CN116184825A - A Trajectory Tracking Control Method Based on Fuzzy Adaptive Sliding Mode for Delta Parallel Robot - Google Patents
A Trajectory Tracking Control Method Based on Fuzzy Adaptive Sliding Mode for Delta Parallel Robot Download PDFInfo
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Abstract
The invention discloses a track tracking control method of a Delta parallel robot based on a fuzzy self-adaptive sliding mode, which comprises the following steps: s1, acquiring a dynamic model and a reference motion trail; s2, mapping is established, and a joint rotation angle is obtained; s3, acquiring a tracking error of the joint angle, designing a sliding mode, and selecting an approach rate to enable the angle tracking error to reach the sliding mode; according to the robot model and a control target of track tracking, designing a control law of a robot track tracking controller, and determining control parameters; s4, introducing a fuzzy self-adaptive control system; s5, analyzing stability and convergence of the fuzzy self-adaptive control system, adjusting control parameters of the controller, and outputting a track tracking result. According to the invention, fuzzy self-adaptive control is introduced on the basis of the sliding mode controller, and discontinuous switching functions in the sliding mode control law are replaced by the output of the fuzzy system, so that smooth output of the robot control moment is realized, and the robustness of the robot system in track tracking is maintained.
Description
Technical Field
The invention relates to the technical field of robot system track tracking, in particular to a track tracking control method of a Delta parallel robot based on a fuzzy self-adaptive sliding mode.
Background
With the progress of technology and the development of the age, the industrial automation degree of a country is also advanced. The robot is a comprehensive system capable of realizing autonomous movement oriented to the target and completing corresponding tasks under the action of a controller according to the state and sensing information of the robot. Motion control is the most fundamental problem in robot autonomy research, as any task that a robot is to autonomously accomplish is motion-based. Because of uncertainty in the working environment of the robot, the robot is often required to track a planned feasible track. Such problems are called trajectory tracking problems, and are hot spot problems in the field of robot motion control research.
For the research of the robot track tracking technology, the more common method is to adopt linear feedback control or nonlinear feedback control, and the main defects are that the method cannot be applied to the motion planning problem in a complex environment, and the robustness of the system and the realization of the control effect are not ideal. With the development of robot technology, the moving and static requirements on the rapidity, the accuracy, the anti-interference capability and the like of the motion trail tracking of a robot system are higher and higher. In reality, the system is likely to be interfered by external environment in the running process, and the sliding mode control has the characteristic of insensitivity to the uncertainty factor of the system and the external disturbance, namely, good robustness can be maintained for the linear system and the nonlinear system. The sliding mode control method can obtain satisfactory dynamic quality through design of a design sliding mode, meanwhile, the control algorithm is simple, the Delta parallel robot is easy to realize track tracking control, the system is influenced by external disturbance, and the sliding mode control strategy is a good choice. However, the discontinuous switching function contained in the approach rate of the slip-mode controller may cause rapid switching of the brake responsible for driving, causing buffeting. In robotic systems, the control input to the system is torque, and severe buffeting can increase the energy loss of the system and affect the accuracy and stability of system trajectory tracking.
Disclosure of Invention
In order to solve the technical problems in the prior art, the invention provides the track tracking control method of the Delta parallel robot based on the fuzzy self-adaptive sliding mode, fuzzy self-adaptive control is introduced on the basis of a sliding mode controller, discontinuous switching functions in a sliding mode control law are replaced by the output of a fuzzy system, smooth output of robot control moment is realized, and robustness of robot system track tracking is maintained.
The invention is realized by adopting the following technical scheme: a track tracking control method of a Delta parallel robot based on a fuzzy self-adaptive sliding mode comprises the following steps:
s1, giving a dynamic model and a reference motion trail Xr of the robot according to the structure of the Delta parallel robot;
s2, establishing a mapping between a robot reference motion track Xr and a driving joint angle according to inverse kinematics solution of the Delta parallel robot, and obtaining a robot expected joint rotation angle qd corresponding to the reference motion track;
s3, measuring the actual rotation angle of a driving joint of the robot, feeding back to the controller, and obtaining a tracking error of the joint angle by making a difference with the expected joint angle in the step S2; according to the angle tracking error information, designing a sliding mode, and selecting an approach rate to enable the angle tracking error to reach the sliding mode; according to the robot model and a control target of track tracking, designing a control law of a robot track tracking controller, and determining control parameters;
s4, introducing a fuzzy self-adaptive control system, and replacing discontinuous switching functions in the synovial membrane control rate by smooth output of the fuzzy self-adaptive control system;
s5, analyzing stability and convergence of the fuzzy self-adaptive control system, adjusting control parameters of the controller, and outputting a track tracking result.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. according to the invention, fuzzy self-adaptive control is introduced on the basis of the sliding mode controller, and discontinuous switching functions in the sliding mode control law are replaced by the output of the fuzzy system, so that smooth output of the robot control moment is realized, and the robustness of the robot system in track tracking is maintained.
