Robot trajectory tracking method, device and medium based on finite-time neural network

Abstract

The present invention discloses a robot trajectory tracking method, device, and medium based on a finite-time neural network. The method comprises: calculating a transformation matrix from the robot base coordinate system to the end effector coordinate system using DH parameters; deriving Cartesian position kinematic equations and setting the robot end effector posture constraint equations; setting the desired Cartesian space trajectory of the robot end effector; describing the robot posture-maintaining trajectory tracking problem as a quadratic programming strategy; designing a finite-time neural network for posture-maintaining trajectory tracking; constructing a finite-time neural network model that solves the specific dynamic parameters of the quadratic programming strategy established in step 4, and using the finite-time neural network model for robot trajectory tracking. Due to the use of dynamic parameter design, the present invention has faster finite-time convergence under any initial error conditions, and it has been verified that the robot trajectory tracking accuracy using this method is relatively high.

Description

Technical Field

[0001] The present invention relates to the field of robot posture constraint motion planning, and in particular to a robot trajectory tracking method based on a finite-time neural network. Background Art

[0002] Robot trajectory tracking is a major branch of robotic motion control. Finite-time zeroing neural networks (FTNNs) can help robots reach their desired trajectory within a finite amount of time and have garnered significant research attention in recent years.

[0003] To facilitate the use of various zeroing neural network solutions, the robot trajectory tracking problem must first be formulated as a quadratic programming problem. Currently, numerous zeroing neural network methods have been proposed for robot trajectory tracking, but few consider the constraints and control of the robot's posture. However, simply considering trajectory tracking speed and accuracy is far from sufficient for effectively executing various practical tasks. Therefore, the present invention proposes a quadratic programming trajectory tracking strategy with posture constraints to avoid unnecessary mission loss and disruption.

[0004] Improving the speed and accuracy of robot trajectory tracking helps robots perform various tasks more efficiently, accurately and stably. Research on various finite-time neural networks provides faster and more accurate solutions for robot trajectory tracking and motion planning. This is due to the efficient parallel computing characteristics and hardware implementation advantages of zero-based neural networks. However, most finite-time neural networks use unbounded activation functions, and their hardware implementation may be difficult. In addition, introducing dynamic parameters in the design of zero-based neural networks can significantly improve the convergence performance of zero-based neural networks. However, there is currently a lack of research on dynamic parameter finite-time neural networks using bounded activation functions and their robot trajectory tracking applications. Therefore, the present invention provides a finite-time neural network with dynamic parameters based on a new bounded activation function to solve the problem of posture-maintaining trajectory tracking of robots. Summary of the Invention

[0005] The object of the present invention is to provide a robot trajectory tracking method, device and medium based on a finite-time neural network to solve the problems raised in the above background technology.

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

[0007] A robot trajectory tracking method based on a finite-time neural network, comprising:

[0008] Step 1, calculate the transformation matrix from the robot base coordinate system to the end effector coordinate system through DH parameters;

[0009] Step 2: Obtain the Cartesian position kinematic equation according to step 1 and set the robot end posture constraint equation;

[0010] Step 3, setting the desired Cartesian space trajectory of the robot's end effector;

[0011] Step 4: describe the robot posture-maintaining trajectory tracking problem as a quadratic programming strategy;

[0012] Step 5: Design a dynamic parameter finite-time neural network for posture-preserving trajectory tracking based on a new bounded activation function;

[0013] In step 6, first, a finite-time neural network model is constructed to solve the specific dynamic parameters of the quadratic programming strategy established in step 4 by defining a reasonable error function; then, the finite-time neural network model is used for robot trajectory tracking.

[0014] Furthermore, the transformation matrix from the robot base coordinate system to the end effector coordinate system in step 1 is .

[0015] Furthermore, the Cartesian position kinematic equation in step 2 is , the robot end posture constraint equation is , where represents the Cartesian position Jacobian matrix, Represent the joint angle and joint angular velocity respectively, Represents the robot end position velocity vector, represents the attitude Jacobian matrix, Represents the direction velocity vector.

[0016] Furthermore, the step 3 includes:

[0017] Set the robot's initial joint angles to , , T represents the transposed matrix; the expected trajectory is a "four-pointed star" trajectory, and the time period of the expected "four-pointed star" trajectory is Expected posture Set to .

[0018] Furthermore, the step 4 includes:

[0019] The quadratic programming strategy for robot posture-maintaining trajectory tracking is:

[0020] (1)

[0021] in, Indicates finding the minimum value of the objective function. The constraints that need to be satisfied by expression (1) are: represents auxiliary variables, , , O c represents the actual direction vector, , Indicates that the dimension of the corresponding vector is 3, η0 is the attitude adjustment parameter, ; ; denote the desired trajectory and the derivative of the desired trajectory respectively; is the Cartesian trajectory of the actual end effector, η p is the trajectory adjustment parameter, ; Represents the desired direction vector, express The derivative of Indicates the direction deviation, If it is 0, it means that the robot's terminal posture is maintained; Represents the position feedback term.

