CN116276986B - Composite learning self-adaptive control method of flexible driving robot - Google Patents

Composite learning self-adaptive control method of flexible driving robot Download PDF

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CN116276986B
CN116276986B CN202310183296.4A CN202310183296A CN116276986B CN 116276986 B CN116276986 B CN 116276986B CN 202310183296 A CN202310183296 A CN 202310183296A CN 116276986 B CN116276986 B CN 116276986B
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robot
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matrix
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CN116276986A (en
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潘永平
时天
黎卫兵
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Sun Yat Sen University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/163—Programme controls characterised by the control loop learning, adaptive, model based, rule based expert control
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

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  • Robotics (AREA)
  • Mechanical Engineering (AREA)
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Abstract

The invention discloses a composite learning self-adaptive control method of a flexible driving robot, which comprises the steps of establishing a CAR model and establishing a CAR controller; based on singular perturbation theory, a first order reduction system and a first boundary layer system are established according to a CAR model, an inner ring linear controller is established according to a CAR controller, a second boundary layer system is determined according to the first boundary layer system and the inner ring linear controller, the CAR controller is combined with the first order reduction system to conduct linear parameterization to obtain a second order reduction system, an outer ring compound learning self-adaptive controller is established according to a compound learning self-adaptive law, a robot system controller is established according to the second order reduction system, the second boundary layer system, the inner ring linear controller and the outer ring compound learning self-adaptive controller, calculation is not needed to be conducted on high-order derivative information of a robot position, and tracking performance and robustness of the flexible driving robot system can be stably and efficiently maintained.

Description

Composite learning self-adaptive control method of flexible driving robot
Technical Field
The invention relates to the technical field of intelligent robots, in particular to a compound learning self-adaptive control method of a flexible driving robot.
Background
A flexible drive robot (compliantly actuated robot, CAR) is driven by a flexible actuator to enable fast and accurate position tracking and secure human-machine interaction. The flexible actuator is a robotic actuator that actively introduces compliant elements between the drive motor and the load. The flexible drive robot typically has greater joint open loop compliance than a rigid robot, which allows the actuator inner loop to use high gain feedback to boost the joint torque control bandwidth, achieve closed loop stability and low output impedance over a wide frequency range, and output low impedance over a frequency band above the control bandwidth. However, the flexible actuator can introduce joint elasticity into the CAR, increasing vibration and settling time of the system during control, and even compromising system stability. Therefore, the influence of joint flexibility is considered in the design of the controller, and the method has important significance for improving the joint tracking precision and transient behavior of the CAR.
The traditional CAR track tracking control method is directly designed on a flexible joint robot model, such as a back-stepping method and a passive method. The design method needs the acceleration and jerk information of the joint, however, the robot is not generally provided with an acceleration sensor, so that the acceleration and jerk are difficult to accurately acquire in practice, are sensitive to measurement noise, and easily influence the control performance and even the stability of the system. Traditional CAR control methods rely on accurate model information, and inaccuracy of the model information can reduce tracking performance and robustness of the system. While adaptation is an effective method of controlling a robot without requiring an accurate robot model, in order to ensure exponential stability of the adaptive control, so as to have sufficient robustness and improve tracking performance, a strict condition of continuous excitation is required. Continuous excitation requires that the position and velocity signals of the robot remain in a state with rich spectral information all the time, and are therefore very demanding to meet in practice. This results in difficulty in convergence of the estimated parameters to the real parameters, which in turn reduces the tracking performance and robustness of the system.
Disclosure of Invention
In view of this, the embodiment of the invention provides a stable and efficient adaptive control method for a flexible driving robot.
The embodiment of the invention provides a compound learning self-adaptive control method of a flexible driving robot, which comprises the following steps: establishing a CAR model and constructing a CAR controller structure; based on a singular perturbation theory, a first order reduction system and a first boundary layer system are established according to the CAR model; constructing an inner loop linear controller according to the CAR controller; determining a second boundary layer system from the first boundary layer system and the inner loop linear controller; performing linear parameterization on the first order reduction system by combining the CAR controller to obtain a second order reduction system; constructing an outer loop compound learning self-adaptive controller according to the compound learning self-adaptive law; and constructing a robot system controller according to the second order reduction system, the second boundary layer system, the inner ring linear controller and the outer ring compound learning self-adaptive controller.
Optionally, the expression of the CAR model is:
wherein q represents the joint position of the robot link side;representing the speed of the robot link side; />Acceleration indicated as robot link side; τ a Representing moment on the side of the articulation link; m represents an inertial matrix of the robot connecting rod side; c is the connecting rod side coriolis Li Juzhen; g represents the gravity moment of the robot connecting rod side; f represents friction force; θ represents a position of the robot motor side; />Representing the speed of the robot motor side; />An acceleration on the robot motor side; b represents the inertia of the robot motor side; d represents damping on the robot motor side; k represents a stiffness matrix of the robot motor side; k (K) -1 An inverse matrix representing the stiffness matrix K; τ represents the torque of the torsion spring; u represents a control law input.
