Trajectory planning control method and system for robot arm based on bafarnn model

Abstract

The application relates to the technical field of robot control, and discloses a mechanical arm trajectory planning control method and system based on a BAFARNN model. The method comprises the following steps: a kinematic model of a mechanical arm is established, a trajectory tracking problem is converted into a time-varying equation; a bounded adaptive function is designed to activate a recursive neural network model, an error function is defined, and a dynamic equation is constructed; a segmented adaptive coefficient function is designed, a gain is dynamically adjusted according to an error norm and time; a Lissajous curve is set as an expected trajectory, and a simulation environment is initialized; joint speed is solved in real time through an ODE numerical method, and the mechanical arm is driven to move; actual motion data is collected, compared with instructions, and closed-loop feedback control is triggered when a threshold is exceeded. The segmented adaptive coefficient function is used for realizing fast convergence, the bounded activation function and the negative feedback mechanism are used for restraining noise, and high-precision and real-time trajectory tracking of the mechanical arm in a dynamic environment is realized.

Description

Technical Field

[0001] This invention relates to the field of robot control technology, specifically to a method and system for trajectory planning and control of a robotic arm based on the BAFARNN model. Background Technology

[0002] As the core execution unit, robotic arms are expanding their applications from traditional structured and deterministic industrial environments to unstructured, dynamically uncertain, and complex scenarios, such as human-robot collaborative assembly, intelligent logistics sorting, medical surgical assistance, and home life services. In these advanced applications, robotic arms not only need to achieve high-precision trajectory tracking, but also face severe challenges such as real-time response to time-varying tasks, strong robustness under model uncertainty and external disturbances, and dynamic replanning capabilities to cope with unexpected situations. Therefore, developing a trajectory planning and control algorithm that can generate high-precision, high-smoothness, and strong anti-interference capabilities online in real time has become a key technological problem urgently needing to be solved in the field of robotic arms. Summary of the Invention

[0003] To address the aforementioned issues, this invention provides a robotic arm trajectory planning and control method and system based on the BAFARNN model. By designing a piecewise adaptive coefficient function to achieve dynamic adjustment of the gain, and employing a bounded activation function and a negative feedback mechanism to suppress noise, the method significantly improves the trajectory tracking accuracy, convergence speed, and robustness of the robotic arm in dynamic environments.

[0004] To achieve the above objectives, the present invention provides the following technical solution:

[0005] On one hand, embodiments of the present invention provide a robotic arm trajectory planning and control method based on a BAFARNN model, the method comprising the following steps:

[0006] S100: Obtain the kinematic parameters, joint displacement range, dynamic constraints, and desired trajectory parameters of the robotic arm;

[0007] S200, establish a kinematic model of the robotic arm based on the kinematic parameters of the robotic arm, and transform the trajectory tracking problem into a time-varying equation;

[0008] S300: Construct a bounded adaptive function to activate the recurrent neural network, define the error function and construct the dynamic equation;

[0009] S400, construct a piecewise adaptive coefficient function based on the norm of the error function and the time variable; the piecewise adaptive coefficient function dynamically adjusts the gain parameter according to the error magnitude and time to achieve fast convergence;

[0010] S500, set the Lissajous curve as the desired trajectory, initialize the simulation environment, and configure the BAFARNN model parameters and the initial state of the robotic arm;

[0011] S600 uses the ODE numerical method to solve the dynamic equations, outputs joint speed control commands in real time, drives the robotic arm actuator to move, and achieves trajectory tracking.

[0012] S700 collects the actual rotation angle of each joint of the robotic arm and the actual position of the end effector, compares them with the joint speed control command, and if the deviation exceeds a preset threshold, triggers closed-loop feedback control to generate feedback control command for real-time adjustment.

[0013] Optionally, the step of establishing a kinematic model of the robotic arm based on its kinematic parameters, transforming the trajectory tracking problem into a time-varying equation, includes:

[0014] S210, Obtain the joint angle vector of the robotic arm. Where n is the number of degrees of freedom, Let T be the angle of the nth joint at time t, and the superscript T indicates transpose.

[0015] S220, establish the forward kinematics model of the robotic arm according to the DH parameter method, and calculate the position and attitude of the end effector in the base coordinate system;

[0016] S230, Calculate the Jacobian matrix Establish kinematic equations Where X is the position and attitude vector of the end effector in the base coordinate system. For joint angle vectors, The desired trajectory velocity at the end point, Let be the joint angle vector at time t. Let be the joint angular velocity vector at time t;

[0017] S240, combined with joint velocity constraints The kinematic equations are transformed into standard time-varying equations. Where E(t) is the Jacobian matrix, Z(t) is the joint velocity vector. V(t) is the negative value of the desired trajectory velocity vector at the end. ; This is the lower limit of joint velocity. This represents the upper limit of joint velocity.

[0018] Optionally, the step of constructing a bounded adaptive function to activate the recurrent neural network, defining an error function, and constructing dynamic equations includes:

[0019] S310, define an error function ζ(t)=E(t)Z(t)+V(t) for measuring the deviation between the actual trajectory and the desired trajectory;

[0020] S320, perform a nonlinear transformation on the error function using a bounded activation function f(ζ)=tanh(ζ), and design a dynamic equation based on the nonlinear transformation result , where Π(ζ(t), t) is a time-varying gain matrix, ζ is a vector value of the error function ζ(t), and tanh() represents a hyperbolic tangent function, is the derivative of the error function ζ(t);

[0021] S330, introduce a negative feedback regulation mechanism to suppress the influence of sensor noise and environmental disturbance on system stability by introducing a negative term -ζ(t);

[0022] S340, construct a Lyapunov function , prove the convergence and robustness of the BAFARNN model by Lyapunov stability theory, and prove the derivative .

[0023] Optionally, in S400, the piecewise adaptive coefficient function is:

[0024] ;

[0025] wherein, is a design parameter, is the Frobenius norm of the error function, , represents the square of the i-th row and j-th column element of the error function ζ(t).

