CN112454349B - Mechanical arm control transformation method considering variable stiffness joint delay characteristics - Google Patents
Mechanical arm control transformation method considering variable stiffness joint delay characteristics Download PDFInfo
- Publication number
- CN112454349B CN112454349B CN202010574622.0A CN202010574622A CN112454349B CN 112454349 B CN112454349 B CN 112454349B CN 202010574622 A CN202010574622 A CN 202010574622A CN 112454349 B CN112454349 B CN 112454349B
- Authority
- CN
- China
- Prior art keywords
- mechanical arm
- joint
- rigidity
- control law
- delay
- 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.)
- Active
Links
Images
Classifications
-
- 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
- B25J9/1646—Programme controls characterised by the control loop variable structure system, sliding mode 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
- B25J9/1602—Programme controls characterised by the control system, structure, architecture
- B25J9/1607—Calculation of inertia, jacobian matrixes and inverses
-
- 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
- B25J9/163—Programme controls characterised by the control loop learning, adaptive, model based, rule based expert control
Landscapes
- Engineering & Computer Science (AREA)
- Robotics (AREA)
- Mechanical Engineering (AREA)
- Physics & Mathematics (AREA)
- Mathematical Physics (AREA)
- Automation & Control Theory (AREA)
- Feedback Control In General (AREA)
Abstract
The invention relates to a mechanical arm control conversion method considering variable stiffness joint delay characteristics, which is realized by the following steps: (1) considering the time delay characteristic of a variable-stiffness joint installed on the mechanical arm, and establishing an n-degree-of-freedom mechanical arm dynamic model; (2) molding the dynamic moldThe delay in the pattern is reduced to the original
Establishing a new dynamic model; m is more than 1; (3) designing a small-delay control law for stabilizing the closed loop of the new dynamic model; (4) and (3) on the basis of the small-delay control law, considering the scaling relation of the two dynamic models in the steps (1) and (2), carrying out scaling transformation, designing a control law which enables the closed loop in the step (1) to be stable, and realizing the control of the mechanical arm by using the control law.
Description
Technical Field
The invention belongs to the field of mechanical arm control, and relates to a mechanical arm control transformation method considering the large delay characteristic of a variable-stiffness joint.
Background
In an unstructured environment, the application of the variable-stiffness joint to an industrial robot or a household robot is more and more extensive to solve the problem of environment interaction completeness, and in the prior art, some robots adopting the variable-stiffness joint or directly neglecting the variable-stiffness delay characteristic cannot ensure the closed-loop stability of an actual system; or the complex variable stiffness dynamics and the robot dynamics are coupled and designed to be controlled, so that the design difficulty of the controller is greatly increased, and the direct popularization and application of the existing control method are limited.
In terms of control input of the mechanical arm, besides joint control of the mechanical arm, rigidity is additionally added as input, and online adjustment of the rigidity enables the application of the robot to be more flexible. Because the dynamics of the robot is very complex, when the rigidity is taken as a control quantity, if the dynamic characteristic of variable rigidity is taken into consideration, the design difficulty of the controller is greatly increased, and the dynamic characteristic is generally neglected for direct design. However, in the variable stiffness joint, the compression of the spring is generally changed or the magnitude of the moment arm is changed to adjust the stiffness by a physical method, so that the response speed of stiffness change is delayed greatly, which brings a large influence on the stability of control.
Disclosure of Invention
The technical problem solved by the invention is as follows: the defects of the prior art are overcome, and the mechanical arm control conversion method considering the variable stiffness joint delay characteristic is provided.
