Trajectory tracking method, tracking device, equipment, storage medium and program product

Abstract

The invention provides a trajectory tracking method, a tracking device, equipment, a storage medium and a program product, and relates to the technical field of robots. The mechanical arm trajectory tracking method comprises the steps that a target equation for solving the joint speed of a mechanical arm is constructed based on a Jacobian matrix and a corresponding pseudo-inverse matrix to be solved, and the Jacobian matrix is used for describing the mapping relation between the joint speed and the tail end speed of a tail end executor of the mechanical arm; a pseudo-inverse matrix to be solved is solved based on the improved anti-noise zero neural network model, the pseudo-inverse matrix is obtained, and the improved anti-noise zero neural network model is configured based on a time-varying parameter and a composite nonlinear activation function; the target equation is solved based on the pseudo-inverse matrix, a time-varying expression of the joint speed is obtained, and a joint control instruction is generated; and obtaining a tracking trajectory of the mechanical arm based on an execution result of the joint control instruction. According to the technical scheme, the mechanical arm can maintain stable trajectory tracking performance in the noise environment.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the technical field of robots, and in particular, to a robot arm trajectory tracking method, a robot arm trajectory tracking device, a robot, an electronic device, a computer readable storage medium, and a computer program product. BACKGROUND

[0002] Robot arm trajectory tracking is one of the core tasks in the field of robot arm control. By controlling the joint movement of the robot arm, the end effector moves according to the preset trajectory in space. However, due to the interference of sensor measurement noise, calculation error and other noises, the actual movement trajectory of the end effector deviates from the preset trajectory, resulting in the need to improve the accuracy and robustness of trajectory tracking.

[0003] It should be noted that the information disclosed in the above background section is only used to strengthen the understanding of the background of the present disclosure, and therefore can include information that does not constitute prior art known to those of ordinary skill in the art. SUMMARY

[0004] The purpose of the present disclosure is to provide a robot arm trajectory tracking method, a tracking device, a robot, an electronic device, a storage medium and a computer program product, which at least partially overcome the problem that the accuracy and robustness of trajectory tracking need to be improved in the related art.

[0005] Other characteristics and advantages of the present disclosure will become apparent from the following detailed description, or will be learned by practice of the present disclosure.

[0006] According to one aspect of the present disclosure, a robot arm trajectory tracking method is provided, comprising: constructing a target equation for solving joint velocity of the robot arm based on a Jacobian matrix and a corresponding pseudo-inverse matrix to be solved, the Jacobian matrix being used to describe a mapping relationship between the joint velocity and an end velocity of an end effector of the robot arm; solving the pseudo-inverse matrix to be solved based on an improved anti-noise nulling neural network model, to obtain the pseudo-inverse matrix with joint angle of the robot arm as a variable, the improved anti-noise nulling neural network model being configured based on time-varying parameters and a composite nonlinear activation function; solving the target equation based on the pseudo-inverse matrix to obtain a time-varying expression of the joint velocity, to generate a joint control instruction based on the time-varying expression of the joint velocity; obtaining a tracking trajectory of the robot arm based on an execution result of the joint control instruction.

[0007] In an embodiment of the present disclosure, before solving the pseudo-inverse matrix to be solved based on the improved anti-noise zeroization neural network model, further comprising: based on the self-reflection that the pseudo-inverse matrix needs to meet, constructing a constraint equation with the pseudo-inverse matrix as the solving target, and configuring the deviation between the constraint equation and the optimization target as an error function, wherein the constraint equation is J (θ (t)) is the Jacobian matrix, J T (θ (t)) is the transpose matrix of the Jacobian matrix; based on the error function, an initial zeroization neural network model is configured, the initial zeroization neural network model includes a fixed gain parameter; the configured time-varying parameter and the composite nonlinear activation function are used to replace the fixed gain parameter, to obtain the improved anti-noise zeroization neural network model, wherein the time-varying parameter is used to enhance the convergence speed of the improved anti-noise zeroization neural network model, and the composite nonlinear activation function is used to enhance the anti-noise of the improved anti-noise zeroization neural network model.

[0008] In an embodiment of the present disclosure, further comprising: configuring an exponential function with a linear growth term and a nonlinear term with saturation characteristics and a constant term as an exponential term, so as to take the negative value of the exponential function as the time-varying parameter.

[0009] In an embodiment of the present disclosure, the linear growth term is determined based on the product of a first gain parameter and a time variable; the nonlinear term with saturation characteristics is determined based on the product of the inverse tangent function of the time variable and a second gain parameter; and the constant term is determined based on a third gain parameter.

[0010] In an embodiment of the present disclosure, further comprising: constructing the composite nonlinear activation function based on a nonlinear enhancement term and a linear stabilization term.

[0011] In an embodiment of the present disclosure, the nonlinear enhancement term is determined based on the sum of a first polynomial group, a second polynomial group and an exponential term, and a sign function, the first polynomial group is represented as α1(|x| m +|x| m+2 +|x| m+4 ), the second polynomial group is represented as α2(|x| n +|x| 2n +|x| 3n ), and the exponential term is represented as α1 is a first coefficient, α2 is a second coefficient, α3 is a third coefficient, x represents the error function, m is a first exponential parameter, n is a second exponential parameter, and k is a third exponential parameter; and the linear stabilization term is determined based on a fourth coefficient and the error function.

[0012] In one embodiment of the present disclosure, the pseudo-inverse matrix to be solved is solved based on an improved anti-noise zeroization neural network model, to obtain the pseudo-inverse matrix with the joint angle of the robot arm as a variable, comprising: in a control period determined based on the time variable of the time-varying expression, iteratively updating the pseudo-inverse matrix to be solved based on the improved anti-noise zeroization neural network model until the constraint equation converges to achieve the optimization target, to obtain the pseudo-inverse matrix with a numerical solution.

[0013] In one embodiment of the present disclosure, a target equation for solving the joint velocity of the robot arm is constructed based on the Jacobian matrix and the corresponding pseudo-inverse matrix to be solved, comprising: based on the kinematic mapping relationship between the position of the end effector and the joint angle, a first correlation expression of the position of the end effector and the joint angle is constructed; the first correlation expression is differentiated based on the time variable to obtain a second correlation expression of the end effector velocity and the joint velocity, wherein the Jacobian matrix is obtained based on the kinematic mapping relationship; the second correlation expression is expressed as a general solution form based on the Jacobian matrix, the pseudo-inverse matrix and the degree of freedom adjustment parameter of the robot arm, to obtain the target equation, which is wherein, is the joint velocity, is the pseudo-inverse matrix, is the expected value of the end effector velocity, J(θ(t)) is the Jacobian matrix, I is a unit matrix consistent with the joint space dimension where the joint velocity is located, and w(t) is a degree of freedom adjustment parameter.

