Method and system for motion planning of redundant parallel manipulator based on quadratic programming and zeroing neural network, and robot

Abstract

The application discloses a kind of redundant parallel manipulator motion planning method, system and robot based on quadratic programming and zero neural network, comprising the following steps: planning joint limited redundant parallel manipulator end effector expected motion trajectory;According to specific parallel manipulator, establish its corresponding quadratic programming control scheme;By solving the first order optimal condition of quadratic programming problem, the constraint optimization problem is converted into nonlinear equations;Nonlinear complement problem function is used to process the first order optimal condition of step three;Error monitoring function is constructed and zero neural network solver is designed;The results obtained are sent to lower computer, and parallel manipulator motion is driven.The application compared with other methods, neural network parameter is less and calculation time is reduced, solving precision is high, without training and iterative calculation, and joint limit avoidance function can be realized, guarantee the safety of parallel manipulator and the high-precision positioning of its end effector.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of robots, in particular to a redundant parallel manipulator motion planning method, system and robot based on quadratic programming and zeroing neural network. BACKGROUND

[0002] Parallel manipulator is an advanced robot technology, widely used in industrial and medical fields. Its unique design makes it have the characteristics of high precision, high stability and high efficiency. Parallel manipulator is composed of a mobile platform, a fixed platform, an end effector and linear drive joints connecting the two platforms, forming a multi-loop closed structure. This structure enables the parallel manipulator to achieve fast, accurate and flexible motion.

[0003] During task execution, the degree of freedom of parallel manipulator is a key factor. When the required degree of freedom is less than its available degree of freedom, this robot becomes a kinematically redundant parallel robot. This brings challenges to the motion control of the robot, but also provides opportunities for optimization and performance improvement. Analyzing the redundancy is one of the core problems of solving kinematically redundant manipulators, which needs in-depth research and discussion.

[0004] Since each joint of the robot has its own limit, once this joint limit is exceeded, it may cause task failure or damage to the robot. In order to effectively handle the joint constraints of redundant robots, it is crucial to solve the inverse kinematics problem. We can transform this problem into a constrained optimization problem, such as a quadratic programming problem, and use neural networks with distributed and parallel computing capabilities to solve it. There are currently a variety of neural network solvers available to solve such problems, including Dynamic Neural Network (DNN) solvers, Gradient-based Neural Network (GNN) solvers, ZNN solvers, and numerical algorithms. Among them, ZNN solvers perform well in solving time-varying optimization problems, with high precision, no need for training, and iterative operations.

[0005] By further studying the redundancy and optimization problems of parallel manipulators, we can further improve the performance and efficiency of robots, providing stronger technical support for the widespread application of industrial and medical fields. SUMMARY

[0006] The main purpose of the present application is to overcome the shortcomings and deficiencies of the prior art, and to provide a redundant parallel manipulator motion planning method, system and robot based on quadratic programming and zeroing neural network. The present application can handle the kinematic control problem of joint-limited redundant parallel manipulators and ensure the safety of the robot during task execution.

[0007] To achieve the above object, the present application adopts the following technical solutions:

[0008] In the first aspect, the present application provides a redundant parallel manipulator motion planning method based on quadratic programming and zero neural network, comprising the following steps:

[0009] Step one, planning the expected motion trajectory of the joint-limited redundant parallel manipulator end effector, i.e. the ideal velocity of the parallel manipulator end effector Setting;

[0010] Step two, establishing the corresponding quadratic programming control scheme according to the specific parallel manipulator; first, the performance index is designed as The equality constraint is And And the double-end constraint is q - ≤q≤q + And Wherein Indicates the velocity of the end effector, W1 and W2 indicate the weighting matrix, q and Respectively represent the length of the driving joint and the length change rate, q - And q + Respectively represent the upper and lower limits of the driving joint length, And Respectively represent the upper and lower limits of the driving joint length change rate, J represents the Jacobian matrix, and K is a constant matrix; Then, the two double-end constraints on the driving joint length and its length change rate are arranged into one double-end constraint Finally, by introducing the matrix W=W1+J T W2J∈R 6×6 And Z=J, the quadratic programming problem with general form is uniformly represented, wherein the performance index is The equality constraint is The double-end constraint is