2. The output of the fuzzy function comprises information of system modeling errors and disturbance errors, and the fuzzy function can be estimated on line, so that the self-adaptive capacity of the system is enhanced.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a three-dimensional perspective view of a reference trajectory in an embodiment of the invention;
FIG. 3 is a schematic view of a desired joint rotation angle in an embodiment of the present invention;
FIG. 4 is a schematic diagram of torque output under the action of a simple sliding mode controller in step S53 according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of torque output under the action of the fuzzy adaptive slip-form controller in step S53 according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of tracking errors of the joint trajectories under the influence of a fuzzy adaptive slip-mode controller in accordance with an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but embodiments of the present invention are not limited thereto.
Examples
As shown in fig. 1, the track tracking control method of the Delta parallel robot based on the fuzzy self-adaptive sliding mode of the embodiment comprises the following steps:
s1, giving a dynamic model and a reference motion trail Xr of the robot according to the structure of the Delta parallel robot;
s2, establishing a mapping between a robot reference motion track Xr and a driving joint angle according to inverse kinematics solution of the Delta parallel robot to obtain a robot expected joint rotation angle qd corresponding to the reference motion track, as shown in FIG. 3;
s3, measuring the actual rotation angle of a driving joint of the robot, feeding back to the controller, and obtaining a tracking error of the joint angle by making a difference with the expected joint angle in the step S2; according to the angle tracking error information, designing a sliding mode, and selecting an approach rate to enable the angle tracking error to reach the sliding mode; according to the robot model and a control target of track tracking, designing a control law of a robot track tracking controller, and determining control parameters;
s4, introducing a fuzzy self-adaptive control system, and replacing discontinuous switching functions in the synovial membrane control rate by smooth output of the fuzzy self-adaptive control system;
s5, analyzing stability and convergence of the fuzzy self-adaptive control system, adjusting control parameters of the controller, and outputting a track tracking result.
Specifically, in this embodiment, the dynamics model of the robot in step S1 is as follows:
where τ is the joint drive torque, τ d Is an external disturbance, q,Represents the driving joint angle, angular velocity and angular acceleration, respectively, M (q) is the mass matrix,/->Is the Kevlar force and centrifugal force matrix, G (q) is the gravity vector;
given reference motion trajectory X r =[x y z] T m; wherein x is an x-axis value, and x=0.3sin5t; y is the y-axis number, and y=0.3 cos5t; z is a z-axis number, and z= -0.5;
as shown in fig. 2, the Delta parallel robot has three moving branched chains, each of which is driven by a motor and can translate in a three-dimensional space; given a reference motion trajectory X r =[0.3sin5t 0.3cos5t -0.5] T 。
Specifically, in this embodiment, the specific procedure of step S3 is as follows:
s31, measuring the rotation angle q= [ q ] of each joint of the Delta parallel robot through a sensor installed in a driving motor 1 q 2 q 3 ] T And joint rotation angular velocityThe parameters of the robot dynamics model are unknown, and external disturbance tau acts on the system d Unknown; estimating the unknown items, taking a control law as u, and obtaining the following control system:
wherein ,the product of the estimated value of the mass matrix and the joint rotation angular acceleration;Is thatThe linear regression form of (2) comprises modeling errors and disturbance estimation errors of a system;Respectively represent M (q), respectively>G(q) and τd Is determined by the estimation error of (a); the relationship between the angular velocity of the drive joint and the control law u is thus obtained:
wherein ,for angular acceleration +.>All disturbance information received by the system is provided;
s32, setting the expected joint rotation angle as q d The actual joint rotation angle of the Delta parallel robot is q, and the tracking error is defined as e=q d -q; the slide surface is then designed:
wherein e is tracking error;is the derivative of the tracking error; lambda is an adjustable parameter;
when s=0, the tracking error of the system enters the sliding mode, at this timeSolving that the tracking error of the system is an exponential function, and gradually converging to 0 along with the time change;
s33, in order to enable the tracking error e of the system to finally converge to 0, the tracking error e is required to move on a sliding mode, namely t & gtto & gtinfinity, and s=0; to meet this condition, it is necessary to design the approach rateFirst derivative is calculated on the sliding mode surface:
wherein ,is the derivative of the slip form surface;Is the second derivative of the error;Is the desired angular acceleration;Is the actual angular acceleration;
the approach rate comprises the control law of the sliding mode controller, and the design problem of the approach rate is related to the control law of the controller at the moment; the approach rate meeting the control requirement is designed, the essence becomes to design a control law u, the track tracking error can be gradually converged, and finally the sliding mode is realized;
s34, in order to finally converge the tracking error e of the system to 0, a control law is designed as follows:
wherein ,is->An upper boundary of the norm; λ and η are adjustable parameters and always satisfy λ > 0, η > 0; sgn(s) is the symbol operation result of taking s; substitution of the control law into the first derivative of the slip plane gives +.>When s is greater than 0, the method comprises the steps of,when s < 0, < ->This ensures that the tracking error of the system always tends towards the sliding mode.
Specifically, in this embodiment, the specific procedure of step S4 is as follows:
s41, replacing discontinuous items contained in the control law u obtained in the step S3 by smooth output of the fuzzy self-adaptive systemThe following blurring function is defined:
K=Θ T ψ(s) (21)
wherein k= [ K ] 1 ,k 2 ,k 3 ] T Representing the output of the fuzzy adaptive system; Θ= [ θ ] 1 ,θ 2 ,…,θ N ] T Free parameters representing the fuzzy adaptive system, which are automatically updated by designing an adaptive law; ψ(s) = [ ψ ] 1 (s),ψ 2 (s),…,ψ N (s)]Is a fuzzy base function, N represents the number of fuzzy logic rules, s is a sliding mode surface, and T is a matrix transposed symbol; the fuzzy basis function is expressed as:
wherein ,is a membership function; l is the number of elements of s; n is any integer from 1 to N; i is any integer from 1 to l;
s42, defining a fuzzy logic rule; specifically, the definition of the fuzzy logic rules is shown in table 1; wherein, the IF column lists all cases, and the THEN column lists rules of corresponding cases; NB represents a large negative number; NS represents a small negative number; ZO represents 0; PB represents a large positive number; PS represents a small positive number.
TABLE 1
S43, adopting a Gaussian membership function, a fuzzy logic rule, a product inference engine and a central average solution moduleThe pasting device obtains a smooth fuzzy function output K; specifically, the membership function isi=1, 2,3; m=n=1, 2,3,4,5, each of the fuzzy function outputs is: />
wherein ,θM The free parameter of the Mth fuzzy system; m is the number of free parameters; j is any integer from 1 to M; a, a i Is the ith adjustable parameter, and a i ∈(0,1];s i Is the ith sliding die surface;
substituting K into equation (7) and replacing the discontinuous term thereofObtaining a control law of the fuzzy self-adaptive sliding mode controller:
specifically, in this embodiment, the specific procedure of step S5 is as follows:
s51, selecting a Lyapunov function as follows:
wherein V is a Lyapunov function;is the estimated deviation value, and +.>θ ki Representing the free parameters; θ kid Is theta ki The adaptive law is selected as:
s52, obtaining a first derivative of the Lyapunov function, and obtaining:
wherein ,a first derivative of the Lyapunov function; s is(s) i Is a sliding die surface;Is disturbance information received by the system; psi phi type ki (s i ) Is a fuzzy basis function; η is an adjustable parameter;
under the action of the control law, the system is stable, the track tracking error of the system is convergent, the convergence speed of the track tracking error of the system is related to the parameter eta, and the larger the eta, the faster the convergence speed of the track tracking error of the system.