Optionally, the establishing a first order reduction system and a first boundary layer system according to the CAR model based on singular perturbation theory includes: according to the CAR model, a robot system model in a singular perturbation form is constructed; obtaining a first order reduction system according to the change of the parameter value in the robot system model; and adjusting the robot system model expression according to an algebraic algorithm to obtain a first boundary layer system.
Optionally, in combination with the CAR controller, the first order reduction system performs linearization parameter processing to obtain a second order reduction system, including: constructing a slow controller according to the CAR controller; combining the slow controller, and constructing an intermediate reduced-order system according to an extended inertia matrix and a control law of the first reduced-order system; and constructing a second order reduction system according to the row vector performance of the intermediate order reduction system.
Optionally, the expression of the second order reduction system is:
wherein v is an auxiliary variable and v ε R; psi is a regression matrix, and hasW e Is a parameter vector to be estimated, and +.>N e For the parameter vector W e Is a dimension of (2); m is M e (q) is an extended inertia matrix corresponding to the first reduced system; />Is a generalized acceleration; />Coriolis Li Juzhen, which is the robot link side; g (q) is the gravitational moment on the robot link side; />Is a moleA wiping force; />Is the speed of the robot link side;
the expression of the second boundary layer system is:
wherein z represents the state of the second boundary layer system; z' represents a first derivative of the state of the second boundary layer system at a fast time scale; z "represents a second derivative of the state of the second boundary layer system at a fast time scale; m is M -1 An inverse matrix representing an inertial matrix M on the robot link side; q represents the joint position on the robot link side; b (B) -1 An inverse matrix representing an inertia matrix B on the robot motor side; k (K) 0 And D 0 Are constant diagonal matrixes; k (K) p And K d Each representing a positive diagonal matrix.
Optionally, the constructing the outer loop composite learning adaptive controller according to the composite learning adaptive law includes: constructing a rigid robot self-adaptive controller; calculating a filtering tracking error of the tracking error information of the robot system; calculating a prediction error at the current moment; performing expansion filtering operation on the regression matrix according to the historical data information of the regression matrix; combining the filtering tracking error, the prediction error and the extended filtering operation to construct a composite learning adaptive law; and updating the prediction error by adopting the composite learning adaptive law to obtain the outer loop composite learning adaptive controller.
Optionally, the expression of the compound learning adaptive law is:
wherein,is the estimated derivative of the parameter vector; Γ is a learning law matrix of positive diagonals; psi is a generalized regression matrix; q is the joint angle of the robot link side; />The joint acceleration of the robot connecting rod side; />Is the joint reference speed of the robot connecting rod side; />Is the reference acceleration of the robot link side; e, e 2 Is a tracking error; k (k) a Sum k b Are all weight factors; psi F Representing a filtered regression matrix; />Representing a generalized parameter estimation error; t represents time; />Representing the interval integral length; />Representing the integral variable.
Optionally, the expression of the robot system controller is:
wherein u represents a control law input; τ represents the torque of the torsion spring; τ r Representing a reference torque; k (K) p And K d All represent positive diagonal matrices; k (K) c Determining a diagonal gain matrix for the positive; k (k) a And k b Are all weight factors; epsilon represents a parameter; e, e 2 Representing tracking errors; q represents the joint position on the robot link side;representing the speed of the robot link side; />Acceleration indicated as robot link side; />A reference acceleration indicating the robot link side; />Representing an estimate of the parameter vector; />Representing the derivative of the complex parameter vector estimate; Γ represents a learning law matrix of positive diagonals; ψ represents the generalized regression matrix; psi F Representing a filtered regression matrix; epsilon represents the torque prediction error; ζ represents the generalized prediction error.
The embodiment of the invention also provides a self-adaptive control system of the flexible driving robot, which comprises the following components: the first module is used for establishing a CAR model and constructing the structure of a CAR controller; the second module is used for establishing a first order reduction system and a first boundary layer system according to the CAR model based on a singular perturbation theory; the third module is used for constructing an inner loop linear controller according to the CAR controller; a fourth module for determining a second boundary layer system from the first boundary layer system and the inner loop linear controller; a fifth module, configured to combine the CAR controller and perform linear parameterization on the first reduced-order system to obtain a second reduced-order system; the sixth module is used for constructing an outer loop composite learning adaptive controller; and a seventh module for constructing a robot system controller according to the second reduced order system, the second boundary layer system, the inner loop linear controller and the outer loop compound learning adaptive controller.
The embodiment of the invention also provides electronic equipment, which comprises a processor and a memory; the memory is used for storing programs; the processor is configured to execute the program to implement the method as described above.
