CN112338913A - Trajectory tracking control method and system of multi-joint flexible mechanical arm - Google Patents

Trajectory tracking control method and system of multi-joint flexible mechanical arm Download PDF

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CN112338913A
CN112338913A CN202011166128.7A CN202011166128A CN112338913A CN 112338913 A CN112338913 A CN 112338913A CN 202011166128 A CN202011166128 A CN 202011166128A CN 112338913 A CN112338913 A CN 112338913A
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mechanical arm
flexible mechanical
track
control law
joint
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CN112338913B (en
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佃松宜
苗佳藤
朱明江
岳宝强
向国菲
钟羽中
马丛俊
杨立超
李景华
崔国柱
李彪
陈玉
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Sichuan University
Linyi Power Supply Co of State Grid Shandong Electric Power Co Ltd
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Sichuan University
Linyi Power Supply Co of State Grid Shandong Electric Power Co Ltd
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—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
    • 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
    • B25J9/161—Hardware, e.g. neural networks, fuzzy logic, interfaces, processor
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/1635—Programme controls characterised by the control loop flexible-arm control
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/1653—Programme controls characterised by the control loop parameters identification, estimation, stiffness, accuracy, error analysis

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  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Automation & Control Theory (AREA)
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Abstract

The invention discloses a track tracking control method and system of a multi-joint flexible mechanical arm, which are characterized in that based on the deviation of an originally set expected track and a real-time track of the flexible mechanical arm, after fusion simplification and self-adaptive processing, two control laws are respectively obtained by using a designed interval type two fuzzy controller and a boundary supervisory controller, and then the track of the flexible mechanical arm is corrected by using the superposition result of the two control laws, so that the real-time tracking of the expected track of the flexible mechanical arm is realized. The method not only improves the approximation precision of the interval two-type fuzzy controller, but also can ensure the effectiveness of track tracking control of the flexible mechanical arm, thereby improving the rapidity, the accuracy and the stability of response of the flexible mechanical arm system.

Description

Trajectory tracking control method and system of multi-joint flexible mechanical arm
Technical Field
The application belongs to the technical field of robots, relates to a track tracking technology of a flexible mechanical arm, and particularly relates to a track control method and system of a multi-joint flexible arm.
Background
Different from the traditional rigid robot fundamentally, the flexible mechanical arm has the advantages of light weight, low power consumption, high load ratio, high precision, compact component design and the like, and can overcome the defects of heavy weight and difficulty in working in a narrow working space of the rigid mechanical arm. However, the flexible elements included in the flexible mechanical arm are low in rigidity, so that the system is easy to be unstable in work, and vibration and bending deformation of the mechanical arm are easily caused, thereby greatly increasing the control difficulty. Therefore, the current mechanical arm research on control has two difficulties: (1) the large flexible mechanical arm generates unstable system internal disturbance due to the existence of flexible components; (2) the flexible mechanical arm can generate elastic and bending deformation in the motion process, and when a complex and accurate control algorithm is designed for the mechanical arm, huge calculation amount can be caused, so that the response speed of the system is reduced.
The complicated nonlinear flexible mechanical arm control mainly controls the coupling motion of a flexible component and a rigid mechanical arm. The desired trajectory cannot be tracked well due to instability of the tip caused by vibration of the flexible joint. At present, researchers aim to find a suitable control algorithm to overcome the problem of inaccurate flexible mechanical arm modeling, and when track control of a flexible mechanical arm is completed, amplitude of the flexible mechanical arm in a motion process is suppressed by controlling input voltage of a servo motor of the flexible mechanical arm to change the magnitude of torque generated by the motor. The current main control methods are PID control, fuzzy self-adaptive control, neural network control, inversion control, synovial membrane control and the like. The fuzzy adaptive control has superiority in processing complex uncertain nonlinear systems, particularly interval two-type fuzzy, and compared with the first-type fuzzy, the fuzzy adaptive control is less influenced by the selection of the membership function, higher in accuracy of approaching unknown disturbance and higher in anti-interference capability.