[0014] In one embodiment of the present disclosure, the target equation is solved based on the pseudo-inverse matrix to obtain a time-varying expression of the joint velocity, to generate a joint control instruction based on the time-varying expression of the joint velocity, comprising: obtaining a time-varying expression of an expected position trajectory of the end effector; determining a time-varying expression of the expected value based on the time-varying expression of the expected position trajectory; introducing the pseudo-inverse matrix and the time-varying expression of the expected value into the target equation to obtain the time-varying expression of the joint velocity.

[0015] In one embodiment of the present disclosure, the tracking trajectory of the robot arm is obtained based on the execution result of the joint control instruction, comprising: driving the joint motion of the robot arm based on the joint control instruction, and measuring the joint angle in real time based on a sensor; determining the actual position of the end effector based on the joint angle and the kinematic mapping relationship, to obtain the tracking trajectory based on the change of the actual position.

[0016] According to another aspect of the present disclosure, a mechanical arm trajectory tracking device is provided, comprising: a construction module configured to construct a target equation for solving joint velocity of the mechanical arm based on a Jacobian matrix and a corresponding pseudo-inverse matrix to be solved, the Jacobian matrix being configured to describe a mapping relationship between the joint velocity and an end velocity of an end effector of the mechanical arm; a first solving module configured to solve the pseudo-inverse matrix to be solved based on an improved anti-noise zeroization neural network model, to obtain the pseudo-inverse matrix with joint angles of the mechanical arm as variables, the improved anti-noise zeroization neural network model being based on time-varying parameters and a composite nonlinear activation function configuration; a second solving module configured to solve the target equation based on the pseudo-inverse matrix, to obtain a time-varying expression of the joint velocity, to generate joint control instructions based on the time-varying expression of the joint velocity; and a tracking trajectory acquisition module configured to obtain a tracking trajectory of the mechanical arm based on an execution result of the joint control instructions.

[0017] According to still another aspect of the present disclosure, a robot is provided, comprising: a mechanical arm body comprising a plurality of joints, an actuator configured to drive movement of the joints, and a sensor configured to detect joint angles of the joints; a control unit connected with the actuator and the sensor, the control unit comprising a processor and a memory; the memory being configured to store executable instructions of the processor; and the processor being configured to generate the mechanical arm trajectory according to any one of the embodiments of the first aspect via execution of the executable instructions.

[0018] According to yet another aspect of the present disclosure, an electronic device is provided, comprising: a processor; and a memory configured to store executable instructions of the processor; the processor being configured to execute the mechanical arm trajectory tracking method of the first aspect via execution of the executable instructions.

[0019] According to yet another aspect of the present disclosure, a computer-readable storage medium is provided, having a computer program stored thereon, the computer program being executed by a processor to implement the mechanical arm trajectory tracking method described above.

[0020] According to yet another aspect of the present disclosure, a computer program product is provided, having a computer program stored thereon, the computer program being executed by a processor to implement the mechanical arm trajectory tracking method described above.

[0021] The mechanical arm trajectory tracking scheme provided by the embodiment of the present disclosure constructs a target equation based on a Jacobian matrix and a pseudo-inverse matrix, combines an improved anti-noise nulling neural network model to solve a time-varying pseudo-inverse matrix in real time, converts an end desired trajectory into a joint control instruction, and finally realizes trajectory tracking of the mechanical arm in a noise environment through actuator driving and feedback correction. The time-varying parameter accelerates the model convergence speed, meets the real-time calculation demand of the mechanical arm trajectory tracking, the composite nonlinear activation function enhances the anti-noise performance of the model, reduces the influence of noise on the result, makes the obtained pseudo-inverse matrix more accurate, and further makes the joint speed time-varying expression obtained by solving the target equation more accurate. The generated joint control instruction can effectively drive the movement of the mechanical arm, and finally realizes more accurate tracking of the preset trajectory by the mechanical arm, improves the robustness and accuracy of the mechanical arm trajectory tracking, and promotes the application of industrial robot technology in a wider range of scenarios.

[0022] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present disclosure. BRIEF DESCRIPTION OF DRAWINGS

[0023] The drawings herein are incorporated into the specification and form part of the specification, show embodiments consistent with the present disclosure, and together with the specification serve to explain the principles of the present disclosure. Obviously, the drawings in the following description are only some embodiments of the present disclosure, and other drawings can be obtained from these drawings without creative labor for those skilled in the art.

[0024] Figure 1 An initial state schematic diagram of a mechanical arm in an embodiment of the present disclosure is shown;

[0025] Figure 2 A mechanical arm trajectory tracking process schematic diagram based on a traditional nulling neural network in an embodiment of the present disclosure is shown;

[0026] Figure 3 A mechanical arm tracking trajectory and desired trajectory comparison schematic diagram based on a traditional anti-noise nulling neural network in an embodiment of the present disclosure is shown;

[0027] Figure 4 A mechanical arm trajectory tracking method flowchart in an embodiment of the present disclosure is shown;

[0028] Figure 5 Another mechanical arm trajectory tracking method flowchart in an embodiment of the present disclosure is shown;

[0029] Figure 6 A mechanical arm trajectory tracking process schematic diagram based on an improved anti-noise nulling neural network in an embodiment of the present disclosure is shown;

[0030] Figure 7 Fig. 9 shows a schematic diagram of a comparison between a tracking trajectory and a desired trajectory of a robot arm based on an improved anti-noise zeroing neural network in an embodiment of the present disclosure;

[0031] Figure 8 Fig. 10 shows a schematic diagram of an error between a tracking trajectory and a desired trajectory of a robot arm based on an improved anti-noise zeroing neural network in a noise-free environment in an embodiment of the present disclosure;

[0032] Figure 9 Fig. 11 shows a schematic diagram of an error between a tracking trajectory and a desired trajectory of a robot arm based on an improved anti-noise zeroing neural network in a noisy environment in an embodiment of the present disclosure;

[0033] Figure 10 Fig. 12 shows a schematic diagram of an error between a tracking trajectory and a desired trajectory of a robot arm based on a traditional zeroing neural network in a noisy environment in an embodiment of the present disclosure;

[0034] Figure 11 Fig. 13 shows a schematic diagram of a change in angle of a robot arm based on an improved anti-noise zeroing neural network in an embodiment of the present disclosure;

[0035] Figure 12 Fig. 14 shows a schematic diagram of a change in angular velocity of a robot arm based on an improved anti-noise zeroing neural network in an embodiment of the present disclosure;

[0036] Figure 13 Fig. 15 shows a schematic diagram of a robot arm trajectory tracking device in an embodiment of the present disclosure;

[0037] Figure 14 Fig. 16 shows a structural block diagram of a computer device in an embodiment of the present disclosure. DETAILED DESCRIPTION

[0038] Example implementations will now be described more fully with reference to the accompanying drawings. Example implementations may, however, be implemented in many different forms and should not be construed as limited to the implementations set forth herein; rather, these implementations are provided so that this disclosure will be thorough and complete, and will fully convey the inventive aspects to those skilled in the art. Features, structures, or characteristics described in connection with one implementation can be combined in any suitable manner with features, structures or characteristics of other implementations.