[0011] Step three, based on the first-order optimization condition, the double-end constraint in the quadratic programming problem is processed, and the constraint optimization problem is converted into a nonlinear equation set; first, the double-end constraint is rewritten by introducing the decision variable y∈R 6 ; Then, by solving the first-order optimal condition of the quadratic programming problem, the original problem is converted into a nonlinear equation set;

[0012] Step four, using the nonlinear complementarity problem function to process the first-order optimal condition of step three, based on the nonlinear complementarity problem NCP function The nonlinear equation set is further converted into g(t,x)=0, wherein

[0013] Step five, constructing error monitoring function and designing ZNN solver; first, define error monitoring function e(t): = g(t,x); second, in order to make error convergence, use evolution rule Wherein, a is convergence parameter, and represents activation function array, derive a new ZNN solver; finally, the optimal solution of constrained optimization problem is obtained by ZNN solver, and the length change rate of parallel manipulator driving joint is obtained

[0014] Step six, the results obtained in step five Or its integral q is sent to the lower computer, and the parallel manipulator is driven to move, thereby completing the expected motion trajectory.

[0015] As a preferred technical scheme, in step one, in the velocity layer kinematics equation of the parallel manipulator, the optimization performance index And considering the upper and lower limit constraints of the driving joint length and its change rate, the constrained optimization control scheme of the redundant parallel manipulator is established;

[0016] After equivalent arrangement, it is mathematically characterized as a quadratic programming problem with a general form, wherein the performance index is The equality constraint is And the double-end constraint is

[0017] As a preferred technical scheme, in step three, by introducing decision variable y∈R 6 , the double-end constraint can be rewritten as Wherein Is a convex set and satisfies

[0018] As a preferred technical scheme, in step three, the first-order optimal condition is:

[0019]

[0020] Wherein Represents the convex set The normal cone of point y.

[0021] As a preferred technical scheme, according to the first-order optimal condition, and using the definition of the normal cone, the condition Is further transformed into:

[0022]

[0023] Wherein And

[0024] ​As a preferred technical solution, in step five, the NCP function is differentiable everywhere.

[0025] As a preferred technical solution, in step five, a novel ZNN solver is derived, which is expressed as follows: Among them are:

[0026]

[0027] Where a1=vy, a2=yu, b1=ω + b2=ω-, D1=Λ(a1. / ζ1), D2=Λ(b1. / ζ1), D3=Λ(a2. / ζ2), D4=Λ(b2. / ζ2), D5=sign(b1).*ω, D6=sign(b2).*ω; where the symbol “.*” represents the element-wise multiplication of two vectors, the symbol “. / ” represents the element-wise division of two vectors, the symbol “sign” represents the sign function, that is, taking the sign of a given number, and Λ represents taking the diagonal matrix of the vectors.

[0028] Secondly, the present invention provides a redundant parallel manipulator motion planning system based on quadratic programming and null neural network, which is applied to the redundant parallel manipulator motion planning method based on quadratic programming and null neural network, including a first planning module, a second planning module, an optimization module, a transformation module, a ZNN construction module and a solution module;

[0029] The first planning module is used to plan the expected motion trajectory of the end effector of the joint-constrained redundant parallel robotic arm, that is, the ideal speed of the end effector of the parallel robotic arm. The settings;

[0030] The second planning module is used to establish a corresponding secondary planning control scheme based on the specific parallel robotic arm; firstly, the design performance indicators are as follows: The equality constraint is and And the two-ended constraint is q - ≤q≤q + and in The speed of the end effector is represented by W1 and W2, which represent the weighting matrices, and q and q represents the length of the driving joint and the rate of change of length, respectively. - and q + These represent the upper and lower limits of the drive joint length, respectively. and respectively represent the upper and lower limits of the driving joint length variation rate, J represents a Jacobian matrix, and K is a constant matrix; then, the two double-end constraints on the driving joint length and the length variation rate thereof are arranged into one double-end constraint through an equivalent transformation method Finally, the matrix W=W1+J T W2J∈R 6×6 and Z=J are introduced to uniformly represent a quadratic programming problem in a general form, wherein a performance index is the equality constraint is the double-end constraint is

[0031] The optimization module is used for processing the double-end constraint in the quadratic programming problem based on a first-order optimization condition, and converting the constraint optimization problem into a nonlinear equation set; first, a decision variable y∈R 6 is introduced to rewrite the double-end constraint; then, the first-order optimal condition of the quadratic programming problem is solved to convert the original problem into a nonlinear equation set;

