joint position q of the single-link mechanical arm tracks and plans the track q with high accuracy d Y in correspondence (4) enables accurate tracking of a given planned trajectory signal y d I.e. there is a position tracking signal with arbitrarily small precision coefficient epsilon > 0 which is consistent and asymptotically stable
|z 1 (t)|＝|y(t)-y d (t)|≤ε (5)
(2) In view of safety, the position variable, the speed variable and the moment variable of each joint of the single-link mechanical arm are all limited by the range, namely a range parameter k according to the actual condition exists ci Satisfy |x i |＜k ci Conditions of (i=1, 2, …, n); (3) all signals of the system are required to be stable and bounded;
(3) Defining tracking error variables of positions, speeds and moments of the joints of the single-link mechanical arm in a Cartesian coordinate system:
wherein x is 1 Representing the position variable of the joint of the single-link mechanical arm acquired in real time through a position sensor, y d A joint trajectory variable representing a given single link mechanical arm, which variable is continuous nth order derivative in actual engineering, and satisfies a bounded condition:
|y d (t)|≤A 0 ＜k c1 ，|y d (i) (t)|≤A i ,i＝1,2,…,n(7)
a herein 0 ,A 1 ,…,A n Is a positive constant; alpha i-1 A virtual control law representing the speed and moment variables in each joint; x is x 2 Representing the speed variable of the joint of the single-link mechanical arm acquired in real time through a speed sensor, alpha 1 Indicating machineVirtual control rate of the robot joint position and speed subsystem;
first position and velocity subsystem control signal
(4) According to the dynamics model of the single-link mechanical arm and the model of the controlled system, the first-order subsystem of the system is a position and speed subsystem of the robot joint, and a joint position track tracking signal is defined as z 1 ＝x 1 -y d Deriving the same and then deriving x in formula (6) 2 ＝z 2 +α 1 Substitution is known
In conventional inversion control strategies, an accurate system function is requiredAnd control function->However, in actual engineering, the function cannot be directly applied to control law design because the function is disturbed by parameters and is unknown; in the technology of the patent, an RBF neural network is used for approaching the unknown function on line; it should be noted that, because the joint position, speed and moment state signal data of the single-link mechanical arm are acquired according to the sensor in real time, the invention is different from the prior art in that the input signal of the neural network controller only needs real-time sensor signal, and the on-line calculation amount of the neural network controller is greatly reduced compared with the prior art, and because the control function is generally reversible, namely >The presence of (8) is obtained by the following treatment
Since the neural network can arbitrarily approximate the unknown function, the method in (9)Respectively using two first order RBF neural network controllers to make on-line approximation to make W 1 * And->Is an unknown uncertainty item->Is the ideal weight coefficient of (1), i.e. exists
And orderAs an estimated value of an ideal weight coefficient, a weight adaptive law will be given in the following steps;
(5) Virtual control law of position and speed subsystems: substituting the neural network approximation result shown in (11) into formula (9),
wherein the input signal of the neural network is a position state data signal Z acquired by a single-link mechanical arm joint position sensor 1 ＝[x 1 ]，d eq1 Is an integrated uncertainty disturbance in the position subsystem neural network approximation error and dynamics model, known from (10), (11) and (12)
Then from the previous step, d eq1 Is bounded, i.eThe control law of the programmable position subsystem of the (12) is as follows:
wherein kappa is 1 > 0 is the controller parameter to be designed, beta 1 ＞0,ρ 1 ＞0，k b1 ＝k c1 -A 0 Is the constraint range of the joint position deviation of the single-link mechanical arm;
(6) Single-link mechanical arm joint position subsystem Lyapunov function design with constraint conditions: defining the weight coefficient error of two first order RBF neural network controllers as
The Lyapunov function of the design location subsystem is:
(7) And (3) self-adaptive law solving of RBF neural network weight of the position and speed subsystem: deriving equation (16) and substituting equations (12) and (14) to obtain
