CN115816453A - TDE-based adaptive supercoiled multivariate fast terminal sliding mode control method - Google Patents
TDE-based adaptive supercoiled multivariate fast terminal sliding mode control method Download PDFInfo
- Publication number
- CN115816453A CN115816453A CN202211531085.7A CN202211531085A CN115816453A CN 115816453 A CN115816453 A CN 115816453A CN 202211531085 A CN202211531085 A CN 202211531085A CN 115816453 A CN115816453 A CN 115816453A
- Authority
- CN
- China
- Prior art keywords
- mechanical arm
- tde
- supercoiled
- constraint
- joint
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Abstract
The invention provides a TDE-based adaptive supercoiled multivariate rapid terminal sliding mode control method, which ensures high-precision trajectory tracking control of a cable-driven mechanical arm under a complex unknown uncertainty condition. Firstly, designing an error range of a joint, ensuring that the deviation between the position of the joint and an expected contour is not too large while ensuring the safety performance of a manipulator, and estimating and compensating the residual lumped system dynamics by using time-lag estimation. Secondly, carrying out design analysis on the angle error expectation by using a safety constraint function, and processing the constraints of different sections in a unified system architecture; through strict analysis, the problem of the motion trail of the mechanical arm with output constraint and uncertainty is solved. The supercoiled adaptive control effectively ensures the algorithm to meet the rapid, accurate and robust convergence under all constraint conditions in operation, and the stability of the closed-loop control system is analyzed by utilizing the Lyapunov method.
Description
Technical Field
The invention belongs to the technical field of mechanical arm control, and relates to a TDE-based adaptive supercoiled multivariable rapid terminal sliding mode control method for a cable-driven mechanical arm with error safety constraint.
Background
Aiming at the problem of control precision of the mechanical arm, a great deal of research is carried out by a plurality of scholars, han S I designs a robust PID controller by combining robust control and PID control to realize the track tracking control [ 1 ] of the mechanical arm, J.xu provides a specified performance controller based on a Linear Extended State Observer (LESO), the problem of stabilization of a complex transformation system is solved, and the control precision [ 2 ] is further improved. Xu provides an orthogonal fuzzy PID intelligent control method [ 3 ], and compared with fuzzy PID orthogonal fuzzy PID, the accuracy of the system can be further improved. Most of the work in the literature that considers the joint tracking problem does not address the problem of error constraints during operation. However, to ensure accurate and safe operation of the cable driven robot, error constraints are required to be non-negligible. In the case of normal control, the control objective can be indicated when the error of the system can be gradually reduced from the initial position to the desired position to a very small value, i.e. the error is within the control range. Some positional ranges are unsafe due to mechanical control structure limitations, and the range is time-varying. If an emergency occurs, a huge deviation is caused, the error floats in an unpredictable range, and people cannot react in time, so that an overlarge movement error of a mechanical system can be caused, the mechanical system collides with the outside, and safety problems and economic losses are caused.
To solve the error constraint problem and to ensure the specified position tracking performance of the robot manipulator, zhou proposes a new constraint error variable [ 4 ] similar to a sliding mode surface. Li Y et al solved the output constraint problem due to physical and environmental limitations by constructing the Lyapunov function of the integral barrier [ 5 ]. And designing a controller by using the traditional logarithm Lyapunov function in the W.He to realize the track tracking control of the robot arm under the full-state constraint. 【6】 However, most of these approaches focus on input or output security constraints, and do not meet time-varying and asymmetric security constraints for position errors.
The control method based on the asymmetric constraint of the mechanical arm has many achievements, and Z.Kai provides a neural adaptive tracking control method aiming at an uncertain robot manipulator constrained in an asymmetric and time-varying holostate under the condition of not relating to feasible conditions, and the scheme can adapt to the asymmetric but time-varying motion constraint [ 7 ]. Xu presents a new Iterative Learning Control (ILC) scheme for tracking the non-repetitive reference trajectory problem of robotic manipulators over iterative domains with different trial lengths, subject to the asymmetric constraint requirements of joint angles [ 8 ]. Zhu proposes a self-adaptive timing estimation algorithm for an uncertain robot, and can avoid measuring acceleration signals (9) in the estimation process.