[0032] The conversion module is used for processing the first-order optimal condition of step three by using a nonlinear complementary problem function, and solving the nonlinear equation set based on a nonlinear complementary problem NCP function g(t,x)=0, wherein

[0033] The ZNN construction module is used for constructing an error monitoring function and designing a ZNN solver; first, an error monitoring function e(t):=g(t,x) is defined; second, in order to make the error converge, an evolution rule is used wherein alpha is a convergence parameter, and Phi(·) represents an activation function array, a new ZNN solver is derived; finally, the optimal solution of the constraint optimization problem is solved by the ZNN solver, and the length variation rate of the driving joint of the parallel manipulator is obtained

[0034] The solving module is used for sending the result obtained in step five or an integral q thereof to a lower computer to drive the parallel manipulator to move, and to complete the expected motion trajectory.

[0035] In a third aspect, the present application provides a computer readable storage medium, which stores a program, and the program is executed by a processor to realize the motion planning method of the redundant parallel manipulator based on the quadratic programming and the zeroization neural network.

[0036] In a fourth aspect, the present application provides a robot, which comprises:

[0037] at least one processor; and

[0038] A memory in communication connection with the at least one processor; wherein

[0039] The memory stores computer program instructions executable by the at least one processor, and the computer program instructions are executed by the at least one processor to enable the at least one processor to execute the redundant parallel manipulator motion planning method based on quadratic programming and zeroing neural network.

[0040] Compared with the prior art, the present application has the following advantages and beneficial effects:

[0041] The present application can effectively overcome the deficiencies in the prior art. Prior to this, the ZNN solver proposed in the prior art needs to convert the double-end constraint into an inequality constraint first when processing the double-end constraint, and then introduces twice the Lagrange multiplier in the process of converting into an inequality equation set using the KKT condition, resulting in an increase in the dimension of the coefficient matrix to be processed, thereby making the neural network more complex. To solve this deficiency, the present application considers using the first-order optimality condition and using the NCP function to process the double-end constraint in the quadratic programming problem, and combines the evolution rule and the activation function to obtain a brand-new ZNN solver. The ZNN solver can obtain the solution of the nonlinear equation set and the optimal solution of the quadratic programming problem with double-end constraints. Compared with other solvers such as DNN and GNN, the ZNN solver only needs one iteration at each time step, is easy to operate, does not need to be trained, and can be used in some applications with strong real-time performance. In addition, the present application can select a suitable activation function to make the method have good noise resistance. Finally, by introducing the first-order optimality condition to process the double-end constraint, the parameters of the neural network are reduced, thereby making the method have lower computational complexity and better real-time performance. The present application provides a motion planning scheme for a joint-limited parallel manipulator, which is easy to operate, does not need to be trained and iteratively calculated, has a standard operation, and is joint-limited. BRIEF DESCRIPTION OF DRAWINGS

[0042] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0043] Figure 1 The flowchart of the redundant parallel manipulator motion planning method based on quadratic programming and zeroing neural network of the embodiment of the present application.

[0044] Figure 2 The model diagram of the simulation Stewart parallel manipulator of the embodiment of the present application.

[0045] Figure 3 A trajectory error plot for a simulated Stewart parallel manipulator arm embodiment of the present application.

[0046] Figure 4 A trajectory error plot for a simulated Stewart parallel manipulator arm embodiment of the present application.

[0047] Figure 5 A drive joint length change plot for a simulated Stewart parallel manipulator arm embodiment of the present application.

[0048] Figure 6 A drive joint length change rate plot for a simulated Stewart parallel manipulator arm embodiment of the present application.

[0049] Figure 7 A solution time change plot for a simulated Stewart parallel manipulator arm embodiment of the present application.

[0050] Figure 8 A structure schematic diagram of a redundant parallel manipulator motion planning system based on quadratic programming and zeroization neural network of an embodiment of the present application.

[0051] Figure 9 A structure schematic diagram of a robot of an embodiment of the present application. DETAILED DESCRIPTION

[0052] In order to enable persons skilled in the art to better understand the scheme of the present application, the technical solutions of the present application will be described clearly and completely in combination with the embodiments in the present application and the drawings. It should be understood that the drawings are only used for illustrative description and cannot be understood as a limitation on the present patent. Obviously, the described embodiments are only some of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0053] In the present application, the phrase "embodiment" means that the specific features, structures or characteristics described in combination with the embodiment can be included in at least one embodiment of the present application. The appearance of this phrase in various places in the specification does not necessarily mean the same embodiment, nor is it an independent or alternative embodiment to other embodiments. Those skilled in the art explicitly and implicitly understand that the embodiments described in the present application can be combined with other embodiments.