The weight self-adaptive law of the RBF neural network of the single-link mechanical arm joint position subsystem controller is known as
σ 11 ＞0,σ 12 > 0 is the parameter to be designed;
(II) Joint speed and Torque subsystem control signals
(8) According to the dynamics model of the single-link mechanical arm and the model of the controlled system, the second subsystem of the system is a joint speed and moment subsystem, and the deviation z of the joint speed of the mechanical arm is known 2 ＝x 2 -α 1 Deriving and knowing
(9) RBF neural network of joint velocity subsystem is designed to makeAnd->Is the ideal weight of the neural network of the joint velocity subsystem, which is used to approximate exactly the unknown uncertainty term +.>Thereby having the following characteristics
Wherein Z is 2 ＝[x 1 ,x 2 ] T Is an input signal of the neural network and is real-time data acquired by a position sensor and a speed sensor of the joint. Substituting (20) into (19) to obtain
Wherein d is eq2 Is joint velocity subsystem neural network approximation error and system unmodeled dynamics and trunkFrom the previous step, the comprehensive term of the disturbance, d eq2 Is bounded, i.e. has
(10) Joint speed controller neural network design: in practical application, let As an estimated value of an ideal weight coefficient, the neural network is used for approximating an unknown system weight adaptive law to be given in the following steps;
the control signal of the available joint speed subsystem in the person (21) is taken as (23)
κ 2 ＞0，β 2 ＞0,ρ 2 > 0, is a parameter to be designed, and k b2 ＝k c2 -A 1 Constraint parameters for joint velocity errors;
(11) Single-link mechanical arm joint speed subsystem obstacle Lyapunov function design with constraint conditions: defining the weight coefficient error of the second order RBF neural network controller as
Designing the Lyapunov function of the joint velocity subsystem as
Is a self-adaptive symmetrical gain matrix to be designed;
(12) Designing a weight self-adaptive law of a RBF neural network of a joint velocity subsystem: deriving (26) to obtain
Then (27) the adaptive law of RBF weight of the joint subsystem is known as
σ 21 ＞0,σ 22 > 0 is the parameter to be designed.
The method comprises the steps of firstly establishing a single-link mechanical arm human dynamics model in a Cartesian space coordinate system, regarding parameter disturbance, mechanical friction and coupling interference among joints in the dynamics nominal model as an unknown finite unmatched uncertain quantity of a system, and taking the moment of a joint servo motor as a control quantity, thereby constructing an equivalent decoupled controlled model. In order to achieve the purpose that the joint track tracks the expected track target with high precision in the safety constraint range, the controller is designed by taking the self-adaptive inversion control strategy as a main control method. In inversion control law design of a position, speed and moment subsystem in a system, a Lyapunov function with constraint performance is constructed for achieving a safety performance constraint target, and virtual control quantity with constraint performance is constructed according to the requirement of system consistent constraint and bounded stability. In addition, in order to enhance the control robustness and overcome the defect of differential explosion caused by repeatedly deriving the virtual control quantity in the traditional inversion control, two RBF neural networks are used for approaching unknown nonlinear items in the decoupled dynamics model, a hyperbolic tangent function is added in each item of the control law to construct a novel structural inversion control law, a first-order RBF neural network controller taking formulas (14) and (18) as the control law and a second-order RBF neural network controller taking formulas (24) and (28) as the control law are obtained, the virtual control law in the controller corresponds to the position, the speed and the moment of a joint respectively, and finally, the desired track is accurately tracked in a safe constraint range by controlling the moment of a servo motor; compared with a conventional joint type mechanical arm self-adaptive control method, the control strategy of the invention not only emphasizes the safety performance of the mechanical arm joint, but also reduces the operation load of the controller, accelerates the operation performance of the controller, enhances the robustness of the system, and has better steady-state precision.