Kelekci Ethem et cl. discloses a novel interval type fuzzy logic controller for real-time trajectory and vibration control of flexible joint manipulators. The controller was designed on a Mamdani-based interval 2 fuzzy logic toolbox developed by Kelekci Ethem et cl. et al, which was designed and developed using an interval triangle membership function and a carrlnickel type reduction algorithm. However, since the section-based fuzzy logic controller designed in the text improves the robustness of the system based on the self-adaptability, the controller has weak adaptability, and thus, the robot arm end tracking deviation cannot be corrected well in real time. In addition, because the flexible mechanical arm is double-joint, the fed back information is the bending angle and the rotation angle omega of the two joints1,ω2,
Figure BDA0002745837110000011
And their derivatives
Figure BDA0002745837110000012
Thus resulting in large computational effort and slow response times.
Disclosure of Invention
The invention aims to solve the problems of insufficient adaptability, slow response time and the like of the conventional flexible mechanical arm track tracking technology, and provides a track tracking control method and a track tracking control system of a multi-joint flexible mechanical arm.
In order to achieve the purpose, the invention idea is as follows: based on the deviation between the originally set expected track and the real-time track of the flexible mechanical arm, after fusion simplification and self-adaptive processing, two control laws are obtained by respectively utilizing a designed interval type fuzzy controller and a designed boundary supervisory controller, and then the track of the flexible mechanical arm is corrected by utilizing the superposition result of the two control laws, so that the real-time tracking of the expected track of the flexible mechanical arm is realized.
The track tracking control method of the multi-joint flexible mechanical arm provided by the invention comprises the following steps:
s1, acquiring state deviation of the expected track and the actual track of the flexible mechanical arm;
s2 performs fusion processing on the state deviations obtained in step S1;
s3, performing adaptive processing by using an adaptive law function according to the state deviation obtained in the step S1;
s4 obtaining a first control law u through the interval type two-type fuzzy controller according to the fusion processing result of the step S2 and the self-adaptive processing result of the step S3D；
S5 is based on the state deviation obtained in step S1 and the first control law u obtained in step S4DObtaining a second control law u by the boundary supervisory controllerC；
S6 shows the first control law u obtained in step S5DAnd a second result obtained in step S6Control law uCSuperposing to obtain a master control law u of the flexible mechanical arm;
s7, correcting the track of the flexible mechanical arm according to the total control law u of the flexible mechanical arm;
and repeating the steps S1-S7 to realize the real-time tracking of the expected track of the flexible mechanical arm.
In the track tracking control method of the multi-joint flexible mechanical arm, in step S1, state variables of each joint of the flexible mechanical arm are obtained based on a dynamic equation of an actual track of the flexible mechanical arm, and an actual pose of the tail end of the flexible mechanical arm is represented by a matrix formed by the state variables of each joint. Expected trajectory Y based on flexible mechanical armmResolving Y by inverse kinematicsmAnd obtaining state variables of all joints of the flexible mechanical arm, and representing the expected pose of the tail end of the flexible mechanical arm by using a matrix formed by the state variables of all the joints. And taking the difference value of the expected pose and the actual pose of the flexible mechanical arm as the state deviation e of the flexible mechanical arm and the actual pose. In the invention, the state variables of each joint of the flexible mechanical arm comprise a bending angle omega and a rotating angle
Figure BDA0002745837110000021
And the first derivatives of both
Figure BDA0002745837110000022
The nonlinear dynamical equation set of the actual track of the multi-joint flexible mechanical arm is as follows:
Figure BDA0002745837110000031
Figure BDA0002745837110000032
Figure BDA0002745837110000033
the above equation set can be obtained in parallel:
Figure BDA0002745837110000034
wherein M (q) represents a symmetric positive definite rigid body inertia matrix,
Figure BDA0002745837110000035
expresses gram force, JmThe inertia matrix of the motor is positively determined, K represents a positive fixed rigidity matrix of the flexible mechanical arm joint, q represents a vector of a motor rotation angle, and q represents the vector of the motor rotation anglemA vector representing the angular displacement of rotation of the motor,
Figure BDA0002745837110000036
respectively represent q and qmU is the overall control law, u is the second derivative and the first derivative ofDDenotes the first control law, ucRepresenting a second control law.
In the trajectory tracking control method of the multi-joint flexible mechanical arm, in step S2, the purpose of performing fusion processing on the state deviation is to simplify the number of state variables and avoid fuzzy rule explosion in the later stage fuzzy processing due to excessive feedback state variables. In the invention, the constructed fusion function matrix is multiplied by the state deviation matrix of the flexible mechanical arm obtained in the step S1 to obtain the state deviation after fusion
Figure BDA0002745837110000037
Figure BDA0002745837110000038
Figure BDA0002745837110000039
Indicates the state deviation of the bend angle after fusion,
Figure BDA00027458371100000310
a state deviation representing the fused rotation angle,
Figure BDA00027458371100000311
representing post-fusion bendsThe deviation of the state of the derivative of the curve angle,
Figure BDA00027458371100000312
a state deviation representing the fused derivative of the rotation angle.
