A spatial continuous path planning method based on curve integral

Abstract

The application discloses a space continuous path planning method based on curve integral, belongs to the technical field of path planning, and is used for intelligent unmanned system path planning, and comprises the following steps: a plane rectangular coordinate system of an environment region is established, environment sub-regions are divided, a first-degree polynomial path function is constructed, and a total path length target function is established by using curve integral; an optimization problem of the target function under double constraint conditions is established to obtain a shortest broken line path; and a cubic polynomial curve is used to perform smoothing processing on the paths of regions near all sharp points to obtain a final planning path. The path planning method of the application utilizes a segmented polynomial function, avoids errors caused by environment gridding, maximally reduces the number of sharp points, shortens the total path length, and avoids the situation that the intelligent unmanned system makes sharp turns in the driving process.

Description

Technical Field

[0001] This invention discloses a spatial continuous path planning method based on curve integral, belonging to the field of path planning technology. Background Technology

[0002] With the rapid development of intelligent unmanned systems such as drones, unmanned ships, robots, and self-driving cars, efficient and smooth path planning technology has become a key research issue. Traditional path planning algorithms, such as Dijkstra's algorithm, While algorithms can perform basic pathfinding in a static environment, they have significant limitations. For example, Dijkstra's algorithm suffers from low computational efficiency due to its global traversal characteristic. While the algorithm improves efficiency through heuristic search, it still cannot solve the problems of excessive redundant points and unsmooth paths. Although existing techniques address these issues... The algorithm has been improved to address the issues of excessive redundancy and non-smooth paths, but it still requires discretization of the environment and cannot avoid discretization errors.

[0003] Existing solutions are mostly based on grid or sampling methods, which require discretizing the continuous environment. This results in the planned path being approximately the shortest, rather than the true shortest path. Secondly, the computational complexity of these path planning methods increases significantly with the increase of environmental resolution, which greatly limits their application in high-precision scenarios. Summary of the Invention

[0004] The purpose of this invention is to provide a spatial continuous path planning method based on curve integrals, in order to solve the problem in the prior art that the continuous environment needs to be discretized, which leads to the planned path being approximately the shortest but not the truly shortest, and the computational complexity increases with the higher the environment resolution.

[0005] A spatially continuous path planning method based on line integrals includes:

[0006] S1. Establish a Cartesian coordinate system for the environmental area, determine the starting and ending points of the path planning, and determine the vertex coordinates of the obstacles in the obstacle set;

[0007] S2. Project the starting point, ending point, and the vertices of each obstacle onto the horizontal axis of a Cartesian coordinate system to obtain a set of projection points. Based on this set of projection points, divide the environment into... Each sub-region is a continuous sub-region, and the coordinates of the intersection points between obstacles within the sub-region and the sub-region boundary are recorded.

[0008] S3. Construct a polynomial path function once in each sub-region, construct the path from the starting point to the ending point based on the path functions of all sub-regions, and use line integrals to establish the objective function of the total path length.

[0009] S4. Establish the optimization problem of the objective function under dual constraints, including path continuity constraints and obstacle avoidance constraints. Solve to obtain the minimum value and optimal value of the independent variable of the objective function under dual constraints. Based on the optimal value of the independent variable of the objective function, obtain the shortest broken line path from the starting point to the ending point that avoids all obstacles.

[0010] S5. Based on the shortest polyline path, a smoothing region is defined with the cusp as the midpoint. A cubic polynomial curve is used to smooth the path within all smoothing regions to obtain the optimization objective function. An optimization problem is then established under triple constraints, including path continuity constraints, path smoothness constraints, and obstacle avoidance constraints. The minimum value and optimal independent variable value of the optimization objective function under the triple constraints are obtained by solving the problem. Based on the optimal independent variable value of the optimization objective function, the final planned path is obtained.

