CN111694273A - Design method for fuzzy self-adaptive control of double-joint manipulator - Google Patents
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Abstract
The invention discloses a design method for fuzzy self-adaptive control of a double-joint manipulator, which is characterized by comprising the following steps of: firstly, establishing a space dynamics model of a double-joint manipulator; secondly, establishing a mathematical model of the double-joint manipulator; and thirdly, establishing the double-joint manipulator fuzzy self-adaptive controller. Compared with the prior art, the invention has the advantages that: the error of the expected track is small, and the convergence speed is high; when the system is suddenly interfered, the system can be restabilized in a shorter time, and the stability and the robustness of the fuzzy controller are reflected.
Description
Technical Field
The invention relates to a design method for fuzzy self-adaptive control of a double-joint manipulator, and relates to the field of stable control of a mobile manipulator.
Background
At present, the robot technology is developing towards high speed, high precision and intellectualization, so higher requirements are put forward on the control precision of the robot. At present, PID control is mostly adopted for typical robot control, and the PID control can meet the requirement on the application occasions with not high track precision requirement. However, if the control accuracy of the robot is to be improved, a control method considering a robot dynamic model, such as torque control, dynamic feedforward control, etc., must be constructed. These control methods are based on a complete kinetic model of the robot. However, the kinetic models obtained by various typical modeling methods are only the result in the ideal case. In practical situations, factors affecting the dynamics of the robot are many, such as deviations caused by machining, assembly, uneven material distribution, and the like; kinematic parameter deviations due to deformations caused by joint elasticity; friction torque due to joint friction; kinematic coupling between different joints caused by the transmission scheme, etc. Many of these factors cannot be modeled accurately. The mapping of the deviation of the dynamic model into the control scheme causes tracking errors of the trajectory.
With the development of robotics, various robots have been developed to meet the demands of various industries, in which a mobile robot becomes an important branch in the development of robotics. The mobile manipulator has almost infinite operation space and high motion redundancy, and has the functions of moving and operating, so that the mobile manipulator is superior to a mobile robot and a traditional manipulator, has wide application prospect, and is widely applied to the fields of service, medical treatment, industry and the like at present. However, due to the problems of complex structure, strong coupling, nonlinearity, non-integrity and the like of the mobile manipulator, the precise control of the mobile manipulator has considerable challenges.
Disclosure of Invention
The invention aims to provide a design method for fuzzy self-adaptive control of a double-joint manipulator.
In order to achieve the purpose of the invention, the technical scheme adopted by the invention is as follows: a design method for fuzzy self-adaptive control of a double-joint manipulator comprises the following steps:
firstly, establishing a space dynamics model of a double-joint manipulator;
secondly, establishing a mathematical model of the double-joint manipulator;
thirdly, establishing a double-joint manipulator fuzzy self-adaptive controller, which comprises the following steps:
s1, performing dimensionality reduction on a system by adopting a fusion function, so that two input variables of the system are obtained after dimensionality reduction;
s2, determining the discourse domain of the input variable and the output variable, wherein the basic discourse domain of the error is set as follows: [ -6,6], the basic domain of error variation is: [ -6,6 ]; the basic discourse domain of the output control quantity is set as follows: [ -6,6 ]; the universe of discourse of the fuzzy subset taken by the error variable is { -6, -4, -2,0,2,4,6 }; the universe of discourse for the fuzzy subset taken by the error variation variable is: -6, -4, -2,0,2,4,6 }; the universe of discourse for the fuzzy subset taken by the control quantity is: { -6, -4, -2,0,2,4,6}, the linguistic variables are all represented by { NB NM NSZE PS PM PB };
s3, determining a membership function, wherein the input variable and the output variable adopt triangular, fully overlapped and uniformly distributed membership functions, and the fuzzy inference system adopts a Mamdani inference method;
s4, formulating a fuzzy control rule table based on the fusion function;
s5, determining a defuzzification method, and realizing fuzzy judgment of output information by adopting a gravity center method, wherein the calculation formula is as follows:
(ii) a Wherein the content of the first and second substances,
in order to be the weighting coefficients,
is a regular back-piece.