In the trajectory tracking control method of the multi-joint flexible mechanical arm, in step S3, the designed adaptive law function is:
Figure BDA00027458371100000313
in the formula, gamma represents a given normal number, eTTranspose, P, representing the state deviation matrix enRepresenting the last column of the positive definite matrix P,
Figure BDA00027458371100000314
represents a fuzzy basis function vector derived from the interval two type fuzzy controller fuzzy rule:
Figure BDA00027458371100000315
in the formula (I), the compound is shown in the specification,
Figure BDA00027458371100000316
two-type fuzzy controller input variable of indication interval
Figure BDA00027458371100000317
In fuzzy sets
Figure BDA00027458371100000318
Membership functions of (a).
The state deviation obtained in step S1 is substituted into the adaptive law function equation obtained above, and an adaptive value set θ is obtained.
The self-adaptive law function designed by the invention contains the variable parameter theta, so that the track tracking efficiency of the flexible mechanical arm is improved, the response rapidity and accuracy of the flexible mechanical arm can be further improved, and the approximation precision is improved.
In the trajectory tracking control method of the multi-joint flexible mechanical arm, in step S4, the output variable of the interval type two fuzzy controller is
Figure BDA0002745837110000041
In the formula (I), the compound is shown in the specification,
Figure BDA0002745837110000042
taking the fusion processing result of the step S2 as an input variable, and bringing the adaptive value set obtained by the adaptive processing of the step S3 into a formula (5) to obtain an output value of the interval type two fuzzy controller, namely a first control law uD。
According to the trajectory tracking control method of the multi-joint flexible mechanical arm, the tracking error is easy to converge under the condition that all variables have boundaries. Therefore, in step S5, a boundary supervisory controller is designed to ensure the state variables are bounded by applying the concept of supervisory control. The boundary supervision controller adopted by the invention is as follows:
Figure BDA0002745837110000043
in the formula ucA second control law representing the input variable e, i.e. the state parameter of the flexible manipulatorindRepresenting an indication function, representing the working state of the supervisory controller, 1 during working, sgn (·) representing a piecewise function, P representing a positive definite matrix which satisfies the Lyapunon equation, bLDenotes an arbitrary constant given, uDDenotes a first control law, fUIt is indicated that the given upper limit value,
Figure BDA0002745837110000044
indicating the desired trajectory Y of the flexible robot armmOf the nth derivative, KTA transpose of a stiffness matrix K representing the flexible joint;
Figure BDA0002745837110000045
judgment of
Figure BDA0002745837110000046
And given
Figure BDA0002745837110000047
Comparing to obtain IindThe indication function value of (2) determines whether the supervisory controller is functional.
Firstly, V is firstlyeAnd
Figure BDA0002745837110000048
comparing and determining the index function IindAnd judging the working state of the boundary monitoring controller according to the I. When the controller works, the state deviation e obtained in the step S1 is further substituted into the formula for expressing the boundary supervisory controller to obtain the output value of the boundary supervisory controller and a second control law uC。
The method converts the set working constraint space of the flexible mechanical arm into the state variable of the flexible mechanical arm system in a function mode, and when the state variable stably tracks an expected track and meets a boundary condition, the boundary supervision controller supervises the running state.
In the track tracking control method for the multi-joint flexible mechanical arm, in step S7, u in the dynamic equation of the flexible mechanical arm in step S1 is updated by using the obtained total control law u, so that the correction of the actual track of the flexible mechanical arm is completed. And then returning to the step S1, re-solving the modified kinematic equation of the flexible mechanical arm, and repeating the steps S1-S7 to realize the real-time tracking of the expected track of each joint of the flexible mechanical arm.
