CN113942010B - Self-adaptive torque control method for multi-station mechanical arm double-side pose positioning - Google Patents

Self-adaptive torque control method for multi-station mechanical arm double-side pose positioning Download PDF

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CN113942010B
CN113942010B CN202111201912.1A CN202111201912A CN113942010B CN 113942010 B CN113942010 B CN 113942010B CN 202111201912 A CN202111201912 A CN 202111201912A CN 113942010 B CN113942010 B CN 113942010B
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mechanical arm
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CN113942010A (en
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张铁荟
李恒宇
刘军
刘靖逸
谢少荣
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Jining University
University of Shanghai for 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
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
    • 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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Abstract

The invention belongs to the technical field of modern industrial intelligent control, and particularly discloses a self-adaptive torque control method for positioning the double-side pose of a multi-station mechanical arm; the problem of excessively rely on the multistation arm position appearance operation control of vision sensor location in industrial flow line production is solved. Firstly, system modeling is carried out, and a sliding mode integral term is embedded into a self-adaptive feedback control protocol of a controlled system to design a closed-loop torque controller; a non-circulation topological structure integrally formed by a production line system is utilized, initial state information is adjusted in advance, a controller algorithm designed by multi-station mechanical arm loading is further evolved to multiple expected groups of bilateral positions, and a method for positioning the pose of the mechanical arm through real-time monitoring of a visual sensor is improved. By the method, the accurate operation of the pose control of the mechanical arm can be conveniently realized, the automation, intellectualization and integration levels of modern industrial production are improved, and the method has good social benefits and economic values.

Description

Self-adaptive torque control method for multi-station mechanical arm double-side pose positioning
Technical Field
The invention belongs to the technical field of modern industrial intelligent control, and particularly relates to a self-adaptive torque control method for positioning double-side poses of a multi-station mechanical arm.
Background
The realization of modern industrial intelligent manufacturing automation, integration and digitization is a necessary way for developing advanced manufacturing technology. The assembly line is an important platform in industrial production, and the intelligent control of the multi-station mechanical arm for executing operation tasks is a key development field of a modern production control system. The multi-station mechanical arm is cooperated with each other to complete task deployment of each link in production, and becomes a key technology of intelligent manufacturing. At present, in industrial flow line production, the position and the posture of each mechanical arm are mostly positioned and monitored in real time by a visual sensor, but the working performance cannot be ensured when the visual sensor fails. In this case, it is very difficult to automatically realize the desired positioning of the robot arm at each station using only the torque controller due to the dynamics of the strong coupling nonlinearity of the robot arm. In addition, when the mechanical arm communication module adopts duplex communication, communication echo crosstalk is easily formed in information transmission at a longer distance, and the task completion effect is influenced.
Disclosure of Invention
The invention aims to provide a self-adaptive moment control method for positioning double-side poses of a multi-station mechanical arm independent of a vision sensor.
Based on the purpose, the invention adopts the following technical scheme:
a self-adaptive torque control method for positioning double-side poses of a multi-station mechanical arm comprises the following steps:
step one, acquiring real-time position information of each mechanical arm; acquiring real-time speed information of each mechanical arm; carrying a communication module on each mechanical arm to perform data interaction with the adjacent mechanical arm;
secondly, modeling a dynamic system of each mechanical arm;
thirdly, marking and grouping the multi-station mechanical arms;
designing a distributed adaptive torque controller of the multi-station mechanical arm;
step five, carrying out stability analysis on the distributed adaptive torque controller;
loading a control algorithm of the distributed adaptive moment controller into a micro-control unit of each mechanical arm, and initializing hardware of the multi-station mechanical arm; and calculating initial position information of each mechanical arm, and writing the initial position information of each mechanical arm into a register.
Further, in the second step, the modeling method is that
Figure GDA0003346354540000011
In the formula, q i As the self-position information of the ith robot arm,
Figure GDA0003346354540000012
is the real-time speed information of the ith mechanical arm, mi is an inertia matrix of the ith mechanical arm, ci is a centrifugal force and Coriolis matrix of the ith mechanical arm, g i Is a generalized potential force matrix, τ, of the ith robot arm i Is the input torque vector of the ith robot arm.