In order to verify the control performance of the neural network controller obtained by the full-state constrained single-rod mechanical arm robust self-adaptive neural network inversion control method, the full-state constrained single-rod mechanical arm robust self-adaptive neural network inversion control method in the patent technology is simulated through MATLAB/SIMULINK. The simulation model adopts a single-connecting-rod mechanical arm model corresponding to the components (3) and (4), and specific parameters are as follows:
A. simulation parameter setting:
the geometrical parameters of the single-link mechanical arm are M=0.5 Kg, m=1, l=1, g=9.8, and the dynamic model of the test model is that
Where x is 1 ＝q,Represents the position and angular velocity of the joint of the mechanical arm, M represents the mass, l represents the length of the connecting rod of the mechanical arm, d 1 ,d 2 Is the comprehensive interference in the model, respectively d 1 ＝0.5sin(t)，d 2 ＝0.5cos(t)；，y d (t) =sin (t) ·rbf neural network hidden layer using gaussianIs modeled as a core function of
c i ＝[c i1 ,c i2 ,…,c ij ] T Is the center of the hidden layer kernel function of the RBF neural network, b i Is a width function, controlling the radial width range of the function. The neural network of the mechanical arm joint position and speed subsystem is an input layer Z 1 ＝[x 1 ]，And->The hidden layer contains 13 nodes (i.e., l 1 =13), the center c of each gaussian Ji Ji function j Randomly distributed in [ -6,6 ]Within the range, select width b j ＝1,(j＝1,2,…,l 1 ). The neural network of the mechanical arm joint speed moment subsystem is provided with two input layers>The hidden layer contains 121 nodes (i.e., l 2 =121), the gaussian basis function center of each node is uniformly distributed at c j [-6,6]×[-6,6]Within the interval, and the center parameter b of the Gaussian basis function j ＝1,(j＝1,2,…,l 2 ) RBF neural network hidden layer weight +.>Random at [ -1,1]Selected in interval +.>The initial value of (1) is randomly 0,1]Internal selection;
the controller parameters were selected as follows: the position and speed constraints of the joints are respectively |x 1 |＜1.8＝k c1 ,|x 2 |＜2.0＝k c2 k b1 ＝0.8k b1 ＝1.20κ 1 ＝3,κ 2 ＝10,β 1 ＝3.0,β 2 ＝3.0,Γ 1 ＝Γ 2 ＝diag{2},α 1 ＝0.1,α 2 ＝0.1,γ 1 ＝0.1,γ 2 ＝0.1,σ 1 ＝0.15,σ 2 ＝0.15。
B. Simulation result analysis:
as can be seen from fig. 2, the arm joint position x 1 The planned track y can be accurately tracked under the conditions of unknown uncertainty and comprehensive interference d And the tracking trajectory is strictly limited in the constraint range |x 1 |＜1.8＝k c1 In FIG. 3, the velocity trace of the arm joint is reflected, the velocity signal is also within the limit of |x 2 |＜2.0＝k c2 Virtual control signal alpha of internal tracking controller 1 . As can be seen from fig. 2 and fig. 3, the single-link mechanical arm position speed subsystem controller and the single-link mechanical arm speed torque subsystem controller obtained by the control algorithm of the invention obtain better constraint performance control, and the positions and the speed tracks of the mechanical arm joints can both track the planned tracks better, so that the system has better robust performance under the conditions of unmodeled dynamics and uncertain interference.
Fig. 4 is a schematic diagram of a torque output signal of an industrial robot mechanical arm, wherein the torque of a joint servo motor is given, and the torque of the servo motor is controlled through voltage, so that the joint speed and the joint position are influenced. As can be seen from fig. 4, the joint torque output signal is smooth and bounded, and in this signal control, the speed and position of the robot arm joint can achieve a better tracking performance within a predetermined constraint range. It is further known from the tracking errors of fig. 5 and 6 that the tracking error remains within the constraint range and that the tracking deviation is stable and bounded.
Fig. 7 and 8 reflect the RBF neural network weight adaptation law employed in the present invention, and the neural network weight update obtained from fig. 7 and 8 satisfies the bounded stable condition, and the adaptive update signal is smooth and bounded. Further, the controller designed by the self-adaptive neural network inversion control method of the single-rod mechanical arm has good control performance and control effect.