[0039] Furthermore, the drawings are not necessarily drawn to scale. Like reference numerals in different drawings denote like or similar parts, and the same will be understood from the following description, and thus a repeated description will be omitted. Some of the block diagrams shown in the drawings are functional entities, which do not necessarily have to correspond to physically or logically independent entities. These functional entities can be implemented in the form of software, or in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0040] Zeroing Neural Network (ZNN) is a neural network method used to solve dynamic matrix problems. The core idea of ​​ZNN is to solve dynamic matrix problems by constructing an error function and making the derivative of the error function tend to zero. ZNN can be applied to solving dynamic matrix linear equations, dynamic matrix inverse, dynamic matrix Moore-Penrose inverse and other problems.

[0041] With the continuous evolution of technology, the annihilation neural network has also developed rapidly. The development of the annihilation neural network currently mainly includes the optimization of activation functions, the improvement of time-varying parameters, the improvement of error functions, and the improvement of the model itself. Aspects to be improved include accelerating the convergence speed and improving the noise resistance performance.

[0042] Robotic arm trajectory tracking is a research hotspot in the field of robotic arm control. Figure 1 As shown in the figure, the two-dimensional coordinate diagram of the trajectory tracking of the six-bar robotic arm shows the motion trajectory of the end effector on the plane. If the precise control and tracking of the motion trajectory of the robotic arm can be achieved, the application of industrial robot technology will be further rapidly developed.

[0043] Figure 2 The figure shows a schematic diagram of the trajectory tracking process of a six-rod robot based on a traditional annihilation neural network. Although the annihilation neural network can solve time-varying problems and converge to an exact solution, the current annihilation neural network requires an infinite amount of time for the error to converge to 0. In addition, in practical applications, noise is inevitable, and the current annihilation neural network is easily affected by noise, such as Figure 3 The comparison diagram of the actual trajectory and the expected trajectory of the six-bar robotic arm shown in the figure shows that there is a large error between the generated result and the expected result. Therefore, a more robust and faster convergence time zeroing neural network model is urgently needed to meet the real-time calculation of the robotic arm trajectory tracking control.

[0044] Below, each step of the robot arm trajectory tracking method in this example implementation will be described in more detail with reference to the accompanying drawings and embodiments.

[0045] Figure 1 A flow chart of a robot arm trajectory tracking method in an embodiment of the present disclosure is shown.

[0046] like Figure 4 As shown, a robot arm trajectory tracking method according to an embodiment of the present disclosure includes:

[0047] Step S402 : constructing a target equation for solving the joint velocity of the robotic arm based on the Jacobian matrix and the corresponding pseudo-inverse matrix to be solved. The Jacobian matrix is ​​used to describe the mapping relationship between the joint velocity and the end velocity of the end effector of the robotic arm.

[0048] In some embodiments, the Jacobian matrix J(0(t)) is a function of the joint angle 0(t), the elements in the Jacobian matrix can be derived by forward kinematics of the robot arm, for quantifying the joint velocity is a linear mapping relationship of the end velocity , that is The corresponding pseudo-inverse matrix is a key parameter for solving the joint velocity, which can be obtained from J(0(t)) by Moore-Penrose pseudo-inverse operation, since the joint angle changes dynamically over time when the robot arm moves, and the pseudo-inverse matrix cannot be directly obtained by a fixed analytical formula, it needs to be calculated in real time based on the current joint angle, therefore the pseudo-inverse matrix is in a to-be-solved state.

[0049] Step S404, solving the to-be-solved pseudo-inverse matrix based on the improved anti-noise zeroing neural network model, to obtain the pseudo-inverse matrix with the joint angle of the robot arm as a variable, wherein the improved anti-noise zeroing neural network model is configured based on time-varying parameters and a composite nonlinear activation function.

[0050] In some embodiments, the zeroing neural network model dynamically adapts the time-varying characteristics of the matrix by introducing time-varying parameters, ensuring that the solving process can track parameter changes in real time during the continuous change of the joint angle, preventing lag or precision decline caused by fixed parameters, in addition, the composite nonlinear activation function is used to enhance the anti-noise ability of the model, so that the model can also stably solve the pseudo-inverse matrix in a noisy environment.

[0051] In some embodiments, the model is based on the constraint equation An error function is constructed, and the improved anti-noise zeroing neural network model can accelerate the convergence of the model and suppress noise interference, and iteratively update the numerical solution of the pseudo-inverse matrix at each control cycle, to ensure the anti-noise and time-varying properties of the pseudo-inverse matrix.

[0052] Step S406, solving the target equation based on the pseudo-inverse matrix to obtain a time-varying expression of the joint velocity, and generating a joint control instruction based on the time-varying expression of the joint velocity.

[0053] In some embodiments, the time-varying expression of the joint velocity is a mathematical description of the change of the joint velocity over time, and the joint control instruction refers to an electrical signal (such as a pulse width modulation signal) generated based on the time-varying expression, which can directly drive the joint actuator (such as a servo motor) to control the joint to move at the calculated speed.

[0054] Step S408, obtaining the tracking trajectory of the robot arm based on the execution result of the joint control instruction.

[0055] In some embodiments, the control instruction drives the joint motor to rotate, the joint angle θ(t) can be collected in real time through a sensor such as an encoder, the end position can be calculated through the forward kinematics formula, the tracking trajectory can be formed, and the closed-loop feedback can be realized by comparing the tracking trajectory with the expected trajectory, and the control instruction can be dynamically adjusted to ensure the trajectory accuracy.

[0056] In this embodiment, the end expected trajectory is converted into joint control instructions by constructing a target equation based on the Jacobian matrix and the pseudo-inverse matrix, and combining the improved anti-noise zeroization neural network model to solve the time-varying pseudo-inverse matrix in real time. Ultimately, the trajectory tracking of the robot arm in the noise environment is realized through the actuator driving and feedback correction. The time-varying parameter accelerates the model convergence speed, meets the real-time calculation demand of the robot arm trajectory tracking, the composite nonlinear activation function enhances the anti-noise performance of the model, reduces the influence of noise on the result, makes the obtained pseudo-inverse matrix more accurate, and further makes the joint speed time-varying expression obtained by solving the target equation more accurate. The generated joint control instruction can effectively drive the robot arm to move, and ultimately realize the relatively accurate tracking of the robot arm to the preset trajectory, improve the robustness and accuracy of the robot arm trajectory tracking, and promote the application of industrial robot technology in a wider range of scenarios.

[0057] In one embodiment of the present disclosure, before the pseudo-inverse matrix to be solved is solved based on the improved anti-noise zeroization neural network model, the following steps are further included:

[0058] Based on the self-reflection required to be met by the pseudo-inverse matrix, a constraint equation taking the pseudo-inverse matrix as the solving target is constructed, and the deviation between the constraint equation and the optimization target is configured as an error function.

