Robot motion planning method and device based on dynamic parameter return-to-zero neural network and medium

Abstract

The invention discloses a robot motion planning method and device based on a dynamic parameter return-to-zero neural network and a medium. The method comprises the steps that 1, an expected track and an expected attitude vector are set; step 2, giving an initial joint angle and an initial attitude vector; 3, reasonable physical limit constraint conditions of the redundant robot joints are set; 4, the redundant robot motion planning considering the joint physical limit constraint and the posture keeping is described as a quadratic planning scheme; and 5, providing a dynamic parameter return-to-zero neural network for the quadratic programming scheme in the step 4, and applying the dynamic parameter return-to-zero neural network to motion programming of the redundant robot. Redundant robot motion planning tasks of joint physical limit constraint and posture keeping are considered, and it can be guaranteed that model errors converge to 0 within finite time.

Description

Technical Field

[0001] The present invention relates to the field of robot motion planning, and specifically to a robot motion planning method, device and medium based on a dynamic parameter zeroing neural network. Background Technique

[0002] The redundant robot has more degrees of freedom than the degrees of freedom required by the target task, with better flexibility and wider application. However, due to the redundant characteristics, the solution of its inverse kinematics is more complex. The traditional method for solving the inverse kinematics of a robot is the pseudo-inverse method, but its calculation is time-consuming and the effect is not good. In addition, the motion planning scheme with the minimum velocity norm as the index function cannot handle the joint repeatability problem. The repeat motion index that adds a joint error feedback term on the basis of the minimum velocity norm can solve the joint angle drift phenomenon of the redundant robot. However, the above methods do not consider the problem of the end effector attitude control of the redundant robot, which is extremely disadvantageous for actual robot operation.

[0003] The present invention takes an index function for maintaining the end effector attitude of a redundant robot as the objective function, and then combines constraints such as kinematic equations and joint physical limits to transform the motion planning problem into a quadratic programming problem, and then uses the proposed recurrent neural network to solve the quadratic programming problem to obtain the redundant analytical solution of the redundant robot.

[0004] Aiming at the problem that the traditional fixed parameter zeroing neural network has a slow convergence speed, the present invention proposes a new dynamic parameter zeroing neural network method, device and medium. The introduction of dynamic parameters makes the zeroing neural network converge faster. In addition, the provided dynamic parameter zeroing neural network method has the characteristic of finite-time convergence, its dynamic parameters will not show the phenomenon of infinite parameter increase, and this method is designed by an activation function with an extreme value. Therefore, this method is more convenient for actual hardware implementation. Summary of the Invention

[0005] The present invention provides a robot motion planning method, device and medium based on a dynamic parameter zeroing neural network for the motion planning of a redundant robot with joint physical limit constraints and attitude maintenance. The invention considers an index function for maintaining the end effector attitude of a redundant robot, describes the motion planning of the redundant robot considering joint physical limit constraints as a quadratic optimization problem, simplifies the original problem into a time-varying nonlinear equation by means of a nonlinear complementary function, and then uses a dynamic parameter zeroing neural network as a solver to realize the motion planning task of the redundant robot with joint physical limit constraints that converges quickly in a finite time when the initial attitude deviates from the target attitude.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A robot motion planning method based on a dynamic parameter zeroing neural network, comprising:

[0008] Step 1, set the desired trajectory and the desired attitude vector;

[0009] Step 2, give the initial joint angles and the initial attitude vector;

[0010] Step 3, set reasonable redundant robot joint physical limit constraint conditions;

[0011] Step 4, describe the redundant robot motion planning considering joint physical limit constraints and attitude maintenance as a quadratic programming scheme;

[0012] Step 5, provide a dynamic parameter zeroing neural network for the quadratic programming scheme in Step 4, and use this dynamic parameter zeroing neural network for the motion planning of the redundant robot.

[0013] Further, the said Step 1 includes:

[0014] Preset the target end trajectory of the redundant robot end effector , where t represents time, and set the desired end effector attitude vector .

[0015] Further, the said Step 2 includes:

[0016] Give the initial joint angles of the redundant robot as , and the initial attitude vector as .

