Path planning method for rotating surface robot based on rectangular mapping and artificial potential field

Abstract

The invention relates to the field of path planning technology, and aims to solve the problem that the existing three-dimensional surface path planning method cannot obtain the shortest path. The present invention adopts a rectangular mapping method to map the three-dimensional rotating surface to a planar rectangular area, and maps the robot task information and obstacle information to the planar area. The three-dimensional surface path planning problem of the pipeline robot is converted into a two-dimensional plane path planning problem, which effectively reduces the complexity of the problem, so that the present invention can plan the shortest path.

Description

Technical Field

[0001] The present invention relates to the technical field of path planning, in particular to a path planning method for a rotating curved surface robot based on rectangular mapping and artificial potential field. Background Art

[0002] With the continuous advancement of robotics technology, robots have been widely used in difficult-to-reach or dangerous environments to perform various non-contact inspection and contact operations. One typical application scenario is pipeline robots. Traditional pipeline maintenance methods are costly and inefficient. Therefore, researchers are using pipeline wall-climbing robots equipped with inspection and operation equipment to enter pipelines and move along the inner wall, performing tasks such as internal damage detection, surface rust removal, and cleaning and maintenance.

[0003] Currently, research on the structural design and motion control of pipeline robots is relatively mature, and they are able to execute basic movement instructions in various types of pipelines. However, research on path planning is not yet mature. When the robot size is large relative to the diameter of the pipeline, the robot can only move forward and backward along the axis, and its range of motion is relatively limited. In this case, the path planning problem is relatively simple. However, for large and complex pipelines, the robot size is small relative to the diameter of the pipeline, and a suitable motion path can significantly improve the efficiency of task execution. Furthermore, there may be obstacles inside the pipeline that can be climbed over, and obstacles that cannot be climbed over and can only be circumvented. It is necessary to implement corresponding obstacle avoidance strategies based on real-time detection results, which brings difficulties and challenges to the path planning problem.

[0004] The path planning problem for pipeline robots is essentially a point-to-point path planning problem on a three-dimensional surface. Existing methods primarily cover the cases where the surface expression is known and the cases where it is unknown. When the surface expression can be precisely determined, analytical or numerical methods are often used to determine the shortest path connecting the start and end points. This shortest path is known as a geodesic. Analytical methods use the geodesic equation or variational methods to obtain the differential equation for the shortest path, substituting the endpoint conditions into the equation to solve for the exact expression. Numerical methods use optimization algorithms such as the particle swarm optimization algorithm to iteratively approximate the shortest path. However, for complex surfaces, the shortest path is difficult to find an analytical solution and cannot account for obstacles, making analytical methods difficult to apply in practice. Existing numerical methods fail to account for various types of obstacles, and the time-consuming iterative process results in low real-time performance, making them difficult to deploy on physical robots. Furthermore, when the surface expression cannot be precisely determined, finite element analysis is often used. Typically, the 3D surface model is segmented into triangular facets, and path planning is performed based on the edges or center points of the facets. However, the resulting path is not the shortest path. Summary of the Invention

[0005] The purpose of the present invention is to provide a rotational surface robot path planning method based on rectangular mapping and artificial potential field to address the problem that existing three-dimensional surface path planning methods cannot obtain the shortest path.

[0006] The technical solution adopted by the present invention to solve the above technical problems is:

[0007] The path planning method for a rotating surface robot based on rectangular mapping and artificial potential field includes the following steps:

[0008] Step 1: Obtain the three-dimensional rotation surface of the inner wall of the pipeline, the robot task information and the obstacle information. The robot task information includes the starting position of the robot (u start ,v start ) and the end position (u end ,v end ), the obstacle information includes information about insurmountable obstacles and information about surmountable obstacles;

[0009] Step 2: Map the three-dimensional rotational surface of the pipe inner wall, the robot task information, and the obstacle information to a flat rectangular area to create a two-dimensional map;

[0010] Step 3: Establish an artificial potential field based on the two-dimensional map;

[0011] Step 4: Start the robot from the starting position and use the artificial potential field to obtain the next expected arrival position of the current position;

[0012] Step 5: Set the desired arrival position as the current position and repeat step 4 until the robot reaches the final position to obtain the path planning result;

[0013] Step 6: Based on the path planning results and the inverse mapping according to the two-dimensional map, each expected arrival position (u next ,v next ).