[0059] In some embodiments, the Jacobian matrix J(θ(t)) belongs to a time-varying matrix, and the time-varying matrix H(t) ∈ R m×n , the pseudo-inverse of the matrix is The pseudo-inverse of the matrix satisfies formula (1) and formula (2).

[0060]

[0061] Based on the actual working condition of the robot arm trajectory tracking, i.e., m < n, the constraint equation obtained is as shown in formula (3).

[0062]

[0063] is the pseudo-inverse matrix, J(θ(t)) is the Jacobian matrix, J T (θ(t)) is the transpose matrix of the Jacobian matrix.

[0064] In some embodiments, the self-reflexivity refers to the operation relationship between the pseudo-inverse matrix and the original matrix, and based on the self-reflexivity required to be met by the pseudo-inverse matrix, a constraint equation taking the pseudo-inverse matrix as a solving target is constructed to ensure the rationality of the pseudo-inverse matrix when solving the joint speed.

[0065] In some embodiments, the error function is as shown in equation (4).

[0066]

[0067] Based on the error function, an initial zeroization neural network model is configured, and the initial zeroization neural network model includes a fixed gain parameter.

[0068] In some embodiments, the initial zeroization neural network model takes the deviation between the constraint equation and the optimization target as the error function, and a dynamic evolution equation of the model is constructed by setting a fixed gain parameter, and the initial zeroization neural network model is as shown in equation (5).

[0069]

[0070] Wherein, the derivative of the error function is taken as the direction of gradient descent, so that the error function can gradually converge to zero along this direction over time, thereby realizing the solving of the pseudo-inverse matrix.

[0071] The fixed gain parameter γ determines the convergence characteristics of the model, but in the noise environment of the trajectory tracking of the robot arm, as it is a constant set in advance, it cannot be adjusted according to the dynamic changes of the error function or the noise interference. When γ is relatively small, the model converges slowly and it is difficult to quickly respond to the time-varying requirements of the pseudo-inverse matrix in the dynamic motion of the robot arm. When γ is relatively large, the convergence speed is accelerated, but under the noise interference, the error function is prone to oscillation, which reduces the solving accuracy of the pseudo-inverse matrix, and further causes the trajectory deviation of the end effector to increase.

[0072] The configured time-varying parameter and the composite nonlinear activation function are used to replace the fixed gain parameter to obtain an improved anti-noise zeroization neural network model, wherein the time-varying parameter is used to enhance the convergence speed of the improved anti-noise zeroization neural network model, and the composite nonlinear activation function is used to anti-noise enhance the improved anti-noise zeroization neural network model.

[0073] In some embodiments, the time-varying parameter dynamically changes over time, which can adjust the evolution rate of the model according to the convergence state of the error function, accelerate the convergence when the error is large, and slow down the rate when approaching the convergence to ensure stability, thereby enhancing the convergence speed of the model.

[0074] In some embodiments, the composite nonlinear activation function suppresses and filters noise interference through the nonlinear characteristic, reduces the influence of noise on the error function convergence process, enables the model to maintain good solving accuracy in the presence of noise, realizes noise-resistant enhancement of the model, and finally obtains an improved noise-resistant zeroization neural network model.

[0075] In this embodiment, the constraint equation and the error function are constructed based on the self-reflection of the pseudo-inverse matrix, the initial zeroization neural network model is configured, and then the initial model is improved by introducing the time-varying parameter and the composite nonlinear activation function to form a model with strong noise-resistant ability and fast convergence speed, thereby being beneficial to solve the problems of insufficient trajectory tracking accuracy and robustness caused by noise interference in the background art. The improved noise-resistant zeroization neural network model can more accurately and quickly solve the pseudo-inverse matrix, providing a reliable joint speed solving basis for the trajectory tracking of the robot arm.

[0076] In one embodiment of the present disclosure, the linear growth term and the nonlinear term with saturation characteristics and the constant term are configured as the exponential function as the exponential term to take the negative value of the exponential function as the time-varying parameter.

[0077] In this embodiment, the linear growth term can monotonically increase with time, can provide strong driving effect in the initial stage of large error to accelerate the convergence speed of the model, the nonlinear term with saturation characteristics grows slowly after the time increases to a certain extent, can prevent system oscillation caused by excessive enhancement of the linear growth term, and ensures convergence stability, and the constant term provides a basic amplitude for the parameter, so that the model can have certain convergence driving force even at the initial time, taking the three terms as the exponential term to configure the exponential function, and taking the negative value of the exponential function as the time-varying parameter, can quickly reduce the error through the linear growth term when the error is large, can suppress excessive adjustment through the saturated nonlinear term when approaching convergence, and can maintain the basic convergence ability through the constant term, realize the dynamic balance of convergence speed and stability, and enhance the adaptability of the model to the time-varying pseudo-inverse matrix.

[0078] In one embodiment of the present disclosure, the linear growth term is determined based on the product of the first gain parameter and the time variable; the nonlinear term with saturation characteristics is determined based on the product of the inverse tangent function of the time variable and the second gain parameter; and the constant term is determined based on the third gain parameter.

[0079] In some embodiments, the time-varying parameter is as shown in formula (6).

[0080]

[0081] wherein γ1 is the first gain parameter, γ2 is the second gain parameter, and γ3 is the third gain parameter, and γ1, γ2, γ3>0.

[0082] In this embodiment, the time-varying parameter p(t) is adaptively adjusted at different stages through three combinations: initial rapid convergence, medium smooth transition, and later fine tuning, achieving a balance that traditional fixed gamma parameters cannot achieve, thereby facilitating the improvement of the solving efficiency and anti-interference ability of the pseudo-inverse matrix in a noisy environment.

[0083] In one embodiment of the present disclosure, the composite nonlinear activation function is constructed based on a nonlinear enhancement term and a linear stabilization term.

[0084] In this embodiment, the activation function is constructed by combining a nonlinear enhancement term and a linear stabilization term. The nonlinear enhancement term is used to optimize different intensities of noise and error ranges. When the error is close to zero, the linear term plays a dominant role, preventing oscillation caused by excessive amplification of the nonlinear term, thereby facilitating the balance between noise suppression and error convergence ability.

[0085] In one embodiment of the present disclosure, the nonlinear enhancement term is determined based on the sum of a first polynomial group, a second polynomial group, and an exponential term, and a sign function, the first polynomial group being represented as α1(|x| m +|x| m+2 +|x| m+4 ), the second polynomial group being represented as α2(|x| n +|x| 2n +|x| 3n ), and the exponential term being α1 is a first coefficient, α2 is a second coefficient, α3 is a third coefficient, k is a third exponential parameter, x represents an error function, and the linear stabilization term is determined based on a fourth coefficient and the error function.

[0086] In some embodiments, the first polynomial group enhances the sensitivity to small errors through high-order polynomial, so that the model still has sufficient adjustment driving force when the error is close to zero, preventing falling into a local minimum.

[0087] In some embodiments, different exponential polynomials are combined to provide nonlinear amplification for moderate intensity errors, enhancing the model's response ability to sudden errors.

