Trajectory planning and optimization control methods for redundant robotic arms

Abstract

This invention discloses a trajectory planning and optimization control method for a redundant robotic arm. The method includes the following steps: Step 1, designing the desired motion trajectory of the robotic arm's end effector; Step 2, establishing a trajectory planning and optimization control scheme based on a specific robotic arm model; Step 3, transforming the constrained optimization problem into an equivalent system of linear equations based on the Cartesian-Kuhn-Tucker (KKT) conditions; Step 4, constructing an error function using the linear equations obtained in Step 3, and designing a nullable neural network solver capable of handling unknown noise and achieving fixed-time convergence based on a new activation function, thereby obtaining the optimal solution to the constrained optimization problem; Step 5, sending the joint angles or joint velocities obtained in Step 4 to a lower-level computer to drive the robotic arm's end effector to move along the designed desired trajectory. Compared with other methods, this invention, in its new algorithm, can handle unknown noise and achieve fixed-time convergence.

Description

Technical Field

[0001] This invention relates to the field of robotics, and more specifically to a trajectory planning and optimization control method for a redundant robotic arm. Background Technology

[0002] Redundant robotic arms have wide applications in many fields. In manufacturing, they are used to automate production lines, performing complex and delicate assembly tasks. In aerospace, redundant robotic arms are used in space exploration missions, performing tasks in extreme environments. In the medical field, redundant robotic arms also play an important role. They are used for surgical assistance and rehabilitation therapy, improving surgical precision and rehabilitation outcomes. In practical applications, quadratic programming can be used to perform inverse kinematics analysis of the robotic arm at the velocity level, and this analysis can be incorporated as a constraint into the quadratic programming problem.

[0003] During task execution by the end effector, despite careful path planning, various noise factors in the real world, such as rounding errors and measurement errors, can cause deviations between the actual path and the planned path, thus affecting the accuracy of task execution. Therefore, improving the accuracy of path planning in noisy environments is an urgent problem to be solved.

[0004] With the increasing capabilities of distributed and parallel processing, neural networks have gradually become a core computational tool for solving inverse kinematics analytical problems. In particular, nullable neural network solvers, with their advantages of high accuracy, no training required, and no iterative computation, are widely used in time-varying optimization problems. However, there is currently a lack of nullable neural network solvers on the market that can simultaneously handle unknown noise, ensure fixed-time convergence, and maintain high solution accuracy. In view of this, this invention proposes a novel nullable neural network solver capable of handling unknown noise and achieving fixed-time convergence for solving quadratic programming problems. The method of this invention not only effectively handles unknown noise and ensures fixed-time convergence but also guarantees high-precision solution performance. Summary of the Invention

[0005] The main objective of this invention is to overcome the shortcomings and deficiencies of the prior art and provide a trajectory planning and optimization control method for redundant robotic arms. This invention has high solution accuracy, can effectively handle unknown noise, and has fixed-time convergence characteristics.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] In a first aspect, the present invention provides a trajectory planning and optimization control method for a redundant robotic arm, comprising the following steps:

[0008] Step 1: Design the desired motion trajectory of the robotic arm's end effector;

[0009] Step 2: Based on the specific robotic arm, establish its corresponding trajectory planning and optimization control scheme, and design a quadratic programming problem to minimize the performance index. The equality constraint is Where A(t) represents the weight matrix, The vector represents the rate of change of the joint angle, and b(t) represents a vector designed for a specific task. T Let J(t) denote the transpose of the matrix and vector, and let J(t) denote the Jacobian matrix of the robotic arm's end effector. This indicates the linear velocity of the end effector of the robotic arm;

[0010] Step 3: Introduce an activation function and Then, based on the KKT conditions, the constrained optimization problem is equivalently transformed into a linear system of equations g(t,y)=0; where the specific expression for each term in the activation function is defined as:

[0011]

[0012] Where f(x) and h(x) represent nonlinear mapping functions, k1, k2, k3, k4, and k5 represent positive constants, and sgn(x) represents the sign function;

[0013] Step 4: Define the error monitoring function e(t):=g(t,y)=0. This error monitoring function is derived from the left-hand side of the linear equation system obtained in Step 3, using the evolutionary rule. Where α(t) and β(t) are adaptive gain coefficients, and the specific expression for the i-th term is defined as follows:

[0014]

[0015] in, Let represent the Hadamard product, n(t) represent unknown noise, and α0, β0, and γ0 represent positive constants. A novel nullable neural network solver capable of handling unknown noise and converging in a fixed time is derived. This solver is used to obtain the optimal solution to the constrained optimization problem, thereby acquiring the angular change rate of the robotic arm's driven joints.