[0026] Optionally, the mathematical expression of the Lissajous curve is:

[0027] ;

[0028] wherein, A, B are amplitude parameters, , is a frequency parameter, φ is a phase difference, and (x0, y0, z0) is a trajectory offset, represents the position coordinates of the end effector in the base coordinate system at time t.

[0029] Optionally, the dynamic equation is solved using an ODE numerical method, real-time output joint speed control instructions are output, the movement of the robot effector is driven, trajectory tracking is achieved, and the method comprises:

[0030] S610, in each control period, the current joint angle θ(t) is collected, the Jacobian matrix J(θ(t)) and the error function ζ(t) are calculated;

[0031] S620, calculating the error norm according to the current time t and the error norm

[0032] S630, solving the dynamic equation to obtain the error change rate , and further calculating the joint speed command ;

[0033] S640, sending the joint speed command to the mechanical arm servo driver to drive the joint motor to move.

[0034] Optionally, the actual rotation angle of each joint of the collection mechanical arm and the actual position of the end effector are compared with the joint speed control command, and if the deviation exceeds a preset threshold, a closed-loop feedback control is triggered to generate a feedback control command for real-time adjustment, including:

[0035] S710, collecting the actual rotation angle of each joint in real time through a high-precision encoder , collecting the actual position of the end through a vision sensor ;

[0036] S720, calculating the position deviation and the angle deviation ; wherein , are the expected end position and joint speed command, respectively;

[0037] S730, when the norm of the position deviation is greater than a first preset threshold or the norm of the angle deviation is greater than a second preset threshold, starting a closed-loop feedback mechanism, and using a second-order low-pass filter to smooth the deviation signal and suppress high-frequency noise interference;

[0038] S740, generating a feedback compensation amount through a PID control algorithm to online correct the joint speed command, obtaining a final control command and sending it to the mechanical arm driver for execution.

[0039] On the other hand, the embodiment of the present application provides a mechanical arm trajectory planning control system based on a BAFARNN model, comprising:

[0040] a data acquisition module for acquiring kinematic parameters, joint displacement range, dynamic constraint conditions and expected trajectory parameters of a mechanical arm;

[0041] a kinematic modeling module for establishing a kinematic model of the mechanical arm according to the kinematic parameters of the mechanical arm, and converting a trajectory tracking problem into a time-varying equation;

[0042] A model construction module is configured to construct a bounded adaptive function activation recurrent neural network, define an error function and construct a dynamic equation.

[0043] An adaptive coefficient construction module is configured to construct a piecewise adaptive coefficient function according to a norm of the error function and a time variable; the piecewise adaptive coefficient function dynamically adjusts a gain parameter according to an error size and a time to achieve fast convergence.

[0044] A trajectory generation module is configured to set a Lissajous curve as the desired trajectory, perform simulation environment initialization, configure BAFARNN model parameters and initial states of a robot arm, and perform simulation environment initialization.

[0045] A solution execution module is configured to solve the dynamic equation by using an ODE numerical method, output joint speed control instructions in real time, drive a robot arm actuator to move, and achieve trajectory tracking.

[0046] A feedback control module is configured to collect actual angles of joints of the robot arm and an actual position of an end effector, compare the actual angles and the actual position with the joint speed control instructions, trigger closed-loop feedback control if a deviation exceeds a preset threshold, and generate feedback control instructions to perform real-time adjustment.

[0047] In another aspect, an embodiment of the present application provides a robot arm trajectory planning control system based on a BAFARNN model, which comprises:

[0048] At least one processor;

[0049] At least one memory configured to store at least one program;

[0050] When the at least one program is executed by the at least one processor, the at least one processor is caused to implement the method described above.

[0051] In another aspect, an embodiment of the present application provides a computer readable storage medium, which stores a program executable by a processor, and the program executable by the processor is used to execute the method described above when executed by the processor.

[0052] The beneficial effects of the present application are: the present application discloses a mechanical arm trajectory planning control method and system based on a BAFARNN model, the present application realizes dynamic adjustment of gain by designing a segmented self-adaptive coefficient function, the function adopts different gain adjustment strategies in different stages according to the norm of an error function and a time variable. At the same time, a bounded activation function is used to perform nonlinear transformation on the error function, so as to limit the output of the neural network within a certain range, avoid the problems of gradient explosion or neuron saturation that may occur in traditional neural networks, and enhance the numerical stability of the model. In addition, by introducing a negative feedback regulation mechanism, the influence of sensor noise and environmental interference on the stability of the system is effectively suppressed, and the anti-interference ability of the mechanical arm in a complex dynamic environment is improved. By constructing a Lyapunov function, the convergence and robustness of the system are strictly guaranteed, so that the end effector of the mechanical arm can quickly and accurately track the desired trajectory, even in the presence of model uncertainty and external disturbances, the trajectory tracking accuracy and dynamic response performance can still be maintained. In summary, the present application can significantly improve the trajectory tracking accuracy, convergence speed and robustness of the mechanical arm in a dynamic environment. BRIEF DESCRIPTION OF DRAWINGS

[0053] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0054] Figure 1 A flowchart of a mechanical arm trajectory planning control method based on a BAFARNN model of the present application;

[0055] Figure 2 A logic block diagram of a mechanical arm trajectory planning control system based on a BAFARNN model of the present application;

[0056] Figure 3 A mechanical arm joint angle response curve, showing the joint angle change of a six-degree-of-freedom mechanical arm in 20 seconds;

[0057] Figure 4 A mechanical arm joint speed response curve, showing the joint speed time domain characteristics based on the BAFARNN control model;

[0058] Figure 5 A mechanical arm joint position curve, showing the position change with time in three degrees of freedom;

[0059] Figure 6 A mechanical arm end effector trajectory tracking diagram, showing the motion trajectory in three-dimensional space;

[0060] Figure 7 The mechanical arm end effector velocity response curve chart shows the velocity changes in X, Y and Z directions;

[0061] Figure 8 The mechanical arm end effector acceleration response curve chart shows the dynamic characteristics of three-axis acceleration;

[0062] Figure 9 The mechanical arm end effector position error analysis chart shows the position tracking errors in X, Y and Z axes;