[0014] Furthermore, the three-dimensional rotation surface of the inner wall of the pipeline is expressed as:

[0015] r(u,v)=[f(v)cosu f(v)sinu v]

[0016] Where (u, v) represents the coordinates of a point on the three-dimensional rotation surface in the three-dimensional orthogonal parameter system, u represents the central angle corresponding to the parallel circle, v represents the coordinate along the axis, and f(v) represents the radius of the parallel circle where (u, v) is located;

[0017] The mapping in step 2 is to establish a mapping from a three-dimensional orthogonal parameter system (u, v) to a two-dimensional orthogonal parameter system (p, q) by expanding along the central angle of the circle, which is expressed as:

[0018]

[0019] Among them, v min and v max Respectively represent the minimum and maximum coordinates of the pipeline along the axis direction, represents the average radius of the three-dimensional rotation surface, arg(z) represents the principal value of the argument, and adjusts the z angle to the interval [0,2π), u adjust represents the coordinate offset, z represents the angle, the sign function sign(z) takes the value of 1 when z is greater than 0 and takes the value of -1 when z is less than or equal to 0, p represents the horizontal coordinate of the two-dimensional orthogonal parameter system, and q represents the vertical coordinate of the two-dimensional orthogonal parameter system.

[0020] Furthermore, the artificial potential field is expressed as:

[0021]

[0022] Among them, V apf represents the artificial potential field, V att Represents the gravitational potential field generated at the end point, V repi Represents the repulsive potential field generated by the insurmountable obstacle, V extj represents the additional potential field generated by surmountable obstacles, N represents the total number of non-surmountable obstacles, M represents the total number of surmountable obstacles, i represents the i-th non-surmountable obstacle, and j represents the j-th surmountable obstacle.

[0023] Furthermore, the gravitational potential field V generated at the end position att Expressed as:

[0024]

[0025] Among them, k att represents the gravitational potential field coefficient, d est It represents the estimated distance from the robot’s current position to the final position without considering environmental obstacles. (p current ,q current ) represents the current position of the robot on the two-dimensional plane, (p end ,q end ) is the end position (u end ,v end ) The position after mapping, f p (q) and f q (q) represents the step factor in the p-direction and the q-direction, and f′(v) represents the derivative of each sub-rotation surface except the endpoints.

[0026] Furthermore, the repulsive potential field V generated at the current position of the robotrepi Expressed as:

[0027]

[0028] Among them, d i Indicates the minimum Euclidean distance between the robot's current position and the collision range of the insurmountable obstacle, k rep represents the repulsive potential field coefficient, R s Indicates the safe distance between the robot and the insurmountable obstacle, (p io ,q io ) represents the center position of the i-th insurmountable obstacle (u io ,v io ) is the mapped position, R represents the collision radius of the pipeline robot itself, R io Indicates the occupied area radius.

[0029] Furthermore, the additional potential field V generated by the surmountable obstacle extj Expressed as:

[0030]

[0031] Among them, D(p jc ,q jc ,R j ' c ) indicates that (p jc ,q jc ) as the center, with R j ' c is the circular area with radius l j It indicates the additional equivalent distance caused by the time spent on climbing over.

[0032] Furthermore, the specific steps of step 4 are:

[0033] Step 41: Determine whether the Euclidean distance between the robot's current position and the end position is less than the set threshold. If so, the end position is used as the next expected arrival position and the path planning algorithm ends. If not, set the number of search directions of the robot to N. s , Set the robot's search step on the three-dimensional surface to l s , Set the robot's forward step length on the three-dimensional surface to l f , l s and l f is a constant and satisfies l f <l s , then, based on the current position of the robot, a uniform search is performed on the two-dimensional plane according to the direction angle to obtain N s search points, where the coordinates of the kth search point in the two-dimensional map are (p searchk ,qsearchk );

[0034] Step 42: Take the position of each search point as the current position of the robot and obtain the corresponding artificial potential field V apfk , then select the artificial potential field V apfk The smallest search point is found, and the search number of the direction angle corresponding to the search point is recorded as t. Then the direction corresponding to the search point is used as the current forward direction of the robot. Finally, the foresight distance method is used to move forward l in this direction. f The distance to the next expected arrival position (p next ,q next ) and add the location to the waypoint sequence.

[0035] Furthermore, the coordinates of the k-th search point in the two-dimensional map (p searchk ,q searchk ) is expressed as:

[0036]

[0037] Among them, θ k represents the direction angle of the k-th search point,

[0038] The next expected arrival position (p next ,q next ) is expressed as:

[0039]

[0040] Among them, θ t Indicates the direction angle of the t-th search point.