Overall, residual linkage dynamics, motor dynamics and collective uncertainty in the model parameters are difficult to obtain with conventional methods, and using TDE can be subject to estimation errors, especially when the system contains fast time-varying dynamics, which can lead to degradation of control performance. It is therefore necessary to develop a TDE-based control scheme with fast convergence and high control accuracy.
The relevant references are as follows:
【1】Han S I，Lee J M.Decentralized neural network control for guaranteed tracking error constraint of a robot manipulator[J].International Journal of Control，Automation and Systems，2015，13(4):906-915.
【2】Xu J，Qiao L.Robust Adaptive PID Control of Robot Manipulator with Bounded Disturbances[J].Mathematical Problems in Engineering，2013，2013(pt.13):1-13.
【3】Xu B，Ji S，Zhang C，et al.Linear-extended-state-observer-based prescribed performance control for trajectory tracking of a robotic manipulator[J].Industrial Robot，2021，ahead-of-print(ahead-of-print).
【4】Zhou，Chen，Liu.Design and Analysis of a Drive System for a Series Manipulator Based on Orthogonal-Fuzzy PID Control[J].Electronics，2019，8(9):1051-
【5】Li Y，Yang C，Yan W，et al.Admittance-based adaptive cooperative control for multiple manipulators with output constraints[J].IEEE transactions on neural networks and learning systems，2019，30(12):3621-3632.
【6】He W，Chen Y，Yin Z.Adaptive neural network control of an uncertain robot with full-state constraints[J].IEEE transactions on cybernetics，2015，46(3):620-629.
【7】Kai Z，Song Y.Neuroadaptive Robotic Control Under TimeVarying Asymmetric Motion Constraints:A Feasibility-Condition-Free Approach[J].IEEE Transactions on Cybernetics，2018，PP:1-10.
【8】Xu J.Iterative Learning Control for Robot Manipulators with NonRepetitive Reference Trajectory，Iteration Varying Trial Lengths，and Asymmetric Output Constraints[C]//2020American Control Conference(ACC).2020.
【9】Zhu C，Jiang Y，Yang C.Fixed-time Parameter Estimation and Control Design for Unknown Robot Manipulators with Asymmetric Motion Constraints[J].International Journal of Control，Automation and Systems，2022，20(1):268-282.
disclosure of Invention
In order to overcome the defects of the prior art, the invention designs the supercoiled controller based on asymmetric error constraint by adopting a time delay estimation method aiming at the problem of high-precision track tracking of the cable driving mechanical arm. According to the method, the error range is controlled by utilizing safety constraint, and the supercoiled design of the controller ensures that the mechanical arm meets the safety constraint in the aspect of control error. Meanwhile, joint position error constraints are designed by utilizing barrier functions. The method reduces the position error of the mechanical arm, and the track of the mechanical arm can be overlapped with the expected track to a great extent.
The technical scheme adopted by the invention is as follows: a TDE-based adaptive supercoiled multivariate fast terminal sliding mode control method comprises the following steps:
step 1, establishing a dynamic model of a mechanical arm, wherein the dynamic model is used for describing the state of the mechanical arm of a machine;
step 2, parameters in the dynamic model are estimated by using TED delay;
step 3, designing the slide film surface to facilitate the design of the next control method, and the method comprises the following substeps;
step 3.1, introducing safety constraint on joint position errors, and setting a safety range for the errors between the actual joint position and the expected joint position, so that the safety range has an upper limit and a lower limit to ensure the accurate and normal operation of the cable-driven mechanical arm;
step 3.2, designing and analyzing the angle error expectation by utilizing a safety constraint function and combining a barrier function, and processing the constraints of different sections in a unified system structure;
3.3, designing a slip form surface according to the joint position kinematics principle of the mechanical arm;
and 4, designing the terminal sliding mode controller by using the sliding film surface.