[0011] S1 includes establishing a Cartesian coordinate system for the environmental region, and determining the starting point, ending point, and obstacle set based on the Cartesian coordinate system for the environmental region. The coordinates of the vertices of each obstacle in the middle, The starting coordinates are The endpoint coordinates are The environmental area is:

[0012] ;

[0013] In the formula, For environmental areas, for Within the coordinate range of the horizontal axis, , for At the maximum value on the horizontal axis, for Within the coordinate range of the vertical axis, , for At the maximum value on the vertical axis, and All are non-negative real numbers. It is a Cartesian product.

[0014] S2 includes S2.1, projecting the start point, end point, and the vertices of each obstacle onto the horizontal axis of a Cartesian coordinate system to obtain the corresponding set of projection points. , ,based on Will Divided into A contiguous subregion:

[0015] ;

[0016] ;

[0017] In the formula, for The Sub-regions for The width.

[0018] S2 includes S2.2, and records. Internal obstacles and The coordinates of the intersection point of the boundary, the first The coordinates of the lower intersection point of the obstacle and the left boundary of the area are: The coordinates of the upper intersection point with the left boundary of the region are: The coordinates of the lower intersection point with the right boundary of the region are: The coordinates of the upper intersection point with the right boundary of the region are: .

[0019] S3 includes, in Construct a linear polynomial path function:

[0020] ;

[0021] In the formula, For path functions, The x-axis is... for Path function, for The slope, for The intercept, and These are coefficients to be determined;

[0022] based on Construct a path function from the starting point to the destination:

[0023] ;

[0024] Establish the objective function for the total path length using line integrals:

[0025] ;

[0026] In the formula, Let be the objective function. To find the derivative, It is a differential.

[0027] S4 includes S4.1, path continuity constraints. and Must meet:

[0028] ;

[0029] ;

[0030] ;

[0031] S4 includes S4.2, obstacle avoidance constraints. When there are obstacles inside, Avoiding obstacles requires that the path endpoints be located on the same side of the obstacle's upper and lower boundary lines. Inside An obstacle, Must meet:

[0032] ;

[0033] ;

[0034] ;

[0035] In the formula, For indexing, ;

[0036] S4 includes S4.3, establishing and solving the optimization problem of the objective function under path continuity and obstacle avoidance constraints, to obtain the minimum objective function. , , for Euclidean space of dimensions;

[0037] S4 includes S4.4, which obtains the optimal values ​​of the independent variables based on the minimum objective function, combined with... Find the shortest polyline path from the starting point to the ending point, avoiding all obstacles. .

[0038] S5 includes S5.1, calculation. and slope difference :

[0039] ;

[0040] In the formula, For the slope difference, for The slope of the inner straight path;

[0041] S5 includes, S5.2, and the following: The threshold for sudden changes in driving direction, when When the intersection of two straight paths is determined to be a cusp, the path needs to be smoothed.

[0042] S5 includes, S5.3, if There is a sharp point at the location; set a smooth distance parameter. :

[0043] ;

[0044] by As the starting point for smoothing, To smoothly handle the endpoint, plan the shortest curved path.

[0045] S5 includes, S5.4, setting a smoothing processing area. for:

[0046] ;

[0047] Smooth the area Divided into and :

[0048] ;

[0049] ;

[0050] In the formula, express area, express Region; the path function after smoothing is:

[0051] ;

[0052] ;

[0053] In the formula, This is the path function after smoothing. for The coefficient of the cubic term affects Overall bending direction and end behavior for The coefficient of the quadratic term affects Symmetry and inflection point for The coefficient of the first term affects The slope and the location of the extreme points, As a constant term, it determines The intersection with the vertical axis, The coefficients are undetermined; the optimized path from the start point to the end point of the smoothing process is:

[0054] ;

[0055] Calculate using line integrals The total length of the path after smoothing is used to obtain the optimization objective function:

[0056] ;

[0057] In the formula, To optimize the objective function.