[0016] Step 5: The results obtained in Step 4 The drive joint angle q(t) obtained by integration is sent to the lower computer to drive the end effector of the robotic arm to move along the desired trajectory.

[0017] As a preferred technical solution, the robotic arm includes a fixed platform, an end effector, and n drive joints q1 to q2. n If n≥6, the kinematic equations of the robot arm velocity layer are as follows: in J(t) represents the Jacobian matrix of the robotic arm's end effector. This indicates the linear velocity of the end effector of the robotic arm.

[0018] As a preferred technical solution, the kinematic equations of the robotic arm velocity layer are designed to minimize performance indices. Considering the kinematic constraints of the robotic arm, a constraint optimization control scheme for the robotic arm is established.

[0019] Based on the KKT conditions, the above quadratic programming problem is equivalently transformed into a linear system of equations g(t,y)=0.

[0020] As a preferred technical solution, in step three, an error monitoring function e(t):=g(t,y) is defined, based on the evolutionary law. We obtain a novel nullable neural network solver capable of handling unknown noise and converging in fixed time:

[0021]

[0022] Among them are:

[0023]

[0024] λ(t) represents the Lagrange multiplier.

[0025] As a preferred technical solution, the nullable neural network solver can handle unknown noise such as constant noise, bounded noise, and unbounded linear noise. It has fixed-time convergence characteristics and can obtain the optimal solution of the quadratic programming problem with high precision, thereby obtaining the angular change rate of the robotic arm's driven joints. By driving the rate of change of the joint angle The drive joint angle q(t) obtained by integration is sent to the lower computer to drive the robotic arm to move according to the designed desired trajectory.

[0026] Secondly, the present invention provides a trajectory planning and optimization control method for a redundant robotic arm, which is applied to the trajectory planning and optimization control method for the redundant robotic arm. The method is characterized by including a trajectory planning module, a kinematic control scheme construction module, an equivalent transformation module, an optimization problem solving module, and a driving module.

[0027] The trajectory planning module is used to design the desired motion trajectory of the robotic arm's end effector;

[0028] The kinematic control scheme construction module is used to establish a corresponding constraint optimization control scheme for a specific robotic arm, and to design a quadratic programming problem whose minimization performance index is: The equality constraint is Where A(t) represents the weighting matrix, J(t) represents the rate of change of the drive joint angle, and J(t) represents the Jacobian matrix of the robotic arm's end effector. This indicates the linear velocity of the end effector of the robotic arm;

[0029] The equivalent transformation module is used to introduce an activation function. and Then, based on the KKT conditions, the constrained optimization problem is equivalently transformed into a linear system of equations g(t,y)=0;

[0030] The optimal solution module is used to define the error monitoring function e(t):=g(t,y)=0, and to use the evolutionary rule. Where α(t) and β(t) are adaptive gain coefficients, Let represent the Hadamard product, n(t) represent unknown noise, and α0, β0, and γ0 represent positive constants. A novel nullable neural network solver capable of handling unknown noise and converging in a fixed time is derived. This solver is used to obtain the optimal solution to the constrained optimization problem, thereby acquiring the angular change rate of the robotic arm's driven joints.

[0031] The driving module is used to process the obtained results. The drive joint angle q(t) obtained by integration is sent to the lower computer to drive the end effector of the robotic arm to move along the desired trajectory.

[0032] Thirdly, the present invention provides a computer-readable storage medium storing a program, which, when executed by a processor, implements the trajectory planning and optimization control method for the redundant robotic arm.

[0033] Fourthly, the present invention provides a redundant robotic arm, the redundant robotic arm comprising:

[0034] At least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores computer program instructions executable by the at least one processor, the computer program instructions being executed by the at least one processor to enable the at least one processor to execute the trajectory planning and optimization control method for the redundant robotic arm.