Further, in the third step, the mechanical arms are grouped according to the stations where the mechanical arms are located; by utilizing the relevant knowledge of graph theory, due to the assembly line operation, a system formed by all mechanical arms corresponds to a non-circular topological graph which is recorded as
Figure GDA00033463545400000211
The number of each station of the production line can be set according to actual requirements; make/combine>
Figure GDA00033463545400000221
Figure GDA00033463545400000222
Is/>
Figure GDA00033463545400000212
In combination with a tone signal, is combined with a tone signal>
Figure GDA00033463545400000220
Represents the l-th group of mechanical arms>
Figure GDA00033463545400000219
Represents the i-th robot arm in the l-th group, i =1,2, …, k, i =1,2, …, w,
Figure GDA0003346354540000021
n l the number of mechanical arms in the first group;
in order to realize accurate positioning of the bilateral pose of the multi-station mechanical arm, the small groups of the mechanical arms at all stations are further divided as follows: will be provided with
Figure GDA00033463545400000223
Division into->
Figure GDA0003346354540000022
And &>
Figure GDA0003346354540000023
If->
Figure GDA0003346354540000024
Phi is then i =1; if it is not
Figure GDA0003346354540000025
Phi is then i ＝-1；
Figure GDA0003346354540000026
Figure GDA0003346354540000027
Figure GDA00033463545400000213
The corresponding laplace matrix->
Figure GDA0003346354540000028
In the formula, L mm Is about a drawing
Figure GDA00033463545400000214
Is based on the Laplace matrix, is based on the evaluation of the status of the evaluation unit>
Figure GDA00033463545400000215
Is a topological graph of the mth group of mechanical arms; l is mn A matrix for information transmission from the nth group of mechanical arms to the mth group of mechanical arms, i, j =1,2, … w; m, n =1,2, … k, n < m; />
Figure GDA00033463545400000216
The row is 0. Because the Laplace matrix is an important carrier for multi-station mechanical arm coupling control, and the structure balance theory is the key for completing multiple groups of symmetrical pose operation in the same working procedure period, each station subgraph is in a sub-picture or a sub-picture state>
Figure GDA00033463545400000217
The corresponding Laplace matrix satisfies
Figure GDA00033463545400000218
The row of (c) is zero, which is a specific quantification of the balance of information exchange of each group of station robot arms when the controller algorithm is designed. Here, equation (1) relates to a constant-value kinetic parameter θ i Can be linearized by a parameter that we ask for each and every->
Figure GDA00033463545400000210
Has spanning tree and balanced structure.
Further, in step four, a distributed adaptive torque controller is designed by using a back stepping method, and the process is as follows:
first, consider the ith robot arm
Figure GDA00033463545400000224
Designing a sliding mode vector
Figure GDA0003346354540000029
The vector is independent of the uncertainty of the matched parameters of the robotic arm system, where j =1,2 …, w; when the j-th mechanical arm transmits information to the i-th mechanical arm, a ij Is constant R when the j-th arm is moved toThe ith mechanical arm has no information transmission, then a ij Is 0; value phi corresponding to each mechanical arm j Are all fixed values (1 or-1), phi at the time of grouping j Already set;
combining sliding mode vector, introducing auxiliary vector
Figure GDA0003346354540000031
Wherein t is time, ζ i Is a constant greater than zero; auxiliary vector
Figure GDA0003346354540000032
Can make s i The asymptote steadily approaches zero.
In addition, in order to enable the mechanical arm to achieve the final expected pose, a second sliding mode vector is designed on the basis
Figure GDA0003346354540000033
By utilizing the overall topological structure of the system, after matrix operation processing is carried out, the integral terms of the formulas (3) and (4) can be designed to conveniently realize the expected pose of any given mechanical arm.