The technical scheme of the invention is as follows: a mechanical arm control transformation method considering variable stiffness joint delay characteristics is realized by the following steps:
(1) considering the time delay characteristic of a variable-stiffness joint installed on the mechanical arm, and establishing an n-degree-of-freedom mechanical arm dynamic model;
(2) reducing the time delay in the kinetic model to the original 
Establishing a new dynamic model; m is more than 1;
(3) designing a small-delay control law for stabilizing the closed loop of the new dynamic model;
(4) and (3) on the basis of the small-delay control law, considering the scaling relation of the two dynamic models in the steps (1) and (2), carrying out scaling transformation, designing a control law which enables the closed loop in the step (1) to be stable, and realizing the control of the mechanical arm by using the control law.
Preferably, before the step (2), analyzing the time delay characteristic of the mechanical arm, and if the time delay is greater than the control period of the mechanical arm, starting to execute the step (2); otherwise, directly designing a small-delay control law which enables the dynamic model in the step (1) to be closed-loop and stable, and controlling the mechanical arm by using the control law.
Preferably, the small delay control law designed in the step (3) is assumed to be:
the control law designed in the step (4) is as follows:
in the formula, u is an n-dimensional torque vector and corresponds to the joint torque of the mechanical arm with n degrees of freedom, k is a l-dimensional rigidity vector and corresponds to the rigidity input of l rigidity-adjustable joints of the mechanical arm with n degrees of freedom, and u is 0 () And k 0 () Control functions, q and q, respectively, referring to the existing moment and stiffness
A joint angle vector and a joint angular velocity vector corresponding to the mechanical arm with n degrees of freedom, G (q) is a gravity gradient vector in a Lagrange equation, and δ q is a deformation angle of l rigidity-adjustable joints; t is time, and B is an n multiplied by n matrix, which describes the effect of the joint moment on the generalized coordinates.
Preferably, the kinetic model in step (1) is as follows:
in the formula, q is a generalized coordinate vector of a structural space, and the dimension is n; d (q) is an inertia matrix;
the method is characterized in that the method is a Coriolis matrix, G (q) is a gradient vector of a gravity potential energy field, B is an n multiplied by n matrix and describes the action effect of joint torque on a generalized coordinate, E (delta q) is an n multiplied by l matrix, the joint deformation action of a joint with variable rigidity is mapped on the generalized coordinate, l is the number of joints with adjustable rigidity and satisfies that l is less than or equal to n, the ith row of the E (delta q) is all zero if the rigidity of the ith joint of an n-degree-of-freedom mechanical arm is not adjustable, the ith row of the E (delta q) is all zero if the rigidity of the ith joint of the n-degree-of-freedom mechanical arm is adjustable, the jth joint of the n-degree-of-freedom mechanical arm is correspondingly the jth joint of the l adjustable rigidity, and the ith row and j column of the E (delta q) is an element of the delta q j The remaining elements in row i are 0; u (t) represents an n-dimensional moment vectorK (T) is the stiffness input of the l stiffness-adjustable joints, T ═ T 1 ,T 2 ,…T l ] T The rigidity adjusting time delay respectively corresponding to the one joint with adjustable rigidity is k (T-T) ═ k 1 (t-T 1 ) k 2 (t-T 2 ) … k l (t-T l )] T 。
Preferably, the new kinetic model in step (2) is as follows:
preferably, m is determined according to the actual time delay T ═ T 1 ,T 2 ,…T l ] T Selecting, wherein generally, it needs to be ensured that the time delay of the established new dynamic model is less than the time length delta T of one control period of the planning controller of the upper computer of the mechanical arm, wherein l is the number of the adjustable rigidity joints in the mechanical arm.
m is preferably within a range
Wherein, T max Is time delay T ═ T 1 ,T 2 ,…T l ] T The largest component of (a).