The embodiment of the invention has the following beneficial effects: by establishing a CAR model and constructing a CAR controller; based on singular perturbation theory, a first order reduction system and a first boundary layer system are established according to a CAR model, an inner ring linear controller is established according to a CAR controller, a second boundary layer system is determined according to the first boundary layer system and the inner ring linear controller, the CAR controller is combined with the first order reduction system to conduct linear parameterization to obtain a second order reduction system, an outer ring compound learning self-adaptive controller is established according to a compound learning self-adaptive law, a robot system controller is established according to the second order reduction system, the second boundary layer system, the inner ring linear controller and the outer ring compound learning self-adaptive controller, calculation is not needed to be conducted on high-order derivative information of a robot position, and tracking performance and robustness of the flexible driving robot system can be stably and efficiently maintained.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of method steps of an embodiment of the present invention;
FIG. 2 is a control process block diagram of an embodiment of the present invention;
FIG. 3 is a graph comparing track following errors in 0-25 seconds for an embodiment of the present invention with a conventional CLRC and MSLC;
FIG. 4 is a graph comparing the tracking error of the present invention with the existing CLRC and MSLC track in 85-105 seconds.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
The embodiment of the invention discloses a self-adaptive control method of a flexible driving robot, which comprises the following steps: establishing a CAR model and constructing a CAR controller structure; based on a singular perturbation theory, a first order reduction system and a first boundary layer system are established according to the CAR model; constructing an inner loop linear controller according to the CAR controller; determining a second boundary layer system from the first boundary layer system and the inner loop linear controller; performing linear parameterization on the first reduced system by combining with the CAR controller to obtain a second reduced system; constructing an outer loop compound learning self-adaptive controller according to the compound learning self-adaptive law; and constructing a robot system controller according to the second order reduction system, the second boundary layer system, the inner ring linear controller and the outer ring compound learning self-adaptive controller.
Specifically, the adaptive control method of the embodiment of the invention is applicable to the hinge type CAR for fixing the flexibility of the joint, and the hinge type CAR for fixing the flexibility of the joint can comprise a medical robot, an industrial robot, a special robot and the like.
Before proceeding to the description, the partial symbols, variables and terms that appear at various points in the description of the invention will be described as follows:
r represents a real number set; r is R + Representing a positive real number set; r is R n Representing an n-dimensional real vector set; m×n represents a real matrix set; l (L) 2 Representing the space formed by the square integrable signals; l (L) ∞ Representing the space constituted by the bounded signals; lambda (lambda) min (A) Representing the minimum eigenvalue of matrix a; lambda (lambda) max (A) Representing the maximum eigenvalue of matrix a; sigma (sigma) min (A) Representing the minimum singular value of matrix a; min { · } represents the minimum operator; max { · } represents the maximum operator; the x is the euclidean norm of x; "x" is a convolution operator; col (x, y) represents [ x ] T ,y T ] T ；x T Representing an n-dimensional row vector;represents x andc is an equivalent infinitesimal relationship; x, y E R n ,A∈R n×n M and n are positive integers.
In the embodiment of the present invention, let t represent a time variable, which is defined as follows:
definition of tracking error e 1 (t)：＝q d (t) -q (t); wherein q (t) is the actual joint angle, q d (t) is the desired joint angle, and q d (t)：＝[q d1 (t),q d2 (t),…,q dn (t)] T ∈R n Satisfies the following conditions Is the desired joint acceleration;
defining a filtered tracking errorWherein (1)>For the actual joint speed +.>Is the joint reference speed, and-> For the desired joint velocity, Λ is the control gain matrix for positive focus, and Λ ε R n×n ；
It should be noted that, the tracking error in the embodiment of the present invention refers to an error between the actual joint angle and the desired joint angle of the robot.
Let the regression matrix be phi (t), sigma be the singular value of the matrix,for the interval integral length, T e Is a positive constant; s is a differential operator, I is an identity matrix, and there are definition 1 and definition 2 as follows:
definition 1 (continuous excitation): regression matrix Φ (t) ∈R N×n The conditions are satisfied: if it isSo thatThe matrix is said to be continuously excited.
Definition 2 (interval excitation): regression matrix Φ (t) ∈R N×n The conditions are satisfied: if it isSo thatThe matrix interval excitation is called.
The following describes in detail a composite learning adaptive control method for a flexible driving robot according to an embodiment of the present invention with reference to fig. 1, and fig. 1 is a flowchart of method steps according to an embodiment of the present invention, including steps S100 to S700:
s100, building a CAR model and constructing a CAR controller structure.