[0035] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0036] This invention effectively overcomes the shortcomings of conventional techniques. Existing nullable neural network solvers with fixed-time or predetermined-time convergence assume that the noise is known when handling noise. However, in reality, noise is random and unknown. Furthermore, although there are models of finite-time convergent nullable neural network solvers capable of handling unknown noise, the upper bound of the convergence time changes with the initial state of the system, thus affecting the system's convergence performance. Therefore, this invention proposes a fixed-time convergent nullable neural network solver capable of handling unknown noise for solving quadratic programming problems. The advantage of this solver is that it not only effectively handles unknown noise and ensures fixed-time convergence, but also guarantees high-precision solution performance. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is a flowchart of the trajectory planning and optimization control method for redundant robotic arms according to an embodiment of the present invention;

[0039] Figure 2 This is a model diagram of the simulated Franka Emika Panda robotic arm according to an embodiment of the present invention;

[0040] Figure 3 This is a simulation of the motion trajectory of the Franka Emika Panda robotic arm end effector in an embodiment of the present invention.

[0041] Figure 4 This is a diagram showing the error between the expected trajectory and the actual path of the simulated Franka Emika Panda robotic arm end effector in an embodiment of the present invention.

[0042] Figure 5 This is a diagram showing the joint angle changes of the simulated Franka Emika Panda robotic arm in an embodiment of the present invention.

[0043] Figure 6 This is a graph showing the rate of change of joint angles of the simulated Franka Emika Panda robotic arm in an embodiment of the present invention.

[0044] Figure 7 This is a schematic diagram of the system for trajectory planning and optimization control of a redundant robotic arm according to an embodiment of the present invention;

[0045] Figure 8 This is a schematic diagram of the structure of the robotic arm according to an embodiment of the present invention. Detailed Implementation

[0046] To enable those skilled in the art to better understand the present application, the technical solution of the present invention will be clearly and completely described below with reference to the embodiments and accompanying drawings. It should be understood that the accompanying drawings are for illustrative purposes only and should not be construed as limiting the present patent. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present application.

[0047] In this application, the reference to "embodiment" means that a specific feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described in this application can be combined with other embodiments.

[0048] Example

[0049] like Figure 1 As shown in the figure, this embodiment is a trajectory planning and optimization control method for a redundant robotic arm. The method includes the following steps:

[0050] Step 1: Design the desired motion trajectory of the robotic arm's end effector;

[0051] Step 2: Establish a corresponding trajectory planning and optimization control scheme for the specific robotic arm, and design a minimum performance index as follows. The equality constraint is Where A(t) represents the weight matrix, The vector represents the rate of change of the joint angle, and b(t) represents a vector designed for a specific task. T Let J(t) denote the transpose of the matrix and vector, and let J(t) denote the Jacobian matrix of the robotic arm's end effector. This indicates the linear velocity of the end effector of the robotic arm;

[0052] Step 3: Introduce an activation function and Then, based on the KKT conditions, the constrained optimization problem is equivalently transformed.

[0053] This is transformed into a linear system of equations g(t,y=0); where each term in the activation function is defined as follows:

[0054]

[0055] Where f(x) and h(x) represent nonlinear mapping functions, k1, k2, k3, k4, and k5 represent positive constants, and sgn(x) represents the sign function.

[0056] Step 4: Define the error monitoring function e(t):=g(t,y)=0. This error monitoring function is derived from the left-hand side of the linear equation system obtained in Step 3, using the evolutionary rule. Where α(t) and β(t) are adaptive gain coefficients, and the specific expression for the i-th term is defined as follows:

[0057]

[0058] in, Let represent the Hadamard product, and n(t) represent unknown noise. A novel nullable neural network solver capable of handling unknown noise and converging in a fixed time is derived. This solver is used to obtain the optimal solution to the constrained optimization problem, and thus the angular change rate of the robotic arm's driven joints is obtained.

[0059] Step 5: The results obtained in Step 4 The drive joint angle q(t) obtained by integration is sent to the lower computer to drive the end effector of the robotic arm to move along the desired trajectory.

[0060] like Figure 2 As shown, in a specific embodiment, the robotic arm includes a fixed platform, an end effector, and seven rotary joints, each composed of joints O1, ..., O7. The kinematic equations of the robotic arm's velocity layer are as follows: in J(t) represents the Jacobian matrix of the robotic arm's end effector. This indicates the linear velocity of the end effector of the robotic arm.

[0061] like Figure 3 As shown, the solid line is the expected trajectory of the end effector of the robotic arm, and the dashed line is the actual trajectory of the end effector of the robotic arm. In the process of completing the trajectory planning task, there is random noise: 0.5 + 1.5cos(2t) + ω(t), ω(t) ∈ (-2, 2). It can be seen from the figure that the actual trajectory and the expected trajectory coincide, indicating that the solver can be used to complete the trajectory planning task of redundant robotic arms.