[0022] Furthermore, the step 5 includes:

[0023] Construct the following finite-time neural network with dynamic parameters to solve the quadratic programming strategy in step 4:

[0024] (2)

[0025] in, Error The ijth element of for The derivative of is a constant parameter, , express The absolute value of Express Power Operation; exp(·) represents the exponential operator with the natural constant e as the base, κ1, κ2, α are positive adjustment parameters, κ1>1, κ2>1, α>1, γ(t) is a dynamic parameter, , q is a positive adjustment parameter, ; sgn(·) represents the sign function.

[0026] Furthermore, the step 6 includes:

[0027] Define the following Lagrangian function:

[0028] (6)

[0029] in, represents the Lagrangian function; represents the Lagrange multiplier vector, express The transposed matrix of About and Find the partial derivative and set it to zero to get the following linear equation:

[0030] (7)

[0031] Among them, M, Y, and W are all intermediate variables. , , , is the identity matrix, for The transposed matrix of for The transposed matrix of

[0032] To solve the quadratic programming strategy in step 4, define is the matrix error function, and Substituting the error function into equation (2) yields the following finite-time neural network model:

[0033] (8)

[0034] in, Respectively The derivative of

[0035] The solution is calculated by formula (8): , the first n items of which are the joint angular velocity vectors of the robot .

[0036] The present invention also provides a robot trajectory tracking device based on a finite-time neural network, comprising one or more processors for implementing the robot trajectory tracking method based on a finite-time neural network as described above.

[0037] The present invention also provides a readable storage medium having a program stored thereon. When the program is executed by a processor, the robot trajectory tracking method based on a finite-time neural network as described above is implemented.

[0038] Compared with the prior art, the present invention has the following advantages: it can quickly achieve trajectory tracking tasks in a finite time under any initial error conditions, and it can maintain the posture of the robot end in the desired posture mode. Compared with existing finite-time neural network methods with fixed parameters, the present invention has faster finite-time convergence under any initial error conditions due to its use of dynamic parameter design. It has also been verified that the robot trajectory tracking accuracy of this method is higher. In addition, the activation function used in the finite-time neural network provided by the present invention has a finite value and the dynamic parameters also have fixed upper and lower bounds, making it more convenient for hardware implementation and meeting the needs of practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a flow chart of the robot posture maintenance trajectory tracking provided by the present invention.

[0040] Figure 2 This is a "four-pointed star" trajectory diagram solved by the finite-time neural network with dynamic parameters designed by the present invention. The dotted line in the figure is the expected trajectory, and the solid line is the actual calculated trajectory.

[0041] Figure 3 This is a graph of joint angles solved by the method of the present invention.

[0042] Figure 4 This is a graph of the joint angular velocity obtained by the method of the present invention.

[0043] Figure 5 This is a graph of posture variables solved by the method of the present invention.

[0044] Figure 6 This is a trajectory error curve diagram solved by the method of the present invention.

[0045] Figure 7 This is a graph of the error norm obtained by the method of the present invention.

[0046] Figure 8 It is a dynamic parameter change curve diagram of the method of the present invention.

[0047] Figure 9 This is a structural schematic diagram of a robot trajectory tracking device based on a finite-time neural network in the present invention. DETAILED DESCRIPTION

[0048] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0049] like Figures 1-8 As shown in Figure 1, a robot trajectory tracking method based on a finite-time neural network consists of the following six steps:

[0050] Step 1: Calculate the transformation matrix from the robot base coordinate system to the end effector coordinate system .

[0051] Step 2: Based on step 1, the Cartesian position kinematic equation is: , and set the robot end posture constraint equation as Where, represents the Cartesian position Jacobian matrix, Represent the joint angle and joint angular velocity respectively, Represents the robot end position velocity vector, represents the attitude Jacobian matrix, Represents the direction velocity vector.

[0052] Step 3: Setting the expected trajectory

[0053] Set the initial joint angle of the robot UR5 to , T represents the transposed matrix; the expected trajectory is a "four-pointed star" trajectory, and the time period of the expected "four-pointed star" trajectory is s, time period Can be adjusted arbitrarily; the desired posture is set to .

[0054] Step 4: Develop a quadratic programming strategy for the robot's posture-maintaining trajectory tracking:

[0055] (1)

[0056] in, Indicates finding the minimum value of the objective function. represents the constraints that need to be satisfied by the optimization formula (1); represents auxiliary variables, , , O c represents the actual direction vector, , Indicates that the dimension of the corresponding vector is 3, η0 is the attitude adjustment parameter, ; , denote the desired trajectory and the derivative of the desired trajectory respectively; is the Cartesian trajectory of the actual end effector, η p is the trajectory adjustment parameter, ; Represents the desired direction vector, express The derivative of Indicates the direction deviation, If it is 0, it means that the robot's terminal posture is maintained; Represents the position feedback term.