Claims (5)
1. A self-adaptive neural network inversion control method of a single-rod mechanical arm is characterized by comprising the following steps of: the method comprises the following steps:
s1, establishing a joint rigid single-link mechanical arm dynamics model of a single-link mechanical arm dynamics system in a Cartesian space coordinate system, and converting the dynamics model into a system state space model; the system state space model is as follows: Wherein x is 1 Position variable signals, x, representing the joints of the single-link mechanical arm acquired in real time through a position sensor 2 The speed variable signals of the single-link mechanical arm joint acquired in real time through the speed sensor are represented, and->Respectively representing a system function and a control function according to the single-link mechanical arm, wherein the system function and the control function are unknown functions; d, d 1 (t) and d 2 (t) each represent a non-matching interfering signal that is bounded but unknown to the world; u represents the output signals of the mechanical arm joint speed and moment subsystem;
s2, the single-link mechanical arm dynamics system comprises a second-order subsystem, wherein the first-order subsystem of the single-link mechanical arm dynamics system is a mechanical arm joint position and speed subsystem, a double RBF neural network online approximation method is adopted to obtain a virtual control law of the mechanical arm joint position and speed subsystem, and the specific process is as follows:
s2.01, acquiring a single-link mechanical arm joint position track tracking deviation signal in real time: z 1 ＝x 1 -y d And a speed trajectory tracking bias signal: z 2 ＝x 2 -α 1 The method comprises the steps of carrying out a first treatment on the surface of the Wherein x is 1 Position variable signals, x, representing the joints of the single-link mechanical arm acquired in real time through a position sensor 2 A speed variable signal, y, representing a single-link mechanical arm joint acquired in real time through a speed sensor d A, representing a desired position track signal of a single-link mechanical arm joint 1 Output signals representing the position and speed subsystem of the mechanical arm joint, namely a virtual speed control law;
s2.02, tracking the deviation signal z of the joint position track obtained in the step S2.01 according to the system state space model 1 Conducting derivation processing to obtain a single-connecting-rod mechanical arm joint position tracking deviation signal model:
wherein (1)>A speed track signal representing a single link mechanical arm joint is represented; />Is the inverse of the control function; z 2 Representing the joint tracking speed error of the single-link mechanical arm;
s2.03, tracking an unknown uncertain function in the deviation signal model of the joint position of the single-link mechanical arm in the step S2.02And->The two first order RBF neural network controllers are used for on-line approximation respectively, and the expression is as follows: />Wherein (1)>And->Respectively representing ideal weight coefficients W of two first-order RBF neural network controllers designed in the position and speed subsystems 1 * And->Is a function of the estimated value of (2); z is Z 1 ＝[x 1 ] T ，Z 1 Input signal representing a first order RBF neural network controller network, < >>And->Neural network kernel functions respectively representing position and speed subsystems of single-link mechanical arm, c 1 Is the center point of the kernel Gaussian basis function, b 1 Width as a gaussian basis function; thereby obtaining approximation results of the two first-order RBF neural network controllers;
s2.04, according to the approximation result obtained in the step S2.03, deriving time from the position tracking deviation signal model of the single-link mechanical arm joint in the step S2.02, and obtaining the position tracking deviation signal model of the single-link mechanical arm joint:wherein Z is 1 Representing the position variable of the joint of the single-link mechanical arm acquired in real time through a position sensor, d eq1 A neural network approximation error and an integrated uncertainty interference portion of a system dynamics model representing a mechanical arm joint position and speed subsystem; />d eq1 Is bounded and is present +.>
S2.05, designing a virtual control law of a mechanical arm joint position and speed subsystem according to an obtained position tracking deviation signal model of the single-link mechanical arm joint, wherein the virtual control law is as follows:wherein,' kappa 1 > 0 represents the speed error adjustment parameter, beta 1 ＞0,ρ 1 > 0 is the parameter to be selected, k b1 Constraint range k representing joint position deviation of single-link mechanical arm b1 ＝k c1 -A 0 ，k c1 A defined range parameter representing position tracking, A 0 Representing a positive constant;
s3, inverting the weight self-adaptive rate of the corresponding double RBF neural network according to the virtual control law of the mechanical arm joint position and speed subsystem obtained in the step S2.05; the specific process is as follows:
S3.01, defining the weight coefficient errors of the two first-order RBF neural network controllers designed in the step S2.03, namely:wherein W is 1 * And->Respectively represent the ideal weight coefficients of two first-order RBF neural network controllers,and->Respectively represent W 1 * And->Is a function of the estimated value of (2);
s3.02, designing a Lyapunov function V of a joint position and speed subsystem of the single-connecting-rod mechanical arm according to the weight coefficient errors of the two first-order RBF neural network controllers defined in the step S3.01 1 ：|z 1 (0)|＜k b1 The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>And->All represent an adaptive gain coefficient matrix, |z 1 (0)|＜k b1 Representing the feasibility condition of joint position constraint, z 1 (0) Representing a position error initial value;
s3.03, deriving the Lyapunov function obtained in the step S3.12 according to the position tracking deviation signal of the single-link mechanical arm joint obtained in the step S2.04 and the control law obtained in the step S2.05 to obtain
S3.04 derivative of Lyapunov function obtained according to step S3.03Obtaining weight self-adaption rates of two first-order RBF neural network controllers of the mechanical arm joint position and speed subsystem: />Wherein sigma 11 Sum sigma 12 Representing the parameters to be designed, sigma 11 ＞0,σ 12 ＞0；/>Representing a matrix of adaptive gain coefficients,and->The weight self-adaptive coefficients of the two designed first-order RBF neural network controllers are represented;
S4, the second order subsystem of the single-link mechanical arm dynamics system is a mechanical arm joint speed and moment subsystem, a control law of the mechanical arm joint speed and moment subsystem is obtained by adopting a double RBF neural network on-line approximation method in the same mode as the steps S2-S3, and the weight self-adaption rate of the corresponding double RBF neural network is obtained according to inversion of the control law of the mechanical arm joint speed and moment subsystem.