Further, the dynamical model of the mechanical arm with n degrees of freedom established in step 1 is represented as:
wherein J and d m Is the motor inertia and damping matrix, q and theta are the joint and motor position vectors,
representing the first and second derivatives of q and theta, respectively, M (q) is an inertia matrix,
is the coriolis/centrifuge matrix, g (q) is the attractive force,
is the friction vector, τ m And τ s Control torque and joint compliance torque, d, respectively, given to the motor s To damp the matrix, k s Is a joint stiffness matrix, τ d Representing a lumped unknown uncertainty;
to facilitate the use of the TDE scheme, substitute (2) into (1), apply constant parameters
Obtaining:
wherein the expression of f is:
further, in step 2, the TED scheme is used to obtain an estimated value of f
Where Δ t is the delay time, the kinetic model (4) is substituted into (6) and is available:
as can be seen from (6) and (7), the purpose of the TED scheme is to estimate the lumped system dynamics using only the time-lag values of the control and acceleration signals, and then to give a model-free scheme;
in engineering applications, u s (t- Δ t) may be represented by u s Is obtained by numerical differentiation
Wherein, the time node t 0 At ≧ 2 Δ t, t ≦ 2 Δ t at the initial stage, q (t) has the actual measurement value, and q (t-2 Δ t) will be manually zeroed, possibly resulting in strong fluctuations, and therefore (8) is used to mitigate the strong fluctuations that may exist.
Further, the specific implementation manner of step 3.1 is as follows;
defining the attitude tracking error of the mechanical arm as follows:
e Q ＝[e q1 ,e q2 ]＝Q-Q di (10)
wherein, Q = [ Q ] 1 ,q 2 ] T ，e q1 ,e q2 Refer to errors of joint one and joint two, Q, respectively di (t)＝[q d1 (t),q d2 (t)] T According to the starting and stopping position, the speed, the acceleration and the ballistic time t, 6 equations can be constructed, 6 coefficients of 5-order polynomial are solved, and Q is obtained di (t)；
The attitude tracking error must satisfy the following condition:
-Ω Li (t)<e qi (t)<Ω Hi (t) (11)
wherein, for all t ≧ 0, the constraint function Ω Li And Ω Hi Is a second order derivative function, satisfies
Safety constraints (10) - (12) require that the attitude tracking error does not exceed a range defined by a user, wherein constraint functions on the profiles of all degrees of freedom are different, and if the constraint requirements (10) are violated, the motion performance of the mechanical arm is influenced, so that the dynamic system of the mechanical arm is unstable, and the system fails;
in this step, the error e of the joint angle Q of the robot arm is defined Q It satisfies e Q ＝Q-Q di Equation (a) of (b), q d Is an artificial expected joint position, and the value range of q is-pi<q i <π；
Defining ω as the derivative of q, obtaining- π by a back-stepping method<q i <π，e ω Error of ω, whose derivative is:
further, the barrier function in step 3.2 is designed as follows;
introducing a transformed error variable for the attitude tracking error constraint condition of the mechanical arm:
Ω qL lower bound for asymmetric constraints, \8230 qH Is an upper bound of asymmetric constraints, η qi Can realize the error e qi Is asymmetrically constrained, η qi A barrier function representing the ith degree of freedom;
in this step, the barrier function η takes into account the safety constraints of the joint position error qi The derivatives of (c) are as follows:
wherein the content of the first and second substances,
defining an asymmetric constraint function:
further, the slip film surface in step 3.3 is designed to:
For convenience of expression, let:
further, the controller in step 4 is designed as follows:
ξ 1 (S) and xi 2 (S) is as follows:
k q1 ,k q2 are adaptive gains and are all greater than 0, k q3 Is a constant parameter;
k q2 ＝ηk q1 (27)
in summary, (25) can be expressed as:
wherein, the ratio of mu to mu,
eta and epsilon are parameters.