[0088] In some embodiments, the exponential term utilizes the explosive growth characteristic of the exponential function to provide super-strong driving force when the error is large, accelerating the convergence process.

[0089] In some embodiments, the sign function ensures that the direction of the activation function is consistent with the direction of the error, so that the model always adjusts in the direction of reducing the error.

[0090] In some embodiments, when the error is close to zero, the linear term plays a dominant role, preventing oscillation caused by excessive amplification of the nonlinear term, ensuring the stability of the system in the steady state.

[0091] In some embodiments, the composite nonlinear activation function is shown in equation (7).

[0092]

[0093] wherein sign(x) is a sign function, a4 is a fourth coefficient, a1, a2, a3, a4 > 0, m > 1, n > 1, 0 < k < 1.

[0094] In some embodiments, the improved anti-noise zeroization neural network model is shown in equations (8) and (9).

[0095]

[0096] In this embodiment, the improved anti-noise zeroization neural network model generated based on the composite nonlinear activation function is suitable for processing time-varying noise and nonlinear dynamic characteristics in robot trajectory tracking.

[0097] In one embodiment of the present disclosure, the pseudo-inverse matrix to be solved is solved based on the improved anti-noise zeroization neural network model, to obtain a pseudo-inverse matrix with joint angles of the robot as variables, comprising: in a control period determined based on a time-varying expression, the pseudo-inverse matrix to be solved is iteratively updated based on the improved anti-noise zeroization neural network model until the constraint equation converges to achieve an optimization objective, to obtain a pseudo-inverse matrix with a numerical solution.

[0098] In some embodiments, the continuous time axis can be divided into fixed length control periods Δt such as 10 ms, and the pseudo-inverse matrix is updated once in each period, in the kth period, the Jacobian matrix J(θ(k)) is calculated based on the joint angle θ(k) at the current time, and is brought into the constraint equation, in each period, the time-varying parameter p(k) is dynamically adjusted according to the configured exponential function, the initial p(k) is larger, the error function converges faster, and the later p(k) automatically decays to prevent overshoot and enhance noise resistance.

[0099] In some embodiments, the error function is input into the composite nonlinear activation function The polynomial set compresses the noise amplitude through nonlinear transformation, preventing noise accumulation.

[0100] In some embodiments, iterative updating and convergence judgment are performed in each period, when ‖E(k+1)‖≤∈ (a preset threshold, such as 10 -6 ), it is determined that the constraint equation converges, the iteration is terminated, and the final pseudo-inverse matrix is output.

[0101] In this embodiment, by quickly solving the pseudo-inverse matrix in each control period, the end effector, such as a welding gun, etc., can accurately track the preset trajectory while suppressing the interference caused by motor vibration and sensor noise.

[0102] As Figure 5 shown in the present disclosure, in one embodiment, the target equation for solving the joint speed of the mechanical arm is constructed based on the Jacobian matrix and the corresponding pseudo-inverse matrix to be solved, including:

[0103] Step S502, based on the kinematic mapping relationship between the position of the end effector and the joint angle, a first correlation relationship between the position of the end effector and the joint angle is constructed.

[0104] In some embodiments, the first correlation relationship is as shown in equation (10).

[0105] d(t)=g(θ(t))(10)

[0106] Wherein, is the position of the end effector, θ(t) is the joint angle, and g() represents the kinematic mapping relationship.

[0107] In some embodiments, taking a six-joint mechanical arm as an example, θ(t)=[θ1(t),θ2(t),θ3(t),θ4(t),θ5(t),θ6(t)] T ∈R 6 .

[0108] The kinematic mapping relationship is as shown in equation (11).

[0109]

[0110] Wherein, l i denotes the length of each of the six rods, c i is the cosine function of the i-th joint angle, s i is the sine function of the i-th joint angle, for describing the effect of joint rotation on the end position.

[0111] Step S504, the first correlation relationship is differentiated based on the time variable to obtain a second correlation relationship between the end velocity and the joint velocity, wherein the Jacobian matrix is obtained based on the kinematic mapping relationship.

[0112] In some embodiments, the position mapping relationship d(t)=g(θ(t)) is differentiated with respect to time t, and according to the derivative rule of composite functions, equation (12) is obtained.

[0113]

[0114] Wherein, the Jacobian matrix J(θ(t)) describes the relationship between the joint velocity and the end velocity The elements of the Jacobian matrix are composed of the partial derivatives of the position function with respect to the joint angles, and reflect the contribution of each joint movement to the end speed.

[0115] In step S506, the second correlation relationship is expressed as a general solution form based on the Jacobian matrix, the pseudo-inverse matrix and the degree of freedom adjustment parameter of the robot arm, and a target equation is obtained.

[0116] In some embodiments, the robot arm may be in a singular configuration or a redundant state in practice, and the pseudo-inverse matrix needs to be introduced and the null space motion is considered.

[0117] In some embodiments, the target equation is as shown in equation (13).

[0118]

[0119] wherein, is the joint speed, is the pseudo-inverse matrix, is the expected value of the end speed, J(θ(t)) is the Jacobian matrix, I is a unit matrix consistent with the joint space dimension of the joint speed, and w(t) is the degree of freedom adjustment parameter.

[0120] In order to calculate the joint speed the pseudo-inverse matrix needs to be calculated first.

[0121] In this embodiment, by converting the complex nonlinear trajectory tracking problem into a linear equation form for solving, the singular and redundant cases are handled through the pseudo-inverse matrix, and the joint trajectory is optimized through the null space motion, for example, when the robot arm performs a welding task, the joint can be adjusted to avoid the limit position under the premise of meeting the end trajectory, thereby improving the reliability of task execution.

[0122] In one embodiment of the present disclosure, the target equation is solved based on the pseudo-inverse matrix to obtain a time-varying expression of the joint speed, and the joint control instruction is generated based on the time-varying expression of the joint speed, including: obtaining a time-varying expression of a desired position trajectory of an end effector; determining a time-varying expression of an expected value based on the time-varying expression of the desired position trajectory; introducing the pseudo-inverse matrix and the time-varying expression of the expected value into the target equation to obtain a time-varying expression of the joint speed.

[0123] In some embodiments, it is assumed that the six-link robot arm θ(0) = [π / 3, -π / 6, -π / 3, π / 3, π / 6, -π / 6] T , l1, l2, l3, l4, l5, l6 = 1, the noise is 0.5*cos(t), and the initial state of the robot arm is as shown in Figure 3The six-bar robot arm is used for trajectory tracking, and a time-varying expression of a desired trajectory of the six-bar robot arm trajectory tracking is shown in formula (14).

[0124]

[0125] In some embodiments, a time-varying expression of a desired value is obtained by derivation of a time-varying expression of a desired position trajectory

[0126] In some embodiments, a pseudo-inverse matrix and a time-varying expression of a desired value are introduced into a target equation to obtain a time-varying expression of joint speed, as shown in formula (13), wherein, It can be understood that the particular solution satisfies the end desired speed, It can be understood as a zero space motion item for optimizing the joint trajectory.

