Full-band error suppression trajectory planning method

Abstract

The invention belongs to the field of ultra-precision optical processing, and particularly relates to a full-band error suppression trajectory planning method, which comprises the following steps of: measuring surface shape data of an optical element, preprocessing and performing surface shape expansion to obtain expanded surface shape data; according to the expanded surface shape condition, a corresponding polishing tool is selected, and a corresponding removal function is determined; residence points are determined according to the machining area, a starting point is selected from the residence points, multi-direction random path planning is implemented, and then the position of a random path point is obtained; the residence time of the residence point is calculated; acquiring the speed and the acceleration of each waypoint according to the random waypoint position and the residence time; and the planned position, speed and acceleration of each path point are sent to a robot controller, and servo control is completed. According to the trajectory planning method provided by the invention, a smoother processing trajectory can be planned according to the residence time of each residence point on the basis of a pseudo-random path, and full-band errors can be quickly and effectively suppressed.

Description

Technical Field

[0001] The present invention belongs to the field of ultra-precision optical processing, and in particular relates to a full-band error suppression trajectory planning method. Background Art

[0002] Computer-aided optical surface shaping (CAO) has become a key technology in optical processing, particularly aspheric processing. It establishes mathematical models to describe the material removal process and achieves quantitative material removal by controlling the grinding head. However, because the grinding head size is often much smaller than the optical component, optical components processed using a regular path inevitably introduce moiré errors at mid- and high-frequency levels. Importantly, these mid- and high-frequency errors, once introduced, are difficult to remove. Therefore, effectively suppressing these errors has become a key research topic in optical processing technology using small grinding heads.

[0003] In recent years, many researchers have optimized machining paths to suppress the moire effect, or mid- and high-frequency errors in surface shape. Dai Yifan and others from the National University of Defense Technology, based on the principle of entropy increase, added random perturbations perpendicular to the path, suppressing mid- and high-frequency errors to a certain extent. Wan Kuiping and others from the Shanghai Institute of Optics and Fine Mechanics proposed a sparse double-step grating path, which effectively reduces moire errors by suppressing the first two-order peaks. Dunn and Walker from ZEEKO proposed a pseudo-random path, which can be applied to areas with arbitrary boundary shapes. Experiments have shown that pseudo-random paths have better mid- and high-frequency suppression than regular paths. Wang Chunjin and others from Xiamen University proposed a novel maze path planning method that can achieve uniform polishing of localized materials. Negi and others from the Indian Council of Scientific and Industrial Research introduced angular randomness to the Hilbert fractal path, combined with the machining boundary to achieve path planning for arbitrary boundary shapes, and experimentally verified the effectiveness of their method. In order to avoid the negative impact of discontinuous path corner speed on equipment and processing, Beaucamp et al. from Kyoto University in Japan proposed a circular random path planning method; Wang Chong et al. from Southwest Jiaotong University proposed a pseudo-random tree path generation method based on the growth law of tree branches in nature, and verified the effectiveness of this method through experiments.

[0004] However, the planned path cannot be directly applied to processing. The processing trajectory should be reasonably planned based on the dwell time of each dwell point and the limitations of the hardware processing equipment. Using the position mode (the grinding head moves between the dwell points at the fastest speed) is a simple way to meet the dwell time, but the processing accuracy will be reduced due to the insufficient smoothness of the speed. Zhou Lin and others from the National University of Defense Technology used the constant acceleration method for trajectory planning (trapezoidal planning), and experimentally proved that the speed processing mode has a faster convergence speed and a larger convergence ratio than the position mode processing, but due to the discontinuous speed, instability will also occur. Wang Tianyi and others from the Brooklyn Haven National Laboratory in the United States used the constant acceleration method for trajectory planning (cubic polynomial planning) and proposed a position-speed-time planning algorithm to better meet the dwell time of the dwell point, but the discontinuous acceleration of the trajectory may excite the vibration mode of the hardware and thus affect the tracking error of the hardware. Summary of the Invention

[0005] The purpose of the present invention is to provide a full-band error suppression trajectory planning method. Through the trajectory planning method, the full-band surface error of the optical element is effectively converged, the processing accuracy and efficiency are improved, and the shortcomings of the trajectory generated by the above-mentioned existing trajectory planning method that is not smooth enough are overcome.

[0006] The technical solution adopted by the present invention to achieve the above-mentioned purpose is: a full-band error suppression trajectory planning method, comprising the following steps:

[0007] 1) measuring an optical element to obtain surface shape data of the optical element, performing a preprocessing operation on the surface shape data, and performing surface shape expansion on the preprocessed surface shape data to obtain expanded surface shape data;

[0008] 2) Select the appropriate polishing tool and determine the corresponding removal function based on the expanded surface shape;

[0009] 3) Determine the dwell points according to the processing area, select the appropriate starting point among the dwell points, implement multi-directional random path planning, and then obtain the random path point positions;

[0010] 4) Calculate the dwell time of the dwell point;

[0011] 5) Perform quintic polynomial trajectory planning based on the random path point positions and dwell times to obtain the velocity and acceleration of each path point;

[0012] 6) According to the robot's control cycle, the position, velocity, and acceleration of each planned path point are sent to the robot controller to complete servo control.

[0013] The preprocessing operations include: rotation, cropping, image denoising, outlier removal, and interpolation operations on the face data;

[0014] The image denoising includes: any one of average filtering, median filtering and composite filtering;

[0015] The removal of outliers adopts a fixed threshold method;

[0016] The interpolation includes any one of preceding interpolation, following interpolation, nearest neighbor interpolation, linear interpolation, cubic spline interpolation and modified Akima cubic Hermite interpolation.

[0017] The surface shape expansion includes any one of Gaussian expansion, nearest neighbor expansion and smooth expansion.

[0018] The pre-processed surface shape data is a rectangular surface shape or a non-rectangular surface shape;

[0019] For rectangular surfaces, the surface expansion is performed directly; for non-rectangular surfaces, the surface is trimmed to obtain a rectangular shape after fitting with Zernike orthogonal polynomials.

[0020] The step 3) is specifically as follows:

[0021] 1-1) Determine the location of the dwell points that need to be passed during the machining process based on the contour of the surface to be machined and the path interval;

[0022] 1-2) Select a dwell point as the starting point, where the dwell point is selected as an edge point and counted as a path point;

[0023] 1-3) Starting from the starting point, select an adjacent dwelling point that has not yet been counted as a path point and does not intersect with the previous path as the next starting point;

[0024] 1-4) When no valid path points can be selected, determine whether the planned number has been reached. If not, go back N steps and continue planning, and continue to execute steps 1-2) to 1-4) until the planned number requirements are met;

[0025] The number of steps N to fall back is the number of consecutive times when the same number of path points encounters a situation where planning is impossible, that is:

[0026] If the current path has M path points and the next path point cannot be planned, the process will regress N=1 steps. If the number of path points is still M and the path planning cannot be completed next time, the process will regress N=2 steps, where N is the number of consecutive times that the process fails to plan for the same number of path points.

[0027] 1-5) On the contrary, if the number of path points reaches the planned number, the path planning is completed, and additional dwell points are added between each dwell point to increase the control frequency and improve the accuracy of trajectory planning.

[0028] The acquisition of the dwell time of the dwell point is specifically as follows:

[0029] Based on the processed surface data and the removal function, the dwell time solution method based on fast Fourier transform is used to obtain the dwell time of the surface measurement point; and the bicubic resampling method is used to upsample the dwell time to the path to obtain the dwell time of each path point.

[0030] In step 4), the quintic polynomial trajectory planning is performed according to the random path point positions and dwell times, specifically:

[0031] 2-1) Define the quintic polynomial trajectory s(t) at time t:

[0032] s(t)=a0+a1t+a2t 2 +a3t 3 +a4t 4 +a5t 5

[0033] 2-2) Establish the position, velocity and acceleration constraints between the i-1th and ith path points:

[0034]

[0035]

[0036]

[0037]

[0038]

[0039]

[0040] where t i-1 , t i represents the time when the polishing head passes the i-1th and i-th path points, respectively, v(t i-1 )、v(t i ) represent the speed of the polishing head passing through the i-1th and i-th path points respectively. Similarly, a(t i-1 )、a(t i ) represent the speeds of the polishing head passing through the i-1th and i-th path points respectively.

[0041] In step 4), the speed and acceleration of each path point are obtained as follows:

[0042] The position, velocity, and acceleration of each path point are obtained by combining the path point with processing experience or surface shape through algorithm optimization. The velocity and acceleration of each path point in the x-axis or y-axis direction are defined as:

[0043]

[0044]

[0045] Among them, v(t i ) is the speed of the polishing head passing the i-th path point, a(t i ) is the acceleration of the polishing head passing the i-th path point, d is the interval of the path points in the x-axis or y-axis direction, α and β are empirical parameters, and they satisfy:

[0046] α i+1 +α i +α i-1 =1

[0047] β i +β i-1 =1

[0048] Among them, i is a path point.

[0049] In step 4), the position of the corner path point is specifically:

[0050] The positions of the corner points in the x-axis or y-axis directions are defined as:

[0051] s(t i )=γ i+1 s(t i+1 )+γ i s(t i )+γ i-1 s(t i-1 )

[0052] Among them, s(t i ) represents the position of the i-th path point, γ is an empirical parameter, and satisfies: γ i+1 +γ i +γ i-1 =1.

[0053] The empirical parameters α, β and γ are obtained from experience, specifically:

[0054]

[0055] The present invention has the following beneficial effects and advantages:

[0056] 1. The present invention can plan a smoother and more accurate trajectory based on the path planning with the introduction of randomness and the combination of the dwell time.

[0057] 2. The present invention largely avoids processing stability problems caused by discontinuities in speed or acceleration, improves surface error convergence efficiency and polishing accuracy, and has important application value in optical processing, especially on robotic processing platforms. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 This is a flow chart of the full-band error suppression trajectory planning method of the present invention;

[0059] Figure 2 This is a flowchart of the multi-directional random path planning of the present invention;

[0060] Figure 3 is the multi-directional path planning result graph of the present invention;

[0061] Figure 4 Schematic diagram of the initial surface shape processing and surface shape expansion process of a plane mirror in an embodiment of the present invention;

[0062] Figure 5 Schematic diagram of the removal function of the wheel polishing head in an embodiment of the present invention;

[0063] Figure 6 This is a graph showing the multi-directional random programming results of a plane mirror according to an embodiment of the present invention;

[0064] Figure 7 This is a dwell time distribution diagram calculated based on the surface shape and removal function in an embodiment of the present invention;

[0065] Figure 8 Graph showing the polynomial trajectory planning results of a plane mirror according to an embodiment of the present invention;

[0066] Figure 9 Graph showing the surface error distribution before and after machining using polynomial planning trajectory in an embodiment of the present invention;

[0067] Figure 10 Graph showing the surface error distribution before and after grating path processing in an embodiment of the present invention;

[0068] Figure 11 1 is a PSD comparison curve diagram after processing using a grating path and a polynomial trajectory in an embodiment of the present invention. DETAILED DESCRIPTION

[0069] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0070] like Figure 1 FIG. 1 is a flow chart of a method for trajectory planning with full-band error suppression according to the present invention. The method for trajectory planning with full-band error suppression provided by the present invention comprises the following steps:

[0071] 1) measuring an optical element to obtain surface shape data of the optical element, performing a preprocessing operation on the surface shape data, and performing surface shape expansion on the preprocessed surface shape data to obtain expanded surface shape data;

[0072] 2) Select the appropriate polishing tool and determine the corresponding removal function based on the expanded surface shape;

[0073] 3) Determine the dwell points according to the processing area, select the appropriate starting point among the dwell points, implement multi-directional random path planning, and then obtain the random path point positions;

[0074] 4) Calculate the dwell time of the dwell point;

[0075] 5) Perform quintic polynomial trajectory planning based on the random path point positions and dwell times to obtain the velocity and acceleration of each path point;

[0076] 6) According to the robot's control cycle, the position, velocity, and acceleration of each planned path point are sent to the robot controller to complete servo control.

[0077] Before processing, the surface shape must be inspected. However, because optical inspection systems can be affected by vibration, light, and even microbial interference, they often cannot obtain complete surface shape data. De-noising, fitting, and interpolation operations are required.

[0078] In the present invention, image denoising can use average filtering, median filtering and composite filtering, etc.; outliers are removed using a fixed threshold method; surface fitting uses the Zernike orthogonal polynomial fitting method; interpolation methods include anterior interpolation, posterior interpolation, nearest neighbor interpolation, linear interpolation, cubic spline interpolation and modified Akima cubic Hermite interpolation, etc. Among the interpolation methods, we found that linear interpolation is more stable and efficient, but it is not effective when there is a large amount of missing surface data. In this case, other interpolation methods or the results of surface fitting can be used. In addition, surface measurement and processing are currently difficult to achieve in-situ or online detection. The optical element needs to be moved to the detection platform for detection after processing. Therefore, before the next processing, it is often necessary to rotate and crop the surface data to obtain surface data within the effective aperture.

[0079] In actual machining, because the removal function itself has a certain size, the machining area needs to be larger than the required effective aperture (to ensure effective aperture edge accuracy), and the area of ​​material removal may also exceed the size of the machining area. Therefore, after obtaining the surface data within the effective aperture, it is necessary to perform reasonable surface expansion. Common expansion methods include Gaussian expansion, nearest neighbor expansion, and smooth expansion. Gaussian expansion is often used to expand circular surface data.

[0080] like Figure 2 The figure shows the multi-directional random path planning flow chart of the present invention. Before planning the processing trajectory, the processing path needs to be determined. The present invention uses a multi-directional random path planning method. In order to avoid the path corner being too large and affecting the stability of the robot processing process, the path is planned in four directions. The specific planning method is as follows:

[0081] 1-1) Determine the location of the dwell points that need to be passed during the machining process based on the contour of the surface to be machined and the path interval;

[0082] 1-2) Select a dwell point as the starting point (usually an edge point) and count it as a path point;

[0083] 1-3) Find a dwell point adjacent to the last waypoint and count it as a waypoint. This point cannot be a previously counted waypoint, and the line connecting the two points cannot intersect with a line already counted.

[0084] 1-4) If no qualified dwelling points can be found, first determine whether a sufficient number of dwelling points have been planned. If not, rewind n steps (n is the number of times the same number of path points cannot be planned) and continue with steps 2-4 until the required number of planned points is met.

[0085] 1-5) Add additional dwell points between each dwell point to increase the control frequency and improve the accuracy of trajectory planning.

[0086] Based on the expanded surface data, dwell time can be calculated using either matrix-based or deconvolution-based methods. Matrix-based methods require more computational resources and memory consumption, so this method uses the latter. The dwell time calculated using deconvolution corresponds to the surface measurement points. To obtain the dwell time corresponding to the path points, the calculated dwell time must be upsampled. This method uses bicubic resampling for this upsampling operation.

[0087] At this point, trajectory planning can be performed by combining dwell time with machining path. Quintic polynomial trajectory planning is a commonly used trajectory planning method for robot motion control, especially in task scenarios that require precise control. Quintic polynomial trajectory planning can ensure the continuity of position, velocity, and acceleration, thereby ensuring machining stability. The specific method of quintic polynomial trajectory planning is as follows:

[0088] 2-1) Define the quintic polynomial trajectory s(t) at time t:

[0089] s(t)=a0+a1t+a2t 2 +a3t 3 +a4t 4 +a5t 5

[0090] 2-2) Establish the constraints of position, velocity and acceleration between the i-1th and i-th path points:

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097] Among them, t i-1 , t i represents the time when the polishing head passes the i-1th and i-th path points, respectively, v(t i-1 )、v(t i ) represent the speed of the polishing head passing through the i-1th and i-th path points respectively. Similarly, a(t i-1 )、a(t i ) represent the speed of the polishing head passing through the i-1th and i-th path points respectively. The position, speed and acceleration of each path point are given by the path point combined with processing experience (or combined with the surface shape through algorithm optimization). The speed and acceleration of the i-th path point on the x-axis (similar to the y-axis) are given by the following formula:

[0098]

[0099]

[0100] Where d represents the interval of path points in the x-axis (or y-axis) direction; α and β are constants and satisfy: α i +α i-1 =1,β i +β i-1 = 1, its value is determined by experience, or by optimizing the parameters using the error margin after trajectory surface processing as the evaluation function through particle swarm optimization, genetic algorithm, simulated annealing algorithm, ant colony optimization algorithm, or neural network. It is worth noting that when the path needs to change direction, replanning the path point position can make the path smoother. If the i-th path point is a turning point, its x-axis position (similar to the y-axis) can be given by the adjacent points:

[0101] s(t i )=γ i+1 s(t i+1 )+γ i s(t i )+γ i-1 s(t i-1 )

[0102] Where γ is a constant and satisfies: i+1 +γ i +γ i-1 =1, the empirical parameters used in the present invention are defined as follows:

[0103]

[0104] The α, β, and γ parameters can be used to introduce a certain degree of randomness into the trajectory through a dynamic optimization algorithm, but this requires additional optimization calculation time.

[0105] like Figure 3 The figure below shows the multi-directional path planning results of the present invention. By pre-setting empirical parameters, the present invention can, to a certain extent, prevent trajectory speed or acceleration from exceeding hardware limitations and significantly improve computational efficiency, especially when there are many path points. These constraints define a linear system with six equations and six unknowns. Solving the linear system yields the planned trajectory. Finally, according to the robot's control cycle, the position of each time point on the trajectory is transmitted to the robot controller to complete servo control.

[0106] Example:

[0107] This example was conducted on a polishing platform based on a domestic collaborative robot. The polishing head was a wheel-type polisher with an 8cm diameter and a 3cm width. The rotation speed was set to 0.5rpm, the applied pressure was 10N, the polishing fluid composition was [ 0.001], and the ambient temperature was 23°C. The test workpieces to be polished were two pieces of quartz glass with an effective aperture of 40mm x 40mm. Both the raster path and the polynomial trajectory were used to process the two workpieces.

[0108] The processing tasks are completed by the following methods:

[0109] The interferometer is used to detect the surface error of the workpiece to be processed, and the obtained data is subjected to rotation, cropping, denoising and interpolation operations, and then the surface data is expanded using the nearest neighbor expansion. The surface data processing and expansion process using polynomial trajectory processing is as follows Figure 4 As shown;

[0110] The wheel polishing removal function used in this experiment is as follows: Figure 5 As shown;

[0111] The machining path interval is set to 0.83 mm, and the multi-directional random path planning method is used to obtain the pseudo-random path in the machining area, such as Figure 6 As shown;

[0112] The residence time is calculated based on the deconvolution method according to the expanded surface data and the removal function. The calculation results are as follows: Figure 7 As shown;

[0113] The dwell time obtained in step 4 is upsampled to the path point determined in step 3, and the trajectory is planned using the polynomial trajectory planning method proposed in this experiment. The planning results are shown in the figure below. Figure 8 As shown;

[0114] The obtained machining trajectory is sent to the robot controller according to the control cycle of the robot machining platform to complete the machining process. After machining twice, the shape quality tends to be stable. The surface shape data before and after machining using the polynomial programming method are as follows: Figure 9 As shown;

[0115] Similarly, the second workpiece is processed according to the above steps, and the path is selected as the grating path. After processing 4 times, the shape quality tends to be stable. The surface data before and after processing are as follows: Figure 10 As shown;

[0116] The power spectrum density curves of the shape data of the two workpieces after processing are as follows: Figure 11 As shown in the figure, it can be found that the surface shape processed using the polynomial trajectory does not have the same bulge as the grating path in the mid-frequency band.

[0117] The trajectory planned by the method proposed in the present invention is smoother, ensuring the stability of processing. According to experimental results, the trajectory planned using polynomials has a stable shape convergence after two processings. The PV value converges from 472.8nm to 178.3nm, with a convergence rate of 37.7%; the RMS value converges from 93.1 to 34.7nm, with a convergence rate of 37.2%. These are respectively greater than the 55.1% PV value convergence rate and the 69.8% RMS value convergence rate of the grating path. In addition, the final surface quality is improved compared to the grating path. This shows that the trajectory planning method proposed by the present invention can plan a smoother processing trajectory based on the dwell time of each dwell point on the basis of a pseudo-random path, and can quickly and effectively suppress errors in the entire frequency band. It has good practical effects and broad application prospects.

Claims

1. A full-band error suppression trajectory planning method, characterized in that: The following steps are involved: 1) measuring an optical element to obtain surface shape data of the optical element, performing a preprocessing operation on the surface shape data, and performing surface shape expansion on the preprocessed surface shape data to obtain expanded surface shape data; 2) Select the appropriate polishing tool and determine the corresponding removal function based on the expanded surface shape; 3) Determine the dwell point according to the processing area, select the starting point from the dwell point, implement multi-directional random path planning, and then obtain the random path point position; 4) Calculate the dwell time of the dwell point; 5) Perform quintic polynomial trajectory planning based on the random path point positions and dwell times to obtain the velocity and acceleration of each path point; 6) According to the robot's control cycle, the position, velocity, and acceleration of each planned path point are sent to the robot controller to complete servo control.

2. The full-band error suppression trajectory planning method according to claim 1, characterized in that: The preprocessing operations include: rotation, cropping, image denoising, outlier removal, and interpolation operations on the face data; The image denoising includes: any one of average filtering, median filtering and composite filtering; The removal of outliers adopts a fixed threshold method; The interpolation includes any one of preceding interpolation, following interpolation, nearest neighbor interpolation, linear interpolation, cubic spline interpolation and modified Akima cubic Hermite interpolation.

3. The full-band error suppression trajectory planning method according to claim 1, characterized in that: The surface shape expansion includes any one of Gaussian expansion, nearest neighbor expansion and smooth expansion.

4. The full-band error suppression trajectory planning method according to claim 1, characterized in that: The pre-processed surface shape data is a rectangular surface shape or a non-rectangular surface shape; For rectangular surfaces, the surface expansion is performed directly; for non-rectangular surfaces, the surface is trimmed to obtain a rectangular shape after fitting with Zernike orthogonal polynomials.

5. The full-band error suppression trajectory planning method according to claim 1, characterized in that: The step 3) is specifically as follows: 1-1) Determine the location of the dwell points that need to be passed during the machining process based on the contour of the surface to be machined and the path interval; 1-2) Select a dwell point as the starting point, where the dwell point is selected as an edge point and counted as a path point; 1-3) Starting from the starting point, select an adjacent dwelling point that has not yet been counted as a path point and does not intersect with the previous path as the next starting point; 1-4) When no valid path points can be selected, determine whether the planned number has been reached. If not, go back N steps and continue planning, and continue to execute steps 1-2) to 1-4) until the planned number requirements are met; The number of steps N to fall back is the number of consecutive times when the same number of path points encounters a situation where planning is impossible, that is: If the current path has M path points and the next path point cannot be planned, the process will regress N=1 steps. If the number of path points is still M and the path planning cannot be completed next time, the process will regress N=2 steps, where N is the number of consecutive times that the process fails to plan for the same number of path points. 1-5) On the contrary, if the number of path points reaches the planned number, the path planning is completed, and additional dwell points are added between each dwell point to increase the control frequency and improve the accuracy of trajectory planning.

6. The full-band error suppression trajectory planning method according to claim 1, characterized in that: The acquisition of the dwell time of the dwell point is specifically as follows: Based on the processed surface data and the removal function, the dwell time solution method based on fast Fourier transform is used to obtain the dwell time of the surface measurement point; and the bicubic resampling method is used to upsample the dwell time to the path to obtain the dwell time of each path point.

7. The full-band error suppression trajectory planning method according to claim 1, characterized in that: In step 4), the quintic polynomial trajectory planning is performed according to the random path point positions and dwell times, specifically: 2-1) Define the quintic polynomial trajectory s(t) at time t: s(t)=a0+a1t+a2t 2 +a3t 3 +a4t 4 +a5t 5 2-2) Establish the position, velocity and acceleration constraints between the i-1th and ith path points: where t i-1 , t i represents the time when the polishing head passes the i-1th and i-th path points, respectively, v(t i-1 )、v(t i ) represent the speed of the polishing head passing through the i-1th and i-th path points respectively. Similarly, a(t i-1 )、a(t i ) represent the speeds of the polishing head passing through the i-1th and i-th path points respectively.

8. The full-band error suppression trajectory planning method according to claim 1, characterized in that: In step 4), the speed and acceleration of each path point are obtained as follows: The position, velocity, and acceleration of each path point are obtained by combining the path point with processing experience or surface shape through algorithm optimization. The velocity and acceleration of each path point in the x-axis or y-axis direction are defined as: Among them, v(t i ) is the speed of the polishing head passing the i-th path point, a(t i ) is the acceleration of the polishing head passing the i-th path point, d is the interval of the path points in the x-axis or y-axis direction, α and β are empirical parameters, and they satisfy: α i+1 +α i +α i-1 ＝1 β i +β i-1 ＝1 Among them, i is a path point.

9. The full-band error suppression trajectory planning method according to claim 1, characterized in that: In step 4), the position of the corner path point is specifically: The positions of the corner points in the x-axis or y-axis directions are defined as: s(t i )=γ i+1 s(t i+1 )+γ i s(t i )+γ i-1 s(t i-1 ) Among them, s(t i ) represents the position of the i-th path point, γ is an empirical parameter, and satisfies: γ i+1 +γ i +γ i-1 =1.

10. A full-band error suppression trajectory planning method according to claim 8 or 9, characterized in that: The empirical parameters α, β and γ are obtained from experience, specifically:

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