2. The adaptive neural network inversion control method of the single-rod mechanical arm according to claim 1, wherein the method comprises the following steps: in step S4, the specific process of obtaining the control law of the mechanical arm joint speed and moment subsystem by adopting the double RBF neural network on-line approximation method includes the following steps:
s4.01, acquiring a joint speed tracking signal in real time: z 2 ＝x 2 -α 1 Wherein z is 2 Speed tracking deviation signal, x, representing a single link mechanical arm joint 2 Representing the speed variable of the joint of the single-link mechanical arm acquired in real time through a speed sensor, alpha 1 A virtual control law representing a mechanical arm joint position and speed subsystem;
s4.02, according to the system state space model, the z in the step S4.01 is calculated 2 Obtaining a speed tracking deviation signal model of the first single-link mechanical arm joint by conducting derivative processing: Wherein (1)>A derivative representing the virtual control law of the position and velocity subsystem designed in step S2.05; />Representing the inverse of the second level subsystem control function; d, d 2 Representing the integrated interference of the second order subsystem, the interference being bounded but the specific threshold is unknown;
s4.03, unknown uncertainty items in the position tracking deviation signal model of the single-link mechanical arm joint in the step S4.02And->The two second order RBF neural network controllers are used for online approximation respectively, and the expression is as follows:wherein (1)>And->Ideal weight coefficient of RBF neural network respectively representing speed moment subsystem of single-link mechanical arm +.>And->Estimated value of ∈10->And->Kernel functions respectively representing neural networks of speed and moment subsystems of single-connecting-rod mechanical arms, c 2 Is the center point of the kernel Gaussian basis function, b 2 Width of Gaussian basis function, Z 2 ＝[x 1 ,x 2 ] T An input signal representing a neural network; obtaining approximation results of two second-order RBF neural network controllers in a second-order subsystem;
s4.04, constructing a speed tracking deviation signal model of the single-link mechanical arm joint obtained in the step S4.02 as a speed tracking deviation signal model of a second single-link mechanical arm joint according to the approximation result obtained in the step S4.03, wherein the speed tracking deviation signal model is as follows: Wherein z is 2 D, representing the speed variable of the joint of the single-link mechanical arm acquired in real time through a speed sensor eq2 Neural network approximation errors and integration uncertainty interference of a system dynamics model of the mechanical arm joint speed and moment subsystem are represented; d, d eq2 Is bounded, i.e. there is +.>
And->Two second-order RBF neural network controls respectively representing second-order subsystemsIdeal weight coefficient of the manufacturing machine;
s4.05, designing a control law of a mechanical arm joint speed and moment subsystem according to the speed tracking deviation signal model of the single-link mechanical arm joint, wherein the control law is as follows:wherein, kappa 2 And beta 2 Representing the parameters to be designed, beta 2 ＞0,ρ 2 ＞0，k b2 Constraint range k representing joint speed deviation of single-link mechanical arm b2 ＝k c2 -A 1 ，k c2 Representing moment constraint coefficients of a mechanical arm joint, A 1 Representing a positive constant.
3. The adaptive neural network inversion control method of the single-rod mechanical arm according to claim 2, wherein the method comprises the following steps: in step S4, the specific process of inverting the weight self-adaptive rate of the corresponding dual RBF neural network according to the control law of the mechanical arm joint speed and moment subsystem includes the following steps:
s4.11, defining the weight coefficient errors of the two second-order RBF neural network controllers in the step S4.02, namely: And->Ideal weight coefficients respectively representing two second-order RBF neural network controllers, +.>And->Respectively indicate->And->Is a function of the estimated value of (2);
s4.12, designing a Lyapunov function V of the mechanical arm joint speed and moment subsystem according to the weight coefficient errors of the two second-order RBF neural network controllers defined in the step S4.11 2 ：|z 2 (0)|＜k b2 The method comprises the steps of carrying out a first treatment on the surface of the Wherein Γ is 21 And Γ 22 Gain matrix representing adaptive symmetry, +.>Is an adaptive gain matrix coefficient; k (k) b2 Constraint range z representing joint speed deviation of single-link mechanical arm 2 (0) Is the initial value of the speed deviation;
s4.13, according to the speed tracking deviation signal model of the single-link mechanical arm joint obtained in the step S4.04 and the control law u obtained in the step S4.05, carrying out derivative processing on the Lyapunov function obtained in the step S4.12 to obtain the Lyapunov function of the second-order subsystem And->Ideal weight coefficient of RBF neural network of speed moment subsystem respectively representing mechanical arm joint, +.>And->Respectively indicate->And->Is a function of the estimated value of (2);
s4.14 Lyapunov function of the second order subsystem obtained according to step S4.13The weight self-adaptive law of the two second-order RBF neural network controllers of the mechanical arm joint speed and moment subsystem is obtained as follows: / >Wherein Γ is 21 ,Γ 22 Representing the adaptive gain matrix coefficients to be selected, σ 21 ＞0,σ 22 > 0 represents the parameters to be designed.