[0127] In this embodiment, the time-varying pseudo-inverse matrix dynamically adapts to the change of the robot arm configuration, ensures that the instruction at each moment is calculated based on the current joint angle, and further converts the desired trajectory of the six-bar robot arm trajectory tracking into a real-time speed instruction of each joint, so that the end effector can accurately track the desired trajectory.

[0128] In one embodiment of the present disclosure, a tracking trajectory of the robot arm is obtained based on an execution result of the joint control instruction, including: driving the joint motion of the robot arm based on the joint control instruction, and measuring the joint angle in real time based on the sensor; determining the actual position of the end effector based on the kinematic mapping relationship of the joint angle, to obtain the tracking trajectory based on the change of the actual position.

[0129] In some embodiments, an error between the desired trajectory and the actual trajectory of the robot arm is shown in formula (15).

[0130]

[0131] In this embodiment, the generation of the tracking trajectory is realized through a closed-loop feedback mechanism: the joint control instruction drives each joint to move at the calculated speed, while the sensor (such as an encoder) collects the actual joint angle in real time; the real-time joint angle is substituted into the forward kinematics equation (i.e., the kinematic mapping relationship) to calculate the actual position coordinates of the end effector; the continuous change of the actual position with time forms the tracking trajectory, and through the comparison of the deviation between the actual position and the desired position, the control instruction can be dynamically corrected to ensure that the tracking trajectory approximates the desired trajectory.

[0132] The robot according to one embodiment of the present disclosure comprises: a robot arm body comprising a plurality of joints, actuators driving the joints, and sensors detecting the joint angles; a control unit comprising a processor and a memory; the memory is used to store executable instructions of the processor; the processor is configured to generate the robot arm trajectory of any one of the embodiments of the first aspect described above by executing the executable instructions.

[0133] In some embodiments, the robot arm body: is composed of a plurality of joints in series, each joint is equipped with an actuator (such as a servo motor) and a sensor (such as an encoder). The actuator is responsible for converting electrical signals into joint rotation, and the sensor measures the joint angle in real time and feeds back to the control unit.

[0134] In some embodiments, the control unit: the processor (such as PLC, industrial computer) executes the trajectory planning algorithm, and the memory stores executable instructions and intermediate data (such as Jacobian matrix, pseudo-inverse matrix).

[0135] In some embodiments, the processor realizes the following steps by executing the instructions in the memory:

[0136] Generate the desired trajectory of the end effector based on the task requirements, as shown in equation (14).

[0137] Real-time calculation of Jacobian pseudo-inverse matrix using improved anti-noise zeroing neural network model Convert the desired trajectory into joint velocity instructions

[0138] Convert the joint velocity instructions into PWM signals to drive the actuators, and collect sensor data to calculate the actual position d(t) to obtain the tracking trajectory, as shown in Figure 6 Adjust the control instructions through closed-loop feedback to reduce tracking errors.

[0139] As shown in Figure 7 The deviation between the expected path and the actual trajectory of the end effector is small, indicating that the actual motion trajectory of the end effector of the robot arm can better fit the desired trajectory, verifying the effectiveness of the trajectory tracking control.

[0140] Among them, the anti-noise characteristics (such as time-varying parameters, composite nonlinear activation functions) are realized through real-time calculation of the processor: based on the time-varying parameters, the convergence rate is dynamically adjusted according to the current error size, which is realized on the hardware by the processor updating the parameters in the control period in real time; and the composite nonlinear activation function suppresses sensor noise through mathematical operation, preventing system oscillation caused by noise amplification.

[0141] Figure 8is a diagram showing the error between the trajectory tracked by the robot arm and the desired trajectory based on the improved anti-noise zeroization neural network in a noise environment, Figure 9 is a diagram showing the error between the trajectory tracked by the robot arm and the desired trajectory based on the improved anti-noise zeroization neural network in a noise environment, Figure 10 is a diagram showing the error between the trajectory tracked by the robot arm and the desired trajectory based on the improved anti-noise zeroization neural network in a noise environment, Figure 8 It can be seen that the model accuracy significantly decreases in the noise, and the improved anti-noise zeroization neural network is based on Figure 9 and Figure 10 It can be seen that the improved anti-noise zeroization neural network has high consistency in the basic tracking characteristics with or without noise, and as shown in Figure 9 Although there is noise interference, the error does not get out of control, indicating that the improved anti-noise zeroization neural network can suppress noise to a certain extent.

[0142] Figure 11 is a diagram showing the angle change of the robot arm based on the improved anti-noise zeroization neural network, Figure 12 is a diagram showing the angular velocity change of the robot arm based on the improved anti-noise zeroization neural network. As shown in Figure 11 and Figure 12 The fluctuation periods of 0-1 seconds, 3-4 seconds, and 6-7 seconds are consistent, indicating that the time-domain characteristics of the angle change and the angular velocity change are matched, and as compared with Figure 11 and Figure 10 It can be seen that the angle does not jump drastically, indicating that the joint angle command solved by the improved model through the pseudo-inverse matrix effectively suppresses the noise interference.

[0143] In this embodiment, the improved anti-noise zeroization neural network model can be applied to the robot arm trajectory tracking, and the time-varying parameters and the activation function in the model make the neural network model have strong robustness and fast convergence properties, so that the neural network model can quickly and accurately solve time-varying problems, improve the anti-noise ability and convergence speed of the model, and enable the robot arm to track the trajectory in a noise environment.

[0144] It should be noted that the above figures are only schematic illustrations of the processes included in the method according to the exemplary embodiments of the present application, and are not for limiting purposes. It is easy to understand that the processes shown in the above figures do not indicate or limit the time sequence of these processes. In addition, it is also easy to understand that these processes can be executed synchronously or asynchronously, for example, in multiple modules.

[0145] The robot arm trajectory tracking device 1300 according to the embodiment of the present application will be described below with reference to Figure 13 Figure 13 The robot arm trajectory tracking device 1300 shown is only an example, and should not limit the functions and use range of the embodiments of the present application.​

[0146] The mechanical arm trajectory tracking apparatus 1300 is in the form of a hardware module. Components of the mechanical arm trajectory tracking apparatus 1300 can include but are not limited to: a construction module 1302 configured to construct a target equation for solving joint velocity of a mechanical arm based on a Jacobian matrix and a corresponding pseudo-inverse matrix to be solved, the Jacobian matrix being used to describe a mapping relationship between joint velocity and end velocity of an end effector of the mechanical arm; a first solving module 1304 configured to solve the pseudo-inverse matrix to be solved based on an improved anti-noise nulling neural network model, to obtain a pseudo-inverse matrix with joint angle of the mechanical arm as a variable, the improved anti-noise nulling neural network model being configured based on time-varying parameters and a composite nonlinear activation function; a second solving module 1306 configured to solve the target equation based on the pseudo-inverse matrix, to obtain a time-varying expression of the joint velocity, and to generate joint control instructions based on the time-varying expression of the joint velocity; and a tracking trajectory obtaining module 1308 configured to obtain a tracking trajectory of the mechanical arm based on an execution result of the joint control instructions.