Specifically, a CAR model is established, and the expression of the CAR model is:
in the formulas (1) and (2), q represents a joint position on the robot link side;representing the speed of the robot link side;/>acceleration indicated as robot link side; τ a Representing moment on the side of the articulation link; m represents an inertial matrix of the robot connecting rod side; c is the connecting rod side coriolis Li Juzhen; g represents the gravity moment of the robot connecting rod side; f represents friction force; θ represents the position of the robot motor side; />Representing the speed of the robot motor side; />Representing acceleration of the robot motor side; b represents an inertial matrix of the robot motor side; d represents damping on the robot motor side; k represents a stiffness matrix of the robot motor side; τ represents the moment of the torsion spring, and τ: =k (θ -q); u represents a control law input.
And constructing the structure of the CAR controller based on the singular perturbation theory. The singular perturbation theory of the embodiment of the invention is based on the control of singular perturbation, namely, the CAR model is divided into two subsystems of a slow time scale model and a fast time scale model, and the control is respectively based on a slow variable and a fast variable, so that the design of the CAR control law without high-order time derivative information such as joint acceleration, jerk and the like becomes possible.
The expression of the CAR controller is:
u(t,e,y)＝u lin (t,e)+u act (y) (3)
in the formula (3), t is time; e is a slow variable; y is a fast variable; u (u) lin Position controller for dynamic link-side robot, and u lin ∈R n ；u act Dynamic moment controller for connecting rod side actuator, u act ∈R n And is also provided withK p And K d Are all positive and negative diagonal matrixes, K -1 Determining an inverse matrix of the diagonal matrix for the positive; />The torque change rate of the torsion spring is obtained; epsilon is a parameter;
s200, based on a singular perturbation theory, a first order reduction system and a first boundary layer system are established according to the CAR model.
Specifically, the CAR model refers to a dynamic model in which the flexible drive robot does not feed back the result of control to affect the current control. Step S200 includes the following steps S210 to S230:
s210, constructing a robot system model in a singular perturbation form according to the CAR model.
Specifically, a robot system model in a singular perturbation form is constructed from expression (1) and expression (2) of the CAR model. In combination with singular perturbation theory, the CAR model expression can be written as the following singular perturbation form:
in the formula (4), e 0 ,y 0 Is in an initial state, and e 0 ,y 0 ∈R 2n The method comprises the steps of carrying out a first treatment on the surface of the e is a slow variable, and e: =col (e) 1 ,e 2 )，e 1 Is tracking error, e 2 Is a filtered tracking error; y is a fast variable, andy 1 is the moment of torsion spring, y 2 Is the product of the torsion spring moment change rate and the parameter epsilon, tau is the moment of the torsion spring, and +.>The torque change rate of the torsion spring is obtained; epsilon is a parameter; f, g is a non-linear mapping, and +.>For f, g also:
in the formula (5) and the formula (6), K 0 And D 0 Are constant diagonal matrixes; u is control law input; m is M -1 Is the inverse matrix of the robot connecting rod side inertia matrix M; b (B) -1 Is the inverse matrix of the inertial matrix B at the motor side of the robot; k (K) 0 An inverse matrix that is a constant diagonal matrix; is a coriolis matrix on the link side.
The singular perturbation form of equation (4) is then a robotic system model expression.
S220, obtaining a first order reduction system according to the change of the parameter values in the robot system model.
Specifically, when the parameter value of the parameter ε of the second equation in equation (4) is 0, a first reduced-order system can be obtained and expressed as:
wherein u is s And Q is the sum of centripetal moment, gravity moment and friction force.
230. And adjusting the model expression of the robot system according to an algebraic algorithm to obtain a first boundary layer system.
Specifically, let the fast time variable t ε : =t/ε, moment control error z (t ε )：＝τ-h(t,e)， A solution of g (t, e, y, u) =0. Substituting τ=z+h into equation (4), replacing the time variable t with t ε And ignoring derivative information of all h to obtain a first boundary layer system, wherein the expression of the first boundary layer system is as follows:
z″+(M -1 (q)+N -1 )(D 0 z′+K 0 z)＝K 0 B -1 u f (8)
in formula (8), z "is the second derivative of the state of the first boundary layer system at a fast time scale; z' is the first derivative of the state of the first boundary layer system on a fast time scale; z': =dz/dt ε The method comprises the steps of carrying out a first treatment on the surface of the z is the state of the first boundary layer system; u (u) f Is a fast controller; and u is f ：＝u-u s For a fast controller, (t, e) is on a fast time scale t ε The following will remain unchanged.
S300, constructing an inner ring linear controller according to the CAR controller.
Specifically, an inner loop linear controller is constructed from the CAR controller, and epsilon=0 and τ=h in the formula (4) are given by:
u s ＝u lin (t,e)-K p h(t,e) (9)
due to u lin (t, e) is independent of ε and is thus the same as in formula (4). According to u f ＝u-u s And formulas (4) and (9) can obtain a controller of the first boundary layer system, namely an inner loop linear controller, wherein the expression of the inner loop linear controller is as follows:
s400, determining a second boundary layer system according to the first boundary layer system and the inner ring linear controller.