[0041] Furthermore, the method further comprises step seven:

[0042] Step 7: The robot reaches the desired position (u next ,v next ) moves along the inner wall of the pipe;

[0043] The specific steps of step seven are:

[0044] Step 71: The robot adjusts the heading angle of the current position to and move forward in this direction f Distance, arrival at the next desired location, heading angle Expressed as:

[0045]

[0046] Step 72: Repeat step 71 to enable the robot to move along the inner wall of the pipe.

[0047] Furthermore, the d est Expressed as:

[0048]

[0049] The beneficial effects of the present invention are:

[0050] This application uses a rectangular mapping method to map the three-dimensional rotating surface to a planar rectangular area, and maps the robot task information and obstacle information to the planar area, thereby converting the three-dimensional surface path planning problem of the pipeline robot into a two-dimensional plane path planning problem, effectively reducing the complexity of the problem, so that this application can plan the shortest path. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 A flowchart of this application;

[0052] Figure 2 To implement the two-dimensional planning results of this application on a conical surface;

[0053] Figure 3 To implement the three-dimensional planning results of this application on a conical surface;

[0054] Figure 4 To implement the two-dimensional planning results of this application on a general surface;

[0055] Figure 5 The three-dimensional planning results of this application are performed on general surfaces. DETAILED DESCRIPTION

[0056] It should be noted that, unless there is any conflict, the various embodiments disclosed in this application can be combined with each other.

[0057] Specific embodiment 1: The rotational curved surface robot path planning method based on rectangular mapping and artificial potential field described in this embodiment includes the following steps:

[0058] Step 1: Input path planning problem information, including three-dimensional environment information, robot task information, and obstacle information.

[0059] The three-dimensional environmental information includes the expression and constraints of the three-dimensional surface of the inner wall of the pipeline. The constraint conditions of the three-dimensional surface of the inner wall of the pipeline are determined as follows: the inner wall of the pipeline can be modeled as a piecewise continuous and smooth three-dimensional rotation surface, that is, it is composed of several sub-rotation surfaces whose main lines are continuous differentiable functions spliced ​​along the axis direction. The coordinates of the points on the three-dimensional rotation surface in the three-dimensional orthogonal parameter system are expressed as (u, v), where u represents the central angle of the parallel circle corresponding to the point, and v represents the coordinate of the point along the axis direction. Then the three-dimensional surface constraint conditions are: 0≤u<2π and v min ≤v≤v max , where v min and v max Respectively represent the minimum and maximum coordinates along the axis of the pipeline, which are obtained by measuring the length of the pipeline in practice. The expression of the three-dimensional surface of the inner wall of the pipeline is determined as follows: let the radius of the parallel circle where the point (u, v) is located be f(v), f(v) is a piecewise continuous differentiable function, and for each sub-rotation surface except the endpoint, its derivative f′(v) exists. The value of f′(v) at the endpoint is supplemented by the value of f′(v) of the sub-rotation surface with smaller v at that point. In practice, the expression of f(v) is obtained by sampling the inner wall of the pipeline and fitting it piecewise, and then the expression of f′(v) is obtained by derivation. Then the expression of the three-dimensional surface of the inner wall of the pipeline is:

[0060] r(u,v)=[f(v)cosu f(v)sinu v] (1)

[0061] The robot mission information includes the starting position and the ending position of the robot. Since the robot is close to the inner wall of the pipe, its position can be described as a point on a three-dimensional surface, that is, in the three-dimensional orthogonal parameter system, the current position of the robot is (u current ,v current ), the starting position is (u start ,v start ), the end point is (u end ,v end The advantage of using a three-dimensional orthogonal parameter system to describe the position of the pipeline robot is that the information acquisition method is simple and will not be affected by the measurement and fitting accuracy of the pipeline inner wall.

[0062] Obstacle information includes information about non-crossable obstacles and surmountable obstacles in a three-dimensional environment. The non-crossable obstacles are specifically inherent parts and large objects in the internal space of the pipeline. The pipeline robot can only adopt a detour strategy. The information is determined as follows: suppose there are N non-crossable obstacles in the space, project the i-th non-surmountable obstacle onto the three-dimensional surface of the inner wall of the pipeline, and obtain the geometric center position of the occupied area as (u io ,v io ), the occupied area radius is R ioThe surmountable obstacle is specifically a small object on the inner wall of the pipeline. The pipeline robot can adopt a surmounting strategy, but it will incur an additional distance cost. The information is determined as follows: suppose there are M surmountable obstacles in the space, project the jth surmountable obstacle onto the three-dimensional surface of the inner wall of the pipeline, and obtain the geometric center position of the occupied area as (u jc ,v jc ), the occupied area radius is R jc .

