CN116872219A - Robot control method based on U-K equation, electronic equipment and storage medium - Google Patents
Robot control method based on U-K equation, electronic equipment and storage medium Download PDFInfo
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- CN116872219A CN116872219A CN202311148664.8A CN202311148664A CN116872219A CN 116872219 A CN116872219 A CN 116872219A CN 202311148664 A CN202311148664 A CN 202311148664A CN 116872219 A CN116872219 A CN 116872219A
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Classifications
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1628—Programme controls characterised by the control loop
- B25J9/163—Programme controls characterised by the control loop learning, adaptive, model based, rule based expert control
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1602—Programme controls characterised by the control system, structure, architecture
- B25J9/1607—Calculation of inertia, jacobian matrixes and inverses
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Abstract
The application relates to a robot control method based on a U-K equation, electronic equipment and a storage medium, wherein the method comprises the following steps: carrying out forward kinematic modeling and dynamic modeling on the mechanical arm to obtain a dynamic equation; processing the dynamics equation to obtain the relation between the acceleration of the system and the external force of the system in an unconstrained state; adding system constraint to the relation between the acceleration of the system and the external force of the system in the constraint state; solving constraint force meeting system constraint through a U-K equation to obtain an accurate expression of the constraint force; and calculating an accurate motion equation of the system motion through an accurate expression of the constraint force, and realizing accurate control of a mechanical system. According to the application, the U-K controller based on the U-K equation is added in the system dynamics solving part, so that the control precision, effect and quick response of the system are improved.
Description
Technical Field
The application relates to the technical field of robot control, in particular to a robot control method based on a U-K equation, electronic equipment and a storage medium.
Background
Currently, motor control methods commonly used in the industry include PID regulator-based control, improved PID control methods, robust control, adaptive control, slip film control, and the like. The PID control is the most common control method which is applied more, and generally consists of three parts, namely a proportional part (P), an integral part (I) and a differential part (D), and the speed of the motor can be stabilized near the set speed by adjusting the parameters of the three parts. In the current research, the mechanical characteristics of the complex multi-lifting mechanism/mechanical system can be changed continuously, more, in the field of medical rehabilitation, the rehabilitation machine can be always contacted with the limb of a patient, so that the traditional control method can not adapt to changeable working conditions, and meanwhile, the working requirements of high speed and high precision cannot be ensured.
Meanwhile, as the traditional dynamic modeling of the mechanical system adopts a Lagrange dynamic modeling method based on the Darby principle, the method can simplify and idealize the related conditions and limitations of the system, thereby causing errors and affecting the accuracy of the model. In the fields of industrial production, robot control, medical rehabilitation and the like, the actual complex and changeable environmental conditions and mechanical structures can bring more uncertain factors to the traditional track tracking. Conventional dynamic modeling methods based on the darabal principle will not solve this problem when non-ideal constraints exist in the system.
Disclosure of Invention
To achieve the above objects and other advantages and in accordance with the purpose of the application, a first object of the application is to provide a robot control method based on a U-K equation, comprising the steps of:
carrying out forward kinematic modeling and dynamic modeling on the mechanical arm to obtain a dynamic equation;
processing the dynamics equation to obtain the relation between the acceleration of the system and the external force of the system in an unconstrained state;
adding system constraint to the relation between the acceleration of the system and the external force of the system in the constraint state;
solving constraint force meeting system constraint through Udwadia-Kalaba equation to obtain an accurate expression of the constraint force;
and calculating an accurate motion equation of the system motion through an accurate expression of the constraint force, and realizing accurate control of a mechanical system.
Further, the forward kinematics modeling and the dynamics modeling of the mechanical arm comprise the following steps:
forward kinematics modeling is carried out on the mechanical arm by adopting a method based on rotation algebra, liqun and Liqun;
and carrying out dynamics modeling by adopting a Lagrange dynamics method to obtain a dynamics equation.
Further, constraint equations of the system are:
；
wherein the matrixFor constraint matrix of system, < >>For acceleration vector +.>Is a constraint vector.
Further, the solving of the constraint force satisfying the system constraint through the Udwadia-Kalaba equation comprises the following steps:
for a six-degree-of-freedom mechanical arm, the expression of the kinetic equation is:
；
wherein ,for the inertia matrix of the system, < > for>For coriolis force, ->For gravity (I)>Is a system control input;
the system is constrained to:
；
the controller and control moment given based on the Udwadia-Kalaba equation are:
；
wherein ,representing the moore-Penrose inverse of the matrix.
Further, the method also comprises the following steps:
adding uncertainty parameters in a controller based on a Udwadia-Kalaba equation;
decomposing the matrix, vector and inverse containing uncertainty parameters;
a robust controller based on the Udwadia-Kalaba equation was designed.
Further, the uncertainty parameter is added in the controller based on the Udwadia-Kalaba equation, and the controller is obtained as follows:
；
wherein ,is an unknown quantity.
Further, the matrix, vector and inverse containing uncertainty parameters are decomposed to obtain:
；
wherein ,、 />、 />is a nominal part, and->，/>、/>、/>Is an uncertainty-containing part;
also included is defining the following formula:
；
。
further, the design of the robust controller based on the U-K equation comprises:
；
wherein ,
；
；
wherein ,is a scalar, is a parameter to be designed; select function->Make->；
Assuming three conditions, for any oneFull rank:
there is a functionMake all->Satisfy the following requirements；
For a given setAnd->Make->；
There is a constantMake->。
Further, the method also comprises a system stability analysis step:
selecting a legal Lyapunov function by using the selecting requirement of the Lyapunov asymptotic stability function;
analysis is carried out by combining with Lyapunov stability judgment theorem, and the robustness controller is proved to meet consistent and final bounded property, so that the control system is asymptotically stable.
A second object of the present application is to provide an electronic device including: a memory having program code stored thereon; a processor coupled with the memory and which, when the program code is executed by the processor, implements a robot control method based on U-K equations.
A third object of the present application is to provide a computer-readable storage medium having stored thereon program instructions that, when executed, implement a robot control method based on the U-K equation.
Compared with the prior art, the application has the beneficial effects that:
the application provides a robot control method based on a U-K equation, electronic equipment and a storage medium, wherein a U-K controller based on the U-K equation is added to a system dynamics solving part, so that the control precision, effect and quick response of a system are improved. Meanwhile, a U-K robust controller which can converge on the inherent uncertain factors is added; the design of the robust controller not only improves the control effect of the system, but also can keep the control effect unchanged for the mechanical system with complex changes, thereby greatly reducing the control cost of the motor when different patients use, and needing no redesign of parameters.
The foregoing description is only an overview of the present application, and is intended to provide a better understanding of the present application, as it is embodied in the following description, with reference to the preferred embodiments of the present application and the accompanying drawings. Specific embodiments of the present application are given in detail by the following examples and the accompanying drawings.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application and do not constitute a limitation on the application. In the drawings:
FIG. 1 is a flow chart of a robot control method based on the U-K equation of embodiment 1;
fig. 2 is a schematic diagram of an electronic device of embodiment 2;
fig. 3 is a schematic diagram of a storage medium of embodiment 3.
Detailed Description
The present application will be further described with reference to the accompanying drawings and detailed description, wherein it is to be understood that, on the premise of no conflict, the following embodiments or technical features may be arbitrarily combined to form new embodiments.
Example 1
The robot control method based on the U-K equation, as shown in FIG. 1, comprises the following steps:
s1, carrying out forward kinematic modeling and dynamic modeling on a mechanical arm to obtain a dynamic equation; specifically, the method comprises the following steps:
forward kinematics modeling is carried out on the mechanical arm by adopting a method based on rotation algebra, liqun and Liqun, so as to provide a mathematical foundation for subsequent track planning;
and carrying out dynamics modeling by adopting a Lagrange dynamics method to obtain a basic dynamics equation.
S2, processing the obtained dynamic equation to obtain the relation between the acceleration of the system and the external force of the system in an unconstrained state;
s3, adding system constraint to the relation between the acceleration of the system and the external force of the system in the constraint state; the constraints of the system generally originate from the mechanical structure of the system itself and from the trajectory constraints generated by trajectories that satisfy the kinematic equations. Both the ideal constraint and the non-ideal constraint of the system can be written in the form of constraint equations as follows.
The constraint equation of the system is:
；
wherein the matrixFor constraint matrix of system, < >>For acceleration vector +.>Is a constraint vector.
S4, solving constraint force meeting system constraint through a Udwadia-Kalaba equation to obtain an accurate expression of the constraint force;
s5, calculating an accurate motion equation of system motion through an accurate expression of the constraint force, and realizing accurate control of a mechanical system.
The method for solving the constraint force meeting the system constraint through the Udwadia-Kalaba equation comprises the following steps:
the main content of the Udwadia-Kalaba equation is that at any time when the constraint is satisfiedIn the system of->Individual particle +.>The vicat velocity vector is given by the equation:
。
for a six-degree-of-freedom mechanical arm, the expression of the kinetic equation is:
；
wherein ,for the inertia matrix of the system, < > for>For coriolis force, ->For gravity (I)>Is a system control input;
the system is constrained to:
；
the controller and control moment given based on the Udwadia-Kalaba equation are:
；
wherein ,the Moore-Penrose inverse of the representation matrix is a generalized inverse matrix, which is the inverse matrix for the reversible square matrix, and for a +.>The vitamin rank is->Matrix->It->Dimensional matrix and satisfies:
；
for any matrix a, its MP inverse exists and is unique, the MP inverse of the zero matrix is the zero matrix.
To account for system uncertainty, a U-K robust controller is added. The method specifically comprises the following steps:
s6, for the six-degree-of-freedom upper limb rehabilitation training mechanical arm, various uncertain factors are required to be considered when the mechanical arm is actually applied to different patients, wherein the quality and the length of the mechanical arm are changed, and uncertainty parameters are required to be added in a controller based on a Udwadia-Kalaba equation, so that the controller is obtained by the following steps:
；
；
wherein ,is an unknown quantity.
S7, considering that the system is stable at the moment, decomposing a matrix, a vector and the inverse containing uncertainty parameters to obtain:
；
wherein ,、 />、 />is a nominal part, and->，/>、/>、/>Is an uncertainty-containing part;
to facilitate the design of the controller, the following formula is specified:
；
。
s8, designing a robust controller based on a Udwadia-Kalaba equation:
；
wherein ,
；
wherein ,is a scalar, is a parameter to be designed; select function->Make->；
Assuming three conditions, for any oneFull rank:
there is a functionMake all->Satisfy the following requirements；
For a given setAnd->Make->；
There is a constantMake->。
The embodiment further includes a system stability analysis step:
s9, selecting a legal Lyapunov function by utilizing the selection requirement of the Lyapunov asymptotic stability function;
s10, analysis is carried out by combining with Lyapunov stability judgment theorem, so that the robust controller can be proved to meet consistent and final bounded properties, and the control system is asymptotically stable.
According to the application, the U-K controller based on the U-K equation is added in the system dynamics solving part, so that the control precision and effect of the system are improved, and the response is quick. And a U-K robust controller which can converge on an inherent uncertainty factor is added. The design of the robust controller not only improves the control effect of the system, but also can keep the control effect unchanged for the mechanical system with complex changes, thereby greatly reducing the control cost of the motor when different patients use, and needing no redesign of parameters.
Example 2
An electronic device 200, as shown in FIG. 2, includes, but is not limited to: a memory 201 having program codes stored thereon; a processor 202 coupled to the memory and which when executed by the processor implements a robot control method based on the U-K equation. For detailed description of the method, reference may be made to corresponding descriptions in the above method embodiments, and details are not repeated here.
Example 3
A computer readable storage medium, as shown in fig. 3, has stored thereon program instructions that when executed implement a robot control method based on the U-K equation. For detailed description of the method, reference may be made to corresponding descriptions in the above method embodiments, and details are not repeated here.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article or apparatus that comprises an element.
In this specification, each embodiment is described in a progressive manner, and identical and similar parts of each embodiment are all referred to each other, and each embodiment mainly describes differences from other embodiments.
The foregoing is illustrative of the embodiments of the present disclosure and is not to be construed as limiting the scope of the one or more embodiments of the present disclosure. Various modifications and alterations to one or more embodiments of this description will be apparent to those skilled in the art. Any modifications, equivalent substitutions, improvements, or the like, which are within the spirit and principles of one or more embodiments of the present disclosure, are intended to be included within the scope of the claims of one or more embodiments of the present disclosure.