In order to suppress the disturbance problem of the mechanical arm, obtain parameter information more quickly and improve system performance, parameters are predicted on line based on self-adaptive characteristics; giving an input torque expression to the ith mechanical arm
Figure GDA0003346354540000034
In the formula, K i In order to be a matrix of gains, the gain matrix,
Figure GDA0003346354540000035
is a kinetic parameter θ i Is evaluated by the evaluation unit>
Figure GDA0003346354540000036
The change rule of (2) adopts a gradient descent method,
since the regression matrix can well reflect the system state information in real time, the self-adaptive law is designed
Figure GDA0003346354540000037
In the formula, Λ i Is a positive definite matrix;
Figure GDA0003346354540000038
is a regression matrix of the kinetic equation. In fact, the dynamic parameters are generally nonlinear functions and can be directly calculated by mechanical arm dynamic equations, and the uncertainty of the system parameters can be suppressed by a designed parameter estimator.
Further, the kinetic model (1) is applied with the formulas (5) and (6) to make
Figure GDA0003346354540000039
Available closed loop system
Figure GDA00033463545400000310
Stability analysis is conveniently carried out to distributed adaptive moment controller.
Further, in step six, the method for calculating the initial position of each mechanical arm comprises the following steps: according to expected pose information to be achieved in actual demand operation, a loop-free topological structure integrally formed by a pipeline system is utilized, a left eigenvector corresponding to a zero eigenvalue of a Laplace matrix is given through a matrix analysis theory, and initial pose and state information of each mechanical arm are obtained. And reading information through the scanning input port, and writing the initial pose and state information of the mechanical arm into a register. And (3) giving a left eigenvector corresponding to a zero eigenvalue of a Laplace matrix formed by k groups of mechanical arms:
Figure GDA0003346354540000041
the component values of the above left eigenvector satisfy the following two equations:
Figure GDA0003346354540000042
Figure GDA0003346354540000043
in the formula, n s The number of the s-th group of arms, n l The number of the l group of mechanical arms.
The following can be obtained through calculation:
Figure GDA0003346354540000044
Figure GDA0003346354540000045
wherein q (0) is a column stack vector of an initial position,
Figure GDA0003346354540000046
to a desired position, I p Is an identity matrix of order p.
Further, in the fifth step, a lyapunov function and an input state stabilization theory are adopted to perform stability analysis on the distributed adaptive torque controller.
Furthermore, the communication modules among the multiple groups of mechanical arms adopt a simplex communication non-circulation transmission mode.
Further, in the first step, an inertial sensor is carried on each mechanical arm to obtain real-time position information; a logic programming controller and a photoelectric encoder are carried on each mechanical arm, and the logic programming controller is used for collecting real-time speed information converted by the photoelectric encoder.
Compared with the prior art, the invention has the following beneficial effects:
1. the motion characteristic of the mechanical arm is related to the self pose and is also limited by factors such as mass inertia, a structural mechanism, an actuator position and the like of the mechanical arm, so that the description of the moment and motion relation is matched in the mechanical arm control based on a kinetic equation, and the motion of the mechanical arm is conveniently controlled.
2. And the self-adaptive moment controller in the fourth step ensures that the station mechanical arm reaches an expected bilateral pose, and adjusts bilateral pose evolution of a plurality of subsequent stations through a special sliding mode vector. The main difficulty of the invention is to design a feasible algorithm to eliminate the mutual influence among different station information and simultaneously realize the bilateral pose positioning of the mechanical arm of each station. The invention introduces the symbol phi i Vector s of sliding mode i Embedding into a given adaptive law theta i In the method, the symbol of information exchange among different stations is automatically adjusted when the behavior of the mechanical arm evolves. In addition, the adopted structural balance topology mechanism also ensures the realization of not damaging the double-side pose target of the mechanical arm at each station. Using kinetic parameters theta i The estimator is convenient for the self-adaptive law to process information in parameter estimation, and accurate control of the final real-time state of the mechanical arm is realized. The Laplace matrix introduced in the third step reflects the coupling relation among multiple mechanical arms, and the dynamic parameter estimator can realize the parameter theta in a self-correcting mode through global information provided by the Laplace matrix i Fast convergence of (2).
3. Sixthly, setting the initial state of each mechanical arm in advance according to the expected pose by combining the property of a zero eigenvalue of a Laplace matrix in the matrix theory, and realizing static positioning of each station mechanical arm through a written controller algorithm; according to expected pose information to be achieved by actual requirements in the operation of the assembly line multi-station mechanical arm, a left eigenvector expression corresponding to a zero eigenvalue of a Laplace matrix is given by self-adaptive control in combination with a sliding mode vector with an integral term, the initial pose and state information of each mechanical arm are obtained, the monitoring of a visual sensor is not required to be relied on in real time, and the working performance of the mechanical arm can still be ensured when the visual sensor breaks down.