S53, in combination with the control law and the analysis of steps S51 and S52, selecting an adjustable parameter as λ=diag (10,10,10),η=60, and an output torque of the Delta parallel robot under the action of the sliding mode controller is obtained, as shown in fig. 4. As can be seen from fig. 5, under the condition that a fuzzy adaptive system is not introduced, the output torque of the robot system generates buffeting, and the severe buffeting can increase the energy loss of the system and affect the accuracy and stability of the track tracking of the system.
After the fuzzy self-adaptive control system is introduced, and the step control law and the analysis of the steps S51 and S52 are combined, the adjustable parameter is selected to be lambda=diag (10,10,10), eta=100, and the output moment of the Delta parallel robot under the action of the fuzzy self-adaptive sliding mode controller is obtained, as shown in fig. 5. As can be seen from fig. 5, after the fuzzy adaptive control system is introduced, the output torque of the robot system is smooth, and the upper bounds of the modeling error and external disturbance of the system are estimated on line through the fuzzy system, so that the difficulty of parameter adjustment is reduced, and the adaptive capacity of the system is enhanced.
S54, the Delta parallel robot outputs smooth moment under the action of the fuzzy sliding mode controller, the joints of the robot are driven to move, the actual rotation angles of the joints of the Delta parallel robot are obtained through measurement of the sensors, and the tracking errors of the angles of the joints are calculated, as shown in FIG. 6.
The above examples are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above examples, and any other changes, modifications, substitutions, combinations, and simplifications that do not depart from the spirit and principle of the present invention should be made in the equivalent manner, and the embodiments are included in the protection scope of the present invention.
Claims (5)
1. A track tracking control method of a Delta parallel robot based on a fuzzy self-adaptive sliding mode is characterized by comprising the following steps:
s1, providing a dynamic model and a reference motion trail X of the robot according to the structure of the Delta parallel robot r ;
S2, establishing a robot reference motion track X according to inverse kinematics solution of the Delta parallel robot r And driving the mapping between joint angles to obtain a desired joint rotation angle q of the robot corresponding to the reference motion trail d ;
S3, measuring the actual rotation angle of a driving joint of the robot, feeding back to the controller, and obtaining a tracking error of the joint angle by making a difference with the expected joint angle in the step S2; according to the angle tracking error information, designing a sliding mode, and selecting an approach rate to enable the angle tracking error to reach the sliding mode; according to the robot model and a control target of track tracking, designing a control law of a robot track tracking controller, and determining control parameters;
s4, introducing a fuzzy self-adaptive control system, and replacing discontinuous switching functions in the synovial membrane control rate by smooth output of the fuzzy self-adaptive control system;
s5, analyzing stability and convergence of the fuzzy self-adaptive control system, adjusting control parameters of the controller, and outputting a track tracking result.
2. The track tracking control method of a Delta parallel robot based on a fuzzy self-adaptive sliding mode as set forth in claim 1, wherein the dynamics model of the robot in step S1 is as follows:
where τ is the joint drive torque, τ d Is an external disturbance, q,Represents the driving joint angle, angular velocity and angular acceleration, respectively, M (q) is the mass matrix,/->Is the Kevlar force and centrifugal force matrix, G (q) is the gravity vector;
given reference motion trajectory X r =[x y z] T m; wherein x is an x-axis value, and x=0.3sin5t; y is the y-axis number, and y=0.3 cos5t; z is a z-axis number, and z= -0.5.