[0062] like Figure 4 As shown, the solid line e x The line e represents the error in the X-direction between the actual trajectory and the desired trajectory of the simulated Panda robotic arm end effector. y The dashed line e represents the error in the Y-direction between the actual trajectory and the expected trajectory of the simulated Panda robot arm end effector. zThis represents the error in the Z-direction between the actual trajectory and the expected trajectory of the simulated Panda robotic arm end effector. During task execution, the absolute error in all three directions is less than or equal to 3 × 10⁻⁶. -5 Meters, with extremely high precision.

[0063] like Figure 5 As shown, q1, q2, q3, q4, q5, q6, and q7 represent the angles of the first rotary joint O1, the second rotary joint O2, the third rotary joint O3, the fourth rotary joint O4, the fifth rotary joint O5, the sixth rotary joint O6, and the seventh rotary joint O7 of the simulated Panda robotic arm, respectively. During task execution, the angles of each joint continuously change, resulting in various different movements of the robotic arm.

[0064] like Figure 6 As shown, where, These represent the angular change rates of the first rotary joint O1, second rotary joint O2, third rotary joint O3, fourth rotary joint O4, fifth rotary joint O5, sixth rotary joint O6, and seventh rotary joint O7 of the simulated Panda robotic arm. Figure 7 As can be seen, during the execution of the task, the rate of change of the angle of each joint changes within a certain range, resulting in various different movements of the robotic arm.

[0065] like Figure 7 As shown, in another embodiment of this application, a trajectory planning and optimization control system 100 for a redundant robotic arm is provided, including a module 101 for designing the desired motion trajectory of the robotic arm end effector, a kinematic control scheme construction module 102, an equivalent transformation module 103, an optimal solution module 104, and a drive module 105.

[0066] The target detection module 101 for the desired motion trajectory of the robotic arm end effector is used to plan the desired motion trajectory of the robotic arm end effector.

[0067] The kinematic control scheme construction module 102 is used to establish a corresponding constraint optimization control scheme for a specific robotic arm, and to design a performance index that is minimized. The equality constraint is Where A(t) represents the weighting matrix, The vector represents the rate of change of the joint angle, and b(t) represents a vector designed for a specific task. T Let J(t) denote the transpose of the matrix and vector, and let J(t) denote the Jacobian matrix of the robotic arm's end effector. This indicates the linear velocity of the end effector of the robotic arm;

[0068] The equivalent transformation module 103 is used to convert the constrained optimization problem into a linear system of equations g(t,y)=0 based on the KKT conditions.

[0069] The optimal solution module 104 is used to define the error monitoring function e(t):=g(t,y)=0, and to use the evolutionary rule. Where α(t) and β(t) are adaptive gain coefficients. Let represent the Hadamard product, and n(t) represent unknown noise. A novel nullable neural network solver capable of handling unknown noise and converging in a fixed time is derived. This solver is used to obtain the optimal solution to the constrained optimization problem, and thus the angular change rate of the robotic arm's driven joints is obtained.

[0070] The driving module 105 is used to process the obtained results. The data is sent to the lower-level machine, which drives the robotic arm to move along the designed trajectory.

[0071] Furthermore, in the implementation of the trajectory planning and optimization control system for the redundant robotic arm in the above embodiments, the logical division of each program module is only an example. In actual applications, the above functions can be assigned to different program modules as needed, for example, for the sake of corresponding hardware configuration requirements or the convenience of software implementation. That is, the internal structure of the trajectory planning and optimization control system for the redundant robotic arm can be divided into different program modules to complete all or part of the functions described above.

[0072] like Figure 8 As shown, in one embodiment, a redundant robotic arm 200 is provided. The redundant robotic arm 200 may include a first processor 201, a first memory 202 and a bus, and may also include a computer program stored in the first memory 202 and executable on the first processor 201, such as a trajectory planning and optimization control program 203 for the redundant robotic arm.

[0073] The first memory 202 includes at least one type of readable storage medium, including flash memory, portable hard drive, multimedia card, card-type memory (e.g., SD or DX memory), magnetic memory, magnetic disk, optical disk, etc. In some embodiments, the first memory 202 can be an internal storage unit of the robotic arm 200, such as the portable hard drive of the robotic arm 200. In other embodiments, the first memory 202 can also be an external storage device of the robotic arm 200, such as a plug-in portable hard drive, smart media card (SMC), secure digital card (SD), flash card, etc., equipped on the robotic arm 200. Furthermore, the first memory 202 can include both internal storage units and external storage devices of the robotic arm 200. The first memory 202 can be used not only to store application software and various types of data installed on the robotic arm 200, such as the code of the redundant robotic arm trajectory planning and optimization control program 203, but also to temporarily store data that has been output or will be output.

