CN116834008A - Different-layer motion control method of redundancy mechanical arm - Google Patents
Different-layer motion control method of redundancy mechanical arm Download PDFInfo
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- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
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- B25J9/00—Programme-controlled manipulators
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- B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
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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
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Abstract
The application discloses a method for controlling the movement of different layers of a redundant mechanical arm, which comprises the following steps: collecting motion data of a redundant mechanical arm; configuring different layer motion schemes of discrete time; acquiring error functions defined by the first moment and the second moment respectively for the joint angle layer, and giving out the equality relation of the error functions of the two adjacent moments; based on the concept of Taylor expansion, the error function of the joint angle layer at the first moment is Taylor expanded at the second moment, and the equation relation of the joint velocity layer at the second moment is obtained; and based on the equation relation of the joint speed layer at the second moment and the equation relation of the joint speed layer in different layer motion schemes, obtaining the discrete time recurrent neural network algorithm for different layer motion control of the redundancy mechanical arm. The application improves the motion instantaneity of the redundant mechanical arm, realizes joint fault tolerance and direction retention of the end effector, and can be widely applied to the technical field of mechanical arm control.
Description
Technical Field
The application relates to the technical field of mechanical arm control, in particular to a method for controlling movement of different layers of a redundant mechanical arm.
Background
The redundancy mechanical arm is widely applied to the fields of industrial production, medical treatment, military, aerospace and the like, can finish tasks with high repeatability, high precision requirement and high risk, and improves production efficiency and safety. With the development of artificial intelligence and machine learning technologies, the application field of the mechanical arm is also expanding continuously, and the mechanical arm becomes an important component of the intelligent manufacturing and service robot in the future.
Motion control of redundant robotic arms typically uses a quadratic programming solver to calculate optimal joint angles, but this approach has some drawbacks, such as high computational complexity, large amounts of memory space required, possible local optimal solutions, etc. In addition, when a certain joint of the mechanical arm is damaged or the direction of the end effector remains unchanged, the mechanical arm may not well complete the tracking task during the movement.
Disclosure of Invention
In view of this, the embodiment of the application provides a method for controlling the movement of different layers of a redundant manipulator, so as to realize the movement control of different layers of the redundant manipulator, improve the movement instantaneity of the redundant manipulator, and realize joint fault tolerance and direction retention of an end effector.
An aspect of an embodiment of the present application provides a method for controlling motion of different layers of a redundant manipulator, including:
collecting motion data of a redundant mechanical arm, wherein the motion data comprise a rod length, an initial joint angle and an expected path;
configuring different layer motion schemes of discrete time;
acquiring error functions defined by adjacent first time and second time respectively for the joint angle layer, and giving out an equality relation of the error functions of the two adjacent time; wherein the first time is a time next to the second time;
based on the concept of Taylor expansion, performing Taylor expansion on the error function of the joint angle layer at the first moment at the second moment to obtain the equation relation of the joint velocity layer at the second moment;
based on the equation relation of the joint speed layer at the second moment and the equation relation of the joint speed layer in different layer motion schemes, applying an Euler forward difference formula to obtain the discrete time recurrent neural network algorithm for controlling different layer motions of the redundancy mechanical arm.
Optionally, in the step of configuring different layer motion schemes of discrete time, the expression of the motion scheme is:
wherein r is actual,k+1 Is the actual position vector of the end effector; r is (r) desired,k+1 Is the desired path for the end effector; a is that k+1 Is a full-line matrix;is the joint velocity vector of the mechanical arm; k is an update index; τ is the sampling interval; t is t final A final time point of the whole calculation time interval; θ k+1 Is the joint angle vector of the mechanical arm; b k+1 Is a vector.