Further, the method for designing the controller is proved by adopting a Lyapunov method.
Compared with the prior art, the invention has the following beneficial effects:
(1) A novel TDE-based adaptive over-torque multivariable rapid terminal sliding mode control scheme is provided, and the scheme has high control precision and robustness.
(2) Asymmetric error constraint is considered, a supercoiling algorithm is improved, and rapid convergence and high control precision are guaranteed.
(3) A general barrier function is employed to address the safety constraints of time-varying and asymmetric position errors.
(4) By using time delay estimation and compensating for overall system dynamics, the error between the actual position and the desired position is reduced.
Detailed Description
The technical solution of the present invention is further explained below.
The invention provides a TDE-based adaptive supercoiled multivariable rapid terminal sliding mode control method, which comprises the following steps:
step 1: establishing a system model for describing the state of the mechanical arm of the machine;
the kinetic model of a mechanical arm with n degrees of freedom is expressed as:
wherein J and d m Is the motor inertia and damping matrix, q and theta are the joint and motor position vectors,
representing the first and second derivatives of q and theta, respectively, M (q) is an inertia matrix,
is the coriolis/centrifuge matrix, g (q) is the attractive force,
is the friction vector, τ m And τ s Control torque and joint compliance torque, d, respectively, given to the motor s To damp the matrix, k s Is a joint stiffness matrix, τ d Representing the lumped unknown uncertainty.
To facilitate the use of the TDE scheme, substitute (2) into (1), apply constant parameters
Obtaining:
wherein the expression of f is:
f, three main components including residual link dynamics, motor dynamics and total uncertainty, which are difficult to obtain using traditional methods, are subsequently estimated using TED.
Step 2: using TED delay time estimation to find the estimated value of f
f is particularly complex and difficult to solve, in this part we will solve using TED scheme
The value:
where Δ t is the delay time, the integrated system dynamics (4) is brought into (6) and is available:
as can be seen from (6) and (7), the main purpose of the TED scheme is to estimate the lumped system dynamics using only the time-lag values of the control and acceleration signals, and then to give a model-free scheme.
In engineering applications, u s (t- Δ t) may be represented by u s Is obtained by numerical differentiation
Wherein, the time node t 0 2 Δ t, t ≦ 2 Δ t at the initial stage, q (t) has the actual measured value, and q (t-2 Δ t) is manually zeroed, possibly leading to strong fluctuations, so (8) is used to mitigate the strong fluctuations that may be present, and in addition (8) and its initial versions are noted:
t>0 (9)
it is widely applied to many robust control schemes based on TDE. If no action is taken, the numerical differentiation (9) can significantly amplify the noise effect, thereby degrading control performance. However, it has been theoretically demonstrated that the gain can be reduced
Or an additional low pass filter may be used to solve this problem.
From (8), the current value of the dynamic model (4) is estimated by the TDE scheme using the time-lag system state, so that the estimation error of the method becomes large when a large disturbance occurs, but the method proposed by the inventor can effectively reduce the estimation error.
And step 3: designing a slide film surface of the system model to facilitate the design of a control method in the next step, wherein the design comprises the following substeps;
and 3.1, introducing safety constraint on joint position errors in a control link, and setting a safety range for the errors between the actual joint position and the expected joint position to enable the safety range to have an upper limit and a lower limit. This upper limit may be given by the actual situation, may be asymmetric, or may vary with time. The purpose of our control is to make it meet safety constraints to ensure accurate and proper operation of the cable driven robotic arm.