[0074] In some embodiments, the first processor 201 may be composed of integrated circuits, such as a single packaged integrated circuit or multiple integrated circuits packaged with the same or different functions, including combinations of one or more central processing units (CPUs), microprocessors, digital processing chips, graphics processors, and various control chips. The first processor 201 is the control unit of the electronic device, connecting various components of the entire electronic device through various interfaces and lines. It executes programs or modules (such as federated learning defense programs) stored in the first memory 202, and calls data stored in the first memory 202 to perform various functions of the robotic arm 200 and process data.

[0075] Figure 8 Only a robotic arm with components is shown; those skilled in the art will understand that... Figure 8 The structure shown does not constitute a limitation on the robotic arm 200, and may include fewer or more parts than shown, or combine certain parts, or have different arrangements of parts.

[0076] The trajectory planning and optimization control program 203 of the redundant robotic arm stored in the first memory 202 of the robotic arm 200 is a combination of multiple instructions. When run in the first processor 201, it can achieve the following:

[0077] Step 1: Design the desired motion trajectory of the robotic arm's end effector;

[0078] Step 2: Based on the specific robotic arm, establish its corresponding trajectory planning and optimization control scheme, and design a quadratic programming problem to minimize the performance index. The equality constraint is Where A(t) represents the weight matrix, The vector represents the rate of change of the joint angle, and b(t) represents a vector designed for a specific task. T Let J(t) denote the transpose of the matrix and vector, and let J(t) denote the Jacobian matrix of the robotic arm's end effector. This indicates the linear velocity of the end effector of the robotic arm;

[0079] Step 3: Introduce an activation function and Then, based on the KKT conditions, the constrained optimization problem is equivalently transformed into a linear system of equations g(t,y)=0; where the specific expression for each term in the activation function is defined as:

[0080]

[0081] Where f(x) and h(x) represent nonlinear mapping functions, k1, k2, k3, k4, and k5 represent positive constants, and sgn(x) represents the sign function;

[0082] Step 4: Define the error monitoring function e(t):=g(t,y)=0. This error monitoring function is derived from the left-hand side of the linear equation system obtained in Step 3, using the evolutionary rule. Where α(t) and β(t) are adaptive gain coefficients, and the specific expression for the i-th term is defined as follows:

[0083]

[0084] in, Let represent the Hadamard product, n(t) represent unknown noise, and α0, β0, and γ0 represent positive constants. A novel nullable neural network solver capable of handling unknown noise and converging in a fixed time is derived. This solver is used to obtain the optimal solution to the constrained optimization problem, thereby acquiring the angular change rate of the robotic arm's driven joints.

[0085] Step 5: The results obtained in Step 4 The drive joint angle q(t) obtained by integration is sent to the lower computer to drive the end effector of the robotic arm to move along the desired trajectory.

[0086] Furthermore, if the modules / units integrated into the robotic arm 200 are implemented as software functional units and sold or used as independent products, they can be stored in a non-volatile computer-readable storage medium. The computer-readable medium may include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, or a read-only memory (ROM).

[0087] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this 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. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM), etc.

[0088] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0089] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A trajectory planning and optimization control method for a redundant robotic arm, characterized in that, Includes the following steps: Step 1: Design the desired motion trajectory of the robotic arm's end effector; Step 2: Based on the specific robotic arm, establish its corresponding trajectory planning and optimization control scheme, and design a quadratic programming problem to minimize the performance index. The equality constraint is Where A(t) represents the weight matrix, Let represent the rate of change of the driven joint angle, b(t) represent a vector designed for a specific task, the superscript T indicates the transpose of the matrix and vector, and J(t) represent the Jacobian matrix of the robotic arm's end effector. This indicates the linear velocity of the end effector of the robotic arm; Step 3: Introduce an activation function and Then, based on the KKT conditions, the constrained optimization problem is equivalently transformed into a linear system of equations g(t,y)=0; where the specific expression for each term in the activation function is defined as: Where f(x) and h(x) represent nonlinear mapping functions, k1, k2, k3, k4, and k5 represent positive constants, and sgn(x) represents the sign function; Step 4: Define the error monitoring function e(t):=g(t,y)=0. This error monitoring function is derived from the left-hand side of the linear equation system obtained in Step 3, using the evolutionary rule. Where α(t) and β(t) are adaptive gain coefficients, and the specific expression for the i-th term is defined as follows: in, Let represent the Hadamard product, n(t) represent unknown noise, and α0, β0, and γ0 represent positive constants. A novel nullable neural network solver capable of handling unknown noise and converging in a fixed time is derived. This solver is used to obtain the optimal solution to the constrained optimization problem, thereby acquiring the angular change rate of the robotic arm's driven joints. Step 5: The results obtained in Step 4 The drive joint angle q(t) obtained by integration is sent to the lower computer to drive the end effector of the robotic arm to move according to the designed desired trajectory; In step three, the error monitoring function e(t) := g(t,y) is defined based on the evolutionary law. We obtain a novel nullable neural network solver capable of handling unknown noise and converging in fixed time: Among them are: λ(t) represents the Lagrange multiplier.