Optionally, the acquiring the error function defined by the adjacent first time and second time respectively for the joint angle layer includes:
defining a first error function for the joint angle layer at a first moment, wherein the expression of the first error function is as follows:
e k+1 ＝f(θ k+1 ,t k+1 )＝r actual,k+1 -r desired,k+1 ，
defining a second error function for the joint angle layer at a second moment, wherein the expression of the second error function is as follows:
e k ＝f(θ k ,t k )＝r actual,k -r desired,k ，
wherein e k+1 ＝(1-h)e k H is a step size parameter; r is (r) actual,k+1 Is the actual position vector of the end effector; r is (r) desired,k+1 Is the desired path for the end effector; θ k+1 Is the joint angle vector of the mechanical arm; t is t k+1 Representing a first moment; t is t k Representing the second moment.
Optionally, based on the concept of taylor expansion, the step of performing taylor expansion on the error function of the joint angle layer at the first moment to obtain the equation relationship of the joint velocity layer at the second moment includes the following expression:
the expression of the equation relation of the joint velocity layer at the second moment is:
wherein O (τ) 2 ) Is a truncation error;J(θ k ) Is a jacobian matrix of the mechanical arm,is the time derivative of the desired path of the end effector.
Optionally, based on the equation relation of the joint speed layer at the second moment and the equation relation of the joint speed layer in the different layer motion schemes, applying an euler forward difference formula to obtain a discrete time recurrent neural network algorithm for different layer motion control of the redundant manipulator, including:
the equality relation of the joint speed layer and the equality relation of the joint speed layer are combined to obtain a combined result;
according to the simultaneous result, applying Euler forward difference formula to design discrete time recurrent neural network algorithm;
and controlling the motions of different layers of the redundancy mechanical arm according to a discrete time recurrent neural network algorithm.
Optionally, the expression of the simultaneous result is:
the expression of the discrete time recurrent neural network algorithm is as follows:
the expression of the Euler forward difference formula is as follows:
wherein τ is the sampling interval; j (theta) k ) Is a jacobian matrix of the mechanical arm; a is that k Is a full-line matrix;is the joint velocity vector of the mechanical arm; />Time derivative of the desired path for the end effector; h is a step size parameter; />Is the pseudo-inverse operator of the matrix.
Another aspect of the embodiments of the present application further provides a device for controlling movement of different layers of a redundant manipulator, including:
the first module is used for collecting motion data of the redundant manipulator, wherein the motion data comprise a rod length, an initial joint angle and an expected path;
a second module for configuring different layer motion schemes of discrete time;
the third module is used for acquiring error functions defined by adjacent first time and second time respectively for the joint angle layer and giving out an equality relation of the error functions of the two adjacent times; wherein the first time is a time next to the second time;
a fourth module, configured to perform taylor expansion on the error function of the joint angle layer at the first moment at the second moment based on the concept of taylor expansion, so as to obtain an equality relationship of the joint velocity layer at the second moment;
and a fifth module, configured to apply an euler forward difference formula based on the equality relation of the joint velocity layer at the second moment and the equality relation of the joint velocity layer in different layer motion schemes, and obtain a discrete time recurrent neural network algorithm for different layer motion control of the redundancy mechanical arm.
Another aspect of the embodiment of the application also provides an electronic device, which includes a processor and a memory;
the memory is used for storing programs;
the processor executes the program to implement the method as described above.
Another aspect of the embodiments of the present application also provides a computer-readable storage medium storing a program that is executed by a processor to implement a method as described above.
Embodiments of the present application also disclose a computer program product or computer program comprising computer instructions stored in a computer readable storage medium. The computer instructions may be read from a computer-readable storage medium by a processor of a computer device, and executed by the processor, to cause the computer device to perform the foregoing method.
The method comprises the steps that firstly, motion data of a redundant mechanical arm are collected, wherein the motion data comprise a rod length, an initial joint angle and an expected path; then configuring different layer motion schemes of discrete time; then, obtaining error functions defined by adjacent first time and second time respectively for the joint angle layer, and giving out the equality relation of the error functions of the two adjacent time; wherein the first time is a time next to the second time; finally, based on the concept of Taylor expansion, performing Taylor expansion on the error function of the joint angle layer at the first moment at the second moment to obtain the equation relation of the joint velocity layer at the second moment; and based on the equation relation of the joint speed layer at the second moment and the equation relation of the joint speed layer in different layer motion schemes, applying an Euler forward difference formula to obtain the discrete time recurrent neural network algorithm for controlling different layer motions of the redundant manipulator. The application can realize different layers of motion control of the redundant mechanical arm, improves the motion instantaneity of the redundant mechanical arm, and realizes joint fault tolerance and direction retention of the end effector.
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In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for the description of the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present application, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flowchart illustrating the overall steps of an embodiment of the present application;
FIG. 2 is a schematic diagram of a simplified model of a redundant manipulator of the present application;
FIG. 3 is a schematic diagram of an actual motion trajectory of a redundant manipulator of the present application;
FIG. 4 is a schematic diagram of the actual trajectory and desired path of the redundant manipulator end effector of the present application;
FIG. 5 is a schematic view of the joint angle of the present application;
FIG. 6 is a schematic representation of the sum of all joint angles of the present application;
FIG. 7 is a schematic diagram of the calculated tracking error of the redundant manipulator in the X-axis direction and the Y-axis direction.
Detailed Description
The present application will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present application more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the application.
In order to solve the problems in the prior art, an aspect of an embodiment of the present application provides a method for controlling motion of different layers of a redundant manipulator, including:
collecting motion data of a redundant mechanical arm, wherein the motion data comprise a rod length, an initial joint angle and an expected path;
configuring different layer motion schemes of discrete time;
acquiring error functions defined by adjacent first time and second time respectively for the joint angle layer, and giving out an equality relation of the error functions of the two adjacent time; wherein the first time is a time next to the second time;
based on the concept of Taylor expansion, performing Taylor expansion on the error function of the joint angle layer at the first moment at the second moment to obtain the equation relation of the joint velocity layer at the second moment;
based on the equation relation of the joint speed layer at the second moment and the equation relation of the joint speed layer in different layer motion schemes, applying an Euler forward difference formula to obtain the discrete time recurrent neural network algorithm for controlling different layer motions of the redundancy mechanical arm.
Optionally, in the step of configuring different layer motion schemes of discrete time, the expression of the motion scheme is:
wherein r is actual,k+1 Is the actual position vector of the end effector; r is (r) desired,k+1 Is the desired path for the end effector; a is that k+1 Is a full-line matrix;is the joint velocity vector of the mechanical arm; k is an update index; τ is the sampling interval; t is t final A final time point of the whole calculation time interval; θ k+1 Is the joint angle vector of the mechanical arm; b k+1 Is a vector.
Optionally, the acquiring the error function defined by the adjacent first time and second time respectively for the joint angle layer includes:
defining a first error function for the joint angle layer at a first moment, wherein the expression of the first error function is as follows:
e k+1 ＝f(θ k+1 ,t k+1 )＝r actual,k+1 -r desired,k+1 ，
defining a second error function for the joint angle layer at a second moment, wherein the expression of the second error function is as follows:
e k ＝f(θ k ,t k )＝r actual,k -r desired,k ，
wherein e k+1 ＝(1-h)e k H is a step size parameter; r is (r) actual,k+1 Is the actual position vector of the end effector; r is (r) desired,k+1 Is the desired path for the end effector; θ k+1 Is the joint angle vector of the mechanical arm; t is t k+1 Representing a first moment; t is t k Representing the second moment.
Optionally, based on the concept of taylor expansion, the step of performing taylor expansion on the error function of the joint angle layer at the first moment to obtain the equation relationship of the joint velocity layer at the second moment includes the following expression:
wherein O (τ) 2 ) Is a truncation error;J(θ k ) Is a jacobian matrix of the mechanical arm, +.>Time derivative of the desired path for the end effector;
the expression of the equation relation of the joint velocity layer at the second moment is:
wherein O (τ) 2 ) Is a truncation error;J(θ k ) Is a jacobian matrix of the mechanical arm, +.>Is the time derivative of the desired path of the end effector.
Optionally, based on the equation relation of the joint speed layer at the second moment and the equation relation of the joint speed layer in the different layer motion schemes, applying an euler forward difference formula to obtain a discrete time recurrent neural network algorithm for different layer motion control of the redundant manipulator, including:
the equality relation of the joint speed layer and the equality relation of the joint speed layer are combined to obtain a combined result;
according to the simultaneous result, applying Euler forward difference formula to design discrete time recurrent neural network algorithm;
and controlling the motions of different layers of the redundancy mechanical arm according to a discrete time recurrent neural network algorithm.
Optionally, the expression of the simultaneous result is:
the expression of the discrete time recurrent neural network algorithm is as follows:
the expression of the Euler forward difference formula is as follows:
wherein τ is the sampling interval; j (theta) k ) Is a jacobian matrix of the mechanical arm; a is that k Is a full-line matrix;is the joint velocity vector of the mechanical arm; />Time derivative of the desired path for the end effector; h is a step size parameter; />Is the pseudo-inverse operator of the matrix.
Another aspect of the embodiments of the present application further provides a device for controlling movement of different layers of a redundant manipulator, including:
the first module is used for collecting motion data of the redundant manipulator, wherein the motion data comprise a rod length, an initial joint angle and an expected path;
a second module for configuring different layer motion schemes of discrete time;
the third module is used for acquiring error functions defined by adjacent first time and second time respectively for the joint angle layer and giving out an equality relation of the error functions of the two adjacent times; wherein the first time is a time next to the second time;
a fourth module, configured to perform taylor expansion on the error function of the joint angle layer at the first moment at the second moment based on the concept of taylor expansion, so as to obtain an equality relationship of the joint velocity layer at the second moment;
and a fifth module, configured to apply an euler forward difference formula based on the equality relation of the joint velocity layer at the second moment and the equality relation of the joint velocity layer in different layer motion schemes, and obtain a discrete time recurrent neural network algorithm for different layer motion control of the redundancy mechanical arm.
Another aspect of the embodiment of the application also provides an electronic device, which includes a processor and a memory;
the memory is used for storing programs;
the processor executes the program to implement the method as described above.
Another aspect of the embodiments of the present application also provides a computer-readable storage medium storing a program that is executed by a processor to implement a method as described above.
Embodiments of the present application also disclose a computer program product or computer program comprising computer instructions stored in a computer readable storage medium. The computer instructions may be read from a computer-readable storage medium by a processor of a computer device, and executed by the processor, to cause the computer device to perform the foregoing method.
The following describes the specific implementation of the present application in detail with reference to the drawings of the specification:
referring to fig. 1, a flow chart of a method for controlling movement of different layers of a redundant manipulator according to an embodiment of the present application is shown.
As an example, the method for controlling the movement of the different layers of the redundant manipulator may include:
s1, acquiring motion data of a redundant mechanical arm, wherein the motion data comprise a rod length, an initial joint angle, an expected path and the like;
s2, designing different discrete time layer motion schemes;
s3, at t k+1 Time sum t k Defining error functions for the joint angle layers at the moment respectively, and giving out the equation relation of the two error functions;
s4, based on the concept of Taylor expansion, t is calculated k+1 The error function of the joint angle layer at time is t k Taylor expansion is carried out at the moment, and then t is obtained k Equation relation of moment joint velocity layer;
s5, based on the t k Equation relation of moment joint velocity layer and equation relation of joint velocity layer in different layer motion schemesAnd applying an Euler forward difference formula, and finally designing and developing a discrete time recurrent neural network algorithm for controlling the motions of different layers of the redundancy mechanical arm.
Wherein at t k+1 ＝(k+1)τ∈[0,t final ]At the moment, the discrete time different layer motion schemes in the step S2 are as follows:
where k is the update index, τ is the sampling interval, t final θ is the final point in time of the entire calculation time interval k+1 Is the joint angle vector of the mechanical arm,is the joint velocity vector of the mechanical arm, r actual,k+1 Is the actual position vector of the end effector, r desired,k+1 For the desired path of the end effector, A k+1 Is a full rank matrix, b k+1 Is a vector. Obviously, the two sets of equations are different layers, the first set of equations being related to the joint angle layer and the second set of equations being related to the joint velocity layer.
Wherein in the step S3, at t k+1 Defining error function e for joint angle layer at time k+1 ＝f(θ k+1 ,t k+1 )＝r actual,k+1 -r desired,k+1 At t k Defining error function e for joint angle layer at time k ＝f(θ k ,t k )＝r actual,k -r desired,k And gives the equality of these two error functions, namely: e, e k+1 ＝(1-h)e k Where h is the step size parameter.
Optionally, in the step S4, based on the concept of taylor expansion, t is set k+1 Error function e of the joint angle layer at time k+1 At t k Taylor expansion is carried out at the moment to obtain
O (τ) in the above formula 2 ) Is a truncation error. In addition, in the case of the optical fiber,wherein J (θ) k ) Is a jacobian matrix of the mechanical arm, +.>Is the time derivative of the desired path of the end effector. Will e k+1 ＝(1-h)e k Substituting the above formula to obtain t k The equality relationship of the moment joint velocity layer is as follows:
optionally, in the step S5, the equation relation and t based on the joint velocity layer in the step S4 k The equality relation of the joint velocity layer in the step S2 at the moment is obtained simultaneously
Applying Euler forward difference formulaAnd finally, developing a discrete time recurrent neural network algorithm:
wherein, the liquid crystal display device comprises a liquid crystal display device,is the pseudo-inverse operator of the matrix.
Referring to fig. 2, a schematic diagram of a simplified model of a redundant manipulator of the present application is shown.
In the simulation experiment, the following correlation settings were used: the expected path of the redundant manipulator end effector is set to be a heart shape, and the expressions are as follows:
wherein, E is 1 Sum epsilon 2 Is a parameter related to the initial position of the desired path; setting the task execution time to be t=t final -0 = 30s; sampling interval τ=0.001 s; step size parameter h=0.1; the initial joint angle of the redundant manipulator is theta 0 ＝[π/6,-π/4,π/6,-π/3] T rad; each rod of the mechanical arm is 1m long; a is that k ＝[0,1,0,0；1,1,1,1]；b k ＝[0；0]I.e. A k And b k Remain unchanged at any one time.
Referring to fig. 3, the actual motion profile of the redundant manipulator is shown, wherein the end effector performs the task of tracking a heart-shaped path.
Referring to fig. 4, the actual trajectory and desired path of the redundant robotic end effector is shown, where the solid line is the actual tracking trajectory of the end effector and the dashed line is the desired path. Referring to fig. 3, after a period of time, the actual trajectory almost coincides with the expected path.
Referring to fig. 5, a variation of the joint angle of the redundant manipulator is shown, wherein the second joint angle remains substantially unchanged, i.e. the second joint angle is limited during the movement, indicating that the developed discrete time recurrent neural network algorithm has a certain joint fault tolerance capability.
Referring to fig. 6, the variation of the sum of all joint angles of the redundant manipulator is shown, and it can be seen that the sum of all joint angles remains substantially unchanged, indicating that the developed discrete time recurrent neural network algorithm can realize the directional control of the end effector.
Referring to FIG. 7, the tracking error of the redundant manipulator in the X-axis and Y-axis directions is shown, and the maximum stability in both directions can be seenThe state tracking error is all 10 -5 m, the tracking accuracy is high as a whole.
In summary, the design method of the application is simple and effective, improves the motion real-time performance of the redundant mechanical arm, and realizes joint fault tolerance and direction retention of the end effector.