Defining the attitude tracking error of the mechanical arm as follows:
e Q ＝[e q1 ,e q2 ]＝Q-Q di (10)
wherein, Q = [ Q ] 1 ,q 2 ] T ，e q1 ,e q2 Refer to errors of joint one and joint two, Q, respectively di (t)＝[q d1 (t),q d2 (t)] T According to the starting and stopping position, the speed, the acceleration and the trajectory time t, 6 equations can be constructed, 6 coefficients of 5-order polynomial are solved, and Q is obtained di (t)；
The attitude tracking error must satisfy the following condition:
-Ω Li (t)<e qi (t)<Ω Hi (t) (11)
wherein, for all t ≧ 0, the constraint function Ω Li And Ω Hi Is a second order derivative function, satisfies
The safety constraints (10) - (12) require that the attitude tracking error does not exceed a user-defined range, where the constraint functions on the respective degree of freedom profiles may be different, the above-mentioned constraint functions may also be time-varying and asymmetric. If the constraint requirement (10) is violated, the motion performance of the mechanical arm is affected, the dynamic system is unstable, and the system fails.
In this step, we define the error e of the joint angle Q of the mechanical arm Q It satisfies e Q ＝Q-Q di Equation (a) of (b), q d Is an artificial expected joint position, and the value range of q is-pi<q i <π；
Defining ω as the derivative of q, obtaining- π by a back-stepping method<q i <π，e ω Error of ω, whose derivative is:
step 3.2, carrying out design analysis on the angle error expectation by using a safety constraint function, and processing the constraints of different sections in a unified system structure;
in order to meet the safety constraint, a barrier function is introduced, the barrier function is a continuous function, an inequality constraint can be replaced by a more easily processed item in an objective function of constraint optimization, and asymmetric constraint is facilitated;
first, the error variables are introduced as follows:
Ω Lij lower bound of asymmetric constraints, Ω Hij Is an upper bound of asymmetric constraints, η ij Can realize the error e ij The asymmetric constraint of (2). It is obvious that if and only if e ij η =0 ij And =0. Furthermore, when e ij →Ω Hij ，η ij → + ∞, or when e ij →Ω Lij Has η ij →-∞；
For the general barrier function V ij If the constraint function is symmetric, i.e. Ω Hij ＝Ω Lij ＝Ω ij Time, barrier function η ij Comprises the following steps:
when e is ij When there is no constraint condition, it can be equivalent to Ω Hij ＝Ω Lij ＝Ω ij → + ∞, at this time:
the above reasoning shows that we can treat a system without output constraint requirements as a special case of the general case of asymmetric constraint requirements.
Introducing a transformed error variable for the attitude tracking error constraint condition of the mechanical arm:
Ω qL lower bound of asymmetric constraints, Ω qH Is an upper bound of asymmetric constraints, η qi Can realize the error e qi The asymmetric constraint of (2). Eta qi A barrier function representing the ith degree of freedom;
in this step, we consider the safety constraint of joint position error, the barrier function eta qi The derivatives of (c) are as follows:
wherein the content of the first and second substances,
defining an asymmetric constraint function:
3.3, designing a slip form surface according to the joint position kinematics principle of the mechanical arm;
in this step, we consider the joint position kinematics problem of the cable-driven mechanical arm, and design the synovial surface as:
The symbol ° represents the hadamard product, i.e. the product between the elements of two matrices having the same dimension, given by:
and 4, step 4: design of controller by using slide film surface
In this step, the overall controller design will proceed, the overall control scheme is as follows:
ξ 1 (S) and xi 2 (S) is as follows:
k q1 ,k q2 are adaptive gains and are all greater than 0, k q3 Is a constant parameter;
k q2 ＝ηk q1 (27)
in summary, (25) can be expressed as:
theorem 1 inIn a system with gain (27), a suitable parameter mu is selected,
η,ε,
the sliding surface S of the system can converge to 0 within a limited time.
