CN115338871A - Limited self-adaptive robust control method and system of two-degree-of-freedom mechanical arm - Google Patents
Limited self-adaptive robust control method and system of two-degree-of-freedom mechanical arm Download PDFInfo
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Abstract
The invention belongs to the field of industrial robots, and particularly relates to a limited self-adaptive robust control method and system for a two-degree-of-freedom mechanical arm. The limited self-adaptive robust control method comprises the following steps: s1: and establishing a physical model of the two-degree-of-freedom mechanical arm, and converting the physical model into a state equation. S2: an outer loop planner is designed based on the physical model. S3: an inner loop controller is designed based on an adaptive robust algorithm. S4: initializing the two-degree-of-freedom mechanical arm. S5: and acquiring state parameters of each joint, acquiring a preset expected track, and generating a reference track and a motor driving moment by using an outer ring planner and an inner ring controller. S6: and the driver of each joint motor generates a corresponding control signal according to the driving torque of the required motor to control the joint rotation and the mechanical arm movement of the two-degree-of-freedom mechanical arm. The invention solves the technical problems of weak robustness and poor real-time performance of the control method under constraint of the traditional two-degree-of-freedom mechanical arm.
Description
Technical Field
The invention belongs to the field of industrial robots, and particularly relates to a limited self-adaptive robust control method and system for a two-degree-of-freedom mechanical arm.
Background
Mechanization and automation are development directions of future intelligent factories, and various robots are adopted in the intelligent factories to replace manual work to complete various work tasks. The mechanical arm is used as a mechanical electronic device simulating the structure of a human body arm and is widely applied to an intelligent factory, and the mechanical arm can obviously improve the production efficiency of a production line and reduce the production cost of products. Robotic arms are also one of the important automated devices in modern manufacturing.
The design of a high-performance control algorithm is a core technology for mechanical arm system development. However, the strong coupling non-linearity and various model uncertainties in the on-line robot arm system pose great difficulties to the robust control algorithm design of the robot arm. In addition, the actual mechanical arm system is also limited by constraints such as working space, safe speed, input torque and the like in the movement process, and once the constraints are violated, the consistent control performance cannot be ensured, even the system is unstable, a hardware system is damaged and the like. Therefore, on the basis of ensuring the constraint condition, the adaptive control of the robot is performed to improve the performance of the robot. Although the existing research results can solve the problem of primary motion control under the constraint of the mechanical arm, the problems of low robustness, poor algorithm real-time performance and the like still exist.
Disclosure of Invention
In order to solve the technical problems of poor robustness and poor real-time performance of the existing control method under the constraint of the two-degree-of-freedom mechanical arm, the invention provides a two-degree-of-freedom mechanical arm limited adaptive robust control method based on a reference regulator.
The invention is realized by adopting the following technical scheme:
a limited self-adaptive robust control method of a two-degree-of-freedom mechanical arm comprises the following steps:
s1: and establishing a physical model of the two-degree-of-freedom mechanical arm, and converting the physical model into a state equation. The physical model comprises a dynamic model of the two-degree-of-freedom mechanical arm and a constraint model thereof.
S2: and designing an outer ring planner based on the physical model, wherein the outer ring planner is used for generating a reference track of the two-degree-of-freedom mechanical arm meeting constraint conditions according to the actual position, the actual speed and the expected track of each joint of the two-degree-of-freedom mechanical arm.
S3: and designing an inner ring controller based on an adaptive robust algorithm, wherein the inner ring controller is used for generating motor driving torque at each joint of the two-freedom-degree mechanical arm meeting an adaptive law according to the actual position, the actual speed and the reference track of the two-freedom-degree mechanical arm.
S4: initializing the two-degree-of-freedom mechanical arm, wherein the initialization content comprises the following steps: resetting the motion state of the mechanical arm and zeroing the absolute encoders in the servo motors at the joints.
S5: presetting a sampling period, and acquiring the actual position and the actual speed of each joint of the two-degree-of-freedom mechanical arm at each sampling moment; and then acquiring a preset expected track, and generating a corresponding reference track and a corresponding motor driving torque at each moment according to a state equation by using an outer ring planner and an inner ring controller.
The sample data in the reference track comprises a reference position, a reference speed and a reference acceleration corresponding to each sampling moment.
S6: the drivers of all joint motors of the two-degree-of-freedom mechanical arm generate corresponding control signals according to the required motor driving torque, and then all joint motors are driven to output torque, so that joint rotation and mechanical arm movement of the two-degree-of-freedom mechanical arm are realized.
As a further improvement of the present invention, in the physical model established in step S1, the dynamic model of the two-degree-of-freedom mechanical arm is:
in the above formula, q = [ q ] 1 ,q 2 ] T The rotation angles of two joints in the two-degree-of-freedom mechanical arm are represented;
representing the rotational speed of each joint;
representing rotational acceleration of each joint; m is the inertial matrix of the system; c is the centrifugal and Coriolis force matrix of the system; g is the gravity matrix of the system, A is the Coulomb friction coefficient;
is used to fit a symbolic function
And satisfies the following:
b is the damping viscous friction coefficient; Δ is the lumped model uncertainty and disturbance on the two degree of freedom manipulator; τ is the motor drive torque at the robot joint.
As a further improvement of the invention, the constraint model of the two-degree-of-freedom mechanical arm is as follows:
in the above formula, q min ＝[q 1min ,q 2min ] T Is the minimum rotation angle of each joint; q. q of max ＝[q 1max ,q 2max ] T The maximum rotation angle of each joint;
is the minimum rotational speed of each joint;
the maximum rotation speed of each joint; tau is max ＝[τ 1max ,τ 2max ] T The maximum input torque of each joint.