S6, determining a quantization factor and a scale factor; the basic discourse domain of error is
The basic argument of the error variation is
The error quantization factor and the error rate quantization factor are represented by Ke and Kc, respectively, and their values are determined by the following two equations:
converting the control quantity given by the fuzzy control algorithm into a basic theory domain accepted by the control object, wherein the theory domain of the fuzzy subset selected by the control quantity is
The basic universe of output control of the fuzzy controller is set as
The scaling factor Ku of the output control amount u is determined by the following equation:
and S7, finally establishing the membership function of the input variable and the output variable of the controller and the fuzzy control rule.
Due to the application of the technical scheme, compared with the prior art, the invention has the following advantages:
compared with the prior art, the invention has the advantages that: the error of the expected track is small, and the convergence speed is high; when the system is suddenly interfered, the system can be restabilized in a shorter time, and the stability and the robustness of the fuzzy controller are reflected.
Drawings
FIG. 1 is a spatial dynamics model diagram of a dual-joint manipulator of the present invention.
FIG. 2 is a schematic diagram of the construction of the fuzzy controller of the present invention.
FIG. 3 is a diagram of a simulation model under the action of a fuzzy control sine input signal.
Fig. 4 shows the position tracking and velocity tracking of the joint 1 under the influence of the fuzzy control sinusoidal input signal in an embodiment of the invention.
Fig. 5 illustrates the position tracking and velocity tracking of the joint 2 under the influence of a fuzzy controlled sinusoidal input signal in one embodiment of the present invention.
Fig. 6 shows the position tracking and velocity tracking of the joint 1 under the action of the PID controlled sinusoidal input signal according to the first embodiment of the present invention.
Fig. 7 illustrates the position tracking and velocity tracking of the joint 2 under the action of the PID controlled sinusoidal input signal according to a first embodiment of the present invention.
Fig. 8 shows the control inputs to joint 1 and joint 2 as a function of a sinusoidal input signal in accordance with one embodiment of the present invention.
Detailed Description
The invention is further described with reference to the following figures and examples:
the first embodiment is as follows:
the dynamic model is mainly used for the design and simulation of the robot, and the relation between the input torque (force) of each joint of the robot and the output motion of the robot can be determined through dynamic research. The robot needs to carry out dynamic simulation according to the quality, the kinematics and the dynamic parameters of the connecting rod, the characteristics of the transmission mechanism and the load in the design process, so that the structural parameters and the transmission scheme of the robot are determined, the rationality and the feasibility of the design scheme are checked, and the structural optimization degree is further checked. In order to estimate the dynamic load and path deviation caused by the high-speed motion of the robot, path control simulation and dynamic model simulation are carried out. These must be based on a robot dynamics model.
Referring to fig. 1, a design method for fuzzy adaptive control of a double-joint manipulator is characterized by comprising the following steps:
firstly, establishing a space dynamics model of a double-joint manipulator;
the first joint of the robot is a driving joint, the second joint is a driven joint, the torque of the driving joint is tau, and the length of the two connecting rods is
Respectively of mass
And
the center of mass is respectively at the joint point of the connecting rod
And
to (3). The arm can be viewed as two particles whose motion is constrained to each other. The dynamic model is shown in figure 1, the concentric circle on the left is the driving joint 1, and the circle on the right is the same as the driving joint 1The heart circle is the passive joint 2.
For any mechanical Lagrange function L is defined as the difference between the total kinetic energy T and the total potential energy V of the system, i.e.:
L=T-V
the kinetic equation for the system can be expressed by the Lagrange equation as follows:
since the present embodiment is a planar robot and elastic friction of each joint is neglected, the system has a potential energy V of zero. The kinetic equation for the system can be written as:
the total kinetic energy T of the system, mass points m1 and m2 are obtained by using a model
The coordinates in the operating space coordinate system XYZ are as follows:
from the above analysis, the kinetic energy of the mechanical arm moving along the horizontal direction is:
the rotation energy of the connecting rod rotating around the mass center is as follows:
in the formula
Moment of inertia of the rod 1
；
So the total kinetic energy of the mechanical arm is:
first, along
The directions are as follows:
wherein:
，
thus, the method can obtain the product,
the kinetic equation for the direction is:
in the same way, along
The directions are as follows:
order to
，
Then the kinetic equation can be written in matrix form:
in the formula:
mass inertia matrix of the system
Secondly, establishing a mathematical model of the double-joint manipulator;
for a double-joint rigid manipulator with plane motion, the dynamic equation is as follows, ignoring gravity:
the above formula can be converted into:
wherein:
taking the system parameters as
Order:
(14)
taking:
the controlled object becomes:
the control objective being to cause the output of the system
Tracking a desired trajectory
。
In the fuzzy control system, a fuzzy controller is the core of the fuzzy control system, and the performance of the fuzzy control system is superior or inferior and mainly depends on the structure of the fuzzy controller, the adopted rules, the synthetic inference algorithm, the fuzzy decision method and other factors. The basic structure of the fuzzy controller is shown in fig. 2, and mainly comprises five parts, namely fuzzification, a database, a rule base, fuzzy reasoning, clarification and the like.