3. The track tracking control method of the Delta parallel robot based on the fuzzy self-adaptive sliding mode according to claim 1, wherein the specific process of the step S3 is as follows:
s31, measuring the rotation angle q= [ q ] of each joint of the Delta parallel robot through a sensor installed in a driving motor 1 q 2 q 3 ] T And joint rotation angular velocityThe parameters of the robot dynamics model are unknown, and external disturbance tau acts on the system d Unknown; estimating the unknown items, taking a control law as u, and obtaining the following control system:
wherein ,the product of the estimated value of the mass matrix and the joint rotation angular acceleration;Is thatThe linear regression form of (2) comprises modeling errors and disturbance estimation errors of a system;Respectively represent M (q), respectively>G(q) and τd Is determined by the estimation error of (a); the relationship between the angular velocity of the drive joint and the control law u is thus obtained:
wherein ,for angular acceleration +.>All disturbance information received by the system is provided;
s32, setting the expected joint rotation angle as q d The actual joint rotation angle of the Delta parallel robot is q, and the tracking error is defined as e=q d -q; the slide surface is then designed:
wherein e is tracking error;is the derivative of the tracking error; lambda is an adjustable parameter;
when s=0, the tracking error of the system enters the sliding mode, at this timeSolving that the tracking error of the system is an exponential function, and gradually converging to 0 along with the time change;
s33, in order to enable the tracking error e of the system to finally converge to 0, the tracking error e is required to move on a sliding mode, namely t & gtto & gtinfinity, and s=0; to meet this condition, it is necessary to design the approach rateFirst derivative is calculated on the sliding mode surface:
wherein ,is the derivative of the slip form surface;Is the second derivative of the error;Is the desired angular acceleration;Is the actual angular acceleration;
s34, in order to finally converge the tracking error e of the system to 0, a control law is designed as follows:
wherein ,is->An upper boundary of the norm; λ and η are adjustable parameters and always satisfy λ > 0, η > 0; sgn(s) is the symbol operation result of taking s; substitution of the control law into the first derivative of the slip plane gives +.>When s > 0, < > and->When s < 0, < ->This ensures that the tracking error of the system always tends to slip modes.
4. The track tracking control method of the Delta parallel robot based on the fuzzy self-adaptive sliding mode according to claim 1, wherein the specific process of the step S4 is as follows:
s41, replacing discontinuous items contained in the control law u obtained in the step S3 by smooth output of the fuzzy self-adaptive systemThe following blurring function is defined:
K=Θ T Ψ(s) (8)
wherein k= [ K ] 1 ,k 2 ,k 3 ] T Representing the output of the fuzzy adaptive system; Θ= [ θ ] 1 ,θ 2 ,…,θ N ] T Free parameters representing the fuzzy adaptive system, which are automatically updated by designing an adaptive law; ψ(s) = [ ψ ] 1 (s),ψ 2 (s),…,ψ N (s)]Is a fuzzy base function, N represents the number of fuzzy logic rules, s is a sliding mode surface, and T is a matrix transposed symbol; the fuzzy basis function is expressed as:
wherein ,is a membership function; l is the number of elements of s; n is any integer from 1 to N; i is any integer from 1 to l;
s42, defining a fuzzy logic rule;
s43, obtaining a smooth fuzzy function output K by using a Gaussian membership function, a fuzzy logic rule and a product inference engine and a central average defuzzifier; membership function ofi=1, 2,3; m=n=1, 2,3,4,5, each of the fuzzy function outputs is: />
wherein ,θM The free parameter of the Mth fuzzy system; m is the number of free parameters; j is any integer from 1 to M; a, a i Is the ith adjustable parameter, and a i ∈(0,1];s i Is the ith sliding die surface;
substituting K into equation (7) and replacing the discontinuous term thereofObtaining a control law of the fuzzy self-adaptive sliding mode controller:
5. the track tracking control method of the Delta parallel robot based on the fuzzy self-adaptive sliding mode according to claim 1, wherein the specific process of the step S5 is as follows:
s51, selecting a Lyapunov function as follows:
wherein V is Lyapunov function;is the estimated deviation value, and +.>θ ki Representing the free parameters; θ kid Is theta ki The adaptive law is selected as:
s52, obtaining a first derivative of the Lyapunov function, and obtaining:
wherein ,a first derivative of the Lyapunov function; s is(s) i Is a sliding die surface;Is disturbance information received by the system; psi phi type ki (s i ) Is a fuzzy basis function; η is an adjustable parameter;
s53, in combination with the control law and the analysis of steps S51 and S52, selecting an adjustable parameter as λ=diag (10,10,10),η=60, obtain Delta parallel robot output moment under the action of slip-form controller;
after a fuzzy self-adaptive control system is introduced, and the adjustable parameters are selected to be lambda=diag (10,10,10) and eta=100 by combining the step control law and the analysis of the steps S51 and S52, so that the output moment of the Delta parallel robot under the action of the fuzzy self-adaptive sliding mode controller is obtained;
s54, the Delta parallel robot outputs smooth moment under the action of the fuzzy sliding mode controller, each joint of the robot is driven to move, the actual rotation angle of each joint of the Delta parallel robot is obtained through measurement of the sensor, and the tracking error of each joint angle is calculated.
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