[0017] Further, the quadratic programming scheme expression in the said Step 4 is as follows:

[0018] (1)

[0019] Wherein, represents minimizing the objective function, represents the constraint conditions that the optimization formula 1 needs to satisfy; T represents the transpose matrix, θ represents the joint angle, is the joint angular velocity, ω represents the real-time attitude vector of the redundant robot end effector, , is the derivative of ω, , ω d represents the desired attitude vector of the end effector, μ ω represents the attitude adjustment parameter, , μ p represents the trajectory adjustment parameter, , represents the deviation between the real-time attitude vector and the desired attitude vector of the end effector; p dRepresents the desired trajectory, is the derivative of p d , represents the position error feedback term of the robot end effector, and its velocity equality constraint form is , respectively represent the actually calculated end effector trajectory and its derivative, and ; J ω (θ) represents the attitude Jacobian matrix, , J(θ) represents the position Jacobian matrix, , J ω (θ) and J(θ) are calculated according to the DH parameters of the redundant robot, represents the real-time trajectory of the redundant robot end effector; respectively represent the upper and lower limits of the robot joints; respectively represent the upper and lower limits of the robot joint angular velocities;

[0020] Unify the joint and joint angular velocity constraints in the quadratic programming scheme into new joint angular velocity constraints through Equation 2:

[0021] (2)

[0022] Among them, respectively represent the actual upper and lower amplitudes of the joint velocity, and , ;

[0023] In the formula, respectively represent the i-th element of; represents the joint angle and angular velocity of the i-th joint; respectively represent the upper amplitudes of the joint and joint velocity preset for the i-th joint, respectively represent the lower amplitudes of the joint and joint velocity preset for the i-th joint; and represent two upper and lower critical values of the joint velocity transformation.

[0024] Furthermore, step 5 includes:

[0025] Construct the following dynamic parameter zeroing neural network to solve the quadratic programming scheme in step 4: (3)

[0026] Among them, represents the error element E ij 's derivative, represents taking the absolute value of the variable ; represents the exponential operator with base a, Denote the variable to the power of; a, β, α are all adjustment parameters, , denotes the exponential operator with the natural constant e as the base, and sgn(·) denotes the sign function; the variable parameter is designed as , where γ is an adjustment parameter, ;

[0027] Next, analyze the finite-time convergence of the dynamic parameter zeroing neural network shown in Equation 3:

[0028] First, assume that the expression of the Lyapunov function is:

[0029] (4)

[0030] The derivative of the Lyapunov function is calculated as:

[0031]

[0032] According to Equation 4, rewrite the above equation into the following two inequalities:

[0033] (5)

[0034] where denotes the initial value of, τ(0) is the initial variable parameter, ;

[0035] Integrate both sides of the equations in the two expressions of Equation 5 to obtain the upper and lower bounds of the convergence time as:

[0036] (6)

[0037] Rewrite Equation 1 into the following form:

[0038] (7)

[0039] where is the transpose matrix of, , denotes that the dimension of the corresponding vector is , Q(t) is an intermediate variable, , denotes the transpose matrix of, M(t) is an intermediate variable, ; A(t) is an intermediate variable, indicates that the dimension of the corresponding matrix is ; b(t) is an intermediate variable, C(t) is a constant matrix, is the identity matrix, d(t) is an intermediate variable, ;

[0040] Define the Lagrangian function as:

[0041] (8)

[0042] where represents the Lagrangian function; respectively represent the Lagrange multiplier vectors of the equality constraint and inequality constraint terms, represents the transpose matrix of; According to the KKT principle, the KKT equation of Equation 7 can be given as:

[0043]

[0044] where the gradient function of the Lagrangian function, is the transpose matrix of, is a non - linear complementary function used to handle the inequality constraint term, and its expression is as follows:

[0045]

[0046] where x, z represent two arbitrary independent variables, represents a positive adjustable parameter, represents the Hadamard product operator;

[0047] According to the KKT equation, Equation 1 is finally converted into the following non - linear equation:

[0048] (9)

[0049] where W(t) is an intermediate variable, , C T (t) is the transpose matrix of C(t), Y(t) is the solution variable, , N is an intermediate variable, , ε(t) is an intermediate variable; , is an intermediate variable, ;

[0050] Define the error function E(t) by Equation 9 as:

[0051]

[0052] Substituting the error function E(t) into Equation 3, the dynamic parameter zeroing neural network model for solving Equation 1 is as follows:

[0053] (10)

[0054] where respectively represent the derivatives of;

[0055] The solution variable , The first n terms of are the calculated joint angular velocities of the redundant robot.

[0056] The present invention also provides a robot motion planning device based on a dynamic parameter zeroing neural network, including one or more processors for implementing the robot motion planning method based on a dynamic parameter zeroing neural network as described above.

