CN113814983A - Multi-single-arm manipulator system control method and system - Google Patents

Multi-single-arm manipulator system control method and system Download PDF

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CN113814983A
CN113814983A CN202111211197.XA CN202111211197A CN113814983A CN 113814983 A CN113814983 A CN 113814983A CN 202111211197 A CN202111211197 A CN 202111211197A CN 113814983 A CN113814983 A CN 113814983A
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tracking error
disturbance observer
arm manipulator
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CN113814983B (en
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周琪
李枝强
刘洋
任鸿儒
鲁仁全
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Guangdong University of Technology
Qingdao University of Science and Technology
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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
    • 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
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • 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
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
    • 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

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Abstract

The invention relates to a multi-single-arm manipulator system control method and a system, which comprises the following steps: establishing a state dynamics model of the multi-single-arm manipulator; acquiring a tracking error after error transformation according to a consistent tracking error model of the single-arm manipulator and a constructed preset finite time performance function; obtaining an identification model and a disturbance observer according to the obtained state dynamics model; obtaining a virtual controller according to a preset finite time performance function, the transformed tracking error and a disturbance observer; filtering a control signal of the virtual controller to obtain a new state variable; the controller of the multi-single-arm manipulator system is obtained according to the new state variable, the recognition model and the disturbance observer, and the method has good control effect.

Description

Multi-single-arm manipulator system control method and system
Technical Field
The invention relates to the technical field of industrial process control, in particular to a multi-single-arm manipulator system control method and system.
Background
With the continuous progress of modern science and technology, manipulators are widely applied, such as mechanical manufacturing, electronic processing, metallurgy, aerospace and the like. The manipulator can replace people to complete repeated and heavy manual labor in a harmful environment. However, with the rapid development of the manipulator, the single-arm manipulator gradually shows the limitations of poor flexibility and low working efficiency, and the cooperative operation of multiple single-arm manipulators has the characteristics of low communication cost, high flexibility and robustness and the like, and can meet the requirements of complex and various tasks, so that the research on the design of the controller for outputting consistent output of the multiple single-arm manipulators is of great significance. One manipulator in the multi-single-arm manipulator cooperative control system is used as a leader, and partial manipulators capable of receiving output signals of the leader or adjacent manipulators are used as followers, wherein all the followers can track the output signals of the leader, so that a control target with consistent output is realized.
In practical application, the multi-single-arm manipulator is limited by external conditions to have high requirements on system performance, and the output error of the manipulator is required to meet certain constraint conditions within a limited time. By selecting the preset finite time performance function and the error transformation, when the output error of the manipulator is close to the boundary condition, the gain of the controller is increased, so that the output error cannot reach the limit boundary. The inventor finds that the finite time of the existing finite time controller design method is influenced by system initial values and design parameters and is more complex to determine.
The system model of the multi-single-arm manipulator often has unknown nonlinearity, and a fuzzy logic system is widely applied to the design of the controller as a common means for processing nonlinearity. The inventor finds that most of the existing approximation methods adopting fuzzy logic systems cannot accurately approximate unknown nonlinearity of the systems, so that the robustness of a controller is weak and the control effect is poor.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a multi-single-arm manipulator system controller acquisition method, which enables a fuzzy logic system to accurately approach unknown nonlinearity of the system and enables the tracking error to be converged within a limited time.
In order to achieve the purpose, the invention adopts the following technical scheme:
in a first aspect, an embodiment of the present invention provides a method for controlling a multi-arm manipulator system, including the following steps:
establishing a state dynamics model of the multi-single-arm manipulator;
carrying out error transformation according to a consistent tracking error model of the multi-single-arm manipulator and a constructed preset finite time performance function to obtain a transformed tracking error;
obtaining an identification model and a disturbance observer according to the obtained state dynamics model;
obtaining a virtual controller according to a preset finite time performance function, the transformed tracking error and a disturbance observer;
filtering a control signal of the virtual controller to obtain a new state variable;
and obtaining the controller of the multi-single-arm manipulator system according to the new state variable, the recognition model and the disturbance observer, and outputting a control signal by using the obtained controller.
Optionally, a system model of the single-arm manipulator is established, and the system model of the single-arm manipulator is converted to obtain a state dynamics model of the single-arm manipulator system.
Optionally, a first-order low-pass filter is used to filter the control signal of the virtual controller.
Optionally, the compensated tracking error is obtained according to the compensation signal, the second error surface is obtained according to the new state variable, and the controller is obtained according to the compensated tracking error, the second error surface, the recognition model and the disturbance observer.
