A uvw parallel platform multi-target trajectory planning method

Abstract

This invention relates to the field of intelligent manufacturing technology, and particularly to a multi-objective trajectory planning method for a UVW parallel platform, comprising the following steps: calculating the target displacements of the U / V / W joints and establishing a mapping relationship between master and slave axis parameters; using the seven-segment asymmetric S-shaped trajectory parameters of the master axis as decision variables, constructing a multi-objective optimization model with the optimization objectives of minimizing motion time, minimizing the peak value of maximum jerky motion, and minimizing the sum of the peak values ​​of the three-axis driving forces, and using the RVS hard constraint function as the mandatory constraint condition for the multi-objective optimization model; using the NSGA-II algorithm to perform global optimization on the multi-objective optimization model to obtain the optimal master axis trajectory parameters; generating the complete motion trajectory of the U / V / W three axes and converting it into PVT trajectory code. Under the premise of satisfying driving and kinematic constraints, this method achieves comprehensive optimization of efficiency, stability, and dynamic load, significantly reducing residual vibration and shortening the total settling time of the system.

Description

Technical Field

[0001] This invention relates to the field of intelligent manufacturing technology, and in particular to a multi-objective trajectory planning method for a UVW parallel platform. Background Technology

[0002] With the development of industrial processing and visual inspection, stringent requirements have been placed on the high speed, high acceleration, and positioning accuracy of motion platforms. UVW parallel platforms, with their compact configuration, high rigidity, and low cumulative error characteristics, have become the core actuators of high-dynamic precision alignment equipment. However, to meet the demands of high production cycles, the platform needs to perform high-frequency, high-acceleration and high-deceleration motions during frequent starts and stops. This easily excites low-order flexible modes of the structure, leading to residual vibrations at the end effector and prolonged settling time, thus affecting positioning efficiency and accuracy. Therefore, how to improve operational efficiency while ensuring motion smoothness and positioning accuracy is a key challenge in the field of precision control.

[0003] In recent years, to achieve a balance between high-speed, high-acceleration motion planning and residual vibration suppression, many scholars have conducted research on trajectory optimization methods that combine trajectory planning and residual vibration suppression. A common approach is to increase the trajectory order to make the trajectory smoother and improve motion stability. However, numerous studies have shown that once the order reaches a certain level, the residual vibration suppression capability no longer improves significantly, and higher-order trajectories increase computational complexity, making it difficult to meet the real-time requirements of online planning. For example, Chinese patent application CN116700151A discloses a precision motion platform motion trajectory planning system and its parameter tuning method. Based on asymmetric S-curve planning, it introduces smoothness and asymmetry parameters, combines flexible system modal information and zero-pole configuration ideas to tune trajectory parameters, achieving maximum suppression of residual vibration.

[0004] During the high-frequency, high-acceleration / deceleration point-to-point motion of the UVW parallel correction platform, after knowing the end-effector's target pose, the required displacement of the joint motor is obtained through inverse kinematics, and joint space trajectory planning is performed accordingly. Existing trajectory planning methods have the following drawbacks: 1. The UVW platform is a strongly coupled system. If each axis is planned independently, phase differences in the planning lead to internal stress and end-effector trajectory deviations. Existing single-axis planning strategies are difficult to directly apply to this type of parallel mechanism. 2. High-order modal parameters are difficult to accurately identify in parallel motion platform systems. Current trajectory optimization methods aimed at reducing system settling time often require knowledge of the high-order dynamic model of the controlled object system to solve for optimal motion parameters, which has certain limitations. 3. Existing multi-objective optimization models ignore the impact of instantaneous driving force peaks on the system. Excessively large driving force peaks are equivalent to applying high-amplitude quasi-step disturbances to the servo system, easily inducing actuator saturation and overload, exacerbating dynamic impacts, and thus reducing the system's control margin and motion stability.

[0005] Therefore, there is an urgent need for a trajectory optimization method that does not rely on the higher-order modal parameters of the system, so as to shorten the total settling time of the system while ensuring motion accuracy, and achieve comprehensive optimization of motion efficiency, stability and dynamic load. Summary of the Invention

[0006] The purpose of this invention is to propose a multi-objective trajectory planning method for a UVW parallel platform. Based on the characteristics of structural flexible modal excitation and multi-axis coupling, it integrates asymmetric S-curve and robust zero-pole vibration suppression hard constraints to optimize multi-objective trajectories. Under the premise of satisfying driving and kinematic constraints, it achieves comprehensive optimization of efficiency, stability and dynamic load, significantly reduces residual vibration and shortens the total settling time of the system.