As a further improvement of the present invention, in step S1, the physical model is converted into a state equation by the following method:
(1) State variables of equation of state
Namely: x is the number of 1 ＝q，
(2) The centralized model uncertainty and the interference delta of the two-degree-of-freedom mechanical arm are divided into a constant and a time-varying function, namely
Δ＝Δ n +Δ t ，
Wherein, delta n To concentrate the constant part of the model uncertainty and disturbance Δ, Δ t Centralizing the time-varying portion of model uncertainty and interference Δ;
(3) The converted state equation of the two-degree-of-freedom mechanical arm is as follows:
as a further improvement of the present invention, the outer loop planner designed in step S2 plans the corresponding reference trajectory by generating the reference position, the reference velocity, and the reference acceleration at each sampling time; in the planning process of the reference track, the outer ring planner takes an expected position approaching the expected track as an initial position, and then continuously carries out iterative updating on the initial position until a position which meets a constraint model and is closest to the expected position is found, and the position is taken as the reference position; meanwhile, the corresponding reference speed and reference acceleration are calculated according to the change of the reference position.
As a further improvement of the invention, the design process of the inner ring controller is as follows:
(1) Definition of x 1r ＝q r ,
The first tracking error z 1 Comprises the following steps:
z 1 ＝x 1 -x 1r
in the above formula q r A reference position output for the outer loop planner;
a reference speed output for the outer loop planner.
(2) Defining a second tracking error z 2 ：
In the above formula, K 1 A 2 x 2 matrix that is an arbitrary non-negative number;
representing a virtual joint velocity; x is the number of 2r Is the reference speed output by the outer loop planner.
(3) The method comprises the following steps of carrying out parameter linearization processing on a dynamic model of the two-degree-of-freedom mechanical arm, wherein the processing formula is as follows:
wherein, f 0 Y is composed of
Is obtained through parameter linearization; beta is a model parameter of the mechanical arm, and the model parameter beta satisfies the following conditions:
β＝[β 1 β 2 β 3 β 4 β 5 β 6 β 7 β 8 β 9 β 10 ] T
(4) The moment calculation formula of the designed inner ring controller is as follows:
in the above-mentioned formula, the compound has the following structure,
are respectively beta, delta n An estimated value of (d); defining a parameter vector
Its estimated value
Satisfy the requirement of
Wherein
To a parameter theta q Is estimated by
The minimum value of (a) is determined,
to a parameter theta q Is estimated value of
Of (c) is calculated.
As a further improvement of the invention, in step S5, the outer loop planner and the inner loop controller generate a reference position q for the next sampling instant T + T at the current instant T r (T + T), reference speed
And a reference acceleration
The process of (2) is as follows:
s51: initializing parameters of an outer loop planner: presetting the sampling period of the outer ring controller as T; defining the iteration turn as N, N is an element of [1, N ∈ max ](ii) a k denotes an approximation coefficient of the reference position with respect to the desired position.
The approximation coefficient k is dynamically updated along with the iteration times, and the updating formula is as follows: k = k 0 N-1 (ii) a Wherein k is 0 Is an initial value of the ratio, k 0 ∈(0,1)。
S52: obtaining a reference position q of a two-degree-of-freedom mechanical arm at the current moment t r (T) determining the desired position q at the next time T + T from the desired trajectory d (T + T), and then calculating the reference position q corresponding to the next sampling time T + T by adopting the following formula r (t+T)：
q r (t+T)＝q r (t)+k(q d (t+T)-q r (t))。
S53: a third order filter is used for obtaining a reference position q corresponding to the next sampling time T + T r (T + T) calculating the corresponding reference speed
And a reference acceleration
S54: calculating the joint acceleration corresponding to the current moment t based on the dynamic model of the two-degree-of-freedom mechanical arm
The following:
wherein, tau N (t) is the joint control moment corresponding to the current moment t; and calculating the joint position q corresponding to the next sampling time T + T N (T + T) and Joint velocity
Wherein q is N (t) is the joint position corresponding to the current time t,
the joint speed corresponding to the current moment t;
s55: generating a joint control moment tau corresponding to the next sampling time T + T by using an inner ring controller according to the actual position and the actual speed of the two-degree-of-freedom mechanical arm and the reference position, the reference speed and the reference acceleration N (T + T), the calculation is as follows:
defining the first tracking error of the Nth round as z 1N ：
z 1N ＝q N (t+T)-q r (t+T)z 1N ＝q N (t+T)-q r (t+T)；
Defining the virtual joint velocity of the Nth round as
In the above formula, K 1 A 2 x 2 matrix that is arbitrary non-negative.
Defining a second tracking error of the Nth round as z 2N ：
Order to
Wherein beta isAs a model parameter of the robot arm, f 0 Y is a group of
And (5) carrying out parameter linearization to obtain a vector function and a matrix function.
Control the moment τ N (T + T) satisfies:
in the above formula,. Tau Na Is the model compensation term; tau is Ns Is a linear feedback term; tau. Nsn Is a robust feedback term; k 2 Is a linear feedback gain, which is a 2 x 2 matrix;
are respectively beta, delta n An estimate of (d).
S56: judging the joint position q of the Nth round N (T + T), joint velocity
And joint control moment tau N (T + T) whether the preset constraint model is satisfied:
(1) If yes, outputting the reference position q of the current round r (T + T), reference speed
And a reference acceleration
As the correlation data of the planned reference trajectory at the next sampling instant T + T.
(2) Otherwise, returning to the step S51, updating the approximation coefficient of the next round, and obtaining the relevant data in the reference track meeting the constraint model again.
(3) When the maximum iteration turns are reached and the constraint model is not met, outputting the reference position q of the current moment t r (t), reference speed
And a reference acceleration
As the correlation data of the planned reference trajectory at the next sampling instant T + T.