[0057] The present invention also provides a readable storage medium, on which a program is stored, and when the program is executed by a processor, it implements the robot motion planning method based on a dynamic parameter zeroing neural network as described above.

[0058] Compared with the prior art, the beneficial effects of the present invention: The present invention considers the redundant robot motion planning tasks with joint physical limit constraints and attitude maintenance, and can ensure that the model error converges to 0 within a finite time. Compared with the traditional fixed parameter zeroing neural network, this method has a faster convergence speed of the zeroing neural network due to the introduction of dynamic parameters, and the accuracy of solving the redundant robot motion planning studied by this method is verified by simulation. In addition, the present invention uses an activation function with an extreme value to construct a dynamic parameter zeroing neural network, and its dynamic parameters will not exhibit the phenomenon of infinite parameter increase. Therefore, this method is more convenient for hardware implementation and is more conducive to popularization to actual engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 is a flowchart of the redundant robot motion planning scheme provided by the present invention.

[0060] Figure 2 is an error norm curve graph of the dynamic parameter zeroing neural network for solving the redundant robot motion planning under different parameter cases.

[0061] Figure 3 is a motion trajectory graph of the seven-axis redundant robot KUKA calculated by the dynamic parameter zeroing neural network.

[0062] Figure 4It is a joint angle curve graph.

[0063] Figure 5 It is a joint angular velocity curve graph.

[0064] Figure 6 It is a posture variable curve graph of the end effector.

[0065] Figure 7 It is a trajectory error curve graph of the end effector.

[0066] Figure 8 It is a dynamic parameter change curve graph of the dynamic parameter zeroing neural network.

[0067] Figure 9 It is a schematic structural diagram of a robot motion planning device based on a dynamic parameter zeroing neural network according to the present invention. Specific implementation manner

[0068] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0069] Such as Figures 1-8 , a robot motion planning method based on a dynamic parameter zeroing neural network, Figure 1 It is a flow chart of a redundant robot motion planning scheme studied by the present invention, specifically including the following steps:

[0070] Step 1, desired trajectory and posture setting

[0071] The desired trajectory is preset as a "hollow double ring" trajectory, and the time period for the end effector to complete the "hollow double ring" trajectory s; and the desired posture vector of the redundant robot is set as .

[0072] Step 2, the initial joint angles and the initial posture vector of the redundant robot KUKA are respectively given as: , .

[0073] Step 3, set the joint physical limits:

[0074] The joint limit is , ; the joint speed limit is . and ​Represent two upper and lower critical values of the joint speed transformation. Respectively represent the upper and lower limits of the angular velocity of the robot joints.

[0075] Step 4, describe the redundant robot motion planning considering joint physical limit constraints and attitude maintenance as the following quadratic programming scheme:

[0076] (1)

[0077] Among them, Represents minimizing the objective function, Represents the constraint conditions that the optimization formula 1 needs to satisfy; T represents the transpose matrix, θ represents the joint angle, Is the joint angular velocity, ω represents the real-time attitude vector of the redundant robot end effector, , Is the derivative of ω, , ω d Represents the desired attitude vector of the end effector, μ ω Represents the attitude adjustment parameter, , μ p Represents the trajectory adjustment parameter, , Represents the deviation between the real-time attitude vector and the desired attitude vector of the end effector; p d Represents the desired trajectory, Is the derivative of p d , Represents the position error feedback term of the robot end effector, and its velocity equality constraint form is , Respectively represent the actually calculated trajectory of the end effector and its derivative, and ; J ω (θ) represents the attitude Jacobian matrix, , J(θ) represents the position Jacobian matrix, , J ω (θ) and J(θ) are calculated according to the redundant robot DH parameters, Represents the real-time trajectory of the redundant robot end effector.

[0078] In particular, since the quadratic programming scheme solves the motion planning problem at the joint speed level, therefore, the following formula unifies the joint and joint angular velocity constraints in the quadratic programming scheme into new joint angular velocity constraints,

[0079] (2)

[0080] Among them, Respectively represent the actual upper and lower amplitudes of the joint speed, and

[0081]

[0082] In the formula, respectively represent the i-th element of represents the joint angle and angular velocity of the i-th joint, respectively represent the upper amplitudes of the joint and joint velocity preset for the i-th joint, respectively represent the lower amplitudes of the joint and joint velocity preset for the i-th joint; and represent two upper and lower critical values for the transformation of the joint velocity.