[0054] EMBODIMENT

[0055] As shown in Figure 1 the present embodiment is a redundant parallel manipulator motion planning method based on quadratic programming and zeroization neural network, which comprises the following steps:

[0056] Step one, plan the expected trajectory of the end-effector of the redundant parallel manipulator with joint limits, i.e. the ideal velocity of the end-effector of the parallel manipulator .

[0057] Step two, establish the corresponding quadratic programming control scheme according to the specific parallel manipulator, as follows:

[0058] First, the performance index is designed as The equality constraints are and and the double-end constraints are q - ≤q≤q + and wherein represents the velocity of the end-effector, W1 and W2 represent the weighting matrices, q and represent the length of the driving joint and the rate of length change, respectively, q - and q + represent the upper and lower limits of the length of the driving joint, and represent the upper and lower limits of the rate of length change of the driving joint, J represents the Jacobian matrix, and K is a constant matrix;

[0059] Then, the two double-end constraints on the length of the driving joint and the rate of length change thereof are arranged into one double-end constraint Finally, by introducing the matrix W = W1 + J T W2J∈R 6×6 and Z = J, the quadratic programming problem with a general form is uniformly represented, wherein the performance index is the equality constraint is and the double-end constraint is

[0060] Step three, by solving the first-order optimal condition of the quadratic programming problem, the constraint optimization problem is converted into a nonlinear equation set, as follows:

[0061] First, by introducing the decision variable y∈R 6 , the double-end constraint can be rewritten as wherein is a convex set and satisfies

[0062] Secondly, the following first-order optimal condition is obtained for the above quadratic programming problem:

[0063]

[0064] wherein, λ∈R 3 and ω∈R 6respectively, are equality constraints and the Lagrange multipliers of denote the normal cone of the convex set at the point y.

[0065] Then, according to the definition of the normal cone, the condition can be further transformed into

[0066]

[0067] where and

[0068] Step four, process the first-order optimal condition of step three using the nonlinear complementarity problem function, as follows:

[0069] First, based on the definition of the nonlinear complementarity problem NCP function the constraint condition obtained in step three can be converted to

[0070]

[0071]

[0072] Then, introduce the nonlinear complementarity function convert the above expression to the equality form ψ(a, b) = 0; and further convert the nonlinear equation set to g(t, x) = 0, where and g(t, x) are:

[0073]

[0074] Step five, construct the error monitoring function and design the ZNN solver. First, define the error monitoring function e(t): = g(t, x); second, to make the error converge, use the evolution rule where α is the convergence parameter, Φ(·) represents the activation function array, and a new ZNN solver is derived:

[0075]

[0076]

[0077] where a1 = v - y, a2 = y - u, b1 = ω + , b2 = ω -, D1 = Λ(a1. / ζ1), D2 = A(b1. / z1), D3 = A(a2. / z2), D4 = A(b2. / z2), D5 = sign(b1).*w, D6 = sign(b2).*w. The symbol ".*" represents the multiplication operation of corresponding elements of two vectors, the symbol " / ." represents the division operation of corresponding elements of two vectors, the symbol "sign" represents the sign function, that is, taking the sign of a given number, and A represents taking the diagonal matrix of a vector. Finally, the optimal solution of the constrained optimization problem is obtained by solving the ZNN solver, and the length change rate of the driving joint of the parallel manipulator is obtained

[0078] Step six, the result obtained in step five or its integral q is sent to the lower computer to drive the parallel manipulator to move, thereby completing the expected motion trajectory.

[0079] As Figure 2 shown, the model of the parallel manipulator is composed of a static platform 8, a moving platform 7, an end effector 9, a first driving rod 1, a second driving rod 2, a third driving rod 3, a fourth driving rod 4, a fifth driving rod 5, and a sixth driving rod 6. The velocity layer kinematics relationship of the parallel manipulator is wherein represents the velocity of the end effector, and the Jacobian matrix J is specifically:

[0080]

[0081] As Figure 3 shown, the solid line is the actual trajectory of the end effector of the simulated Stewart parallel manipulator, and the dashed line is the target trajectory of the end effector of the simulated Stewart parallel manipulator. It can be seen from the figure that the target trajectory and the actual trajectory almost completely coincide, indicating that the method can achieve high-precision control of the motion of the manipulator.