Compared with the prior art, the invention has the beneficial effects that:
the variable stiffness joint adopted by the mechanical arm generally changes the tension force of a spring or changes the force arm of a supporting point by a physical method to adjust the stiffness, the response speed of the stiffness change is delayed greatly, if the dynamic characteristic of the variable stiffness is taken into account, the design difficulty of the controller is greatly increased, and the dynamic characteristic of the controller is generally neglected in the existing control law design to be directly designed. However, in practical applications, the larger delay may make the system unstable. In order to guarantee stability and operation precision when the mechanical arm performs relevant operation, the time scaling method is provided, dynamic characteristics of the variable-stiffness joints are taken into consideration, a control law directly designed by neglecting the dynamic characteristics can be converted into practical control through corresponding control transformation, and stability and steady-state precision of the mechanical arm with the variable-stiffness joints in the operation process are guaranteed by sacrificing certain dynamic performance.
The invention provides a control transformation method considering variable stiffness regulation delay, which can directly popularize and apply some existing control laws to the condition of considering variable stiffness large delay characteristics and can ensure the stability and steady-state precision of the mechanical arm in the operation process.
Drawings
FIG. 1 is a flow chart of the present invention.
Detailed Description
The invention is further illustrated by the following examples.
The basic principle of the invention is as follows: by adopting a time scaling method, the dynamic characteristics of the variable-stiffness joint are considered in the control design of the mechanical arm, and the stability and the steady-state precision of the system can be ensured under the condition of sacrificing a certain response speed.
As shown in fig. 1, a mechanical arm control transformation method considering variable stiffness joint delay characteristics is realized by the following steps:
(1) considering the time delay characteristic of a variable-stiffness joint installed on the mechanical arm, and establishing an n-degree-of-freedom mechanical arm dynamic model;
(2) reducing the time delay in the kinetic model to the original
Establishing a new dynamic model; m is more than 1;
(3) designing a small-delay control law for stabilizing the closed loop of the new dynamic model:
(4) based on the small delay control law, considering the scaling relation of the two dynamic models in the steps (1) and (2), carrying out scaling transformation, and designing a control law which enables the closed loop in the step (1) to be stable:
Scheme verification
Considering a general model of an n-degree-of-freedom mechanical arm, q is a generalized coordinate vector of a structural space, the dimension is n, u is an n-dimensional moment vector, and a mathematical model of the robot can be described as a controlled Lagrange system
Where D (q) is the inertial matrix of the system.
Is a matrix of coriolis-type signals,
the method is characterized in that the method is a gradient vector of a gravitational potential energy field, V (q) is system gravitational potential energy, B is an n multiplied by n matrix which describes the effect of joint moment on generalized coordinates, and u is an input n-dimensional moment vector.
When a certain joint or certain joints of the mechanical arm are provided with variable-rigidity joints, dynamics become
k is the rigidity input of l rigidity-adjustable joints, E (delta q) is an n multiplied by l matrix, the joint deformation action of the rigidity-variable joints is mapped to a generalized coordinate, l is the rigidity-adjustable joint number, l is equal to or less than n, the ith joint rigidity of the n-freedom-degree mechanical arm is not adjustable, the ith row of the E (delta q) is all zero, the ith joint rigidity of the n-freedom-degree mechanical arm is adjustable, the jth joint in the l rigidity-adjustable joints is correspondingly arranged, and the ith row and the jth column of the E (delta q) are delta q j The remaining elements in row i are 0.
Then both u and k can be used as system inputs to adjust the motion of the robotic arm. In fact, of mechanical armsJoint stiffness k ═ k 1 k 2 … k l ] T The change of the variable stiffness motor is obtained by adjusting the angular position of the variable stiffness motor, the response speed of the stiffness has larger delay compared with the response speed of the input u, the delay is related to the joint position, the deformation quantity of the deformation element and the dynamic response speed of the variable stiffness motor, modeling is quite complicated, the duration delta T of one control period of a planning controller of the mechanical arm upper computer is set, the value of the time delay of the variable stiffness joint is larger than delta T, and the vector T is set as [ T ═ T [ T [ ] 1 ,T 2 ,…T l ] T Respectively corresponding to the rigidity adjustment time delay of the joints with adjustable rigidity, a system dynamics model can be written (called a system (3) below)
Wherein k (T-T) ═ k 1 (t-T 1 ) k 2 (t-T 2 ) … k l (t-T l )] T 。
Now a new variable is introduced
Wherein m is>1, defining variables
s(τ)＝q(t) (4)
Is provided with
Then can obtain
When neglecting the system (3) delay, consider the following control law,
note u 0 And k 0 The expression is a function of the system state and time, has generality and can represent any state feedback or output feedback control law designed by adopting the existing theoretical method under the condition of neglecting the joint delay characteristic.
