Planar cable-driven platform based on recurrent neural network and control method thereof

Abstract

The application discloses a planar cable driving platform based on a recurrent neural network and a control method thereof, and the platform comprises a support frame, a planar workboard, a left driving assembly, a right driving assembly, a cable transmission mechanism and an end execution mechanism; a continuous form integral reinforcement recurrent neural network model is established; a continuous form error dynamic model containing disturbance is established; a continuous form control model is obtained in combination with the kinematic relationship of the planar cable driving platform; a four-step ZeaD discretization formula is introduced; a four-step discrete integral reinforcement recurrent neural network control law is constructed; actual trajectory of the end is calculated according to the cable length change; and trajectory tracking control results of the planar cable driving platform are output. Through the comprehensive application of the integral reinforcement mechanism, the four-step discretization method and the recurrent neural network, the control precision and the anti-interference ability of the cable driving platform in a complex dynamic environment are remarkably improved, and an efficient and robust control scheme is provided for cable driving parallel robot technology.

Description

Technical Field

[0001] This invention relates to the field of robot control technology, and in particular to a planar cable-driven platform based on a recurrent neural network and its control method. Background Technology

[0002] In modern robot control systems, cable-driven parallel robots are widely used in logistics warehousing, construction engineering, medical, and precision manufacturing due to their advantages of simple structure, high load capacity, and high flexibility. Especially in planar cable-driven platforms, high-precision trajectory tracking control can be achieved through the coordinated control of two cables and stepper motors. Planar cable-driven platforms offer high workspace flexibility and a small mechanical structure, making them widely used in various complex environments, such as warehouse management and medical operations. However, existing technologies still face many technical challenges in trajectory tracking control of planar cable-driven platforms, particularly in the following aspects:

[0003] 1) Low trajectory tracking accuracy: Most existing planar cable-driven platforms use traditional PID control or other classic control methods to achieve trajectory tracking, which perform well in ideal environments. However, due to the strong flexibility and complex dynamic characteristics of cable-driven platforms, traditional control methods often struggle to maintain high trajectory tracking accuracy in complex, nonlinear environments, especially when subjected to external disturbances (such as environmental interference, measurement noise, etc.). Specifically, external disturbances may cause dynamic changes in the system, leading to the gradual accumulation of position errors, affecting the system's stability and accuracy, and thus failing to meet the requirements of high-precision control.

[0004] 2) Poor System Robustness: The control performance of cable-driven platforms heavily depends on changes in cable tension, flexible deformation, and system dynamics. Most existing methods fail to adequately consider non-ideal disturbances that the system may encounter during actual operation, such as low-frequency disturbances and external physical interference. These disturbances often lead to system instability, especially in complex and dynamically changing environments. Existing methods have failed to effectively enhance the system's ability to suppress these disturbances, thus limiting their application and widespread adoption in complex scenarios such as logistics, healthcare, and construction engineering.

[0005] 3) Challenges of Discrete-Time Control and Disturbance Suppression: Most existing control strategies focus on continuous-time control systems. Although some methods have addressed discrete-time system control, these methods typically neglect the impact of time-varying disturbances or fail to effectively integrate disturbance suppression mechanisms. Especially in practical applications, the control of discrete-time systems often faces interference factors such as measurement noise, system uncertainties, and external disturbances. Existing discrete control methods often fail to balance control accuracy and system robustness, resulting in an inability to effectively address these challenges in practical applications and causing the actual system performance to fall far short of theoretical expectations.

[0006] 4) Insufficient interference suppression mechanisms: Although some studies have proposed intelligent control methods based on recurrent neural networks, which can handle time-varying trajectory planning and trajectory tracking problems to some extent, most methods focus on control problems under ideal environments. In practical applications, the nonlinear dynamics and uncertainties of planar cable-driven platforms mean that traditional recurrent neural network methods often fail to meet the requirements for robustness and stability when facing complex interference, noise, and non-ideal environments, making it difficult to effectively suppress the system's trajectory tracking error. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention provides a planar cable-driven platform and its control method based on a recurrent neural network. By introducing a four-step discrete integral method to enhance the recurrent neural network, the anti-interference capability of the system is effectively enhanced, ensuring that the system can operate stably in complex environments, while significantly improving the accuracy and reliability of trajectory tracking control.

[0008] The objective of this invention is achieved in one respect as follows: a planar cable drive platform based on a recurrent neural network, comprising a support frame, a planar work plate, a left drive assembly, a right drive assembly, a cable transmission mechanism, and an end effector.

[0009] The support frame is used to support and install various functional components; the planar working plate is installed on the front side of the support frame to form a two-dimensional planar motion area.

[0010] The left drive assembly and the right drive assembly are respectively installed on the left and right sides of the upper end of the support frame; each of the left drive assembly and the right drive assembly includes a progress motor, a winding reel and a mounting bracket, the progress motor is connected to the winding reel for driving the winding reel to rotate to realize the winding and unwinding of the cable;

[0011] The cable drive mechanism includes a left cable and a right cable. One end of the left cable is wound around the reel of the left drive assembly, and the other end is connected to the end effector. One end of the right cable is wound around the reel of the right drive assembly, and the other end is connected to the end effector.

[0012] The end effector is located in the front area of ​​the planar working plate and is suspended in front of the planar working plate by the traction of the left and right cables, so that the end effector can move in the two-dimensional plane corresponding to the planar working plate.

[0013] The end effector is equipped with a writing tool mounting mechanism driven by a servo motor, which is used to fix a writing pen or drawing tool to draw a trajectory on the flat work plate.

[0014] By controlling the rotation of the progress motors in the left and right drive components, the lengths of the left and right cables are changed, thereby driving the end effector to perform two-dimensional trajectory motion on the planar work plate.

[0015] Furthermore, it also includes a control system, which includes a controller, a progressive motor drive module, a motor interface, a power interface, and connecting wires;

[0016] The controller is connected to an external computer via a USB interface to receive control data calculated by the host computer. The host computer calculates the target length sequence of the two cables based on the platform's desired trajectory and system state information using a four-step discrete integral enhanced recurrent neural network control algorithm, and sends the corresponding cable length data to the controller.

[0017] The controller is electrically connected to the first stepper motor interface and the second stepper motor interface via connecting wires. The first stepper motor interface and the second stepper motor interface are respectively connected to the stepper motors in the left drive assembly and the right drive assembly, and are used to drive the corresponding stepper motors to rotate.

[0018] The controller is also connected to a servo motor to control the lifting and lowering of the writing pen, thereby drawing the corresponding trajectory on the flat work surface.

[0019] Another aspect of the objective of this invention is achieved as follows: a control method for a planar cable-driven platform based on a recurrent neural network, characterized by comprising the following steps:

[0020] Step 1) Establish a continuous integral reinforcement recurrent neural network model;

[0021] Step 2) Construct a continuous-form error dynamic model with perturbations;

[0022] Step 3) Combining the kinematic relationships of the planar cable-driven platform, a continuous form control model is obtained;

[0023] Step 4) Introduce the four-step ZeaD discretization formula to transform the continuous integral-enhanced recurrent neural network into a discrete form suitable for digital controller implementation;

[0024] Step 5) Construct a four-step discrete integral reinforced recurrent neural network control law and calculate the discrete integral error term;

[0025] Step 6) Calculate the actual trajectory at the end of the cable based on the change in cable length to achieve discrete disturbance rejection control under disturbance conditions;

[0026] Step 7) Analyze the stability, convergence and anti-disturbance performance, and output the trajectory tracking control results of the planar cable-driven platform.

[0027] Furthermore, step 1) includes: Regarding the trajectory tracking error of the planar cable-driven platform, firstly, the error function between the actual trajectory and the desired trajectory is defined as:

[0028]

[0029] Among them, v a (t) represents the actual position of the end effector, v d (t) represents the desired position of the end effector. This represents the trajectory tracking error; an integral reinforcement term is introduced into the error dynamics of the recurrent neural network to construct a continuous-form integral reinforcement recurrent neural network model:

[0030]

[0031] in, This is a proportionality coefficient used to accelerate error convergence. This is the integral coefficient, used to accumulate historical tracking errors.

[0032] Furthermore, step 2) includes: when the system is subjected to an external disturbance, introducing the disturbance term d(t) into the error dynamic equation to obtain a continuous-form integral-enhanced recurrent neural network model containing the disturbance.

[0033]

[0034] The model adjusts the error dynamics through both proportional and integral terms, with the integral term providing compensation for both constant and slowly changing disturbances.

[0035] Furthermore, step 3) includes: based on the kinematic relationship of the planar cable-driven platform, the rate of change of cable length and the speed of the end effector satisfy the following:

[0036]

[0037] in, Let the length of the cable be a vector. This is the position matrix of the end effector in the global coordinate system. The system kinematic coefficient matrix is ​​determined by the cable length and end position; This represents the actual velocity vector of the end effector.

[0038] Substituting the integral reinforcement error dynamically into the above kinematic equations, we obtain the continuous form integral reinforcement recurrent neural network control method:

[0039]

[0040] in, This represents the desired velocity vector of the end effector.

[0041] Furthermore, step 4) includes: introducing a general four-step ZeaD discretization formula to transform the continuous-form integral-enhanced recurrent neural network into a discrete form suitable for digital controller implementation. The general four-step ZeaD discretization formula is as follows:

[0042]

[0043] in, The sampling interval is... To select parameters for discretization, This indicates the higher-order truncation error term, with the error order in parentheses related to the sampling interval g.

[0044] Furthermore, step 5) includes: applying the four-step ZeaD discretization formula to the continuous-form integral-enhanced recurrent neural network control model to obtain the four-step discrete-integral-enhanced recurrent neural network control method.

[0045]

[0046] in, This represents the integral reinforcement term, used to record and compensate for historical tracking errors;

[0047] The discrete integral error term is updated using the same four-step ZeaD discretization formula, ensuring that the integral term has a consistent discrete implementation form with the main control law:

[0048] .

[0049] Furthermore, step 6) includes: in the kinematic matrix Under the condition that a pseudo-inverse exists, the actual speed of the end effector is calculated from the rate of change of cable length:

[0050]

[0051] in, Let be the actual velocity vector of the end effector at the k-th sampling time. The Moore-Penrose pseudo-inverse operator for the kinematic coefficient matrix.

[0052] Further update the actual trajectory using the four-step ZeaD discretization formula:

[0053]

[0054] When the system is subjected to discrete disturbances When applied, the disturbance term is added to the desired velocity input, resulting in a four-step discrete integral reinforced recurrent neural network control law with disturbance:

[0055]

[0056] in, Representing the discrete time-varying perturbation vector, through the integration enhancement term Accumulate the history of errors.

[0057] Furthermore, step 7) includes: for the constructed four-step discrete integral reinforcement recurrent neural network method, its characteristic polynomial is:

[0058]

[0059] when When the root of the characteristic polynomial satisfies the zero stability condition, the global truncation error order is... Based on the recursive process of the four-step ZeaD discretization, discrete control law construction, and actual trajectory update in steps 4) to 6), at each sampling time... Calculate tracking error Points-based enhancement items Cable length status and actual trajectory By continuously updating the cable length control input, the end effector of the planar cable-driven platform tracks the desired trajectory, maintaining a bounded steady-state error even under constant and linear time-varying disturbances, with its upper bound determined by the global truncation error order. Together with integral reinforcement disturbance compensation residual, it enables discrete trajectory tracking control with disturbance rejection capability.

[0060] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention first adopts a four-step discrete integral enhanced recurrent neural network method, which significantly improves the trajectory tracking accuracy of the planar cable-driven platform; by introducing a recurrent neural network and combining it with an integral enhancement mechanism, the present invention can effectively handle the dynamic changes of the platform, correct errors in real time, and eliminate steady-state errors caused by interference or noise; this enables the platform to track the predetermined trajectory more accurately in complex dynamic environments, significantly improving the trajectory tracking accuracy.

[0061] Secondly, the integral enhancement mechanism of this invention strengthens the system's ability to suppress external disturbances, solving the problem of poor system robustness in existing technologies. By adding an integral term to the recurrent neural network, this invention can accumulate historical errors and adjust the control signal in real time, thereby effectively eliminating error accumulation caused by low-frequency disturbances, measurement noise, and other interferences. Compared with traditional control methods, this invention can maintain the stability and accuracy of the system when facing complex working environments and variable external disturbances, greatly improving the system's robustness.

[0062] Furthermore, the application of the four-step discretization formula enables this invention to possess extremely high stability and numerical accuracy in discrete-time control systems. By employing the four-step discretization formula, this invention can efficiently transform continuous-time control systems into discrete-time systems, ensuring efficient and accurate trajectory tracking even in discrete control environments. This discretization method not only improves computational efficiency and reduces system energy consumption but also reduces the burden on hardware resources.

[0063] In terms of control efficiency and response speed, this invention utilizes the adaptive adjustment capability of a recurrent neural network, enabling the system to respond to changes in platform state in real time and quickly optimize control signals. Compared with traditional methods, this invention not only reduces adjustment time but also effectively handles the complex dynamics of cable-driven platforms, improving the real-time performance and dynamic response speed of the control system.

[0064] Finally, this invention also offers significant advantages in simplifying operation and control. By introducing a recurrent neural network, the invention can automatically adjust the control strategy without relying heavily on manual intervention, greatly simplifying the operation of the control system. Users only need to set the target trajectory, and the system can automatically optimize the control process through neural network self-learning, improving operational convenience and system applicability. Attached Figure Description

[0065] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0066] Figure 1 A schematic diagram of the structure of the platform of this invention.

[0067] Figure 2 Block diagram of the control system of this invention.

[0068] Figure 3 Simulation results of the method of this invention.

[0069] Figure 4 A comparison diagram of the trajectory generated by the method of this invention and the trajectory of a common control algorithm. Detailed Implementation

[0070] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0071] like Figure 1 The planar cable drive platform based on a recurrent neural network shown includes a support frame, a planar work plate, a left drive assembly, a right drive assembly, a cable transmission mechanism, and an end effector.

[0072] The support frame is used to support and install various functional components; the flat working plate is installed on the front side of the support frame to form a two-dimensional planar motion area;

[0073] The left drive assembly and the right drive assembly are respectively installed on the left and right sides of the upper end of the support frame; both the left drive assembly and the right drive assembly include a progress motor, a winding reel and a mounting bracket. The progress motor is connected to the winding reel for driving the winding reel to rotate and realize the winding and unwinding of the cable.

[0074] The cable drive mechanism includes a left cable and a right cable. One end of the left cable is wound around the reel of the left drive assembly, and the other end is connected to the end effector. One end of the right cable is wound around the reel of the right drive assembly, and the other end is connected to the end effector.

[0075] The end effector is located in the front area of ​​the flat working plate and is suspended in front of the flat working plate by the traction of the left and right cables, so that the end effector can move in the two-dimensional plane corresponding to the flat working plate.

[0076] The end effector is equipped with a writing instrument mounting mechanism driven by a servo motor, which is used to fix a writing pen or drawing tool to draw a trajectory on a flat work surface.

[0077] By controlling the rotation of the progress motors in the left and right drive components, the lengths of the left and right cables are changed, thereby driving the end effector to perform two-dimensional trajectory motion on the planar work plate.

[0078] like Figure 2 As shown, it also includes a control system, which includes a controller, a progressive motor drive module, a motor interface, a power interface, and connecting wires.

[0079] The controller connects to an external computer via a USB interface to receive control data calculated by the host computer. The host computer calculates the target length sequence of the two cables based on the platform's desired trajectory and system state information using a four-step discrete integral enhanced recurrent neural network control algorithm, and sends the corresponding cable length data to the controller.

[0080] The controller is electrically connected to the first stepper motor interface and the second stepper motor interface via connecting wires. The first stepper motor interface and the second stepper motor interface are respectively connected to the stepper motors in the left drive assembly and the right drive assembly, and are used to drive the corresponding stepper motors to rotate.

[0081] The controller is also connected to a servo motor to control the lifting and lowering of the writing pen, thereby drawing the corresponding trajectory on the flat work surface.

[0082] During the control process, the controller converts the cable length into the number of drive steps for the stepper motor based on the received cable length data and the geometric parameters of the planar cable drive platform. By controlling the forward and reverse rotation of the stepper motor, the cable is wound up and unwound, thereby driving the end effector to move within the planar working area.

[0083] To improve the smoothness and stability of the motion process, the control program adopts a segmented control strategy, dividing the change in the length of the target cable into multiple segments and driving the stepper motor segment by segment to make the end effector move continuously along the predetermined trajectory.

[0084] Through the above control system, the host computer uses a four-step discrete integral enhanced recurrent neural network control algorithm to calculate the cable length sequence, which can drive the stepper motor to change the cable length in real time, thereby realizing high-precision trajectory tracking control of the end effector of the planar cable drive platform.

[0085] Another aspect of the objective of this invention is achieved as follows: a control method for a planar cable-driven platform based on a recurrent neural network, characterized by comprising the following steps:

[0086] Step 1) Establish a continuous integral reinforcement recurrent neural network model;

[0087] To address the trajectory tracking error of a planar cable-driven platform, the error function between the actual trajectory and the desired trajectory is first defined as follows:

[0088]

[0089] Among them, v a (t) represents the actual position of the end effector, v d (t) represents the desired position of the end effector. This represents the trajectory tracking error. To improve the system's ability to suppress continuous disturbances, an integral reinforcement term is introduced into the error dynamics of the recurrent neural network, constructing a continuous-form integral reinforcement recurrent neural network model:

[0090]

[0091] in, This is a proportionality coefficient used to accelerate error convergence. The integral coefficient is used to accumulate historical tracking errors, thereby suppressing continuous disturbances and reducing steady-state errors.

[0092] Step 2) Construct a continuous-form error dynamic model with perturbations;

[0093] When the system is subjected to external disturbances, the disturbance term d(t) is introduced into the error dynamic equation, resulting in a continuous integral-enhanced recurrent neural network model containing the disturbance:

[0094]

[0095] The model adjusts the error dynamics through both proportional and integral terms. The integral term can compensate for constant disturbances and slowly changing disturbances, thereby improving the anti-disturbance performance of the trajectory tracking system.

[0096] Step 3) Combining the kinematic relationships of the planar cable-driven platform, a continuous form control model is obtained;

[0097] Based on the kinematic relationship of the planar cable-driven platform, the rate of change of cable length and the speed of the end effector satisfy the following:

[0098]

[0099] in, Let the length of the cable be a vector. This is the position matrix of the end effector in the global coordinate system. The system kinematic coefficient matrix is ​​determined by the cable length and end position; This represents the actual velocity vector of the end effector.

[0100] Substituting the integral reinforcement error dynamically into the above kinematic equations, we obtain the continuous form integral reinforcement recurrent neural network control method:

[0101]

[0102] in, This represents the desired velocity vector of the end effector.

[0103] Step 4) Introduce the four-step ZeaD discretization formula to transform the continuous integral-enhanced recurrent neural network into a discrete form suitable for digital controller implementation;

[0104] The general four-step ZeaD discretization formula is introduced to transform the continuous-form integral-enhanced recurrent neural network into a discrete form suitable for digital controller implementation. The general four-step ZeaD discretization formula is as follows:

[0105]

[0106] in, The sampling interval is... To select parameters for discretization, This represents the higher-order truncation error term, with the error order in parentheses relating to the sampling interval g. When... When the four-step discrete formula has zero stability and convergence, it can be used to construct high-precision discrete control models.

[0107] Step 5) Construct a four-step discrete integral reinforced recurrent neural network control law and calculate the discrete integral error term;

[0108] Applying the four-step ZeaD discretization formula to the continuous-form integral-enhanced recurrent neural network control model yields a four-step discrete-integral-enhanced recurrent neural network control method:

[0109]

[0110] in, This represents the integral reinforcement term, used to record and compensate for historical tracking errors;

[0111] The discrete integral error term is updated using the same four-step ZeaD discretization formula, ensuring that the integral term has a consistent discrete implementation form with the main control law:

[0112] .

[0113] Therefore, the integral term is no longer obtained by approximation through simple Euler integral, but is recursively derived from the main system state using a unified four-step discretization scheme, thereby improving the numerical accuracy and consistency of the discrete control system.

[0114] Step 6) Calculate the actual trajectory at the end of the cable based on the change in cable length to achieve discrete disturbance rejection control under disturbance conditions;

[0115] In the kinematic matrix Under the condition that a pseudo-inverse exists, the actual speed of the end effector is calculated from the rate of change of cable length:

[0116]

[0117] in, Let be the actual velocity vector of the end effector at the k-th sampling time. The Moore-Penrose pseudo-inverse operator for the kinematic coefficient matrix.

[0118] Further update the actual trajectory using the four-step ZeaD discretization formula:

[0119]

[0120] When the system is subjected to discrete disturbances When applied, the disturbance term is added to the desired velocity input, resulting in a four-step discrete integral reinforced recurrent neural network control law with disturbance:

[0121]

[0122] in, Representing the discrete time-varying perturbation vector, through the integration enhancement term By accumulating the history of errors, this method can reduce steady-state deviations caused by persistent disturbances.

[0123] Step 7) Analyze the stability, convergence and anti-disturbance performance, and output the trajectory tracking control results of the planar cable-driven platform.

[0124] The characteristic polynomial of the constructed four-step discrete integral reinforcement recurrent neural network method is:

[0125]

[0126] when When the root of the characteristic polynomial satisfies the zero stability condition, the proposed four-step discrete integral enhanced recurrent neural network method possesses zero stability, consistency, and convergence, and its global truncation error order is . Meanwhile, under constant discrete perturbation or linear time-varying discrete perturbation, the method can maintain convergence and limit the steady-state residual to a bounded range.

[0127] Based on the recursive process of the four-step ZeaD discretization, discrete control law construction, and actual trajectory update in steps 4) to 6), at each sampling time... Calculate tracking error Points-based enhancement items Cable length status and actual trajectory By continuously updating the cable length control input, the end effector of the planar cable-driven platform tracks the desired trajectory, maintaining a bounded steady-state error even under constant and linear time-varying disturbances, with its upper bound determined by the global truncation error order. Together with integral reinforcement disturbance compensation residual, it enables discrete trajectory tracking control with disturbance rejection capability.

[0128] like Figure 3 The image shows the tracking control performed on the following trajectory:

[0129]

[0130] It can be seen that the four-step discrete integral enhanced recurrent neural network control algorithm achieves the tracking control of the above trajectory, and the actual trajectory coincides with the desired trajectory.

[0131] like Figure 4 As shown in the figure, the trajectory tracking results of different control algorithms under linear disturbances are presented. In the figure, the blue trajectory represents the proposed four-step discrete integral enhanced recurrent neural network control algorithm (DF-IR-RNN), the red trajectory represents the ordinary discrete recurrent neural network control algorithm (DF-C-RNN) without the integral enhancement mechanism, and the black trajectory represents the gradient neural network (GNN) method. As can be seen from the figure, under the influence of linear disturbances, the actual trajectories of DF-C-RNN and GNN deviate from the desired trajectory to varying degrees, especially in areas with sharp trajectory angles and large curvature changes, where the tracking error is more pronounced. In contrast, DF-IR-RNN can better maintain the target trajectory contour and effectively reduce the trajectory deviation caused by linear disturbances. Experimental results show that the proposed four-step discrete integral enhanced recurrent neural network control algorithm has strong linear disturbance suppression capabilities and can achieve stable tracking control of the desired trajectory.

[0132] This invention provides a planar cable-driven platform and its control method based on a recurrent neural network, solving problems such as low trajectory tracking accuracy, poor system robustness, and insufficient discrete-time control and interference suppression in existing technologies. By introducing an integral enhancement mechanism, a four-step discretization method, and the comprehensive application of a recurrent neural network, this invention significantly improves the control accuracy and anti-interference capability of the cable-driven platform in complex dynamic environments. It provides an efficient and robust control scheme for cable-driven parallel robot technology, possessing significant theoretical importance and broad application prospects.

[0133] The above description of the embodiments is only for the purpose of helping to understand the method and core ideas of the present invention. It should be noted that those skilled in the art can make several improvements and modifications to the present invention without departing from the principles of the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Claims

1. A planar cable-driven platform based on a recurrent neural network, characterized in that, It includes a support frame, a flat working plate, a left drive assembly, a right drive assembly, a cable drive mechanism, and an end effector. The support frame is used to support and install various functional components; the planar working plate is installed on the front side of the support frame to form a two-dimensional planar motion area. The left drive assembly and the right drive assembly are respectively installed on the left and right sides of the upper end of the support frame; each of the left drive assembly and the right drive assembly includes a progress motor, a winding reel and a mounting bracket, the progress motor is connected to the winding reel for driving the winding reel to rotate to realize the winding and unwinding of the cable; The cable drive mechanism includes a left cable and a right cable. One end of the left cable is wound around the reel of the left drive assembly, and the other end is connected to the end effector. One end of the right cable is wound around the reel of the right drive assembly, and the other end is connected to the end effector. The end effector is located in the front area of ​​the planar working plate and is suspended in front of the planar working plate by the traction of the left and right cables, so that the end effector can move in the two-dimensional plane corresponding to the planar working plate. The end effector is equipped with a writing tool mounting mechanism driven by a servo motor, which is used to fix a writing pen or drawing tool to draw a trajectory on the flat work plate. By controlling the rotation of the progress motors in the left and right drive components, the lengths of the left and right cables are changed, thereby driving the end effector to perform two-dimensional trajectory motion on the planar work plate.

2. The planar cable-driven platform based on a recurrent neural network according to claim 1, characterized in that, It also includes a control system, which includes a controller, a progressive motor drive module, a motor interface, a power interface, and connecting wires; The controller is connected to an external computer via a USB interface to receive control data calculated by the host computer. The host computer calculates the target length sequence of the two cables based on the platform's desired trajectory and system state information using a four-step discrete integral enhanced recurrent neural network control algorithm, and sends the corresponding cable length data to the controller. The controller is electrically connected to the first stepper motor interface and the second stepper motor interface via connecting wires. The first stepper motor interface and the second stepper motor interface are respectively connected to the stepper motors in the left drive assembly and the right drive assembly, and are used to drive the corresponding stepper motors to rotate. The controller is also connected to a servo motor to control the lifting and lowering of the writing pen, thereby drawing the corresponding trajectory on the flat work surface.

3. A control method for a planar cable-driven platform based on a recurrent neural network, characterized in that, Includes the following steps: Step 1) Establish a continuous integral reinforcement recurrent neural network model; Step 2) Construct a continuous-form error dynamic model with perturbations; Step 3) Combining the kinematic relationships of the planar cable-driven platform, a continuous form control model is obtained; Step 4) Introduce the four-step ZeaD discretization formula to transform the continuous integral-enhanced recurrent neural network into a discrete form suitable for digital controller implementation; Step 5) Construct a four-step discrete integral reinforced recurrent neural network control law and calculate the discrete integral error term; Step 6) Calculate the actual trajectory at the end of the cable based on the change in cable length to achieve discrete disturbance rejection control under disturbance conditions; Step 7) Analyze the stability, convergence and anti-disturbance performance, and output the trajectory tracking control results of the planar cable-driven platform.