4. The adaptive neural network inversion control method of the single-rod mechanical arm according to claim 1, wherein the method comprises the following steps: in step S1, the specific process of establishing a dynamics model of the joint rigid single-link mechanical arm of the single-link mechanical arm dynamics system in the cartesian space coordinate system and converting the dynamics model into a system state space model includes the following steps:
s1.1, establishing a first dynamics model of the joint rigidity single-link mechanical arm in a Cartesian space coordinate system:wherein (1)>Respectively representing the position, the speed and the acceleration variables of the joints of the single-link mechanical arm, < >>M(q)＝M 0 (q)+δM(q)∈R n×n M (q) represents a symmetrical positive definite inertia matrix vector,matrix vectors representing centripetal and coriolis moments, G (q) =g 0 (q)+δG(q)∈R n G (q) represents a gravity moment matrix vector, τ d Respectively representing moment vector matrix of joint servo motor and bounded external disturbance moment vector, tau and tau d ∈R n And meet the following i tau d ||≤γ；M 0 (q),/>G 0 (q) each represent an exact portion of a nominal model of a single link mechanical arm dynamics system δM 0 (q),/>δG 0 (q) each represent an uncertainty term in the first kinetic model;
S1.2, uncertainty term δM 0 (q),δG 0 (q) is equivalent to a comprehensive uncertain disturbance term, which is recorded asWherein (1)>There is an unknown upper bound, namely: />
S1.3, converting the first dynamics model into a second dynamics model of the joint rigidity single-link mechanical arm according to the comprehensive uncertain disturbance item:
s1.4, converting the dynamic model in the step S1.3 into a system state space model:wherein x is 1 Representing the position variable, x, of a single-link mechanical arm joint acquired in real time through a position sensor 2 Speed variable representing the joint of the single link mechanical arm acquired in real time by the speed sensor, ++>And->The system function and the control function according to the single link mechanical arm are shown as unknown functions, respectively.
5. An adaptive neural network control system of a single-rod mechanical arm, for implementing the adaptive neural network inversion control method of a single-rod mechanical arm according to any one of claims 1 to 4, the system comprises a single-rod joint mechanical arm, a joint servo motor position sensor installed on the single-rod joint mechanical arm, a joint servo motor speed sensor installed on the single-rod joint mechanical arm, a preset joint track module, a mechanical arm joint position and speed subsystem, a first order RBF neural network controller acting on the mechanical arm joint position and speed subsystem, and a mechanical arm joint speed and moment connected with the mechanical arm joint position and speed subsystem The second-order RBF neural network controller acts on the mechanical arm joint speed and moment subsystem; the joint servo motor position sensor is used for collecting position signals of the operation of the single-link joint mechanical arm in real time, the joint servo motor speed sensor is used for collecting speed signals of the operation of the single-link joint mechanical arm in real time, the preset joint track module is used for outputting set joint track signals, the first-order RBF neural network controller is used for receiving the collected position signals and the joint track signals, controlling the position and speed subsystem of the joint of the mechanical arm and outputting control signals alpha by the position and speed subsystem of the joint of the mechanical arm 1 The speed and moment subsystem of the mechanical arm joint receives the control signal alpha 1 The method comprises the steps of carrying out a first treatment on the surface of the The second order RBF neural network controller is used for receiving the acquired speed signal and the control signal alpha 1 The speed and moment subsystem of the mechanical arm joint is controlled, and a control signal u is output by the speed and moment subsystem of the mechanical arm joint; the single-link joint mechanical arm receives the control signal u and performs operation.
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