A trajectory planning method, system, device and medium without a dynamics model

Abstract

The application discloses a kind of trajectory planning methods, systems, equipment and medium without kinetics model, method includes: the objective function of quadratic open-loop trajectory planning is constructed;According to spline curve, control input profile is constructed;According to the first sampling point of a plurality of first sampling points determined according to point sampling criterion;Obtain initial sampling point, construct kriging model according to the initial sampling point, and then construct system proxy model;Based on control input profile, the first sampling point is input into the system proxy model and the optimal trajectory planning strategy is determined according to the objective function.The trajectory planning result can be obtained based on the input and output of the embodiment of the application, without establishing kinetic model, the required data quantity is small, the realizability is strong, can realize quick learning and application deployment in engineering application, can be widely applied in trajectory planning technical field.

Description

Technical Field

[0001] This invention relates to the field of trajectory planning technology, and in particular to a trajectory planning method, system, device and medium without a dynamic model. Background Technology

[0002] Smart material-driven flexible deformable structures can significantly improve the performance of future industrial equipment and have great application potential in aerospace and robotics. Due to their inherent structural characteristics, flexible deformable structures are prone to transient and residual vibrations during deformation. If left uncontrolled, these vibrations can severely impair the structure's shape accuracy and performance. Therefore, feedback control methods are typically used to actively suppress vibrations after they occur or are subjected to external disturbances. However, feedback control cannot prevent vibrations from occurring in advance. In contrast, trajectory planning and optimization of control input signals can, to some extent, prevent vibration excitation. This method can avoid vibrations before they occur, thus maintaining a smooth and stable deformation process.

[0003] Flexible deformable structures are difficult to model accurately due to structural and material nonlinearities, making control methods relying on precise mathematical models unreliable in ensuring control accuracy. For piezoelectrically driven flexible deformable structures, current shape control methods typically depend on precise mathematical models. Furthermore, some stochastic algorithms for trajectory optimization without dynamic models, such as Genetic Algorithms (GA) and Particle Swarm Optimization (PSO), are computationally intensive and costly, requiring extensive sampling and cannot be directly implemented based on experimental data. With the development of artificial intelligence, reinforcement learning methods based on neural networks are gradually emerging as a new approach for trajectory planning without dynamic models. However, reinforcement learning requires a large amount of data samples for training, making rapid deployment in engineering applications difficult. Summary of the Invention

[0004] This invention aims to at least partially solve one of the technical problems in related technologies. To this end, this invention proposes a method, system, electronic device, and storage medium for trajectory planning without dynamics models, requiring a small amount of data.

[0005] On one hand, embodiments of the present invention provide a trajectory planning method without a dynamic model, including:

[0006] Construct the objective function for quadratic open-loop trajectory programming;

[0007] Construct the control input contour based on the spline curve;

[0008] Several first sampling points are determined based on the sampling criteria.

[0009] Obtain initial sampling points, construct a kriging model based on the initial sampling points, and then construct a system proxy model;

[0010] Based on the control input profile, the first sampling point is input into the system proxy model, and the optimal trajectory planning strategy is determined according to the objective function.

[0011] Optionally, the expression for the objective function of the quadratic open-loop trajectory is:

[0012]

[0013] Where J represents the objective function of the quadratic open-loop trajectory; t0 represents the initial moment when the motion begins; t f This indicates the moment when the deformation motion control signal loading process ends and the steady-state control signal loading process begins; t r It is selected at t for calculating the residual response of the system. f Subsequent time points; The velocity at the system state measurement point is represented; Q1 and Q2 are both constants, representing positive weighting coefficients; the first term... For the voltage loading process [t0 t] f Transient vibrational energy within a time period; second term For voltage over time interval [t] f ,t f +t r The residual vibration energy after the target value is reached.

[0014] Optionally, constructing the control input contour based on the spline curve includes:

[0015] Determine the spline curve;

[0016] Based on the spline curve, the motion time is divided into several time segments with equal time intervals;

[0017] Determine the actuator voltage distribution and the voltage at the control point;

[0018] Construct an input trajectory polynomial, calculate the coefficients of the input trajectory polynomial according to the first expression, and then determine the control input profile.