Optionally, a consistent tracking error model of the multi-single-arm manipulator is obtained according to the knowledge of the graph theory.
Optionally, the preset finite time performance function is obtained according to the finite time for which the consistent tracking error is stable.
Optionally, the disturbance observer includes a connecting rod angular velocity disturbance observer and a connecting rod angular acceleration disturbance observer of a single-arm manipulator.
Optionally, an unknown nonlinear function of the fuzzy logic system approximation system is obtained according to the basis function vector, the optimal weight vector and the approximation error, and the identification model is obtained according to the multi-single-arm manipulator system dynamics model.
Optionally, a gaussian function is used to obtain the basis function vector.
In a second aspect, an embodiment of the present invention provides a multi-single arm robot system control system, including:
a modeling module: the system is used for establishing a state dynamic model of the multi-single-arm manipulator system;
a tracking error acquisition module: the system comprises a single-arm manipulator, a tracking error model, a finite time performance function and a time domain model, wherein the single-arm manipulator is used for constructing the finite time performance function;
the identification model and disturbance observer acquisition module: the disturbance observer is used for obtaining an identification model and a disturbance observer according to the obtained state dynamics model;
the virtual controller obtains a model: the virtual controller is obtained according to a preset finite time performance function, the transformed tracking error and the disturbance observer;
a state variable acquisition module: the virtual controller is used for filtering a control signal of the virtual controller to obtain a new state variable;
a control module: and the controller is used for obtaining the controller of the multi-single-arm manipulator system according to the new state variable, the recognition model and the disturbance observer, and outputting a control signal by using the obtained controller.
The invention has the beneficial effects that:
1. according to the method, the fuzzy logic system can accurately approach the unknown nonlinear function of the system by using the identification model, so that the robustness of the controller obtained according to the identification model is stronger, and the control effect is better.
2. According to the method, the error change model is obtained according to the consistent tracking error of the multi-single-arm manipulator and the constructed finite time performance function, so that the consistent tracking error meets the limiting condition and reaches a stable state within the preset time, the multi-single-arm manipulator can effectively track the given signal, and the finite time setting of the method is more flexible and is irrelevant to the initial value and the setting parameter of the system.
3. According to the method, the problem of time-varying disturbance is considered by designing the disturbance observer, so that the obtained controller can meet the requirement of a multi-single-arm manipulator for working in a more complex environment.
4. The method of the invention filters the control signal of the virtual controller, introduces the dynamic surface technology to solve the problem of 'computing explosion' in the traditional backstepping method, and eliminates the influence caused by the filtering error in the dynamic surface technology through the error compensation model.
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The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the application and, together with the description, serve to explain the application and are not intended to limit the application.
FIG. 1 is a flowchart of a control method according to embodiment 1 of the present invention;
FIG. 2 is a communication topology diagram between single-arm robots according to embodiment 1 of the present invention;
FIG. 3 is a flowchart illustrating a control procedure performed by the ith single-arm manipulator for a predetermined limited time period according to embodiment 1 of the present invention;
FIG. 4 is a graph of the tracking effect of the simulation test in embodiment 1 of the present invention;
FIG. 5 is a schematic diagram of a tracking error of a simulation test in embodiment 1 of the present invention;
FIG. 6 shows a time-varying disturbance d in a simulation test according to embodiment 1 of the present inventioni,1A schematic view of the observation;
FIG. 7 shows an unknown nonlinear function and a time-varying disturbance f of a simulation test system in embodiment 1 of the present inventioni,2+di,2Schematic diagram of the estimation result.
Detailed Description
Example 1
The embodiment provides a control method for a multi-single-arm manipulator system, where the multi-single-arm manipulator system includes a leader manipulator and N following manipulators, and the following manipulators are single-arm manipulators with unknown non-linearity and time-varying disturbance, as shown in fig. 1, the control method includes the following steps:
step 1: and establishing a state dynamics model of the multi-single-arm manipulator.
The specific method comprises the following steps: as a single arm robot system model of the following robot, which has been widely recognized in the related art, as shown in fig. 1, a system model of an i-th single arm robot among the following robots is:
Figure BDA0003308922090000051
wherein,
Figure BDA0003308922090000052
the angular position, angular velocity and angular acceleration, m, of the connecting rod of the single-arm manipulatoriIs the total mass of the connecting rod, MiIs the total moment of inertia of the connecting rod, g is the acceleration of gravity, DiAs a total damping coefficient,/iIs the distance from the joint axis to the center of mass of the connecting rod.