[0007] To achieve this objective, the present invention adopts the following technical solution:

[0008] A multi-objective trajectory planning method for a UVW parallel platform includes the following steps:

[0009] S1: Obtain the end-effector pose and perform inverse kinematics calculation of the U / V / W joint target displacement;

[0010] S2: Initialize the parameters of the seven-segment asymmetric S-shaped trajectory, select the axis with the largest absolute displacement as the master axis, and the other axes as slave axes. Use the master-slave axis time scaling full-dimensional synchronization strategy to establish the master-slave axis parameter mapping relationship.

[0011] S3: Using the seven-segment asymmetric S-shaped trajectory parameters of the main axis as decision variables, a multi-objective optimization model is constructed with the objectives of minimizing motion time, minimizing the peak value of maximum jerkyity, and minimizing the sum of the peak values ​​of the three-axis driving forces. The RVS hard constraint function is used as the mandatory constraint condition for the multi-objective optimization model.

[0012] S4: The NSGA-II algorithm is used to perform global optimization on the multi-objective optimization model to obtain the Pareto optimal solution set. According to the weight requirements of the current working condition, the best compromise solution is selected from the Pareto optimal solution set to obtain the optimal spindle trajectory parameters.

[0013] S5: Based on the optimal master axis trajectory parameters and the mapping relationship between the master and slave axis parameters, generate the complete motion trajectory of the U / V / W three axes and convert it into PVT trajectory code.

[0014] Furthermore, in step S2, the ratio of the maximum acceleration in the acceleration phase to the maximum acceleration in the deceleration phase is used as the asymmetry factor K of the seven-segment asymmetric S-shaped trajectory.

[0015] Furthermore, in step S2, the method for establishing the master-slave axis parameter mapping relationship includes:

[0016] Select the axis with the largest absolute displacement as the principal axis M, and specify its index and displacement. Defined as:

[0017] ,

[0018] in, For the first The target displacement of the axis;

[0019] Synchronization ratio coefficient of slave axis relative to master axis for:

[0020] ,

[0021] For the spindle, And for any x, always holds ;

[0022] The master-slave axis parameter mapping relationship is as follows:

[0023] ,

[0024] in, , , For the velocity, acceleration, and jerk of the shaft, , , The maximum speed, maximum acceleration, and maximum jerk of the shaft are given. , , The main axis's velocity, acceleration, and jerk. , , The maximum speed, maximum acceleration, and maximum jerk of the main axis.

[0025] Furthermore, in step S3, the instantaneous driving forces of the principal axis and the slave axis are calculated using a rigid body dynamics model with nonlinear perturbation.

[0026] The rigid body dynamics model of the nonlinear disturbance includes nonlinear friction and linear motor cogging effect.

[0027] Furthermore, the method for constructing the rigid body dynamics model of the nonlinear perturbation includes:

[0028] The inverse kinematic equations of the UVW parallel platform are derived and differentiated to obtain the Jacobian matrix between the joint space and the operation space.

[0029] A basic rigid body dynamics model of the system is established using the Lagrange method combined with the principle of virtual work:

[0030] ,

[0031] in, For the operation space inertia matrix, Let J be the Coriolis / eccentricity matrix, and J be the Jacobian matrix. This is the magnetic reluctance disturbance term. For friction disturbance term, This is the ideal driving force term for the motor. Let be the inverse of the transpose of the Jacobian matrix. For the joint motor speed matrix, The acceleration matrix of the joint motor. It is the inverse of the Jacobian matrix;

[0032] Nonlinear perturbation terms are superimposed on the basic rigid body dynamics model:

[0033] The cogging magnetic resistance of the linear motor was fitted using a third-order Fourier series.

[0034] The basic friction of the guide rail is described by a combined model of Coulomb friction and viscous friction, and the coupled friction component of the driven chain friction mapped back to the driving shaft through the end platform is included to obtain the total friction force.

[0035] By superimposing the coarse magnetic reluctance and total frictional force onto the basic rigid body dynamics model, the final inverse rigid body dynamics model is obtained:

[0036] ,

[0037] in, This is the ideal driving force term for the motor. This is the magnetic reluctance disturbance term. This represents the friction disturbance term.

[0038] Furthermore, the method for constructing the RVS hard constraint function in step S3 includes:

[0039] S301: A seven-segment S-shaped trajectory is used to traverse the feature points of the platform's workspace and collect residual vibration signals after the trajectory is in place.