As a further improvement of the present invention, in step S53, the state equation of the third-order filter is:
in the above formula, let y i ＝q ri (t+T)，x i1 ,x i2 ,x i3 Respectively representing a filtered reference position, a reference velocity and a reference acceleration; wherein i represents the joint serial number of the two-degree-of-freedom mechanical arm, and i =1,2; q. q.s r1 (T + T) is q r The first element of (T + T), q r2 (T + T) is q r A second element of (T + T);
the reference speed of the next sampling instant T + T
And a reference acceleration
Comprises the following steps:
wherein, the parameter a in the state equation of the third-order filter 1 ,a 2 ,a 3 Can be obtained by first constructing y i To x i1 And then pole allocation is carried out on the transfer function to obtain the pole allocation.
As a further improvement of the present invention, the inner loop controller is designed to estimate the value
Is controlled by the adaptation law
To obtain gamma-gamma 1 Is a positive definite gain matrix.
The mapping function corresponding to the adaptive law is as follows:
in the above formula, j represents the number of the model parameter; the model parameters comprise 10 beta parameters and external interference corresponding to the two joints; theta qmaxj ，θ qminj Are each theta q Maximum and minimum values of the jth element, · j Is an independent variable.
Wherein, order:
then, the robust feedback term τ sn Satisfies the following conditions:
in the above formula, I 2*2 Represents a 2 × 2 identity matrix; phi is a unit of 1 Representing a regression quantity matrix;
is equal to the estimated value
Minus the actual value theta q A difference of (d); ε is a threshold and is an arbitrary non-negative number.
The invention also comprises an adaptive robust control system of the two-degree-of-freedom mechanical arm, which adopts the limited adaptive robust control method to carry out adaptive robust control on the two-degree-of-freedom mechanical arm, so that the two-degree-of-freedom mechanical arm can accurately follow a preset expected track under the condition of meeting the constraint. The adaptive robust control system includes: an expected track acquisition module, an outer ring planner and an inner ring controller.
The expected track acquiring module is used for acquiring an expected track of the motion process of the two-degree-of-freedom mechanical arm. The outer ring planner is used for taking the actual position, the actual speed and the expected track of each joint of the two-freedom-degree mechanical arm as input, and then outputting the reference track of each joint of the two-freedom-degree mechanical arm. The inner ring controller is used for taking the actual position and the actual speed of each joint of the two-freedom-degree mechanical arm and the reference track output by the outer ring planner as input and outputting the motor driving torque of each joint of the two-freedom-degree mechanical arm.
The actual position and the actual speed of each joint of the two-degree-of-freedom mechanical arm are obtained through an absolute encoder. The motor driving torque output by the inner ring controller is sent to the controller of the driving motor at each joint, and the controller is used for controlling the actual motion track of the two-degree-of-freedom mechanical arm to accurately follow the expected track.
The technical scheme provided by the invention has the following beneficial effects:
the invention provides a two-degree-of-freedom mechanical arm limited adaptive robust control method based on reference regulator design, which mainly aims at the problems of strong coupling nonlinearity, model uncertainty and motion control under various constraints of the two-degree-of-freedom mechanical arm. The control method adopts a double-loop structure, and respectively comprises the step of designing an outer loop planner based on a reference Regulator (RG), so that the track planning can be carried out on the mechanical arm in real time, and the problem of mechanical arm system constraint is effectively solved. And an inner ring controller designed by adopting a self-adaptive robust control algorithm effectively overcomes the influences of joint coupling, nonlinearity and model uncertainty of a two-degree-of-freedom mechanical arm system.
The control method designed by the invention can perform feedforward compensation on the control model to ensure zero tracking error under a static state, and ensure the dynamic characteristic and stability of the two-degree-of-freedom mechanical arm system through the designed robust feedback, thereby solving the technical problem of weak robust performance in the control method under the constraint of the existing mechanical arm, realizing the tracking effect of high precision and strong robustness on the mechanical arm, and having simple design, better real-time performance, easy engineering realization and stronger application value.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:
fig. 1 is a schematic structural diagram of a two-degree-of-freedom mechanical arm employed in the present invention.
Fig. 2 is a flowchart illustrating steps of a method for controlling a limited adaptive robust of a two-degree-of-freedom robot arm according to embodiment 1 of the present invention.
Fig. 3 is a flowchart of dynamically updating a reference trajectory by the outer loop planner and the inner loop controller in embodiment 1 of the present invention.
Fig. 4 is a schematic diagram of an adaptive robust control system provided in embodiment 2 of the present invention.
Fig. 5 is a motion flow diagram of a robot employing an adaptive robust control system.
Labeled as:
1. a base; 2. a first servo motor; 3. a first robot arm; 4. a second servo motor; 5. a second mechanical arm.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Example 1
Fig. 1 is a schematic structural diagram of a typical actual product of a two-degree-of-freedom robot arm used in this embodiment. In the figure, the two-degree-of-freedom mechanical arm is composed of a base 1, a first mechanical arm 3 and a second mechanical arm 5, wherein a first servo motor 2 is adopted between the base 1 and the first mechanical arm 3 for motion control, and a second servo motor 4 is adopted between the first mechanical arm 3 and the second mechanical arm 5 for motion control. The first servomotor 2 and the second servomotor 4 have absolute encoders built therein. The first servo motor 2 and the second servo motor 4 are also driven by motor drivers, the motor drivers are electrically connected with a real-time controller, and the real-time controller is used for coordinating and adjusting the motion state of each electric control assembly. In the two-degree-of-freedom mechanical arm product of the embodiment, the product model of the real-time controller is cSPACE-RT. The servo motor is a TS 4607N 7191E 200 type product of a Mokawa precision motor. The motor driver adopts a product which is produced by high-tech technology and has the model of GTHD-003-2AEC 2.
In order to overcome the strong coupling nonlinearity and model uncertainty of the two-degree-of-freedom mechanical arm in the modeling process and the influence of various constraints in actual work, the good motion control effect of the mechanical arm is realized. The limited adaptive robust control method for the two-degree-of-freedom mechanical arm provided by the embodiment is applied to a reference Regulator (RG) which can be greatly influenced by a process constraint and a related technology of Adaptive Robust Control (ARC) which can overcome uncertainty and nonlinear influence; and an outer ring planner and an inner ring controller are designed based on the principles of two technologies.