The establishment steps of the state dynamics model are as follows:
step 1.1: establishing graph theory knowledge for describing the communication relationship between the multiple single-arm manipulators:
in order to facilitate the description of the communication relationship between the manipulators in the topological diagram of fig. 2, relevant knowledge of algebraic graph theory needs to be introduced. The directed graph is defined as G ═ (V, E, a). Wherein V ═ V (V)1,v2,...,vN) Is a non-empty set of N manipulators,
Figure BDA0003308922090000053
is a set of edges, (v)i,vj) E represents that manipulator i can receive the information of manipulator j. The set of adjacent nodes for manipulator i is denoted Ni＝{vj∈|(vi,vj) E, i ≠ j }. Defining a weight adjacency matrix as
Figure BDA0003308922090000056
If (v)i,vj) E, then ai,j>0; otherwise ai,j0. Suppose that there is no self-loop in the topology, i.e. ai,i＝0，
Figure BDA0003308922090000055
Define the in-degree matrix of node i as
Figure BDA0003308922090000054
In-degree diagonal matrix R ═ diag { b ═ diag }1,b2,...,bNAnd G, the laplacian matrix of the graph G is L ═ R- A. Definition H ═ diag { a1,0,a2,0,...,aN,0H, if the node i can receive the information of the leader 0, ai,0>0; otherwise, ai,0＝0；
Step 1.2: converting a system model of the single-arm manipulator obtained by modeling into a state dynamic mechanical model:
Figure BDA0003308922090000061
wherein x isi,1＝qi,1,
Figure BDA0003308922090000062
The rotation angle position and the angular velocity of a connecting rod of a single-arm manipulator and an unknown nonlinear function of a system
Figure BDA0003308922090000063
di,1(t),di,2(t) represents an unknown time-varying disturbance.
Step 2: and acquiring a tracking error according to a consistent tracking error model of the multi-single-arm manipulator and a constructed finite time performance function, and performing coordinate transformation to obtain a transformed tracking error.
Step 2.1: the ith multiple-arm manipulator consistent tracking error model is defined by the knowledge of graph theory as follows:
Figure BDA0003308922090000064
wherein, yiIndicating link angle position output, y, of the i-th manipulator0Indicating the angular position of the connecting rod of the leader manipulator as a reference signal for the system tracking, ai,0,ai,jCommunication information between manipulators is contained, and is defined by the graph theory knowledge;
step 2.2, designing a preset finite time performance function:
Figure BDA0003308922090000065
wherein,
Figure BDA0003308922090000066
is a design parameter; t isiThe method is a finite time for tracking error stability, can be flexibly set and is irrelevant to the initial value of the system, and the determination method is simpler.
And 2.3, changing the following errors to obtain the transformed tracking error.
Figure BDA0003308922090000067
And step 3: designing an identification model based on a fuzzy logic system according to the state dynamics model obtained in the step 1, and designing a disturbance observer according to the state dynamics model obtained in the step 1.
Step 3.1, designing a fuzzy logic system to approximate an unknown nonlinear function of the system:
the system unknown nonlinear function is:
Figure BDA0003308922090000071
wherein,
Figure BDA0003308922090000072
for the optimal weight vector, θi,2Is a baseThe function vector, ε is the approximation error.
Selecting a basis function vector:
Figure BDA0003308922090000073
wherein, N is the number of fuzzy rules, and the following Gaussian function is used:
Figure BDA0003308922090000074
wherein,
Figure BDA0003308922090000075
is the center point, oiIs the width of a gaussian function.
Step 3.2: and designing the recognition model according to the unknown nonlinear function of the designed fuzzy logic system approximation system.
The designed recognition model is as follows:
Figure BDA0003308922090000076
wherein,
Figure BDA0003308922090000077
is the optimal weight vector
Figure BDA0003308922090000078
Is determined by the estimated value of (c),
Figure BDA0003308922090000079
is to the disturbance di，2Is determined by the estimated value of (c),
Figure BDA00033089220900000710
to predict the state, βi，2,γi，2,δi，2>0 is the parameter to be designed.
And 3.3, designing a disturbance observer which comprises a connecting rod angular velocity disturbance observer and a connecting rod angular acceleration disturbance observer of the single-arm manipulator.