[0063] Step 2: Perform rectangular mapping to map the three-dimensional rotation surface to a flat rectangular area to create a two-dimensional map for path planning. Use the method of expanding along the central angle to establish a mapping from the three-dimensional orthogonal parameter system (u, v) to the two-dimensional orthogonal parameter system (p, q):

[0064]

[0065] in, Select as the average radius of the three-dimensional rotation surface, which is calculated as:

[0066]

[0067] The symbol arg(z) means taking the principal value of the argument and adjusting the z angle to the interval [0,2π). The coordinate offset u adjust The introduction of is to make the shortest path connecting the starting point and the end point of the robot located in the middle of the two-dimensional map, without reaching the two ends of the map. The calculation method is:

[0068]

[0069] The sign function sign(z) takes the value of 1 when z is greater than 0, and takes the value of -1 when z is less than or equal to 0.

[0070] After the above rectangular mapping, the three-dimensional rotation surface of the inner wall of the pipe is mapped into a flat rectangular area, and the length of the flat rectangular area is the average perimeter of all sub-rotation surfaces. The width is the interval span v in the axis direction max -v min The essence of the rectangular mapping algorithm is to project the three-dimensional rotation surface onto the cylindrical surface and then unfold it into a plane.

[0071] According to the rectangular mapping method of formula (2), the robot task information and obstacle information input in step 1 are mapped to the plane rectangular area respectively. Among them, the current position of the robot is (u current ,v current ) is mapped to (p current ,q current ), starting position (u start ,vstart ) is mapped to (p start ,q start ), end position (u end ,v end ) is mapped to (p end ,q end The center position of the i-th insurmountable obstacle (u io ,v io ) is mapped to (p io ,q io ), the center position of the jth surmountable obstacle (u jc ,v jc ) is mapped to (p jc ,q jc After rectangular mapping, the collision radius of the obstacle also needs to be changed. The calculation method is: consider the collision radius of the pipeline robot itself as R, which needs to be superimposed on the non-crossable obstacle. Therefore, the collision radius of the i-th non-crossable obstacle in the plane rectangular area changes to The radius of the jth surmountable obstacle changes to It should be noted that the mapping method of the above obstacle collision radius has a certain safety margin. As long as the path planned based on the two-dimensional plane and the collision range of the insurmountable obstacle do not intersect, the pipeline robot can bypass the insurmountable obstacle and reach the end point.

[0072] Through the above-mentioned rectangular mapping method, the three-dimensional surface path planning problem of the pipeline robot is transformed into a two-dimensional plane path planning problem, which can effectively reduce the complexity of the problem and is conducive to building a corresponding planar scene for early algorithm verification.

[0073] Step 3: Establish an artificial potential field based on the two-dimensional map, including the gravitational potential field generated by the end point, the repulsive potential field generated by the insurmountable obstacle, and the additional potential field generated by the surmountable obstacle.

[0074] The calculation method of the gravitational potential field value generated at the end point is:

[0075]

[0076] where k att is the gravitational potential field coefficient to be set, d estIt represents the estimated distance from the robot's current position to the final position without considering environmental obstacles. For traditional planar path planning, this estimated distance can be calculated as the Euclidean distance between two points. However, for the plane area obtained by rectangular mapping of the three-dimensional rotation surface, the robot moves the same distance in different directions, and the corresponding movement distance on the actual three-dimensional surface is not equal, that is, it no longer has the property of isometric mapping. At this time, if the Euclidean distance is still used, the actual distance of the robot will be significantly different from the shortest distance. To solve this problem, the step size factor in two directions of the two-dimensional orthogonal parameter system is introduced:

[0077]

[0078] Then the current position on the two-dimensional plane is (p current ,q current ) of the robot, and its estimated distance d from the end position est The calculation method is:

[0079]

[0080] It should be noted that the above-mentioned evaluation distance function is essentially based on the Euclidean distance metric function, multiplied by the step size factor of the current position in both directions. This setting allows the robot to make a good estimate of the shortest distance between two points on the actual three-dimensional surface even when the current position is far from the end position.

[0081] The following analysis proves the rationality of the evaluation distance setting form.

[0082] According to formula (1), the first basic form of the three-dimensional surface of the inner wall of the pipe is:

[0083] I=E(du) 2 +G(dv) 2 =f 2 (v)(du) 2 +[1+f′ 2 (q)](dv) 2 (8)

[0084] The shortest path connecting two points on a three-dimensional surface is a geodesic. Using the Liouville formula for geodesics, the differential equation of the geodesic can be written as:

[0085]

[0086] Where s represents the arc length parameter, and θ represents the angle between the geodesic and the u-curve, which is the heading angle of the pipeline robot moving on the three-dimensional surface. Substituting the first basic form of the three-dimensional surface (8) into formula (9) yields:

[0087]

[0088] According to formula (10), we can get:

[0089]

[0090] Since the two ends of the geodesic are the current position and the end position of the robot, we can get:

[0091]

[0092] Then when the distance between the two ends of the geodesic is close, the length L of the geodesic on the three-dimensional surface satisfies the following relationship:

[0093]

[0094] Therefore, we have the relationship L≈d est , indicating that the design of the evaluation distance equation (7) can be used as an approximate replacement for the geodesic equation connecting two points on a three-dimensional rotation surface. It should be noted that in the approximation process, the variables E and G are replaced by constants at the current robot position, and the closer the robot's current position is to the end position, the more accurate the estimate.

[0095] The calculation method of the repulsive potential field value generated by the non-crossable obstacle is: for the i-th non-crossable obstacle, the repulsive potential field value generated at the current position of the robot is:

[0096]

[0097] in The minimum Euclidean distance between the robot's current position and the collision range of the insurmountable obstacle is represented here. The Euclidean distance is used here instead of the weighted distance that takes into account the step size factor. This is because when the repulsive potential field of the insurmountable obstacle takes effect, the distance between the two on the two-dimensional map is relatively close. rep is the repulsive potential field coefficient to be set, R s The safe distance between the robot and the insurmountable obstacle. The robot will only be affected by the repulsive field of the insurmountable obstacle when the collision range between the robot's current position and the insurmountable obstacle is smaller than the safe distance.

[0098] The calculation method of the additional potential field value generated by the surmountable obstacle is as follows: D(p jc ,q jc ,R j ' c ) indicates that (p jc ,q jc ) as the center, with R j ' cIf the motion path of the pipeline robot is within the radius of the jth surmountable obstacle, an additional equivalent distance l will be generated due to the time taken to climb over it. j , then the additional potential field generated by the surmountable obstacle is:

[0099]

[0100] Then the artificial potential field value at the robot's location is the sum of the gravitational potential field generated by the end point, the repulsive potential field generated by all insurmountable obstacles, and the additional potential field value generated by all surmountable obstacles. The calculation method is:

[0101]

[0102] Step 4: The robot starts from the starting position and continuously executes the path planning algorithm based on the rectangular mapping and artificial potential field during the movement towards the end position to obtain the next expected arrival position of the current position. The path planning algorithm is as follows: first, determine whether the distance between the robot's current position and the end position is less than the set threshold. If so, it means that the robot is close to the end position, and the end position is directly used as the next expected arrival position, and the path planning algorithm ends; if not, since the robot should try to maintain a uniform speed, set the number of search directions of the robot to N s , the robot's search step on the three-dimensional surface is a constant l s , the actual forward step length of the robot on the three-dimensional surface is a constant l f , and satisfy the relationship l f <l s For the current position of the robot, a uniform search is performed on the two-dimensional plane according to the direction angle, and a certain distance is deduced in different directions as the search point, so that N s search points, the coordinates of the kth search point in the two-dimensional map are (p searchk ,q searchk ), whose coordinates are:

[0103]

[0104] In formula (18) Then the distances between these search points and the current position on the three-dimensional surface are approximately l s This is because the corresponding step size factors need to be multiplied in both directions, which means that an equidistant search in space is achieved.

[0105] Next, the positions of these search points are taken as the current positions of the robot, and the artificial potential field value V of each search point is calculated according to the calculation method of the artificial potential field value in step 3 and formula (17). apfk , and then select the artificial potential field value V apfkThe smallest search point, the direction angle search number is t, its direction is the current robot's forward direction, according to the idea of ​​the foresight distance method, move along this direction in space l f The distance, then get the next expected arrival position (p next ,q next ) and add a sequence of path points, whose coordinates are:

[0106]

[0107] During the execution of the path planning algorithm, if the number of program iterations exceeds the set maximum number of iterations, it means that the path connecting the starting point and the end point has not been found, and the path planning algorithm terminates. To prevent falling into a local minimum, the following formula can be used instead when substituting the search point into the evaluation distance formula (7):

[0108]

[0109] The path planning algorithm in this step, through reasonable parameter settings, can generate a better point-to-point path for the robot. The total length of the path is as short as possible, and it will not collide with non-crossable obstacles during operation, and try to avoid climbing over crossable obstacles.

[0110] Step 5: According to the path planning result based on the two-dimensional map in step 4, the robot's path points are remapped to the three-dimensional surface and actually executed by the pipeline robot. The specific method is: for the current position in the two-dimensional map (p current ,q current ), expected arrival position (p next ,q next ) robot, the inverse mapping relationship of formula (2) can be obtained (u next ,v next ), according to formula (1), the expected arrival position of the robot in three-dimensional space is:

[0111] r(u next ,v next )=[f(v next )cosu next f(v next )sinu next v next ] (twenty one)

[0112] When the robot actually executes on the three-dimensional surface of the inner wall of the pipe, its heading angle is adjusted to and move forward in this direction f Distance is enough, The calculation expression is:

[0113]

[0114] The proposed pipeline robot path planning algorithm based on rectangular mapping and artificial potential field, if the number of generated path point sequences N total , then the total distance L of the robot from the starting point to the end point total The estimated value is:

[0115]

[0116] The symbol II(z) takes the value 1 when the proposition z holds, and takes the value 0 otherwise.

[0117] It's important to note that this algorithm operates in real time and effectively addresses local uncertainties within the pipe's inner surface. When the robot detects discrepancies between the local f(v) and f′(v) values ​​and the sampled fitted values ​​during operation, the actual values ​​can be substituted into the calculation. When the robot encounters an unknown obstacle, it only needs to make corresponding corrections to the two-dimensional map. Because the artificial potential field values ​​experienced by the robot are only related to its current position and do not require representations of the entire three-dimensional surface, the robot can simultaneously perform subsequent path planning and execution to reach the next desired position. In summary, this algorithm demonstrates high real-time performance.

[0118] This application can also be improved or expanded in the following areas:

[0119] (1) Using different artificial potential field function designs to prevent the algorithm from falling into local minima and causing oscillations;

[0120] (2) The algorithm can be applied to rust removal on the outer wall of a pipe, or path planning of similar three-dimensional surface operation robots with segmented continuous smooth rotating surface features.

[0121] This application also provides two specific examples to illustrate the effectiveness of the algorithm:

[0122] The first embodiment is to use the pipeline robot path planning algorithm based on rectangular mapping and artificial potential field of the present invention on the conical surface. The input path planning problem information is: the expression of the three-dimensional surface of the inner wall of the pipeline is The constraints are The robot's starting position is The end position is The robot's collision radius is 0.05, and there are three insurmountable obstacles in the space, occupying the center positions of the areas on the three-dimensional surface. The occupied area radius is 0.05; there is a surmountable obstacle in the space, and the center of its occupied area is The occupied area radius is 0.2. Based on the input path planning problem information, the two-dimensional diagram of the path planning result is shown in the attached figure. Figure 2The three-dimensional diagram of the path planning result is shown in the attached Figure 3 As shown in the figure, it can be seen that the robot successfully reaches the end position from the starting position and does not collide with the non-crossable obstacle during the movement. Since the extra distance cost of executing the climbing strategy for the surmountable obstacle is relatively large, the planned path implements the detour strategy for the surmountable obstacle. Finally, the total path length of the pipeline robot on the three-dimensional surface is 2.6476. It should be noted that in this embodiment, without considering the surmountable and non-surmountable obstacles, based on the property that the conical surface is a developable surface, the theoretical shortest path between the starting point and the end point is 2.2361, and the path length obtained by the algorithm of the present invention is 2.2590. In comparison, if the evaluation distance of formula (7) is changed to Euclidean distance, the path length obtained is 2.6979. From this result, it can be seen that the distance evaluation function setting form considering the step size factor of the present invention can make the path length and the geodesic length in the absence of obstacles closer, which illustrates the effectiveness of the algorithm of the present invention.

[0123] The second embodiment is to use the pipeline robot path planning algorithm based on rectangular mapping and artificial potential field of the present invention on a general curved surface. There are three non-crossable obstacles and one crossable obstacle in the space. The two-dimensional diagram of the path planning result is shown in the attached figure. Figure 4 The three-dimensional diagram of the path planning result is shown in the attached Figure 5 As shown in the figure, it can be seen that the robot successfully reaches the end position from the starting position and does not collide with the non-crossable obstacles during the movement. Since the additional distance cost of executing the climbing strategy for the surmountable obstacles is relatively small, the planned path executes the climbing strategy for the surmountable obstacles. Finally, the total path length of the pipeline robot on the three-dimensional surface is 17.8525.

[0124] The above two specific embodiments illustrate the effectiveness of the pipeline robot path planning algorithm based on rectangular mapping and artificial potential field of the present invention.

[0125] This application establishes an artificial potential field based on a two-dimensional map after rectangular mapping, including the gravitational potential field generated by the end point position, the repulsive potential field generated by the insurmountable obstacle, and the additional potential field generated by the surmountable obstacle, and designs a distance evaluation function with a step factor. Theoretical analysis and simulation results show that the distance evaluation function can serve as a good estimate of the length of the geodesic connecting two points on the three-dimensional rotating surface, so that this application can plan the shortest path.

[0126] This application adopts the directional angle uniform search and foresight distance method based on the two-dimensional map after rectangular mapping, and finds the search point with the smallest artificial potential field value from several search points as the robot's next expected arrival position. It also provides a distance evaluation function correction method to avoid falling into the local minimum, so that the pipeline robot can maintain uniform motion on the three-dimensional surface as much as possible, effectively improving the performance of the path planning algorithm.

[0127] The pipeline robot path planning algorithm based on rectangular mapping and artificial potential fields, described in this application, takes into account both impassable and traversable obstacles in three-dimensional space. It generates an optimal point-to-point path for the robot, minimizing its total length while avoiding collisions with impassable obstacles and minimizing the need to traverse traversable obstacles. This algorithm balances speed, safety, and smoothness, offering advantages such as simple implementation, high performance, and high real-time performance.

[0128] It should be noted that the specific embodiments are merely explanations and illustrations of the technical solutions of the present invention and cannot be used to limit the scope of protection. Any minor changes made based on the claims and description of the present invention shall still fall within the scope of protection of the present invention.

Claims

1. A rotational surface robot path planning method based on rectangular mapping and artificial potential field, characterized by The following steps are involved: Step 1: Obtain the three-dimensional rotation surface of the inner wall of the pipeline, the robot task information and the obstacle information. The robot task information includes the starting position of the robot (u start ,v start ) and the end position (u end ,v end ), the obstacle information includes information about insurmountable obstacles and information about surmountable obstacles; Step 2: Map the three-dimensional rotational surface of the pipe inner wall, the robot task information, and the obstacle information to a flat rectangular area to create a two-dimensional map; Step 3: Establish an artificial potential field based on the two-dimensional map; Step 4: Start the robot from the starting position and use the artificial potential field to obtain the next expected arrival position of the current position; Step 5: Set the desired arrival position as the current position and repeat step 4 until the robot reaches the final position to obtain the path planning result; Step 6: Based on the path planning results and the inverse mapping according to the two-dimensional map, each expected arrival position (u next ,v next ).

2. The method for path planning of a rotating curved surface robot based on rectangular mapping and artificial potential field according to claim 1 is characterized in that The three-dimensional rotation surface of the inner wall of the pipe is expressed as: r(u,v)=[f(v)cosu f(v)sinu v] Where (u, v) represents the coordinates of a point on the three-dimensional rotation surface in the three-dimensional orthogonal parameter system, u represents the central angle corresponding to the parallel circle, v represents the coordinate along the axis, and f(v) represents the radius of the parallel circle where (u, v) is located; The mapping in step 2 is to establish a mapping from a three-dimensional orthogonal parameter system (u, v) to a two-dimensional orthogonal parameter system (p, q) by expanding along the central angle of the circle, which is expressed as: Among them, v min and v max Respectively represent the minimum and maximum coordinates of the pipeline along the axis direction, represents the average radius of the three-dimensional rotation surface, arg(z) represents the principal value of the argument, and adjusts the z angle to the interval [0,2π), u adjust represents the coordinate offset, z represents the angle, the sign function sign(z) takes the value of 1 when z is greater than 0 and takes the value of -1 when z is less than or equal to 0, p represents the horizontal coordinate of the two-dimensional orthogonal parameter system, and q represents the vertical coordinate of the two-dimensional orthogonal parameter system.

3. The method for rotating curved surface robot path planning based on rectangular mapping and artificial potential field according to claim 2 is characterized in that The artificial potential field is expressed as: Among them, V apf represents the artificial potential field, V att Represents the gravitational potential field generated at the end point, V repi Represents the repulsive potential field generated by the insurmountable obstacle, V extj represents the additional potential field generated by surmountable obstacles, N represents the total number of non-surmountable obstacles, M represents the total number of surmountable obstacles, i represents the i-th non-surmountable obstacle, and j represents the j-th surmountable obstacle.

4. The method for rotating curved surface robot path planning based on rectangular mapping and artificial potential field according to claim 3 is characterized in that The gravitational potential field V generated at the end position att Expressed as: Among them, k att represents the gravitational potential field coefficient, d est It represents the estimated distance from the robot’s current position to the final position without considering environmental obstacles. (p current ,q current ) represents the current position of the robot on the two-dimensional plane, (p end ,q end ) is the end position (u end ,v end ) The position after mapping, f p (q) and f q (q) represents the step factor in the p-direction and the q-direction, and f′(v) represents the derivative of each sub-rotation surface except the endpoints.

5. The method for rotating curved surface robot path planning based on rectangular mapping and artificial potential field according to claim 4 is characterized in that The repulsive potential field V generated at the current position of the robot repi Expressed as: Among them, d i Indicates the minimum Euclidean distance between the robot's current position and the collision range of the insurmountable obstacle, k rep represents the repulsive potential field coefficient, R s Indicates the safe distance between the robot and the insurmountable obstacle, (p io ,q io ) represents the center position of the i-th insurmountable obstacle (u io ,v io ) is the mapped position, R represents the collision radius of the pipeline robot itself, R io Indicates the occupied area radius.

6. The method for rotating curved surface robot path planning based on rectangular mapping and artificial potential field according to claim 5 is characterized in that The additional potential field V generated by the surmountable obstacle extj Expressed as: Among them, D(p jc ,q jc ,R j ' c ) indicates that (p jc ,q jc ) as the center, with R j ' c is the circular area with radius l j It indicates the additional equivalent distance caused by the time spent on climbing over.

7. The method for rotating curved surface robot path planning based on rectangular mapping and artificial potential field according to claim 6 is characterized in that The specific steps of step 4 are: Step 41: Determine whether the Euclidean distance between the robot's current position and the end position is less than the set threshold. If so, the end position is used as the next expected arrival position and the path planning algorithm ends. If not, set the number of search directions of the robot to N. s , Set the robot's search step on the three-dimensional surface to l s , Set the robot's forward step length on the three-dimensional surface to l f , l s and l f is a constant and satisfies l f <l s , then, based on the current position of the robot, a uniform search is performed on the two-dimensional plane according to the direction angle to obtain N s search points, where the coordinates of the kth search point in the two-dimensional map are (p searchk ,q searchk ); Step 42: Take the position of each search point as the current position of the robot and obtain the corresponding artificial potential field V apfk , then select the artificial potential field V apfk The smallest search point is found, and the search number of the direction angle corresponding to the search point is recorded as t. Then the direction corresponding to the search point is used as the current forward direction of the robot. Finally, the foresight distance method is used to move forward l in this direction. f The distance to the next expected arrival position (p next ,q next ) and add the location to the waypoint sequence.

8. The method for path planning of a rotating curved surface robot based on rectangular mapping and artificial potential field according to claim 7 is characterized in that The coordinates of the k-th search point in the two-dimensional map (p searchk ,q searchk ) is expressed as: Among them, θ k represents the direction angle of the k-th search point, The next expected arrival position (p next ,q next ) is expressed as: Among them, θ t Indicates the direction angle of the t-th search point.

9. The method for rotating curved surface robot path planning based on rectangular mapping and artificial potential field according to claim 8, characterized in that The method further comprises step seven: Step 7: The robot reaches the desired position (u next ,v next ) moves along the inner wall of the pipe; The specific steps of step seven are: Step 71: The robot adjusts the heading angle of the current position to θ and moves forward in this direction. f Distance, to reach the next expected arrival position, the heading angle θ is expressed as: Step 72: Repeat step 71 to enable the robot to move along the inner wall of the pipe.

10. The method for path planning of a rotating curved surface robot based on rectangular mapping and artificial potential field according to claim 9, characterized in that The d est Expressed as:

Images