And 5: making valid proof of the above controller
For the system (10), the analysis was performed using the Lyapunov method, and the Lyapunov candidate function was chosen as follows:
in the formula, k q1 ，
Is a constant greater than 0:
is a symmetric positive definite matrix, in which λ>0，ε>0；
Derivation on both sides of equation (29):
order to
Can be converted into:
wherein, Q is a symmetric matrix,
wherein:
c 1 ＝k q1 λ 2 +4k q1 ε-λk 2 ＝a 1 k q1 -λk 2
c 3 ＝λ
if it is not
Negative, then the matrix Q is positive with a determinant greater than zero. If det (Q) is to be guaranteed>0, then the root discriminant λ k 2 (k q1 -λ)>0. And because of
So k 2 >0, thereby
k q1 >λ。
Wherein k is 2 The value range is as follows:
let k q1 = λ + τ, where τ>0, then det [ Q ]]The solution of =0 is:
if ρ 1 Has a value range of
At this time det [ Q ]]>0. When in use
The existence of the root can be guaranteed. Let k 2 ＝κ 2 Obtaining:
thereby pushing to
Thus, it is possible to provide
Let λ max { P } and λ min { P } is the maximum eigenvalue and minimum eigenvalue of the matrix, then (33) can be:
in the formula, xi 1 Is xi 1 The amount of the characteristic(s),
thus, it is possible to provide
(35) The method can be characterized in that:
in the formula, beta η ＝min{η 1 ,β 1 ,β 2 }，
To ensure k q1 And k q2 Are respectively represented by k q1 - | S | and η k q1 The slope of | S | is increased to satisfy | S! non-calculation>ε, when the following conditions are met:
can obtain zeta 1 >0 and ζ 2 >0；
Thus, it is possible to provide
Therefore | S | can converge to the interval | S | in a limited time<ε 2 Internal; if | S |<ε 2 Then ζ 1 <0，ζ 2 <0，
Is unknown, the rate of change of gain becomes-k q1 - | S | and-. Eta.k q1 G | S | when the gain is reduced to the interval | S |, the Y ray<ε 2 The gain will be at k q1 - | S | and η · k q1 The slope of | S | increases.
Claims (8)
1. The TDE-based adaptive supercoiled multivariate fast terminal sliding mode control method is characterized by comprising the following steps of:
step 1, establishing a dynamic model of a mechanical arm, wherein the dynamic model is used for describing the state of the mechanical arm of a machine;
step 2, parameters in the dynamic model are estimated by using TED delay;
step 3, designing the slide film surface to facilitate the design of the next control method, and the method comprises the following substeps;
step 3.1, introducing safety constraint on joint position errors, and setting a safety range for the errors between the actual joint position and the expected joint position, so that the safety range has an upper limit and a lower limit to ensure the accurate and normal operation of the cable-driven mechanical arm;
step 3.2, designing and analyzing the angle error expectation by utilizing a safety constraint function and combining a barrier function, and processing the constraints of different sections in a unified system structure;
3.3, designing a slip form surface according to the joint position kinematics principle of the mechanical arm;
and 4, designing the terminal sliding mode controller by using the sliding film surface.
2. The TDE-based adaptive supercoiled multivariate fast terminal sliding-mode control method according to claim 1, characterized in that: the kinetic model of the mechanical arm with n degrees of freedom established in step 1 is represented as:
wherein J and d m Is the motor inertia and damping matrix, q and theta are the joint and motor position vectors,
representing the first and second derivatives of q and theta, respectively, M (q) is an inertia matrix,
is the Coriolis/centrifuge matrix, g (q) is the gravitational force,
is the friction vector, τ m And τ s Control torque and joint compliance torque, d, respectively, given to the motor s To damp the matrix, k s Is a joint stiffness matrix, τ d Representing a lumped unknown uncertainty;
to facilitate the use of the TDE scheme, substitute (2) into (1), apply constant parameters
Obtaining:
wherein the expression of f is:
3. the TDE-based adaptive supercoiled multivariate fast terminal sliding-mode control method according to claim 2, characterized in that: step 2, using TED scheme to obtain f estimation value
Where Δ t is the delay time, the kinetic model (4) is substituted (6) to obtain:
as can be seen from (6) and (7), the purpose of the TED scheme is to estimate the lumped system dynamics using only the time-lag values of the control and acceleration signals, and then to give a model-free scheme;
in engineering applications, u s (t- Δ t) may be represented by u s Is obtained by numerical differentiation
Wherein, the time node t 0 At ≧ 2 Δ t, t ≦ 2 Δ t at the initial stage, q (t) has the actual measurement value, and q (t-2 Δ t) will be manually zeroed, possibly resulting in strong fluctuations, and therefore (8) is used to mitigate the strong fluctuations that may exist.