Wherein, the connecting rod angular velocity disturbance observer is:
Figure BDA0003308922090000081
the connecting rod angular acceleration disturbance observer is as follows:
Figure BDA0003308922090000082
wherein,
Figure BDA0003308922090000083
and
Figure BDA0003308922090000084
is to the disturbance di，1，di，2Is observed value of si，1And si，2For the disturbance observer the state of the auxiliary system is transformed according to the derivative of the disturbance observer design, lambdai，1,λi，2>0 is the parameter to be designed.
And 4, step 4: obtaining a virtual controller according to a preset finite time performance function, the transformed tracking error and a disturbance observer
The virtual controller is designed as follows:
Figure BDA0003308922090000085
wherein,
Figure BDA0003308922090000086
ki,1>0 is a design parameter.
The control method of the embodiment is designed based on a backstepping method, and the traditional backstepping method needs a virtual controller
Figure BDA0003308922090000087
Repeatedly differentiate to causeThe problem of "differential explosion". Therefore, a dynamic surface technology is introduced, and the dynamic surface inputs the signal of the virtual controller into a first-order low-pass filter to obtain a new state variable
Figure BDA0003308922090000088
The next calculation is performed instead of the first virtual controller, so that the processing has the advantage of reducing the calculation amount of the multi-arm manipulator system, and specifically comprises the following steps:
and 4.1, filtering the control signal of the virtual controller by adopting a first-order low-pass filter.
The first order low pass filter is designed as follows:
Figure BDA0003308922090000089
wherein new state variables are obtained
Figure BDA00033089220900000810
τi，1>0 is a design parameter.
Step 4.2, in order to eliminate the influence of the filtering error, the transformed tracking error is compensated, and the compensated tracking error is defined as:
vi,1＝ξi,1-zi,1
wherein z isi,1A compensation signal designed for filtering errors.
The derivative of the compensation signal designed in step 4.3 is:
Figure BDA0003308922090000091
step 4.4: defining a second error surface based on the new state variables as:
Figure BDA0003308922090000092
and 5: and obtaining the controller of the multi-single-arm manipulator system according to the new state variable, the recognition model and the disturbance observer.
Controller uiComprises the following steps:
Figure BDA0003308922090000093
wherein k isi,2>0 is a design parameter.
The whole control method is realized as shown in fig. 3.
And controlling the system to work by using a control signal output by the controller, detecting whether the tracking error meets the requirement, and if not, circulating the steps to form a closed-loop system until the requirement is met.
In a simulation test of this example:
the control objective of the simulation experiment is to make the angle q of the connecting rodiTracking an upper given track signal y00.5sin (t) + sin (0.5t), considering unknown time-varying perturbations, d can be assumed for the purpose of verifying the validity of the methodi,1＝sin(t)-0.5sin(1.5t)；di,2＝-0.8[sin(t-0.6)-sin(t-0.8)]。
According to the actual system, the related parameter is the total mass m of the connecting rodi2kg total moment of inertia M of the connecting rodi＝2kg·m2Acceleration of gravity g 10m/s2Total damping coefficient DiDistance l from joint axis to center of mass 2i1m, system unknown nonlinear function
Figure BDA0003308922090000101
The initial simulation conditions are as follows: x is the number ofi,1(0)＝[0.1,0.2,0.1,0.3]；xi,2(0)＝[0.2,0.1,0.2,0]；si,1(0)＝[0,0,0,0]；si,2(0)＝[0,0,0,0]；
Figure BDA0003308922090000102
wi,2(0)＝[0,0,0,0,0,0,0,0,0,0]；
Figure BDA0003308922090000103
The relevant parameters are set as follows: rhoi,0＝1；ρi,T＝0.05；Ti＝0.1；βi,2＝1；γi,2＝50；δi,2＝20；λi,1＝10；λi,2＝10；ki,1＝20；ki,2＝20；τi,1＝0.005。
The simulation results are shown in fig. 4-7. FIG. 4 is a diagram showing the tracking effect of a multi-arm manipulator, which gives a given track y in an extremely short tracking time0. As can be seen from the tracking error performance constraint map of fig. 5, the preset finite time performance constraint method makes the consistent tracking error within the specified boundary and reach a steady state at a given time. FIG. 6 shows a time-varying disturbance di,1The disturbance observation can accurately estimate the time-varying disturbance. FIG. 7 is a diagram for simultaneously estimating an unknown nonlinear function and a time-varying disturbance f of a systemi,1+di,1The combination of the fuzzy logic system and the disturbance observer can accurately estimate the unknown part f of the systemi,1+di,1. Numerical simulations therefore demonstrate the effectiveness of the proposed control method.