The invention further provides a track tracking control system of the multi-joint flexible mechanical arm, which comprises:
the state deviation acquiring module is used for acquiring the state deviation of the expected track and the actual track of the flexible mechanical arm;
the fusion module is used for carrying out fusion processing on the state deviation obtained by the state deviation acquisition module;
the self-adaptive processing module is used for carrying out self-adaptive processing according to the state deviation obtained by the state deviation obtaining module;
an interval type two fuzzy controller for obtaining a first control law u according to the fusion processing result obtained by the fusion and the adaptive processing result obtained by the adaptive processing moduleD；
A boundary monitor controller for obtaining the state deviation of the module according to the state deviation and the first control law u obtained in step S4DObtaining a second control law u by the boundary supervisory controllerC；
A superposition module for obtaining a first control law u obtained by the interval type two fuzzy controllerDAnd a second control law u derived by the boundary supervisory controllerCSuperposing to obtain a master control law u of the flexible mechanical arm;
and the correction module is used for correcting the track of the flexible mechanical arm according to the master control law u of the flexible mechanical arm.
The invention further provides a multi-joint flexible mechanical arm provided with the track tracking control system. The track tracking control system corrects the actual track of the flexible mechanical arm in real time according to the track tracking control method, and realizes real-time tracking of the expected track of the flexible mechanical arm.
The track tracking control method of the multi-joint flexible mechanical arm provided by the invention at least has the following advantages or beneficial effects:
1. according to the invention, adaptive law control is added into the interval two-type fuzzy controller, so that the approximation precision of the interval two-type fuzzy controller is improved, and the response rapidity and accuracy of the flexible mechanical arm system are further improved.
2. In the aspect of processing interference, the internal disturbance and the external disturbance of the system are uniformly regarded as generalized disturbance, and the generalized disturbance is approximated by selecting a proper membership function, so that errors caused by the generalized disturbance can be compensated, and the anti-interference capability of the flexible mechanical arm system is improved.
3. The invention simplifies and fuses the deviation of the actual track and the expected track of the flexible mechanical arm through the designed fusion function, greatly simplifies the operation process of the interval two-type fuzzy controller, improves the working efficiency of the controller, further accelerates the response speed of the flexible mechanical arm system, and avoids fuzzy rule explosion in later-stage fuzzy processing caused by excessive feedback state variables.
4. According to the invention, by designing the interval two-type fuzzy controller and the boundary supervision controller, the effectiveness of track tracking control of the flexible mechanical arm can be ensured, the problem of large tracking error of the flexible mechanical arm in boundary motion is solved, and the track tracking stability of the flexible mechanical arm is improved.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.
FIG. 1 is a schematic diagram of the principle of the trajectory tracking control method of the multi-joint flexible mechanical arm.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
The track tracking method of the multi-joint flexible mechanical arm provided by the embodiment is as follows: the two-type fuzzy controller with the self-adaptive function is designed and combined with a boundary supervision controller to realize real-time tracking of the track of the flexible mechanical arm.
1. Two type fuzzy controller
The two-type fuzzy controller converts the precise input variable into the fuzzy input variable through the membership function, and obtains the final output variable through the fuzzy inference mechanism, the degradation type, the solution of the fuzzy and the like.
The two types of fuzzy controllers involved are:
Figure BDA0002745837110000061
wherein x is a fuzzy set of two types
Figure BDA0002745837110000062
X is a first set of variables, uDIs a fuzzy set of two types
Figure BDA0002745837110000063
H is a second set of variables, JxIs a first degree of membership of x,
Figure BDA0002745837110000064
a second degree of membership of x; the present embodiment takes the state deviation after the fusion processing as the first variable. Interval type-two fuzzy is a special case of type-two fuzzy, the second degree of membership of which
Figure BDA0002745837110000065
Are all equal to 1.
(1) A rule base.
The rules in the rule base are generally established by expert knowledge and are generally represented by IF-THEN statements.
For input variable
Figure BDA0002745837110000071
Definition hiA fuzzy set
Figure BDA0002745837110000072
Then it is first
Figure BDA0002745837110000073
The rule has the following form:
Figure BDA0002745837110000074
wherein the content of the first and second substances,
Figure BDA0002745837110000075
front element, u, called interval type two fuzzy setDCorresponding to the final output of the interval type two fuzzy controller.
(2) And acquiring the activation interval of each rule input variable.
Input variable
Figure BDA0002745837110000076
The corresponding activation intervals are:
Figure BDA0002745837110000077
Figure BDA0002745837110000078
and
Figure BDA0002745837110000079
are respectively input variables
Figure BDA00027458371100000710
In fuzzy sets
Figure BDA00027458371100000711
The upper membership function and the lower membership function are Gaussian membership functions, and the upper membership and the lower membership which meet the requirements are obtained by adjusting the power exponent of the membership function. What is needed isThe gaussian membership function is:
Figure BDA00027458371100000712
in the formula, c and σ are given constants.