In particular, if the boundary layer system and the reduced order system are exponentially stable, the overall system will achieve a practical exponential stability. Inner loop linear controller u f Substituting into the expression of the first boundary layer system to obtain a second boundary layer system, andthe boundary layer system is a closed loop system, and the expression of the second boundary layer system is:
the system corresponds to a time scale t ε Lower linear time-invariant system by selecting proper gain K p And K d It can be ensured that the second boundary layer system is exponentially stable.
S500, combining the CAR controller, and carrying out linear parameterization on the first order reduction system to obtain a second order reduction system.
Specifically, step S500 includes the following step S530:
s510, constructing a slow controller according to the CAR controller.
Specifically, according to formulas (9) and (II)A slow controller may be derived, the expression of which is:
in the formula (12), the amino acid sequence of the compound,a derivative of the tracking error for filtering; />Is the reference acceleration; (I+K) p ) -1 K p ＝I-(I+K p ) -1 ，u lin (t,e)＝I+K p )τ r ，τ r Is a rigid robot controller to be designed.
S520, combining the slow controller, and constructing an intermediate reduced-order system according to the extended inertia matrix and the control law of the first reduced-order system.
Specifically, u is lin (t, e) substituting into the expression of CAR controller(3) The method comprises the following steps:
the controller u (tau) r Y) may be a PD torque regulator for actuator dynamics, and τ r Corresponding to the reference moment.
According to (7) and (12), determining an intermediate reduction system, the expression of which is:
in the formula (14), M e (q) is an extended inertia matrix corresponding to the first reduced-order system, and M e (q)：＝M(q)+I+K p ) -1 B, a step of preparing a composite material; g (q) is the gravity moment of the robot connecting rod side;coriolis Li Juzhen, which is the robot link side; τ r Is a control law to be designed. In the robot control strategy, the control law is generally moment.
S530, constructing a second order reduction system according to the row vector performance of the intermediate order reduction system.
In particular, the linear parameterization of the link-side dynamics model in general can be expressed as:
in the formula (15), v is an auxiliary variable, and v ε R n The method comprises the steps of carrying out a first treatment on the surface of the Phi is a regression matrix and hasW is the parameter vector to be estimated, and W εR N 。
The intermediate reduced-order system expression (14) is more than the connecting rod side dynamics model expression (15) Wherein b e ：＝[b e1 ,b e2 ,…,b en ] T ，b ek Is (I+K) p ) -1 B kth diagonal element, k=1, 2, …, n.
For each ofIf there is a certain row vector of +.>Then the corresponding parameter b ei And->Add, wherein->Is->Is the i-th row vector of (c).
If it isFailing to combine with phi, then ∈>Corresponding parameter b ei Expanding into phi and W as new regression channels and parameters to form new regression matrix ψ and parameter vector W e 。
Thus, the expression for determining the second reduced-order system is:
in formula (16), v is an auxiliary variable, and v ε R; psi is a regression matrix, and hasW e Is a parameter vector to be estimated, and +.>N e For the parameter vector W e Is a dimension of (c).
In the case of the embodiment of the invention, ψ is known, W e Unknown.
S600, constructing an outer loop compound learning self-adaptive controller according to the compound learning self-adaptive law.
Specifically, step S600 includes the following steps S610 to S660:
s610, constructing a self-adaptive controller of the rigid robot.
Specifically, a rigid robot adaptive controller is constructed, and the expression is:
in the formula (17), K c For positive and negative diagonal gain matrix, and K c ∈R n×n ；Ψ r Is a generalized regression matrix, and is W e And> the update mode of (2) is as follows:
in the formula (18), Γ is a learning law matrix of positive and negative angles, and Γ ε R N×N ；k a ,k b Are all weight factors, and k a ,k b ∈R + The method comprises the steps of carrying out a first treatment on the surface of the ζ is the generalized prediction error; epsilon is the torque prediction error.
S620, calculating a filtering tracking error of the tracking error information of the robot system.
S630, calculating the prediction error of the current moment.
S640, performing expansion filtering operation on the regression matrix according to the historical data information of the regression matrix.
Specifically, for steps S620 to S640, the prediction error at the current time includes a moment prediction error and a generalized moment prediction error, and the calculation formula of the moment prediction error is:
the generalized prediction error is calculated by the following formula:
in the formula (19) and the formula (20), t e Is the time of meeting the interval excitation, andT e ，σ，so that the section excitation condition Θ (T e ) Is equal to or more than sigma I; Θ (t) is the excitation matrix, and as integral variable, ψ F Is a filtering regression matrix; />Is the integration interval of the regression matrix and the moment product, and +.> τ rF Representation of the pair tau r And τ rF ：＝αe -αt *τ r ；/>Representation pair->Is a first order low pass filter of (a), andperforming first order low pass filtering can eliminate the dependence on acceleration.