[0058] S5 includes S5.5, establishing path continuity constraints:

[0059] ;

[0060] ;

[0061] ;

[0062] Establish path smoothness constraints:

[0063] ;

[0064] ;

[0065] ;

[0066] S5 includes S5.6, establishing obstacle avoidance constraints and setting obstacle avoidance constraints. for Let the set of internal obstacle avoidance constraints be denoted as follows. The number of obstacles is Set obstacle avoidance constraints. for Let the set of internal obstacle avoidance constraints be denoted as follows. The number of obstacles is The obstacle avoidance constraints are: the two endpoints of the curve are on the same side of the upper and lower boundary lines of all obstacles; and the points on the curve whose tangents are parallel to the boundary lines of the obstacles are on the same side of the upper and lower boundary lines of the obstacles as the two endpoints of the curve.

[0067] Obstacle avoidance constraints for:

[0068] ;

[0069] ;

[0070] ;

[0071] ;

[0072] ;

[0073] In the formula, For obstacle boundary functions, For indexing, , for Inner The lower boundary function of an obstacle for Inner The upper boundary function of the obstacle, For indexing, , for The path curve satisfies the condition that the tangent line is perpendicular to the first line. The x-coordinate of a point parallel to the lower boundary line of an obstacle. And satisfy ; for The path curve satisfies the condition that the tangent line is perpendicular to the first line. The x-coordinate of a point parallel to the upper boundary line of an obstacle. And satisfy ; The boundary function for the internal obstacle is:

[0074] ;

[0075] ;

[0076] In the formula, , , and These are parameters to be determined, and are obtained from the coordinates of the lower and upper boundary endpoints of the obstacle.

[0077] Obstacle avoidance constraints for:

[0078] ;

[0079] ;

[0080] ;

[0081] ;

[0082] ;

[0083] In the formula, For indexing, ; for Inner The lower boundary function of an obstacle for Inner The upper boundary function of the obstacle, for The path curve satisfies the condition that the tangent line is perpendicular to the first line. The x-coordinate of a point parallel to the lower boundary line of an obstacle. And satisfy ; for The path curve satisfies the condition that the tangent line is perpendicular to the first line. The x-coordinate of a point parallel to the upper boundary line of an obstacle. And satisfy ; The boundary function for the internal obstacle is:

[0084] ;

[0085] ;

[0086] In the formula, , , and These are parameters to be determined, and are obtained from the coordinates of the lower and upper boundary endpoints of the obstacle.

[0087] S5 includes S5.7, establishing and solving the optimization problem under the constraints of path continuity, path smoothness, and obstacle avoidance, to obtain the minimum optimization objective function:

[0088] ;

[0089] ;

[0090] ;

[0091] ;

[0092] ;

[0093] ;

[0094] ;

[0095] Obstacle avoidance constraints ;

[0096] Obstacle avoidance constraints ;

[0097] ;

[0098] In the formula, for Euclidean space of dimensions;

[0099] based on ,get The optimal value of the independent variable, combined with Find the shortest smooth path from the starting point to the ending point that avoids all obstacles. .

[0100] Compared with the prior art, the present invention has the following advantages: The present invention uses a path planning method based on piecewise polynomial functions to avoid errors caused by environmental gridding, minimizes the number of cusps, fundamentally shortens the total path length, and uses piecewise cubic polynomials to achieve path smoothing at cusps, which can avoid sharp turns in the intelligent unmanned system during driving. Through local area optimization, it effectively solves the discrete error problem caused by smoothing at path cusps in traditional methods. Attached Figure Description

[0101] Figure 1 This is a diagram showing the division of regions;

[0102] Figure 2 This is a schematic diagram of the shortest broken line path;

[0103] Figure 3 This is a schematic diagram of the final planned smooth path;

[0104] Figure 4 A smoothing effect diagram of the path around the first cusp;

[0105] Figure 5 The smoothing effect of the path around the second cusp;