4. The TDE-based adaptive supercoiled multivariate fast terminal sliding-mode control method according to claim 3, characterized in that: the specific implementation of step 3.1 is as follows;
defining the attitude tracking error of the mechanical arm as follows:
e Q ＝[e q1 ,e q2 ]＝Q-Q di (10)
wherein, Q = [ Q ] 1 ,q 2 ] T ，e q1 ,e q2 Refer to errors of joint one and joint two, Q, respectively di (t)＝[q d1 (t),q d2 (t)] T According to the starting and stopping position, the speed, the acceleration and the ballistic time t, 6 equations can be constructed, 6 coefficients of 5-order polynomial are solved, and Q is obtained di (t)；
The attitude tracking error must satisfy the following condition:
-Ω Li (t)<e qi (t)<Ω Hi (t) (11)
wherein, for all t ≧ 0, the constraint function Ω Li And Ω Hi Is a second order derivative function, satisfies
Safety constraints (10) - (12) require that the attitude tracking error does not exceed a range defined by a user, wherein constraint functions on the profiles of all degrees of freedom are different, and if the constraint requirements (10) are violated, the motion performance of the mechanical arm is influenced, so that the dynamic system of the mechanical arm is unstable, and the system fails;
in this step, the error e of the joint angle Q of the robot arm is defined Q It satisfies e Q ＝Q-Q di Equation (a) of (b), q d Is an artificial expected joint position, and the value range of q is-pi<q i <π；
Defining ω as the derivative of q, obtaining- π by a back-stepping method<q i <π，e ω Error at ω, whose derivative is:
5. the TDE-based adaptive supercoiled multivariate fast terminal sliding-mode control method of claim 4, characterized in that: the barrier function in step 3.2 is designed as follows;
introducing a transformed error variable for the attitude tracking error constraint condition of the mechanical arm:
Ω qL lower bound of asymmetric constraints, Ω qH Is an upper bound of asymmetric constraints, η qi Can realize the error e qi Is asymmetrically constrained, η qi A barrier function representing the ith degree of freedom;
in this step, the barrier function η takes into account the safety constraints of the joint position error qi The derivatives of (c) are as follows:
wherein the content of the first and second substances,
defining an asymmetric constraint function:
6. the TDE-based adaptive supercoiled multivariate fast terminal sliding-mode control method according to claim 5, characterized in that: in step 3.3 the slip film surface is designed as follows:
For convenience of expression, let:
7. the TDE-based adaptive supercoiled multivariate fast terminal sliding-mode control method according to claim 6, characterized in that: the controller in step 4 is designed as follows:
ξ 1 (S) and xi 2 (S) is as follows:
k q1 ,k q2 are adaptive gains and are all greater than 0, k q3 Is a constant parameter;
k q2 ＝ηk q1 (27)
in summary, (25) can be expressed as:
wherein the content of the first and second substances,
are all parameters.