[0019] Optionally, in the step of constructing the input trajectory polynomial, calculating the coefficients of the input trajectory polynomial according to the first expression, and then determining the input trajectory, the first expression is:

[0020]

[0021] Among them, u n (t f ) represents t f Voltage value at time; U n This indicates the voltage value for the preset steady-state control phase; Indicates tf The rate of change of voltage at any given moment;

[0022] The expression for the control input contour is:

[0023] u(t)=f(U)=f(U1…U n )

[0024] Where u(t) represents the control input contour; f(U) and f(U1…U n All represent the voltage input profile constructed based on each control point; U represents a control point; U1 represents the first control point; U n This represents the nth control point.

[0025] Optionally, the determination of several first sampling points according to the point addition criteria includes one of the following:

[0026] Several first sampling points were determined based on the EI addition criteria;

[0027] Alternatively, determine several first sampling points based on the MSP addition criteria;

[0028] Alternatively, determine several first sampling points based on the MSE addition criteria;

[0029] Alternatively, several first sampling points can be determined based on the PI addition criterion.

[0030] Optionally, the step of obtaining initial sampling points, constructing a kriging model based on the initial sampling points, and then constructing a system agent model includes:

[0031] The initial sampling points were determined using the Latin hypercube sampling method;

[0032] Construct an initial kriging model based on the initial sampling points;

[0033] The initial kriging model is used to construct a proxy between the control input profile and the objective function, thus obtaining the system proxy model.

[0034] Optionally, the step of inputting the first sampling point into the system proxy model based on the control input contour and determining the trajectory planning strategy according to the objective function includes:

[0035] The system agent model is run based on the control input profile;

[0036] The first sampling point is input into the system proxy model to calculate the value of the objective function;

[0037] Repeat the step of inputting the first sampling point into the system proxy model to calculate the value of the objective function until the minimum value of the objective function remains unchanged or the number of iterations reaches a preset iteration threshold to obtain the trajectory planning strategy.

[0038] On the other hand, embodiments of the present invention also provide a trajectory planning system without a dynamic model, comprising:

[0039] The first module is used to construct the objective function for quadratic open-loop trajectory planning;

[0040] The second module is used to construct the control input contour based on the spline curve;

[0041] The third module is used to determine several first sampling points according to the sampling criteria.

[0042] The fourth module is used to obtain initial sampling points, construct a kriging model based on the initial sampling points, and then construct a system agent model.

[0043] The fifth module is used to input the first sampling point into the system proxy model based on the control input contour and determine the optimal trajectory planning strategy according to the objective function.

[0044] On the other hand, embodiments of the present invention also provide an electronic device, including: a processor and a memory; the memory is used to store a program; the processor executes the program to implement the method described above.

[0045] On the other hand, embodiments of the present invention also provide a computer storage medium storing a processor-executable program, which, when executed by a processor, is used to implement the method described above.

[0046] The embodiments of the present invention have the following beneficial effects: the embodiments of the present invention can calculate the trajectory planning result based on the input and output, without the need to establish a dynamic model, requiring a small amount of data, and are highly feasible, enabling rapid learning and application deployment in engineering applications. Attached Figure Description

[0047] The accompanying drawings are provided to further understand the technical solutions of the present invention and constitute a part of the specification. They are used together with the embodiments of the present invention to explain the technical solutions of the present invention, and do not constitute a limitation on the technical solutions of the present invention.

[0048] Figure 1 This is a flowchart illustrating the steps of the trajectory planning method without dynamics provided in this embodiment of the invention.

[0049] Figure 2 This is a schematic diagram of a cubic spline curve describing voltage distribution provided in an embodiment of the present invention;

[0050] Figure 3 This is a schematic diagram of a non-dynamic model trajectory planning framework based on input and output data provided in an embodiment of the present invention;

[0051] Figure 4 This is a structural diagram of a cantilever plate driven by a piezoelectric fiber composite material MFC actuator provided in an embodiment of the present invention;

[0052] Figure 5 This is a schematic diagram of the design domain of candidate control points provided in an embodiment of the present invention;

[0053] Figure 6 This is an optimization flowchart based on online experimental data provided in an embodiment of the present invention;

[0054] Figure 7 This is a graph showing the evolution of the objective function based on online experimental data, provided in an embodiment of the present invention.

[0055] Figure 8 This is a graph showing the evolution of the optimal value distribution provided in an embodiment of the present invention;

[0056] Figure 9 This is a voltage-time relationship diagram under optimal input and ramp voltage input provided by an embodiment of the present invention;

[0057] Figure 10 This is a graph showing the relationship between deflection and time under optimal input and ramp voltage input provided in an embodiment of the present invention;

[0058] Figure 11 This is a graph showing the speed-time relationship under optimal input and ramp voltage input provided in an embodiment of the present invention;

[0059] Figure 12 This is a schematic diagram of the structure of a trajectory planning system without a dynamic model provided in an embodiment of the present invention;

[0060] Figure 13 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0061] 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.

[0062] It should be noted that although functional modules are divided in the system diagram and the logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the system or the order in the flowchart. The terms "first / S100," "second / S200," etc., in the specification, claims, and the aforementioned figures are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0063] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0064] To address the issues of transient and residual vibrations during the deformation process of deformable structures, this invention proposes a dynamic model-free trajectory planning method and, based on the Kriging surrogate model and spline curves, presents a high-precision dynamic shape control and vibration minimization dynamic model-free fast trajectory planning framework. The trajectory planning problem is transformed into an optimization problem of minimizing vibration during deformation within a specified time. A spline curve with several control points (i.e., design variables) is used to define the actuator's voltage distribution, and a surrogate model-based optimization method based on the Kriging model and the EI filling sampling criterion is constructed. This method can find the global optimum using only input and output data obtained from simulation or experiments.

[0065] Reference Figure 1 and Figure 2 The method includes the following steps:

[0066] S100, Construct the objective function for quadratic open-loop trajectory programming.

[0067] Specifically, the expression for the quadratic open-loop trajectory planning objective function constructed in this embodiment of the invention can be:

[0068]

[0069] Where t0 represents the initial time at which the motion begins, t f t represents the moment when the deformation motion control signal loading process ends and the steady-state control signal loading process begins. r The time t was chosen to facilitate consideration of the system's residual response. f A specific point in time thereafter. The velocity at the system state measurement point is represented by Q1 and Q2, which are constants representing positive weighting coefficients. The first term represents the voltage loading process [t0 t].f The transient vibrational energy within a time interval [t], the second term is the voltage over the time interval [t]. f ,t f +t r The residual vibration energy after the target value is reached.

[0070] As can be seen from equation (1), the embodiments of the present invention consider transient vibration and residual vibration while performing trajectory planning.

[0071] In other embodiments, the expression for the quadratic open-loop trajectory planning objective function can also be represented modally as follows:

[0072]

[0073] in, The system velocity matrix is ​​based on modal representation. Q1 and Q2 are constants, representing the positive weighting coefficient matrix. The remaining parameters have the same meaning as in formula (2). Model-based objective functions are easy to implement in numerical studies, while directly measurable physical quantities are more feasible in both numerical and experimental studies. In addition, control costs can also be added to the objective function, i.e. Where u represents the control voltage and R is the correlation coefficient.

[0074] S200: Construct the control input contour based on the spline curve.

[0075] This invention embodiment performs feedforward trajectory planning by constructing a control input contour to find the time interval [t0, t... f The optimal control input u(t) is within the range 0 ≤ t ≤ t. f This minimizes the objective function to obtain the final trajectory planning result.

[0076] S210. Determine the spline curve.

[0077] To efficiently implement the trajectory planning method without dynamics, this embodiment of the invention uses cubic spline curves to construct the control input contour. Based on the cubic spline curves, the motion time [t0 t] is obtained. f The actuator is divided into several parts, each with the same time interval Δt. The voltage distribution u(t) of the actuator can be defined by a cubic polynomial, with its control point time t... i The corresponding voltage is U i For specific examples, please refer to Figure 2 As shown.

[0078] In other embodiments, other spline curves may be used for processing, such as quintic spline curves, B-spline curves, or other spline curves.

[0079] S220. Based on the spline curve, the motion time is divided into several time segments with the same time interval.

[0080] S230. Determine the actuator voltage distribution and the voltage at the control point.

[0081] In [t] i t i+1 The formula for calculating the control input within [ ] can be:

[0082] u(t) = a0 + a1t + a2t 2 +a3t 3 (3)

[0083] S240. Construct an input trajectory polynomial, calculate the coefficients of the input trajectory polynomial according to the first expression, and then determine the control input profile.

[0084] The coefficients of the polynomial are determined by considering the continuity of the first and second derivatives of the voltage distribution u(t) and the following first expression (final condition):

[0085]

[0086] Among them, u n (t f ) represents t f Voltage value at time; U n This indicates the voltage value for the preset steady-state control phase; Indicates t f The rate of change of voltage at any given moment.

[0087] Based on this, the continuously input contour u(t) can be represented by several control points U = [U1 … U2]. n ] is represented as:

[0088] u(t)=f(U)=f(U1 … U n (5)

[0089] Where u(t) represents the control input contour; f(U) and f(U1 … U n All represent the voltage input profile constructed based on each control point; U represents a control point; U1 represents the first control point; U n This represents the nth control point.

[0090] Specifically, step S300 may include one of the following steps S310 to S340.

[0091] S310. Determine several first sampling points according to the EI addition criteria.

[0092] The EI addition criterion, also known as the efficient global optimization (EGO) method, refers to the improvement expectation criterion. It obtains new sample points by solving a sub-optimization problem that maximizes the EI value.

[0093] S320, or, determine several first sampling points according to the MSP point addition criterion.

[0094] The MSP (Minimize Proxy Model Prediction) criterion, also known as the Minimize Proxy Model Prediction Criterion, works by directly finding the minimum value of the objective function on the Proxy Model.

[0095] S330, or, determine several first sampling points according to the MSE point addition criteria.

[0096] The MSE (Mean Squared Error) criterion, also known as the mean squared error criterion, is a criterion that directly uses the mean squared error estimate provided by the Kriging model to improve the global accuracy of the surrogate model. In other words, it uses a sub-optimization algorithm to solve the sub-optimization problem.

[0097] S340, or, determine several first sampling points according to the PI addition criterion.

[0098] The PI plus point criterion refers to the probability of improvement criterion method, which is a derivative of the EI method. Similar to the EI criterion, this criterion calculates the probability of improvement of the objective function and takes the point with the maximum improvement probability as the new sample point.

[0099] S400. Obtain initial sampling points, construct a kriging model based on the initial sampling points, and then construct a system agent model.

[0100] This invention employs the Kriging model to establish a proxy between the design variable U and the objective function J. The expression for this proxy model is:

[0101]

[0102] in, f(U) is an approximation of the objective function J. T The trend of the model can be represented by a function of any linear or nonlinear design variables; β is a vector of unknown coefficients; f(U) T β forms the regression term; z(U) is the random error. This embodiment of the invention uses a Gaussian distribution with a mean of zero.

[0103] The formula for calculating the covariance between two sampling points is:

[0104]

[0105] In equation (7), Represents variance; R(U) a U bThe correlation function defined for the anisotropic Gaussian model is expressed as follows:

[0106]

[0107] In equation (8), N is the number of design variables. [θ1 θ2 … θ N ] is the n-dimensional parameter vector that needs to be solved.

[0108] For a series of sampling points, the correlation matrix R can be expressed as:

[0109]

[0110] In equation (9), N s This represents the number of sampling points.

[0111] Using the generalized least squares method, we can obtain β in equation (6) and β in equation (7). β and The calculation formulas are as follows:

[0112] β=(X T R -1 X) -1 (X T R -1 Y) (10)

[0113]

[0114] in:

[0115] For any design variable U within the feasible region, the corresponding voltage distribution u(t) can be uniquely determined. Then, the deformation response w can be directly obtained through numerical simulation or experimental testing. p The time history of (t) is obtained. Therefore, the objective function value J is calculated according to equation (1). It should be emphasized that these steps are a forward process, without complex backward problems. Now, the key to establishing the Kriging model is to solve for the parameter vector [θ1 θ2 … θ n This is crucial for determining the correlation between sampling points. Here, the likelihood function of equation (12) is used to obtain the most suitable θ. i value:

[0116]

[0117] Where |R| is the determinant of the correlation matrix.

[0118] For a new sampling point U # The Kriging model can not only provide predicted response values The mean square error of the predicted points can also be given:

[0119]

[0120] Where μ = X T R -1 rf(U # ); This represents the correlation vector between the predicted point and the sampled point.

[0121] Based on the established Kriging model, it is easy to find the minimum of the response surface, i.e., an approximation of the objective function. However, this direct method heavily relies on the distribution of sampling points, which may prevent finding the true minimum solution. Therefore, a specific strategy should be implemented to add some carefully selected sampling points to improve the accuracy of the Kriging model. The EI filling sampling criterion is used to determine the addition points by maximizing the expected value of the improved function. Its main idea is to find the special sampling point U with the highest probability of the expected value or producing a better solution. ## :

[0122]

[0123] in, This represents the minimum value of the current Kriging model. Since the surrogate model based on Kriging is explicit, its minimum value can be easily found using traditional algorithms.

[0124] Based on this, step S400 includes the following steps S410 to S430.

[0125] S410. The initial sampling points are determined using the Latin hypercube sampling method.

[0126] Latin hypercube sampling is a commonly used experimental design and initial sample selection method that aims to achieve maximum uniform coverage of the design domain with as few sample points as possible.

[0127] S420. Construct an initial kriging model based on the initial sampling points.

[0128] S430. Using the initial kriging model, construct a proxy between the control input profile and the objective function to obtain the system proxy model.

[0129] S500: Based on the control input profile, input the first sampling point into the system proxy model and determine the optimal trajectory planning strategy according to the objective function.

[0130] S510. Run the system agent model based on the control input profile.

[0131] S520. Input the first sampling point into the system proxy model to calculate the value of the objective function.

[0132] A series of new sampling points are determined based on the EI filling sampling criterion, which gradually approach the true optimal solution.

[0133] S530. Repeat the step of inputting the first sampling point into the system proxy model to calculate the value of the objective function until the minimum value of the objective function remains unchanged or the number of iterations reaches a preset iteration threshold, to obtain the trajectory planning strategy.

[0134] When the maximum number of iterations or the minimum objective function remains constant within a predefined continuous time, optimization will stop, and the optimal trajectory planning strategy will be obtained. The trajectory input scheme includes the control input profile and the running trajectory.

[0135] In summary, the flowchart of the trajectory planning method based on spline curves, Kriging models, and EI filling sampling criteria in this invention can be referred to... Figure 2 .from Figure 2 As can be seen from this, the method of this embodiment of the invention is a non-dynamic model method based on input and output data, which can be generated through theoretical models or experimental tests.

[0136] On the other hand, such as Figure 12 As shown, this embodiment of the invention provides a trajectory planning system without a dynamic model, comprising:

[0137] The first module is used to construct the objective function for quadratic open-loop trajectory planning;

[0138] The second module is used to construct the control input contour based on the spline curve;

[0139] The third module is used to determine several first sampling points according to the sampling criteria.

[0140] The fourth module is used to obtain initial sampling points, construct a kriging model based on the initial sampling points, and then construct a system agent model.

[0141] The fifth module is used to input the first sampling point into the system proxy model based on the control input contour and determine the optimal trajectory planning strategy according to the objective function.

[0142] On the other hand, such as Figure 13 As shown, this embodiment of the invention also provides an electronic device, including: a processor and a memory; the memory is used to store a program; the processor executes the program to implement the method described above.

[0143] On the other hand, embodiments of the present invention also provide a computer storage medium storing a processor-executable program, which, when executed by a processor, is used to implement the method described above.

[0144] The embodiments of the present invention have the following beneficial effects: The embodiments of the present invention provide a fast trajectory planning method for a non-dynamic model that can be implemented based on input and output data. It requires a small amount of data, is highly feasible, and can achieve rapid learning and application deployment in engineering applications.

[0145] The technical effects of the embodiments of the present invention will be further described below in conjunction with specific application scenarios:

[0146] 1. Scene Description:

[0147] A flexible cantilever plate structure driven by a piezoelectric fiber composite material (MFC, Macro Fiber Composites, a type of piezoelectric fiber composite actuator that can bend and deform under external voltage excitation) actuator, the M8528P1 type MFC actuator is bonded to the root region of the cantilever plate, including rectangular cross-section piezoelectric ceramic fibers embedded in an epoxy resin matrix and cross electrodes, the matrix structure is a 500mm*35mm*1mm cantilever aluminum plate structure.

[0148] Reference Figure 4 Driven by the MFC actuator, the structure will undergo bending deformation. The control objective of this embodiment is to design the input voltage so that the measurement point of the substrate structure moves to a specified position within a specified time (exemplarily, this embodiment sets the target to the measurement point moving 5mm), and ensures that the movement trajectory of the measurement point is continuous and smooth, avoiding transient vibration and residual vibration during the movement process.

[0149] For the sake of simplicity, the embodiments specifically consider the dynamic shape control problem aimed at minimizing residual vibration. Therefore, the parameter configuration of the embodiments is u. f =500V,t f =1s,t r =1s, Q1=0, Q2=1. To reduce the amount of computation, t f The voltage after a given time step is set to a stable value, and can be easily estimated using pre-static shape control. To construct the spline voltage curve, the time interval is set to Δt = 0.25 s, meaning only n = 4 control points need to be designed. Using n... s =Construct the initial Kriging model with 80 initial sampling points. Set the maximum number of sampling times for the EI point addition criterion to be [value missing]. When the defined maximum number of iterations is reached or continuous Optimization will stop when the minimum value of the secondary objective function remains unchanged. To accelerate convergence and avoid invalid design domains, the design domain of the candidate control points is given based on a ramp voltage of ±100V, such as... Figure 5 As shown.

[0150] 2. Implementation process and results:

[0151] This embodiment uses a non-dynamic model based on real-time input and output data to optimize the data flow, such as... Figure 6 As shown, SBO trajectory planning is implemented in MATLAB to generate the voltage loading history, i.e., the input data. LabVIEW (graphical programming environment) is used to output the generated voltage signal to drive the MFC actuator. This control signal is converted into analog voltage form by the input / output board and then amplified by a high-voltage amplifier. The amplified voltage is applied to the MFC actuator, driving the flexible cantilever plate to produce elastic deformation. The displacement and velocity response of the measuring point are measured in real time by a laser displacement sensor and transmitted back to the control program in the computer for new iterations until optimization is completed.

[0152] First, sampling points were collected from online experiments to construct an initial Kriging model. Then, the Kriging model was iteratively updated based on the added sampling points according to the EI filling sampling criterion. To ensure the independence of the two experiments and avoid the influence of the previous experiment, the time interval between the two experiments was set to 1.5 minutes. (Refer to...) Figure 7 and Figure 8 As can be seen, after adding sampling points, the objective function tends to decrease significantly, and the optimal control trajectory can be obtained within 150 iterations.

[0153] Figure 9 , Figure 10 and Figure 11 The measured dynamic response based on ramp voltage and optimal voltage trajectory is displayed. Comparing the displacement responses of the structural measurement points obtained with ramp voltage and optimal voltage, it can be seen that the optimized control trajectory achieves a smoother dynamic trajectory control effect. The residual vibration energy of the structure decreased from 6.8834e-6 to 8.6679e-8, which is approximately two orders of magnitude lower than the ramp voltage response result. The examples based on online experimental data demonstrate that the dynamic model-free trajectory planning method proposed in this invention can quickly achieve continuous, smooth, and vibration-free motion effects.

[0154] In some alternative embodiments, the functions / operations mentioned in the block diagrams may not occur in the order shown in the operation diagrams. For example, depending on the functions / operations involved, two consecutively shown blocks may actually be executed substantially simultaneously, or the blocks may sometimes be executed in reverse order. Furthermore, the embodiments presented and described in the flowcharts of this invention are provided by way of example to provide a more comprehensive understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is altered and sub-operations described as part of a larger operation are executed independently.

[0155] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, essentially, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0156] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0157] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0158] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0159] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

[0160] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of the present invention.

Claims

1. A trajectory planning method without a dynamic model, characterized in that, include: Construct the objective function for quadratic open-loop trajectory programming; Construct the control input contour based on the spline curve; Several first sampling points are determined based on the sampling criteria. Obtain initial sampling points, construct a kriging model based on the initial sampling points, and then construct a system proxy model; Based on the control input profile, the first sampling point is input into the system proxy model and the optimal trajectory planning strategy is determined according to the objective function; The objective function of the quadratic open-loop trajectory planning is expressed as follows: Where J represents the objective function of quadratic open-loop trajectory planning; Indicates the initial moment when the motion begins; This indicates the moment when the deformation motion control signal loading process ends and the steady-state control signal loading process begins; It was selected for calculating the residual response of the system. Subsequent time points; Indicates the velocity at the system state measurement point; , All are constants, representing positive weighting coefficients; the first term For voltage loading process Transient vibrational energy within a time period; second term For voltage at time intervals The residual vibration energy after the target value is reached; The process of obtaining initial sampling points, constructing a kriging model based on the initial sampling points, and then constructing a system agent model includes: The initial sampling points were determined using the Latin hypercube sampling method; Construct an initial kriging model based on the initial sampling points; The initial kriging model is used to construct a proxy between the control input profile and the objective function to obtain a system proxy model. The step of inputting the first sampling point into the system proxy model based on the control input contour and determining the trajectory planning strategy according to the objective function includes: The system agent model is run based on the control input profile; The first sampling point is input into the system proxy model to calculate the value of the objective function; Repeat the step of inputting the first sampling point into the system proxy model to calculate the value of the objective function until the minimum value of the objective function remains unchanged or the number of iterations reaches a preset iteration threshold to obtain the trajectory planning strategy.

2. The trajectory planning method without a dynamic model according to claim 1, characterized in that, The construction of the control input contour based on the spline curve includes: Determine the spline curve; Based on the spline curve, the motion time is divided into several time segments with equal time intervals; Determine the actuator voltage distribution and the voltage at the control point; Construct an input trajectory polynomial, calculate the coefficients of the input trajectory polynomial according to the first expression, and then determine the control input profile.

3. The trajectory planning method without a dynamic model according to claim 2, characterized in that, In the step of constructing the input trajectory polynomial, calculating the coefficients of the input trajectory polynomial based on the first expression, and then determining the input trajectory, the first expression is: in, express The voltage value at that moment; This indicates the voltage value for the preset steady-state control phase; express The rate of change of voltage at any given moment; The expression for the control input contour is: in, Indicates the control input contour; and All represent the voltage input profile constructed based on each control point; U represents the control point; Indicates the first control point; This represents the nth control point.

4. The trajectory planning method without a dynamic model according to claim 1, characterized in that, The determination of several first sampling points according to the sampling criteria includes one of the following: Several first sampling points were determined based on the EI addition criteria; Alternatively, determine several first sampling points based on the MSP addition criteria; Alternatively, determine several first sampling points based on the MSE addition criteria; Alternatively, several first sampling points can be determined based on the PI addition criterion.

5. A system for implementing the trajectory planning method without a dynamic model as described in any one of claims 1-4, characterized in that, include: The first module is used to construct the objective function for quadratic open-loop trajectory planning; The second module is used to construct the control input contour based on the spline curve; The third module is used to determine several first sampling points according to the sampling criteria. The fourth module is used to obtain initial sampling points, construct a kriging model based on the initial sampling points, and then construct a system agent model. The fifth module is used to input the first sampling point into the system proxy model based on the control input contour and determine the optimal trajectory planning strategy according to the objective function.

6. An electronic device, characterized in that, Including the processor and memory; The memory is used to store programs; The processor executes the program to implement the method as described in any one of claims 1 to 4.

7. A computer storage medium storing a processor-executable program, characterized in that, The processor-executable program, when executed by the processor, is used to implement the method as described in any one of claims 1 to 4.

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