The outer ring planner can judge whether the mechanical arm violates the constraint condition or not through the expected position and the reference position at the previous moment, and continuously plan out the reference position, the speed and the acceleration which accord with the constraint at the current moment by using the bisection method. The inner ring controller can continuously adjust model parameters through a designed self-adaptive law, feed-forward compensation is carried out on a control model to ensure zero tracking error under a static state, and dynamic characteristics and stability of a two-degree-of-freedom mechanical arm system are ensured through designed robust feedback.
By using the designed outer ring planner and inner ring controller, the limited adaptive robust control method provided by the embodiment can perform online trajectory planning and real-time trajectory tracking on the two-degree-of-freedom mechanical arm by using a double-loop control structure, thereby realizing the tracking effect of high precision and strong robustness on the mechanical arm. Meanwhile, the control method designed by the embodiment has simple control logic, good real-time performance and easy engineering realization.
Based on the two-degree-of-freedom mechanical arm shown in fig. 1, the present embodiment provides a limited adaptive robust control method for a two-degree-of-freedom mechanical arm; and carrying out experimental simulation aiming at the designed limited self-adaptive robust control method. As shown in fig. 2, the limited adaptive robust control method includes the following steps:
s1: and establishing a physical model of the two-degree-of-freedom mechanical arm, and converting the physical model into a state equation. The physical model comprises a dynamic model and a constraint model of the two-degree-of-freedom mechanical arm.
Specifically, in the physical model of this embodiment, the dynamic model of the two-degree-of-freedom mechanical arm is:
in the above formula, q = [ q ] 1 ,q 2 ] T Representing the rotation angles of two joints in the two-degree-of-freedom mechanical arm;
representing the rotational speed of each joint;
representing rotational acceleration of each joint; m is the inertial matrix of the system; c is the centrifugal and Coriolis force matrix of the system; g is the gravity matrix of the system, A is the Coulomb friction coefficient;
is used to fit a symbolic function
And satisfies the following:
b is the damping viscous friction coefficient; delta is a concentrating die on a two-degree-of-freedom mechanical armType uncertainty and interference; τ is the motor drive torque at the robot joint.
The constraint model of the two-degree-of-freedom mechanical arm is as follows:
in the above formula, q min ＝[q 1min ,q 2min ] T Is the minimum rotation angle of each joint; q. q.s max ＝[q 1max ,q 2max ] T The maximum rotation angle of each joint;
the minimum rotation speed of each joint;
the maximum rotation speed of each joint; tau is max ＝[τ 1max ,τ 2max ] T The maximum input torque of each joint.
In the experimental simulation of this embodiment, according to the actual scene, the threshold values of the parameters in the constraint model are set as follows: q. q of 1min ＝-0.7854，q 2min ＝-0.8814，q 1max ＝1.1340，q 2max ＝0.6196，
q 2max ＝2.182，τ 1max ＝120，τ 2max ＝48。
The constructed physical model is converted into a state equation through the following processes:
(1) State variables of the order of state equations
Namely: x is a radical of a fluorine atom 1 ＝q，
(2) The centralized model uncertainty and the interference delta of the two-degree-of-freedom mechanical arm are divided into a constant and a time-varying function, namely
Δ＝Δ n +Δ t ，
Wherein, delta n To concentrate the constant part of the model uncertainty and disturbance Δ, Δ t Centralizing the time-varying portion of model uncertainty and interference Δ;
(3) The converted state equation of the two-degree-of-freedom mechanical arm is as follows:
accordingly, the state equation of the constraint model of the two-degree-of-freedom mechanical arm is:
in this embodiment, τ is chosen max ＝[120 48] T ，x 1min ＝[-0.7854 -0.8814] T ，x 1max ＝[1.1340 0.6196] T ，x 2min ＝[-2.007 -2.082] T ，x 2max ＝[2.007 2.182] T 。
S2: and designing an outer ring planner based on the physical model, wherein the outer ring planner is used for generating a reference track of the two-degree-of-freedom mechanical arm meeting constraint conditions according to the actual position, the actual speed and the expected track of each joint of the two-degree-of-freedom mechanical arm.
The outer ring planner designed in this embodiment plans a corresponding reference track by generating a reference position, a reference speed, and a reference acceleration at each sampling time; in the planning process of the reference track, the outer ring planner takes an expected position approaching the expected track as an initial position, and then continuously carries out iterative updating on the initial position until a position which meets a constraint model and is closest to the expected position is found, and the position is taken as the reference position; meanwhile, the corresponding reference speed and reference acceleration are calculated according to the change of the reference position.
S3: an inner ring controller is designed based on an adaptive robust algorithm, and the inner ring controller is used for generating motor driving torque at each joint of the two-freedom-degree mechanical arm meeting an adaptive law according to the actual position, the actual speed and the reference track of the two-freedom-degree mechanical arm.
The design process of the inner ring controller is as follows:
(1) Definition of x 1r ＝q r ,
The first tracking error z 1 Comprises the following steps:
z 1 ＝x 1 -x 1r
in the above formula, q r A reference position output for the outer loop planner;
a reference speed output for the outer loop planner. (2) Defining a second tracking error z 2 ：
In the above formula, K 1 A 2 x 2 matrix that is an arbitrary non-negative number; get the
Representing a virtual joint velocity; x is the number of 2r A reference speed output for the outer loop planner.