New variable
(4) Substitution of equations (3) into (5) and (6)
If (7) is replaced by the following control law
Substituted into formula (3) and changed into new variable
Defining a correlation system (hereinafter system (11))
It can be seen that the variable stiffness dynamic time delay is smaller and is the time delay of the original system (3)
If the initially defined control law (7) is substituted, a closed system loop of
It can be observed that equations (10) and (12) have identical dynamic evolution behavior except that variables s and τ are replaced by q and t, respectively, that is, if the system (11) with small dynamic time delay of system stiffness is closed-loop stable under the action of the control law (7), the dynamic equation (10) is closed-loop stable. Note that the closed-loop behavior of the system (3) with large dynamic time delay of system stiffness under the control law (9) is equivalent to equation (10), which is obtained by applying a time scaling transform. It can be concluded that if the control law (7) stabilizes the system (11), the control law (9) stabilizes the system (3). Therefore, for the control problem of the system (3) with large variable stiffness dynamic time delay, the method provided by the application can be converted into the control problem of the system (11) with small variable stiffness dynamic time delay.
For the problem of mechanical arm joint tracking, if the small time delay system (11) can asymptotically and stably track the reference output q under the action of the control law (7) d (mt), then the large time delay system (3) can track the reference output q under the action of the control law (9) d (T), in such scaling, the value of m may be determined according to the actual time delay T ═ T 1 ,T 2 ,…T l ] T Selected as appropriate, and set T max Is time delay T ═ T 1 ,T 2 ,…T l ] T The maximum component of (1) is selected empirically
In time, the system can be generally stabilized by setting other control parameters, but the system robustness is limited; selecting
When the value of m is selected to be too large, the dynamic response of the system is too slow. In general, selecting
Thus, the design of the controller (7) for the system (11) becomes very easy, and the existing control laws mostly follow the assumed conditionsThe design is that the transformation relation provided by the invention is applied, the control law (9) can be obtained through transformation according to the control law (7), and the control law (9) can be suitable for an actual system (3) with large variable-rigidity time delay characteristics.
The invention provides a method based on time scaling transformation, which can convert a control law directly designed by neglecting dynamic characteristics into practical control taking the larger time delay characteristic of variable rigidity into consideration through corresponding control transformation, and ensure the stability and steady-state precision of the mechanical arm in the operation process by sacrificing certain dynamic performance.
The control conversion method provided by the invention can be used for controlling various mechanical arms adopting variable-stiffness joints, has clear results and generality, and can solve the problem of variable-stiffness delay characteristics in the existing control law design. The invention has wide application range and strong practicability, can be widely applied to the motion control of industrial robots or household robots with variable-rigidity joints in unstructured environments, and has better application prospect.
The invention has not been described in detail in part in the common general knowledge of a person skilled in the art.