[0083] Step 5, construct the following dynamic parameter zeroing neural network to solve the quadratic programming scheme in Step 4:

[0084] (3)

[0085] Among them, represents the derivative of the error element E ij of represents taking the absolute value of the variable ; represents the exponential operator with base a, represents performing a power operation on the variable ; a, β, α are all adjustment parameters, , represents the exponential operator with the natural constant e as the base, sgn(·) represents the sign function; the variable parameter is designed as , γ is an adjustment parameter, ; The whole function term is used as the dynamic parameter term, and obviously it changes dynamically with the error. In particular, since the absolute value of the initial error is fixed and the error will converge to 0 within a finite time, the initial variable parameter has a fixed bounded range, that is ; Therefore, the parameters of this method will not increase infinitely; in addition, the parameter

[0086] The finite-time convergence of the dynamic parameter zeroing neural network shown in Equation 3 is analyzed as follows:

[0087] First, assume that the expression of the Lyapunov function is:

[0088] (4)

[0089] In the formula, t represents time.

[0090] Derivative of the Lyapunov function is calculated as:

[0091]

[0092] It can be observed from the above formula that when , is always satisfied; and only when , holds. Therefore, it can be determined that the dynamic parameter zeroing neural network (3) is asymptotically convergent.

[0093] Since , the above formula is written as the following two inequalities:

[0094] (5)

[0095] Among them, represents the initial value of, τ(0) is the initial variable parameter, ;

[0096] Integrating both sides of the two expressions in Equation 5, the upper and lower bounds of the convergence time can be obtained as:

[0097] (6)

[0098] Rewrite Equation 1 in the following form:

[0099] (7)

[0100] Among them, is the transpose matrix of, , represents that the dimension of the corresponding vector is , Q(t) is an intermediate variable, , represents the transpose matrix of, M(t) is an intermediate variable, , A(t) is an intermediate variable, b(t) is an intermediate variable, constant matrix is the identity matrix, intermediate variable ;

[0101] Define the Lagrangian function as follows:

[0102] (8)

[0103] where, represents the Lagrangian function; respectively represent the Lagrange multiplier vectors of the equality constraint and the inequality constraint terms, represents the transpose matrix of; According to the KKT principle, the KKT equation of Equation (7) can be given as:

[0104]

[0105] where, the gradient function of the Lagrangian function, is the transpose matrix of, is a non - linear complementary function used to handle the inequality constraint terms, and its expression is as follows:

[0106]

[0107] where, x and z represent two arbitrary independent variables, represents a positive adjustable parameter, represents the Hadamard product operator;

[0108] It can be seen that introducing can transform the inequality constraint terms into the form of an equation.

[0109] According to the KKT equation, Equation (1) is finally transformed into the following non - linear equation:

[0110] (9)

[0111] where, W(t) is an intermediate variable, , A T (t) is the transpose matrix of A(t), C T (t) is the transpose matrix of C(t), Y(t) is the solution variable, , N is an intermediate variable, , ε(t) is an intermediate variable; , is an intermediate variable, .

[0112] is the quadratic programming scheme in Solving Step 4. Define the error function E(t) by Equation (9) as:

[0113]

[0114] Substituting the error function \(E(t)\) into Equation (3), the dynamic parameter zeroing neural network model for solving Equation (1) is as follows:

[0115] (10)

[0116] Among them, respectively represent the derivatives of.

[0117] The solution variable , The first \(n\) terms of are the calculated joint angular velocities of the redundant robot.

[0118] For the motion planning problem of the KUKA redundant robot, a simulation environment of the neural network model shown in Equation (10) is built in the MATLAB software and tested, and the test results are presented in the accompanying drawings of the specification.

[0119] The relevant simulation parameters in the accompanying drawings of the specification are selected as follows: .

[0120] Figure 2 is for taking different values, the error norm curve of the dynamic parameter zeroing neural network for solving the motion planning of the redundant robot; it can be found that the larger, the smaller, the faster the error curve converges; in addition, when the larger, the smaller, the error curve will also converge faster.

[0121] Figure 3 is the motion trajectory of the seven-degree-of-freedom redundant robot KUKA calculated by the dynamic parameter zeroing neural network, which is the blue solid line curve in the figure. It quickly tracks the desired trajectory under the condition of initial deviation from the desired trajectory (the black dashed line curve in the figure).

[0122] Figure 4 is the joint angle curve, and it can be found that the joints are strictly kept within the joint limit range.

[0123] Figure 5 The joint angular velocity curves in also remain within the joint velocity limit range.