8. The TDE-based adaptive supercoiled multivariate fast terminal sliding-mode control method according to claim 1, characterized in that: the method also comprises the step of proving the design method of the controller by adopting a Lyapunov method.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211531085.7A CN115816453A (en) | 2022-12-01 | 2022-12-01 | TDE-based adaptive supercoiled multivariate fast terminal sliding mode control method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211531085.7A CN115816453A (en) | 2022-12-01 | 2022-12-01 | TDE-based adaptive supercoiled multivariate fast terminal sliding mode control method |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN115816453A true CN115816453A (en) | 2023-03-21 |
Family
ID=85533564
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202211531085.7A Pending CN115816453A (en) | 2022-12-01 | 2022-12-01 | TDE-based adaptive supercoiled multivariate fast terminal sliding mode control method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115816453A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116141339A (en) * | 2023-04-19 | 2023-05-23 | 珞石（北京）科技有限公司 | Seven-degree-of-freedom mechanical arm preset time track tracking control method |
-
2022
- 2022-12-01 CN CN202211531085.7A patent/CN115816453A/en active Pending
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116141339A (en) * | 2023-04-19 | 2023-05-23 | 珞石（北京）科技有限公司 | Seven-degree-of-freedom mechanical arm preset time track tracking control method |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN112180729B (en) | Self-adaptive trajectory tracking control method for mechanical arm | |
| Zhu et al. | Output feedback adaptive dynamic surface sliding-mode control for quadrotor UAVs with tracking error constraints | |
| Slotine et al. | Adaptive manipulator control: A case study | |
| CN112363519B (en) | Four-rotor unmanned aerial vehicle reinforcement learning nonlinear attitude control method | |
| Butt et al. | Multi-variable integral sliding mode control of a two degrees of freedom helicopter | |
| CN110673472B (en) | Adaptive robust control method based on neural network compensation dead zone inversion error | |
| CN113183154B (en) | Adaptive inversion control method of flexible joint mechanical arm | |
| CN111965976B (en) | Robot joint sliding mode control method and system based on neural network observer | |
| CN111941432A (en) | Artificial intelligence output feedback control method for high-performance mechanical arm | |
| Xia et al. | Fuzzy neural-network friction compensation-based singularity avoidance energy swing-up to nonequilibrium unstable position control of pendubot | |
| CN115816453A (en) | TDE-based adaptive supercoiled multivariate fast terminal sliding mode control method | |
| CN113759722B (en) | Unmanned aerial vehicle active disturbance rejection controller parameter optimization method | |
| Zhang et al. | Variable gain based composite trajectory tracking control for 4-wheel skid-steering mobile robots with unknown disturbances | |
| Chen et al. | Robust trajectory tracking control of underactuated underwater vehicle subject to uncertainties | |
| Zeghlache et al. | Adaptive type-2 fuzzy sliding mode control using supervisory type-2 fuzzy control for 6 DOF octorotor aircraft | |
| CN112936277A (en) | Underwater robot-manipulator system fixed time trajectory tracking method | |
| CN111857172B (en) | Four-rotor dynamic surface integral sliding mode controller based on preset tracking error | |
| Zhu et al. | A PID based approximation-free controller with prescribed performance function for model helicopter attitude control | |
| Ma et al. | Finite-time trajectory tracking control of quadrotor UAV via adaptive RBF neural network with lumped uncertainties | |
| Peng et al. | Robust quadratic stabilization tracking control for mobile robot with nonholonomic constraint | |
| CN110209055B (en) | Second-order system controller and control method based on reference model and disturbance observation | |
| Liu et al. | Adaptive Fuzzy Finite Time Prescribed Performance Control for Long Stroke Hybrid Robots | |
| Li et al. | Trajectory tracking control of robot manipulators using a neural-network-based torque compensator | |
| Zhu et al. | Trajectory Tracking Control Strategy Based on Model-Free Adaptive Sliding Mode Control Approach for Robot Manipulator | |
| Lee et al. | Model-Free Attitude Control of Quadcopter using Disturbance Observer and Integral Reinforcement Learning |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |