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

Abstract

The invention discloses a robot trajectory tracking method and device based on a finite time neural network, and a medium. The method comprises the following steps: calculating a conversion matrix from a robot base coordinate system to an end effector coordinate through a DH parameter; a Cartesian position kinematics equation is obtained, and a robot tail end posture constraint equation is set; setting a Cartesian space expected trajectory of an end effector of the robot; describing a robot attitude keeping trajectory tracking problem as a quadratic programming strategy; designing a finite time neural network for attitude keeping trajectory tracking; and 4, constructing a finite time neural network model for solving the specific dynamic parameters of the quadratic programming strategy established in the step 4, and applying the finite time neural network model to trajectory tracking of the robot. According to the method, due to the fact that dynamic parameter design is adopted, faster finite time convergence is achieved under any initial error condition, and it is verified that the robot trajectory tracking precision is high through the method.

Description

Technical Field

[0001] The 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] The robot trajectory tracking problem is a major branch of the field of robot motion control. Finite time zeroing neural network (referred to as finite time neural network) can make the robot trajectory reach the desired trajectory within a finite time, and has received widespread attention from researchers in recent years.

[0003] In order to facilitate the use of various zeroing neural networks for solving, it is first necessary to describe the robot trajectory tracking problem as a quadratic programming. At present, there are many zeroing neural network methods for the robot trajectory tracking problem, but few consider the constraints and control of the robot's posture. However, only considering the trajectory tracking speed and accuracy is far from enough for the effective execution of various practical tasks. Therefore, the present invention considers a quadratic programming trajectory tracking strategy with posture constraints, which can avoid unnecessary task losses and damage.

[0004] Improving the speed and accuracy of robot trajectory tracking helps the robot to perform various tasks more efficiently, accurately and stably. The research on various finite-time neural networks provides a faster and more accurate solution method for robot trajectory tracking and motion planning. This is due to the efficient parallel computing characteristics and hardware implementation advantages of zeroing 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 zeroing neural networks can significantly improve the convergence performance of zeroing 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, which is used to solve the problem of posture-maintaining trajectory tracking of robots. Summary of the invention

[0005] The purpose 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: Step 1, calculate the transformation matrix from the robot base coordinate system to the end effector coordinate system through DH parameters; Step 2, according to step 1, obtain the Cartesian position kinematic equation and set the robot end posture constraint equation; Step 3, setting the desired trajectory of the robot's end effector in Cartesian space; Step 4, describe the robot posture-maintaining trajectory tracking problem as a quadratic programming strategy; Step 5, design a dynamic parameter finite-time neural network for posture-preserving trajectory tracking based on a new bounded activation function; Step 6, first, a finite-time neural network model for solving the specific dynamic parameters of the quadratic programming strategy established in step 4 is constructed by defining a reasonable error function; then, the finite-time neural network model is used for trajectory tracking of the robot.

[0008] Furthermore, the transformation matrix from the robot base coordinate system to the end effector coordinate system in step 1 is .

[0009] 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 angular velocity of the joint respectively, represents the velocity vector of the robot end position, represents the attitude Jacobian matrix, Represents the direction velocity vector.

[0010] Furthermore, the step 3 comprises:

[0011] 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 .

[0012] Furthermore, the step 4 comprises:

[0013] The secondary programming strategy for robot posture-maintaining trajectory tracking is formulated as:

[0014] (1)

[0015] in, It means to find the minimum value of the objective function. The constraints that need to be satisfied in 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.

[0016] Furthermore, the step 5 comprises:

[0017] Construct the following finite-time neural network with dynamic parameters to solve the quadratic programming strategy in step 4:

[0018] (2)

[0019] 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.

[0020] Further, the step 6 comprises:

[0021] Define the following Lagrangian function:

[0022] (6)

[0023] 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:

[0024] (7)

[0025] Among them, M, Y, and W are all intermediate variables. , , , is the identity matrix, for The transposed matrix of for The transposed matrix of

[0026] 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:

[0027] (8)

[0028] in, Respectively The derivative of

[0029] The solution is calculated by formula (8): , whose first n items are the joint angular velocity vectors of the robot .

[0030] The present invention also provides a robot trajectory tracking device based on a finite-time neural network, comprising one or more processors for implementing a robot trajectory tracking method based on a finite-time neural network as described above.

[0031] The present invention also provides a readable storage medium having a program stored thereon, and 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.

[0032] Compared with the prior art, the beneficial effects of the present invention are: the present invention can quickly realize the trajectory tracking task in a finite time under any initial error condition, and it can keep the posture of the robot end in the desired posture mode. Compared with the existing finite time neural network method with fixed parameters, the present invention has faster finite time convergence under any initial error condition due to the use of dynamic parameter design, and it has been verified that the robot trajectory tracking accuracy using 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, so it is more convenient for hardware implementation and meets the needs of actual applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 A flow chart of the robot posture-maintaining trajectory tracking provided by the present invention.

[0034] 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.

[0035] Figure 3 This is a graph of joint angles solved by the method of the present invention.

[0036] Figure 4 This is a graph of the joint angular velocity solved by the method of the present invention.

[0037] Figure 5 This is a graph of posture variables solved by the method of the present invention.