[0063] Figure 10 The mechanical arm end effector velocity error analysis chart shows the high convergence characteristics of velocity error;

[0064] Figure 11 The mechanical arm two-dimensional trajectory tracking accuracy verification chart compares the expected path and the actual trajectory;

[0065] Figure 12 The mechanical arm three-dimensional motion trajectory simulation analysis chart shows the space motion trajectory of the UR5 mechanical arm;

[0066] Figure 13 The mechanical arm high-precision trajectory drawing demonstration chart shows the scene of the industrial mechanical arm performing the precise drawing task. DETAILED DESCRIPTION

[0067] The disclosed concept, specific structure and generated technical effects will be described clearly and completely in combination with the embodiments and the drawings, so as to fully understand the purposes, schemes and effects of the present disclosure. It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0068] In order to make the purposes, technical schemes and advantages of the present application clearer, the present application will be further described in combination with the drawings and examples. It should be understood that the specific examples described herein are only used to explain the present application and do not limit the present application. When the following description refers to the drawings, the same numbers in different drawings represent the same or similar elements unless otherwise indicated. The implementation described in the following exemplary embodiments does not represent all the implementations consistent with the embodiments of the present application, but is only an example of devices and methods consistent with some aspects of the embodiments of the present application as described in the appended claims.

[0069] It can be understood that the terms "first", "second", and the like used in the present application can be used herein to describe various concepts, but unless specifically stated, these concepts are not limited by these terms. These terms are only used to distinguish one concept from another. For example, without departing from the scope of embodiments of the present application, the first information can also be referred to as the second information, and similarly, the second information can also be referred to as the first information. Depending on the context, the word "if" as used herein can be interpreted as "when" or "upon determining" or "in response to determining".

[0070] The terms "at least one", "multiple", "each", "any" and the like used in the present application include one, two or more than two, multiple includes two or more than two, each refers to each of the corresponding multiple, and any refers to any one of the multiple.

[0071] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as understood by a person skilled in the art to which the present application belongs. The terms used herein are only for the purpose of describing the embodiments of the present application and are not intended to limit the present application.

[0072] The technical terms related to the present application are explained as follows:

[0073] ZNN (Zeroing Neural Network): Zeroing Neural Network, which is a recurrent neural network, and the design purpose is to solve time-varying problems in real time. This method converts the problem into a dynamic system, and by constructing and zeroing the error function, the system state is forced to converge to the theoretical solution of the time-varying problem in a limited time.

[0074] BAFRNN (Bounded Adaptive Function Activated Recurrent Neural Network): Bounded Adaptive Function Activated Recurrent Neural Network model, which has high adaptability of related parameters, can be adjusted according to different application scenarios, and is more suitable for basic research field. BAFRNN model is an improved version of ZNN model with limited adaptive function, and compared with OZNN model, the innovative activation function has better convergence speed and calculation accuracy.

[0075] The technical solutions in the related art mainly focus on the trajectory planner based on ZNN. The most representative is to use the traditional ZNN model or the improved ZNN model based on the monotonic increasing activation function, such as OZNN.

[0076] Traditional ZNN model: This model is the foundational framework for solving time-varying problems. Its core idea is to construct a scalar or vector form of error function for time-varying problems, and then design a dynamic evolution law that forces the error function to converge to zero exponentially. Although this model provides a theoretical foundation for real-time solving, its convergence speed is relatively slow, and the convergence accuracy and stability will decrease significantly when there are external disturbances or computational noise.

[0077] OZNN model: To accelerate convergence, researchers propose introducing nonlinear activation functions into the dynamic equations of ZNN. OZNN is the most typical representative. By using these nonlinear functions, the model can obtain greater convergence driving force when the error is large, thereby accelerating the convergence speed to some extent.

[0078] In summary, the related art has the following disadvantages:

[0079] Slow convergence speed: The traditional ZNN model (such as OZNN) uses a fixed gain coefficient, which cannot be dynamically adjusted according to the error, resulting in a delay in solving.

[0080] Poor noise resistance: Under sensor noise or environmental interference, the existing model (such as NTZNN) diverges in error and cannot maintain stability.

[0081] Low resource efficiency: Fixed parameter models consume excessive computational resources during solving, making them unsuitable for real-time control.

[0082] Insufficient constraint handling: Existing methods have difficulty handling inequality constraints such as joint velocity of a robotic arm.

[0083] To address these technical problems, the present application proposes a mechanical arm trajectory planning control method and system based on a bounded adaptive function activated recurrent neural network (BAFARNN).

[0084] The essence of trajectory planning and control is to solve a time-varying mathematical problem, i.e., how to calculate the optimal motion instructions for each joint of the mechanical arm in real time based on time-varying task objectives. Traditional control methods often struggle when faced with nonlinear, strongly coupled robot dynamics and time-varying tasks, making it difficult to ensure convergence speed, accuracy, and robustness simultaneously. Therefore, researchers have turned their attention to intelligent computing, particularly neural network methods that have parallel processing capabilities and strong function approximation capabilities.

[0085] Mechanical arm trajectory tracking control technology is the core of industrial automation and robotics, widely used in welding, spraying, assembly and precision drawing scenarios. In dynamic environment, the mechanical arm needs to track complex trajectories (such as curved paths) with high precision, while meeting joint speed, angle and other constraint conditions. Traditional methods such as gradient method or double neural network model are based on static optimization assumption, which produces lag error under time-varying trajectory, and is sensitive to noise. The invention is based on the BAFARNN model proposed in annex II, which realizes high-precision, real-time trajectory tracking of the mechanical arm through adaptive coefficient and negative feedback adjustment, suitable for noisy industrial environment.

[0086] The purpose of the present invention is:

[0087] The adaptive coefficient function of the BAFARNN model is used to dynamically adjust the gain and accelerate the convergence.

[0088] The noise is suppressed by the bounded function and negative feedback mechanism, and the robustness is improved.

[0089] Optimize the efficiency of the algorithm, reduce the dependence on hardware, and realize real-time drawing tracking of the mechanical arm in dynamic environment.