[0106] Figure 6 A smoothing effect diagram of the path around the third cusp;

[0107] Figure 7 The smoothing effect of the path around the fourth cusp. Detailed Implementation

[0108] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0109] A spatially continuous path planning method based on line integrals includes:

[0110] S1. Establish a Cartesian coordinate system for the environmental area, determine the starting and ending points of the path planning, and determine the vertex coordinates of the obstacles in the obstacle set;

[0111] S2. Project the starting point, ending point, and the vertices of each obstacle onto the horizontal axis of a Cartesian coordinate system to obtain a set of projection points. Based on this set of projection points, divide the environment into... Each sub-region is a continuous sub-region, and the coordinates of the intersection points between obstacles within the sub-region and the sub-region boundary are recorded.

[0112] S3. Construct a polynomial path function once in each sub-region, construct the path from the starting point to the ending point based on the path functions of all sub-regions, and use line integrals to establish the objective function of the total path length.

[0113] S4. Establish the optimization problem of the objective function under dual constraints, including path continuity constraints and obstacle avoidance constraints. Solve to obtain the minimum value and optimal value of the independent variable of the objective function under dual constraints. Based on the optimal value of the independent variable of the objective function, obtain the shortest broken line path from the starting point to the ending point that avoids all obstacles.

[0114] S5. Based on the shortest polyline path, a smoothing region is defined with the cusp as the midpoint. A cubic polynomial curve is used to smooth the path within all smoothing regions to obtain the optimization objective function. An optimization problem is then established under triple constraints, including path continuity constraints, path smoothness constraints, and obstacle avoidance constraints. The minimum value and optimal independent variable value of the optimization objective function under the triple constraints are obtained by solving the problem. Based on the optimal independent variable value of the optimization objective function, the final planned path is obtained.

[0115] S1 includes establishing a Cartesian coordinate system for the environmental region, and determining the starting point, ending point, and obstacle set based on the Cartesian coordinate system for the environmental region. The coordinates of the vertices of each obstacle in the middle, The starting coordinates are The endpoint coordinates are The environmental area is:

[0116] ;

[0117] In the formula, For environmental areas, for Within the coordinate range of the horizontal axis, , for At the maximum value on the horizontal axis, for Within the coordinate range of the vertical axis, , for At the maximum value on the vertical axis, and All are non-negative real numbers. It is a Cartesian product.

[0118] S2 includes S2.1, projecting the start point, end point, and the vertices of each obstacle onto the horizontal axis of a Cartesian coordinate system to obtain the corresponding set of projection points. , ,based on Will Divided into A contiguous subregion:

[0119] ;

[0120] ;

[0121] In the formula, for The Sub-regions for The width.

[0122] S2 includes S2.2, and records. Internal obstacles and The coordinates of the intersection point of the boundary, the first The coordinates of the lower intersection point of the obstacle and the left boundary of the area are: The coordinates of the upper intersection point with the left boundary of the region are: The coordinates of the lower intersection point with the right boundary of the region are: The coordinates of the upper intersection point with the right boundary of the region are: .

[0123] S3 includes, in Construct a linear polynomial path function:

[0124] ;

[0125] In the formula, For path functions, The x-axis is... for Path function, for The slope, for The intercept, and These are coefficients to be determined;

[0126] based on Construct a path function from the starting point to the destination:

[0127] ;

[0128] Establish the objective function for the total path length using line integrals:

[0129] ;

[0130] In the formula, Let be the objective function. To find the derivative, It is a differential.

[0131] S4 includes S4.1, path continuity constraints. and Must meet:

[0132] ;

[0133] ;

[0134] ;

[0135] S4 includes S4.2, obstacle avoidance constraints. When there are obstacles inside, Avoiding obstacles requires that the path endpoints be located on the same side of the obstacle's upper and lower boundary lines. Inside An obstacle, Must meet:

[0136] ;

[0137] ;

[0138] ;

[0139] In the formula, For indexing, ;

[0140] S4 includes S4.3, establishing and solving the optimization problem of the objective function under path continuity and obstacle avoidance constraints, to obtain the minimum objective function. , , for Euclidean space of dimensions;

[0141] S4 includes S4.4, which obtains the optimal values ​​of the independent variables based on the minimum objective function, combined with... Find the shortest polyline path from the starting point to the ending point, avoiding all obstacles. .