[0147] Those skilled in the art can understand that the various aspects of the present application can be implemented as a system, a method or a program product. Therefore, the various aspects of the present application can be embodied as a complete hardware implementation, a complete software implementation (including firmware, microcode, etc.), or an implementation combined with hardware and software aspects, which can be collectively referred to as "circuitry", "module" or "system" here.

[0148] The electronic device 1400 according to this embodiment of the present application will be described below with reference to Figure 14 The electronic device 1400 can be a computer device or a robot. Figure 14 The electronic device 1400 shown is merely an example and should not impose any limitation on the functions and use range of the embodiments of the present application.

[0149] As shown in Figure 14 The electronic device 1400 is in the form of a general-purpose computing device. Components of the electronic device 1400 can include but are not limited to: the above-mentioned at least one processing unit 1410, the above-mentioned at least one storage unit 1420, and a bus 1430 connecting different system components including the storage unit 1420 and the processing unit 1410.

[0150] The storage unit stores program code which can be executed by the processing unit 1410, so that the processing unit 1410 performs the steps according to various exemplary embodiments of the present application described in the above "Exemplary Method" section of the present specification. For example, the processing unit 1410 can execute the schemes as Figure 3 described.

[0151] The storage unit 1420 can include a readable medium in the form of volatile storage such as random access memory (RAM) 14201 and / or cache memory 14202, and also can include a non-volatile storage such as read only memory (ROM) 14203.

[0152] The storage unit 1420 also can include a program / utility 14204 having a set (at least one) of program modules 14205, including an operating system, one or more application programs, other program modules, and program data, each of which can give the electronic device 1400 its functionality, or some combination thereof.

[0153] The bus 1430 can represent one or more of several types of bus structures, including a storage bus or bus controller, a peripheral bus, a graphics acceleration port, a processor or local bus using any of a variety of bus architectures.

[0154] The electronic device 1400 also can communicate with one or more external devices 1470, such as a keyboard or a pointing device, via an I / O interface 1450. Additionally, an electronic device 1400 can communicate with one or more devices that enable a user to interact with the electronic device 1400 in a network environment or to display information related to the electronic device 1400 on an external device, such as an interactive television. In one embodiment, the electronic device 1400 can communicate with one or more devices via an RF interface 1452. In some embodiments, the electronic device 1400 can include one or more communication interfaces 1454, such as a wireless communication interface, a USB interface, a Bluetooth® interface, and / or an infrared interface.

[0155] Those skilled in the art will readily recognize that the example embodiments described herein can be implemented using software and / or hardware in combination with software. Thus, the technical solutions according to the embodiments of the present disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, a USB flash drive, a mobile hard disk, etc.) or a network, and includes a number of instructions to make a computing device (such as a personal computer, a server, a terminal device, or a network device, etc.) execute the methods according to the embodiments of the present disclosure.

[0156] In the exemplary embodiments of the present disclosure, a computer readable storage medium having stored thereon a program product capable of implementing the above-described method of the present specification is also provided. In some possible implementations, various aspects of the present application can also be implemented in the form of a program product including program code, which, when run on an electronic device, causes the electronic device to perform the steps described in the above "Exemplary Methods" section according to various exemplary embodiments of the present application.

[0157] The program product for implementing the above-described method according to the embodiments of the present application can take the form of a portable compact disc read-only memory (CD-ROM) and include program code, and can be run on an electronic device, such as a personal computer. However, the program product of the present application is not limited thereto, and in the present document, the readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0158] The program product can take any combination of one or more readable media. The readable medium can be a readable signal medium or a readable storage medium. The readable storage medium, for example, can be, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples (a non-exhaustive list) of the readable storage medium include an electrical connection having one or more wires, a portable disc, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof. The computer readable signal medium can include a data signal borne in a baseband or as a part of a carrier wave, in which readable program code is borne. Such a propagated data signal can take various forms, including but not limited to an electromagnetic signal, an optical signal, or any suitable combination thereof. The readable signal medium can also be any readable medium other than the readable storage medium, which can send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, apparatus, or device.

[0159] The program code embodied on the computer readable medium can be transmitted using any appropriate medium, including but not limited to wireless, wired, optical fiber cable, RF, etc., or any suitable combination of the foregoing. Computer program code for carrying out operations for aspects of the present application can be written in any combination of one or more programming languages, including an object oriented programming language such as Java, C++ or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code can execute entirely on the user's computing device, partly on the user's computing device, as a stand-alone software package, partly on the user's computing device and partly on a remote computing device or entirely on the remote computing device or server. In the latter scenario, the remote computing device can be connected to the user's computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection can be made to an external computing device, such as through the Internet using an Internet Service Provider.

[0160] It should be noted that, although several modules or units of the devices for action execution are mentioned in the foregoing detailed description, such a division is not mandatory. Indeed, according to an embodiment of the present disclosure, the features and functionalities of two or more modules or units described above can be embodied in one module or unit. Conversely, the features and functionalities of one module or unit described above can be further divided into embodied by a plurality of modules or units.

[0161] In addition, although the various steps of the methods in the present disclosure are described in a particular order in the drawings, this does not require or imply that the steps must be performed in this particular order, or that all of the steps must be performed to achieve the desired result. Additionally or alternatively, certain steps can be omitted, multiple steps can be combined into one step, one step can be split into multiple steps, etc. Through the above description of the embodiments, those skilled in the art can easily understand that the example embodiments described herein can be implemented by software, or by software in combination with necessary hardware. Therefore, the technical solutions according to the embodiments of the present disclosure can be embodied in the form of a software product. The software product can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash disk, a mobile hard disk, etc.) or a network, and includes a number of instructions to enable a computing device (which can be a personal computer, a server, a mobile terminal, or a network device, etc.) to perform the methods according to the embodiments of the present disclosure. Those skilled in the art will easily derive other embodiments of the present disclosure after considering the specification and practicing the invention disclosed herein. The present application is intended to cover any variations, uses, or adaptive changes of the present disclosure that follow the general principles of the present disclosure and include common knowledge or conventional technical means in the technical field that are not disclosed by the present disclosure. The specification and examples are only considered as exemplary, and the true scope and spirit of the present disclosure are indicated by the appended claims.

Claims

1. A robot arm trajectory tracking method, characterized in that: include: Constructing a target equation for solving the joint velocity of the robotic arm based on a Jacobian matrix and a corresponding pseudo-inverse matrix to be solved, wherein the Jacobian matrix is ​​used to describe a mapping relationship between the joint velocity and the end velocity of the end effector of the robotic arm; Solving the pseudo-inverse matrix to be solved based on an improved noise-resistant annihilation neural network model to obtain the pseudo-inverse matrix with the joint angle of the robotic arm as a variable, wherein the improved noise-resistant annihilation neural network model is configured based on time-varying parameters and a composite nonlinear activation function; Solving the target equation based on the pseudo-inverse matrix to obtain a time-varying expression of the joint velocity, and generating a joint control instruction based on the time-varying expression of the joint velocity; The tracking trajectory of the robotic arm is obtained based on the execution result of the joint control instruction.