[0090] Adapt the BAFARNN model to handle the kinematic constraints of the mechanical arm, and improve the flexibility of application.

[0091] Reference Figure 1 As Figure 1 The method comprises the following steps:

[0092] S100, obtain the kinematic parameters, joint displacement range, dynamic constraint conditions and expected trajectory parameters of the mechanical arm.

[0093] It should be noted that the kinematic parameters of the mechanical arm include link length, joint type, number of degrees of freedom, etc., which determine the kinematic characteristics of the mechanical arm. The joint displacement range refers to the maximum and minimum angle range that each joint can move, which is a physical constraint condition for motion planning of the mechanical arm. The dynamic constraint conditions include the load capacity, maximum acceleration and maximum speed limit of the mechanical arm, which directly affect the motion stability and tracking accuracy of the mechanical arm. The expected trajectory parameters involve trajectory shape, amplitude, frequency, etc., which determine the motion path of the end effector of the mechanical arm.

[0094] Exemplarily, taking a UR5 six-degree-of-freedom mechanical arm as an example, the joint displacement range is ±360°, the maximum joint speed is 180° / s, and the maximum joint acceleration is 900° / s². The expected trajectory adopts a Lissajous curve, and the parameters are set as A=0.03m, B=0.03m, , rad / s.

[0095] S200, according to the kinematics parameters of the robot arm, a kinematics model of the robot arm is established, and a trajectory tracking problem is converted into a time-varying equation.

[0096] In some embodiments, S200 specifically includes the following steps:

[0097] S210, obtaining a joint angle vector of the robot arm , where n is the number of degrees of freedom, is the angle of the nth joint at time t, and the superscript T represents transposition;

[0098] S220, according to the D-H parameter method, a forward kinematics model of the robot arm is established, and the position and attitude of the end effector in the base coordinate system are calculated;

[0099] S230, calculating the Jacobian matrix , establishing a kinematics equation , where X is the position and attitude vector of the end effector in the base coordinate system, is the joint angle vector, is the expected trajectory velocity of the end, is the joint angle vector at time t, is the joint angular velocity vector at time t;

[0100] S240, combining joint velocity constraints , the kinematics equation is converted into a standard time-varying equation form , where E(t) is the Jacobian matrix, , Z(t) is the joint velocity vector, , V(t) is the negative value of the expected trajectory velocity vector of the end, ; is the lower limit of joint velocity, is the upper limit of joint velocity.

[0101] The specific implementation process includes: first, obtaining a joint angle vector of the robot arm , where n is the number of degrees of freedom. Then, according to the D-H parameter method, a forward kinematics model of the robot arm is established, and the position and attitude of the end effector in the base coordinate system are calculated. Further, the Jacobian matrix is calculated, and a kinematics equation is established, where is the expected trajectory velocity of the end. Combining joint velocity constraints , the kinematics equation is converted into a standard time-varying equation form E(t)Z(t)+V(t)=0, where E(t)=J(θ(t)), , .

[0102] S300, constructing a bounded activation function adaptive recurrent neural network (BAFARNN) model, defining an error function ζ(t)=E(t)Z(t)+V(t), and constructing a dynamic equation .

[0103] In some embodiments, S300 specifically comprises the following steps:

[0104] S310, defining an error function ζ(t)=E(t)Z(t)+V(t) for measuring the deviation between the actual trajectory and the desired trajectory;

[0105] S320, performing a nonlinear transformation on the error function using a bounded activation function f(ζ)=tanh(ζ), and designing a dynamic equation based on the nonlinear transformation result , where Π(ζ(t), t) is a time-varying gain matrix, ζ is a vector value of the error function ζ(t), and tanh() represents a hyperbolic tangent function, is the derivative of the error function ζ(t);

[0106] S330, introducing a negative feedback regulation mechanism to suppress the influence of sensor noise and environmental disturbance on system stability by introducing a negative term -ζ(t);

[0107] S340, constructing a Lyapunov function , proving the convergence and robustness of the BAFARNN model by Lyapunov stability theory, and proving its derivative .

[0108] The specific design process includes: defining an error function ζ(t)=E(t)Z(t)+V(t) for measuring the deviation between the actual trajectory and the desired trajectory. The error function is a vector-valued function whose dimension is related to the degree of freedom of the robot arm. Design a dynamic equation , where Π(ζ(t), t) is a time-varying gain matrix. A bounded activation function f(ζ)=tanh(ζ) is used to perform a nonlinear transformation on the error function to ensure that the error converges to zero within a finite time. A negative feedback regulation mechanism is introduced to suppress the influence of sensor noise and environmental disturbance on system stability by introducing a negative term -ζ(t). The convergence and robustness of the BAFARNN model are proved by Lyapunov stability theory, and a Lyapunov function is constructed, and its derivative .

[0109] S400, constructing a piecewise adaptive coefficient function according to the norm of the error function and the time variable.

[0110] The piecewise adaptive coefficient function Π(ζ(t),t) is the core component that determines the performance of the BAFARNN model, and its design needs to consider convergence speed, stability and computational complexity. The piecewise function form proposed by the application is as follows:

[0111] ;

[0112] wherein, is a design parameter, is the Frobenius norm of the error function, defined as , represents the square of the i-th row and j-th column element of the error function ζ(t). The design principle of the piecewise function is: in the initial stage 0<t<0.005, a smaller gain +2 is used to ensure the stability of system startup; in the main convergence stage 0.005≤t≤1, a larger gain +12 is used to accelerate error convergence; in the steady state stage t>1, a pure adaptive gain is used to maintain tracking accuracy. Parameters c1, c2, c3 can be adjusted according to specific application scenarios, for example, for high-precision drawing tasks, c1, c2, c3 can be set to .

[0113] S500, set the Lissajous curve as the expected trajectory, initialize the simulation environment, and configure the BAFARNN model parameters and the initial state of the robot arm.