Claims (6)
1. A mechanical arm control transformation method considering variable stiffness joint delay characteristics is characterized by being realized by the following modes:
(1) considering the time delay characteristic of a variable-stiffness joint installed on the mechanical arm, and establishing an n-degree-of-freedom mechanical arm dynamic model;
(2) reducing the time delay in the kinetic model to the original
Establishing a new dynamic model; m is more than 1;
(3) designing a small-delay control law for stabilizing the closed loop of the new dynamic model;
(4) based on the small delay control law, considering the scaling relation of the two dynamic models in the steps (1) and (2), carrying out scaling transformation, designing a control law which enables the closed loop in the step (1) to be stable, and realizing the control of the mechanical arm by using the control law;
Assuming that the small delay control law designed in the step (3) is as follows:
the control law designed in the step (4) is as follows:
in the formula, u is an n-dimensional torque vector and corresponds to the joint torque of the mechanical arm with n degrees of freedom, k is a l-dimensional rigidity vector and corresponds to the rigidity input of l rigidity-adjustable joints of the mechanical arm with n degrees of freedom, and u is 0 () And k 0 () Control functions, q and q, respectively, referring to the existing moment and stiffness
A joint angle vector and a joint angular velocity vector corresponding to the mechanical arm with n degrees of freedom, G (q) is a gravity gradient vector in a Lagrange equation, and δ q is a deformation angle of l rigidity-adjustable joints; t is time, and B is an n multiplied by n matrix, which describes the effect of the joint moment on the generalized coordinates.
2. The method of claim 1, wherein: analyzing the time delay characteristic of the mechanical arm before the step (2), and starting to execute the step (2) if the time delay is greater than the control period of the mechanical arm; otherwise, directly designing a small-delay control law which enables the dynamic model in the step (1) to be closed-loop and stable, and controlling the mechanical arm by using the control law.
3. The method according to claim 1 or 2, characterized in that: the kinetic model in step (1) is as follows:
in the formula, q is a generalized coordinate vector of a structural space, and the dimension is n; d (q) is an inertia matrix; 
The method is characterized in that the method is a Coriolis matrix, G (q) is a gradient vector of a gravity potential energy field, B is an n multiplied by n matrix and describes the action effect of joint torque on a generalized coordinate, E (delta q) is an n multiplied by l matrix, the joint deformation action of a joint with variable rigidity is mapped on the generalized coordinate, l is the number of joints with adjustable rigidity and satisfies that l is less than or equal to n, the ith row of the E (delta q) is all zero if the rigidity of the ith joint of an n-degree-of-freedom mechanical arm is not adjustable, the ith row of the E (delta q) is all zero if the rigidity of the ith joint of the n-degree-of-freedom mechanical arm is adjustable, the jth joint of the n-degree-of-freedom mechanical arm is correspondingly the jth joint of the l adjustable rigidity, and the ith row and j column of the E (delta q) is an element of the delta q j The remaining elements in row i are 0; u (T) represents n-dimensional moment vector, k (T) is the rigidity input of l rigidity-adjustable joints, and T is [ T ═ T [ ] 1 ,T 2 ,…T l ] T The rigidity adjusting time delay respectively corresponding to the one joint with adjustable rigidity is k (T-T) ═ k 1 (t-T 1 ) k 2 (t-T 2 )…k l (t-T l )] T 。
4. The method of claim 3, wherein: the new kinetic model in step (2) is as follows:
5. the method according to claim 1 or 2, characterized in that: m is determined according to the actual time delay T ═ T 1 ,T 2 ,…T l ] T Selecting, wherein the time delay of the new dynamic model to be established is ensured to be less than the time length delta T of one control period of the planning controller of the upper computer of the mechanical arm, wherein l is the number of the adjustable rigidity joints in the mechanical arm.
6. The method of claim 5, wherein: m is preferably within a range
Wherein, T max Is time delay T ═ T 1 ,T 2 ,…T l ] T The largest component of (a).