[0082] As Figure 4 shown, wherein the solid line e x represents the error of the end effector of the simulated Stewart parallel manipulator in the X direction, the dotted line e y represents the error of the end effector of the simulated Stewart parallel manipulator in the Y direction, and the dashed line e z represents the error of the end effector of the simulated Stewart parallel manipulator in the Z direction. During the task execution, the errors in the three directions are all less than or equal to 6x10 -4 meters, with a sub-millimeter level of high positioning accuracy.

[0083] As Figure 5are shown in the figure, wherein q1, q2, q3, q4, q5, q6 respectively represent the lengths of the first driving rod 1, the second driving rod 2, the third driving rod 3, the fourth driving rod 4, the fifth driving rod 5 and the sixth driving rod 6 of the simulated Stewart parallel mechanism. During the execution of the task, the lengths of the respective driving rods are constantly changing, and various different motions of the mechanical arm occur.

[0084] As shown in the figure, Figure 6 wherein, respectively represent the length change rates of the first driving rod 1, the second driving rod 2, the third driving rod 3, the fourth driving rod 4, the fifth driving rod 5 and the sixth driving rod 6 of the simulated Stewart parallel mechanism. As can be seen from the figure, during the execution of the task, the length change rates of the respective driving rods can be ensured to change within a certain range, thereby illustrating the effectiveness of the application for the handling of double-end constraints and joint limit avoidance in the quadratic programming problem.

[0085] As shown in the figure, Figure 7 the solving time reaches the millisecond level, thereby illustrating the high real-time performance of the application for solving the quadratic programming problem.

[0086] As shown in the figure, Figure 8 in another embodiment of the present application, a redundant parallel manipulator motion planning system 100 based on quadratic programming and zeroization neural network is provided, which is applied to the redundant parallel manipulator motion planning method based on quadratic programming and zeroization neural network, and includes a first planning module 101, a second planning module 102, an optimization module 103, a conversion module 104, a ZNN construction module 105 and a solving module 106.

[0087] The first planning module 101 is used for planning the expected motion trajectory of the joint-limited redundant parallel manipulator end effector, i.e. the setting of the ideal velocity of the parallel manipulator end effector .

[0088] The second planning module 102 is used for establishing the corresponding quadratic programming control scheme according to the specific parallel manipulator; first, the performance index is designed as the equality constraint is and and the double-end constraint is q - ≤q≤q + and wherein represents the velocity of the end effector, W1 and W2 represent the weighting matrix, q and respectively represent the driving joint length and the length change rate, q - and q + respectively represent the upper and lower limits of the driving joint length, and Let J and K represent the upper and lower limits of the rate of change of the driving joint length, respectively; J represents the Jacobian matrix; and K is a constant matrix. Then, the two double-ended constraints on the driving joint length and its rate of change are transformed into a single double-ended constraint using an equivalent transformation method. Finally, by introducing the matrix W = W1 + J T W2J∈R 6×6 And Z = J is uniformly represented as a quadratic programming problem with a general form, where the performance index is The equality constraint is Two-ended constraints are

[0089] The optimization module 103 is used to process the double-ended constraints in the quadratic programming problem based on the first-order optimization conditions, transforming the constrained optimization problem into a system of nonlinear equations; firstly, by introducing the decision variable y∈R 6 The double-ended constraints are rewritten; then, by obtaining the first-order optimal conditions of the quadratic programming problem, the original problem is transformed into a system of nonlinear equations.

[0090] The transformation module 104 is used to process the first-order optimal conditions in step three using a nonlinear complementarity problem function, based on the nonlinear complementarity problem NCP function. The nonlinear equation system is further transformed into g(t,x)=0, where

[0091] The ZNN construction module 105 is used to construct the error monitoring function and design the ZNN solver. First, the error monitoring function e(t) := g(t,x) is defined. Second, to ensure error convergence, an evolutionary rule is used. Where α is the convergence parameter and Φ(·) represents the activation function array, a novel ZNN solver is derived. Finally, the optimal solution to the constrained optimization problem is obtained through the ZNN solver, thereby obtaining the length change rate of the parallel robotic arm's drive joint.