[0114] The Lissajous curve, as a typical parametric curve, has periodicity and complexity, and is suitable for testing dynamic tracking capability. Its mathematical expression is:

[0115] ;

[0116] wherein, A, B are amplitude parameters, , are frequency parameters, φ is a phase difference, (x0, y0, z0) is a trajectory offset, represents the position coordinates of the end effector in the base coordinate system at time t. The preferred parameter settings are A=0.03m, B=0.03m, , , φ=π / 2, (x0, y0, z0)=(0, 0, 0.2m), which ensures smooth change of the trajectory in the robot arm workspace and avoids singular points.

[0117] The simulation environment initialization includes: setting the initial joint angle of the robot arm , which can ensure that the robot arm is in the central region of the workspace; the BAFARNN model parameters c1=4, c2=4, and c3=6 are configured to balance the convergence speed and stability; the simulation time step Δt=0.001 seconds and the total simulation time T=20 seconds are set to ensure sufficient simulation accuracy; a noise model is established to simulate sensor measurement noise and environmental interference, with a noise amplitude of ±0.01 and a signal-to-noise ratio of 40 dB; and the ODE45 numerical integration method is used to solve the dynamic equation, which is a variant of the Runge-Kutta method and has high calculation accuracy and stability.

[0118] S600, the ODE numerical method is used to solve the dynamic equation, and joint speed control instructions are output in real time to drive the robot arm actuator to move and achieve trajectory tracking.

[0119] In some embodiments, S600 specifically includes the following steps:

[0120] S610, in each control cycle, the current joint angle θ(t) is collected, the Jacobian matrix J(θ(t)) and the error function ζ(t) are calculated;

[0121] S620, the current time t and the error norm are used to calculate the piecewise adaptive coefficient Π(ζ(t), t);

[0122] S630, the dynamic equation is solved to obtain the error change rate , and then the joint speed instruction is calculated;

[0123] S640, the joint speed instruction is sent to the robot arm servo driver to drive the joint motor to move.

[0124] Specific implementation includes: in each control cycle, the current joint angle θ(t) is collected, the Jacobian matrix J(θ(t)) and the error function ζ(t) are calculated. The current time t and the error norm are used to calculate the piecewise adaptive coefficient Π(ζ(t), t). The dynamic equation is solved to obtain the error change rate, and then the joint speed instruction is calculated. The instruction is sent to the robot arm servo driver to drive the joint motor to move. This process is executed in a loop at a frequency of 1000 Hz to achieve real-time control.

[0125] S700, the actual angles of the joints of the robot arm and the actual position of the end effector are collected, and are compared with the joint speed control instructions. If the deviation exceeds a preset threshold, a closed-loop feedback control is triggered to generate a feedback control instruction for real-time adjustment.

[0126] In some embodiments, S700 specifically comprises the following steps:

[0127] S710, collecting actual rotation angles of each joint in real time through a high-precision encoder , collecting actual end position through a visual sensor ;

[0128] S720, calculating position deviation and angle deviation ; wherein , are expected end position and joint speed instruction respectively;

[0129] S730, when the norm of the position deviation is greater than a first preset threshold or the norm of the angle deviation is greater than a second preset threshold, starting a closed-loop feedback mechanism, and smoothing the deviation signal through a second-order low-pass filter to suppress high-frequency noise interference;

[0130] S740, generating a feedback compensation amount through a PID control algorithm to correct the joint speed instruction online, obtaining a final control instruction and sending it to the robot arm driver for execution.

[0131] The closed-loop feedback control is specifically implemented as follows: the actual rotation angles of each joint are collected in real time through a high-precision encoder (resolution 0.001°) , the actual end position is collected through a visual sensor (accuracy 0.01mm) . The position deviation and the angle deviation are calculated. When or , the closed-loop feedback mechanism is started. The deviation signal is smoothed through a second-order low-pass filter (cutoff frequency 50Hz) to suppress high-frequency noise interference. The feedback compensation amount is generated through a PID control algorithm, wherein , , are proportional, integral and differential coefficients respectively, which can be adjusted according to the system response characteristics, for example, set , , . The joint speed instruction is corrected online to obtain a final control instruction , which is sent to the robot arm driver for execution.

[0132] Referring to Figure 2 , the application provides a robot arm trajectory planning control system based on a BAFARNN model, comprising:

[0133] a data acquisition module, configured to acquire kinematics parameters, joint displacement ranges, dynamics constraint conditions and expected trajectory parameters of the robot arm;

[0134] The kinematic modeling module is used to establish a kinematic model of the robotic arm based on its kinematic parameters, transforming the trajectory tracking problem into a time-varying equation.

[0135] The model building module is used to build a bounded adaptive function-activated recurrent neural network, define the error function, and construct the dynamic equations.

[0136] An adaptive coefficient construction module is used to construct a piecewise adaptive coefficient function based on the norm of the error function and the time variable; the piecewise adaptive coefficient function dynamically adjusts the gain parameter according to the error magnitude and time to achieve fast convergence;

[0137] The trajectory generation module is used to set the Lissajous curve as the desired trajectory, initialize the simulation environment, and configure the BAFARNN model parameters and the initial state of the robotic arm.

[0138] The solution execution module is used to solve the dynamic equations using the ODE numerical method, output joint speed control commands in real time, drive the robotic arm actuator to move, and achieve trajectory tracking.

[0139] The feedback control module is used to collect the actual rotation angle of each joint of the robotic arm and the actual position of the end effector, and compare them with the joint speed control command. If the deviation exceeds a preset threshold, closed-loop feedback control is triggered to generate feedback control command for real-time adjustment.

[0140] The content of the above method embodiments is applicable to this embodiment. The specific functions implemented in this embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments. Therefore, they will not be repeated here.

[0141] The following is combined with Figures 3 to 13 The simulation results and performance analysis of the present invention are described in detail.

[0142] Figure 3 The curves showing the change of joint angles q1 to q6 of a six-DOF robotic arm over a 20-second time interval are presented. The horizontal axis represents time (seconds), and the vertical axis represents the joint angle (radians). All joints, starting from their initial values, exhibit a smooth and continuous evolution trend without drastic jumps or divergence. The small fluctuations in the curves reflect the stability of the control algorithm in simulated noise environments, while the overall convergence trend indicates that the BAFARNN model can effectively generate stable commands, ensuring coordinated joint movements and providing internal state guarantees for high-precision trajectory tracking. This result confirms the model's robustness and real-time performance in dynamic environments.