[0040] S302: Perform FFT spectrum analysis on the residual vibration segment signals at each feature point, and extract the common peak frequency with the largest amplitude at all feature points as the first-order dominant resonance frequency of the system. And introduce a robust tolerance band. The target vibration suppression frequency band is obtained. ;

[0041] S303: Defines the fundamental frequency of the S-curve:

[0042] ,

[0043] in, To achieve the maximum speed during the acceleration phase, This is the maximum acceleration during the acceleration phase;

[0044] S304: Calculate the fundamental frequency of the current trajectory With dominant resonant frequency Normalized notch distance This is used to quantify the alignment between the spectral zeros and the resonant poles;

[0045] S305: Define the asymmetry factor K as the ratio of the maximum acceleration during the acceleration phase to the maximum acceleration during the deceleration phase, and calculate the ideal reference value that makes the time-domain phase of the acceleration and deceleration phases satisfy the cancellation condition. And construct a soft penalty term for asymmetric factor time-domain phase coordination. ;

[0046] S306: Synthetic Normalized Notch Range Soft penalty item with time domain coordination The RVS hard constraint function is obtained as follows:

[0047] ,

[0048] in, and These are the weighting coefficients. This is the constraint threshold.

[0049] Furthermore, the ideal vibration condition for the fundamental frequency of the S-curve in S303 is:

[0050] ,

[0051] Where n is the frequency alignment order, and the ideal vibration conditions are substituted into step S304.

[0052] In step S304, the nearest integer multiple n corresponding to the current solution is calculated:

[0053] ,

[0054] Define target alignment frequency The normalized notch distance is expressed as:

[0055] ;

[0056] In step S305, the ideal reference value is:

[0057] ;

[0058] Soft penalty items The formula is:

[0059] .

[0060] Furthermore, the method for constructing the multi-objective optimization model in step S3 includes:

[0061] Decision variables are ,in It is the planned maximum speed value. It is the planned maximum acceleration value, It is the maximum urgency value in the plan;

[0062] Motion efficiency goals To minimize the total motion time :

[0063] ,

[0064] in, Indicates the decision variables The determined first Duration of segment These correspond to the seven time periods of the seven-segment asymmetric S-shaped trajectory;

[0065] Motion stability target use Minimize the norm to the peak of maximum jerkiness:

[0066] ,

[0067] in, Indicates the principal axis trajectory at time [time]. The degree of urgency; The maximum abrupt change during the main shaft acceleration phase; Indicates according to asymmetric factors The calculated maximum abruptness of the deceleration phase;

[0068] Peak driving force and suppression target The optimization objective is to minimize the sum of the maximum peak values ​​of the three-axis driving forces.

[0069] ,

[0070] in, Indicated in decision variables The corresponding trajectory under the first axis at time The instantaneous driving force;

[0071] The multi-objective optimization model is described as follows:

[0072] .

[0073] The technical solution provided by this invention may include the following beneficial effects:

[0074] This invention reduces internal stress and end-point trajectory deviation caused by asynchronous motion by employing a time-scaling master-slave axis synchronization strategy. For the low-order flexible modes of the platform structure, an asymmetric S-curve parameter constraint is constructed to force the zero points of the trajectory spectrum to precisely correspond with the poles (resonance frequencies) of the system. Through the zero-pole cancellation principle, residual vibration after the system reaches its final position is fundamentally suppressed. Under the above constraints, a multi-objective optimization model is established with time efficiency, jerkiness, and peak driving force as optimization indicators. By solving for the optimal solution of the curve parameters, the overall optimization of efficiency, stability, and dynamic load is achieved.

[0075] This invention is particularly suitable for high-speed start-stop point movement and micron-level precision alignment of UVW parallel precision alignment platforms. It can also be extended to other multi-axis precision positioning equipment with significant structural resonance modes and strict requirements for settling time and residual vibration. Attached Figure Description

[0076] Figure 1 This is a schematic diagram of the structure of the UVW parallel platform of the present invention;

[0077] Figure 2 This is a schematic diagram of the motion of the UVW parallel platform of the present invention;

[0078] Figure 3 This is a flowchart illustrating the multi-target trajectory planning method of the UVW parallel platform of the present invention. Detailed Implementation

[0079] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that the specific embodiments described herein are for illustrative and explanatory purposes only and are not intended to limit the present invention.

[0080] An embodiment of the present invention provides a multi-objective trajectory planning method for a UVW parallel platform, characterized by comprising the following steps:

[0081] S1: Obtain the end-effector pose and perform inverse kinematics calculation of the U / V / W joint target displacement;

[0082] S2: Initialize the parameters of the seven-segment asymmetric S-shaped trajectory, select the axis with the largest absolute displacement as the master axis, and the other axes as slave axes. Use the master-slave axis time scaling full-dimensional synchronization strategy to establish the master-slave axis parameter mapping relationship.

[0083] S3: Using the seven-segment asymmetric S-shaped trajectory parameters of the main axis as decision variables, a multi-objective optimization model is constructed with the objectives of minimizing motion time, minimizing the peak value of maximum jerkyity, and minimizing the sum of the peak values ​​of the three-axis driving forces. The RVS hard constraint function is used as the mandatory constraint condition for the multi-objective optimization model.

[0084] S4: The NSGA-II algorithm is used to perform global optimization on the multi-objective optimization model to obtain the Pareto optimal solution set. According to the weight requirements of the current working condition, the best compromise solution is selected from the Pareto optimal solution set to obtain the optimal spindle trajectory parameters.

[0085] S5: Based on the optimal master axis trajectory parameters and the mapping relationship between the master and slave axis parameters, generate the complete motion trajectory of the U / V / W three axes and convert it into PVT trajectory code.

[0086] This invention employs a seven-segment asymmetric S-shaped velocity curve as the trajectory primitive and uses a time-scaling master-slave axis synchronization strategy to ensure multi-axis coordination. It avoids complex flexible modeling by utilizing only FFT to extract the dominant frequency and forces precise matching between the trajectory zeros and the system's resonant frequency poles through robust zero-pole hard constraints. Based on this, a multi-objective optimization model is established with time efficiency, jerkiness, and peak and suppressed driving force as indicators, and the NSGA-II algorithm is used to optimize and solve for the trajectory motion parameters.

[0087] Reference Figure 1 and Figure 2 The UVW parallel platform includes a moving platform, driven branches, and a base. Each driven branch contains a slider assembly, a linear motor, and a linear scale. Multiple driven branches move along the U-axis, V-axis, and W-axis, respectively.

[0088] In one embodiment of the present invention, in step S2, the ratio of the maximum acceleration of the acceleration phase to the maximum acceleration of the deceleration phase is used as the asymmetry factor K of the seven-segment asymmetric S-shaped trajectory. The asymmetry factor K is used to characterize the degree of asymmetry between acceleration and deceleration capabilities. When K=1, the trajectory degenerates into a symmetric S-shaped curve; when K>1, it indicates an asymmetric trajectory with high acceleration for start-up and low acceleration for stop-down. During the optimization process, K, as one of the principal axis decision variables, together with the principal axis maximum speed, maximum acceleration, and maximum jerkness, determines the duration of each sub-stage of the seven-segment trajectory, and calculates the deceleration phase parameters accordingly, thereby adjusting the temporal phase relationship and the position of the spectral zero point while ensuring that the total displacement remains unchanged.

[0089] To avoid phase differences caused by independent planning of the three axes, which could lead to deviations in internal stress and end trajectory, the axis with the largest displacement stroke is selected as the master axis, which determines the total system time. The remaining axes are designated as slave axes. The velocity, acceleration, and jerk parameters of the master axis are scaled proportionally using a synchronization scaling factor to achieve full-dimensional synchronous arrival of position, velocity, acceleration, and jerk. In one embodiment of the present invention, the method for establishing the master-slave axis parameter mapping relationship in step S2 includes:

[0090] The axis with the largest absolute displacement is selected as the principal axis M. The principal axis is subject to the most stringent kinematic constraints and determines the total motion time of the entire system. The motion plan of the principal axis will serve as the baseline timing for the system, and the other axes are defined as slave axes. Principal axis index and its displacement are described below. Defined as:

[0091] ,

[0092] in, For the first The target displacement of the axis;

[0093] Synchronization ratio coefficient of slave axis relative to master axis for:

[0094] ,

[0095] For the spindle, And for any x, always holds The definition of the synchronization proportional coefficient enables multi-axis synchronization in all dimensions, including position, velocity, acceleration, and abrupt change. For the master axis, And for any x, always holds ;

[0096] The master-slave axis parameter mapping relationship is as follows:

[0097] ,

[0098] in, , , For the velocity, acceleration, and jerk of the shaft, , , The maximum speed, maximum acceleration, and maximum jerk of the shaft are given. , , The main axis's velocity, acceleration, and jerk. , , The maximum speed, maximum acceleration, and maximum jerk of the main axis.