S650, combining the filtering tracking error, the prediction error and the extended filtering operation to construct a compound learning adaptive law.
Specifically, a composite learning adaptive law is constructed by combining a filtering tracking error, a prediction error and an extended filtering operation, and the composite learning adaptive law is as follows:
in the formula (21), the amino acid sequence of the amino acid,filtering tracking errors including system tracking error information;is the prediction error of the current moment,/>Is a generalized parameter estimation error;then the regression matrix is subjected to extended filtering operation, and the historical data information of the regression matrix is utilized.
And S660, updating the prediction error by adopting a compound learning self-adaptive law to obtain the outer loop compound learning self-adaptive controller.
Specifically, a composite learning adaptive law is adopted to update a prediction error, and an outer loop composite learning adaptive controller is obtained, wherein the expression of the composite learning adaptive controller is as follows:
s700, constructing a robot system controller according to the second order reduction system, the second boundary layer system, the inner ring linear controller and the outer ring compound learning self-adaptive controller.
Specifically, a robot system controller is constructed according to a second order reduction system, a second boundary layer system, an inner ring linear controller and an outer ring compound learning adaptive controller, and the robot system controller has the expression:
in the formula (23), u represents a control law input; τ represents the torque of the torsion spring; τ r Representing a reference torque;representing the moment change rate of the torsion spring; k (K) p And K d All represent positive diagonal matrices; k (K) c To increase diagonallyA benefit matrix; k (k) a And k b Are all weight factors; epsilon represents a parameter; e, e 2 Representing tracking errors; q represents the joint position on the robot link side; />Representing the speed of the robot link side; />Acceleration indicated as robot link side; />Representing a reference acceleration; />Representing an estimate of the parameter vector; />A derivative representing the parameter vector estimate; Γ represents a learning law matrix of positive diagonals; ψ represents the regression matrix; psi F Representing a filtered regression matrix; epsilon represents the torque prediction error; ζ represents the generalized prediction error.
The embodiment of the invention also provides a self-adaptive control system of the flexible driving robot, which comprises the following components: the first module is used for establishing a CAR model and constructing the structure of a CAR controller; the second module is used for establishing a first order reduction system and a first boundary layer system according to the CAR model based on the singular perturbation theory; the third module is used for constructing an inner ring linear controller according to the CAR controller; a fourth module for determining a second boundary layer system based on the first boundary layer system and the inner loop linear controller; the fifth module is used for carrying out linear parameterization on the first order reduction system by combining with the CAR controller to obtain a second order reduction system; the sixth module is used for constructing an outer loop composite learning self-adaptive controller; and the seventh module is used for constructing a robot system controller according to the second order reduction system, the second boundary layer system, the inner ring linear controller and the outer ring compound learning self-adaptive controller.
The embodiment of the invention also provides electronic equipment, which comprises a processor and a memory; the memory is used for storing programs; the processor executes the program to implement the method as described above.
The embodiment of the invention has the following beneficial effects:
1. the CAR is reduced to two second-order differential equations through a singular perturbation theory, the two second-order differential equations correspond to a boundary layer system and a reduced-order system respectively, an inner loop linear controller and an outer loop composite learning self-adaptive controller are designed, the CAR controller is determined according to the two controllers, and track tracking control of the CAR flexible joint can be realized without acceleration, jerk and model information;
2. the composite learning adaptive law is constructed, the regression matrix is subjected to expansion filtering operation by utilizing the historical data information of the regression matrix, the historical data can be fully utilized, and the accuracy and the efficiency of track tracking control can be improved.
The control procedure of the embodiment of the present invention is described below with reference to the accompanying drawings:
referring to fig. 2, fig. 2 is a control process block diagram of an embodiment of the present invention. Firstly, obtaining joint angle and acceleration at the current moment through a sensor, and initializing estimated parametersCalculating the control moment tau on the connecting rod side from the formula (17) r And transmitted to an inner loop control system; calculating an actuator moment u according to the formula (13), and sending the actuator moment u to the robot as a control signal; then the joint angle and the acceleration at the next moment are obtained and combined with the control moment tau at the side of the current connecting rod r Updating the model parameters using equation (18)>Sent to the self-adaptive control law (17) and calculates the control moment tau of the connecting rod side at the next moment r 。
The effects of the embodiments of the present invention are described below with reference to the drawings and experimental data:
referring to fig. 3 and 4, fig. 3 is a graph showing a trace tracking error between 0 and 25 seconds between the embodiment of the present invention and the existing CLRC and MSLC, and fig. 4 is a graph showing a trace tracking error between 85 and 105 seconds between the embodiment of the present invention and the existing CLRC and MSLC. It can be seen from the figure that within 0-25 seconds, both SP-CLRC and CLRC tracking errors are greater than MSLC (see FIG. 3) because they are in the learning phase. When the estimated parameters converged, the tracking error of the SP-CLRC was smaller than that of MSLC and CLRC in 85-105 seconds (see FIG. 4). Therefore, the tracking effect of the invention is superior to that of the existing composite learning controller and model-based controller.