[0143] Figure 4The time-domain response curve of joint velocity (dq1~dq6) of the six-degree-of-freedom robot arm based on the BAFARNN control model is shown. Within a 20-second simulation period, each joint velocity presents regular oscillation within the range of ±0.2 rad / s, and the waveform shows typical sinusoidal characteristics. There is a clear phase difference and amplitude difference between each joint. This coordinated velocity change pattern reflects the dynamic response characteristics of each joint servo system when the robot arm performs a trajectory tracking task. The continuous and smooth curve verifies that the control algorithm can effectively generate coordinated motion instructions to ensure that the end effector achieves precise trajectory tracking. Through the periodic change of joint velocity, it can be further inferred that the robot arm is performing a cyclic operation task. This motion characteristic has important reference value for evaluating the dynamic performance of the system.

[0144] Figure 5 The joint position curves of the robot arm in three degrees of freedom (X, Y, Z directions) over time under BAFARNN control are shown. Within a 10-second simulation period, each joint position presents a smooth change trend within the range of 0~0.65 m. The three curves all show good convergence characteristics, verifying the precise adjustment capability of the control algorithm for joint position.

[0145] Figure 6 The motion trajectory of the robot arm end effector in three-dimensional space using the BAFARNN control algorithm is shown. The position curves in the X and Y directions show regular sinusoidal fluctuation characteristics, and the motion in each direction maintains a stable phase relationship, indicating that the end effector is performing the expected periodic trajectory tracking task. The three curves all show good smoothness and continuity, and the trajectory amplitude changes are coordinated and consistent, verifying that the BAFARNN control algorithm can effectively maintain the motion stability of the end effector. This precise trajectory tracking performance provides reliable protection for high-precision operation tasks of the robot arm, such as trajectory drawing and precision assembly.

[0146] Figure 7 The velocity change curves of the six-degree-of-freedom robot arm end effector in X, Y, and Z directions are shown. Within a 20-second motion period, the velocities in the three directions all present regular periodic fluctuations within the range of ±0.1 m / s, and the velocity curves in each direction maintain a stable phase relationship. This coordinated velocity change pattern indicates that the end effector is performing the expected trajectory tracking task, and verifies that the BAFARNN control algorithm can effectively maintain the coordination of multi-degree-of-freedom motion. The continuous and smooth characteristics of the velocity curve reflect the good dynamic performance of the control system, providing an important guarantee for high-precision operation of the robot arm.

[0147] Figure 8The three-axis acceleration response characteristics of the manipulator end-effector under the BAFARNN controller are presented. The dynamic response within 20 seconds is observed, and the acceleration curves of X (ddX), Y (ddY), and Z (ddZ) axes within the range of ±0.6 m / s² show regular oscillation. The acceleration changes of each axis are smooth and continuous, and the phases are coordinated, indicating that the end-effector is in a stable periodic motion state. The acceleration curves have no sudden jumps or divergence, verifying that the BAFARNN control algorithm can effectively suppress dynamic impact during the motion of the manipulator, ensuring the smoothness of the end-effector motion. This excellent acceleration response characteristic provides an important guarantee for high-precision trajectory tracking tasks, reflecting the robustness and real-time performance of the control system.

[0148] Figure 9 The position tracking error of the manipulator end-effector in X, Y, and Z axes over time is shown. Within the 20-second motion period, the three-axis errors are effectively controlled within the order of m, with the Z-axis (ez) error being the most stable, always maintaining a small fluctuation around zero. The X-axis (ex) error shows a convergent and stable trend, while the Y-axis (ey) error has obvious fluctuations but still maintains a convergent characteristic. This result verifies that the BAFARNN control algorithm can achieve high-precision trajectory tracking of the manipulator end-effector, and the differentiated performance of each axis error reflects the influence of system dynamics on control accuracy, providing an important basis for algorithm optimization.

[0149] Figure 10 The velocity error of the manipulator end-effector in X, Y, and Z directions based on the BAFARNN control model is shown. Within the 20-second observation period, the three error curves (edx, edy, edz) quickly converge and fluctuate within a small interval close to zero, and the errors almost completely coincide and closely follow the zero line. This highly convergent error characteristic indicates that the BAFARNN control algorithm can effectively suppress system disturbances and achieve precise tracking of the end-effector velocity, providing a reliable guarantee for high-precision trajectory control of the manipulator.

[0150] Figure 11 The trajectory tracking effect of the manipulator end-effector in a two-dimensional plane is compared, with the blue curve representing the desired path and the red curve representing the actual motion trajectory. Both complex closed trajectories exhibit smooth Lissajous figure characteristics, and the actual path highly coincides with the desired path in overall shape, but there is a small deviation in local areas. This uniform and non-accumulative deviation distribution indicates that the BAFARNN-based control system can effectively track complex trajectories, and the actual path always fluctuates slightly around the desired path. The smoothness and closeness of the trajectory verify that the control algorithm has good dynamic performance and steady-state accuracy, meeting the application requirements of high-precision trajectory tracking.

[0151] Figure 12 The simulation results of the UR5 six-degree-of-freedom robot arm end effector motion trajectory in three-dimensional Cartesian space are shown. It can be observed from the multiple color trajectory curves that the robot arm forms a complex spatial motion trajectory in the range of X-axis direction (0 to 0.6 m), Y-axis direction (-0.1 to 0.1 m) and Z-axis direction (-0.2 to 0.8 m) from the vicinity of the coordinate system origin. These trajectory curves exhibit continuous and smooth characteristics, indicating that the joints of the robot arm coordinate well during motion, achieving smooth motion without abrupt changes. Different colors of trajectories may correspond to different motion modes or time stages, demonstrating the path planning effect of the robot arm when completing specific tasks. The distribution pattern of the trajectory in space reflects the unique motion flexibility of the UR5 robot arm spherical wrist structure, which can achieve multi-directional work tasks. The simulation results verify the correctness of the kinematics model of the robot arm, providing an intuitive visual basis for the optimization of trajectory planning and control algorithms. The complex spatial distribution of the trajectory also reflects the good motion ability of the six-degree-of-freedom robot arm in the workspace.

