Parallel robot time delay prediction control method and system

Abstract

The application belongs to the technical field of robot control, and discloses a parallel robot time delay prediction control method and system, which comprises the following steps: constructing a nonlinear state equation of a parallel robot system; performing real-time linearization and discretization on the nonlinear state equation to obtain a basic discrete linear state equation; deriving a discrete equation of a lag control instruction sequence based on the lag control instruction sequence that has been issued but not executed at a current control time; constructing an extended state vector based on the lag control instruction sequence and a state vector, and constructing an extended state discrete linear state equation; and optimizing and outputting a control variable by using an MPC prediction control method based on the extended state discrete linear state equation. The application constructs an extended state vector, internalizes time delay through state extension, reconstructs an extended state discrete linear state equation, and realizes early calculation of a control instruction by MPC rolling optimization to eliminate phase lag and improve control precision.

Description

Technical Field

[0001] This invention belongs to the field of robot control technology, and more specifically, relates to a method and system for predictive control of time delay in parallel robots. Background Technology

[0002] Parallel robots have numerous applications in various fields, such as treatment beds for respiratory compensation in radiotherapy. These beds are supported and driven by multiple parallel linear modules that change posture. In precise radiotherapy for thoracic and abdominal tumors, aligning the radiation beam or the patient with the target tumor is crucial. To support the patient's weight, treatment beds are often of parallel structure. Utilizing parallel treatment beds to compensate for the patient's respiratory movements is a method of precise radiotherapy, offering advantages such as high rigidity, high load capacity, and no cumulative error, making it the mainstream actuator for respiratory motion compensation. However, existing parallel robots, such as parallel treatment beds for respiratory motion compensation, generally face the following bottlenecks in application control: System latency caused by link delay: For example, a radiotherapy compensation system involves multiple stages such as image acquisition, target localization, correlation model calculation, and control command transmission, resulting in inherent physical delays that cannot be ignored. Traditional robot feedback control logic struggles to eliminate phase lag during tracking without sacrificing stability when dealing with such delays.

[0003] Multi-axis nonlinear coupling: The linear drive parallel configuration has highly nonlinear kinematic characteristics, and the motion of each axis is coupled with each other. Conventional single-axis control methods are difficult to maintain the spatial pose of the moving platform accurately in dynamic tracking.

[0004] Strict constraints when applied in medical settings: Radiotherapy requires extremely high operational stability, and the terminal acceleration must be strictly limited to ensure patient safety and beam stability. At the same time, each linear drive axis has physical travel limits, and conventional control methods are prone to safety risks such as control saturation and overtravel impact. Summary of the Invention

[0005] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a delay prediction control method and system for parallel robots. This method solves the problem that link delays commonly occur in the application control of existing parallel robots, such as parallel treatment beds for respiratory compensation movements, leading to system latency and phase lag, which in turn affects control accuracy.

[0006] To achieve the above objectives, according to one aspect of the present invention, a method for predictive control of delay in a parallel robot is provided, comprising: Construct the nonlinear state equations for the parallel robot system, where the nonlinear state equations are the relationship between the derivative of the system's state vector with respect to time and the state vector and control variables; The nonlinear state equation is linearized and discretized in real time to obtain the basic discrete linear state equation at any control moment; Based on the sequence of delayed control commands that have been issued but not yet executed at the current control moment, the discretization equation of the delayed control command sequence is derived. Based on the sequence of delayed control commands issued but not yet executed at the current control time and the state vector at the current control time, an extended state vector is constructed; the basic discrete linear state equation and the discretized equation of the delayed control command sequence are merged to construct the extended state discrete linear state equation. Based on the extended state discrete linear state equation, the MPC predictive control method is used to optimize the output of the control variables, and the parallel robot system is controlled according to the output control variables.

[0007] According to the delay prediction control method for parallel robots provided by the present invention, the parallel robot system includes a parallel robot and a moving platform driven by the parallel robot. The state vector of the system includes the position, attitude, velocity and angular velocity of the moving platform; the control variable is the acceleration of the parallel robot.

[0008] According to the time-delay prediction control method for parallel robots provided by this invention, the nonlinear state equation is linearized in real time to obtain a locally linear continuous model as follows: ; in, State vector Regarding continuous time t The derivative; It is a continuous state matrix; For continuous control input matrix; k To control the timing; The state equations are nonlinear. For control variables; Discretizing the locally linear continuous model yields the following basic discrete linear state equations: ; in, The discrete state transition matrix, To control the cycle, It is the identity matrix; For discrete control input matrix; It is a time delay control variable. For the inherent physical delay of the system The corresponding number of discrete lag periods.

[0009] According to the time delay prediction control method for parallel robots provided by the present invention, a sequence of delayed control commands that has been issued but not yet executed at the current control time is... for: ; Always ; The discretized equations for the hysteresis control command sequence are as follows: ; in, yes The sliding matrix, yes The input embedding matrix.

[0010] According to the parallel robot delay prediction control method provided by the present invention, the system's first... k State vector at control time With delayed control command sequence Concatenate to construct an expanded state vector as follows: ; The extended state discrete linear state equations are constructed as follows:

[0011] Simplifying, we get: ; in, This is the extended state transition matrix; For expanding the control input matrix; Function is from Extract .

[0012] According to the parallel robot delay prediction control method provided by the present invention, the optimization of the control variables output using the MPC predictive control method specifically includes: Based on the extended state discrete linear state equation, the extended state vector is predicted using the state vector and control variables, thereby obtaining the predicted state vector at multiple control times in the prediction time domain. An objective function is constructed based on the error between multiple predicted state vectors and their corresponding reference state vectors, and the output control variables are optimized based on the objective function.

[0013] According to the parallel robot delay prediction control method provided by the present invention, the optimization output of the control variables using the MPC predictive control method further includes: The objective function takes the control variable increment sequence in the control time domain as the optimization variable and also includes the L2 norm sum of squares of the control variable increment sequence. The control variable increment sequence includes multiple control variable increments within the control time domain, with each control variable increment being the increase in the control variable compared to the previous control time. Multiple control variables within the control time domain are obtained sequentially based on the control variable increment sequence and the control variables of the previous control time.

[0014] According to the time delay prediction control method for parallel robots provided by the present invention, the objective function is specifically: minimizing the sum of the weighted L2 norm squares of the differences between multiple predicted state vectors and their corresponding reference state vectors, and the sum of the weighted L2 norm squares of the control variable increment sequence. The specific calculation formula is as follows: ; in, For prediction in the time domain; In order to be in Time prediction The predicted state vector at time step; for The reference state vector at time t; To control the time domain; In order to be in Time prediction Increment of control variables at any given time; and This is the weight matrix.

[0015] According to the parallel robot delay prediction control method provided by the present invention, the optimization output of the control variables using the MPC predictive control method further includes: The physical travel limits and control variable ranges of the parallel robot system are used as constraints for selecting optimization variables; among them, the control variable range constraints are verified based on the values ​​of the control variables. After obtaining the predicted state vector, the predicted displacement of the parallel robot is obtained based on the predicted state vector in order to verify the physical travel limit constraints of the parallel robot system.

[0016] According to another aspect of the present invention, a delay prediction and control system for a parallel robot is provided, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor, when executing the program, implements the steps of any of the above-described delay prediction and control methods for a parallel robot.

[0017] Overall, compared with the prior art, the parallel robot delay prediction and control method and system provided by this invention offer the following advantages: 1. This invention constructs an extended state vector by splicing together a sequence of delayed control commands that have been issued but not yet executed and a state vector. The time delay is internalized through state expansion. Then, by reconstructing the extended state prediction model, i.e. the extended state discrete linear state equation, and using MPC rolling optimization, the control commands, i.e. the control variables, are calculated in advance to eliminate phase lag and improve control accuracy. 2. When used for radiotherapy bed control, the inherent link delay of the radiotherapy system is transformed into a predictable parameter within the MPC model through the active compensation mechanism of state expansion delay. This fundamentally solves the inherent contradiction of traditional feedback control, eliminates phase lag, significantly improves the accuracy of tumor target tracking, helps ensure a high degree of synchronization between the motion of the treatment bed and the respiratory motion of the tumor, and significantly reduces the radiation dose to normal tissues. 3. This invention achieves high-precision decoupling of strong multi-axis coupling in parallel robots, enhancing their ability to maintain pose on complex trajectories. Leveraging the multiple-input multiple-output (MIMO) global optimization capabilities of MPC, combined with a real-time updated kinematic model of the parallel robot, this invention automatically handles nonlinear motion coupling between multiple drive axes. Compared to traditional single-axis independent control, this solution avoids motion distortion caused by asynchrony between axes in three-dimensional respiratory trajectory tracking of thoracic and abdominal tumors, adapting to the clinical needs of multi-degree-of-freedom dynamic respiratory compensation. 4. Ensures safety and stability during clinical operation; This invention, through full-time-domain predictive safety constraints, can anticipate and avoid risks such as drive shaft overtravel and acceleration exceeding limits, completely avoiding the violent shutdown and control saturation problems that are prone to occur in traditional control algorithms; At the same time, this solution directly uses drive shaft acceleration as the control input, i.e., the control variable, and achieves direct smooth constraint on drive impact through the cost function weight matrix, meeting the clinical requirements of radiotherapy scenarios for patient comfort, body position stability, and radiation beam stability; 5. It has strong robustness and clinical versatility, and can quickly adapt to the application needs of multiple scenarios; the present invention has scenario adaptability. Only the time delay parameters and weight matrix in the prediction model need to be adjusted to quickly adapt to the latency of different devices and the load characteristics of patients with different weights. There is no need to readjust the entire set of control parameters, which greatly reduces the clinical debugging cost. It is compatible with mainstream medical parallel radiotherapy treatment beds and has extremely strong clinical versatility and environmental robustness. Attached Figure Description

[0018] Figure 1 This is a logical architecture diagram of the delay prediction control method for parallel robots provided by the present invention.

[0019] Figure 2 This is a structural illustration of the six-degree-of-freedom parallel robot provided by the present invention.

[0020] Figure 3 This is a schematic diagram of the MPC prediction time domain and compensation principle provided by the present invention.

[0021] Figure 4 This is a curve showing the dynamic tracking effect of the control method provided by this invention.

[0022] In all the accompanying drawings, the same reference numerals are used to denote the same elements or structures, wherein: 1-Moving platform; 2-Connecting rod; 3-Linear module; 4-Static platform. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0024] Please see Figure 1 This embodiment provides a delay prediction control method for parallel robots, which includes: Construct the nonlinear state equations for the parallel robot system, where the nonlinear state equations are the relationship between the derivative of the system's state vector with respect to time and the state vector and control variables; The nonlinear state equation is linearized and discretized in real time to obtain the basic discrete linear state equation at any control moment; Based on the sequence of delayed control commands that have been issued but not yet executed at the current control moment, the discretization equation of the delayed control command sequence is derived. Based on the sequence of delayed control commands issued but not yet executed at the current control time and the state vector at the current control time, an extended state vector is constructed; the basic discrete linear state equation and the discretized equation of the delayed control command sequence are merged to construct the extended state discrete linear state equation. Based on the extended state discrete linear state equation, the MPC predictive control method is used to optimize the output of the control variables, and the parallel robot system is controlled according to the output control variables.

[0025] In this embodiment, the basic discrete linear state equation is the relationship between the state vector at the next control time and the state vector and control variables at the current time; the discretized equation of the lag control command sequence is the relationship between the lag control command sequence at the next control time and the lag control command sequence and control variables at the current time; the extended state discrete linear state equation is the relationship between the extended state vector at the next control time and the extended state vector and control variables at the current time. This embodiment proposes a state-extended active delay compensation mechanism for radiotherapy links. Unlike traditional feedback control, which suffers from the technical bottleneck of failing to balance delay compensation and system stability, this embodiment addresses the inherent delay of parallel robot systems, such as radiotherapy systems, by proposing a state-extended active delay compensation method. By concatenating the issued but ineffective delayed control command sequence with the robot's pose state to form an extended state vector, the external system delay is transformed into internal state parameters of the MPC model. By modifying the discrete state space equations to construct an extended state prediction model, i.e., an extended state discrete linear state equation, the advanced periodic prediction of the future execution effect of delayed commands is achieved. Active cancellation of physical delay is completed at the stage of outputting control variables upon issuance of control commands, fundamentally solving the phase lag problem in respiratory compensation.

[0026] In some embodiments, the parallel robot system includes a parallel robot and a moving platform driven by the parallel robot. The state vector of the system includes the position, attitude, velocity, and angular velocity of the moving platform; the control variable is the acceleration of the parallel robot.

[0027] refer to Figure 2 Taking a treatment bed for radiotherapy respiratory compensation as an example, the treatment bed is a six-degree-of-freedom parallel robot system comprising a moving platform 1 (upper platform) and a stationary platform 4 (lower platform). The moving platform 1 is supported and driven by multiple parallel linear modules 3 (multiple outriggers) to change its posture. The multiple parallel linear modules 3 are mounted on the stationary platform 4, and the sliders of the linear modules 3 are hinged to the moving platform 1 via connecting rods 2. Specifically, this embodiment provides a motion control method for a six-degree-of-freedom parallel robot used in tumor radiotherapy, particularly relating to a predictive control technology capable of actively compensating for system delays and achieving multi-constraint optimization.

[0028] First, the robot's kinematic mapping and state space construction are as follows: Set a static platform coordinate system Dynamic platform coordinate system upper hinge point lower hinge point ; has the velocity at the upper hinge point lower hinge point velocity ; Support vector ; i Indicates the first i One support leg; unit vector of movement direction of the lower hinge point locating joint. ,by Figure 2 For example, , .

[0029] The inverse kinematics solution process for determining the displacement of the parallel robot, i.e., the displacement of the lower hinge point, based on the pose of the moving platform is as follows: Using the pose of the moving platform... Calculate the distance that the six linear modules need to move from their initial positions. .

[0030] The position vector of the upper hinge point in the stationary frame is , The homogeneous transformation matrix is ​​defined by the superscript O on the left, which represents the reference coordinate system, and the subscript D on the left, which represents the coordinate system being described. This is the homogeneous transformation matrix of the moving platform relative to the static platform. Let the position of the upper hinge point be in the coordinate system of the moving platform; let the initial position of the lower hinge point be... The position after moving is The outrigger length is set to a fixed value. Satisfying geometric constraints: .

[0031] Define vector Its length is The angle between the moving joint direction and the moving joint direction satisfy: ; The inverse solution formula can be derived from geometric relationships; substituting it into... And organize the information available about The equation: .

[0032] The forward kinematics solution, i.e., the solution process for the moving platform pose, is as follows: First, a pose error function is established based on the aforementioned inverse kinematics model. For any false pose during the iteration process... It can be achieved through rotation matrix and translation vector Calculate the corresponding upper hinge point position Then, the theoretical vector is obtained. length and included angle The theoretical displacement can be calculated by substituting it into the inverse solution formula. : ; Define nonlinear error function For theoretical calculation of displacement Compared with the actual measured displacement Difference:

[0033] Indicates the first i The error function of each drive shaft; the forward kinematics solution is to solve the system of nonlinear equations. The root is obtained. The Newton-Raphson numerical method is used for iteration, the core of which is to approximate the Jacobian matrix of the pose vector using a first-order Taylor expansion of the objective function. The iterative update formula is: ; ; In the formula, It is the correction amount for the false positioning pose; It is the first The false localization pose in the next iteration; Error function For generalized pose vectors The partial derivative matrix: ; The process of solving the velocity Jacobian matrix is ​​as follows: The generalized velocity of the moving platform's operational space is established using the velocity Jacobian matrix. With drive speed The mapping relationship is , For platform speed; The angular velocity of the moving platform; This is the velocity Jacobian matrix; thus, the tangential velocity requirements of the tumor target trajectory are calculated in real time and applied to each drive axis. The velocity Jacobian matrix is ​​specifically:

[0034] set up , ,have: The following are listed: ,Right now , . It is a translation vector; The Jacobian matrix is ​​the operation space matrix; Let be the Jacobian matrix of the joint space.

[0035] The continuous-time nonlinear state-space equations are constructed as follows: Constructing the state vector. Control input is the control variable. , To drive acceleration, the following nonlinear state equation is established: ; Among them, the location of the moving platform The dynamic platform xyz Euler angle ; It is a nonlinear state equation.

[0036] The transformation matrix mapping Euler's rate of change of angle to angular velocity ; , , refer to Dimensions 1 to 3 refer to Dimensions 4 to 6.

[0037] The specific logic of the prediction model discretization and time delay compensation is as follows: This step is the core time delay compensation module, which solves the phase lag problem caused by the inherent link delay of the radiotherapy system, and at the same time transforms the nonlinear model into a linear discrete model that can be solved in real time by MPC.

[0038] First, model linearization and discretization: This step transforms the continuous nonlinear model into a discrete linear model that can be handled by MPC through real-time linearization and zero-order preserved discretization.

[0039] Real-time linearization: The 6-DOF linearly driven parallel robot used in this embodiment is a strongly nonlinear system. Only within the neighborhood of the current state can the linearization model accurately approximate the actual motion characteristics of the system. Therefore, in each control cycle, i.e., at each control moment... Based on the current actual state fed back by the sensors For continuous nonlinear state equations Performing a first-order Taylor expansion and ignoring higher-order terms yields a locally linearly continuous model in the neighborhood of the current state. This involves real-time linearization of the nonlinear state equations, resulting in the following locally linearly continuous model: ; in, State vector Regarding continuous time t The derivative; It is a continuous state matrix; For continuous control input matrix; k To control the timing; The state equations are nonlinear. For control variables. The velocity Jacobian matrix of the parallel robot. Euler angle transformation matrix All follow the platform pose The system's nonlinear characteristics change dynamically with the pose, changing in real time. Only by relinearizing based on the current pose in each control cycle can we ensure that the linear model closely matches the robot's actual motion characteristics, avoid prediction bias and motion distortion, and adapt to the control requirements of highly nonlinear parallel configurations.

[0040] Zero-order hold discretization: Using the zero-order hold method (ZOH), commonly used in industrial control, the above linear continuous model is discretized to obtain the basic discrete linear state equations with system time delay. That is, the basic discrete linear state equations are obtained by discretizing the locally linear continuous model as follows: ; in, It is a discrete state transition matrix, which is the core coefficient connecting the states of two adjacent periodic systems; To control the cycle, It is the identity matrix; As a discrete control input matrix, it directly determines the control effect of the drive shaft acceleration command on the pose state of the moving platform; The delay control variable is the delay term. For the inherent physical delay of the system The corresponding discrete lag period number varies due to delays in various components of the system. Control commands issued at any time The timing of the actual action on the parallel robot is the core source of the system's dynamic tracking phase lag.

[0041] Delay Compensation Based on State Expansion: This step utilizes state expansion technology to transform the external physical delay of the system into internal state variables of the MPC model, achieving internalization and active compensation of the delay. The delay of the radiotherapy system is... Discrete lag period number The current control time contains a sequence of delayed control commands that have been issued but not yet executed. for: ; Always ; The discretized equation of the lag control command sequence, i.e., the sliding relationship between the lag control command sequence at the current control moment and the lag control command sequence at the next control moment, can be obtained as follows: ; in, yes The sliding matrix, yes The input embedding matrix.

[0042] The system number k State vector at control time With delayed control command sequence Concatenate to construct an expanded state vector as follows: ; This operation transforms external time delays into observable and predictable state variables within the model, achieving "internalization" of time delays. This allows the MPC model to directly predict the future execution effects of delayed instructions. Based on the expansion vector, the expanded state discrete linear state equations are constructed as follows:

[0043] Simplifying, we get: ; in, Let be the extended state transition matrix, which describes the one-step evolution characteristics of the extended state; To expand the control input matrix, the control input calculated at the current time is... Incorporate it into the expansion phase to enable prediction of future execution results; Function is from Extract The delayed control input in the original model Converted into control inputs calculated at the current moment Control over the expansion state allows the MPC model to directly predict... The actual state of the system after one cycle lays the foundation for the calculation of the lead control command.

[0044] In some embodiments, optimizing the output of the control variable using the MPC predictive control method specifically includes: Based on the extended state discrete linear state equation, the extended state vector is predicted using the state vector and control variables, thereby obtaining the predicted state vector at multiple control times in the prediction time domain. An objective function is constructed based on the error between multiple predicted state vectors and their corresponding reference state vectors, and the output control variables are optimized based on the objective function.

[0045] Optimizing the output of control variables using the MPC predictive control method also includes: The objective function takes the control variable increment sequence in the control time domain as the optimization variable and also includes the L2 norm sum of squares of the control variable increment sequence. The control variable increment sequence includes multiple control variable increments within the control time domain, with each control variable increment being the increase in the control variable compared to the previous control time. Multiple control variables within the control time domain are obtained sequentially based on the control variable increment sequence and the control variables of the previous control time.

[0046] refer to Figure 3 In this embodiment, an extended state vector is constructed. Then, the optimal acceleration control command for the current moment is obtained through the following closed-loop calculation, which is fully compatible with the MPC rolling optimization logic: State prediction: based on the current time. expansion state Compared with the extended state prediction model, in the prediction time domain Internal prediction of the future System state in each cycle ,in Indicates in Time Prediction The state at each time step. Specifically, using the extended state prediction model, multiple recursive steps are taken. The extended vector includes the state vector. The original basic discrete linear state equations are used to predict the state vector at the next control time step. The expansion vector contains Therefore, the expanded state prediction model can use the current input control variables. Control future expansion and make predictions.

[0047] Optimize objective construction: embed the predicted state into the MPC cost function, so as to After a certain time From any moment on, the system status is accurately tracked using reference trajectories. With the core objective, construct a quadratic optimization problem with physical hard constraints; The term "moment after time" refers to tracking future moments. The starting point of optimization refers to the moment when the instruction takes effect.

[0048] Quadratic Programming Solution: The optimization problem is transformed into a standard quadratic programming (QP) problem by using hard constraints such as the physical travel limit of the drive shaft and the extreme value of acceleration. The effective set method or interior point method is used to solve it in real time, obtaining the control time domain solution. The optimal control increment sequence within: ; in, To control the input increment, .

[0049] Current instruction calculation: Based on the optimal control increment sequence, the current time step is calculated. Optimal acceleration control command: ; Scroll execution: The instruction is sent to the instruction buffer and executed after the delay ends; then the next control cycle begins. Repeat the entire process described above to achieve closed-loop rolling control and active time delay compensation. (Reference) Figure 4 This is a schematic diagram of the dynamic tracking effect curve, demonstrating that this control method can achieve precise tracking.

[0050] The cost function is designed as follows: a quadratic cost function is adopted. As the objective function for MPC rolling optimization, by minimizing Solving for the optimal control sequence, the objective function is specifically: minimizing the sum of the weighted L2 norm squares of the differences between multiple predicted state vectors and their corresponding reference state vectors, and the sum of the weighted L2 norm squares of the control variable increment sequence. The specific calculation formula is as follows: ; The optimization variable in this formula is the control increment sequence within the control time domain M: ; in, For prediction in the time domain; In order to be in Time prediction The predicted state vector at time step; for The reference state vector at time t; To control the time domain; In order to be in Time prediction Increment of control variables at any given time; and This is the weight matrix. The cost function is minimized. The optimal sequence of acceleration control increments for the drive axes of the six-DOF parallel robot is obtained through calculation, and the acceleration control command for the current moment is finally output. Weight matrix Ensure the breathing trajectory High-precision tracking; weight matrix For driving acceleration Apply smooth constraints to ensure stable operation of the radiotherapy bed.

[0051] Specifically, optimizing the output of control variables using the MPC predictive control method also includes: The physical travel limits and control variable ranges of the parallel robot system are used as constraints for selecting optimization variables; among them, the control variable range constraints are verified based on the values ​​of the control variables. After obtaining the predicted state vector, the predicted displacement of the parallel robot is obtained based on the predicted state vector in order to verify the physical travel limit constraints of the parallel robot system.

[0052] In some embodiments, a parallel robot delay prediction control system is also provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the program to implement the steps of any of the above-described parallel robot delay prediction control methods.

[0053] This embodiment addresses the inherent contradiction between large latency and high precision in parallel robot systems such as those for radiotherapy respiratory compensation tasks, as well as the challenges of multi-axis coupling in parallel robots. It proposes a latency prediction control method for radiotherapy respiratory compensation parallel robots based on model predictive control (MPC). This method internalizes system latency through state expansion technology, achieving active phase alignment; it decouples the nonlinear coupling of the parallel robot in real time through a real-time linearized prediction model; and it balances tracking accuracy, operational stability, and clinical safety within a unified framework through rolling optimization with hard constraints.

[0054] Among them, a deep integration and decoupling mechanism between the 6-rail-6-link parallel configuration and MPC is proposed: Addressing the strong nonlinearity and multi-axis strong coupling characteristics of the 6-rail-6-link linear drive parallel robot, a real-time update method for the prediction model is proposed. Within each control cycle, the velocity Jacobian matrix is ​​calculated in real-time based on the current dynamic platform pose, and directly embedded into the linearization, state transition matrix, and control input matrix calculation processes of the MPC prediction model. That is, the velocity Jacobian matrix is ​​recalculated in each control cycle, and the state transition matrix and control input matrix are updated. Then, combined with an extended state prediction model, the system state for P cycles is predicted, and the result is obtained through quadratic programming. , It takes effect after a certain number of cycles, with cycle iterations and real-time model updates; it can achieve deep adaptation of the control algorithm to specific parallel mechanical configurations, as well as real-time decoupling of the nonlinear motion of the 6 drive axes, solving the motion distortion problem caused by multi-axis coupling that traditional single-axis control cannot handle.

[0055] It also enables a proactive safety envelope control mechanism based on full-time-domain prediction: Full-time-domain predictive hard constraints are introduced during MPC rolling optimization, overcoming the limitation of traditional control which can only constrain the current output. The system not only performs safety checks on the current control commands but also conducts a full-cycle assessment of physical limits such as drive shaft travel and acceleration at all intermediate moments within the prediction time domain. This allows for the early identification of potential safety risks such as slider overtravel impacts and excessive acceleration. During the optimization process, it automatically calculates the optimal smooth motion trajectory that satisfies all constraints, achieving proactive prediction and pre-emptive control of radiotherapy clinical safety.

[0056] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A delay prediction control method for parallel robots, characterized in that, include: Construct the nonlinear state equations for the parallel robot system, where the nonlinear state equations are the relationship between the derivative of the system's state vector with respect to time and the state vector and control variables; The nonlinear state equation is linearized and discretized in real time to obtain the basic discrete linear state equation at any control moment; Based on the sequence of delayed control commands that have been issued but not yet executed at the current control moment, the discretization equation of the delayed control command sequence is derived. Based on the sequence of delayed control commands issued but not yet executed at the current control time and the state vector at the current control time, an extended state vector is constructed; the basic discrete linear state equation and the discretized equation of the delayed control command sequence are merged to construct the extended state discrete linear state equation. Based on the extended state discrete linear state equation, the MPC predictive control method is used to optimize the output of the control variables, and the parallel robot system is controlled according to the output control variables.

2. The delay prediction control method for parallel robots as described in claim 1, characterized in that, The parallel robot system includes a parallel robot and a moving platform driven by the parallel robot. The state vector of the system includes the position, attitude, velocity and angular velocity of the moving platform; the control variable is the acceleration of the parallel robot.

3. The delay prediction control method for parallel robots as described in claim 1, characterized in that, The nonlinear state equations are linearized in real time to obtain a locally linear continuous model as follows: ； in, State vector Regarding continuous time t The derivative; It is a continuous state matrix; For continuous control input matrix; k To control the timing; The state equations are nonlinear. For control variables; Discretizing the locally linear continuous model yields the following basic discrete linear state equations: ； in, The discrete state transition matrix, To control the cycle, It is the identity matrix; For discrete control input matrix; It is a time delay control variable. For the inherent physical delay of the system The corresponding number of discrete lag periods.

4. The delay prediction control method for parallel robots as described in claim 3, characterized in that, Lag control command sequence that has been issued but not yet executed at the current control moment for: ； Always ; The discretized equations for the hysteresis control command sequence are as follows: ； in, yes The sliding matrix, yes The input embedding matrix.

5. The delay prediction and control method for parallel robots as described in claim 4, characterized in that, The system number k State vector at control time With delayed control command sequence Concatenate to construct an expanded state vector as follows: ； The extended state discrete linear state equations are constructed as follows: Simplifying, we get: ； in, This is the extended state transition matrix; For expanding the control input matrix; Function is from Extract .

6. The delay prediction control method for parallel robots as described in claim 1, characterized in that, The optimization of control variables using the MPC predictive control method specifically includes: Based on the extended state discrete linear state equation, the extended state vector is predicted using the state vector and control variables, thereby obtaining the predicted state vector at multiple control times in the prediction time domain. An objective function is constructed based on the error between multiple predicted state vectors and their corresponding reference state vectors, and the output control variables are optimized based on the objective function.

7. The delay prediction control method for parallel robots as described in claim 6, characterized in that, Optimizing the output of control variables using the MPC predictive control method also includes: The objective function takes the control variable increment sequence in the control time domain as the optimization variable and also includes the L2 norm sum of squares of the control variable increment sequence. The control variable increment sequence includes multiple control variable increments within the control time domain, with each control variable increment being the increase in the control variable compared to the previous control time. Multiple control variables within the control time domain are obtained sequentially based on the control variable increment sequence and the control variables of the previous control time.

8. The delay prediction control method for parallel robots as described in claim 7, characterized in that, The objective function is specifically defined as minimizing the sum of the weighted squared L2 norms of the differences between multiple predicted state vectors and their corresponding reference state vectors, as well as the sum of the weighted squared L2 norms of the control variable increment sequences. The specific calculation formula is as follows: ； in, For prediction in the time domain; In order to be in Time prediction The predicted state vector at time step; for The reference state vector at time t; To control the time domain; In order to be in Time prediction Increment of control variables at any given time; and This is the weight matrix.

9. The delay prediction control method for parallel robots as described in claim 6, characterized in that, Optimizing the output of control variables using the MPC predictive control method also includes: The physical travel limits and control variable ranges of the parallel robot system are used as constraints for selecting optimization variables; among them, the control variable range constraints are verified based on the values ​​of the control variables. After obtaining the predicted state vector, the predicted displacement of the parallel robot is obtained based on the predicted state vector in order to verify the physical travel limit constraints of the parallel robot system.

10. A time delay prediction and control system for parallel robots, characterized in that, The system includes a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor, when executing the program, implements the steps of the parallel robot delay prediction control method as described in any one of claims 1 to 9.

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