Rotating curved surface robot path planning method based on rectangular mapping and artificial potential field

Abstract

The invention discloses a rotating curved surface robot path planning method based on rectangular mapping and an artificial potential field, relates to the technical field of path planning, and aims to solve the problem that a shortest path cannot be obtained by an existing three-dimensional curved surface path planning method. According to the method, a rectangular mapping mode is adopted, the three-dimensional rotating curved surface is mapped to the plane rectangular area, the robot task information and the obstacle information are mapped to the plane area, the three-dimensional curved surface path planning problem of the pipeline robot is converted into the two-dimensional plane path planning problem, the complexity of the problem is effectively reduced, and the path planning efficiency is improved. Therefore, the shortest path can be planned.

Description

Technical Field

[0001] The 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 scenarios that are difficult to reach or dangerous to perform various non-contact detection and contact operation tasks. One typical application scenario is pipeline robots. Traditional pipeline maintenance methods have disadvantages such as high cost and low efficiency. Therefore, researchers use pipeline wall-climbing robots with detection and operation devices to enter the pipeline and move along the inner wall of the pipeline to achieve functions such as damage exploration, surface rust removal, cleaning and maintenance inside the pipeline.

[0003] At present, the research on the structural design and motion control of pipeline robots is relatively mature, and they can execute basic movement instructions in various pipelines. However, the research on path planning is not mature enough. When the size of the robot is large relative to the diameter of the pipeline, the robot can only move forward and backward along the axis, and the range of motion is relatively limited. At this time, the path planning problem is relatively simple. However, for large and complex pipelines, the size of the robot is small relative to the diameter of the pipeline, and a suitable motion path can significantly improve the efficiency of task execution. Moreover, there may be obstacles that can be climbed over and obstacles that cannot be climbed over and can only be bypassed inside the pipeline. It is necessary to execute 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 of pipeline robots is essentially a point-to-point path planning problem on a three-dimensional surface. The existing methods mainly include two cases: when the surface expression is known and when it is unknown. When the surface expression can be accurately obtained, analytical methods or numerical methods are often used to obtain the shortest path connecting the starting point and the end point. The shortest path is the geodesic. The analytical method is to use the geodesic equation or the variational method to obtain the differential equation of the shortest path, and substitute the endpoint conditions to solve the exact expression of the shortest path. The numerical method is to use optimization algorithms such as particle swarm optimization to iteratively approximate the shortest path. However, for surfaces with more complex forms, it is difficult to find an analytical solution for the shortest path, and it is impossible to consider the situation where there are obstacles. Therefore, the analytical method is difficult to apply in practice. The existing numerical methods do not consider various types of obstacles, and the iterative process is time-consuming, resulting in low real-time performance and difficult to deploy to physical robots. In addition, when the surface expression cannot be accurately obtained, the finite element analysis method is often used. The typical approach is to divide the three-dimensional surface model into triangular facets, and then perform path planning based on the edges or center points of the triangular facets. However, the path obtained in this way 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 in order to solve the problem that the existing three-dimensional surface path planning method 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 of a rotating surface robot based on rectangular mapping and artificial potential field comprises the following steps:

[0008] Step 1: Obtain the three-dimensional rotation surface of the inner wall of the pipeline, robot task information, and obstacle information. The robot task information includes the robot's starting position (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 rotation surface of the inner wall of the pipeline, the robot task information and the obstacle information to the plane rectangular area respectively, so as to establish 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 expected 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 direction, and f(v) represents the radius of the parallel circle where (u, v) is located;

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

[0018]

[0019] Among them, v min and v max They 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 angle, 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 It is 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 It is 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, and R io Indicates the occupied area radius.

[0029] Furthermore, the additional potential field V generated by the surmountable obstacle extj It is 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 taken 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 length 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 , and 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 robot's forward direction. Finally, the foresight distance method is used to move forward l in this direction. f distance, and obtain 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 kth 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 tth search point.

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

[0042] Step 7: The robot reaches each 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 expected arrival position, heading angle It is expressed as:

[0045]

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

[0047] Furthermore, the d est It is expressed as:

[0048]

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

[0050] This application 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, 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 a general surface. DETAILED DESCRIPTION

[0056] It should be particularly noted that, in the absence of conflict, the various embodiments disclosed in this application can be combined with each other.

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

[0058] Step 1: Input the path planning problem information, including 3D 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 generatrix is ​​a continuous differentiable function 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 center 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 of the pipeline along the axis direction, 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 this point. In practice, the expression of f(v) is obtained by sampling the inner wall of the pipeline and fitting it piecewise, and 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 task information includes the starting position and the end 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 a 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 three-dimensional orthogonal parameter system is used to describe the position of the pipeline robot. The advantage 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 insurmountable obstacles and surmountable obstacles in a three-dimensional environment. The insurmountable obstacles are specifically inherent parts and large-sized 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 insurmountable obstacles in the space, project the i-th insurmountable 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 a small object on the inner wall of the pipeline. The pipeline robot can adopt a surmounting strategy, but it will cause additional travel 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 and establish 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 angle and adjusting the z angle to the interval [0,2π). 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, and will not reach 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 planar rectangular area, and the length of the planar 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: Considering the collision radius of the pipeline robot itself is R, this radius 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 there is no intersection between the path planned based on the two-dimensional plane and the collision range of the insurmountable obstacle, 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 the 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 obstacles, and the additional potential field generated by the surmountable obstacles.

