Pipeline layout planning method and system considering bending curvature

Abstract

The invention belongs to the field of pipeline design planning, and particularly relates to a pipeline layout planning method and system considering a bending curvature, and the method comprises the following steps: S1, determining an expansion path of a three-dimensional laying environment based on an undirected graph, and completing the two-dimensional equivalent processing of a wall-attached laying environment through homogeneous transformation; s2, in the two-dimensional plane, performing pipeline path planning by adopting a Dubins curve generation method with multiple passing points; s3, adopting a pipeline forward layout planning method to realize pipeline layout planning considering the bending curvature in a plane; s4, realizing backtracking of a pipeline path from a two-dimensional space to a three-dimensional space through homogeneous transformation; and S5, completing local post-processing of the three-dimensional space pipeline path by adopting a three-dimensional Dubins method. According to the method, the bending curvature constraint and the start-stop direction constraint can be considered at the same time in the planning stage, the laying performance and the length prediction precision of the path are improved, and the calculation efficiency is high.

Description

Technical Field

[0001] This invention belongs to the field of pipeline design and planning, specifically a pipeline layout planning method and system that takes into account bending curvature. Background Technology

[0002] Pipeline layout planning has wide applications in engineering fields such as machinery, aviation, shipbuilding, and construction. Its goal is to plan an optimal or feasible laying path for pipelines (such as cables, hydraulic pipes, and optical fibers) from their starting point to their destination under complex spatial constraints. Traditional pipeline layout methods largely rely on classic path planning algorithms, such as the A* algorithm based on grid search, the Rapid Expanding Random Tree (RRT) algorithm, and its variants. These algorithms can generate a connected path that avoids obstacles in two-dimensional or three-dimensional space, essentially solving the "path existence" problem. However, these algorithms cannot consider pipeline bending curvature constraints and cable start-end direction vector constraints, leading to significant discrepancies between the theoretical path generated and the actual laying path. Furthermore, pipeline path planning in three-dimensional space typically involves high computational costs and makes it difficult to accurately control pipeline length during the path generation stage, which is detrimental to material budgeting and engineering implementation.

[0003] Therefore, there is an urgent need for a forward layout planning method that can consider bending curvature constraints and pipeline start and end point direction vectors during the path planning stage, has high computational efficiency, and can accurately plan the required length of pipelines. This would enable the precise customization of pipeline materials during the planning stage and ensure that the laying path closely matches the planned path. Summary of the Invention

[0004] The purpose of this invention is to provide a pipeline forward layout planning method and system that takes into account the bending curvature, thereby solving the problem that existing pipeline path planning technologies ignore the direction vectors of the pipeline's start and end points and the pipeline's bending curvature, resulting in discrepancies between the actual laying results and the planned path.

[0005] The technical solution adopted by the present invention to achieve the above objectives is: a pipeline layout planning method considering bending curvature, comprising the following steps:

[0006] S1: The development path of the three-dimensional laying environment is determined based on the undirected graph. The wall-mounted laying environment is processed into two-dimensional equivalent through homogeneous transformation. The homogeneous transformation matrix realizes coordinate mapping based on Denavit-Hartenberg parameters.

[0007] S2: In the two-dimensional plane, the Dubins curve generation method with multiple waypoints is used for pipeline path planning. The optimization variable is the set of waypoint direction angles, and the total arc length of the path is minimized by the particle swarm optimization algorithm.

[0008] S3: Employs a forward pipeline layout planning method to achieve in-plane pipeline layout planning that takes into account bending curvature, including obstacle sorting, interference detection and detour path generation;

[0009] S4: Through homogeneous transformation, the pipeline path can be traced back from two-dimensional space to three-dimensional space;

[0010] S5: The three-dimensional Dubins method is used to complete the local post-processing of the three-dimensional spatial pipeline path, and to handle the working conditions where the direction vectors of the pipeline start and end points are not in the laying plane and the curvature constraint problem at the wall fold.

[0011] The specific approach for determining the three-dimensional laying environment based on undirected graphs is as follows:

[0012] S1-1: The undirected graph spanning tree method is used to expand the wiring space in a plane. The boundary surface of the three-dimensional wiring space is abstracted as the vertices of the undirected graph. The adjacency matrix digitally represents the adjacency relationship of the surface. The effective surface traversal sequence is enumerated by graph theory algorithm.

[0013] S1-2: Based on the traversal surface sequence, the coordinate transformation is defined using the Denavit-Hartenberg parameters, and the homogeneous transformation matrix of adjacent reference frames is:

[0014] ;

[0015] Among them, the linkage angle Indicates circling Shaft from Turn to axis The included angle; the length of the connecting rod Indicates along Shaft from Move to Distance; joint offset for and Distance between common perpendiculars; joint angle From arrive The included angle;

[0016] S1-3: Multiply the transformations of each link to obtain the transformation matrix of the {k} coordinate system relative to the {0} coordinate system:

[0017] ;

[0018] S1-4: For a point in the k-coordinate system Its coordinates in the {0} coordinate system It can be represented as:

[0019] ;

[0020] S1-5: When the 3D environment is unfolded in a plane according to the given wiring unfolding path, the common edge between two adjacent faces is equivalent to the linkage axis. Each face is established as its own reference system, and each face is equivalent to a link. According to the DH parameter rules, the reference system corresponding to each face is established. The process of unfolding each face to the same plane is achieved by adjusting the θ angle between the links.

[0021] In step S2, the pipeline path planning is performed using the Dubins curve generation method with multiple waypoints, specifically as follows:

[0022] S2-1: Model the pipeline path as a composite path, introducing a direction angle variable for each path point, and defining path points as vectors. ;

[0023] S2-2: To ensure the path meets the minimum bending radius constraint, the optimization objective is defined as:

[0024] );

[0025] in, This indicates the calculation of the length of the shortest Dubins curve connecting two vector points. and These represent fixed start and end points, respectively. Ensure the path meets the minimum bending radius constraint of the cable, i.e., the actual radius of curvature r ≥ r for all Dubins curve segments. min At the same time, optimize the variables to satisfy θ i ∈[0, 2π];

[0026] S2-3: The optimization problem is solved using the particle swarm optimization algorithm, with inertia weights. An adaptive update strategy is used, namely:

[0027] ;

[0028] Where ω is the inertia weight, t is the current iteration number, and maxgen is the maximum iteration number;

[0029] S2-4: Obtain the optimal solution of the direction angle of the waypoint with the shortest total path length through iterative calculation, thereby generating a globally optimal smooth pipeline path that satisfies curvature constraints and passes through all specified waypoints.

[0030] In step S3, the pipeline forward layout planning method includes the following steps:

[0031] Step S3-1: Generate the initial Dubins path based on the position and direction vector of the pipeline's start and end points;

[0032] Step S3-2: Based on the distance from the obstacle center to the end point of the path. Distance to the starting point The difference Sort the obstacles in descending order of their values;

[0033] Step S3-3: Perform interference detection between the current path and obstacles in the sorted order; if interference occurs, select detour points and update the path using the pipeline path planning method with Dubins curve generation method with multiple detour points;

[0034] Step S3-4: Try to remove the added waypoints in a backtracking manner, generate a temporary path and verify whether it interferes with the corresponding obstacle; if there is no interference, delete the waypoint and update the path; if there is interference, keep it.

[0035] Step S3-5: Record the feasible paths without redundant waypoints and their detour direction selection sequence;

[0036] Step S3-6: Use a binary tree to traverse all possible detour direction selection sequences, repeat steps S3-3 to S3-5, and finally select the shortest path as the optimal solution from all feasible paths.

[0037] In step S3-3, the interference detection specifically includes the following steps:

[0038] Step a. Decompose the generated multi-segment Dubins path into several straight line segments and circular arc segments as the discrimination set, and decompose the convex bounding contour of the obstacle into several line segments as the discrimination object set;

[0039] Step b. For line segment interference detection, first calculate the projection range of the line segment on the coordinate axis for rapid rejection; let the coordinates of the line segment endpoints be... , Its projected boundary is:

[0040]

[0041] in, , , , They represent line segments respectively. Maximum and minimum projected values ​​on the x-axis and y-axis; and For line segments The x-coordinates of endpoint 1 and endpoint 2, and These are the y-coordinates of endpoint 1 and endpoint 2;

[0042] If two line segments satisfy one of the following conditions, they are determined to be non-intersecting; otherwise, proceed to step c for the straddle experiment:

[0043]

[0044] Step c. The straddle experiment is determined by calculating the cross product of vectors; for line segments AB and CD, a scalar function is defined:

[0045]

[0046] Two line segments intersect if and only if both of the following conditions are met:

[0047] ;

[0048] Step d. For interference detection between the circular arc segment and the polygonal edge, calculate the center O(O) of the circle. x O y The minimum distance d to each side of the polygon min If d min If r > 0, there is no interference; otherwise, solve for the intersection of the edge parametric equation and the circle. The edge parametric equation is:

[0049]

[0050] Among them, ( , ) represents the coordinates of the starting point of the edge segment, Δx and Δy represent the coordinate difference between the two endpoints of the edge, and t is a parameter with a value range of [0,1].

[0051] Substitute into the circle equation The quadratic equation is obtained. ,in:

[0052]

[0053] If there are real roots Then calculate the intersection point Q and its angle relative to the center of the circle. ,like Located in the arc corner region [ , [Interference is determined within the scope of the law;]

[0054] Step e: When interference is detected, select a detour point based on the vertex set V of the convex polygon; let the current nearest path point be Me, and for a vertex, its adjacent vertices are: A=V i-1 and B=V i+1 Then the following condition is met: The vertex is the left tangent point L(M) e );satisfy: The vertex is the right tangent point R(Me); generate a sequence of path points for left or right detours based on the left and right tangent points.

[0055] Step S5 includes:

[0056] Step S5-1: For cases where the direction vectors of the start and end points are not in the laying plane, the path is planned based on their projection in the plane. Then, a reference circle is drawn with the point as the center and 3r as the radius, which intersects the plane path at the transition point. Finally, a three-dimensional Dubins path segment is generated from the actual start and end points to the transition point.

[0057] Step S5-2: For the case where the wall fold edge bends outward and cannot be attached to the wall, in the wall surface on both sides of the fold edge, draw reference circles with the intersection point of the pipeline and the fold edge as the center and 3r as the radius, and intersect with the path in the corresponding wall surface at the transition point, and then generate a three-dimensional Dubins path segment between the two points.

[0058] Step S5-3: The method for generating the three-dimensional Dubins path segment is as follows:

[0059] Let the starting point P0 be the direction vector d̂0, and the ending point P1 be the direction vector d̂1. The path consists of the starting arc S0 and the straight line segment. It is formed by the terminating arc S1; by solving the parameters Determine the coordinates of connecting points E and F:

[0060] ;

[0061] ;

[0062] Where α is the rotation angle of arc S0 about axis d̂0, β is the rotation angle of arc S1 about axis d̂1, γ is the radian of arc S0, and δ is the radian of arc S1; vector The local right-handed orthonormal unit basis is formed at point Pᵢ;

[0063] With the goal of minimizing the tangential continuity error, a fitness function is established and its parameters are optimized. for:

[0064]

[0065] in, For arc The unit tangent vector at point E, For arc The unit tangent vector at point F, Let F be the normalized direction vector pointing from E to F;

[0066] Step S5-4: Solve the problem using the particle swarm optimization algorithm. Minimum parameter This determines the coordinates of points E and F, and generates a three-dimensional Dubins path segment.

[0067] In step S5-3, the vector Constructed in the following way:

[0068] The vector for:

[0069]

[0070] The vector for:

[0071]

[0072] The vector for:

[0073]

[0074] Wherein, auxiliary vector according to The absolute value of the dot product with the reference vector is chosen as follows:

[0075] .

[0076] A system for pipeline layout planning that considers bending curvature includes:

[0077] The environment modeling and unfolding module is used to perform topological modeling of the wall-mounted surfaces in the 3D pipeline laying environment, construct a graph model based on the surface adjacency relationship, and unfold all related surfaces to the same 2D planning plane through coordinate transformation based on the selected surface traversal sequence.

[0078] The two-dimensional curvature constraint path planning module is used to generate a smooth two-dimensional path that satisfies curvature constraints and is collision-free within the two-dimensional planning plane, using the starting and ending points and directions of the pipeline and the minimum bending radius as constraints, combined with obstacle information in the plane, by optimizing the direction angle of the path points.

[0079] The 3D path reconstruction and local optimization module is used to map the 2D path back to 3D space through inverse coordinate transformation to form a preliminary path. For local sections that do not meet the wall-hugging or curvature constraints due to non-coplanar direction vectors or abrupt changes in wall geometry, the module replaces and smoothly connects them with straight line segments and arc segments in 3D space to generate the final 3D laying path.

[0080] The present invention has the following beneficial effects and advantages:

[0081] 1. This invention combines the Particle Swarm Optimization (PSO) algorithm with multi-segment Dubins curves for pipeline routing. Compared with existing path planning methods based on grid search and sampling methods, its planned path can highly overlap with the actual laying path in the project, and the estimated required pipeline length is more accurate.

[0082] 2. The forward layout algorithm used in this invention first generates an initial pipeline path, and then adds discrete obstacles one by one within the cabling environment. Compared with traditional cable layout planning methods, this method requires less computation and can solve the pipeline layout path problem more quickly.

[0083] 3. This invention significantly reduces the dimensionality and computational complexity of the problem by mapping the complex three-dimensional wall-mounted laying environment to a two-dimensional plane for path planning. Within the two-dimensional plane, the modeling, representation, and optimization of direction vectors and curvature constraints are more intuitive and efficient, enabling the algorithm to significantly improve computational speed while ensuring planning accuracy. This makes it more suitable for engineering design scenarios or iterative optimization processes that require real-time performance or fast response.

[0084] 4. This invention provides a complete technical process from 3D environment processing and 2D path planning to 3D path generation and post-processing, forming a systematic pipeline layout planning solution. This method not only focuses on the geometric feasibility of the path but also comprehensively solves multiple practical engineering problems such as wall-mounted laying, curvature constraints, start and end direction constraints, obstacle avoidance, and length control through forward layout strategies and local post-processing mechanisms, enhancing the overall integrity, reliability, and engineering practical value of the planning results. Attached Figure Description

[0085] Figure 1 This is a design flowchart of the pipeline forward layout planning of the present invention;

[0086] Figure 2 This is a schematic diagram illustrating the geometric meaning of the analytical solution obtained by the three-dimensional Dubins path segment generation method in this invention. Detailed Implementation

[0087] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0088] Example:

[0089] like Figure 1 As shown, a pipeline layout planning method considering bending curvature specifically includes the following steps:

[0090] S1: Determine the three-dimensional laying environment development path based on the undirected graph, and complete the two-dimensional equivalent processing of the wall-mounted laying environment through homogeneous transformation;

[0091] A1: An undirected graph spanning tree method is used to unfold the routing space in a plane to aid path planning. The boundary surfaces of the 3D routing space are abstracted as an undirected graph G=<V, E> Let V be a set of vertices, where each vertex represents a boundary surface. If two boundary surfaces are adjacent in 3D space, an edge is established between their corresponding vertices in the undirected graph, forming an edge set E. This adjacency relationship is digitally represented by an adjacency matrix A, where A(i,j)=1 indicates that surfaces i and j are adjacent, and A(i,j)=0 indicates that they are not adjacent. Based on the undirected graph, a graph theory algorithm is used to enumerate all valid surface traversal sequences from the starting surface to the target surface. Among all valid surface traversal sequences, the sequence with the fewest traversed surfaces is selected as the target expansion path.

[0092] A2: Based on the traversal sequence, a coordinate transformation method based on Denavit-Hartenberg parameters is used to unfold the three-dimensional wiring space into a two-dimensional plane. The Denavit-Hartenberg parameters are expressed through four parameters. The connection relationship between the coordinate system {i-1} fixed on link i-1 and the coordinate system {i} fixed on link i is defined. The link rotation angle is also defined. Indicates circling Shaft from Turn to axis The included angle; the length of the connecting rod Indicates along Shaft from Move to Distance; joint offset for and Distance between common perpendiculars; joint angle From arrive The included angle.

[0093] The homogeneous transformation matrix of adjacent reference frames is:

[0094] (1)

[0095] Multiplying the transformations of each link together, we obtain the transformation matrix of the {k} coordinate system relative to the {0} coordinate system:

[0096] (2)

[0097] For a point in the k-coordinate system Its coordinates in the {0} coordinate system It can be represented as:

[0098] (3)

[0099] When a 3D environment is unfolded in a plane according to a given wiring unfolding path, the common edge between two adjacent faces is equivalent to a link and a pivot. Each face is established as its own reference system, and each face is equivalent to a link. According to the DH parameter rules, the reference system corresponding to each face is established. The process of unfolding each face to the same plane can be achieved by adjusting the θ angle between the links.

[0100] S2: In the two-dimensional plane, the Dubins curve generation method with multiple path points is used for pipeline path planning;

[0101] B1: The pipeline path is modeled as a composite path consisting of n+1 Dubins curves connected end to end, defined by a starting point, an ending point, and n fixed coordinate transit points in between. At each transit point Pi (xi, yi), a direction angle variable θi to be optimized is introduced, thus defining the path point as a vector form Pi(xi, yi, θi) containing position and direction.

[0102] B2: The optimization variable for this method is the set of orientation angles of all passing points, i.e. The optimization objective is to minimize the total arc length of the entire composite path.

[0103] (4)

[0104] in, This indicates the calculation of the length of the shortest Dubins curve connecting two vector points. and These represent fixed start and end points, respectively. Ensure the path meets the minimum bending radius constraint of the cable, i.e., the actual radius of curvature r ≥ r for all Dubins curve segments. min At the same time, optimize the variables to satisfy θ i ∈[0, 2π].

[0105] B3: The Particle Swarm Optimization (PSO) algorithm is used to solve the above high-dimensional non-convex optimization problem. Through information sharing and cooperation among particles, the optimal combination of orientation angles is searched in parallel. Specifically, this includes: initializing the particle swarm, where each particle's position represents a set of candidate orientation angle solutions for a path; evaluating the fitness of each particle according to the objective function; iteratively updating the particle state according to the velocity and position update formula based on the individual's historical best solution and the swarm's global best solution; and balancing the global exploration and local exploitation capabilities of the algorithm using an adaptive weight strategy, with the update formula being:

[0106] (5)

[0107] Where ω is the inertia weight, t is the current iteration number, and maxgen is the maximum iteration number.

[0108] The optimal solution of the direction angle of the waypoint with the shortest total path length is obtained by iterative calculation, thereby generating a globally optimal smooth pipeline path that satisfies curvature constraints and passes through all specified waypoints.

[0109] S3: Employ the forward pipeline layout planning method to achieve in-plane pipeline layout planning that takes into account bending curvature;

[0110] C1: Generate a Dubins path based on the location and direction vector information of the pipeline's start and end points, which serves as the initial path for forward layout planning.

[0111] C2: Sort the obstacles according to their planar coordinates between the start and end points of the path planning. The specific sorting coefficients are as follows:

[0112] (6)

[0113] in, This indicates the distance from the center of the obstacle material to the end point of the pipeline path. This represents the distance from the center of the obstacle material to the starting point of the pipeline path, based on a coefficient. The values ​​are sorted in descending order for the obstacles.

[0114] C3: Sort by obstacles and perform interference detection on the current path and obstacles in turn. If interference occurs, select a detour point and update the detour path using the method described in S2.

[0115] D1: Decompose the multi-segment Dubins path generated by step S2 into several straight line segments and arc segments as the discrimination set, and decompose the convex bounding contour of the obstacle into several line segments as the discrimination object set.

[0116] D2: When determining whether a line segment interferes with an obstacle, the bounding box test method is first used to quickly eliminate obviously non-intersecting line segment pairs, thereby reducing the computational load. If the orthogonal projections of two line segments on the x-axis and y-axis do not overlap, then these two line segments cannot intersect; otherwise, further geometric verification is required. The projection of a line segment can be calculated as follows:

[0117] (7)

[0118] in, , , , They represent line segments respectively. Maximum and minimum projected values ​​on the x-axis and y-axis; and For line segments The x-coordinates of endpoint 1 and endpoint 2, and These are the y-coordinates of endpoint 1 and endpoint 2.

[0119] Based on the above calculations, the line segments can be determined to be non-intersecting if any one of the following conditions is met. If none of the conditions are met, the straddle experiment will continue.

[0120] (8)

[0121] D3: Cross-tabulation experiment to determine the positional relationship of the endpoints of a line segment using the cross product of vectors. In a two-dimensional plane, given two line segments:

[0122] Line segment AB: endpoints

[0123] Line segment CD: endpoint

[0124] vector and The cross product is a scalar, defined as:

[0125] (9)

[0126] For line segments AB and CD, geometric relations show that if points C and D are located on opposite sides of the line containing line segment AB, then... .

[0127] Therefore, two line segments intersect if and only if the following two conditions are met simultaneously:

[0128] (10)

[0129] D4: When determining whether the arc segment interferes with the sides of the obstacle, first calculate the minimum distance d from the center of the arc to each side of the polygonal obstacle. min If d min If d > r (where r is the radius of the arc), then no interference occurs; if d min If the value is less than or equal to r, further checks are needed on the intersections of the arc and each side of the polygon. For each side segment of the obstacle, calculate the intersection of the circle and the line segment. If the intersection point is located on the side segment, determine its angular position θ relative to the center O of the arc, and compare this angle with the angular range of the arc to ultimately determine whether there is interference. The specific calculation process is as follows:

[0130] Let the arc start from the center point O (O x O yThe polygonal obstacle consists of a vertex set {V0, V1, …, V}, a radius r, a starting angle θ1, and a ending angle θ2. n} indicates that edge E i =(V i V i+1 ), where V n+1 =V0. The intersection point of the edge and the circle can be derived through parametric equations:

[0131] (11)

[0132] Where (x1, y1) are the coordinates of the starting point of the edge segment, Δx and Δy represent the coordinate difference between the two endpoints of the edge, and t is a parameter with a value range of [0,1].

[0133] Substitute the parametric equation into the circle equation:

[0134] (12)

[0135] We can obtain the quadratic equation:

[0136] (13)

[0137] The coefficients are:

[0138] (14)

[0139] When a real root t∈[0,1] exists, the coordinates of the intersection point can be calculated as follows:

[0140] (15)

[0141] This allows us to determine the angular position of the intersection point Q relative to the center O of the circle:

[0142] (16)

[0143] The validity of the intersection point is determined according to the following rules. If the rules are satisfied, it proves that α is located within the arc angle domain.

[0144] (17)

[0145] D5: When interference between the current path segment and a polygonal obstacle has been determined, the new waypoint selection method is as follows: Let V represent the set of vertices of the convex polygonal obstacle sorted counterclockwise. For any vertex V... i Let A = V be the adjacent vertex of ∈V. i-1 and B=V i+1 Let Me be the shortest path point from the starting point of the path to the interference position. Based on the properties of convex polygons, the left and right tangent points on the obstacle polygon can be determined.

[0146] From Me to the left tangent point L(M) of the polygon e This can be determined based on the following conditions:

[0147] (18)

[0148] The right tangent point R(Me) from Me to the polygon can be determined by the following condition:

[0149] (19)

[0150] To avoid the obstacle and determine the waypoints, we can draw an analogy to the case where the two endpoints S and T of the known Dubins curve are both located outside the obstacle. Using the aforementioned method of left and right tangency points, the tangency points L(S), R(S), L(T), and R(T) corresponding to points S and T can be easily obtained. Therefore, there are usually two obstacle avoidance paths on the plane: a left avoidance path and a right avoidance path. When avoiding the obstacle to the left, the path passes through the point sequence S→L(S)→R(T)→T; when avoiding the obstacle to the right, the path passes through the point sequence S→R(S)→L(T)→T. If L(S)=R(T) or R(S)=L(T), the left and right tangency points may coincide, and the path degenerates into a form containing only a single waypoint.

[0151] C4: Attempt to remove previously added waypoints using a backtracking approach, and generate corresponding temporary discrimination paths using the method described in S2. Then, use the interference detection method described in C3 to verify whether the temporary discrimination paths interfere with the obstacles where the deleted waypoints are located. If no interference occurs, delete the waypoint and assign the temporary discrimination path to the current path, then return to step C3; if interference occurs, it proves that the previous waypoints were not redundant.

[0152] C5: Record the path that has been proven to have no redundant waypoints through step C4 as a feasible path, and record the sequence of detour direction choices (left detour or right detour) made by the feasible path each time it detours around an obstacle.

[0153] C6: Use the binary tree method to update the detour selection sequence, and then return to step C3; if all detour selection sequences on the binary tree have been traversed, select the shortest path as the optimal solution from the list of feasible solutions.

[0154] S4. Through homogeneous transformation, the pipeline path is traced back from two-dimensional space to three-dimensional space. The homogeneous transformation matrix used for traversal is the inverse of the homogeneous transformation matrix described in A2.

[0155] S5: The three-dimensional Dubins method is used to complete the local post-processing of the three-dimensional spatial pipeline path. Specifically, this includes the case where the direction vector of the pipeline's start and end points is not in the laying plane, and the local area where the wall cannot be attached to the wall due to the bending curvature factor at the wall fold.

[0156] E1: For cases where the pipeline start and end points themselves or the direction vectors of the start and end points are not in the laying plane, first use the point and the projection of the direction vector of the point in the laying plane as the initial point and the initial direction vector, and plan the laying path in the plane according to the S3 method. Then, with the initial point as the center and 3r as the radius (r is the constraint curvature radius), draw a reference circle and intersect the laying path at the transition point. The direction vector of the transition point is the tangent vector of the laying path at this point. Finally, generate a three-dimensional Dubins path segment from the starting point to the transition point.

[0157] E2: For local areas where pipelines cannot be laid close to the wall due to curvature limitations caused by bending outwards along the folded edge of the wall, the pipeline path on the wall before the folded edge remains unchanged. The intersection point of the folded edge and the pipeline is taken as the starting point of the local processing path. The direction vector of the starting point is the same as the original pipeline direction vector at this point. Then, with the initial point as the center, a reference circle is drawn with a radius of 3r (r is the constraint curvature radius) in the wall after the folded edge and intersects the pipeline wall path in the wall after the fold at the transition point. The direction vector of the transition point is the tangent vector of the laying path at this point. Finally, a three-dimensional Dubins path segment is generated from the starting point to the transition point.

[0158] F1: As Figure 2 As shown, let P0 be the starting point and P1 be the ending point of the three-dimensional Dubins path segment involved in E1 and E2, with corresponding direction vectors d̂0 and d̂1 respectively. Let the three-dimensional Dubins path segment consist of the starting circular arc S0 and the straight line segment... It is formed by the arc S1 at the end, and the arc S0 starts at point P0 and ends at point E. The straight line segment Starting at point E and ending at point F, arc S1 starts at point F and ends at point P1. Based on the above path geometry and the tangential continuity at the connection points, the coordinates of the endpoint E of arc S0 and the starting point F of arc S1 can be expressed as:

[0159] (20)

[0160] (twenty one)

[0161] Where α is the rotation angle of arc S0 about axis d̂0, β is the rotation angle of arc S1 about axis d̂1, γ is the radian of arc S0, and δ is the radian of arc S1. Vectors 𝐮̂ᵢ, 𝐯̂ᵢ, and 𝐰̂ᵢ constitute a local right-handed orthonormal unit basis at point Pᵢ.

[0162] It can be calculated using the following expression:

[0163] , (twenty two)

[0164] The derivation of 𝐫̂ᵢ here is as follows:

[0165] (twenty three)

[0166] F2: Based on the calculation methods for points E and F above, calculate the tangent vectors at points E and F and the line... , Tangential continuity is evaluated by checking if the dot product of the direction vectors equals 1. Therefore, the minimum error is chosen as the fitness function to find the coordinate parameters of points E and F that minimize the tangential continuity error:

[0167] Variable: x=(α, β, γ, δ);

[0168] Fitness function:

[0169] (twenty four)

[0170] in, For arc The unit tangent vector at point E, For arc The unit tangent vector at point F, Let F be the normalized direction vector pointing from E to F.

[0171] (25)

[0172] (26)

[0173] Normalized direction vector of line EF It can be represented as:

[0174] = (27)

[0175] F3: For the fitness function described above, the particle swarm optimization algorithm described in B3 is used to solve it, and the final three-dimensional Dubins path segment is obtained.

[0176] E3: For local areas where pipelines cannot be laid close to the wall due to curvature limitations due to folding edges along the wall, the minimum bending radius R of the cable can be used to smoothly transition the bend, based on spatial geometry. This method is not discussed here.

[0177] In summary, this invention provides a systematic and high-precision forward pipeline layout planning method. This method creatively transforms the crucial pipeline bending curvature and start / end direction constraints from "post-hoc verification" to "pre-hoc core," integrating them into the entire planning process. Through a technical path of "3D surface topology unfolding—2D curvature constraint optimization—3D path reconstruction and correction," it successfully transforms the complex 3D laying problem into a more easily solvable 2D planar planning problem. This significantly improves computational efficiency while ensuring the high feasibility of the planned path at the geometric, physical, and engineering implementation levels. This invention not only effectively overcomes the shortcomings of traditional planning methods that ignore cable curvature constraints and the direction vectors of laying start and end points, but also provides reliable technical support for achieving precise customization of pipeline materials, reducing engineering costs, and improving the first-time design success rate. It has broad application prospects in the manufacturing of complex equipment such as machinery, aviation, and shipbuilding.

[0178] Those skilled in the art will understand that the above description is merely a preferred embodiment of the present invention, and the features described in the various embodiments and / or claims of this disclosure can be combined or combined in various ways, even if such combinations or combinations are not explicitly described in this disclosure. This is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0179] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if these modifications and modifications of the invention fall within the scope of the claims and their equivalents, the invention is also intended to include these modifications and modifications.

Claims

1. A pipeline layout planning method considering bending curvature, characterized in that, Includes the following steps: S1: The development path of the three-dimensional laying environment is determined based on the undirected graph. The wall-mounted laying environment is processed into two-dimensional equivalent through homogeneous transformation. The homogeneous transformation matrix realizes coordinate mapping based on Denavit-Hartenberg parameters. S2: In the two-dimensional plane, the Dubins curve generation method with multiple waypoints is used for pipeline path planning. The optimization variable is the set of waypoint direction angles, and the total arc length of the path is minimized by the particle swarm optimization algorithm. S3: Employs a forward pipeline layout planning method to achieve in-plane pipeline layout planning that takes into account bending curvature, including obstacle sorting, interference detection and detour path generation; S4: Through homogeneous transformation, the pipeline path can be traced back from two-dimensional space to three-dimensional space; S5: The three-dimensional Dubins method is used to complete the local post-processing of the three-dimensional spatial pipeline path, and to handle the working conditions where the direction vectors of the pipeline start and end points are not in the laying plane and the curvature constraint problem at the wall fold.

2. The pipeline layout planning method considering bending curvature according to claim 1, characterized in that, In step S1, the method for determining the unfolding path of the three-dimensional laying environment based on the undirected graph is specifically as follows: S1-1: The undirected graph spanning tree method is used to expand the wiring space in a plane. The boundary surface of the three-dimensional wiring space is abstracted as the vertices of the undirected graph. The adjacency matrix digitally represents the adjacency relationship of the surface. The effective surface traversal sequence is enumerated by graph theory algorithm. S1-2: Based on the traversal surface sequence, the coordinate transformation is defined using the Denavit-Hartenberg parameters, and the homogeneous transformation matrix of adjacent reference frames is: ； Among them, the linkage angle Indicates circling Shaft from Turn to axis The included angle; the length of the connecting rod Indicates along Shaft from Move to Distance; joint offset for and Distance between common perpendiculars; joint angle From arrive The included angle; S1-3: Multiply the transformations of each link to obtain the transformation matrix of the {k} coordinate system relative to the {0} coordinate system: ； S1-4: For a point in the k-coordinate system Its coordinates in the {0} coordinate system It can be represented as: ; S1-5: When the 3D environment is unfolded in a plane according to the given wiring unfolding path, the common edge between two adjacent faces is equivalent to the linkage axis. Each face is established as its own reference system, and each face is equivalent to a link. According to the DH parameter rules, the reference system corresponding to each face is established. The process of unfolding each face to the same plane is achieved by adjusting the θ angle between the links.

3. The pipeline layout planning method considering bending curvature according to claim 1, characterized in that, In step S2, the pipeline path planning is performed using the Dubins curve generation method with multiple waypoints, specifically as follows: S2-1: Model the pipeline path as a composite path, introducing a direction angle variable for each path point, and defining path points as vectors. ; S2-2: To ensure the path meets the minimum bending radius constraint, the optimization objective is defined as: )； in, This indicates the calculation of the length of the shortest Dubins curve connecting two vector points. and These represent fixed start and end points, respectively. Ensure the path meets the minimum bending radius constraint of the cable, i.e., the actual radius of curvature r ≥ r for all Dubins curve segments. min At the same time, optimize the variables to satisfy θ i ∈[0, 2π]; S2-3: The optimization problem is solved using the particle swarm optimization algorithm, with inertia weights. An adaptive update strategy is used, namely: ； Where ω is the inertia weight, t is the current iteration number, and maxgen is the maximum iteration number; S2-4: Obtain the optimal solution of the direction angle of the waypoint with the shortest total path length through iterative calculation, thereby generating a globally optimal smooth pipeline path that satisfies curvature constraints and passes through all specified waypoints.

4. The pipeline layout planning method considering bending curvature according to claim 1, characterized in that, In step S3, the pipeline forward layout planning method includes the following steps: Step S3-1: Generate the initial Dubins path based on the position and direction vector of the pipeline's start and end points; Step S3-2: Based on the distance from the obstacle center to the end point of the path. Distance to the starting point The difference Sort the obstacles in descending order of their values; Step S3-3: Perform interference detection between the current path and obstacles in the sorted order; if interference occurs, select detour points and update the path using the pipeline path planning method with Dubins curve generation method with multiple detour points; Step S3-4: Try to remove the added waypoints in a backtracking manner, generate a temporary path and verify whether it interferes with the corresponding obstacle; if there is no interference, delete the waypoint and update the path; if there is interference, keep it. Step S3-5: Record the feasible paths without redundant waypoints and their detour direction selection sequence; Step S3-6: Use a binary tree to traverse all possible detour direction selection sequences, repeat steps S3-3 to S3-5, and finally select the shortest path as the optimal solution from all feasible paths.

5. The pipeline layout planning method considering bending curvature according to claim 4, characterized in that, In step S3-3, the interference detection specifically includes the following steps: Step a. Decompose the generated multi-segment Dubins path into several straight line segments and circular arc segments as the discrimination set, and decompose the convex bounding contour of the obstacle into several line segments as the discrimination object set; Step b. For line segment interference detection, first calculate the projection range of the line segment on the coordinate axis for rapid rejection; let the coordinates of the line segment endpoints be... , Its projected boundary is: ； in, , , , They represent line segments respectively. Maximum and minimum projected values ​​on the x-axis and y-axis; and For line segments The x-coordinates of endpoint 1 and endpoint 2, and These are the y-coordinates of endpoint 1 and endpoint 2; If two line segments satisfy one of the following conditions, they are determined to be non-intersecting; otherwise, proceed to step c for the straddle experiment: ； Step c. The straddle experiment is determined by calculating the cross product of vectors; for line segments AB and CD, a scalar function is defined: ； Two line segments intersect if and only if both of the following conditions are met: ； Step d. For interference detection between the circular arc segment and the polygonal edge, calculate the center O(O) of the circle. x O y The minimum distance d to each side of the polygon min If d min If r > 0, there is no interference; otherwise, solve for the intersection of the edge parametric equation and the circle. The edge parametric equation is: ； Among them, ( , ) represents the coordinates of the starting point of the edge segment, Δx and Δy represent the coordinate difference between the two endpoints of the edge, and t is a parameter with a value range of [0,1]. Substitute into the circle equation The quadratic equation is obtained. ,in: ； If there are real roots Then calculate the intersection point Q and its angle relative to the center of the circle. ,like Located in the arc corner region [ , [Interference is determined within the scope of the law;] Step e: When interference is detected, select a detour point based on the vertex set V of the convex polygon; let the current nearest path point be Me, and for a vertex, its adjacent vertices are: A=V i-1 and B=V i+1 Then the following condition is met: The vertex is the left tangent point L(M) e );satisfy: The vertex is the right tangent point R(Me); generate a sequence of path points for left or right detours based on the left and right tangent points.

6. The pipeline layout planning method considering bending curvature according to claim 4, characterized in that, Step S5 includes: Step S5-1: For cases where the direction vectors of the start and end points are not in the laying plane, the path is planned based on their projection in the plane. Then, a reference circle is drawn with the point as the center and 3r as the radius, which intersects the plane path at the transition point. Finally, a three-dimensional Dubins path segment is generated from the actual start and end points to the transition point. Step S5-2: For the case where the wall fold edge bends outward and cannot be attached to the wall, in the wall surface on both sides of the fold edge, draw reference circles with the intersection point of the pipeline and the fold edge as the center and 3r as the radius, and intersect with the path in the corresponding wall surface at the transition point, and then generate a three-dimensional Dubins path segment between the two points. Step S5-3: The method for generating the three-dimensional Dubins path segment is as follows: Let the starting point P0 be the direction vector d̂0, and the ending point P1 be the direction vector d̂1. The path consists of the starting arc S0 and the straight line segment. It is formed by the terminating arc S1; by solving the parameters Determine the coordinates of connecting points E and F: ； ； Where α is the rotation angle of arc S0 about axis d̂0, β is the rotation angle of arc S1 about axis d̂1, γ is the radian of arc S0, and δ is the radian of arc S1; vector The local right-handed orthonormal unit basis is formed at point Pᵢ; With the goal of minimizing the tangential continuity error, a fitness function is established and its parameters are optimized. for: ； in, For arc The unit tangent vector at point E, For arc The unit tangent vector at point F, Let F be the normalized direction vector pointing from E to F; Step S5-4: Solve the problem using the particle swarm optimization algorithm. Minimum parameter This determines the coordinates of points E and F, and generates a three-dimensional Dubins path segment.

7. A pipeline layout planning method considering bending curvature according to claim 6, characterized in that, In step S5-3, the vector Constructed in the following way: The vector for: ； The vector for: ； The vector for: ； Wherein, auxiliary vector according to The absolute value of the dot product with the reference vector is chosen as follows: 。 8. The system for pipeline layout planning considering bending curvature according to claim 6, characterized in that, include: The environment modeling and unfolding module is used to perform topological modeling of the wall-mounted surfaces in the 3D pipeline laying environment, construct a graph model based on the surface adjacency relationship, and unfold all related surfaces to the same 2D planning plane through coordinate transformation based on the selected surface traversal sequence. The two-dimensional curvature constraint path planning module is used to generate a smooth two-dimensional path that satisfies curvature constraints and is collision-free within the two-dimensional planning plane, using the starting and ending points and directions of the pipeline, and the minimum bending radius as constraints, combined with obstacle information in the plane, by optimizing the direction angle of the path points. The 3D path reconstruction and local optimization module is used to map the 2D path back to 3D space through inverse coordinate transformation to form a preliminary path. For local sections that do not meet the wall-hugging or curvature constraints due to non-coplanar direction vectors or abrupt changes in wall geometry, the module replaces and smoothly connects them with straight line segments and arc segments in 3D space to generate the final 3D laying path.

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