阅读说明：本技术 一种土壤侵蚀量定时测量装置 (Soil erosion amount timing measuring device ) 是由 朱昊宇 夏小林 姬钰 汪邦稳 张世杰 张靖雨 刘旦旦 张卫 赵黎明 龙昶宇 王浩 于 2021-08-09 设计创作，主要内容包括：本发明涉及一种土壤侵蚀量定时测量装置,包括激光测距器、测量机器人、定时控制模块、数据临时存储模块、数据远程传送模块、控制终端。所述测量机器人控制激光测距器按照指定轨迹与指定频率对坡面进行第一轮扫描,采集得到第一轮间距测量值；通过定时控制模块控制第二轮扫描的时间间隔,所述测量机器人控制激光测距器按照指定轨迹与指定频率对坡面进行第二轮扫描,采集得到第二轮间距测量值；通过数据远程传送模块将第一轮间距测量值和第二轮间距测量值发送至控制终端,在控制终端处进行运算,得到坡面的土壤侵蚀量。本发明不需在坡面上布置传感器或测钉,不易发生丢失,且测量点密度更大,更能保证实验和测量结果。(The invention relates to a soil erosion amount timing measuring device which comprises a laser range finder, a measuring robot, a timing control module, a data temporary storage module, a data remote transmission module and a control terminal. The measuring robot controls the laser range finder to perform first scanning on the slope surface according to the specified track and the specified frequency, and a first round of distance measurement value is acquired; controlling the time interval of second round scanning by a timing control module, and controlling a laser range finder to perform second round scanning on the slope surface by the measuring robot according to the specified track and the specified frequency, and acquiring a second round distance measurement value; and sending the first wheel interval measurement value and the second wheel interval measurement value to a control terminal through a data remote transmission module, and calculating at the control terminal to obtain the soil erosion amount of the slope. According to the invention, a sensor or a measuring nail is not required to be arranged on the slope, the loss is not easy to occur, the density of measuring points is higher, and the experiment and measuring results can be better ensured.)

1. A soil erosion amount timing measuring device, comprising:

the laser range finder is used for measuring the distance between the laser range finder and the slope surface to obtain a distance measurement value;

the laser range finder is fixedly arranged at the moving end of the measuring robot and is controlled by the measuring robot to scan the slope surface according to the specified track and frequency and collect the distance measurement value;

the timing control module is used for controlling the time interval of the measurement of two adjacent wheels;

the data temporary storage module is used for temporarily storing data;

the data remote transmission module is used for transmitting the temporary storage data to the control terminal;

and a control terminal for calculating the transmitted data.

2. A soil erosion amount timing measuring device according to claim 1, wherein: the measuring robot controls the laser range finder to perform first scanning on the slope surface according to the specified track and the specified frequency, and a first round of distance measurement value is acquired; controlling the time interval of second round scanning by a timing control module, and controlling a laser range finder to perform second round scanning on the slope surface by the measuring robot according to the specified track and the specified frequency, and acquiring a second round distance measurement value; the designated track in the first scanning process is the same as the designated track in the second scanning process, and the designated frequency in the first scanning process is equal to the designated frequency in the second scanning process; and sending the first wheel interval measurement value and the second wheel interval measurement value to a control terminal through a data remote transmission module, and calculating at the control terminal to obtain the soil erosion amount of the slope.

3. A soil erosion amount timing measuring device according to claim 2, wherein: the operation method of the control terminal comprises the following processes:

the absolute value of the difference between the first round spacing measurement and the second round spacing measurement for the same measurement point is deltah,

V_d＝∑Δh·ΔS，

the total number of the slope units is equal to the number of all measuring points in the first round/second round measuring process;

Q_d＝V_drho, rho is the volume weight of the soil at the slope, V_dThe total volume of water and soil loss, Q_dThe amount of soil erosion of the slope.

4. A soil erosion amount timing measuring device according to claim 3, wherein: the designated track in the first round/second round scanning process is one of a Chinese character 'ji' shaped structure, a concentric circle shaped structure and a spiral structure; in each scanning process, adjacent measuring points are arranged at equal intervals.

5. A soil erosion amount timing measuring device according to claim 2, wherein: in each scanning process, the density of the measuring points is 300-350/square meter.

6. A soil erosion amount timing measuring device according to claim 1, wherein: if a plurality of slopes needing to be measured exist, the soil erosion amount timing measuring device further comprises an industrial camera arranged at the measuring robot; three fixed marks which are arranged in a triangular shape are arranged on each slope surface to be measured, after the last slope surface is measured by the measuring robot and the laser range finder, the laser range finder and the industrial camera are controlled by the measuring robot to be aligned to a second slope surface, the industrial camera respectively shoots three fixed marks on the second slope surface to obtain a real-time adjusting image, and the real-time adjusting image and a preset image stored in the temporary data storage module are subjected to similarity operation to obtain a similarity value corresponding to the fixed marks;

when the similarity values corresponding to the three fixed marks are all larger than a preset threshold value, judging that the industrial camera and the laser range finder at the moment are aligned to a second slope;

and if the similarity value corresponding to any fixed mark is smaller than a preset threshold value, judging that the industrial camera and the laser range finder are not aligned with the second slope surface at the moment, and readjusting the positions of the industrial camera and the laser range finder by the measuring robot until the industrial camera and the laser range finder are aligned with the second slope surface.

7. A soil erosion amount timing measuring device according to claim 6, wherein: the fixed mark is one of a cross shape, a meter shape, an X shape, a Y shape and an O shape, and the three fixed marks of a single slope are different from each other.

8. A soil erosion amount timing measuring device according to claim 1, wherein: in the first round of scanning and the second round of scanning, the motion tracks of the laser range finder are in the same vertical plane.

9. A soil erosion amount timing measuring device according to claim 1, wherein: the measuring robot is a four-axis robot or a six-axis robot.

Technical Field

The invention relates to a soil erosion amount timing measuring device, and belongs to the technical field of water and soil conservation monitoring.

Background

The traditional soil erosion amount is measured by a steel chisel method. The most important monitoring index of the water and soil conservation monitoring work in the development and construction project is the monitoring of the soil erosion amount, and the method is that each instrument to be monitored is manually and periodically brought to a monitoring point, each instrument works independently, and the monitoring result is recorded. The method requires that a measurer arrives at the site regularly for monitoring, simultaneously, a large amount of instruments and equipment are required to be carried each time, and the manual measurement and recording have large errors and a plurality of uncertain factors, so that the monitoring accuracy is seriously influenced.

The existing "steel chisel method" is a mature technology for measuring soil erosion amount, for example, refer to journal "technical and market" 2013, at stage 08, the author: the paper of Liu Jiming and Wang Qiang Ying (English before China) is about the determination of the amount of water and soil loss in hydraulic engineering construction.

In the drill rod method, because the measuring nails (drill rods) are vertically jacked into the slope, the slope unit where one measuring nail is taken as an example for explanation, as shown in fig. 1, the original slope of the slope unit is a solid oblique line, the slope after water and soil loss is an imaginary oblique line, beta is a slope angle after water and soil loss, and gamma is the slope between the measuring nail and the slope after water and soil lossThe included angle between beta and gamma is complementary; the change value of the slope surface at the position of the measuring nail, namely H, is measured at present; from this, the vertical distance between the point of penetration of the original nail on the slope and the slope after water and soil loss is calculated as H, H · sin γ ═ H · cos β, and β and H are the current measured values. Then the water flow rate Q of the slope unit is equal to vp, and ρ is the volume weight of the soil; q is dependent on V, which is S · H · cos β, S is the area of the regular pattern of the unit in which the pin is located, e.g. a rectangle centered on the pin, S can also be calculated. Therefore, the water and soil flow rate Q and the total water and soil loss Q of the unit where the single measuring nail is located can be calculated_dThe water flow Q of the water and soil in the unit where all the measuring nails are located is added.

Measurement of soil erosion amount by the above-mentioned "Steel chisel method", the obtained Q_dDepending primarily on β, H, S, the variables that need to be measured are many; moreover, the corresponding beta and H, S need to be measured manually for each measuring nail, and the operation is complicated; in addition, due to the slope limitation, the number of inserted steel pins is limited, 80m²The slope surface of the slope is provided with 12 slope angles, and the slope angles corresponding to different areas of the whole slope surface are possibly different, namely, the sizes of beta at different positions are possibly different, and the calculated H is H & cos beta, and the precision of H is also influenced to a certain extent by beta; the current measurement method ignores the influence of the value. Therefore, the sample amount is small (the number of the steel rods), the error of the calculated h value is large, and the accuracy error of the finally measured soil erosion amount is large.

For the existing "steel rod method", if the measurement error is to be reduced, theoretically the most feasible operation is to ensure that the length direction of the "steel rod" is always perpendicular to the slope surface during each measurement, and the operation is obviously unrealistic because the slope surface often has rugged parts.

Disclosure of Invention

Aiming at the defects in the prior art, the invention provides a device for measuring the soil erosion amount at regular time, which has the following specific technical scheme:

the soil erosion amount timing measuring device comprises:

the laser range finder is used for measuring the distance between the laser range finder and the slope surface to obtain a distance measurement value;

the laser range finder is fixedly arranged at the moving end of the measuring robot and is controlled by the measuring robot to scan the slope surface according to the specified track and frequency and collect the distance measurement value;

the timing control module is used for controlling the time interval of the measurement of two adjacent wheels;

the data temporary storage module is used for temporarily storing data;

the data remote transmission module is used for transmitting the temporary storage data to the control terminal;

and a control terminal for calculating the transmitted data.

As an improvement of the above technical scheme, the measuring robot controls the laser range finder to perform a first round of scanning on the slope surface according to a specified track and a specified frequency, and a first round of distance measurement value is acquired; controlling the time interval of second round scanning by a timing control module, and controlling a laser range finder to perform second round scanning on the slope surface by the measuring robot according to the specified track and the specified frequency, and acquiring a second round distance measurement value; the designated track in the first scanning process is the same as the designated track in the second scanning process, and the designated frequency in the first scanning process is equal to the designated frequency in the second scanning process; and sending the first wheel interval measurement value and the second wheel interval measurement value to a control terminal through a data remote transmission module, and calculating at the control terminal to obtain the soil erosion amount of the slope.

As an improvement of the above technical solution, the operation method of the control terminal includes the following processes:

the absolute value of the difference between the first round spacing measurement and the second round spacing measurement for the same measurement point is deltah,

V_d＝∑Δh·ΔS，

the total number of the slope units is equal to the number of all measuring points in the first round/second round measuring process;

Q_d＝V_drho, rho is the volume weight of the soil at the slope, V_dThe total volume of water and soil loss, Q_dThe soil erosion amount of the slope surface.

As an improvement of the above technical solution, the designated track in the first/second scanning process is one of a "hex" shaped structure, a concentric circle shaped structure, and a helical structure; in each scanning process, adjacent measuring points are arranged at equal intervals.

As an improvement of the technical scheme, in each scanning process, the density of the measuring points is 300-350/square meter.

As an improvement of the above technical solution, if there are a plurality of slopes to be measured, the soil erosion amount timing measuring device further comprises an industrial camera installed at the measuring robot; three fixed marks which are arranged in a triangular shape are arranged on each slope surface to be measured, after the last slope surface is measured by the measuring robot and the laser range finder, the laser range finder and the industrial camera are controlled by the measuring robot to be aligned to a second slope surface, the industrial camera respectively shoots three fixed marks on the second slope surface to obtain a real-time adjusting image, and the real-time adjusting image and a preset image stored in the temporary data storage module are subjected to similarity operation to obtain a similarity value corresponding to the fixed marks;

when the similarity values corresponding to the three fixed marks are all larger than a preset threshold value, judging that the industrial camera and the laser range finder at the moment are aligned to a second slope;

and if the similarity value corresponding to any fixed mark is smaller than a preset threshold value, judging that the industrial camera and the laser range finder are not aligned with the second slope surface at the moment, and readjusting the positions of the industrial camera and the laser range finder by the measuring robot until the industrial camera and the laser range finder are aligned with the second slope surface.

As an improvement of the above technical solution, the fixed mark is one of a cross shape, a meter shape, an X shape, a Y shape and an O shape, and three fixed marks of a single slope are different from each other.

As an improvement of the above technical solution, in the first round of scanning and the second round of scanning, the movement tracks of the laser range finder are all in the same vertical plane.

As an improvement of the above technical solution, the measuring robot is a four-axis robot or a six-axis robot.

The invention has the beneficial effects that:

1) the soil erosion amount timing measuring device and the corresponding measuring method are compared with a steel rod method, the traditional steel rod method is upgraded and modified, and the soil erosion amount timing measuring device and the corresponding measuring method are superior to the traditional steel rod method. Compared with a simple slope surface measuring method (a steel chisel method), the method does not need to arrange a sensor or a measuring nail on the slope surface, is not easy to lose, has higher density of measuring points, and can better ensure the experiment and the measuring result.

2) Compared with the existing steel chisel method, the method has the advantages that the collected sample amount is huge in one-time measurement process, and the data collection amount in the prior art cannot be reached; in addition, the invention enables direct measurement of Δ h, which is more accurate than the existing calculated values of h! Therefore, the soil erosion amount measured by the method is more accurate.

3) Although the data sample amount required to be measured is large, the measuring robot is adopted for remote and automatic measurement and collection, the operation is simple and convenient, manpower and material resources are saved, and the measuring efficiency is high. The device can realize measurement automation, manually adjust the measurement frequency to meet the measurement requirement, realize remote data receiving, reduce the manual field measurement frequency and save the labor cost.

4) Laser rangefinder can remote measurement, can adapt to the monitoring of different slope types, simultaneously, can also measure simple operation convenience to the domatic batch of difference with the region.

5) Compared with a slope erosion gully measuring method, the method can measure not only the slope with the erosion gully but also the slope without the erosion gully, and is more accurate and practical compared with the traditional method of measuring the erosion gully by using a tape.

6) Compared with a sand settling tank method, the method does not need to develop a drainage ditch and a sand settling tank, and reduces errors caused by artificial disturbance.

7) Compared with the runoff plot method, the runoff plot is specially laid without spending large manpower and material resources, the engineering construction progress cannot be influenced by the protection of the runoff plot, and the method is more suitable for construction and production projects.

8) The data obtained by measurement can be temporarily stored and wirelessly transmitted, and can be exported on site, so that data loss caused by unexpected faults is reduced.

Drawings

FIG. 1 is a schematic diagram of a conventional "steel bar method" measurement;

FIG. 2 is a schematic structural view of a soil erosion amount timing measuring device according to the present invention;

FIG. 3 is a schematic diagram of a laser rangefinder according to the present invention for measuring the distance between slopes;

FIG. 4 is a schematic view of the present invention illustrating the slope divided into slope units;

FIG. 5 is a schematic diagram of specifying a track according to embodiment 2;

FIG. 6 is a schematic diagram of specifying a track according to embodiment 3;

FIG. 7 is a diagram illustrating the designated trajectory according to embodiment 4;

FIG. 8 is a graph showing the measurement error in test A and the number of pins;

FIG. 9 is a graph of measurement error versus measurement spot density for test B.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

Example 1

As shown in fig. 2, the soil erosion amount timing measuring apparatus includes:

the laser range finder 10 is used for measuring the distance between the laser range finder and the slope surface to obtain a distance measurement value;

the measuring robot 20 is characterized in that the laser range finder 10 is fixedly arranged at the moving end of the measuring robot 20, and the measuring robot 20 controls the laser range finder 10 to scan the slope surface according to the specified track and frequency and collect the distance measurement value;

the timing control module is used for controlling the time interval of the measurement of two adjacent wheels;

the data temporary storage module is used for temporarily storing data;

the data remote transmission module is used for transmitting the temporary storage data to the control terminal;

and a control terminal for calculating the transmitted data.

The measuring principle of the soil erosion amount timing measuring device is as follows:

the measuring robot 20 controls the laser range finder 10 to perform first round scanning on the slope surface according to the specified track and the specified frequency, and a first round distance measurement value is acquired; controlling the time interval of second round scanning by the timing control module, and controlling the laser range finder 10 to perform second round scanning on the slope surface by the measuring robot 20 according to the specified track and the specified frequency, and acquiring a second round distance measurement value; the designated track in the first scanning process is the same as the designated track in the second scanning process, and the designated frequency in the first scanning process is equal to the designated frequency in the second scanning process; and sending the first wheel interval measurement value and the second wheel interval measurement value to a control terminal through a data remote transmission module, and calculating at the control terminal to obtain the soil erosion amount of the slope.

Wherein, in order to ensure that the front and the back two scanning processes, the front and the back two measuring points are at the same position and are in one-to-one correspondence; in the first round of scanning and the second round of scanning, the movement tracks of the laser range finder 10 are all in the same vertical plane.

Further, the measuring robot 20 is a four-axis robot or a six-axis robot.

Further, the operation method of the control terminal includes the following processes:

the absolute value of the difference between the first round spacing measurement and the second round spacing measurement for the same measurement point is deltah,

V_d＝∑Δh·ΔS，

the total number of the slope units is equal to the number of all measuring points in the first round/second round measuring process;

Q_d＝V_drho, rho is the volume weight of the soil at the slope, V_dThe total volume of water and soil loss, Q_dThe soil erosion amount of the slope surface.

In the data acquisition process of the present invention, in this embodiment, Δ h is used to represent the data acquisition process for convenience of distinguishing from h in the background art. H in the prior art is obtained by calculation, and h is also limited by beta. In this embodiment, the laser rangefinder 10 measures the slope to obtain a distance measurement, the principle of which is shown in fig. 3. In the present embodiment, since there are hundreds, thousands or even tens of thousands of scanning points (measurement points) in the scanning trajectory (designated trajectory), each scanning point corresponds to one slope unit (see fig. 4). According to experimental research, the method has the following discovery that: if the number of the slope units is large enough, the slope units can be approximately considered as a regular pattern (such as a cuboid or cube structure, rather than a structure with an inclined plane), and the influence caused by the inclined plane is ignored to the maximum extent, as shown in fig. 4; in this case, the influence of the change in the slope angle of the slope surface is negligible for Δ h, which corresponds to h in the prior art. Thus, V_dSigma delta h delta S, delta h delta S is the volume corresponding to one slope surface unit, and the total water and soil loss volume V is obtained through final summation operation_dAnd multiplying by the volume weight rho of the soil to obtain the water flow and soil flow. Thus, in contrast to the prior art, the volume of soil erosion V_dDepends mainly on Δ h; that is, Q finally obtained in the present invention_dThe corresponding variable is only delta h, the delta h is not influenced by the change of the slope angle of the slope, the difference between the distance measurement values obtained by measuring twice before and after the same measurement point is only needed, and the absolute value operation is carried out by aligning to ensure that the value is a positive valueAnd calculating to obtain the delta h. Theoretically, Q_dOnly one variable is corresponded, and the prior art has three variables of beta and H, S; therefore, the water and soil loss Q finally measured by the invention_dThe accuracy of (2) is remarkably improved.

Example 2

In this embodiment, the designated track during the first/second scanning rounds described in embodiment 1 is a "hex" shaped structure, as shown in fig. 5. In each scanning process, adjacent measuring points are arranged at equal intervals. In this embodiment, the density of the measurement points is 300/m per scan.

Example 3

In this embodiment, the designated tracks during the first/second scanning round described in embodiment 1 are in concentric circle-like structures, as shown in fig. 6. In each scanning process, adjacent measuring points are arranged at equal intervals.

In this embodiment, the density of the measurement points is 300/m per scan.

Example 4

In this embodiment, the designated track during the first/second scanning rounds described in embodiment 1 is a spiral structure, as shown in fig. 7. In each scanning process, adjacent measuring points are arranged at equal intervals.

In this embodiment, the density of the measurement points is 300/m per scan.

Example 5

When the slope is measured in the same area, the slope is measured; the method comprises the following steps:

if there are a plurality of slopes to be measured, the soil erosion amount timing measuring apparatus further includes an industrial camera 21 installed at the measuring robot 20; three fixed marks which are arranged in a triangular shape are arranged on each slope surface to be measured; after the last slope is measured by the measuring robot 20 and the laser range finder 10, the measuring robot 20 controls the laser range finder 10 and the industrial camera 21 to align to a second slope, the industrial camera 21 respectively photographs three fixed marks on the second slope to obtain a real-time adjustment image, and performs similarity calculation on the real-time adjustment image and a preset image stored in the temporary data storage module to obtain a similarity value corresponding to the fixed mark (for example, photographing the first fixed mark to obtain a real-time adjustment image of the first fixed mark, and performing similarity calculation on the real-time adjustment image of the first fixed mark and the preset image of the first fixed mark to obtain a similarity value of the first fixed mark);

when the similarity values corresponding to the three fixed marks are all larger than a preset threshold value, judging that the industrial camera 21 and the laser range finder 10 at the moment are aligned to a second slope;

if the similarity value corresponding to any fixed mark is smaller than a preset threshold value, the industrial camera 21 and the laser range finder 10 are judged not to be aligned with the second slope at the moment; thereafter, the positions of the industrial camera 21 and the laser rangefinder 10 are readjusted by the measuring robot 20 until the industrial camera 21 and the laser rangefinder 10 are aligned to the second slope surface.

The fixed mark is one of a cross shape, a meter shape, an X shape, a Y shape and an O shape, and the three fixed marks of a single slope are different from each other.

For example: the three fixed marks on the first slope surface to be measured are respectively in a cross shape, a meter shape and an X shape; the three fixed marks cannot be of the same shape, which is to improve the accuracy of the similarity algorithm. The triangular arrangement allows a plane to be defined using a minimum number of fixed markings, thereby facilitating the movement of the laser rangefinder 10 in the same vertical plane.

The preset image stored in the temporary data storage module is obtained by determining the positions corresponding to all the slopes to be measured in a manual calibration mode before the test is started, and shooting three fixed marks at the specified positions by using an industrial camera 21 respectively, wherein the shot image is the preset image.

When the similarity values corresponding to the three fixed marks are all larger than the preset threshold value, it is indicated that the plane determined by the three fixed marks corresponds to the plane where the motion track of the laser range finder 10 is located.

Thus, by the method, the slope at the second place can be remotely and automatically determined, and the laser range finder 10 at the moment is used for carrying out remote data acquisition.

Example 6

Test for verifying measurement results

Making a standard runoff plot (straight slope) by referring to 'water and soil conservation test regulation' SL419-2007, and performing first round scanning and measurement on the initial slope surface of the standard runoff plot by using the soil erosion amount timing measurement device; simulating water and soil loss, and measuring the corresponding water and soil loss according to the method in the rule 3.3.6, wherein the water and soil loss is the theoretical water and soil loss; the numerical value measured by the method of the invention and the steel chisel method is the actual water and soil loss. The measurement error is the absolute value of the difference between the theoretical water and soil loss and the actual water and soil loss and the percentage value between the theoretical water and soil loss.

Test A

The area of the slope to be measured is 80m²The number of steel pins measured according to the "drill method" is in turn 6, 12, 20, 35, 42, 56, 72, 90, 110, and the corresponding measurement error versus the number of steel pins is shown in fig. 8. As can be seen from fig. 8:

in the measuring process by adopting the steel chisel method, even if the number of the steel chisels is increased, the measuring error can be reduced to a certain degree, and the measuring precision is improved; however, the number of the steel rods is increased to a certain degree, and the measurement error is increased, so that the measurement accuracy is reduced. In the test, when the number of steel pins was 12 in the measurement of the "drill method", the measurement error was 8.5%.

Test B

The area of the slope to be measured is 80m²Measuring according to the embodiment 1, in each scanning process, designating a track as a Chinese character 'ji' shaped structure, respectively changing the density of measuring points, and obtaining corresponding measuring errors according to a measuring result verification test; wherein, the density of the measuring points is the total number of the measuring points/to-be-measured slope surface to be measured in one round of scanning processMeasuring the area of the slope surface; the curve between the density of the measurement points and the measurement error is shown in fig. 9.

In the invention, the density of the measuring point is not as high as possible, the density of the measuring point is in the range of 300-350/square meter, and the measuring error is 0.7% -0.9%, namely, the actual water and soil loss is very close to the theoretical water and soil loss. Therefore, the measurement point density is preferably 300 per square meter. When the density of the measuring points is more than 350/square meter, the fluctuation of the measuring result is large because the measuring points of the whole system are too dense.

Test C

For examples 2 to 4, the corresponding measurement errors were obtained according to "test for verification of measurement results", and the measurement errors were measured 5 times at the minimum, and the average values of the measurement errors and the standard deviation results thereof are shown in table 1.

TABLE 1

	Example 2	Example 3	Example 4
				Average value of measurement errors	0.8％	0.9％	0.9％
Standard deviation of	1.92％	6％	9.12％

As can be seen from table 1, in a limited area, the designated locus is a "hex" shaped structure, the average of the measurement errors and the standard deviation thereof are minimal. Thus, the specified trajectory is preferably a "hex" like structure.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.