(3) Output variable
The embodiment is based on a fuzzy inference engine, a single-valued fuzzifier and a center average defuzzifier, and obtains the following output variables:
Figure BDA00027458371100000713
in the formula (I), the compound is shown in the specification,
Figure BDA00027458371100000714
representing the free parameters.
This embodiment will be described
Figure BDA00027458371100000715
Put into adaptive value set
Figure BDA00027458371100000716
And order:
Figure BDA0002745837110000081
then:
Figure BDA0002745837110000082
2. adaptive law design
In this embodiment, the adaptive value set θ is obtained in an adaptive manner, and the adaptive value set satisfies the Lyapunov equation:
Figure BDA0002745837110000083
in the formula, theta*The initial value to be set, which may be given by expert experience, is generally set as an integer matrix,
Figure BDA0002745837110000084
p is a positive definite matrix.
Derivation of the Lyapunov equation yields:
Figure BDA0002745837110000085
in the formula, gamma represents a given normal number, eTTranspose, P, representing the state deviation matrix enRepresenting the last column of the positive definite matrix P,
Figure BDA0002745837110000086
representing the vector of the fuzzy basis function,
Figure BDA0002745837110000087
in this embodiment, ω simplified calculation is set to 1, and in order to satisfy vmin, the available adaptive law function is:
Figure BDA0002745837110000088
3. boundary supervision controller
The boundary supervisory controller adopted in this embodiment is:
Figure BDA0002745837110000089
in the formula ucA second control law representing the input variable e, i.e. the state parameter of the flexible manipulatorindRepresenting an indication function, representing the working state of the supervisory controller, 1 during working, sgn (·) representing a piecewise function, P representing a positive definite matrix which satisfies the Lyapunon equation, bLDenotes an arbitrary constant given, uDDenotes a first control law, fUIt is indicated that the given upper limit value,
Figure BDA0002745837110000091
indicating the desired trajectory Y of the flexible robot armmOf the nth derivative, KTRepresenting the transpose of the stiffness matrix K of the flexible joint.
Figure BDA0002745837110000092
Judgment of
Figure BDA0002745837110000093
And given
Figure BDA0002745837110000094
And comparing to obtain the indication function value of I and deciding whether the supervisory controller is in action.
In this embodiment, a flexible mechanical arm with two joints is taken as an example, and the track tracking control method of the multi-joint flexible mechanical arm provided by the present invention is explained in detail.
The trajectory tracking control method for the double-joint flexible mechanical arm provided by the embodiment, as shown in fig. 1, includes the following steps:
s1 obtains a state deviation of the expected trajectory from the actual trajectory of the flexible robot arm.
In the step, state variables of all joints of the flexible mechanical arm are obtained based on a dynamic equation of an actual track of the flexible mechanical arm, and an actual pose of the tail end of the flexible mechanical arm is represented by a matrix formed by the state variables of all the joints. Expected trajectory Y based on flexible mechanical armmResolving Y by inverse kinematicsmAnd obtaining state variables of all joints of the flexible mechanical arm, and representing the expected pose of the tail end of the flexible mechanical arm by using a matrix formed by the state variables of all the joints. And taking the difference value of the expected pose and the actual pose of the flexible mechanical arm as the state deviation e of the flexible mechanical arm and the actual pose. In the invention, the state variables of each joint of the flexible mechanical arm comprise a bending angle omega and a rotating angle
Figure BDA0002745837110000095
Andfirst derivative of both
Figure BDA0002745837110000096
In this embodiment, assuming that each joint is modeled as a linear torsion spring with constant stiffness, a nonlinear dynamical equation set of the actual trajectory of the multi-joint flexible mechanical arm is obtained from the angles of power and potential energy by using an euler-lagrange formula:
Figure BDA0002745837110000097
Figure BDA0002745837110000098
Figure BDA0002745837110000099
the above equation set can be obtained in parallel:
Figure BDA00027458371100000910
wherein M (q) represents a symmetric positive definite rigid body inertia matrix,
Figure BDA00027458371100000911
expresses gram force, JmThe inertia matrix of the motor is positively determined, K represents a positive fixed rigidity matrix of the flexible mechanical arm joint, q represents a vector of a motor rotation angle, and q represents the vector of the motor rotation anglemA vector representing the angular displacement of rotation of the motor,
Figure BDA00027458371100000912
respectively represent q and qmU is the overall control law, u is the second derivative and the first derivative ofDDenotes the first control law, uCRepresenting a second control law. For a double-joint flexible mechanical arm, the bending angle (namely, rotation angle) and the rotation angle (namely, rotation angular displacement) of two joints) Are respectively omega1,ω2,
Figure BDA0002745837110000101
Therefore, it is
Figure BDA0002745837110000102
M (q) and
Figure BDA0002745837110000103
is represented as follows:
Figure BDA0002745837110000104
Figure BDA0002745837110000105
Figure BDA0002745837110000106
in the formula, m1、m2Respectively representing the mass, r, of a first joint and a second joint of a flexible manipulator1、r2Respectively represents the lengths L from the center of gravity of a first mechanical arm rod and a second mechanical arm rod of the flexible mechanical arm to a first joint and a second joint1、L2Respectively showing the arm lengths of the first joint and the second joint of the flexible mechanical arm, I1、I2Respectively representing the moment of inertia of the first joint and the second joint of the flexible mechanical arm.
The method comprises the steps of resolving a nonlinear dynamical equation set of a double-joint flexible mechanical arm to obtain state variables of all joints of the flexible mechanical arm, and representing an actual pose Y of the tail end of the flexible mechanical arm by a matrix formed by the state variables of all the joints. The state variables used for representing the actual track of the double-joint flexible mechanical arm in the embodiment comprise omega1,ω2,
Figure BDA0002745837110000107
And
Figure BDA0002745837110000108
8 variables, wherein the state variables for representing the expected track of the double-joint flexible mechanical arm comprise omega1m,ω2m,
Figure BDA0002745837110000109
And
Figure BDA00027458371100001010
8 variables, then:
Figure BDA00027458371100001011
in the formula, for the first joint of the flexible mechanical arm,
Figure BDA00027458371100001014
Figure BDA00027458371100001013
the second joint is similar and will not be described in detail here.
S2 performs fusion processing on the state deviations obtained in step S1.
In this step, the constructed fusion function matrix is multiplied by the state variables of the flexible mechanical arm respectively to obtain the fused state variables.
For example, 8 state deviation variables are fused into 4 state deviation variables by an information fusion method, that is:
Figure BDA0002745837110000111
wherein k is a state feedback gain matrix, and can be obtained by a linear quadratic programming method (see Wang L, Zheng S, Wang X, inverted pendant based Fan L. fuzzy control of a double on information fusion);
Figure BDA0002745837110000112
is a new state deviation variable after fusion. Here will be
Figure BDA0002745837110000113
As the fused principal variable, the fused principal variable has the same physical meaning as the principal variable before the fusion.
In order to ensure that the water-soluble organic acid,
Figure BDA0002745837110000114
[Ke1 Kec1 Ke2 Kec2]i.e., a fusion function, which can scale the input variables (here, the state deviation of the flexible manipulator obtained in step S1) from the physical domain into the fuzzy domain.
Figure BDA0002745837110000115
Namely the fuzzy set of the interval type two fuzzy controller.
S3 performs adaptive processing using an adaptive law function according to the state deviation obtained in step S1.
Firstly, obtaining fuzzy basis function vector by interval two-type fuzzy controller fuzzy rule (see formula (5))
Figure BDA0002745837110000116
Then the state deviation e and the fuzzy basis function vector obtained in step S1
Figure BDA0002745837110000117
The adaptive value set theta can be obtained by substituting the above obtained adaptive law function formula (9).
S4 obtaining a first control law u through the interval type two-type fuzzy controller according to the fusion processing result of the step S2 and the self-adaptive processing result of the step S3D。
In this step, the result of the fusion process in step S2 is used as an input variable (N is 4), that is, the result is
Figure BDA0002745837110000118
Is interval type two fuzzyFuzzy sets of controllers.
Substituting the adaptive value set theta obtained by the adaptive processing in the step S3 into a formula (6) to obtain an output value of the interval type two-model fuzzy controller, namely a first control law uD。
S5 is based on the state deviation obtained in step S1 and the first control law u obtained in step S4DObtaining a second control law u by the boundary supervisory controllerC。
Firstly, V is firstlyeAnd
Figure BDA0002745837110000121
and comparing, determining an index function I, and judging the working state of the boundary supervisory controller according to the index function I. When it is operated, the state deviation e obtained in step S2 is substituted into the above formula (9) for expressing the boundary supervisory controller to obtain the output value of the boundary supervisory controller, and the second control law uC。
S6 shows the first control law u obtained in step S5DAnd the second control law u obtained in step S6CAnd (5) superposing to obtain the master control law u of the flexible mechanical arm.
u is an ideal overall control law to be obtained in this embodiment, and u is equal to uD+uCWherein u isDFor the two-type fuzzy controller in step S4, uCObtained for the boundary supervisory controller in step S5.
And S7, correcting the track of the flexible mechanical arm according to the total control law u of the flexible mechanical arm.
In this step, the obtained total control law u is used to update u in the dynamic equation of the flexible mechanical arm in step S1, so that the correction of the actual track of the flexible mechanical arm is completed.
And then returning to the step S1, re-solving the modified kinematic equation of the flexible mechanical arm, and repeating the steps S1-S7 to realize the real-time tracking of the expected track of each joint of the flexible mechanical arm until the operation of the flexible mechanical arm is completed.
Example 2
The embodiment provides a track following control system of multi-joint flexible mechanical arm, which includes:
the state deviation acquiring module is used for acquiring the state deviation of the expected track and the actual track of the flexible mechanical arm;
the fusion module is used for carrying out fusion processing on the state deviation obtained by the state deviation acquisition module;
the self-adaptive processing module is used for carrying out self-adaptive processing according to the state deviation obtained by the state deviation obtaining module;
an interval type two fuzzy controller for obtaining a first control law u according to the fusion processing result obtained by the fusion and the adaptive processing result obtained by the adaptive processing moduleD；
A boundary monitor controller for obtaining the state deviation of the module according to the state deviation and the first control law u obtained in step S4DObtaining a second control law u by the boundary supervisory controllerC；
A superposition module for obtaining a first control law u obtained by the interval type two fuzzy controllerDAnd a second control law u derived by the boundary supervisory controllerCSuperposing to obtain a master control law u of the flexible mechanical arm;
and the correction module is used for correcting the track of the flexible mechanical arm according to the master control law u of the flexible mechanical arm.
The operation steps of the trajectory tracking control system of the multi-joint flexible mechanical arm correspond to those of embodiment 1, and specific implementation can be referred to the relevant description part of the first embodiment.
Example 3
The present embodiment provides a multi-joint flexible robot arm equipped with the trajectory tracking control system provided in embodiment 2.
Taking a double-joint flexible mechanical arm as an example, the trajectory tracking control system can be in communication connection with servo motors of the double-joint flexible mechanical arms for controlling the mechanical arms, and the trajectory tracking control system corrects the actual trajectory of the flexible mechanical arm in real time according to the trajectory tracking control method provided in embodiment 1, and controls the servo motors of the mechanical arms to operate according to the corrected trajectory, so as to realize real-time tracking of the expected trajectory of the flexible mechanical arm.
The invention is mainly based on a traditional interval two-type fuzzy controller, combines the characteristics of a flexible mechanical arm, designs a related fusion function, a self-adaptive law function and a boundary supervision controller, provides a track tracking method suitable for a multi-joint flexible mechanical arm, can realize stable control on the multi-joint flexible mechanical arm, and further improves the response speed and accuracy of a flexible mechanical arm system.
The above is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes will occur to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (9)

1. A trajectory tracking control method of a multi-joint flexible mechanical arm is characterized by comprising the following steps:
s1, acquiring state deviation of the expected track and the actual track of the flexible mechanical arm;
s2 performs fusion processing on the state deviations obtained in step S1;
s3, performing self-adaptive processing according to the state deviation obtained in the step S1;
s4 obtaining a first control law u through the interval type two-type fuzzy controller according to the fusion processing result of the step S2 and the self-adaptive processing result of the step S3D；
S5 is based on the state deviation obtained in step S1 and the first control law u obtained in step S4DObtaining a second control law u by the boundary supervisory controllerC；
S6 shows the first control law u obtained in step S5DAnd the second control law u obtained in step S6CSuperposing to obtain a master control law u of the flexible mechanical arm;
s7, correcting the track of the flexible mechanical arm according to the total control law u of the flexible mechanical arm;
and repeating the steps S1-S7 to realize the real-time tracking of the expected track of the flexible mechanical arm.
2. The trajectory tracking control method of the multi-joint flexible mechanical arm according to claim 1, characterized in that: in the step S1, state variables of all joints of the flexible mechanical arm are obtained based on a dynamic equation of an actual track of the flexible mechanical arm, and an actual pose of the tail end of the flexible mechanical arm is represented by a matrix formed by the state variables of all the joints; obtaining state variables of all joints based on the expected track of the flexible mechanical arm, and representing the expected pose of the tail end of the flexible mechanical arm by a matrix formed by the state variables of all the joints; and taking the difference value of the expected pose and the actual pose of the flexible mechanical arm as the state deviation of the flexible mechanical arm and the actual pose.
3. The trajectory tracking control method of the multi-joint flexible mechanical arm according to claim 2, characterized in that: in step S2, the constructed fusion function matrix is multiplied by the state deviation matrix of the flexible manipulator obtained in step S1 to obtain the state deviation after fusion
Figure RE-FDA0002788577620000011
4. The trajectory tracking control method of the multi-joint flexible mechanical arm according to claim 3, characterized in that: in step S3, the state deviation is adaptively processed by using an adaptive law function, which is:
Figure RE-FDA0002788577620000012
in the formula, gamma represents a given normal number, eTTranspose, P, representing the state deviation matrix enRepresenting the last column of the positive definite matrix P,
Figure RE-FDA0002788577620000013
represents a fuzzy basis function vector derived from the interval two type fuzzy controller fuzzy rule:
Figure RE-FDA0002788577620000014
in the formula (I), the compound is shown in the specification,
Figure RE-FDA0002788577620000021
two-type fuzzy controller input variable of indication interval
Figure RE-FDA0002788577620000022
In fuzzy sets
Figure RE-FDA0002788577620000023
Membership functions of (a).
5. The trajectory tracking control method of the multi-joint flexible mechanical arm according to claim 4, characterized in that: in step S4, the output variable of the interval type two fuzzy controller is
Figure RE-FDA0002788577620000024
6. The trajectory tracking control method of the multi-joint flexible mechanical arm according to claim 5, characterized in that: in step S5, the boundary supervisory controller is used:
Figure RE-FDA0002788577620000025
in the formula ucA second control law representing the input variable e, i.e. the state parameter of the flexible manipulatorindRepresenting an indication function, representing the working state of the supervisory controller, 1 during working, sgn (·) representing a piecewise function, P representing a positive definite matrix which satisfies the Lyapunon equation, bLDenotes an arbitrary constant given, uDDenotes a first control law, fUIt is indicated that the given upper limit value,
Figure RE-FDA0002788577620000026
indicating the desired trajectory Y of the flexible robot armmOf the nth derivative, KTA transpose of a stiffness matrix K representing the flexible joint;
Figure RE-FDA0002788577620000027
judgment of
Figure RE-FDA0002788577620000028
And given
Figure RE-FDA0002788577620000029
Comparing to obtain IindThe indication function value of (2) determines whether the supervisory controller is functional.
7. A trajectory tracking control system of a multi-joint flexible mechanical arm is characterized by comprising:
the state deviation acquiring module is used for acquiring the state deviation of the expected track and the actual track of the flexible mechanical arm;
the fusion module is used for carrying out fusion processing on the state deviation obtained by the state deviation acquisition module;
the self-adaptive processing module is used for carrying out self-adaptive processing according to the state deviation obtained by the state deviation obtaining module;
an interval type two fuzzy controller for obtaining a first control law u according to the fusion processing result obtained by the fusion and the adaptive processing result obtained by the adaptive processing moduleD；
A boundary monitor controller for obtaining the state deviation of the module according to the state deviation and the first control law u obtained in step S4DObtaining a second control law u by the boundary supervisory controllerC；
A superposition module for obtaining a first control law u obtained by the interval type two fuzzy controllerDAnd a second control law u derived by the boundary supervisory controllerCSuperposing to obtain a master control law u of the flexible mechanical arm;
and the correction module is used for correcting the track of the flexible mechanical arm according to the master control law u of the flexible mechanical arm.
8. A multi-joint flexible robot arm characterized by being equipped with the trajectory tracking control system according to claim 7.
9. The multi-joint flexible mechanical arm as claimed in claim 8, wherein the trajectory tracking control system corrects the actual trajectory of the flexible mechanical arm in real time according to the trajectory tracking control method as claimed in any one of claims 1 to 6, so as to realize real-time tracking of the desired trajectory of the flexible mechanical arm.
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