[0092] The solution module 106 is used to process the results obtained in step five. The integral q is sent to the lower-level machine to drive the parallel robotic arm to move, thereby completing the expected motion trajectory.

[0093] It should be noted that the redundant parallel manipulator motion planning system based on quadratic programming and zeroization neural network of the present application corresponds to the redundant parallel manipulator motion planning method based on quadratic programming and zeroization neural network of the present application, the technical features and advantages described in the above embodiment of the redundant parallel manipulator motion planning method based on quadratic programming and zeroization neural network are applicable to the embodiment of the redundant parallel manipulator motion planning method based on quadratic programming and zeroization neural network, and the specific content can be referred to the description in the method embodiment of the present application, which will not be described here again, and hereby declared.

[0094] In addition, in the embodiment of the redundant parallel manipulator motion planning system based on quadratic programming and zeroization neural network of the above embodiment, the logical division of each program module is only illustrative, and in actual application, the above function allocation can be completed by different program modules according to needs, for example, considering the configuration requirements of the corresponding hardware or the convenience of software implementation, that is, the internal structure of the redundant parallel manipulator motion planning system based on quadratic programming and zeroization neural network is divided into different program modules to complete all or part of the functions described above.

[0095] As shown in Figure 9 In one embodiment, a robot 200 is provided, which can include a first processor 201, a first memory 202 and a bus, and can further include a computer program stored in the first memory 202 and executable on the first processor 201, such as a redundant parallel manipulator motion planning program based on quadratic programming and zeroization neural network 203.

[0096] The first memory 202 includes at least one type of readable storage medium, including flash memory, mobile hard disk, multimedia card, card-type memory (such as SD or DX memory, etc.), magnetic memory, disk, optical disk, etc. The first memory 202 can be an internal storage unit of the robot 200 in some embodiments, for example, a mobile hard disk of the robot 200. The first memory 202 can also be an external storage device of the robot 200 in other embodiments, for example, a plug-in mobile hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, etc. equipped on the robot 200. Further, the first memory 202 can include both the internal storage unit and the external storage device of the robot 200. The first memory 202 can be used not only to store application software and various data installed on the robot 200, such as the code of the redundant parallel manipulator motion planning program based on quadratic programming and zeroization neural network 203, but also to temporarily store data that has been output or will be output.

[0097] The first processor 201 may, in some embodiments, be composed of integrated circuits, for example, may be composed of a single packaged integrated circuit, or may be composed of multiple packaged integrated circuits of the same function or different functions, including one or more central processing units (CPUs), microprocessors, digital processing chips, graphics processors, and combinations of various control chips, etc. The first processor 201 is the control unit of the electronic device, which connects various components of the entire electronic device through various interfaces and lines, and executes various functions of the robot 200 and processes data by running or executing programs or modules stored in the first memory 202 and calling data stored in the first memory 202.

[0098] Figure 9 Only the robot with components is shown, and those skilled in the art can understand that, Figure 9 The structure shown does not constitute a limitation on the robot 200, and can include fewer or more components than shown, or combine certain components, or different component arrangements.

[0099] The second storage 202 in the robot 200 stores a redundant parallel manipulator motion planning program 203 based on quadratic programming and zeroization neural network, which is a combination of multiple instructions and can realize:

[0100] Step one, planning the expected motion trajectory of the joint-limited redundant parallel manipulator end effector, i.e., setting the ideal velocity of the parallel manipulator end effector ;

[0101] Step two, establish the corresponding quadratic programming control scheme according to the specific parallel manipulator; first, design the performance index as The equality constraint is and and the double-end constraint is q - ≤q≤q + and Where represents the velocity of the end effector, W1 and W2 represent the weighting matrix, q and respectively represent the length of the driving joint and the rate of change of the length, - and q + respectively represent the upper and lower limits of the length of the driving joint, and respectively represent the upper and lower limits of the driving joint length variation rate, J represents the Jacobian matrix, and K is a constant matrix; then, the two double-end constraints on the driving joint length and its length variation rate are arranged into one double-end constraint through an equivalent transformation method Finally, the matrix W = W1 + J T W2J ∈ R 6×6 and Z = J are introduced to uniformly represent a quadratic programming problem with a general form, where the performance index is The equality constraint is The double-end constraint is