[0124] Figure 6 is the curve of the attitude vector of the end effector. Among them, respectively are the coordinates of on the x, y, and z axes. Therefore all have no units; it can be observed that the attitude of the end effector quickly reaches and remains within the vicinity of the desired attitude.

[0125] Figure 7 is the trajectory error curve of the end effector, where represents the trajectory error , with the unit of meter (m), are respectively the error components on the x, y, and z axes; it can be seen from Figure 7 that the trajectory tracking accuracy of the dynamic parameter zeroing neural network is relatively high, that is .

[0126] Figure 8 are the dynamic parameters when the dynamic parameter zeroing neural network generates the redundant robot KUKA motion trajectory changing with time (where ), and the parameters 1 - 7 in the figure are seven parameters related to the change of the joint angle , that is, the first to seventh elements of the dynamic parameter ; it can be seen that the dynamic parameters quickly decay to a small constant value as the error converges.

[0127] See Figure 9 , an embodiment of a robot motion planning device based on a dynamic parameter zeroing neural network provided by the present invention includes one or more processors for implementing a redundant robot attitude - constrained motion planning method based on a dynamic parameter zeroing neural network in the above - mentioned embodiment.

[0128] An embodiment of a robot motion planning device based on a dynamic parameter zeroing neural network provided by the present invention can be applied to any device with data - processing capabilities, and the any device with data - processing capabilities can be a device or equipment such as a computer. The device embodiment can be implemented through software, or through hardware or a combination of software and hardware. Taking software implementation as an example, as a logically - defined device, it is formed by the processor of any device with data - processing capabilities where it is located reading the corresponding computer program instructions in the non - volatile memory into the memory for operation. From the hardware level, as Figure 9 shown, it is a hardware structure diagram of any device with data - processing capabilities where a robot motion planning device based on a dynamic parameter zeroing neural network provided by the present invention is located. In addition to Figure 9 the shown processor, memory, network interface, and non - volatile memory, any device with data - processing capabilities where the device in the embodiment is located usually also includes other hardware according to the actual functions of the any device with data - processing capabilities, which will not be elaborated here.

[0129] For the specific implementation process of the functions and roles of each unit in the above - mentioned device, please refer to the implementation process of the corresponding steps in the above - mentioned method, which will not be elaborated here.

[0130] The technical features of the above-described embodiments can be combined arbitrarily. For the sake of brevity of description, 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, it should be considered to be within the scope described in this specification.

[0131] The embodiment of the present invention also provides a readable storage medium, on which a program is stored. When the program is executed by a processor, it implements a robot motion planning method based on a dynamic parameter zeroing neural network in the above embodiment.

[0132] The readable storage medium may be an internal storage unit of any device with data processing capabilities described in any of the foregoing embodiments, such as a hard disk or memory. The readable storage medium may also be an external storage device, such as a plug-in hard disk, a smart media card (SMC), an SD card, a flash card, etc. equipped on the device. Further, the readable storage medium may also include both an internal storage unit of any device with data processing capabilities and an external storage device. The readable storage medium is used to store the computer program and other programs and data required by any device with data processing capabilities, and can also be used to temporarily store data that has been output or will be output.

[0133] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A robot motion planning method based on a dynamic parameter zeroing neural network, characterized in that, Including: Step 1: Set the desired trajectory and the desired attitude vector; Step 2: Given the initial joint angles and the initial attitude vector; Step 3: Set reasonable redundant robot joint physical limit constraint conditions; Step 4: Describe the redundant robot motion planning considering joint physical limit constraints and attitude maintenance as a quadratic programming scheme; Step 5: Provide a dynamic parameter zeroing neural network for the quadratic programming scheme in Step 4, and use this dynamic parameter zeroing neural network for the motion planning of the redundant robot.

2. The robot motion planning method based on a dynamic parameter zeroing neural network according to claim 1, wherein The said Step 1 includes: Preset the target end trajectory of the redundant robot end effector , where t represents time, and set the desired end effector attitude vector .

3. A robot motion planning method based on a dynamic parameter zeroing neural network according to claim 1, characterized in that, The said Step 2 includes: The initial joint angles of the given redundant robot are , and the initial attitude vector is .