[0152] Figure 13 The instantaneous scene of the industrial robot performing precise drawing task is shown, which shows the excellent motion control ability of modern industrial robots. The light blue modules at the joints of the robot arm form a sharp contrast with the gray body, reflecting its flexible joint configuration. This visualization result verifies that the robot arm based on advanced control algorithm can achieve high-precision reproduction of complex trajectories, providing a reliable technical solution for automated drawing, precision machining and other industrial applications.

[0153] Performance comparison analysis: Compared with the traditional ZNN model, the BAFARNN model of the present application improves the convergence speed by about 10 times, and the convergence time is shortened from 0.1 seconds to 0.01 seconds. In terms of noise resistance, when a random noise with an amplitude of ±0.01 is applied, the position error of the traditional OZNN model can reach 0.02 m, while the error of the method of the present application remains within m, with an accuracy improvement of about 50 times. In terms of resource consumption, the execution time of the algorithm on an ARM Cortex-M4 processor (168 MHz) is only 0.8 ms, meeting the real-time requirement of 1 ms control period, while the traditional method requires a higher performance processor to achieve it.

[0154] Application example: In the precision electronic component assembly task, the robot arm is required to move along a complex trajectory at a speed of 0.05 m / s, with a position accuracy requirement of ±0.01 mm. Using the BAFARNN control method of the present application, setting parameters c1=4, c2=4, c3=6, the simulation results show that the position tracking error is stable at m (i.e. 0.08mm), fully meeting the accuracy requirements. In the presence of mechanical vibration interference (frequency 10Hz, amplitude 0.01mm), the system can still maintain the error within 0.1mm, showing excellent anti-interference ability.

[0155] Compared with the related art, the present application has the following improvements:

[0156] 1. BAFARNN model application: adapt bounded adaptive function activation recurrent neural network to robot trajectory tracking, dynamically adjust gain through segmented adaptive coefficient function.

[0157] 2. Adaptive coefficient function design: use segmented function to optimize convergence speed according to error norm and time.

[0158] 3. Noise suppression mechanism: combine negative feedback regulation to suppress sensor noise and environmental interference.

[0159] 4. Robot drawing integration: the method is designed for dynamic trajectory, suitable for high-precision drawing tasks such as Lissajous curve tracking.

[0160] 5. Simulation initialization process: including parameter configuration, environment setting, ensuring experimental repeatability.

[0161] The BAFARNN model of the present application has the following advantages:

[0162] Fast convergence speed: adaptive coefficient function makes error converge quickly, time only 0.01 seconds.

[0163] Strong noise resistance: under constant and time-varying noise, error is stable at level, better than traditional models.

[0164] High resource efficiency: dynamic parameter adjustment reduces computational consumption, suitable for low-cost hardware.

[0165] Flexible application: the model can handle robot constraints and adapt to complex drawing paths such as Lissajous curves.

[0166] High precision: tracking error reaches level, meeting the needs of high-precision drawing.

[0167] The embodiment of the present application also provides a robot trajectory planning control system based on the BAFARNN model, comprising:

[0168] At least one processor;

[0169] At least one memory for storing at least one program;

[0170] When the at least one program is executed by the at least one processor, the at least one processor implements the above method.

[0171] The contents in the above method embodiments are applicable to the present embodiment, the present embodiment specifically implements the same functions as the above method embodiments, and achieves the same beneficial effects as the above method embodiments, which will not be described herein again.

[0172] The present embodiment further provides an electronic device, which includes a memory and a processor, the memory stores a computer program, and the processor implements the above method when executing the computer program. The electronic device can be any intelligent terminal including a tablet computer, a vehicle-mounted computer, etc.

[0173] It can be understood that the contents in the above method embodiments are applicable to the present device embodiment, the present device embodiment specifically implements the same functions as the above method embodiments, and achieves the same beneficial effects as the above method embodiments.

[0174] The present embodiment further provides a computer readable storage medium, which stores a computer program, and the computer program implements the above method when executed by a processor.

[0175] It can be understood that the contents in the above method embodiments are applicable to the present storage medium embodiment, the present storage medium embodiment specifically implements the same functions as the above method embodiments, and achieves the same beneficial effects as the above method embodiments.

[0176] The present embodiment further provides a computer program product, which includes a computer program or computer instructions, the computer program or computer instructions are stored in a memory, a processor of a computer device reads the computer program or computer instructions from the memory, and the processor executes the computer program or computer instructions, so that the computer device executes the above method.

[0177] It can be understood that the contents in the above method embodiments are applicable to the present program product embodiment, the present program product embodiment specifically implements the same functions as the above method embodiments, and achieves the same beneficial effects as the above method embodiments.

[0178] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0179] It will be understood by those skilled in the art that all or some of the steps and systems in the methods disclosed above can be implemented as software, firmware, hardware, and suitable combinations thereof. Some or all of the physical components can be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit. Such software can be distributed on a computer-readable medium, which can include computer storage media (or non-transitory media) and communication media (or transient media). As is known to those skilled in the art, the term computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules, or other data). Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and is accessible to a computer. Furthermore, as is known to those skilled in the art, communication media typically include computer-readable instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