Model-based Slot-Li controller (MSLC) relies on accurate model information for offline parameter identification, whereas existing compound learning robot controllers (composite learning robot controller, CLRC) can guarantee parameter convergence only by interval excitation conditions, but rigid-flexible coupling problem is not considered, and stability of the whole system cannot be established. The method of the embodiment of the invention can ensure the convergence of parameters and the (practical index) stability of the whole system only by interval excitation conditions. In the actual CAR working process, the continuous excitation condition is generally difficult to realize, but the interval excitation condition is easier to meet, so that the algorithm provided by the embodiment of the invention can more easily realize parameter convergence, thereby fundamentally improving the tracking performance and robustness of the system.
In some alternative embodiments, the functions/acts noted in the block diagrams may occur out of the order noted in the operational illustrations. For example, two blocks shown in succession may in fact be executed substantially concurrently or the blocks may sometimes be executed in the reverse order, depending upon the functionality/acts involved. Furthermore, the embodiments presented and described in the flowcharts of the present invention are provided by way of example in order to provide a more thorough understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is changed, and in which sub-operations described as part of a larger operation are performed independently.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that: many changes, modifications, substitutions and variations may be made to the embodiments without departing from the spirit and principles of the invention, the scope of which is defined by the claims and their equivalents.
While the preferred embodiment of the present invention has been described in detail, the present invention is not limited to the embodiments described above, and those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention, and these equivalent modifications or substitutions are included in the scope of the present invention as defined in the appended claims.

Claims (7)

1. The compound learning self-adaptive control method of the flexible driving robot is characterized by comprising the following steps of:
establishing a CAR model and constructing a CAR controller structure;
based on a singular perturbation theory, a first order reduction system and a first boundary layer system are established according to the CAR model;
constructing an inner loop linear controller according to the CAR controller;
determining a second boundary layer system from the first boundary layer system and the inner loop linear controller;
performing linear parameterization on the first order reduction system by combining the CAR controller to obtain a second order reduction system;
constructing an outer loop compound learning self-adaptive controller according to the compound learning self-adaptive law;
constructing a robot system controller according to the second order reduction system, the second boundary layer system, the inner ring linear controller and the outer ring compound learning self-adaptive controller;
the method for establishing the first order reduction system and the first boundary layer system based on the singular perturbation theory according to the CAR model comprises the following steps:
according to the CAR model, a robot system model in a singular perturbation form is constructed;
obtaining a first order reduction system according to the change of the parameter value in the robot system model;
adjusting the robot system model expression according to an algebraic algorithm to obtain a first boundary layer system;
and combining the CAR controller to linearize the first order reduction system to obtain a second order reduction system, wherein the method comprises the following steps:
constructing a slow controller according to the CAR controller;
combining the slow controller, and constructing an intermediate reduced-order system according to the first reduced-order system expansion inertia matrix and a control law;
constructing a second order reduction system according to the row vector performance of the intermediate order reduction system;
the method for constructing the outer loop compound learning self-adaptive controller according to the compound learning self-adaptive law comprises the following steps:
constructing a rigid robot self-adaptive controller;
calculating a filtering tracking error of the tracking error information of the robot system;
calculating a prediction error at the current moment;
performing expansion filtering operation on the regression matrix according to the historical data information of the regression matrix;
combining the filtering tracking error, the prediction error and the extended filtering operation to construct a composite learning adaptive law;
and updating parameters by adopting the composite learning self-adaptive law to obtain the outer loop composite learning self-adaptive controller.
2. The method for composite learning adaptive control of a flexible drive robot of claim 1, wherein the expression of the CAR model is:
wherein q represents the joint position of the robot link side;representing the speed of the robot link side; />Acceleration indicated as robot link side; τ a Representing moment on the side of the articulation link; m represents an inertial matrix of the robot connecting rod side; c is the connecting rod side coriolis Li Juzhen; g (q) represents a gravitational moment on the robot link side; f represents friction force; θ represents a position of the robot motor side; />Representing the speed of the robot motor side; />An acceleration on the robot motor side; b represents the inertia of the robot motor side; d represents damping on the robot motor side; k represents a stiffness matrix of the robot motor side; k (K) -1 An inverse matrix representing the stiffness matrix K; τ represents the torque of the torsion spring; u represents a control law input.