4. According to actual requirements, the assembly line multi-station mechanical arm can automatically run to an expected pose, static positioning of the mechanical arm at each station is achieved through a written controller algorithm, namely the speed of the mechanical arm at the expected pose gradually converges to zero, and the pose of each mechanical arm does not need to be monitored by a visual sensor in real time. In many practical applications, it is very convenient if the final pose of each group of mechanical arms can be predicted in advance. However, it should be noted here that the mechanical arm dynamics system is a high-order nonlinear system, and has the characteristics of strong coupling and nonlinearity, and the linear system explicit solution method and convergence analysis cannot be applied. The basic principle of the invention for solving the problems is that a left characteristic vector expression corresponding to a zero characteristic value of a Laplace matrix is given by combining self-adaptive control with a sliding mode vector with an integral term, and initial state information of each mechanical arm is obtained according to an expected pose after matrix operation processing is carried out by utilizing the overall topological structure of the system. The realization of the final target of the invention only depends on the network topology structure of the no-cycle division of the production line, so that the invention can flexibly respond to different production target conditions, the applicable conditions are very common, the automation and intellectualization degrees are improved, the use is more convenient and humanized, and the invention has higher practicability.
5. In the production process of the production line, the mechanical arm operation of the previous station can influence the subsequent station, but because the production line is in one-way information transmission, the data operated by the subsequent station can not be transmitted back to the previous station, therefore, the communication module can adopt simplex communication, and communication echo crosstalk is avoided.
6. The stability analysis adopts modern control theory methods such as Lyapunov function and input state stability theory, and theoretically supports the goal that the multi-station mechanical arm can stably realize static pose positioning.
In conclusion, the designed algorithm is integrated in the adaptive torque controller, the streamline platform is described by adopting a topological structure without cyclic division in combination with the graph theory, multiple groups of bilateral positioning of the multi-station mechanical arm in the same working procedure can be realized, the mechanical arm of each station is guaranteed to evolve to a static expected pose, and the method for positioning the pose of the mechanical arm through real-time monitoring by the vision sensor is improved. The self-adaptive moment controller used in the invention ensures that the station mechanical arm reaches an expected bilateral pose, and regulates the bilateral pose evolution of a plurality of subsequent stations through a novel sliding mode control technology with integral terms, thereby solving the problem of operation control of the pose of the multi-station mechanical arm excessively depending on the positioning of a vision sensor in industrial flow line production. Furthermore, according to expected pose information to be achieved by actual requirements in assembly line multi-station mechanical arm operation, initial state information of each mechanical arm can be preset in advance, and accurate operation of mechanical arm pose control is achieved conveniently. The realization of the final target of the invention only depends on the network topology structure of the no-cycle division of the assembly line, which leads the invention to be capable of flexibly changing according to different production target conditions, the application condition is very common, and the invention has higher practicability. By the method, the accurate operation of the pose control of the mechanical arm can be conveniently realized, the automation level of an assembly line is better applied and improved, the controller function of the industrial mechanical arm is integrated, the automation, intellectualization and system integration level of modern industrial production is improved, the application of a new generation of information technology in high-end manufacturing equipment industry is further promoted, the cost is reduced, and the method has good social benefit and economic value.
Drawings
Fig. 1 is a schematic view of a multi-station robot arm production line according to embodiment 1 of the present invention;
fig. 2 is a schematic diagram illustrating a pose positioning target of the mechanical arm in embodiment 1 of the present invention.
Detailed Description
Example 1
The self-adaptive torque control for positioning the double-side pose of the multi-station mechanical arm comprises the following steps:
step one, each mechanical arm (mechanical arm joint) is provided with an inertial sensor, and the self pose q is determined in real time i Monitoring is carried out; each mechanical arm is provided with a logic programming controller for collecting real-time speed information converted by a photoelectric encoder of the motor actuator
Figure GDA0003346354540000069
The carried communication module can carry out data interaction with the adjacent mechanical arm. The communication module between two stations (two groups of mechanical arms) adopts simplex communication, thereby avoiding communication echo and crosstalk.