[0102] Step three, process the double-end constraint in the quadratic programming problem based on the first-order optimization condition, and convert the constraint optimization problem into a nonlinear equation set; first, the decision variable y ∈ R 6 is introduced to rewrite the double-end constraint; then, the first-order optimal condition of the quadratic programming problem is obtained to convert the original problem into a nonlinear equation set;

[0103] Step four, process the first-order optimal condition of step three using a nonlinear complementarity problem function, based on the nonlinear complementarity problem NCP function The nonlinear equation set is further converted into g(t, x) = 0, where

[0104] Step five, construct an error monitoring function and design a ZNN solver; first, define the error monitoring function e(t): = g(t, x); second, to make the error converge, use the evolution rule where α is a convergence parameter, and Φ(·) represents an activation function array, and a new ZNN solver is derived; finally, the optimal solution of the constraint optimization problem is obtained by solving the ZNN solver, and the length variation rate of the driving joint of the parallel manipulator is obtained

[0105] Step six, send the results obtained in step five or the integral q to the lower computer to drive the parallel manipulator to move, and thus complete the expected motion trajectory.

[0106] Further, the modules / units integrated by the robot 200, if realized in the form of a software function unit and sold or used as an independent product, can be stored in a nonvolatile computer readable storage medium. The computer readable medium can include any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM, Read-Only Memory).

[0107] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by a computer program instructing relevant hardware. The program can be stored in a non-volatile computer readable storage medium, and when executed, can include the processes of the above-mentioned embodiment methods. Any reference to memory, storage, database or other medium used in the embodiments provided by the present application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. As an illustration but not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0108] Any combination of the technical features of the above embodiments can be made. In order to make the description simple, all possible combinations of the technical features in the above embodiments are not described, however, as long as the combination of the technical features does not exist, it should be considered as the scope of the present application.

[0109] The above embodiments are the preferred embodiments of the present application, but the embodiments of the present application are not limited to the above embodiments, and any changes, modifications, substitutions, combinations and simplifications made without departing from the spirit and principles of the present application shall be equivalent replacement methods and shall be within the scope of protection of the present application.

Claims

1. A redundant parallel manipulator motion planning method based on quadratic programming and zeroing neural network, characterized in that, comprising the following steps: Step one, planning the expected motion trajectory of the joint-limited redundant parallel manipulator end effector, that is, the ideal velocity of the parallel manipulator end effector setting; Step two, establish the corresponding quadratic programming control scheme for each parallel manipulator according to the specific parallel manipulator; first, design the performance index as The equality constraint is and and the double-end constraint is q - ≤q≤q + and wherein represents the velocity of the end effector, W1 and W2 represent the weighting matrix, q and respectively represent the driving joint length and the length change rate, q - and q + respectively represent the upper and lower limits of the driving joint length, and respectively represent the upper and lower limits of the driving joint length change rate, J represents the Jacobian matrix, and K is a constant matrix; then, the two double-end constraints on the driving joint length and the length change rate thereof are arranged into one double-end constraint through an equivalent transformation method Finally, the matrix W=W1+J T W2J∈R 6×6 is introduced again, and Z=J is uniformly represented as a quadratic programming problem with a general form, wherein the performance index is the equality constraint is and the double-end constraint is Step three, based on the first order optimization condition to deal with the double end constraints in the quadratic programming problem, the constraint optimization problem is converted into a nonlinear equation system; first, by introducing the decision variable y e R 6 , the double end constraint is rewritten; then, by obtaining the first order optimal condition of the quadratic programming problem, the original problem is converted into a nonlinear equation system; By introducing decision variables y ∈ R 6 The double-sided constraints are Rewrite as where is a convex set and satisfies The first-order optimality conditions are: wherein denotes a convex set The normal cone at point y, λ and ω represent Lagrange multipliers; Step four, processing the first order optimality conditions of Step three using a nonlinear complementarity problem function, based on the nonlinear complementarity problem NCP function The nonlinear system of equations is further transformed into g(t,x) = 0, where Step five, constructing error monitor function and designing ZNN solver; first, define error monitor function e(t):=g(t,x); second, to make error convergence, use evolution law where α is convergence parameter, Φ(·) represents activation function array, derive a new ZNN solver; finally, solve the optimal solution of constrained optimization problem through ZNN solver, and then obtain the length change rate of parallel manipulator driving joint Step six, send the result of step five to the lower computer, drive the parallel robot to move, and then complete the expected trajectory. or its integral q to the lower computer, drive the parallel robot to move, and then complete the expected trajectory.