3. The method for adaptively controlling compound learning of a flexible driving robot according to claim 1, wherein the expression of the second order reduction system is:
wherein v is an auxiliary variable and v ε R; ψ is the generalized regression matrix, and there are ψ:W e is a parameter vector to be estimated, and +.>N e For the parameter vector W e Is a dimension of (2); m is M e (q) is an extended inertia matrix corresponding to the first reduced system; />Is a generalized acceleration; />Coriolis Li Juzhen, which is the robot link side; g (q) is the gravitational moment on the robot link side; />Is a friction force; />Is the speed of the robot link side;
the expression of the second boundary layer system is:
wherein z represents the state of the second boundary layer system; z' represents a first derivative of the state of the second boundary layer system at a fast time scale; z "represents a second derivative of the state of the second boundary layer system at a fast time scale; m is M -1 An inverse matrix representing an inertial matrix M on the robot link side; q represents the joint position on the robot link side; b (B) -1 An inverse matrix representing an inertia matrix B on the robot motor side; k (K) 0 And D 0 Are constant diagonal matrixes; k (K) p And K d Each representing a positive diagonal matrix.
4. The method for adaptively controlling compound learning of a flexible driving robot according to claim 1, wherein the expression of the compound learning adaptive law is:
wherein,is the derivative of the estimated value of the parameter vector; Γ is a learning law matrix of positive diagonals; psi is a generalized regression matrix; q is the joint position on the robot link side; />Is the speed of the robot link side; />Is the joint reference speed of the robot connecting rod side; />Is the reference acceleration of the robot link side; e, e 2 Is a tracking error; k (k) a Sum k b Are all weight factors; psi F Representing a filtered regression matrix; />Representing a generalized parameter estimation error; t represents time; />Representing the interval integral length; />Representing the integral variable.
5. The method for compound learning adaptive control of a flexible drive robot of claim 1, wherein the expression of the robot system controller is:
wherein u represents a control law input; τ represents the torque of the torsion spring; τ r Representing a reference torque;representing the moment change rate of the torsion spring; k (K) p And K d All represent positive diagonal matrices; k (K) c Determining a diagonal gain matrix for the positive; k (k) a And k b Are all weight factors; epsilon represents a parameter; e, e 2 Representing tracking errors; q represents the joint position on the robot link side; />Representing the speed of the robot link side; />Acceleration indicated as robot link side; />A reference acceleration indicating the robot link side; />Representing an estimate of the parameter vector; />A derivative representing an estimated value of the parameter vector; Γ represents a learning law matrix of positive diagonals; ψ represents the generalized regression matrix; psi F Representing a filtered regression matrix; e represents the torque prediction errorThe method comprises the steps of carrying out a first treatment on the surface of the ζ represents a generalized moment prediction error.
6. An adaptive control system for a flexible drive robot, comprising:
the first module is used for establishing a CAR model and constructing the structure of a CAR controller;
the second module is used for establishing a first order reduction system and a first boundary layer system according to the CAR model based on a singular perturbation theory;
the third module is used for constructing an inner loop linear controller according to the CAR controller;
a fourth module for determining a second boundary layer system from the first boundary layer system and the inner loop linear controller;
a fifth module, configured to combine the CAR controller and perform linear parameterization on the first reduced-order system to obtain a second reduced-order system;
the sixth module is used for constructing an outer loop composite learning adaptive controller;
a seventh module for constructing a robotic system controller from the second reduced order system, the second boundary layer system, the inner loop linear controller, and the outer loop compound learning adaptive controller;
the method for establishing the first order reduction system and the first boundary layer system based on the singular perturbation theory according to the CAR model comprises the following steps:
according to the CAR model, a robot system model in a singular perturbation form is constructed;
obtaining a first order reduction system according to the change of the parameter value in the robot system model;
adjusting the robot system model expression according to an algebraic algorithm to obtain a first boundary layer system;
and combining the CAR controller to linearize the first order reduction system to obtain a second order reduction system, wherein the method comprises the following steps:
constructing a slow controller according to the CAR controller;
combining the slow controller, and constructing an intermediate reduced-order system according to the first reduced-order system expansion inertia matrix and a control law;
constructing a second order reduction system according to the row vector performance of the intermediate order reduction system;
the construction of the outer loop composite learning self-adaptive controller comprises the following steps:
constructing a rigid robot self-adaptive controller;
calculating a filtering tracking error of the tracking error information of the robot system;
calculating a prediction error at the current moment;
performing expansion filtering operation on the regression matrix according to the historical data information of the regression matrix;
combining the filtering tracking error, the prediction error and the extended filtering operation to construct a composite learning adaptive law;
and updating parameters by adopting the composite learning self-adaptive law to obtain the outer loop composite learning self-adaptive controller.
7. An electronic device comprising a processor and a memory;
the memory is used for storing programs;
the processor executing the program implements the method of any one of claims 1 to 5.
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