(3) The method comprises the following steps of carrying out parameter linearization processing on a dynamic model of the two-degree-of-freedom mechanical arm, wherein a processing formula is as follows:
wherein f is 0 Y is composed of
Obtaining a vector function and a matrix function through parameter linearization; beta is a model parameter of the mechanical arm, and the model parameter beta satisfies the following conditions:
β＝[β 1 β 2 β 3 β 4 β 5 β 6 β 7 β 8 β 9 β 10 ] T
(4) The moment calculation formula of the designed inner ring controller is as follows:
in the above formula, the first and second carbon atoms are,
are respectively beta, delta n An estimated value of (d); defining a parameter vector
Its estimated value
Satisfy the requirement of
Wherein
To a parameter theta q Is estimated value of
The minimum value of (a) is determined,
to a parameter theta q Is estimated by
Is measured. The values of the two thresholds are as follows:
in the present embodiment, it is preferred that,
taking the initial value as:
wherein the estimated value in the inner loop controller is designed
Is controlled by the adaptation law
To obtain gamma-ray diffraction grating 1 Is a positive definite gain matrix. In the present embodiment, F is selected as 1 ＝diag{10,10,10,10,10,10,10,10,10,10,120,40}
The mapping function corresponding to the adaptive law is as follows:
in the above formula, j represents the number of the model parameter; the model parameters comprise 10 beta parameters and external interference corresponding to the two joints; theta qmaxj ，θ qminj Are respectively theta q Maximum and minimum values of the jth element, · j Is an independent variable.
Wherein, order:
in the above formula, I 2*2 Represents a 2 × 2 identity matrix; phi is a 1 Representing a regression quantity matrix;
then, the robust feedback term τ sn Satisfies the following conditions:
in the above formula, the first and second carbon atoms are,
is equal to the estimated value
Minus the actual value theta q A difference of (d); ε is a threshold and is an arbitrary non-negative number. In this embodiment, ε = [1 ] is selected] T ；τ sn ＝[0 0] T 。
S4: initializing the two-degree-of-freedom mechanical arm, wherein the initialization content comprises the following steps: resetting the motion state of the mechanical arm and zeroing the absolute encoders in the servo motors at the joints.
S5: presetting a sampling period, and acquiring the actual position and the actual speed of each joint of the two-degree-of-freedom mechanical arm at each sampling moment; and then acquiring a preset expected track, and generating a corresponding reference track and a motor driving torque corresponding to each moment by using an outer ring planner and an inner ring controller according to a state equation.
The sample data in the reference track comprises a reference position, a reference speed and a reference acceleration corresponding to each sampling moment. As shown in fig. 3, the outer loop planner and the inner loop controller generate a reference position q corresponding to the next sampling time T + T at the current time T r (T + T), reference speed
And a reference acceleration
The process is as follows:
s51: initializing parameters of an outer loop planner: presetting the sampling period of an outer ring controller as T; defining the iteration turn as N, N is an element of [1, N ∈ max ](ii) a k denotes an approximation coefficient of the reference position with respect to the desired position. In this embodiment, the sampling period T is set to 4ms, and the maximum iteration round N max Set to 40 times. The approximation coefficient k is dynamically updated along with the iteration times, and the updating formula is as follows: k = k 0 N-1 (ii) a Wherein k is 0 Is an initial value of the ratio, k 0 E (0, 1). In the present embodiment, k is set in consideration of the fact that the dichotomy approximation is adopted 0 The value is 0.5.
S52: acquiring reference position q of two-degree-of-freedom mechanical arm at current moment t r (T) determining a desired position q at a next time T + T from the desired trajectory d (T + T), and then calculating the reference position q corresponding to the next sampling time T + T by adopting the following formula r (t+T)：
q r (t+T)＝q r (t)+k(q d (t+T)-q r (t))。
S53: a third-order filter is used for obtaining a reference position q corresponding to the next sampling time T + T r (T + T) calculating the corresponding reference speed
And a reference acceleration
The equation of state of the third-order filter in this embodiment is:
in the above formula, let y i ＝q ri (T + T), then x i1 ,x i2 ,x i3 Respectively representing a filtered reference position, a reference velocity and a reference acceleration; wherein i represents a two-degree-of-freedom machineThe joint number of the arm, i =1,2; q. q.s r1 (T + T) is q r First parameter of (T + T), q r2 (T + T) is q r (T + T).
Then, the reference velocity of the next sampling instant T + T is generated by a third order filter
And a reference acceleration
Respectively as follows:
wherein, the parameter a in the state equation of the third-order filter 1 ,a 2 ,a 3 Can be obtained by first constructing y i To x i1 And then pole allocation is carried out on the transfer function to obtain the pole allocation.
In the pole allocation process, let y i (s)＝q ri (T + T)(s), then y i To x i1 The transfer function of (a) is:
in this embodiment, a is obtained by setting the closed loop pole to 20 radians per second 1 ,a 2 ,a 3 Respectively is a 1 ＝80,a 2 ＝2400,a 3 ＝32000。
S54: calculating the joint acceleration corresponding to the current moment t based on the dynamic model of the two-degree-of-freedom mechanical arm
The following were used:
wherein, tau N (t) is the joint control moment corresponding to the current moment t; and calculating the joint position q corresponding to the next sampling time T + T N (T + T) and Joint velocity
Wherein q is N (t) is the joint position corresponding to the current time t,
the joint speed corresponding to the current moment t;
s55: generating a joint control moment tau corresponding to the next sampling time T + T by using an inner ring controller according to the actual position and the actual speed of the two-degree-of-freedom mechanical arm and the reference position, the reference speed and the reference acceleration N (T + T), the calculation is as follows:
defining the first tracking error of the Nth round as z 1N ：
z 1N ＝q N (t+T)-q r (t+T)；
Defining the virtual joint velocity of the Nth round as
In the above formula, K 1 A 2 x 2 matrix that is arbitrary non-negative.
Defining a second tracking error of the Nth round as z 2N ：
Order to
Wherein beta is a model parameter of the mechanical arm, f 0 Y is composed of
And (5) carrying out parameter linearization to obtain a vector function and a matrix function.