In some alternative embodiments, the functions/acts noted in the block diagrams may occur out of the order noted in the operational illustrations. For example, two blocks shown in succession may in fact be executed substantially concurrently or the blocks may sometimes be executed in the reverse order, depending upon the functionality/acts involved. Furthermore, the embodiments presented and described in the flowcharts of the present application are provided by way of example in order to provide a more thorough understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is changed, and in which sub-operations described as part of a larger operation are performed independently.
Furthermore, while the application is described in the context of functional modules, it should be appreciated that, unless otherwise indicated, one or more of the described functions and/or features may be integrated in a single physical device and/or software module or one or more functions and/or features may be implemented in separate physical devices or software modules. It will also be appreciated that a detailed discussion of the actual implementation of each module is not necessary to an understanding of the present application. Rather, the actual implementation of the various functional modules in the apparatus disclosed herein will be apparent to those skilled in the art from consideration of their attributes, functions and internal relationships. Accordingly, one of ordinary skill in the art can implement the application as set forth in the claims without undue experimentation. It is also to be understood that the specific concepts disclosed are merely illustrative and are not intended to be limiting upon the scope of the application, which is to be defined in the appended claims and their full scope of equivalents.
The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present application. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
Logic and/or steps represented in the flowcharts or otherwise described herein, e.g., a ordered listing of executable instructions for implementing logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For the purposes of this description, a "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device.
More specific examples (a non-exhaustive list) of the computer-readable medium would include the following: an electrical connection (electronic device) having one or more wires, a portable computer diskette (magnetic device), a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). In addition, the computer readable medium may even be paper or other suitable medium on which the program is printed, as the program may be electronically captured, via, for instance, optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner, if necessary, and then stored in a computer memory.
It is to be understood that portions of the present application may be implemented in hardware, software, firmware, or a combination thereof. In the above-described embodiments, the various steps or methods may be implemented in software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, may be implemented using any one or combination of the following techniques, as is well known in the art: discrete logic circuits having logic gates for implementing logic functions on data signals, application specific integrated circuits having suitable combinational logic gates, programmable Gate Arrays (PGAs), field Programmable Gate Arrays (FPGAs), and the like.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present application. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the present application have been shown and described, it will be understood by those of ordinary skill in the art that: many changes, modifications, substitutions and variations may be made to the embodiments without departing from the spirit and principles of the application, the scope of which is defined by the claims and their equivalents.
While the preferred embodiment of the present application has been described in detail, the present application is not limited to the embodiments described above, and those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present application, and these equivalent modifications or substitutions are included in the scope of the present application as defined in the appended claims.
Claims (10)
1. The method for controlling the movement of different layers of the redundant mechanical arm is characterized by comprising the following steps of:
collecting motion data of a redundant mechanical arm, wherein the motion data comprise a rod length, an initial joint angle and an expected path;
configuring different layer motion schemes of discrete time;
acquiring error functions defined by adjacent first time and second time respectively for the joint angle layer, and giving out an equality relation of the error functions of the two adjacent time; wherein the first time is a time next to the second time;
based on the concept of Taylor expansion, performing Taylor expansion on the error function of the joint angle layer at the first moment at the second moment to obtain the equation relation of the joint velocity layer at the second moment;
based on the equation relation of the joint speed layer at the second moment and the equation relation of the joint speed layer in different layer motion schemes, applying an Euler forward difference formula to obtain the discrete time recurrent neural network algorithm for controlling different layer motions of the redundancy mechanical arm.
2. The method for controlling motion of different layers of a redundant manipulator according to claim 1, wherein in the step of configuring a discrete-time different layer motion scheme, an expression of the motion scheme is:
wherein r is actual,k+1 Is the actual position vector of the end effector; r is (r) desired,k+1 Is the desired path for the end effector; a is that k+1 Is a full-line matrix;is the joint velocity vector of the mechanical arm; k is moreA new index; τ is the sampling interval; t is t final A final time point of the whole calculation time interval; θ k+1 Is the joint angle vector of the mechanical arm; b k+1 Is a vector.