2. The robot arm trajectory tracking method according to claim 1, characterized in that: Before solving the pseudo-inverse matrix to be solved based on the improved noise-resistant annihilation neural network model, the method further includes: Based on the reflexivity that the pseudo-inverse matrix needs to satisfy, a constraint equation with the pseudo-inverse matrix as the solution target is constructed, and the deviation between the constraint equation and the optimization target is configured as the error function, where the constraint equation is is the pseudo-inverse matrix, J(θ(t)) is the Jacobian matrix, J T (θ(t)) is the transposed matrix of the Jacobian matrix; Configuring an initial annihilation neural network model based on the error function, wherein the initial annihilation neural network model includes a fixed gain parameter; The configured time-varying parameters and the composite nonlinear activation function are used to replace the fixed gain parameters to obtain the improved noise-resistant annihilation neural network model, wherein the time-varying parameters are used to enhance the convergence speed of the improved noise-resistant annihilation neural network model, and the composite nonlinear activation function is used to perform noise-resistant enhancement on the improved noise-resistant annihilation neural network model.

3. The robot arm trajectory tracking method according to claim 2, characterized in that: Also includes: An exponential function is configured by using a linear growth term, a nonlinear term with a saturation characteristic, and a constant term as exponential terms, so that a negative value of the exponential function is used as the time-varying parameter.

4. The robot arm trajectory tracking method according to claim 3, characterized in that: The linear growth term is determined based on the product of the first gain parameter and the time variable; A nonlinear term having a saturation characteristic is determined based on a product of an arc tangent function of the time variable and a second gain parameter; The constant term is determined based on a third gain parameter.

5. The robot arm trajectory tracking method according to claim 2, characterized in that: Also includes: The composite nonlinear activation function is constructed based on the nonlinear enhancement term and the linear stabilization term.

6. The robot arm trajectory tracking method according to claim 5, characterized in that: The nonlinear enhancement term is determined based on the sum of a first polynomial group, a second polynomial group, an exponential term, and a sign function, wherein the first polynomial group is represented by α1(|x| m +|x| m+2 +|x| m+4 ), the second polynomial group is expressed as α2(|x| n +|x| 2n +|x| 3n ), the exponential term is expressed as α1 is the first coefficient, α2 is the second coefficient, α3 is the third coefficient, x represents the error function, m is the first exponential parameter, n is the second exponential parameter, k is the third exponential parameter, and the linear stability term is determined based on the fourth coefficient and the error function.

7. The robot arm trajectory tracking method according to claim 2, characterized in that: Solving the pseudo-inverse matrix to be solved based on the improved noise-resistant annihilation neural network model to obtain the pseudo-inverse matrix with the joint angle of the robotic arm as a variable, including: In a control cycle determined based on the time variable of the time-varying expression, the pseudo-inverse matrix to be solved is iteratively updated based on the improved noise-resistant annihilation neural network model until the constraint equation converges to achieve the optimization goal, thereby obtaining the pseudo-inverse matrix with a numerical solution.

8. The robot arm trajectory tracking method according to claim 1, characterized in that: Based on the Jacobian matrix and the corresponding pseudo-inverse matrix to be solved, a target equation for solving the joint velocity of the robotic arm is constructed, including: Constructing a first association relationship between the position of the end effector and the joint angle based on a kinematic mapping relationship between the position of the end effector and the joint angle; Derivative the first association relationship based on a time variable to obtain a second association relationship between the terminal velocity and the joint velocity, wherein the Jacobian matrix is ​​obtained based on the kinematic mapping relationship; The second association relationship is expressed as a general solution based on the Jacobian matrix, the pseudo-inverse matrix and the degree of freedom adjustment parameters of the manipulator to obtain the target equation, which is: in, is the joint velocity, is the pseudo-inverse matrix, is the expected value of the terminal velocity, J(θ(t)) is the Jacobian matrix, I is the unit matrix consistent with the joint space dimension of the joint velocity, and w(t) is the degree of freedom adjustment parameter.

9. The robot arm trajectory tracking method according to claim 8, characterized in that: Solving the target equation based on the pseudo-inverse matrix to obtain a time-varying expression of the joint velocity, and generating a joint control instruction based on the time-varying expression of the joint velocity, including: Obtaining a time-varying expression of a desired position trajectory of the end effector; Determining a time-varying expression for the expected value based on the time-varying expression for the expected position trajectory; The pseudo-inverse matrix and the time-varying expression of the expected value are introduced into the target equation to obtain the time-varying expression of the joint velocity.

10. The robot arm trajectory tracking method according to claim 9, characterized in that: Obtaining a tracking trajectory of the robotic arm based on an execution result of the joint control instruction, including: driving the joint motion of the robotic arm based on the joint control instruction, and measuring the joint angle in real time based on a sensor; The actual position of the end effector is determined based on the joint angle and the kinematic mapping relationship, so as to obtain the tracking trajectory based on the change of the actual position.

11. A robot arm trajectory tracking device, characterized in that: include: A construction module is used to construct a target equation for solving the joint velocity of the robotic arm based on a Jacobian matrix and a corresponding pseudo-inverse matrix to be solved, wherein the Jacobian matrix is ​​used to describe the mapping relationship between the joint velocity and the end velocity of the end effector of the robotic arm; a first solving module, configured to solve the pseudo-inverse matrix to be solved based on an improved noise-resistant annihilation neural network model to obtain the pseudo-inverse matrix with the joint angle of the robotic arm as a variable, wherein the improved noise-resistant annihilation neural network model is configured based on time-varying parameters and a composite nonlinear activation function; a second solving module, configured to solve the target equation based on the pseudo-inverse matrix to obtain a time-varying expression of the joint velocity, and generate a joint control instruction based on the time-varying expression of the joint velocity; A tracking trajectory acquisition module is used to obtain the tracking trajectory of the robotic arm based on the execution result of the joint control instruction.

12. A robot, characterized in that: include: A robotic arm body, the robotic arm body comprising a plurality of joints, actuators for driving the joints to move, and sensors for detecting joint angles of the joints; a control unit connected to the actuator and the sensor, the control unit comprising a processor and a memory; The memory is used to store executable instructions of the processor; The processor is configured to execute the robot arm trajectory tracking method according to any one of claims 1 to 10 by executing the executable instructions.

13. An electronic device, characterized in that: include: processor; as well as a memory for storing executable instructions of the processor; The processor is configured to execute the robot arm trajectory tracking method according to any one of claims 1 to 10 by executing the executable instructions.

14. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the robot arm trajectory tracking method according to any one of claims 1 to 10 is implemented.

15. A computer program product having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the robot arm trajectory tracking method according to any one of claims 1 to 10 is implemented.

Images