Control the moment τ N (T + T) satisfies:
in the above formula, τ Na Is the model compensation term; tau. Ns Is a linear feedback term; tau is Nsn Is a robust feedback term; k 2 Is a linear feedback gain, which is a 2 x 2 matrix;
are respectively beta, delta n An estimate of (d).
S56: determining the joint position q of the Nth round N (T + T), joint velocity
And joint control moment tau N (T + T) whether the preset constraint model is satisfied:
(1) If yes, outputting the reference position q of the current round r (T + T), reference speed
And a reference acceleration
As planningThe correlation data of the reference trajectory at the next sampling instant T + T.
(2) Otherwise, returning to the step S51, updating the approximation coefficient of the next round, and obtaining the relevant data in the reference track meeting the constraint model again.
(3) When the maximum iteration round is reached and the constraint model is not met, outputting a reference position q of the current moment t r (t), reference speed
And a reference acceleration
And (4) relevant data at the next sampling time T + T as a planned reference track.
S6: the drivers of the joint motors of the two-degree-of-freedom mechanical arm generate corresponding control signals according to the driving torque of the motors, and then the motors of the joints are driven to output torque, so that joint rotation and mechanical arm movement of the two-degree-of-freedom mechanical arm are realized.
Example 2
On the basis of embodiment 1, this embodiment further provides an adaptive robust control system for a two-degree-of-freedom robot arm, where the system performs adaptive robust control on the two-degree-of-freedom robot arm by using the limited adaptive robust control method as in embodiment 1, so that the two-degree-of-freedom robot arm can accurately follow a preset expected trajectory under a condition that a constraint is satisfied. As shown in fig. 4, the adaptive robust control system provided by the present embodiment includes: an expected track acquisition module, an outer ring planner and an inner ring controller.
The expected track acquiring module is used for acquiring an expected track of the motion process of the two-degree-of-freedom mechanical arm. The outer ring planner is used for taking the actual position, the actual speed and the expected track of each joint of the two-freedom-degree mechanical arm as input so as to output the reference track of each joint of the two-freedom-degree mechanical arm. The inner ring controller is used for taking the actual position and the actual speed of each joint of the two-degree-of-freedom mechanical arm and the reference track output by the outer ring planner as input and outputting the motor driving torque at each joint of the two-degree-of-freedom mechanical arm.
The actual position and the actual speed of each joint of the two-degree-of-freedom mechanical arm are obtained through an absolute encoder. The motor driving torque output by the inner ring controller is sent to the controller of the driving motor at each joint, and the controller is used for controlling the actual motion track of the two-degree-of-freedom mechanical arm to accurately follow the expected track.
Fig. 5 shows a control flow chart of a robot system adopting the adaptive robust control system provided by the embodiment. As shown in fig. 5, the robot system first determines the sampling period in the real-time controller when running, and then initializes the absolute encoders at each joint. Next, during each step of movement, the system will detect the data of the absolute encoder and will give the desired trajectory; the outer ring planning area continuously generates a corresponding reference track according to a given expected track, and the inner ring controller calculates a corresponding motor torque according to the reference track. The motor driver converts the corresponding motor torque into motor current and outputs the motor current to the servo motor to control the joint motor to execute corresponding actions.
The above description is intended to be illustrative of the preferred embodiment of the present invention and should not be taken as limiting the invention, but rather, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention.
Claims (10)
1. A limited adaptive robust control method of a two-degree-of-freedom mechanical arm is characterized by comprising the following steps of:
s1: establishing a physical model of the two-degree-of-freedom mechanical arm, and converting the physical model into a state equation; the physical model comprises a dynamic model of the two-degree-of-freedom mechanical arm and a constraint model thereof;
s2: designing an outer ring planner based on the physical model, wherein the outer ring planner is used for generating a reference track of the two-degree-of-freedom mechanical arm meeting constraint conditions according to the actual position, the actual speed and the expected track of each joint of the two-degree-of-freedom mechanical arm;
s3: designing an inner ring controller based on an adaptive robust algorithm, wherein the inner ring controller is used for generating motor driving torque at each joint of the two-degree-of-freedom mechanical arm according to the actual position, the actual speed and the reference track of the two-degree-of-freedom mechanical arm, and the motor driving torque meets an adaptive law;
s4: initializing the two-degree-of-freedom mechanical arm, wherein the initialization content comprises the following steps: resetting the motion state of the mechanical arm and zeroing an absolute encoder in a servo motor at each joint;
s5: presetting a sampling period, and acquiring the actual position and the actual speed of each joint of the two-degree-of-freedom mechanical arm at each sampling moment; then acquiring a preset expected track, and generating a corresponding reference track and a motor driving moment corresponding to each moment by using the outer ring planner and the inner ring controller according to the state equation; sample data in the reference track comprises a reference position, a reference speed and a reference acceleration corresponding to each sampling moment;
s6: and the drivers of all joint motors of the two-degree-of-freedom mechanical arm generate corresponding control signals according to the required motor driving torque, so that all joint motors are driven to output torque, and joint rotation and mechanical arm movement of the two-degree-of-freedom mechanical arm are realized.
2. The limited adaptive robust control method of a two-degree-of-freedom mechanical arm according to claim 1, characterized in that: in the physical model established in step S1, the dynamic model of the two-degree-of-freedom mechanical arm is:
in the above formula, q = [ q ] 1 ,q 2 ] T Representing the rotation angles of two joints in the two-degree-of-freedom mechanical arm;
representing the rotational speed of each joint;
representing rotational acceleration of each joint; m is the inertial matrix of the system; c is the centrifugal and Coriolis force matrix of the system; g is the gravity matrix of the system, A is the Coulomb friction coefficient;
is used to fit a symbolic function
And satisfies the following:
b is the damping viscous friction coefficient; Δ is the lumped model uncertainty and disturbance on the two-degree-of-freedom mechanical arm; τ is the motor drive torque at the robot joint.