Thirdly, establishing a double-joint manipulator fuzzy self-adaptive controller, which comprises the following steps:
s1, performing dimensionality reduction on a system by adopting a fusion function, so that two input variables of the system are obtained after dimensionality reduction, and only a common two-dimensional fuzzy controller needs to be designed;
s2, determining the discourse domain of the input variable and the output variable, wherein the basic discourse domain of the error is set as follows: [ -6,6], the basic domain of error variation is: [ -6,6 ]; the basic discourse domain of the output control quantity is set as follows: [ -6,6 ]; the universe of discourse of the fuzzy subset taken by the error variable is { -6, -4, -2,0,2,4,6 }; the universe of discourse for the fuzzy subset taken by the error variation variable is: -6, -4, -2,0,2,4,6 }; the universe of discourse for the fuzzy subset taken by the control quantity is: { -6, -4, -2,0,2,4,6}, the linguistic variables are all represented by { NB NM NSZE PS PM PB };
s3, determining a membership function, wherein the input variable and the output variable adopt triangular, fully overlapped and uniformly distributed membership functions, and the fuzzy inference system adopts a Mamdani inference method;
s4, formulating a fuzzy control rule table based on the fusion function;
as shown in table 1.
TABLE 1 fuzzy control rules Table
S5, determining a defuzzification method, and realizing fuzzy judgment of output information by adopting a gravity center method, wherein the calculation formula is as follows:
s6, determining a quantization factor and a scale factor; for the fuzzification process, the input variable must be converted from the fundamental domain to the corresponding domain of the fuzzy set, in which the input variable must be multiplied by the corresponding quantization factor, where the error quantization factor and the error rate quantization factor are respectively represented by Ke and Kc, and their values are determined by the following two equations:
the quantization factor and the scale factor are both derived for the purpose of implementing the conversion of the corresponding variable from the basic domain of discourse to the discrete domain of discourse, the larger the quantization factor, the larger the corresponding linguistic value, and vice versa, for the input variable. When Ke is larger, overshoot of the system is larger, and the transition process is longer; when the Kc is larger, the overshoot is reduced, but the response speed of the system is slow, and the suppression effect of the Kc on the overshoot is very obvious.
And S7, finally establishing the membership function of the input variable and the output variable of the controller and the fuzzy control rule.
The fuzzy adaptive control of the present embodiment is performed to perform a double-joint manipulator simulation.
And (3) simulation result analysis:
respectively adopting fuzzy adaptive control and a PID controller to carry out simulation analysis on the multi-joint motion platform, wherein a fuzzy adaptive control simulation model is shown in figure 3, the given input is a sine signal, and the simulation result is shown in figures 4 and 5; the Fuzzy controller Fuzzy _ ctrl in fig. 3 is changed into PID control, and when the input is given as a sinusoidal signal, the simulation is performed again, and the results are shown in fig. 6 and 7. As can be seen from fig. 6-7: under the action of the PID controller, when an input signal is a sinusoidal signal, position tracking curves and speed tracking curves of the joint 1 and the joint 2 can not be completely overlapped, and a certain deviation always exists, which shows that the conventional PID control method can not achieve a satisfactory effect on the control of a multi-input multi-output manipulator system, and the limitation except for the PID control method is reflected. As can be seen from fig. 4-5: under the action of the fuzzy controller, when the input signal is a sinusoidal signal, the track tracking curve error is relatively large at the simulation starting moment, and then the actual output tracks of the joint 1 and the joint 2 in fig. 8 almost completely coincide with the expected output track. The designed system has good tracking performance. It can be seen from the figure that the control input curve change rule of the joint 1 and the joint 2 has small disturbance, which shows that the output of the controller is relatively stable.
The double-joint manipulator system is a typical multi-input nonlinear system, and a double-joint manipulator simulation mathematical model is deduced by simplifying input variables of the double-joint manipulator system. Then, a fuzzy controller is designed aiming at the simplified model, a simulation model is built by utilizing a Matlab/Simulink module and a written S function, and the following simulation results can be easily seen: the fuzzy control has the advantage of small error of the expected track tracked by the double-joint manipulator.
Claims (1)
1. A design method for fuzzy self-adaptive control of a double-joint manipulator is characterized by comprising the following steps:
firstly, establishing a space dynamics model of a double-joint manipulator;
secondly, establishing a mathematical model of the double-joint manipulator;
thirdly, establishing a double-joint manipulator fuzzy self-adaptive controller, which comprises the following steps:
s1, performing dimensionality reduction on a system by adopting a fusion function, so that two input variables of the system are obtained after dimensionality reduction;
s2, determining the discourse domain of the input variable and the output variable, wherein the basic discourse domain of the error is set as follows: [ -6,6], the basic domain of error variation is: [ -6,6 ]; the basic discourse domain of the output control quantity is set as follows: [ -6,6 ]; the universe of discourse of the fuzzy subset taken by the error variable is { -6, -4, -2,0,2,4,6 }; the universe of discourse for the fuzzy subset taken by the error variation variable is: -6, -4, -2,0,2,4,6 }; the universe of discourse for the fuzzy subset taken by the control quantity is: { -6, -4, -2,0,2,4,6}, the linguistic variables are all represented by { NB NM NSZE PS PM PB };
s3, determining a membership function, wherein the input variable and the output variable adopt triangular, fully overlapped and uniformly distributed membership functions, and the fuzzy inference system adopts a Mamdani inference method;
s4, formulating a fuzzy control rule table based on the fusion function;
s5, determining defuzzification method and adopting weightThe fuzzy judgment of the output information is realized by a heart method, and the calculation formula is as follows:
(ii) a Wherein the content of the first and second substances,
in order to be the weighting coefficients,
in order to be a regular back-piece,
s6, determining a quantization factor and a scale factor; the basic discourse domain of error is
The basic argument of the error variation is
The error quantization factor and the error rate quantization factor are represented by Ke and Kc, respectively, and their values are determined by the following two equations:
converting the control quantity given by the fuzzy control algorithm into a basic theory domain accepted by the control object, wherein the theory domain of the fuzzy subset selected by the control quantity is
The basic universe of output control of the fuzzy controller is set as
The scaling factor Ku of the output control amount u is determined by the following equation:
and S7, finally establishing the membership function of the input variable and the output variable of the controller and the fuzzy control rule.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102621892A (en) * | 2012-04-06 | 2012-08-01 | 杭州电子科技大学 | Control method of speed regulator of servo system of flat knitting machine |
| CN103309233A (en) * | 2013-05-13 | 2013-09-18 | 陕西国防工业职业技术学院 | Designing method of fuzzy PID (Proportion-Integration-Differential) controller |
| CN105652667A (en) * | 2016-03-31 | 2016-06-08 | 西南石油大学 | High-precision path tracking control method for uncertain-model double-joint mechanical arms |
| CN107390528A (en) * | 2017-08-23 | 2017-11-24 | 华南理工大学 | A kind of adaptive fuzzy control method of weld joint tracking application |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102621892A (en) * | 2012-04-06 | 2012-08-01 | 杭州电子科技大学 | Control method of speed regulator of servo system of flat knitting machine |
| CN103309233A (en) * | 2013-05-13 | 2013-09-18 | 陕西国防工业职业技术学院 | Designing method of fuzzy PID (Proportion-Integration-Differential) controller |
| CN105652667A (en) * | 2016-03-31 | 2016-06-08 | 西南石油大学 | High-precision path tracking control method for uncertain-model double-joint mechanical arms |
| CN107390528A (en) * | 2017-08-23 | 2017-11-24 | 华南理工大学 | A kind of adaptive fuzzy control method of weld joint tracking application |
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Application publication date: 20200922 |