Step two, performing system modeling on mechanical arm dynamics for Matlab or Python by using mathematical software:
Figure GDA0003346354540000061
and thirdly, marking and grouping the multi-station mechanical arms. FIG. 1 is an environment of assembly line robot arm operation, grouping the robot arms according to the stations where the robot arms are located. By utilizing the relevant knowledge of graph theory, due to the pipeline operation, a system consisting of w mechanical arms is correspondingly provided with a topological graph without circulation
Figure GDA00033463545400000610
Make->
Figure GDA00033463545400000613
Figure GDA00033463545400000615
Represents->
Figure GDA00033463545400000614
Is selected, and the ith packet of>
Figure GDA00033463545400000616
Represents that the i-th mechanical arm is positioned in the l-th group, i =1,2, …, k, i =1,2, …, w, called &/>
Figure GDA00033463545400000617
Is/>
Figure GDA00033463545400000611
In combination with a tone signal, is combined with a tone signal>
Figure GDA00033463545400000619
Corresponding diagram->
Figure GDA00033463545400000612
For convenience, order
Figure GDA0003346354540000062
n l Number of arms of group l.
In order to realize accurate positioning of the bilateral pose of the multi-station mechanical arm, the following steps of further dividing each station mechanical arm group:
Figure GDA00033463545400000618
can be divided into>
Figure GDA0003346354540000063
And &>
Figure GDA0003346354540000064
Satisfy->
Figure GDA0003346354540000065
Wherein if->
Figure GDA0003346354540000066
Definition of phi i =1; if->
Figure GDA0003346354540000067
Definition of phi i And (4) = -1. Order to
Figure GDA0003346354540000068
/>
Definition of
Figure GDA0003346354540000079
The corresponding laplace matrix->
Figure GDA0003346354540000071
Where L is mm Is related to the map->
Figure GDA00033463545400000710
Is based on the Laplace matrix, is based on the evaluation of the status of the evaluation unit>
Figure GDA00033463545400000712
Is a topological graph of the mth group of mechanical arms; l is mn A matrix for information transmission from the nth group of arms to the mth group of arms, i, j =1,2, … w; m, n =1,2, … k, n < m. Here->
Figure GDA00033463545400000713
Rows and columns are 0,m ≠ n, m, n =1,2, …, k. We ask for each and every one>
Figure GDA00033463545400000711
Has spanning tree and balanced structure.
Step four, designing a distributed controller; the controller is designed using the principle of the backstepping method. First, consider the ith robot arm
Figure GDA00033463545400000714
Design a sliding mode vector
Figure GDA0003346354540000072
This vector is independent of the matching parameter uncertainty of the robotic arm system. Wherein j =1,2 …, w; when the j th mechanical arm has information transmission to the i th mechanical arm, a ij Constant R, when there is no information transmission from the jth arm to the ith arm, a ij Is 0; value phi corresponding to each mechanical arm j Are all fixed values (1 or-1), phi at the time of grouping j Has already been set.
Combining the sliding mode vector formula (2) and introducing an auxiliary vector with an integral term form
Figure GDA0003346354540000073
Wherein t is time, and after the robot arm is initialized, t =0, ζ i Is a constant greater than zero; auxiliary vector
Figure GDA0003346354540000074
Can make s i Asymptotic steadily approaches zero.
In addition, in order to enable the mechanical arm to achieve the final expected pose, a second sliding mode vector is designed on the basis
Figure GDA0003346354540000075
By using the overall topological structure of the system, after matrix operation processing is carried out, the integral terms of the formulas (3) and (4) can be designed to conveniently realize the expected pose of any given mechanical arm.