3. The limited adaptive robust control method of a two-degree-of-freedom mechanical arm according to claim 2, characterized in that: the constraint model of the two-degree-of-freedom mechanical arm is as follows:
in the above formula, q min ＝[q 1min ,q 2min ] T The minimum rotation angle of each joint; q. q.s max ＝[q 1max ,q 2max ] T The maximum rotation angle of each joint;
is the minimum rotational speed of each joint;
the maximum rotation speed of each joint; tau is max ＝[τ 1max ,τ 2max ] T For each jointThe maximum input torque.
4. The constrained adaptive robust control method of a two degree-of-freedom robotic arm of claim 3, characterized by: in step S1, the physical model is converted into a state equation by the following method:
(1) State variables of equation of state
Namely: x is a radical of a fluorine atom 1 ＝q，
(2) The centralized model uncertainty and the interference delta of the two-degree-of-freedom mechanical arm are divided into a constant and a time-varying function, namely
Δ＝Δ n +Δ t ，
Wherein, delta n To concentrate the constant part of the model uncertainty and disturbance Δ, Δ t Centralizing the time-varying portion of model uncertainty and interference Δ;
(3) The converted state equation of the two-degree-of-freedom mechanical arm is as follows:
5. the constrained adaptive robust control method of a two degree-of-freedom robotic arm of claim 4, wherein: the outer ring planner designed in the step S2 plans a corresponding reference track by generating a reference position, a reference speed and a reference acceleration at each sampling moment; in the planning process of the reference track, the outer ring planner takes an expected position approaching the expected track as an initial position, and then continuously carries out iterative updating on the initial position until a position which meets a constraint model and is closest to the expected position is found, and the position is taken as the reference position; meanwhile, the corresponding reference speed and reference acceleration are calculated according to the change of the reference position.
6. The constrained adaptive robust control method of a two degree-of-freedom robotic arm of claim 4, wherein: in step S3, the design process of the inner ring controller is as follows:
(1) Definition of x 1r ＝q r ,
The first tracking error z 1 Comprises the following steps:
z 1 ＝x 1 -x 1r
in the above formula, q r A reference position output for the outer loop planner;
a reference speed output for the outer loop planner;
(2) Defining a second tracking error z 2 ：
In the above formula, K 1 A 2 x 2 matrix that is an arbitrary non-negative number;
representing a virtual joint velocity; x is a radical of a fluorine atom 2r A reference speed output for the outer loop planner;
(3) And carrying out parameter linearization processing on the dynamic model of the two-degree-of-freedom mechanical arm, wherein the processing formula is as follows:
wherein, f 0 Y is a group of
Is prepared from radix GinsengPerforming number linearization to obtain a vector function and a matrix function; beta is a model parameter of the mechanical arm, and the model parameter beta satisfies the following conditions:
β＝[β 1 β 2 β 3 β 4 β 5 β 6 β 7 β 8 β 9 β 10 ] T
(4) The moment calculation formula of the designed inner ring controller is as follows:
in the above formula, the first and second carbon atoms are,
are respectively beta, delta n An estimated value of (d); defining a parameter vector
Its estimated value
Satisfy the requirements of
Wherein,
to a parameter theta q Is estimated value of
The minimum value of (a) is determined,
to a parameter theta q Is estimated value of
Is measured.
7. The constrained adaptive robust control method of a two degree-of-freedom robotic arm of claim 6, characterized in that: in step S5, the outer loop planner and the inner loop controller generate a reference position q of the next sampling time T + T at the current time T r (T + T), reference speed
And a reference acceleration
The process of (2) is as follows:
s51: initializing parameters of an outer loop planner: presetting the sampling period of an outer ring controller as T; defining the iteration turn as N, N is an element of [1, N ∈ max ](ii) a k represents an approximation coefficient of the reference position with respect to the desired position; the approximation coefficient k is dynamically updated along with the iteration times, and the updating formula is as follows: k = k 0 N-1 (ii) a Wherein k is 0 Is an initial value of the ratio, k 0 ∈(0,1)；
S52: obtaining a reference position q of a two-degree-of-freedom mechanical arm at the current moment t r (T) determining a desired position q at a next time T + T from the desired trajectory d (T + T), and then calculating the reference position q corresponding to the next sampling time T + T by adopting the following formula r (t+T)：
q r (t+T)＝q r (t)+k(q d (t+T)-q r (t))；
S53: a third order filter is used for obtaining a reference position q corresponding to the next sampling time T + T r (T + T) calculating a corresponding reference speed
And a reference acceleration
S54: calculating the joint acceleration corresponding to the current moment t based on the dynamic model of the two-degree-of-freedom mechanical arm
The following:
wherein, tau N (t) is the joint control moment corresponding to the current moment t; and calculating the joint position q corresponding to the next sampling time T + T N (T + T) and Joint velocity
Wherein q is N (t) is the joint position corresponding to the current time t,
the joint speed corresponding to the current moment t;
s55: according to the actual position and the actual speed of the two-degree-of-freedom mechanical arm and the reference position, the reference speed and the reference acceleration, a joint control torque tau corresponding to the next sampling time T + T is generated by using an inner ring controller N (T + T), the calculation is as follows:
defining the first tracking error of the Nth round as z 1N ：
z 1N ＝q N (t+T)-q r (t+T)；
Defining the virtual joint velocity of the Nth round as
In the above formula, K 1 A 2 x 2 matrix that is an arbitrary non-negative number;
defining a second tracking error of the Nth round as z 2N ：
Order to
Wherein beta is a model parameter of the mechanical arm, f 0 And Y is respectively composed of
A vector function and a matrix function are obtained by parameter linearization;
then, the torque τ is controlled N (T + T) satisfies:
in the above formula, τ Na Is the model compensation term; tau. Ns Is a linear feedback term; tau is Nsn Is a robust feedback term; k 2 Is a linear feedback gain, which is a 2 x 2 matrix;
are respectively beta, delta n An estimated value of (d);
s56: judging the joint position q of the Nth round N (T + T), joint velocity
And joint control moment tau N (T + T) whether the preset constraint model is satisfied:
(1) If yes, outputting the reference position q of the current round r (T + T), reference speed
And a reference acceleration
The correlation data serving as the planned reference track at the next sampling time T + T;
(2) Otherwise, returning to the step S51, updating the approximation coefficient of the next round, and obtaining the relevant data in the reference track meeting the constraint model again;
(3) When the maximum iteration turns are reached and the constraint model is not met, outputting the reference position q of the current moment t r (t), reference speed
And a reference acceleration
As the correlation data of the planned reference trajectory at the next sampling instant T + T.