[0038] Figure 6 This is a trajectory error curve diagram solved by the method of the present invention.

[0039] Figure 7 This is a graph of the error norm solved by the method of the present invention.

[0040] Figure 8 It is a dynamic parameter change curve diagram of the method of the present invention.

[0041] Fig. 9 The present invention is a schematic structural diagram of a robot trajectory tracking device based on a finite-time neural network. DETAILED DESCRIPTION

[0042] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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 creative work are within the scope of protection of the present invention.

[0043] like Figure 1-Figure 8 As shown in Figure 1, a robot trajectory tracking method based on a finite-time neural network consists of the following six steps:

[0044] Step 1: Calculate the transformation matrix from the robot base coordinate system to the end effector coordinate system .

[0045] Step 2: Based on step 1, the Cartesian position kinematic equation is: , and set the robot end posture constraint equation as In the formula, represents the Cartesian position Jacobian matrix, Represent the joint angle and angular velocity of the joint respectively, represents the velocity vector of the robot end position, represents the attitude Jacobian matrix, Represents the direction velocity vector.

[0046] Step 3: Setting the expected trajectory

[0047] Set the initial joint angle of 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 .

[0048] Step 4: Formulate the secondary programming strategy for the robot's posture-maintaining trajectory tracking as follows:

[0049] (1)

[0050] in, It means to find 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.

[0051] Step 5, construct the following finite-time neural network with dynamic parameters to solve the quadratic programming strategy in step 4:

[0052] (2)

[0053] 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 convergent in finite time, then we have ,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.

[0054] 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:

[0055] Define the following Lagrangian function:

[0056] (6)

[0057] 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:

[0058] (7)

[0059] Among them, M, Y, and W are all intermediate variables. , , ; is the identity matrix, for The transposed matrix of for The transposed matrix of .

[0060] 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)

[0061] in, Respectively The derivative of

[0062] The solution is calculated by formula (8): , whose first n items are the joint angular velocity vectors of the robot .

[0063] 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.

[0064] The simulation related parameters in the attached drawings of the specification are selected as follows: ; .

[0065] 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).

[0066] 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 respectively.

[0067] 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 joint velocities are restored to 0. Figure 4 middle Represent the joint angular velocities of the six joints in the robot respectively.

[0068] 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.

[0069] Figure 6 is the trajectory error curve solved by the method of the present invention, where: Represents 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 .

[0070] Figure 7 This is the error norm curve of the method of the present invention for solving the robot posture-maintaining 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.

[0071] 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 changing with time, where parameters 1-6 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.

[0072] See also Fig. 9 A neural network device for robot posture-maintaining trajectory tracking provided by an embodiment of the present invention includes one or more processors for implementing a robot trajectory tracking method based on a finite-time neural network in the above-mentioned embodiment.

[0073] 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 internal memory for execution. From a hardware perspective, if Fig. 9As shown in FIG. 1 , a hardware structure diagram of a robot trajectory tracking device based on a finite time neural network according to the present invention is provided in any device with data processing capability, except Fig. 9 In addition to the processor, memory, network interface, and non-volatile memory shown, any device with data processing capabilities in the embodiments may also include other hardware, usually based on the actual functions of the device with data processing capabilities, which will not be described in detail.

[0074] 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.

[0075] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described 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.

[0076] 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.

[0077] The readable storage medium may be an internal storage unit of any device with data processing capability described in any of the aforementioned embodiments, such as a hard disk or a 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 of any device with data processing capability 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 capability, and may also be used to temporarily store data that has been output or is to be output.

[0078] Although 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 the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present 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, according to step 1, obtain the Cartesian position kinematic equation and set the robot end posture constraint equation; Step 3, setting the desired trajectory of the robot's end effector in Cartesian space; Step 4, describe the robot posture-maintaining trajectory tracking problem as a quadratic programming strategy; Step 5, design a dynamic parameter finite-time neural network for posture-preserving trajectory tracking based on a new bounded activation function; Step 6, first, a finite-time neural network model for solving the specific dynamic parameters of the quadratic programming strategy established in step 4 is constructed by defining a reasonable error function; then, the finite-time neural network model is used for trajectory tracking of the robot.

2. A 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 is characterized in that: 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 angular velocity of the joint respectively, represents the velocity vector of the robot end position, represents the attitude Jacobian matrix, Represents the direction velocity vector.

4. The robot trajectory tracking method based on finite time neural network according to claim 1 is 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 .

5. The robot trajectory tracking method based on finite time neural network according to claim 3 is characterized in that: The step 4 comprises: The secondary programming strategy for robot posture-maintaining trajectory tracking is formulated as: (1) in, It means to find the minimum value of the objective function. The constraints that need to be satisfied in 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.

6. The robot trajectory tracking method based on finite time neural network according to claim 5 is characterized in that: The step 5 comprises: 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.

7. The robot trajectory tracking method based on finite time neural network according to claim 6 is characterized in that: The step 6 comprises: 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): , whose first n items are the joint angular velocity vectors of the robot .

8. A robot trajectory tracking device based on a finite time neural network, characterized in that: It comprises one or more processors for implementing a robot trajectory tracking method based on a finite-time neural network as described in any one of claims 1 to 7.

9. 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 as described in any one of claims 1 to 7 is implemented.

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