[0057] Step 5: Construct the following finite-time neural network with dynamic parameters to solve the quadratic programming strategy in step 4:

[0058] (2)

[0059] in, is the ijth element of error E, for The derivative of is a constant parameter, , express The absolute value of Express Power Operation; exp(·) represents the exponential operator with the natural constant e as the base, κ1, κ2, α are positive adjustment parameters, κ1>1, κ2>1, α>1, γ(t) is a dynamic parameter, , positive adjustment parameter ; sgn (dot) represents the symbolic function. In particular, the function As a whole, it is considered as a time-varying gain parameter function. Since the error function is finite-time convergent, then ,and is a fixed parameter because the initial error is fixed, the initial dynamic parameters Therefore, the parameter There are fixed upper and lower bounds. This dynamic parameter design is more in line with actual hardware implementation, and it can adaptively adjust parameters as the error changes in order to obtain a more satisfactory convergence rate.

[0060] Step 6: First, a finite-time neural network model is constructed to solve the specific dynamic parameters of the quadratic programming strategy established in step 4 by defining a reasonable error function; then, the finite-time neural network model is used for robot trajectory tracking. Specifically, it includes:

[0061] Define the following Lagrangian function:

[0062] (6)

[0063] in, represents the Lagrangian function; represents the Lagrange multiplier vector, express The transposed matrix of About and Find the partial derivative and set it to zero to get the following linear equation:

[0064] (7)

[0065] Among them, M, Y, and W are all intermediate variables. , , ; is the identity matrix, for The transposed matrix of for The transposed matrix of .

[0066] To solve the quadratic programming strategy for attitude-maintaining trajectory tracking in step 4, define is the matrix error function, and Substituting the error function into equation (2) yields the following finite-time neural network model: (8)

[0067] in, Respectively The derivative of

[0068] The solution is calculated by formula (8): , the first n items of which are the joint angular velocity vectors of the robot .

[0069] The specific implementation method of this step is: for the posture-maintaining trajectory tracking problem of the UR5 robot, a simulation environment for robot posture-maintaining trajectory tracking is built in MATLAB software and the proposed finite-time neural network method with dynamic parameters is tested. The simulation results are presented in the attached figure of the specification.

[0070] The simulation related parameters in the drawings of the specification are selected as follows: ; .

[0071] in, Figure 2 This is the result of the end effector tracking the "four-pointed star" trajectory. It can be seen that the real-time motion trajectory of the end effector in the figure (the blue dotted line in the figure) perfectly tracks the expected "four-pointed star" trajectory (the black solid line in the figure).

[0072] Figure 3 is the joint angle curve solved by the method of the present invention, Figure 3 middle Represent the joint angles of the six joints in the robot.

[0073] Figure 4 This is the joint angular velocity curve solved by the method of the present invention. It can be seen that after executing the "four-pointed star" trajectory task, the robot's joint velocities are restored to 0. Figure 4 middle Represent the joint angular velocities of the six joints in the robot.

[0074] Figure 5 From the posture variable curve solved by the method of the present invention, it can be found that the posture of the robot quickly reaches and remains in the desired posture state. Figure 5 middle Represents the direction vector The three coordinate elements of are all constants.

[0075] Figure 6 is the trajectory error curve solved by the method of the present invention, where Representative trajectory error , the unit is meter (m), They are The error components in the x, y, and z axes; it can be found that the finite time neural network with dynamic parameters achieves a higher trajectory tracking accuracy, which is .

[0076] Figure 7 This is the error norm curve of the method of the present invention for solving the robot posture maintenance trajectory tracking problem. Figure 7 middle ; It can be seen that the error norm converges to 0 quickly, so the judgment error function also converges to 0 quickly.

[0077] Figure 8 The dynamic parameters generated by the method of the present invention for solving the robot posture maintenance trajectory tracking problem (Graphical solution to the problem ) curves that change with time. Parameters 1-6 in the figure are related to joint angles. Six parameters related to changes, also known as dynamic parameters ; It can be observed that the dynamic parameters gradually decrease and tend to a constant value, and there will be no infinite increase in gain.

[0078] See also Figure 9 An embodiment of the present invention provides a neural network device for robot posture maintenance trajectory tracking, including one or more processors for implementing a robot trajectory tracking method based on a finite-time neural network in the above embodiment.