Claims (11)
1. The robot control method based on the U-K equation is characterized by comprising the following steps of:
carrying out forward kinematic modeling and dynamic modeling on the mechanical arm to obtain a dynamic equation;
processing the dynamics equation to obtain the relation between the acceleration of the system and the external force of the system in an unconstrained state;
adding system constraint to the relation between the acceleration of the system and the external force of the system in the constraint state;
solving constraint force meeting system constraint through Udwadia-Kalaba equation to obtain an accurate expression of the constraint force;
and calculating an accurate motion equation of the system motion through an accurate expression of the constraint force, and realizing accurate control of a mechanical system.
2. The robot control method based on the U-K equation according to claim 1, wherein: the forward kinematics modeling and the dynamics modeling of the mechanical arm comprise the following steps:
forward kinematics modeling is carried out on the mechanical arm by adopting a method based on rotation algebra, liqun and Liqun;
and carrying out dynamics modeling by adopting a Lagrange dynamics method to obtain a dynamics equation.
3. The robot control method based on the U-K equation according to claim 1, wherein: the constraint equation of the system is:
；
wherein the matrixFor constraint matrix of system, < >>For acceleration vector +.>Is a constraint vector.
4. A method of controlling a robot based on the U-K equation according to claim 3, wherein: the solving of the constraint force meeting the system constraint through the Udwadia-Kalaba equation comprises the following steps:
for a six-degree-of-freedom mechanical arm, the expression of the kinetic equation is:
；
wherein ,for the inertia matrix of the system, < > for>For coriolis force, ->For gravity (I)>Is a system control input;
the system is constrained to:
；
the controller and control moment given based on the Udwadia-Kalaba equation are:
；
wherein ,representing the moore-Penrose inverse of the matrix.
5. The robot control method based on the U-K equation according to claim 4, wherein: the method also comprises the following steps:
adding uncertainty parameters in a controller based on a Udwadia-Kalaba equation;
decomposing the matrix, vector and inverse containing uncertainty parameters;
a robust controller based on the Udwadia-Kalaba equation was designed.
6. The robot control method based on the U-K equation according to claim 5, wherein: the uncertainty parameter is added into the controller based on the Udwadia-Kalaba equation, and the controller is obtained as follows:
；
wherein ,is an unknown quantity.
7. The robot control method based on the U-K equation according to claim 6, wherein: and decomposing the matrix, the vector and the inverse containing the uncertainty parameters to obtain:
；
wherein ,、 />、 />is a nominal part, and->，/>、/>、/>Is an uncertainty-containing part;
also included is defining the following formula:
；
。
8. the robot control method based on the U-K equation according to claim 7, wherein: the robust controller based on U-K equation comprises:
；
wherein ,
；
wherein ,is a scalar, is a parameter to be designed; select function->Make the following；
Assuming three conditions, for any oneFull rank:
there is a functionMake all->Satisfy the following requirements；
For a given setAnd->Make->；
There is a constantMake->。
9. The robot control method based on the U-K equation according to claim 8, wherein: the method also comprises the step of analyzing the system stability:
selecting a legal Lyapunov function by using the selecting requirement of the Lyapunov asymptotic stability function;
analysis is carried out by combining with Lyapunov stability judgment theorem, and the robustness controller is proved to meet consistent and final bounded property, so that the control system is asymptotically stable.
10. An electronic device, comprising: a memory having program code stored thereon; a processor connected to the memory and which, when executed by the processor, implements the method of any one of claims 1 to 9.
11. A computer readable storage medium, having stored thereon program instructions which, when executed, implement the method of any of claims 1-9.
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| CN117654000A (en) * | 2024-01-31 | 2024-03-08 | 中国科学院苏州生物医学工程技术研究所 | Active and passive rehabilitation training control method, system, equipment and medium for robot |
| CN118650636A (en) * | 2024-08-20 | 2024-09-17 | 中国交通信息科技集团有限公司 | Segment waterproof material pasting robot control method based on generalized U-K equation |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN117647985A (en) * | 2024-01-30 | 2024-03-05 | 中国科学院苏州生物医学工程技术研究所 | Power-assisted robot track tracking control method, system, equipment and medium |
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| CN118650636A (en) * | 2024-08-20 | 2024-09-17 | 中国交通信息科技集团有限公司 | Segment waterproof material pasting robot control method based on generalized U-K equation |
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Application publication date: 20231013 |