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010574622.0A CN112454349B (en) | 2020-06-22 | 2020-06-22 | Mechanical arm control transformation method considering variable stiffness joint delay characteristics |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010574622.0A CN112454349B (en) | 2020-06-22 | 2020-06-22 | Mechanical arm control transformation method considering variable stiffness joint delay characteristics |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN112454349A CN112454349A (en) | 2021-03-09 |
| CN112454349B true CN112454349B (en) | 2022-07-29 |
Family
ID=74833558
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010574622.0A Active CN112454349B (en) | 2020-06-22 | 2020-06-22 | Mechanical arm control transformation method considering variable stiffness joint delay characteristics |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112454349B (en) |
Family Cites Families (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR101141917B1 (en) * | 2009-12-03 | 2012-05-03 | 한국과학기술원 | Time delay control with gradient estimator for robot manipulator and robot manipulator controller using the same |
| CN103412567A (en) * | 2013-04-15 | 2013-11-27 | 上海大学 | Underwater robot depth control device based on linear active disturbance rejection technology and method thereof |
| CN105459118B (en) * | 2016-01-07 | 2018-05-22 | 北京邮电大学 | A kind of wave variables four-way bilateral control method based on main side power buffering |
| CN106584455B (en) * | 2016-10-11 | 2019-06-11 | 苏州继企机电科技有限公司 | A kind of delay control method of remote operating mechanical arm system |
| CN107577147B (en) * | 2017-09-08 | 2020-07-03 | 北京邮电大学 | Teleoperation bilateral PID control method based on self-adaptive Smith predictor |
| CN110026981B (en) * | 2019-04-19 | 2021-09-17 | 中科新松有限公司 | Mechanical arm collision detection method based on model self-adaptation |
-
2020
- 2020-06-22 CN CN202010574622.0A patent/CN112454349B/en active Active
Also Published As
| Publication number | Publication date |
|---|---|
| CN112454349A (en) | 2021-03-09 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Lai et al. | Comprehensive unified control strategy for underactuated two-link manipulators | |
| Hu et al. | Robust adaptive fixed-time sliding-mode control for uncertain robotic systems with input saturation | |
| Maalini et al. | Modelling and control of ball and beam system using PID controller | |
| Cheng et al. | Non-linear bandwidth extended-state-observer based non-smooth funnel control for motor-drive servo systems | |
| CN107263483B (en) | The control method for coordinating of two degrees of freedom articulated robot track | |
| CN105446348A (en) | Distributed control method capable of improving control precision of flexible spacecraft | |
| CN110842913B (en) | Adaptive sliding mode iterative learning control method of single-joint mechanical arm | |
| Cho et al. | An indirect model reference adaptive fuzzy control for SISO Takagi–Sugeno model | |
| CN109828468A (en) | A kind of control method for the non-linear robot system of magnetic hysteresis | |
| Sun et al. | Research on the trajectory tracking control of a 6-dof manipulator based on fully-actuated system models | |
| Rhee et al. | Hybrid impedance and admittance control of robot manipulator with unknown environment | |
| Zhen et al. | Model‐based robust control design and experimental validation of collaborative industrial robot system with uncertainty | |
| Hu et al. | Impedance with finite-time control scheme for robot-environment interaction | |
| CN112454349B (en) | Mechanical arm control transformation method considering variable stiffness joint delay characteristics | |
| Singh et al. | Modeling, analysis and control of a single stage linear inverted pendulum | |
| Dangol et al. | A hzd-based framework for the real-time, optimization-free enforcement of gait feasibility constraints | |
| Zhang et al. | A practical PID variable stiffness control and its enhancement for compliant force-tracking interactions with unknown environments | |
| Wang et al. | A new model-free trajectory tracking control for robot manipulators | |
| Al-hadithy et al. | Two-Link Robot Through Strong and Stable Adaptive Sliding Mode Controller | |
| CN117484499B (en) | SCARA robot for tracking robust track of mechanical arm | |
| Lin et al. | On a new CMAC control scheme, and its comparisons with the PID controllers | |
| Wang et al. | Variable Impedance Force Tracking with a Collaborative Joint Based on Second-Order Momentum Observer Under Uncertain Environment | |
| Qin et al. | Friction compensation control of space manipulator considering the effects of gravity | |
| Song et al. | LQR Optimal Control Method Based on Two-Degree-of Freedom Manipulator | |
| Lai et al. | Intelligent Control of Underactuated Mechanical System |
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 | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |