Digging track calculation method

Abstract

The invention discloses a digging track calculation method, which is applied to a digging tool to dig a pipeline, and comprises the following steps: setting a digging direction and a digging depth, and constructing a parameterized transition curve; planning a digging track according to the parameterized transition curve, including: calculating a deflection angle of a digging tool according to the digging depth and the parameterized transition curve; and controlling the digging tool to dig the pipeline along the set digging direction according to the calculated deflection angle so as to ensure that the digging track of the digging tool is consistent with the parameterized transition curve. According to the method, the parameterized transition curve is constructed according to the digging direction and the digging depth, and the digging track is quantified. And the deflection angle of the digging tool is calculated according to the parameterized transition curve and the digging depth, so that the digging tool is prevented from damaging the pipeline body outside the digging track in the digging process, the digging precision is improved, the digging forming quality is ensured, and a guarantee is provided for subsequent pipeline welding.

Description

Technical Field

[0001] This application relates to the field of pipeline excavation technology, and in particular to a method for calculating excavation trajectory. Background Technology

[0002] In the installation and maintenance of industrial pipeline systems (such as petrochemical, natural gas transmission, and power generation), the butt weld is the most critical connection form connecting pipe sections and forming a pressure-bearing system. Especially in the case of transporting high-temperature, high-pressure, flammable, explosive, or toxic media, the quality of the butt weld is directly related to the safety and reliability of the entire pipeline system.

[0003] When the welding quality of a pipe butt weld fails to meet standard requirements, the original weld must be removed and re-welded. The specific procedure involves first grinding the weld surface smooth, then using a chisel to further excavate and create an opening for subsequent welding. The opening is typically located circumferentially around the pipe, gradually transitioning from the innermost side (bottom) to the outer wall to ensure the quality of the weld and the safety of the pipe structure. Currently, this work is usually done manually by workers using handheld angle grinders. This process is not only time-consuming and labor-intensive, but also lacks precise control, making it difficult to quantify the excavated surface and resulting in an uneven opening surface, making it difficult to control the final weld quality.

[0004] Although drilling robots have now replaced manual handheld angle grinders for weld seam drilling, there is still a lack of high-precision drilling paths to quantify the drilling surface and ensure the forming quality after secondary welding. Summary of the Invention

[0005] This application aims to at least solve one of the aforementioned technical problems existing in the prior art. The purpose of this application is to provide a method for calculating excavation trajectories, in order to address the problem that the lack of excavation surface quantification in the prior art makes it difficult to control the forming quality of the pipeline after excavation.

[0006] To achieve the above objectives, the technical solution adopted in this application is as follows: A method for calculating excavation trajectory, applied to excavation tools for excavating pipelines, includes: Set the excavation direction and depth, and construct a parametric transition curve; Based on the parametric transition curve, the excavation trajectory is planned, including: The yaw angle of the digging tool is calculated based on the digging depth and the parametric transition curve. The calculated yaw angle controls the digging tool to dig along the set digging direction to ensure that the digging trajectory of the digging tool is consistent with the parameterized transition curve.

[0007] According to some embodiments of this application, setting the excavation direction and excavation depth includes: The excavation direction includes a first direction and a second direction, the first direction being the radial direction of the pipe, the second direction being the circumferential direction of the pipe, and the excavation depth being the distance from the outer wall surface to the inner wall surface of the pipe along the first direction.

[0008] According to some embodiments of this application, the construction of the parameterized transition curve includes: A polar coordinate system is established with the center of the cross-section of the pipe as the origin, relating to the pipe radius and angle. The parameterized transition curve is set as a continuous function of the pipe radius and angle; Discrete sampling is performed on the continuous function to obtain several polar coordinate points; By transforming coordinates, several polar coordinate points are mapped to a Cartesian coordinate system with the center of the pipe circle as the origin, thereby forming the parameterized transition curve.

[0009] According to some embodiments of this application, the digging depth is divided into several digging layers, and each digging layer is stacked layer by layer according to a set feed depth. The digging tool determines the movement limit position of the digging tool in the second direction according to the yaw angle corresponding to the current digging layer on each digging layer, and the digging tool reciprocates along the second direction between the movement limit positions.

[0010] According to some embodiments of this application, the calculation of the yaw angle of the digging tool based on the digging depth and the parameterized transition curve includes: The selected excavation tool intersects with the parameterized transition curve at a first position; The digging tool intersects the parameterized transition curve at a first intersection point and a second intersection point at a first position; Determine the first included angle of the first intersection point in the polar coordinate system, and its coordinates in the Cartesian coordinate system; Calculate the coordinates of the center of the digging tool in the Cartesian coordinate system based on the first included angle and the coordinates of the first intersection point. Divide the arc between the first intersection point and the second intersection point into n arc segments according to the arc length step; Calculate the intersection point of each arc segment in the n arc segments with the parameterized transition curve, and determine the second included angle of the intersection point in the polar coordinate system and its coordinates in the Cartesian coordinate system; Construct a reference circle with the current excavation depth of the excavation layer as its radius. Each of the n arc segments intersects the reference circle and the excavation tool, namely the third intersection point and the fourth intersection point. Calculate the coordinates of the third and fourth intersection points in the Cartesian coordinate system, and select the intersection point with the larger value in the X-axis direction. The angle between this intersection point and the line connecting the center of the pipe is the third angle. The yaw angle is calculated based on the first included angle, the second included angle, and the third included angle.

[0011] According to some embodiments of this application, the excavating tool is positioned at a first position, such that one edge of the excavating tool intersects the parametric transition curve at a first intersection point, and the other edge extends beyond the parametric transition curve and enters the pipe body, and the other edge intersects the parametric transition curve at a second intersection point.

[0012] According to some embodiments of this application, the formula for calculating the yaw angle is as follows:

[0013] Where β is the yaw angle; θ is the first included angle; e i The second included angle; m i It is the third included angle.

[0014] According to some embodiments of this application, the yaw angle of the digging tool at each digging layer is calculated, and the movement limit position of the digging tool along the second direction is determined based on the yaw angle. The digging tool reciprocates between the movement limit positions to achieve a smooth transition from the outer diameter to the inner diameter of the pipe.

[0015] According to some embodiments of this application, the formula for calculating the third included angle is:

[0016] Where α is the single-sided angle to be excavated at the bottom of the pipe, and x and y are the x-coordinate and y-coordinate of the third intersection point and the fourth intersection point in the Cartesian coordinate system, respectively, in the coordinates of the larger value in the X-axis direction.

[0017] According to some embodiments of this application, a point S1 is provided on the inner diameter of the pipe, a point E1 is provided on the outer diameter of the pipe, and a point A is provided on the line connecting point S1 and point E1, the slope of the line being k. The coordinates of point A in the polar coordinate system are expressed as follows: R A =kt1 Among them, R A t1 represents the position of point A on the line connecting the two points, and t1 represents the polar angle of point A in the polar coordinate system. The coordinates of point A in the Cartesian coordinate system are then expressed as: X A=kt1*cos(t1) Y A =kt1*sin(t1) X A Let X be the coordinates of point A on the Cartesian coordinate system, and Y be the coordinates of point A on the Cartesian coordinate system. A Let be the Y-coordinate of point A in the Cartesian coordinate system. The beneficial effects of this application are: This application constructs a parametric transition curve based on the excavation direction and depth to quantify the excavation trajectory. Furthermore, it calculates the yaw angle of the excavation tool based on the parametric transition curve and the excavation depth, preventing damage to the pipeline body outside the excavation trajectory during the excavation process, improving excavation accuracy, ensuring the quality of the excavated structure, and providing a guarantee for subsequent pipeline welding.

[0018] Additional aspects and advantages of this application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this application. Attached Figure Description

[0019] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which: Figure 1 This is a flowchart of a method for calculating the excavation trajectory according to this application.

[0020] Figure 2 This is a schematic diagram of the layout of the excavation tools on the pipeline excavation trajectory.

[0021] Figure 3 This is a schematic diagram of the parametric transition curve.

[0022] Figure 4 This is a schematic diagram of the pipe cross-section in polar coordinates.

[0023] Figure 5 This is a diagram showing the ideal state of the excavation tool at the current excavation layer.

[0024] Figure 6 This is a schematic diagram showing how a digging tool damages the pipeline body at the current digging layer.

[0025] Figure 7 This is an enlarged schematic diagram of n arc segments.

[0026] Figure label: 100, Excavation tool; 200, Pipeline; 300, First direction; 400, Second direction; 500, Parametric transition curve. Detailed Implementation

[0027] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application.

[0028] In the description of this application, it should be understood that if directional descriptions are involved, such as up, down, front, back, left, right, etc., indicating the directional or positional relationship based on the directional or positional relationship shown in the accompanying drawings, it is only for the convenience of describing this application and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application.

[0029] In the description of this application, if words such as several, greater than, less than, exceeding, above, below, or within appear, "several" means one or more, "more than" means two or more, "greater than," "less than," "exceeding," etc. are understood to exclude the number itself, and "above," "below," "within," etc. are understood to include the number itself.

[0030] In the description of this application, the use of terms such as "first" and "second" is for the purpose of distinguishing technical features only, and should not be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated or the order of the technical features indicated.

[0031] In the description of this application, unless otherwise expressly defined, terms such as "setup," "installation," and "connection" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this application in conjunction with the specific content of the technical solution.

[0032] Reference Figures 1 to 7 The following are specific embodiments of this application.

[0033] like Figure 1 As shown, this application provides a method for calculating the excavation trajectory, applied to an excavation tool 100 for excavating a pipe 200, including: S100, set the excavation direction and depth, and construct the parameterized transition curve 500.

[0034] Based on the parametric transition curve 500, plan the excavation trajectory, including: S200, calculate the yaw angle of the digging tool 100 based on the digging depth and the parameterized transition curve 500.

[0035] S300: Control the digging tool 100 to dig along the set digging direction according to the calculated yaw angle, so as to ensure that the digging trajectory of the digging tool is consistent with the parameterized transition curve 500.

[0036] Depend on Figure 2 As shown, the excavation direction includes a first direction 300 and a second direction 400. The first direction 300 is the radial direction of the pipe 200, that is, the outer radial direction and inner diameter direction of the pipe 200. The second direction 400 is the circumferential direction of the pipe 200, and the excavation depth is the distance from the outer wall surface to the inner wall surface of the pipe 200 along the first direction 300.

[0037] Depend on Figure 3 and Figure 4 As shown, in some embodiments, the specific steps for constructing the parameterized transition curve 500 are as follows: S110. Establish a polar coordinate system with the center of the 200mm cross-section of the pipe as the origin.

[0038] S120. Set the parameterized transition curve 500 as a continuous function of the pipe radius and angle, and enable a smooth transition from the outer diameter of the pipe 200 to the inner diameter of the pipe 200. S130. Discretely sample the continuous function to obtain several polar coordinate points; S140. Through coordinate transformation, several polar coordinate points are mapped to a Cartesian coordinate system with the pipe center as the origin, thus forming a parameterized transition curve 500. The x and y coordinates of points corresponding to different angles in the polar coordinate equation in the Cartesian coordinate system are calculated, and then these points are connected to form a curve, thus creating the parameterized transition curve. Figure 3 As shown.

[0039] In some embodiments, in S110, the pipe radius is r and the angle is t, and a polar coordinate system about r and t is established accordingly, such as... Figure 4 As shown.

[0040] Let R1 represent the inner diameter of pipe 200 and R2 represent the outer diameter of pipe 200. In order to achieve a smooth transition from the outer diameter of pipe to the inner diameter of pipe during the excavation process, a linear transition method in polar coordinates is adopted to achieve a smooth transition from the outer diameter of pipe to the inner diameter of pipe.

[0041] Specifically, in S120, a point S1 is selected on the inner diameter of the pipe, and a point E1 is selected on the outer diameter of the pipe. A straight line with slope k connects points S1 and E1. Therefore, the straight line with slope k in the polar coordinate system is the parameterized transition curve, which is a continuous function of the pipe radius and angle, expressed as: R=kt The value of k ranges from 1.0 to 2.0. The value of k affects the appearance of the smooth transition of the parameterized transition curve. The appearance is determined empirically based on the diameter of the pipe, the depth of the excavation (which depends on the depth of the welding defect detection) and the angle at which the excavation needs to be carried out. As long as it can meet the process requirements of subsequent repair welding, it is acceptable.

[0042] In S130, suppose there is a point A on the straight line, located on the line connecting points S1 and E1. The coordinates of point A in the polar coordinate system are: R A =kt1 Among them, R A t1 represents the position of point A on the line connecting the two points, and t1 represents the polar angle of point A in the polar coordinate system.

[0043] Establish a Cartesian coordinate system with the center of pipe 200 as the origin. Then, the coordinates of point A in the Cartesian coordinate system are represented as follows: X A =kt1*cos(t1) Y A =kt1*sin(t1) X A Let X be the coordinates of point A on the Cartesian coordinate system, and Y be the coordinates of point A on the Cartesian coordinate system. A Let be the Y-coordinate of point A in the Cartesian coordinate system.

[0044] In some embodiments, the digging depth is divided into several digging layers, and each digging layer is stacked layer by layer according to a set feed depth. The digging tool 100 determines the movement limit position of the digging tool 100 in the second direction according to the yaw angle corresponding to the current digging layer in each digging layer. The digging tool reciprocates between the movement limit positions along the second direction.

[0045] Specifically: the excavation tool 100 is an angle grinder or an excavation robot. The angle grinder or excavation robot uses a grinding wheel to excavate the pipe 200 in layers. When the grinding wheel is excavating, it first sets the feed depth of the current excavation layer along the first direction. On the excavation layer, the grinding wheel reciprocates along the second direction to complete the transverse cutting of the layer. Then, according to the feed depth, it feeds downward along the first direction to the next excavation layer, repeating the reciprocating motion along the second direction, thus grinding layer by layer until the bottom of the parameterized transition curve 500 is reached.

[0046] In some embodiments, the sway angle is the angle at which the digging tool 100 symmetrically deflects to both sides along the second direction 400 on each digging layer, and the movement limit position is the position of the two side boundaries corresponding to the sway angle of the digging tool 100 deflecting to both sides along the second direction 400 on the current digging layer.

[0047] The excavation depth is represented by R. dThis indicates that the feed depth is 0.1 mm.

[0048] according to Figure 5 As shown, combining the parametric transition curve with the pipe cross-section diagram, the parametric transition curve 500 is symmetrically distributed across the pipe's cross-section. When the excavating tool 100 grinds the pipe along the parametric transition curve, the outer contour of the excavating tool 100 interacts with the radius R... d The circle and the parameterized transition curve are tangent at points A and B, respectively. At this point, the digging tool 100 can grind to the digging depth and just touch the parameterized transition curve without interfering with it.

[0049] Where O0 is the center of pipe 200, and points S2 and E2 are the points symmetrical about the center of point S1 and point E1 about the cross-section of pipe 200, respectively.

[0050] O t Let α be the center of the excavation tool 100, β be the set angle of the bottom of the pipe excavation, and β be the sway angle of the excavation tool on one side. S1S2 is the length of the pipe inner diameter excavation, and E1E2 is the length of the pipe outer diameter excavation.

[0051] However, in the actual excavation process, the excavation tool 100 is a circular grinding wheel with a geometric profile of finite dimensions, rather than a theoretical point contact model. Therefore, it is necessary to consider the interference between the excavated pipes 200 and the pipes 200 to avoid excessive grinding during the excavation process.

[0052] according to Figure 6 As shown, the digging tool 100 has interfered with the parametric transition curve. At this point, the intersection of the outer contour of the digging tool 100 and the parametric transition curve is point C, and the corresponding angle is θ. The magnified view of the interference area is shown below. Figure 7 As shown.

[0053] To ensure that the excavation tool 100 does not interfere with the pipeline outside the parameterized transition curve, thereby damaging the pipeline body, it is necessary to calculate the yaw angle of the excavation tool 100 on the current excavation layer.

[0054] In some embodiments, S200, calculating the yaw angle of the digging tool 100 based on the digging depth and the parameterized transition curve specifically includes the following steps: S210, Select the first position where the digging tool 100 intersects with the parametric transition curve: like Figure 6 As shown, the first position is the location where the digging tool 100 interferes with the parametric transition curve. The digging tool 100 is set to intersect the parametric transition curve at the first intersection point and the second intersection point at the first position, respectively. Figure 6 Points C and D in the diagram.

[0055] S210. Determine the first included angle of the first intersection point in the polar coordinate system and its coordinates in the Cartesian coordinate system.

[0056] Specifically, the formula for calculating the first included angle is: θ=R d / k The coordinates of the first intersection point in the Cartesian coordinate system are: D x =R d *cos(θ) D y =R d *sin(θ) D x Let D be the x-coordinate of point D in the Cartesian coordinate system. y Let be the Y-coordinate of point D in the Cartesian coordinate system.

[0057] S220. Calculate the coordinates of the center of the digging tool 100 in the Cartesian coordinate system based on the first included angle and the coordinates of the first intersection point: R t Let R be the radius of the digging tool, and R be the distance between the center of the digging tool and the center of the pipe. d +R t Then O t The formula for calculating coordinates in the Cartesian coordinate system is as follows: O tx =(R d +R t )*cos(θ) O ty =(R d +R t sin(θ) S230. Divide the arc between the first and second intersection points into n arc segments according to the arc length step. Based on... Figure 7 It can be seen that, given a step size of d, along the first direction, from the current digging depth R... d To outer diameter R t The distance, that is, the interference area between the excavation tool and the parameterized transition curve, is defined by n arcs. Each arc represents the length of interference between the excavation tool 100 and the pipe 200 on this arc. This length is determined by the rotation angle of the excavation tool 100. By analyzing the interference angles corresponding to each arc, the maximum rotation angle at which the excavation tool and the parameterized transition curve do not interfere with each other at the current excavation depth can be determined.

[0058] S240. Calculate the intersection point of each arc segment and the parameterized transition curve in the n arc segments, and determine the second included angle of the intersection point in the polar coordinate system and its coordinates in the Cartesian coordinate system.

[0059] The formula for calculating the second included angle is: e i =R dn / k Among them, e i R is the second included angle. dn This represents the current excavation depth of the excavated layer.

[0060] S250. Construct a reference circle with the current excavation depth as its radius, i.e., R. d A circle. Each of the n arc segments intersects R. d The circle and the outer contour of the digging tool 100 intersect at points, namely the third and fourth intersections, by... Figure 7 As shown, the third intersection point is points E and F.

[0061] S260. Calculate the coordinates of the third and fourth intersection points in the Cartesian coordinate system, and select the intersection point with the larger value in the X-axis direction. The angle between this intersection point and the center of the pipe is the third angle.

[0062] The specific calculation steps are as follows: The center of a reference circle with radius r1 is set to (x1, y1) in a Cartesian coordinate system, with the current excavation depth as the reference circle.

[0063] The center of the digging tool 100 is located at (x2, y2) in a Cartesian coordinate system, and its radius is r2. Therefore,

[0064] The solution expression is:

[0065] x and y represent the coordinates of the third and fourth intersection points in the Cartesian coordinate system.

[0066] Among these, the intersection point with the larger value in the X-axis direction between the third and fourth intersection points is selected, and the angle between this intersection point and the center of the pipe 200 is calculated as the third angle. The third angle is represented by m. i express.

[0067] The formula for calculating the third included angle is:

[0068] Where α is the single-sided angle to be excavated at the bottom of the pipe, and x and y are the x and y coordinates of the third and fourth intersection points in the Cartesian coordinate system, respectively, in the direction of the X-axis where the x-coordinate is larger.

[0069] S270. Calculate the sway angle based on the first included angle, the second included angle, and the third included angle.

[0070] The formula for calculating the yaw angle is:

[0071] Where β is the yaw angle; θ is the first included angle; e i The second included angle; m i The included angle is the third angle; Max is the maximum value; Abs is the absolute value function. S300. Based on the calculated yaw angle, control the excavation tool 100 to excavate the pipeline 200 along the excavation direction to ensure that the excavation trajectory of the excavation tool 100 is consistent with the parameterized transition curve.

[0072] Specifically, the sway angle of the digging tool 100 on each digging layer is calculated layer by layer by digging depth. The movement limit position is determined based on the sway angle. The grinding trajectory of the digging tool 100 can be controlled based on the movement limit position, thereby achieving a smooth transition in digging.

[0073] The excavation trajectory calculation method of this application is applicable to excavation of pipe surfaces after weld grinding and smoothing or to completely smooth pipe surfaces.

[0074] This application discloses a method for calculating a digging trajectory. Based on the digging direction and depth, a parametric transition curve is constructed to quantify the digging trajectory. The method then calculates the yaw angle of the digging tool based on the parametric transition curve and the digging depth. This prevents damage to the pipeline body outside the digging trajectory during the digging process, improves digging accuracy, ensures the quality of the excavated material, and provides a guarantee for subsequent pipeline welding.

[0075] In the description of this specification, the use of terms such as "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," and "some examples" indicates that the specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. 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.

[0076] Although embodiments of this application 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 this application, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for calculating excavation trajectory, characterized in that, Tools used for digging pipes include: Set the excavation direction and depth, and construct a parametric transition curve; Based on the parametric transition curve, the excavation trajectory is planned, including: The yaw angle of the digging tool is calculated based on the digging depth and the parametric transition curve. The calculated yaw angle controls the digging tool to dig along the set digging direction to ensure that the digging trajectory of the digging tool is consistent with the parameterized transition curve.

2. The method for calculating excavation trajectory according to claim 1, characterized in that, The setting of the excavation direction and excavation depth includes: The excavation direction includes a first direction and a second direction, the first direction being the radial direction of the pipe, the second direction being the circumferential direction of the pipe, and the excavation depth being the distance from the outer wall surface to the inner wall surface of the pipe along the first direction.

3. The method for calculating excavation trajectory according to claim 1, characterized in that, The construction of the parameterized transition curve includes: A polar coordinate system is established with the center of the cross-section of the pipe as the origin, relating to the pipe radius and angle. The parameterized transition curve is set as a continuous function of the pipe radius and angle; Discrete sampling is performed on the continuous function to obtain several polar coordinate points; By transforming coordinates, several polar coordinate points are mapped to a Cartesian coordinate system with the center of the pipe circle as the origin, thereby forming the parameterized transition curve.

4. The method for calculating excavation trajectory according to claim 2, characterized in that, The digging depth is divided into several digging layers. Each digging layer is stacked layer by layer according to a set feed depth. The digging tool determines the movement limit position of the digging tool in the second direction according to the yaw angle corresponding to the current digging layer on each digging layer. The digging tool reciprocates along the second direction between the movement limit positions.

5. The method for calculating excavation trajectory according to claim 4, characterized in that, The calculation of the yaw angle of the digging tool based on the digging depth and the parametric transition curve includes: The selected excavation tool intersects with the parameterized transition curve at a first position; The digging tool intersects the parameterized transition curve at a first intersection point and a second intersection point at a first position; Determine the first included angle of the first intersection point in the polar coordinate system, and its coordinates in the Cartesian coordinate system; Calculate the coordinates of the center of the digging tool in the Cartesian coordinate system based on the first included angle and the coordinates of the first intersection point. Divide the arc between the first intersection point and the second intersection point into n arc segments according to the arc length step; Calculate the intersection point of each arc segment in the n arc segments with the parameterized transition curve, and determine the second included angle of the intersection point in the polar coordinate system and its coordinates in the Cartesian coordinate system; Construct a reference circle with the current excavation depth of the excavation layer as its radius. Each of the n arc segments intersects the reference circle and the excavation tool, namely the third intersection point and the fourth intersection point. Calculate the coordinates of the third and fourth intersection points in the Cartesian coordinate system, and select the intersection point with the larger value in the X-axis direction. The angle between this intersection point and the line connecting the center of the pipe is the third angle. The yaw angle is calculated based on the first included angle, the second included angle, and the third included angle.

6. The method for calculating excavation trajectory according to claim 5, characterized in that, The excavating tool is positioned at a first position, such that one edge of the excavating tool intersects the parametric transition curve at a first intersection point, and the other edge extends beyond the parametric transition curve and enters the pipe body, and the other edge intersects the parametric transition curve at a second intersection point.

7. The method for calculating excavation trajectory according to claim 5, characterized in that, The formula for calculating the yaw angle is: Where β is the yaw angle; θ is the first included angle; e i The second included angle; m i It is the third included angle.

8. The method for calculating excavation trajectory according to claim 7, characterized in that, The yaw angle of the digging tool at each digging layer is calculated, and the movement limit position of the digging tool along the second direction is determined based on the yaw angle. The digging tool reciprocates between the movement limit positions to achieve a smooth transition from the outer diameter to the inner diameter of the pipe.

9. The method for calculating excavation trajectory according to claim 7, characterized in that, The formula for calculating the third included angle is: Where α is the single-sided angle to be excavated at the bottom of the pipe, and x and y are the x-coordinate and y-coordinate of the third intersection point and the fourth intersection point in the Cartesian coordinate system, respectively, in the coordinates of the larger value in the X-axis direction.

10. The method for calculating excavation trajectory according to claim 3, characterized in that, Point S1 is located on the inner diameter of the pipe, and point E1 is located on the outer diameter of the pipe. Point A is located on the line connecting point S1 and point E1, and the slope of the line is k. The coordinates of point A in the polar coordinate system are expressed as follows: R A =kt1 Among them, R A t1 represents the position of point A on the line connecting the two points, and t1 represents the polar angle of point A in the polar coordinate system. The coordinates of point A in the Cartesian coordinate system are then expressed as: X A =kt1*cos(t1) AND A =kt1*sin(t1) X A Let X be the coordinates of point A on the Cartesian coordinate system, and Y be the coordinates of point A on the Cartesian coordinate system. A Let be the Y-coordinate of point A in the Cartesian coordinate system.

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