In order to suppress the disturbance problem of the mechanical arm, obtain parameter information more quickly and improve system performance, parameters are predicted online based on adaptive characteristics. Giving an input torque expression to the ith mechanical arm
Figure GDA0003346354540000076
Equation (1) here relates to a constant kinetic parameter θ i Can be parametrically linearized, wherein K i In order to be a matrix of gains, the gain matrix,
Figure GDA0003346354540000077
is a kinetic parameter θ i An estimate of (d). />
Figure GDA0003346354540000078
The change rule of (2) adopts a gradient descent method, and since the regression matrix can well reflect the system state information in real time, the self-adaptation law is designed
Figure GDA0003346354540000081
Here Λ i Is a positive definite matrix;
Figure GDA0003346354540000082
the system is a regression matrix of a kinetic equation, in fact, kinetic parameters are generally nonlinear functions and can be directly obtained by calculation of the mechanical arm kinetic equation, and uncertainty of system parameters can be suppressed through a designed parameter estimator.
And fifthly, carrying out stability analysis on the adaptive torque controller. The kinetic model (1) is acted on by the formulae (5) and (6) in order
Figure GDA0003346354540000083
Available closed loop system
Figure GDA0003346354540000084
Stability analysis is conveniently carried out to distributed adaptive moment controller.
And step six, loading the algorithm information of the distributed adaptive moment controller into the micro-control unit of each mechanical arm and initializing the hardware of the multi-station mechanical arm. FIG. 2 is a pose positioning target demonstration of the robotic arm. And initializing and setting a hardware system of the mechanical arm of each station. According to expected pose information to be achieved in actual demand operation, a loop-free topological structure integrally formed by a pipeline system is utilized, a left eigenvector corresponding to a zero eigenvalue of a Laplace matrix is given through a matrix analysis theory, and initial pose and state information of each mechanical arm are obtained. And reading information through the scanning input port, and writing the initial pose and state information of the mechanical arm into a register. And (3) giving a left eigenvector corresponding to a zero eigenvalue of a Laplace matrix formed by k groups of mechanical arms:
Figure GDA0003346354540000085
the component values of the above left eigenvector satisfy the following two equations:
Figure GDA0003346354540000086
Figure GDA0003346354540000087
in the formula, n s The number of the s-th group of arms, n l Number of the first group of mechanical arms
By using matrix transformation and solving for the limit with respect to time t through the integral term in equations (3) and (4), the target position and velocity of the ith robot arm can be obtained as follows:
Figure GDA0003346354540000088
Figure GDA0003346354540000089
where q (0) is the column stack vector for the initial position,
Figure GDA00033463545400000810
to a desired position, I p Is an identity matrix of order p. The initial position information can be obtained by inputting the expected position information of the mechanical arm, the obtained initial position information is input into the register, and the distributed adaptive torque controller can control the mechanical arm to move to the expected position according to the initial position information. />

Claims (7)

1. A self-adaptive torque control method for positioning double-side pose of a multi-station mechanical arm comprises the following steps:
step one, acquiring real-time position information of each mechanical arm; acquiring real-time speed information of each mechanical arm; carrying a communication module on each mechanical arm to perform data interaction with the adjacent mechanical arm;
step two, modeling a dynamic system of each mechanical arm;
step three, marking and dividing the multi-station mechanical armGroup (d); the mechanical arms are grouped according to the stations, and a system formed by all the mechanical arms corresponds to a non-circular topological graph and is recorded as
Figure FDA0004128007800000011
Make->
Figure FDA0004128007800000012
Figure FDA0004128007800000013
Is->
Figure FDA0004128007800000014
In combination with a tone signal, is combined with a tone signal>
Figure FDA0004128007800000015
Represents the l-th group of mechanical arms>
Figure FDA0004128007800000016
Representing the i-th arm in the l-th group, l =1,2, …, k, i =1,2, …, w,
Figure FDA0004128007800000017
n l the number of mechanical arms in the first group; w is the number of mechanical arms;
will be provided with
Figure FDA0004128007800000018
Divide into->
Figure FDA0004128007800000019
And &>
Figure FDA00041280078000000110
If->
Figure FDA00041280078000000111
Phi is then i =1; if->
Figure FDA00041280078000000112
Phi is then i ＝-1；
Figure FDA00041280078000000113
Figure FDA00041280078000000114
Figure FDA00041280078000000115
The corresponding laplace matrix->
Figure FDA00041280078000000116
In the formula, L mm Is about a drawing
Figure FDA00041280078000000117
Is based on the Laplace matrix, is based on the evaluation of the status of the evaluation unit>
Figure FDA00041280078000000118
Is a topological graph of the mth group of mechanical arms; l is mn A matrix for information transmission from the nth group of mechanical arms to the mth group of mechanical arms, i, j =1,2, … w; m, n =1,2, … k, n < m; />
Figure FDA00041280078000000119
The row and is 0;
designing a distributed adaptive torque controller of the multi-station mechanical arm;
fifthly, carrying out stability analysis on the distributed adaptive torque controller;
loading a control algorithm of the distributed adaptive moment controller into a micro-control unit of each mechanical arm, and initializing hardware of the multi-station mechanical arm; and calculating initial position information of each mechanical arm, and writing the initial position information of each mechanical arm into a register.