4. The control method for a planar cable-driven platform based on a recurrent neural network according to claim 3, characterized in that, Step 1) includes: Regarding the trajectory tracking error of the planar cable-driven platform, firstly, the error function between the actual trajectory and the desired trajectory is defined as: ； Among them, v a (t) represents the actual position of the end effector, v d (t) represents the desired position of the end effector. This represents the trajectory tracking error; an integral reinforcement term is introduced into the error dynamics of the recurrent neural network to construct a continuous-form integral reinforcement recurrent neural network model: ； in, This is a proportionality coefficient used to accelerate error convergence. This is the integral coefficient, used to accumulate historical tracking errors.

5. The control method for a planar cable-driven platform based on a recurrent neural network according to claim 3, characterized in that, Step 2) includes: when the system is subjected to external disturbances, the disturbance term d(t) is introduced into the error dynamic equation to obtain a continuous integral-enhanced recurrent neural network model containing the disturbance. ； The model adjusts the error dynamics through both proportional and integral terms, with the integral term providing compensation for both constant and slowly changing disturbances.

6. The control method for a planar cable-driven platform based on a recurrent neural network according to claim 3, characterized in that, Step 3) includes: based on the kinematic relationship of the planar cable-driven platform, the rate of change of cable length and the speed of the end effector satisfy the following: ； in, Let the length of the cable be a vector. This is the position matrix of the end effector in the global coordinate system. The system kinematic coefficient matrix is ​​determined by the cable length and end position; This represents the actual velocity vector of the end effector. Substituting the integral reinforcement error dynamically into the above kinematic equations, we obtain the continuous form integral reinforcement recurrent neural network control method: ； in, This represents the desired velocity vector of the end effector.

7. The control method for a planar cable-driven platform based on a recurrent neural network according to claim 3, characterized in that, Step 4) includes: introducing a general four-step ZeaD discretization formula to transform the continuous-form integral-enhanced recurrent neural network into a discrete form suitable for digital controller implementation. The general four-step ZeaD discretization formula is as follows: ； in, The sampling interval is... To select parameters for discretization, This indicates the higher-order truncation error term, with the error order in parentheses related to the sampling interval g.

8. The control method for a planar cable-driven platform based on a recurrent neural network according to claim 3, characterized in that, Step 5) includes: applying the four-step ZeaD discretization formula to the continuous-form integral-enhanced recurrent neural network control model to obtain the four-step discrete integral-enhanced recurrent neural network control method. ； in, This represents the integral reinforcement term, used to record and compensate for historical tracking errors; The discrete integral error term is updated using the same four-step ZeaD discretization formula, ensuring that the integral term has a consistent discrete implementation form with the main control law: 。 9. The control method for a planar cable-driven platform based on a recurrent neural network according to claim 3, characterized in that, Step 6) includes: in the kinematic matrix Under the condition that a pseudo-inverse exists, the actual speed of the end effector is calculated from the rate of change of cable length: ； in, Let be the actual velocity vector of the end effector at the k-th sampling time. (·) is the Moore-Penrose pseudo-inverse operator for the kinematic coefficient matrix; Further update the actual trajectory using the four-step ZeaD discretization formula: ； When the system is subjected to discrete disturbances When applied, the disturbance term is added to the desired velocity input, resulting in a four-step discrete integral reinforced recurrent neural network control law with disturbance: ； in, Representing the discrete time-varying perturbation vector, through the integration enhancement term Accumulate errors historically.

10. The control method for a planar cable-driven platform based on a recurrent neural network according to claim 3, characterized in that, Step 7) includes: For the constructed four-step discrete integral reinforcement recurrent neural network method, its characteristic polynomial is: ； when When the root of the characteristic polynomial satisfies the zero stability condition, the global truncation error order is... Based on the recursive process of the four-step ZeaD discretization, discrete control law construction, and actual trajectory update in steps 4) to 6), at each sampling time... Calculate tracking error Points-based enhancement items Cable length status and actual trajectory By continuously updating the cable length control input, the end effector of the planar cable-driven platform tracks the desired trajectory, maintaining a bounded steady-state error even under constant and linear time-varying disturbances, with its upper bound determined by the global truncation error order. Together with integral reinforcement disturbance compensation residual, it enables discrete trajectory tracking control with disturbance rejection capability.

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