2. The trajectory planning and optimization control method for the redundant robotic arm according to claim 1, characterized in that, The robotic arm includes a fixed platform, an end effector, and n drive joints q1 to q2. n If n≥6, the kinematic equations of the robot arm velocity layer are as follows: in J(t) represents the Jacobian matrix of the robotic arm's end effector. This indicates the linear velocity of the end effector of the robotic arm.

3. The trajectory planning and optimization control method for the redundant robotic arm according to claim 2, characterized in that, In the kinematic equations of the robotic arm's velocity layer, a performance index is designed to be minimized. Considering the kinematic constraints of the robotic arm, a constraint optimization control scheme for the robotic arm is established. Based on the KKT conditions, the above quadratic programming problem is equivalently transformed into a linear system of equations g(t,y)=0.

4. The trajectory planning and optimization control method for the redundant robotic arm according to claim 1, characterized in that, The nullable neural network solver can handle unknown noise, including constant noise, bounded noise, and unbounded linear noise. It has fixed-time convergence characteristics and can obtain the optimal solution to the quadratic programming problem with high accuracy, thereby obtaining the angular change rate of the robotic arm's driven joints. By driving the rate of change of the joint angle The drive joint angle q(t) obtained by integration is sent to the lower computer to drive the robotic arm to move according to the designed desired trajectory.

5. A trajectory planning and optimization control system for a redundant robotic arm, applied to the trajectory planning and optimization control method for the redundant robotic arm according to any one of claims 1-4, characterized in that, It includes a trajectory planning module, a kinematic control scheme construction module, an equivalent transformation module, an optimization problem solving module, and a driving module; The trajectory planning module is used to design the desired motion trajectory of the robotic arm's end effector; The kinematic control scheme construction module is used to establish a corresponding constraint optimization control scheme for a specific robotic arm, and to design a quadratic programming problem whose minimization performance index is: The equality constraint is Where A(t) represents the weighting matrix, J(t) represents the rate of change of the drive joint angle, and J(t) represents the Jacobian matrix of the robotic arm's end effector. This indicates the linear velocity of the end effector of the robotic arm; The equivalent transformation module is used to introduce an activation function. and Then, based on the KKT conditions, the constrained optimization problem is equivalently transformed into a linear system of equations g(t,y)=0; The optimization problem-solving module is used to define the error monitoring function e(t):=g(t,y)=0, and to use the evolutionary rule. Where α(t) and β(t) are adaptive gain coefficients, Let represent the Hadamard product, n(t) represent unknown noise, and α0, β0, and γ0 represent positive constants. A novel nullable neural network solver capable of handling unknown noise and converging in a fixed time is derived. This solver is used to obtain the optimal solution to the constrained optimization problem, thereby acquiring the angular change rate of the robotic arm's driven joints. The driving module is used to process the obtained results. The drive joint angle q(t) obtained by integration is sent to the lower computer to drive the end effector of the robotic arm to move along the desired trajectory.

6. A computer-readable storage medium storing a program, characterized in that, When the program is executed by the processor, it implements the trajectory planning and optimization control method for the redundant robotic arm as described in any one of claims 1-4.

7. A redundant robotic arm, characterized in that, The redundant robotic arm includes: At least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores computer program instructions executable by the at least one processor, the computer program instructions being executed by the at least one processor to enable the at least one processor to perform the trajectory planning and optimization control method for a redundant robotic arm as described in any one of claims 1-4.

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