4. A robot motion planning method based on a dynamic parameter zeroing neural network according to claim 1, characterized in that The expression of the quadratic programming scheme in Step 4 is as follows: （1） Among them, represents minimizing the objective function, represents the constraint conditions that the optimization formula 1 needs to satisfy; T represents the transpose matrix, θ represents the joint angle, is the joint angular velocity, ω represents the real-time attitude vector of the redundant robot's end effector, , is the derivative of ω, , ω d represents the desired attitude vector of the end effector, μ ω represents the attitude adjustment parameter, , μ p represents the trajectory adjustment parameter, , represents the deviation between the real-time attitude vector and the desired attitude vector of the end effector; p d represents the desired trajectory, is the derivative of p d , represents the position error feedback term of the robot's end effector, and its velocity equality constraint form is , respectively represent the actually calculated trajectory of the end effector and its derivative, and ; J ω (θ) represents the attitude Jacobian matrix, , J(θ) represents the position Jacobian matrix, , J ω (θ) and J(θ) are calculated according to the DH parameters of the redundant robot, represents the real-time trajectory of the redundant robot's end effector; respectively represent the upper and lower limits of the robot joints; respectively represent the upper and lower limits of the robot joint angular velocities; Unify the joint and joint angular velocity constraints in the quadratic programming scheme into new joint angular velocity constraints through Equation 2: (2) Among them, respectively represent the actual upper and lower amplitudes of the joint velocity, and ， ； wherein, respectively represent the i-th element of the joint angle and angular velocity of the i-th joint; respectively represent the upper amplitudes of the joints and joint velocities preset for the i-th joint, respectively represent the lower amplitudes of the joints and joint velocities preset for the i-th joint; and represent two upper and lower critical values for the transformation of the joint velocity.

5. A robot motion planning method based on a dynamic parameter zeroing neural network according to claim 1, characterized in that, The said Step 5 includes: Construct the following dynamic parameter zeroing neural network to solve the quadratic programming scheme in Step 4: (3) Among them, represents the derivative of the error element E ij , represents taking the absolute value of the variable ; represents the exponential operator with base a, represents performing a power operation on the variable ; a, β, and α are all adjustment parameters, , represents the exponential operator with base e, the natural constant, and sgn(·) represents the sign function; the variable parameter is designed as , where γ is an adjustment parameter, ; Analyze the finite-time convergence of the dynamic parameter zeroing neural network shown in Equation 3 below: First, assume the Lyapunov function has the following expression: (4) Derivative of the Lyapunov function Calculated as: According to Equation 4, rewrite the above formula into the following two inequalities: (5) Among them, represents the initial value of, τ(0) is the initial variable parameter, ; Integrating both sides of the equations in the two expressions of Equation 5, the upper and lower bounds of the convergence time can be obtained are as follows: (6) Rewrite Equation 1 into the following form: (7) Among them, is the transpose matrix of, , indicates that the dimension of the corresponding vector is , Q(t) is an intermediate variable, , indicates the transpose matrix of, M(t) is an intermediate variable, ; A(t) is an intermediate variable, indicates that the dimension of the corresponding matrix is ; b(t) is an intermediate variable, C(t) is a constant matrix, is an identity matrix, d(t) is an intermediate variable, ; Define the Lagrangian function as: (8) Among them, represents the Lagrangian function; respectively represent the Lagrange multiplier vectors of the equality constraint and inequality constraint terms, represents the transpose matrix of; According to the KKT principle, the KKT equation of Equation 7 can be given as: Among them, The gradient function of the Lagrangian function, is the transpose matrix of a non-linear complementary function used to handle the inequality constraint terms, and its expression is as follows: where x and z represent two arbitrary independent variables, represents a positive adjustable parameter, represents the Hadamard product operator; According to the KKT equation, finally convert Equation 1 into the following nonlinear equation: (9) Among them, W(t) is an intermediate variable, , C T (t) is the transpose matrix of C(t), Y(t) is the solution variable, , N is an intermediate variable, , ε(t) is an intermediate variable; , is an intermediate variable, ; Define the error function E(t) by Equation 9 as: Substitute the error function E(t) into Equation 3 to obtain the dynamic parameter zeroing neural network model for solving Equation 1 as: (10) Among them, respectively represent the derivative of The solution variables are calculated by the neural network shown in Equation 10 , The first n terms of are the calculated joint angular velocities of the redundant robot .

6. A robot motion planning device based on a dynamic parameter zeroing neural network, characterized in that, Including one or more processors for implementing a robot motion planning method based on a dynamic parameter zeroing neural network according to any one of claims 1-5.

7. A readable storage medium, characterized in that, Stored thereon is a program which, when executed by the processor, implements a robot motion planning method based on a dynamic parameter zeroing neural network according to any one of claims 1-5.

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