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

[0075]

[0076] where k att is the gravitational potential field coefficient to be set, d estIt represents the evaluation distance from the current position of the robot to the end position without considering environmental obstacles. For traditional plane path planning, this evaluation 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 moving 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 greatly different from the shortest distance. In order 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, its estimated distance d from the end position est The calculation method is:

[0079]

[0080] It should be noted that the above 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 enables the robot to make a good estimate of the shortest distance connecting two points in the actual three-dimensional surface when the current position of the robot is far away 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 pipeline 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. The differential equation of a geodesic can be written as follows using the Liouville formula of the geodesic:

[0085]

[0086] Where s represents the arc length parameter, 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 formula (7) can be used as an approximate substitute 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 the values ​​at the current robot position as constants, 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 as follows: for the i-th non-crossable obstacle, the repulsive potential field value generated at the current position of the robot is:

[0096]

[0097] in Indicates the minimum Euclidean distance between the robot's current position and the collision range of the insurmountable obstacle. The Euclidean distance is used here instead of the weighted distance considering 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. k rep is the repulsive potential field coefficient to be set, R s is 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: In the two-dimensional map, 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 position, 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 to 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, the number of search directions of the robot is set to N s , the robot's search step length 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 relation 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 realizes equidistant search in space.

[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, and its direction is the current robot's forward direction. According to the idea of ​​the foresight distance method, the robot moves forward in space along this direction l f distance, then 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 iterations of the program exceeds the set maximum number of iterations, it means that the path connecting the starting point and the end point cannot be found, and the path planning algorithm terminates. To prevent falling into the local minimum, the following formula can be used to substitute the search point when calculating the evaluation distance formula (7):

[0108]

[0109] The path planning algorithm in this step can generate a point-to-point optimal path for the robot through reasonable parameter settings. 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 is actually executing on the three-dimensional curved surface of the inner wall of the pipeline, 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 of the robot from the starting point to the end point is L total The estimated values ​​are:

[0115]

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

[0117] It should be noted that this algorithm can run in real time and effectively deal with local uncertainties on the inner wall of the pipeline. When the robot finds that the local values ​​of f(v) and f′(v) differ from the sampled fitting values ​​during operation, the actual values ​​can be used for 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 value to which the robot is subjected is only related to the current position, and does not need to use the expression 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 is a highly real-time algorithm.

[0118] This application can also be improved or expanded in application areas as follows:

[0119] (1) Different artificial potential field function designs are used 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 piecewise 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 a conical surface, and 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. There are three insurmountable obstacles in the space. The center positions of the areas occupied on the three-dimensional surface are The radius of the occupied area is 0.05; there is one 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, 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 generated by executing the climbing strategy for the surmountable obstacle is relatively large, the planned path implements the detour strategy for the surmountable obstacle, and 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 obstacles and the 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 can be obtained to be 2.2361, and the path length obtained by the algorithm of the present invention is 2.2590. In contrast, if the evaluation distance of formula (7) is changed to the 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 closer in the absence of obstacles, 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. Three non-crossable obstacles and one crossable obstacle are set in 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, it can be seen that the robot successfully reaches the end position from the starting position and does not collide with non-crossable obstacles during the movement. Since the additional distance cost of executing the climbing strategy for the crossable obstacles is relatively small, the planned path implements the climbing strategy for the crossable 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 an insurmountable obstacle, and the additional potential field generated by a 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 a 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, and 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 field described in this application takes into account both the non-crossable obstacles and the surmountable obstacles in three-dimensional space, and can generate a point-to-point optimal path for the robot, with the total path length as short as possible, and will not collide with non-surmountable obstacles during operation, and try to avoid climbing over surmountable obstacles. The algorithm takes into account speed, safety, and smoothness, and has the advantages of simple implementation, good performance, and high real-time performance.

[0128] It should be noted that the specific implementation is only an explanation and description of the technical solution of the present invention, and cannot be used to limit the scope of protection of the rights. Any partial changes made according to the claims and description of the present invention should still fall within the scope of protection of the present invention.

Claims

1. A rotating surface robot path planning method based on rectangular mapping and artificial potential field, characterized in that The following steps are involved: Step 1: Obtain the three-dimensional rotation surface of the inner wall of the pipeline, robot task information, and obstacle information. The robot task information includes the robot's starting position (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 rotation surface of the inner wall of the pipeline, the robot task information and the obstacle information to the plane rectangular area respectively, so as to establish 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 expected 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 rotating surface robot path planning method 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 pipeline 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 direction, and f(v) represents the radius of the parallel circle where (u, v) is located; In the step 2, the mapping is established by expanding along the central angle to establish the mapping from the three-dimensional orthogonal parameter system (u, v) to the two-dimensional orthogonal parameter system (p, q), which is expressed as: Among them, v min and v max They 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 angle, 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 rotating surface robot path planning method 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 rotating surface robot path planning method 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 It is 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 rotating surface robot path planning method 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 It is 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, and R io Indicates the occupied area radius.

6. The rotating surface robot path planning method 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 It is 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 rotating surface robot path planning method 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 taken 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 length 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 , and 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 robot's forward direction. Finally, the foresight distance method is used to move forward l in this direction. f distance, and obtain the next expected arrival position (p next ,q next ) and add the location to the waypoint sequence.

8. The rotating surface robot path planning method 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 kth search point, The next expected arrival position (p next ,q next ) is expressed as: Among them, θ t Indicates the direction angle of the tth search point.

9. The rotating surface robot path planning method based on rectangular mapping and artificial potential field according to claim 8 is characterized in that The method further comprises step seven: Step 7: The robot reaches each 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 on the inner wall of the pipe.

10. The rotating surface robot path planning method based on rectangular mapping and artificial potential field according to claim 9 is characterized in that The d est It is expressed as:

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