[0099] This invention employs a synchronization planning mechanism based on master-slave axis time scaling, which ensures strict matching of the motion timing of the UVW three axes, effectively eliminates coupling shocks caused by phase differences, and improves the tracking accuracy and motion smoothness of the end trajectory.

[0100] Understandably, in multi-objective optimization models, the decision variable vector... For planning main shaft only ( The asymmetric S-shaped trajectory of the axis. Motion parameters (velocity) of each axis. acceleration Swiftness All are passed through the proportional coefficient. Obtained from the spindle parameter mapping.

[0101] To accurately calculate the peak driving force in subsequent optimizations, this invention establishes system dynamic equations in the operating space and maps them to the joint space. Simultaneously, it introduces nonlinear friction and linear motor cogging force models to establish a dynamic model capable of calculating the platform's instantaneous driving force—that is, a rigid body dynamic model incorporating nonlinear disturbances. In one embodiment of this invention, in step S3, the instantaneous driving forces of the master and slave axes are calculated using the rigid body dynamic model with nonlinear disturbances, respectively.

[0102] The rigid body dynamics model of the nonlinear disturbance includes nonlinear friction and linear motor cogging effect.

[0103] Specifically, methods for constructing rigid body dynamics models of nonlinear perturbations include:

[0104] The inverse kinematic equations of the UVW parallel platform are derived and differentiated to obtain the Jacobian matrix between the joint space and the operation space.

[0105] A basic rigid body dynamics model of the system is established using the Lagrange method combined with the principle of virtual work:

[0106]

[0107] in, For the operation space inertia matrix, Let J be the Coriolis / eccentricity matrix, and J be the Jacobian matrix. This is the ideal driving force term for the motor. Let be the inverse of the transpose of the Jacobian matrix. For the joint motor speed matrix, The acceleration matrix of the joint motor. It is the inverse of the Jacobian matrix;

[0108] Nonlinear perturbation terms are superimposed on the basic rigid body dynamics model:

[0109] The cogging magnetic resistance of the linear motor was fitted using a third-order Fourier series.

[0110] The basic friction of the guide rail is described by a combined model of Coulomb friction and viscous friction, and the coupled friction component of the driven chain friction mapped back to the driving shaft through the end platform is included to obtain the total friction force.

[0111] By superimposing the coarse magnetic reluctance and total frictional force onto the basic rigid body dynamics model, the final inverse rigid body dynamics model is obtained:

[0112] ,

[0113] in, This is the ideal driving force term for the motor. This is the magnetic reluctance disturbance term. This represents the friction disturbance term.

[0114] In one embodiment of the present invention, the method for constructing the RVS hard constraint function in step S3 includes:

[0115] S301: A seven-segment S-shaped trajectory is used to traverse the feature points of the platform's workspace and collect residual vibration signals after the trajectory is in place.

[0116] S302: Perform FFT spectrum analysis on the residual vibration segment signals at each feature point, and extract the common peak frequency with the largest amplitude at all feature points as the first-order dominant resonance frequency of the system. And introduce a robust tolerance band. The target vibration suppression frequency band is obtained. ;

[0117] S303: Defines the fundamental frequency of the S-curve:

[0118] ,

[0119] in, To achieve the maximum speed during the acceleration phase, This is the maximum acceleration during the acceleration phase;

[0120] S304: Calculate the fundamental frequency of the current trajectory With dominant resonant frequency Normalized notch distance This is used to quantify the alignment between the spectral zeros and the resonant poles;

[0121] S305: Define the asymmetry factor K as the ratio of the maximum acceleration during the acceleration phase to the maximum acceleration during the deceleration phase, and calculate the ideal reference value that makes the time-domain phase of the acceleration and deceleration phases satisfy the cancellation condition. And construct a soft penalty term for asymmetric factor time-domain phase coordination. ;

[0122] S306: Synthetic Normalized Notch Range Soft penalty item with time domain coordination The RVS hard constraint function is obtained as follows:

[0123] ,

[0124] in, and These are the weighting coefficients. This is the constraint threshold. This constraint forces all feasible solutions to simultaneously possess the optimal vibration suppression characteristics, transforming the vibration suppression trajectory parameter conditions into hard constraints for subsequent multi-objective optimization models.

[0125] This invention only requires identifying the first-order dominant frequency of the system. By introducing robust zero-pole hard constraints, residual vibration is suppressed from the source. Without the need to establish a complex high-order dynamic model, it ensures that the optimized solution of trajectory planning parameters has vibration suppression capability within the dominant mode frequency band, which significantly reduces residual vibration and shortens the tuning time.