8. The limited adaptive robust control method of a two degree-of-freedom robotic arm of claim 7, wherein: in step S53, the state equation of the third-order filter is:
in the above formula, let y i ＝q ri (t+T)，x i1 ,x i2 ,x i3 Respectively representing a filtered reference position, a reference velocity and a reference acceleration; wherein i represents the joint serial number of the two-degree-of-freedom mechanical arm, and i =1,2; q. q of r1 (T + T) is q r The first element of (T + T), q r2 (T + T) is q r A second element of (T + T);
the reference speed of the next sampling instant T + T
And a reference acceleration
Comprises the following steps:
wherein, the parameter a in the state equation of the third-order filter 1 ,a 2 ,a 3 Can be obtained by first constructing y i To x i1 And then pole allocation is carried out on the transfer function to obtain the pole allocation.
9. The limited adaptive robust control method of a two degree-of-freedom robotic arm of claim 8, wherein: in the designed inner loop controller, the estimated value
Is controlled by an adaptive law
To obtain gamma-ray diffraction grating 1 Is a matrix of positive definite gains and is,
the mapping function corresponding to the adaptive law is as follows:
in the above formula, j represents the number of the model parameter; the model parameters comprise 10 beta parameters and external interference corresponding to the two joints; theta qmaxj ，θ qminj Are each theta q Maximum of jth elementValue and minimum value, · j Is an independent variable;
wherein, order:
then, the robust feedback term τ sn Satisfies the following conditions:
in the above formula, I 2*2 Represents a 2 × 2 identity matrix; phi is a unit of 1 Representing a regression quantity matrix;
is equal to the estimated value
Minus the actual value theta q A difference of (d); ε is a threshold and is an arbitrary non-negative number.
10. A self-adaptive robust control system of a two-degree-of-freedom mechanical arm is characterized in that: the adaptive robust control method is adopted to carry out adaptive robust control on the two-degree-of-freedom mechanical arm, so that the two-degree-of-freedom mechanical arm can accurately follow a preset expected track under the condition of meeting the constraint; the adaptive robust control system comprises:
the expected track acquisition module is used for acquiring an expected track of the motion process of the two-degree-of-freedom mechanical arm;
the outer ring planner is used for taking the actual position, the actual speed and the expected track of each joint of the two-degree-of-freedom mechanical arm as input and further outputting the reference track of each joint of the two-degree-of-freedom mechanical arm;
the inner ring controller is used for taking the actual position and the actual speed of each joint of the two-degree-of-freedom mechanical arm and the reference track output by the outer ring planner as input and outputting motor driving torque at each joint of the two-degree-of-freedom mechanical arm;
the actual position and the actual speed of each joint of the two-degree-of-freedom mechanical arm are obtained through an absolute encoder; the motor driving torque output by the inner ring controller is sent to the controller of the driving motor at each joint, and the controller is used for controlling the actual motion track of the two-degree-of-freedom mechanical arm to accurately follow the expected track.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20060116783A1 (en) * | 2004-12-01 | 2006-06-01 | Canadian Space Agency | Method and system for torque/force control of hydraulic actuators |
| CN106842954A (en) * | 2017-03-14 | 2017-06-13 | 北京理工大学 | A kind of control method of semi-flexible mechanical arm system |
| CN114888806A (en) * | 2022-05-25 | 2022-08-12 | 合肥工业大学 | Robust control method and device for under-actuated single-leg support hydraulic power-assisted exoskeleton |
-
2022
- 2022-09-16 CN CN202211133071.XA patent/CN115338871B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20060116783A1 (en) * | 2004-12-01 | 2006-06-01 | Canadian Space Agency | Method and system for torque/force control of hydraulic actuators |
| CN106842954A (en) * | 2017-03-14 | 2017-06-13 | 北京理工大学 | A kind of control method of semi-flexible mechanical arm system |
| CN114888806A (en) * | 2022-05-25 | 2022-08-12 | 合肥工业大学 | Robust control method and device for under-actuated single-leg support hydraulic power-assisted exoskeleton |
Non-Patent Citations (2)
| Title |
|---|
| SHAN CHEN; TENGHUI HAN; FANGFANG DONG; JIANG HAN; LEI LU; HAIJUN LIU: "Adaptive Robust Force Control of an Underactuated Stance Leg Exoskeleton for Human Performance Augmentation", 《2021 IEEE INTERNATIONAL CONFERENCE ON MECHATRONICS (ICM)》, 30 March 2021 (2021-03-30) * |
| 韩江;魏光耀;董方方;夏链: "打磨机器人自适应鲁棒约束跟踪控制", 《合肥工业大学学报(自然科学版)》, 28 July 2022 (2022-07-28) * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN118331168A (en) * | 2024-04-30 | 2024-07-12 | 上海卫尼医疗器械有限公司 | Motion control method and system |
| CN118331168B (en) * | 2024-04-30 | 2024-10-11 | 上海卫尼医疗器械有限公司 | Motion control method and system |
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