In summary, the method of the present embodiment has the following advantages:
(1) and designing a preset finite time performance constraint method to ensure that the consistent tracking error meets the external limiting condition and reaches a stable state within the required finite time.
(2) And establishing an identification model based on the fuzzy logic system, so that the fuzzy logic system accurately approaches unknown nonlinearity of the system. The problem of unknown model of the controlled system is solved, the robustness of the controlled system is enhanced by the designed controller, and the method can be popularized to wider systems.
(3) The designed disturbance observer can effectively compensate the influence caused by time-varying disturbance, so that the multi-single-arm manipulator is suitable for more complex environments.
Example 2:
the embodiment discloses a many single armed manipulator system control system includes:
a modeling module: the system is used for establishing a state dynamic model of the multi-single-arm manipulator system;
a tracking error acquisition module: the system comprises a single-arm manipulator, a tracking error model, a finite time performance function and a coordinate transformation module, wherein the single-arm manipulator is used for carrying out coordinate transformation according to the consistent tracking error model of the single-arm manipulator and the constructed finite time performance function to obtain a transformed tracking error;
the identification model and disturbance observer acquisition module: the disturbance observer is used for obtaining an identification model and a disturbance observer according to the obtained state dynamics model;
the virtual controller obtains a model: the virtual controller is obtained according to a preset finite time performance function, the transformed tracking error and the disturbance observer;
a state variable acquisition module: the virtual controller is used for filtering a control signal of the virtual controller to obtain a new state variable;
a control module: and the controller is used for obtaining the multi-single-arm manipulator system according to the new state variable, the recognition model and the disturbance observer.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts by those skilled in the art based on the technical solution of the present invention.

Claims (10)

1. A multi-single-arm manipulator system control method is characterized by comprising the following steps:
establishing a state dynamics model of the multi-single-arm manipulator;
performing error transformation according to a consistent tracking error model of the single-arm manipulator and a constructed preset finite time performance function to obtain a transformed tracking error;
obtaining an identification model and a disturbance observer according to the obtained state dynamics model;
obtaining a virtual controller according to a preset finite time performance function, the transformed tracking error and a disturbance observer;
filtering a control signal of the virtual controller to obtain a new state variable;
and obtaining a controller of the multi-single-arm manipulator system according to the new state variable, the recognition model and the disturbance observer, and outputting a control signal by using the controller.
2. The method of claim 1, wherein the system model of the single-arm robot is created, and the system model of the single-arm robot is transformed to obtain the state dynamics model of the single-arm robot system.
3. The method of claim 1, wherein the control signal of the virtual controller is filtered by a first order low pass filter.
4. The method of claim 1, wherein the compensated tracking error is obtained from the compensation signal, the second error plane is obtained from the new state variable, and the controller is obtained from the compensated tracking error, the second error plane, the recognition model, and the disturbance observer.
5. The method of claim 1, wherein the consistent tracking error model of the single-arm robot is obtained based on knowledge of graph theory.
6. The method of claim 1, wherein the predetermined finite time performance function is obtained according to a finite time during which the consistent tracking error is stable.
7. The method of claim 1, wherein the disturbance observer comprises a link angular velocity disturbance observer and a link angular acceleration disturbance observer of the single-arm robot.
8. The method of claim 1, wherein the unknown nonlinear function of the fuzzy logic system approximation system is obtained according to the basis function vector, the optimal weight vector and the approximation error, and the recognition model is obtained according to the state dynamics model of the multi-arm manipulator.
9. The method of claim 8, wherein the basis function vector is obtained using a gaussian function.
10. A multi-arm robot system control system, comprising:
a modeling module: the system is used for establishing a state dynamic model of the multi-single-arm manipulator system;
a tracking error acquisition module: the system comprises a single-arm manipulator, a tracking error model, a finite time performance function and a coordinate transformation module, wherein the single-arm manipulator is used for carrying out coordinate transformation according to the consistent tracking error model of the single-arm manipulator and the constructed finite time performance function to obtain a transformed tracking error;
the identification model and disturbance observer acquisition module: the disturbance observer is used for obtaining an identification model and a disturbance observer according to the obtained state dynamics model;
the virtual controller obtains a model: the virtual controller is obtained according to a preset finite time performance function, the transformed tracking error and the disturbance observer;
a state variable acquisition module: the virtual controller is used for filtering a control signal of the virtual controller to obtain a new state variable;
a control module: and the controller is used for obtaining the controller of the multi-single-arm manipulator system according to the new state variable, the recognition model and the disturbance observer, and outputting a control signal by using the controller.
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