3. The method for controlling motion of different layers of a redundant manipulator according to claim 2, wherein said obtaining error functions defined by adjacent first and second moments for the joint angle layers, respectively, comprises:
defining a first error function for the joint angle layer at a first moment, wherein the expression of the first error function is as follows:
e k+1 ＝f(θ k+1 ,t k+1 )＝r actual,k+1 -r desired,k+1 ，
defining a second error function for the joint angle layer at a second moment, wherein the expression of the second error function is as follows:
e k ＝f(θ k ,t k )＝r actual,k -r desired,k ，
wherein e k+1 ＝(1-h)e k H is a step size parameter; r is (r) actual,k+1 Is the actual position vector of the end effector; r is (r) desired,k+1 Is the desired path for the end effector; θ k+1 Is the joint angle vector of the mechanical arm; t is t k+1 Representing a first moment; t is t k Representing the second moment.
4. The method for controlling different layer motions of a redundant manipulator according to claim 3, wherein, based on the concept of taylor expansion, the error function of the joint angle layer at the first moment is taylor expanded at the second moment, and the expression of taylor expansion is as follows:
the expression of the equation relation of the joint velocity layer at the second moment is:
wherein O (τ) 2 ) Is a truncation error;J(θ k ) Is a jacobian matrix of the mechanical arm, +.>Is the time derivative of the desired path of the end effector.
5. The method for controlling different layer motions of a redundant manipulator according to claim 4, wherein the applying the euler forward difference formula to derive the discrete time recurrent neural network algorithm for controlling different layer motions of the redundant manipulator based on the equality relation of the joint velocity layer at the second moment and the equality relation of the joint velocity layer in different layer motion schemes comprises:
the equality relation of the joint speed layer and the equality relation of the joint speed layer are combined to obtain a combined result;
according to the simultaneous result, applying Euler forward difference formula to design discrete time recurrent neural network algorithm;
and controlling the motions of different layers of the redundancy mechanical arm according to a discrete time recurrent neural network algorithm.
6. The method of claim 5, wherein,
the expression of the simultaneous result is:
the expression of the discrete time recurrent neural network algorithm is as follows:
the expression of the Euler forward difference formula is as follows:
wherein τ is the sampling interval; j (theta) k ) Is a jacobian matrix of the mechanical arm; a is that k Is a full-line matrix;is the joint velocity vector of the mechanical arm; />Time derivative of the desired path for the end effector; h is a step size parameter; />Is the pseudo-inverse operator of the matrix.
7. A device for controlling movement of different layers of a redundant manipulator, comprising:
the first module is used for collecting motion data of the redundant manipulator, wherein the motion data comprise a rod length, an initial joint angle and an expected path;
a second module for configuring different layer motion schemes of discrete time;
the third module is used for acquiring error functions defined by adjacent first time and second time respectively for the joint angle layer and giving out an equality relation of the error functions of the two adjacent times; wherein the first time is a time next to the second time;
a fourth module, configured to perform taylor expansion on the error function of the joint angle layer at the first moment at the second moment based on the concept of taylor expansion, so as to obtain an equality relationship of the joint velocity layer at the second moment;
and a fifth module, configured to apply an euler forward difference formula based on the equality relation of the joint velocity layer at the second moment and the equality relation of the joint velocity layer in different layer motion schemes, and obtain a discrete time recurrent neural network algorithm for different layer motion control of the redundancy mechanical arm.
8. An electronic device comprising a processor and a memory;
the memory is used for storing programs;
the processor executing the program implements the method of any one of claims 1 to 6.
9. A computer-readable storage medium, characterized in that the storage medium stores a program that is executed by a processor to implement the method of any one of claims 1 to 6.
10. A computer program product comprising a computer program which, when executed by a processor, implements the method of any one of claims 1 to 6.
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