2. The method for controlling the adaptive torque for the bilateral pose positioning of the multi-station mechanical arm according to claim 1, wherein in the second step, the modeling method is that
Figure FDA0004128007800000021
In the formula, q i As the self-position information of the ith robot arm,
Figure FDA0004128007800000022
for real-time velocity information of the ith robot, M i Is the inertia matrix of the ith arm, C i Is a matrix of centrifugal force and Coriolis force of the ith robot arm, q i Is a generalized potential force matrix, τ, of the ith robot arm i Is the input torque vector of the ith robot arm.
3. The self-adaptive torque control method for the double-side pose positioning of the multi-station mechanical arm according to claim 2 is characterized in that in the fourth step, a distributed self-adaptive torque controller is designed by a back-stepping method, and the process is as follows:
firstly, designing a sliding mode vector related to the ith mechanical arm
Figure FDA0004128007800000023
Wherein j =1,2 …, w; when the j-th mechanical arm transmits information to the i-th mechanical arm, a ij Is constant R, when the j mechanical arm to the i mechanical arm has no information transmission, a ij Is 0;
combining sliding mode vectors, introducing auxiliary vectors
Figure FDA0004128007800000024
Wherein t is time, ζ i Is a constant greater than zero;
then, a second sliding mode vector is designed
Figure FDA0004128007800000025
Finally, the input torque vector of the ith mechanical arm is obtained, and the expression is
Figure FDA0004128007800000026
In the formula, K i In order to be a matrix of gains, the gain matrix,
Figure FDA0004128007800000027
is a kinetic parameter θ i Is estimated by
Law of design adaptation
Figure FDA0004128007800000028
In the formula, Λ i Is a positive definite matrix;
Figure FDA0004128007800000029
is a regression matrix of the kinetic equation.
4. The self-adaptive torque control method for the multi-station mechanical arm double-side pose positioning according to claim 3, wherein in the sixth step, the method for calculating the initial position of each mechanical arm is as follows: and (3) giving a left eigenvector corresponding to a zero eigenvalue of a Laplace matrix formed by k groups of mechanical arms:
Figure FDA0004128007800000031
the component values of the above left eigenvector satisfy the following two equations:
Figure FDA0004128007800000032
Figure FDA0004128007800000033
the following are obtained through calculation:
Figure FDA0004128007800000034
Figure FDA0004128007800000035
wherein q (0) is a column stack vector of the initial position,
Figure FDA0004128007800000036
to the desired position, I p Is an identity matrix of order p.
5. The self-adaptive torque control method for the double-side pose positioning of the multi-station mechanical arm according to any one of claims 1 to 4, characterized in that in the fifth step, a Lyapunov function and an input state stabilization theory are adopted to perform stability analysis on the distributed self-adaptive torque controller.
6. The self-adaptive torque control method for the bilateral pose positioning of the multi-station mechanical arms according to any one of claims 1 to 4, wherein communication modules among the multiple groups of mechanical arms adopt a simplex communication non-cyclic transmission mode.
7. The self-adaptive torque control method for the bilateral pose positioning of the multi-station mechanical arm according to any one of claims 1 to 4, characterized in that in the first step, an inertial sensor is carried on each mechanical arm to acquire real-time position information; a logic programming controller and a photoelectric encoder are carried on each mechanical arm, and the logic programming controller is used for collecting real-time speed information converted by the photoelectric encoder.
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