[0126] Specifically, in step S302, the high-speed, high-acceleration S-shaped trajectory used for frequency identification preferably has the same trajectory primitives as the seven-segment asymmetric S-shaped trajectory used in subsequent optimization. The velocity, acceleration, and jerk are set near the upper limit allowed by the device to fully excite the main structural mode. The preferred feature points in the workspace are the platform center point, the midpoints of the four boundaries, and the four corner points, covering multiple representative poses in both the central and boundary areas. For each feature point, a reciprocating motion is performed, and position errors from the grating ruler or acceleration sensor signals are collected. When the trajectory command reaches the target position, the free decay segment from the first crossing of the position error threshold to the amplitude decay before entering the steady-state threshold is extracted as the residual vibration segment. A fast Fourier transform is performed on this residual vibration segment, and the common peak frequency with the largest amplitude at multiple feature points is counted as the platform's dominant resonance frequency. Considering frequency drift caused by pose changes, load variations, and temperature rise, robust tolerance bands are introduced on both sides of the dominant frequency. ,form The target vibration suppression frequency band.

[0127] The ideal vibration condition for the fundamental frequency of the S-curve in S303 is:

[0128] ,

[0129] Where n is the frequency alignment order, substituted into step S304 with ideal vibration conditions; it is understandable that the dominant resonant frequency... It is not only used for frequency identification, but also further used in subsequent equations (4) to (8) to calculate the nearest integer multiple n and the target alignment frequency. and normalized notch distance Finally, the results are substituted into the RVS constraint function for trajectory optimization.

[0130] In steps S303 and S304, to expand the multi-objective optimization solution space for trajectory parameters, a fixed fundamental frequency is not enforced. Instead, an alignment metric is defined: first, the nearest integer multiple is calculated, then the normalized notch distance is defined. The smaller the distance, the more accurately the zeros are aligned with the resonant poles. (Definition of normalized notch distance) To quantify the current trajectory fundamental frequency and the system's natural frequency The degree of alignment.

[0131] In step S304, the nearest integer multiple n corresponding to the current solution is calculated:

[0132] ,

[0133] Define target alignment frequency The normalized notch distance is expressed as:

[0134] .

[0135] The smaller the value, the more precisely the zero point of the trajectory's spectrum aligns with the pole of the system's resonant frequency.

[0136] In step S305, to improve robustness to parameter drift, a time-domain phase coordination penalty term related to the asymmetry factor is introduced, and the RVS constraint function is synthesized as a hard constraint threshold for optimization, which requires that the feasible solution must meet the vibration suppression requirements.

[0137] In step S305, through constraints Approaching the ideal benchmark value This effectively corrects time-domain phase deviation, ensuring the algorithm operates within the system's inherent frequency parameters. Robustness under drift conditions. Ideal baseline value:

[0138] ;

[0139] Construct a soft penalty function in cosine form To guide the optimization algorithm to prioritize the search Value close to Integer multiples of the solution soft penalty term The formula is:

[0140] .

[0141] During optimization, start with the current solution. , and the identified calculate Then, NSGA-II jointly optimizes K within a given search interval, so that it simultaneously takes into account objectives such as temporal phase coordination, motion efficiency, and peak driving force.

[0142] In one embodiment of the present invention, the method for constructing a multi-objective optimization model in step S3 includes:

[0143] The key parameters of the asymmetric S-shaped trajectory along the principal axis are selected as decision variables. ,in It is the planned maximum speed value. It is the planned maximum acceleration value, It is the maximum jerk value of the plan, and this vector uniquely determines all time-domain parameters of the three-axis synchronous motion;

[0144] Motion efficiency goals To minimize the total motion time :

[0145] ,

[0146] in, Indicates the decision variables The determined first Duration of segment These correspond to the seven time periods of the seven-segment asymmetric S-shaped trajectory;

[0147] Motion stability target use Minimize the norm to the peak of maximum jerkiness:

[0148] ,

[0149] in, Indicates the principal axis trajectory at time [time]. The degree of urgency; The maximum abrupt change during the main shaft acceleration phase; Indicates according to asymmetric factors The calculated maximum abruptness of the deceleration phase;

[0150] Peak driving force and suppression target The optimization objective is to minimize the sum of the maximum peak values ​​of the three-axis driving forces.

[0151] ,

[0152] in, Indicated in decision variables The corresponding trajectory under the first axis at time The instantaneous driving force.

[0153] To ensure the planned S-curve of velocity has complete uniform acceleration and deceleration segments and prevent degradation due to excessively short travel, the total target travel must meet the minimum displacement required to reach the set maximum acceleration. Joint motor constraints and robust vibration suppression hard constraints (RVS hard constraints) are also required. Joint motor constraints prevent the instantaneous motion parameters of each axis from exceeding the kinematic constraints and physical limits of the drive motor during motion. Robust vibration suppression hard constraints (RVS hard constraints) require all feasible solutions to strictly satisfy the robust zero-pole constraint condition. This constraint forces the optimization algorithm to search for feasible solutions only in the solution space where the planned poles are aligned with the dominant modal frequencies of the system, ensuring that vibration suppression is achieved at a fundamental level. Residual vibration at the location.

[0154] The multi-objective optimization model is described as follows:

[0155] .

[0156] The constructed optimization model exhibits highly nonlinear, multi-objective conflict, and strong constraint characteristics, making it prone to getting trapped in local optima using traditional gradient-based algorithms. Therefore, the Non-Dominated Sorting Genetic Algorithm (NSGA-II) is selected to perform global optimization on the model, obtaining the optimal solution set.

[0157] This invention introduces robust zero-pole vibration suppression conditions as hard constraints into the multi-objective optimization process. During the planning phase, an asymmetric S-shaped trajectory is generated using a master-slave axis synchronization strategy. A multi-objective optimization algorithm simultaneously optimizes the motion time, maximum jerk, and peak driving force, directly outputting trajectory parameters that balance efficiency, stability, and dynamic load while possessing vibration suppression capabilities. The hard constraint in this invention is a specific method for constructing vibration suppression constraints. Instead of fixing the fundamental frequency, it constructs inequality constraints by calculating the normalized notch distance between the trajectory's fundamental frequency and the system's first-order dominant frequency, combined with a time-domain coordination penalty term for the asymmetric factor. This method allows for effective notch filtering even when frequency uncertainties exist.

[0158] As an example, the executable instructions of the method of the present invention can be deployed to be executed on a computing device, or on multiple computing devices located at one location, or on multiple computing devices distributed in multiple locations and interconnected by a communication network.

[0159] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0160] The sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0161] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as read-only memory / random access memory, magnetic disk, optical disk) and includes several instructions to cause a multimedia terminal device (which may be a mobile phone, computer, television receiver, or network device, etc.) to execute the methods described in the various embodiments of this application.

[0162] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A method for multi-target trajectory planning of a UVW parallel platform, characterized in that, Includes the following steps: S1: Obtain the end-effector pose and perform inverse kinematics calculation of the U / V / W joint target displacement; S2: Initialize the parameters of the seven-segment asymmetric S-shaped trajectory, select the axis with the largest absolute displacement as the master axis, and the other axes as slave axes. Use the master-slave axis time scaling full-dimensional synchronization strategy to establish the master-slave axis parameter mapping relationship. S3: Using the seven-segment asymmetric S-shaped trajectory parameters of the main axis as decision variables, a multi-objective optimization model is constructed with the objectives of minimizing motion time, minimizing the peak value of maximum jerkyity, and minimizing the sum of the peak values ​​of the three-axis driving forces. The RVS hard constraint function is used as the mandatory constraint condition for the multi-objective optimization model. S4: The NSGA-II algorithm is used to perform global optimization on the multi-objective optimization model to obtain the Pareto optimal solution set. According to the weight requirements of the current working condition, the best compromise solution is selected from the Pareto optimal solution set to obtain the optimal spindle trajectory parameters. S5: Based on the optimal master axis trajectory parameters and the mapping relationship between the master and slave axis parameters, generate the complete motion trajectory of the U / V / W three axes and convert it into PVT trajectory code.

2. The method according to claim 1, characterized in that, In step S2, the ratio of the maximum acceleration in the acceleration phase to the maximum acceleration in the deceleration phase is used as the asymmetry factor K of the seven-segment asymmetric S-shaped trajectory.

3. The method according to claim 1, characterized in that, In step S2, the method for establishing the master-slave axis parameter mapping relationship includes: Select the axis with the largest absolute displacement as the principal axis M, and specify its index and displacement. Defined as: ， in, For the first The target displacement of the axis; Synchronization ratio coefficient of slave axis relative to master axis for: ， For the spindle, And for any x, always holds ; The master-slave axis parameter mapping relationship is as follows: ， in, , , For the velocity, acceleration, and jerk of the shaft, , , The maximum speed, maximum acceleration, and maximum jerk of the shaft are given. , , The main axis's velocity, acceleration, and jerk. , , The maximum speed, maximum acceleration, and maximum jerk of the main axis.

4. The method according to claim 1, characterized in that, In step S3, the instantaneous driving forces of the principal axis and the slave axis are calculated using a rigid body dynamics model with nonlinear perturbation. The rigid body dynamics model of the nonlinear disturbance includes nonlinear friction and linear motor cogging effect.

5. The method according to claim 4, characterized in that, The method for constructing the rigid body dynamics model of the nonlinear perturbation includes: The inverse kinematic equations of the UVW parallel platform are derived and differentiated to obtain the Jacobian matrix between the joint space and the operation space. A basic rigid body dynamics model of the system is established using the Lagrange method combined with the principle of virtual work: ， in, For the operation space inertia matrix, Let J be the Coriolis / eccentricity matrix, and J be the Jacobian matrix. This is the magnetic reluctance disturbance term. For friction disturbance term, This is the ideal driving force term for the motor. Let be the inverse of the transpose of the Jacobian matrix. For the joint motor speed matrix, The acceleration matrix of the joint motor. It is the inverse of the Jacobian matrix; Nonlinear perturbation terms are superimposed on the basic rigid body dynamics model: The cogging magnetic resistance of the linear motor was fitted using a third-order Fourier series. The basic friction of the guide rail is described by a combined model of Coulomb friction and viscous friction, and the coupled friction component of the driven chain friction mapped back to the driving shaft through the end platform is included to obtain the total friction force. By superimposing the coarse magnetic reluctance and total frictional force onto the basic rigid body dynamics model, the final inverse rigid body dynamics model is obtained: ， in, This is the ideal driving force term for the motor. This is the magnetic reluctance disturbance term. This represents the friction disturbance term.

6. The method according to claim 4, characterized in that, The method for constructing the RVS hard constraint function in step S3 includes: S301: A seven-segment S-shaped trajectory is used to traverse the feature points of the platform's workspace and collect residual vibration signals after the trajectory is in place. S302: Perform FFT spectrum analysis on the residual vibration segment signals at each feature point, and extract the common peak frequency with the largest amplitude at all feature points as the first-order dominant resonance frequency of the system. And introduce a robust tolerance band. The target vibration suppression frequency band is obtained. ; S303: Defines the fundamental frequency of the S-curve: ， in, To achieve the maximum speed during the acceleration phase, This is the maximum acceleration during the acceleration phase; S304: Calculate the fundamental frequency of the current trajectory With dominant resonant frequency Normalized notch distance This is used to quantify the alignment between the spectral zeros and the resonant poles; S305: Define the asymmetry factor K as the ratio of the maximum acceleration during the acceleration phase to the maximum acceleration during the deceleration phase, and calculate the ideal reference value that makes the time-domain phase of the acceleration and deceleration phases satisfy the cancellation condition. And construct a soft penalty term for asymmetric factor time-domain phase coordination. ; S306: Synthetic Normalized Notch Range Soft penalty item with time domain coordination The RVS hard constraint function is obtained as follows: ， in, and These are the weighting coefficients. This is the constraint threshold.

7. The method according to claim 6, characterized in that, The ideal vibration condition for the fundamental frequency of the S-curve in S303 is: ， Where n is the frequency alignment order, and the ideal vibration conditions are substituted into step S304. In step S304, the nearest integer multiple n corresponding to the current solution is calculated: ， Define target alignment frequency The normalized notch distance is expressed as: ； In step S305, the ideal reference value is: ； Soft penalty items The formula is: 。 8. The method according to claim 6, characterized in that, The method for constructing the multi-objective optimization model in step S3 includes: Decision variables are ,in It is the planned maximum speed value. It is the planned maximum acceleration value, It is the maximum urgency value in the plan; Motion efficiency goals To minimize the total motion time : ， in, Indicates the decision variables The determined first Duration of segment These correspond to the seven time periods of the seven-segment asymmetric S-shaped trajectory; Motion stability target use Minimize the norm to the peak of maximum jerkiness: ， in, Indicates the principal axis trajectory at time [time]. The degree of urgency; The maximum abrupt change during the main shaft acceleration phase; Indicates according to asymmetric factors The calculated maximum abruptness of the deceleration phase; Peak driving force and suppression target The optimization objective is to minimize the sum of the maximum peak values ​​of the three-axis driving forces. ， in, Indicated in decision variables The corresponding trajectory under the first axis at time The instantaneous driving force; The multi-objective optimization model is described as follows: 。

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