Rigid-flexible composite flight positioning platform motion planning method based on input shaping theory and S-shaped curve

Abstract

The invention relates to the technical field of high-precision motion control, in particular to a rigid-flexible composite flight positioning platform motion planning method based on an input shaping theory and an S-shaped curve. According to the technical scheme, the method comprises the following steps that parameterization is conducted on an S-shaped curve, and multi-stage motion parameters including the inherent frequency f of the flexible platform are defined; setting a residual vibration minimization condition; establishing an optimization model; solving an optimal time parameter by adopting an intelligent optimization algorithm; and calculating displacement contributed by the initial speed and the acceleration according to the optimal time parameter, solving the maximum acceleration, and generating an optimal motion planning curve. Through phase offset and time symmetry design, the vibration energy at the inherent frequency is remarkably reduced, the maximum acceleration required by platform movement is calculated within extremely short time, then the optimal movement curve of the platform is obtained, the platform can make a quick decision within several milliseconds, meanwhile, the displacement error can be smaller than 10 micrometers, and the stability of the platform is improved. The method is suitable for high-precision manufacturing, optical alignment and other harsh scenes.

Description

Technical Field

[0001] The present invention relates to the technical field of high-precision motion control, and in particular to a motion planning method for a rigid-flexible composite flight positioning platform based on input shaping theory and S-shaped curves. Background Art

[0002] In the field of high-speed, high-precision motion control, the rigid-flexible composite flight positioning platform combines the stability of the rigid structure with the flexibility of the flexible structure, and can achieve high-efficiency, high-precision positioning under high-frequency conditions.

[0003] Most existing rigid-flexible hybrid motion platforms perform positioning motion at a constant speed and with equal spacing. However, in actual engineering applications, manufacturing deviations can occur between operating points, resulting in unequal distances between workpiece operating points. This patent addresses the problem of how to quickly adjust the platform's speed in these unequal spacing conditions without generating additional vibrations.

[0004] At present, the Chinese invention patent application (application publication number CN118280431A, publication date July 2, 2024) discloses a rigid-flexible composite flight positioning platform and its implementation method. The main problem with this patent document is that it does not provide a practical operation method for quickly adjusting the speed of the platform under unequal spacing conditions, nor does it consider the impact of speed adjustment on the flexible platform.

[0005] Furthermore, a Chinese invention patent application (publication number CN106054605A, published on October 16, 2016) discloses a highly precise positioning motion planning algorithm based on damping attenuation. By considering the damping attenuation effect and the system dynamics, a motion planning curve that better meets actual working conditions is obtained, which is a non-online motion planning algorithm. The main problem with the above patent document is its high computational complexity and inability to achieve rapid decision-making within a few milliseconds. Therefore, there is an urgent need for a computationally efficient motion planning algorithm that can achieve rapid speed regulation and effectively suppress vibration in unequal spacing scenarios. Summary of the Invention

[0006] In order to solve the shortcomings and deficiencies in the above-mentioned prior art, the present invention proposes a motion planning algorithm that combines input shaping theory and S-shaped curve motion planning, which can solve the problems of rapid speed regulation and vibration suppression during unequal spacing positioning in the prior art, and realize high-precision, low-vibration rapid positioning control, and is suitable for high-precision motion control scenarios.

[0007] The technical solution of the present invention is a motion planning method for a rigid-flexible composite flying positioning platform based on input shaping theory and S-shaped curves, comprising the following steps:

[0008] S1. Parameterize the S-shaped curve and define multi-stage motion parameters including the natural frequency f of the flexible platform;

[0009] S2. Set the residual vibration minimization conditions, including:

[0010] Phase cancellation, the Fourier transform of the acceleration signal has zero amplitude at the natural frequency f of the flexible platform:

[0011] Time symmetry, the time of each stage satisfies: t i =n i T, where n i is an integer;

[0012] S3. Establish an optimization model with the goal of minimizing the amplitude of the acceleration spectrum at the natural frequency f of the flexible platform. Constraints include total time, displacement, velocity continuity, and upper limits of acceleration and jerk.

[0013] S4, using intelligent optimization algorithm to solve the optimal time parameters;

[0014] S5. Calculate the initial velocity and the displacement contributed by acceleration according to the optimal time parameters, and solve the maximum acceleration a max , generate the optimal motion planning curve.

[0015] Optionally, in S1, the multi-stage motion parameters defined also include initial velocity v0, maximum acceleration a max , maximum jerk J max , total displacement Q, total platform speed regulation time t total , and the time of each stage t1, t2, t3, t4, t5, where t1 is the acceleration increase period, t2 is the acceleration constant period, t3 is the acceleration decrease period, t4 is the jerk decrease period, and t5 is the jerk increase period.

[0016] Optionally, in S4, the intelligent optimization algorithm is used to solve the optimal time parameters to allocate the time t1, t2, t3, t4, and t5 to each stage.

[0017] Optionally, in S1, the calculation formula of the natural frequency f of the flexible platform is: Where k is the system stiffness and m is the moving mass.

[0018] Optionally, in S2, the Fourier transform of the acceleration signal is: Where j is the imaginary unit, t total Expressed as the total movement time, t total =t1+t2+t3+t4+t5;

[0019] The amplitude of the acceleration spectrum is the modulus of the Fourier transform, that is,

[0020] Optionally, in S2, the time symmetry constraint is achieved by adjusting t1=t3 and t4=t5, where t2 is the maximum allowed time of the constant acceleration segment.

[0021] Optionally, in S3, the optimization model is expressed as:

[0022]

[0023] Among them, s(t) is the displacement function; v(τ) is the velocity function; v(t end ) is the end time of the movement; dτ is the time element; a(τ) is the acceleration function that changes with time; J(t) is the rate of change of acceleration.

[0024] Optionally, in S4, the intelligent optimization algorithm adopts a particle swarm optimization algorithm, a gradient descent method or a genetic algorithm.

[0025] Optionally, in S5, if the target displacement is known to be S, then the displacement contributed by the initial velocity is: S initial =v0·t total ; Displacement contributed by acceleration: S acceleration =SS initial .

[0026] Optionally, the displacement S contributed by the acceleration acceleration With the maximum acceleration a max satisfy:

[0027] Compared with the prior art, this application has at least one of the following beneficial technical effects:

[0028] 1. The purpose of this invention is to significantly reduce the vibration energy at the natural frequency through phase cancellation and time symmetry design. The residual vibration amplitude can be reduced by more than 80%, so that the final optimized motion curve of the motion planning algorithm is more consistent with actual working conditions.

[0029] 2. After obtaining the optimal time parameters, the present invention uses fixed time parameters and adopts an offline method. That is, based on the displacement formula of acceleration contribution, the maximum acceleration required for platform movement can be calculated in a very short time, thereby obtaining the optimal motion curve of the platform;

[0030] 3. This invention enables the platform to make rapid decisions within milliseconds, while maintaining a displacement error of less than 10 microns, making it suitable for demanding scenarios such as high-precision manufacturing and optical alignment.

[0031] 4. A rigid-flexible composite platform that can flexibly adapt to different target displacements and natural frequencies, achieving stable control across working conditions through a fixed time parameter strategy. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 is a schematic diagram of acceleration spectrum amplitude corresponding to an embodiment of the present invention;

[0033] Figure 2 It is the algorithm flow chart of the present invention. DETAILED DESCRIPTION

[0034] The technical solution of the present invention is further described below with reference to the accompanying drawings and specific embodiments.

[0035] Example

[0036] See also Figure 1 The motion planning algorithm of this embodiment includes the following steps:

[0037] S1. Parameterize the S-shaped curve. Suppose the S-shaped curve contains 5, and the parameters are: initial velocity v0, maximum acceleration a max , maximum jerk J max , total displacement Q, natural frequency of flexible platform The time of each stage is t1, t2, t3, t4, t5, where the initial speed v0 = 125 mm / s and the maximum acceleration a max =2000m / s 2 , maximum jerk J max =90000m / s 3 , total displacement Q = 1.01 mm, natural frequency of the flexible platform f = 100 Hz, total platform speed regulation time t total Since the actual working time of the platform is 2ms, the total adjustable time is 8ms, that is, t total =8ms;

[0038] S2. Set the residual vibration minimization condition. Design the S-shaped curve so that its acceleration spectrum has the minimum energy at the natural frequency f of the flexible platform. The key constraints are:

[0039] (1) Phase cancellation: The Fourier transform of the acceleration excitation signal has a zero amplitude at f = 100 Hz:

[0040] (2) Time symmetry: Due to t total <Τ, so the following strategy is adopted to meet the time symmetry as much as possible. Specifically, t1 = t3 = 1ms, t4 = t5 = 2ms, t2 = 2ms;

[0041] S3. Establish an optimization model with the goal of minimizing the amplitude of the acceleration spectrum at the natural frequency f of the flexible platform. The constraints include total time, displacement, velocity continuity, and upper limits of acceleration and jerk, as follows:

[0042]

[0043] S4. The optimal time parameter distribution is obtained by using the optimization algorithm as follows: t1 = 0.000242 s, t2 = 0.000937 s, t3 = 0.000067 s, t4 = 0.006080 s, t5 = 0.000674 s (the time parameter is the time period of each movement);

[0044] S5. Calculate the total movement time t according to the optimal time parameters t1, t2...t5 obtained in step S4. total =t1+t2+t3+t4+t5=0.000242+0.000937+0.000067+0.006080+

[0045] 0.000674=0.008s;

[0046] S5. Assuming that the distance to the next operating point is 0.99 mm, that is, the target displacement S = 0.99 mm, the total movement time t obtained in step S5 is total , calculate the displacement contributed by the initial velocity and acceleration.

[0047] (1) Displacement contributed by initial velocity: S initial =v0·t total =125mm / s·0.008s=1.0mm;

[0048] (2) Displacement contributed by acceleration: S acceleration =SS initial =0.99-1.0=-0.01mm;

[0049] S6. Displacement S contributed by acceleration obtained in step S5 acceleration To solve the maximum acceleration a max . The displacement formula of acceleration contribution is:

[0050] Substitute the optimal time parameter distribution t1, t2...t5 obtained in step S4 to solve the maximum acceleration a max =443.4594mm / s 2 , and obtain the optimal motion planning curve.

[0051] The technical solution of this embodiment is further explained below:

[0052] like Figure 2 The curve shown is a schematic diagram of the acceleration spectrum amplitude. The Fourier transform of the acceleration signal is: The amplitude of the acceleration spectrum is the modulus of the Fourier transform, that is, Represents the vibration characteristics of the system. Figure 2 In the figure, the amplitude of the acceleration spectrum at 100 Hz is 3.468822, which is about 80% lower than that of the traditional method, indicating that the residual vibration is effectively suppressed. The displacement error is measured to be 8 microns, indicating that the vibration energy of the system at this frequency is low and the residual vibration is small, meeting the high-precision requirements.

[0053] The above specific embodiments are merely several optional embodiments of the present invention. Based on the technical solutions of the present invention and the relevant inspirations of the above embodiments, those skilled in the art may make various alternative improvements and combinations to the above specific embodiments.

Claims

1. A motion planning method for a rigid-flexible composite flying positioning platform based on input shaping theory and S-shaped curves, characterized by: The following steps are involved: S1. Parameterize the S-shaped curve and define multi-stage motion parameters including the natural frequency f of the flexible platform; S2. Set the residual vibration minimization conditions, including: Phase cancellation, the Fourier transform of the acceleration signal has zero amplitude at the natural frequency f of the flexible platform: Where a(t) is the acceleration function that changes with time; Time symmetry, the time of each stage satisfies: t i =n i T, where n i is an integer; S3. Establish an optimization model with the goal of minimizing the amplitude of the acceleration spectrum at the natural frequency f of the flexible platform. Constraints include total time, displacement, velocity continuity, and upper limits of acceleration and jerk. S4, using intelligent optimization algorithm to solve the optimal time parameters; S5. Calculate the initial velocity and the displacement contributed by acceleration according to the optimal time parameters, and solve the maximum acceleration a max , generate the optimal motion planning curve.

2. The motion planning method for a rigid-flexible composite flying positioning platform based on input shaping theory and S-shaped curve according to claim 1 is characterized in that: In S1, the multi-stage motion parameters are defined, including the initial velocity v0, the maximum acceleration a max , maximum jerk J max , total displacement Q, total platform speed regulation time t total , and the time of each stage t1, t2, t3, t4, t5, where t1 is the acceleration increase period, t2 is the acceleration constant period, t3 is the acceleration decrease period, t4 is the jerk decrease period, and t5 is the jerk increase period.

3. The motion planning method for a rigid-flexible composite flying positioning platform based on input shaping theory and S-shaped curve according to claim 2, characterized in that: In S4, the intelligent optimization algorithm is used to solve the optimal time parameters to allocate the time t1, t2, t3, t4, and t5 to each stage.

4. The motion planning method for a rigid-flexible composite flying positioning platform based on input shaping theory and S-shaped curve according to claim 1, characterized in that: In S1, the calculation formula of the flexible platform natural frequency f is: Where k is the system stiffness and m is the moving mass.

5. The motion planning method for a rigid-flexible composite flying positioning platform based on input shaping theory and S-shaped curve according to claim 2, characterized in that: In S2, the Fourier transform of the acceleration signal is: Where j is the imaginary unit, t total Expressed as the total movement time, t total =t1+t2+t3+t4+t5; The amplitude of the acceleration spectrum is the modulus of the Fourier transform, that is, 6. The motion planning method for a rigid-flexible composite flying positioning platform based on input shaping theory and S-shaped curve according to claim 5, characterized in that: In S2, the time symmetry constraint is achieved by adjusting t1 = t3 and t4 = t5, where t2 is the maximum allowed time of the constant acceleration segment.

7. The motion planning method for a rigid-flexible composite flying positioning platform based on input shaping theory and S-shaped curve according to claim 5, characterized in that: In S3, the optimization model is expressed as: Among them, s(t) is the displacement function; v(τ) is the velocity function; v(t end ) is the end time of the movement; dτ is the time element; a(τ) is the acceleration function that changes with time; J(t) is the rate of change of acceleration.

8. The motion planning method for a rigid-flexible composite flying positioning platform based on input shaping theory and S-shaped curve according to claim 6, characterized in that: In S4, the intelligent optimization algorithm adopts a particle swarm optimization algorithm, a gradient descent method or a genetic algorithm.

9. The motion planning method for a rigid-flexible composite flying positioning platform based on input shaping theory and S-shaped curve according to claim 7, characterized in that: In S5, the target displacement is known to be S, and the displacement contributed by the initial velocity is: S initial =v0·t total ; Displacement contributed by acceleration: S acceleration =SS initial .

10. The motion planning method for a rigid-flexible composite flying positioning platform based on input shaping theory and S-shaped curve according to claim 9, characterized in that: The acceleration contributes to the displacement S acceleration With the maximum acceleration a max satisfy:

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