2. The redundant parallel manipulator motion planning method based on quadratic programming and null-space neural network according to claim 1, wherein, According to the first order optimality condition, and using the definition of the normal cone, the condition is further transformed into: wherein and 3. The method of claim 1, wherein, In step five, the NCP function is everywhere differentiable.

4. The method of claim 2, wherein, In step five, a new ZNN solver is derived, which is denoted as wherein: wherein a1 = v - y, a2 = y - u, b1 = ω + , b2 = ω - , D2 = Λ(b1. / ζ1), D3 = Λ(a2. / ζ2), D4 = Λ(b2. / ζ2), D5 = sign(b1).*ω, D6 = sign(b2).*ω; where the symbol ".*" represents the multiplication of corresponding elements of two vectors, the symbol " / " represents the division of corresponding elements of two vectors, the symbol "sign" represents the sign function, i.e., taking the sign of a given number, and Λ represents taking the diagonal matrix of a vector.

5. A redundant parallel manipulator motion planning system based on quadratic programming and zeroing neural network, characterized in that, The redundant parallel manipulator motion planning method based on quadratic programming and zero neural network according to any one of claims 1-4 comprises a first planning module, a second planning module, an optimization module, a transformation module, a ZNN construction module, and a solving module. The first planning module is configured to plan an expected motion trajectory of the joint-limited redundant parallel manipulator end effector, i.e., to set an ideal velocity of the parallel manipulator end effector . The second programming module is configured to establish a corresponding quadratic programming control scheme for each parallel robot according to the specific parallel robot; first, a performance index is designed as An equation constraint is and and a double-end constraint is q - ≤q≤q + and wherein represents the velocity of an end effector, W1 and W2 represent weighting matrices, q and respectively represent the length of a driving joint and the length change rate, q - and q + respectively represent the upper and lower limits of the length of the driving joint, and respectively represent the upper and lower limits of the length change rate of the driving joint, J represents a Jacobian matrix, and K is a constant matrix; then, the two double-end constraints on the length of the driving joint and the length change rate thereof are arranged into one double-end constraint by an equivalent conversion method Finally, the matrix W = W1 + J T W2J∈R 6×6 and Z = J are introduced to uniformly represent a quadratic programming problem with a general form, wherein the performance index is the equation constraint is and the double-end constraint is The optimization module is used for processing the double-end constraint in the quadratic programming problem based on the first-order optimization condition, converting the constraint optimization problem into a nonlinear equation set; first, the double-end constraint is rewritten by introducing a decision variable y∈R 6 ; then, the original problem is converted into a nonlinear equation set by obtaining the first-order optimal condition of the quadratic programming problem; the transformation module is configured to process the first order optimality conditions of step three using a nonlinear complementarity problem function based on a nonlinear complementarity problem NCP function the nonlinear equations are further transformed into g(t,x) = 0, where The ZNN construction module is configured to construct an error monitoring function and design a ZNN solver; first, an error monitoring function e(t):=g(t,x) is defined; second, in order to make the error converge, an evolution rule is used Wherein, α is a convergence parameter, and Φ(·) represents an activation function array, a new ZNN solver is derived; finally, the optimal solution of the constrained optimization problem is obtained by solving the ZNN solver, and the length change rate of the driving joint of the parallel manipulator is obtained The solution module is used to process the results obtained in step five. The integral q is sent to the lower-level machine to drive the parallel robotic arm to move, thereby completing the expected motion trajectory.

6. A computer-readable storage medium storing a program, characterized in that, The program is executed by the processor to implement the redundant parallel manipulator motion planning method based on quadratic programming and zero neural network according to any one of claims 1-4.

7. A robot, characterized in that The robot comprises: at least one processor; and a memory connected to the at least one processor in communication; wherein The memory stores computer program instructions executable by the at least one processor, and the computer program instructions are executed by the at least one processor to enable the at least one processor to perform the redundant parallel manipulator motion planning method based on quadratic programming and zero neural network according to any one of claims 1-4. The robot comprises: at least one processor; and a memory connected to the at least one processor in communication; wherein The memory stores computer program instructions executable by the at least one processor, and the computer program instructions are executed by the at least one processor to enable the at least one processor to perform the redundant parallel manipulator motion planning method based on quadratic programming and zero neural network according to any one of claims 1-4.

Images