[0079] An embodiment of a robot trajectory tracking device based on a finite-time neural network of the present invention can be applied to any device with data processing capabilities, and the device with data processing capabilities can be a device or apparatus 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 device in a logical sense, it is formed by the processor of any device with data processing capabilities in which it is located reading the corresponding computer program instructions in the non-volatile memory into the memory for execution. From the hardware level, if Figure 9 As shown in the figure, it is a hardware structure diagram of a robot trajectory tracking device based on a finite time neural network of the present invention, in which any device with data processing capability is located. Figure 9 In addition to the processor, memory, network interface, and non-volatile memory shown, any device with data processing capabilities in the embodiment may also include other hardware according to the actual function of the device with data processing capabilities, which will not be described in detail.

[0080] The implementation process of the functions and effects of each unit in the above-mentioned device is specifically described in the implementation process of the corresponding steps in the above-mentioned method, and will not be repeated here.

[0081] The technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above-mentioned 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.

[0082] An embodiment of the present invention further provides a readable storage medium having a program stored thereon. When the program is executed by a processor, a robot trajectory tracking method based on a finite-time neural network in the above embodiment is implemented.

[0083] The readable storage medium may be an internal storage unit of any device with data processing capabilities described in any of the aforementioned 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. Furthermore, the readable storage medium may also include both an internal storage unit and an external storage device of any device with data processing capabilities. 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 may also be used to temporarily store data that has been output or is to be output.

[0084] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A robot trajectory tracking method based on finite time neural network, characterized in that: include: Step 1, calculate the transformation matrix from the robot base coordinate system to the end effector coordinate system through DH parameters; Step 2: Obtain the Cartesian position kinematic equation according to step 1 and set the robot end posture constraint equation, where the Cartesian position kinematic equation is: , the robot end posture constraint equation is , where represents the Cartesian position Jacobian matrix, Represent the joint angle and joint angular velocity respectively, Represents the robot end position velocity vector, represents the attitude Jacobian matrix, represents the direction velocity vector; Step 3, setting the desired Cartesian space trajectory of the robot's end effector; Step 4: Describe the robot posture-maintaining trajectory tracking problem as a quadratic programming strategy, including: The quadratic programming strategy for robot posture-maintaining trajectory tracking is: (1) in, Indicates finding the minimum value of the objective function. The constraints that need to be satisfied by expression (1) are: represents auxiliary variables, , , O c represents the actual direction vector, , Indicates that the dimension of the corresponding vector is 3, η0 is the attitude adjustment parameter, ; ; denote the desired trajectory and the derivative of the desired trajectory respectively; is the Cartesian trajectory of the actual end effector, η p is the trajectory adjustment parameter, ; Represents the desired direction vector, express The derivative of Indicates the direction deviation, If it is 0, it means that the robot's terminal posture is maintained; represents the position feedback item; Step 5: Design a dynamic parameter finite-time neural network for posture-preserving trajectory tracking based on a new bounded activation function, including: Construct the following finite-time neural network with dynamic parameters to solve the quadratic programming strategy in step 4: (2) in, Error The ijth element of for The derivative of is a constant parameter, , express The absolute value of Express Power Operation; exp(·) represents the exponential operator with the natural constant e as the base, κ1, κ2, α are positive adjustment parameters, κ1>1, κ2>1, α>1, γ(t) is a dynamic parameter, , q is a positive adjustment parameter, ; sgn(·) represents the sign function; Step 6: First, a finite-time neural network model is constructed to solve the specific dynamic parameters of the quadratic programming strategy established in step 4 by defining a reasonable error function; then, the finite-time neural network model is used for robot trajectory tracking, including: Define the following Lagrangian function: (6) in, represents the Lagrangian function; represents the Lagrange multiplier vector, express The transposed matrix of About and Find the partial derivative and set it to zero to get the following linear equation: (7) Among them, M, Y, and W are all intermediate variables. , , , is the identity matrix, for The transposed matrix of for The transposed matrix of To solve the quadratic programming strategy in step 4, define is the matrix error function, and Substituting the error function into equation (2) yields the following finite-time neural network model: (8) in, Respectively The derivative of The solution is calculated by formula (8): , the first n items of which are the joint angular velocity vectors of the robot .

2. The robot trajectory tracking method based on finite time neural network according to claim 1, characterized in that: The transformation matrix from the robot base coordinate system to the end effector coordinate system in step 1 is .

3. The robot trajectory tracking method based on finite time neural network according to claim 1, characterized in that: The step 3 comprises: Set the robot's initial joint angles to , , T represents the transposed matrix; the expected trajectory is a "four-pointed star" trajectory, and the time period of the expected "four-pointed star" trajectory is Expected posture Set to .

4. A robot trajectory tracking device based on a finite time neural network, characterized in that: The method comprises one or more processors for implementing a robot trajectory tracking method based on a finite-time neural network according to any one of claims 1 to 3.

5. A readable storage medium, characterized in that: A program is stored thereon, and when the program is executed by a processor, a robot trajectory tracking method based on a finite-time neural network according to any one of claims 1 to 3 is implemented.

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