[0180] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

Claims

1. A robotic arm trajectory planning and control method based on a BAFARNN model, characterized in that, The method includes the following steps: S100: Obtain the kinematic parameters, joint displacement range, dynamic constraints, and desired trajectory parameters of the robotic arm; S200, establish a kinematic model of the robotic arm based on the kinematic parameters of the robotic arm, and transform the trajectory tracking problem into a time-varying equation; S300: Construct a bounded adaptive function to activate the recurrent neural network, define the error function and construct the dynamic equation; S400, construct a piecewise adaptive coefficient function based on the norm of the error function and the time variable; the piecewise adaptive coefficient function dynamically adjusts the gain parameter according to the error magnitude and time to achieve fast convergence; S500, set the Lissajous curve as the desired trajectory, initialize the simulation environment, and configure the BAFARNN model parameters and the initial state of the robotic arm; S600 uses the ODE numerical method to solve the dynamic equations, outputs joint speed control commands in real time, drives the robotic arm actuator to move, and achieves trajectory tracking. S700: Collect the actual rotation angle of each joint of the robotic arm and the actual position of the end effector, and compare them with the joint speed control command. If the deviation exceeds the preset threshold, trigger closed-loop feedback control and generate feedback control command for real-time adjustment. The step of establishing a kinematic model of the robotic arm based on its kinematic parameters, transforming the trajectory tracking problem into a time-varying equation, includes: S210, Obtain the joint angle vector of the robotic arm. Where n is the number of degrees of freedom, Let T be the angle of the nth joint at time t, and the superscript T indicates transpose. S220, establish the forward kinematics model of the robotic arm according to the DH parameter method, and calculate the position and attitude of the end effector in the base coordinate system; S230, Calculate the Jacobian matrix Establish kinematic equations Where X is the position and attitude vector of the end effector in the base coordinate system. The joint angle vector. The desired trajectory velocity at the end point, Let be the joint angle vector at time t. Let be the joint angular velocity vector at time t; S240, combined with joint velocity constraints The kinematic equations are transformed into the standard time-varying equation form E(t)Z(t)+V(t)=0, where E(t) is the Jacobian matrix, E(t)=J(θ(t)), and Z(t) is the joint velocity vector. V(t) is the negative value of the desired trajectory velocity vector at the end. ; This is the lower limit of joint velocity. This represents the upper limit of joint velocity.

2. The method according to claim 1, characterized in that, The construction of a bounded adaptive function to activate the recurrent neural network, defining the error function and constructing the dynamic equation, includes: S310, Define the error function It is used to measure the deviation between the actual trajectory and the expected trajectory; S320 uses a bounded activation function. The error function is subjected to a nonlinear transformation, and a dynamic equation is designed based on the result of the nonlinear transformation. ,in The time-varying gain matrix, Error function The vector value of tanh() represents the hyperbolic tangent function. Error function The derivative; S330 introduces a negative feedback regulation mechanism, which suppresses the impact of sensor noise and environmental interference on system stability by introducing a negative fixed term -ζ(t); S340, Constructing Lyapunov functions The convergence and robustness of the BAFARNN model are proved using Lyapunov stability theory, and its derivative is also proven. .

3. The method according to claim 2, characterized in that, In S400, the piecewise adaptive coefficient function is: ； in, For design parameters, Let Frobenius norm be the error function. , Let ζ(t) represent the square of the element in the i-th row and j-th column of the error function ζ(t).

4. The method according to claim 3, characterized in that, The mathematical expression for the Lissajous curve is: ； Where A and B are amplitude parameters, , For frequency parameters, The phase difference is represented by x0, y0, and z0, which are all trajectory offsets. This represents the position coordinates of the end effector in the base coordinate system at time t.

5. The method according to claim 4, characterized in that, The process of solving the dynamic equations using the ODE numerical method and outputting joint speed control commands in real time to drive the robotic arm actuator to move and achieve trajectory tracking includes: S610: In each control cycle, the current joint angle θ(t) is collected, and the Jacobian matrix J(θ(t)) and error function ζ(t) are calculated. S620, based on the current time t and the error norm Calculate the piecewise adaptive coefficient Π(ζ(t),t); S630, Solve the dynamic equation to obtain the rate of change of error. Then, the joint speed command is calculated. ; S640, joint speed command The signal is sent to the robotic arm's servo driver, which then drives the joint motors to move.

6. The method according to claim 1, characterized in that, The actual rotation angles of each joint of the robotic arm and the actual positions of the end effector are collected and compared with the joint speed control commands. If the deviation exceeds a preset threshold, closed-loop feedback control is triggered, generating feedback control commands for real-time adjustment, including: The S710 uses a high-precision encoder to collect the actual rotation angle of each joint in real time. The actual position of the end is collected by a vision sensor. ; S720, Calculate position deviation and angle deviation ;in , These are the desired end-effector position and joint velocity commands, respectively. S730: When the norm of the position deviation is greater than the first preset threshold or the norm of the angle deviation is greater than the second preset threshold, the closed-loop feedback mechanism is activated, and a second-order low-pass filter is used to smooth the deviation signal and suppress high-frequency noise interference. The S740 generates feedback compensation through a PID control algorithm, corrects the joint speed command online, obtains the final control command, and sends it to the robotic arm driver for execution.

7. A robotic arm trajectory planning and control system based on a BAFARNN model, used to implement the method as described in any one of claims 1 to 6, characterized in that, include: The data acquisition module is used to acquire the kinematic parameters, joint displacement range, dynamic constraints, and desired trajectory parameters of the robotic arm. The kinematic modeling module is used to establish a kinematic model of the robotic arm based on its kinematic parameters, transforming the trajectory tracking problem into a time-varying equation. The model building module is used to build a bounded adaptive function-activated recurrent neural network, define the error function, and construct the dynamic equations. An adaptive coefficient construction module is used to construct a piecewise adaptive coefficient function based on the norm of the error function and the time variable; the piecewise adaptive coefficient function dynamically adjusts the gain parameter according to the error magnitude and time to achieve fast convergence; The trajectory generation module is used to set the Lissajous curve as the desired trajectory, initialize the simulation environment, and configure the BAFARNN model parameters and the initial state of the robotic arm. The solution execution module is used to solve the dynamic equations using the ODE numerical method, output joint speed control commands in real time, drive the robotic arm actuator to move, and achieve trajectory tracking. The feedback control module is used to collect the actual rotation angle of each joint of the robotic arm and the actual position of the end effector, and compare them with the joint speed control command. If the deviation exceeds a preset threshold, closed-loop feedback control is triggered to generate feedback control command for real-time adjustment.

8. A robotic arm trajectory planning and control system based on a BAFARNN model, characterized in that, include: At least one processor; At least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor performs the method as described in any one of claims 1 to 6.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 6.

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