[0142] S5 includes S5.1, calculation. and slope difference :

[0143] ;

[0144] In the formula, For the slope difference, for The slope of the inner straight path;

[0145] S5 includes, S5.2, and the following: The threshold for sudden changes in driving direction, when When the intersection of two straight paths is determined to be a cusp, the path needs to be smoothed.

[0146] S5 includes, S5.3, if There is a sharp point at the location; set a smooth distance parameter. :

[0147] ;

[0148] by As the starting point for smoothing, To smoothly handle the endpoint, plan the shortest curved path.

[0149] S5 includes, S5.4, setting a smoothing processing area. for:

[0150] ;

[0151] Smooth the area Divided into and :

[0152] ;

[0153] ;

[0154] In the formula, express area, express Region; the path function after smoothing is:

[0155] ;

[0156] ;

[0157] In the formula, This is the path function after smoothing. for The coefficient of the cubic term affects Overall bending direction and end behavior for The coefficient of the quadratic term affects Symmetry and inflection point for The coefficient of the first term affects The slope and the location of the extreme points, As a constant term, it determines The intersection with the vertical axis, The coefficients are undetermined; the optimized path from the start point to the end point of the smoothing process is:

[0158] ;

[0159] Calculate using line integrals The total length of the path after smoothing is used to obtain the optimization objective function:

[0160] ;

[0161] In the formula, To optimize the objective function.

[0162] S5 includes S5.5, establishing path continuity constraints:

[0163] ;

[0164] ;

[0165] ;

[0166] Establish path smoothness constraints:

[0167] ;

[0168] ;

[0169] ;

[0170] S5 includes S5.6, establishing obstacle avoidance constraints and setting obstacle avoidance constraints. for Let the set of internal obstacle avoidance constraints be denoted as follows. The number of obstacles is Set obstacle avoidance constraints. for Let the set of internal obstacle avoidance constraints be denoted as follows. The number of obstacles is The obstacle avoidance constraints are: the two endpoints of the curve are on the same side of the upper and lower boundary lines of all obstacles; and the points on the curve whose tangents are parallel to the boundary lines of the obstacles are on the same side of the upper and lower boundary lines of the obstacles as the two endpoints of the curve.

[0171] Obstacle avoidance constraints for:

[0172] ;

[0173] ;

[0174] ;

[0175] ;

[0176] ;

[0177] In the formula, For obstacle boundary functions, For indexing, , for Inner The lower boundary function of an obstacle for Inner The upper boundary function of the obstacle, For indexing, , for The path curve satisfies the condition that the tangent line is perpendicular to the first line. The x-coordinate of a point parallel to the lower boundary line of an obstacle. And satisfy ; for The path curve satisfies the condition that the tangent line is perpendicular to the first line. The x-coordinate of a point parallel to the upper boundary line of an obstacle. And satisfy ; The boundary function for the internal obstacle is:

[0178] ;

[0179] ;

[0180] In the formula, , , and These are parameters to be determined, and are obtained from the coordinates of the lower and upper boundary endpoints of the obstacle.

[0181] Obstacle avoidance constraints for:

[0182] ;

[0183] ;

[0184] ;

[0185] ;

[0186] ;

[0187] In the formula, For indexing, ; for Inner The lower boundary function of an obstacle for Inner The upper boundary function of the obstacle, for The path curve satisfies the condition that the tangent line is perpendicular to the first line. The x-coordinate of a point parallel to the lower boundary line of an obstacle. And satisfy ; for The path curve satisfies the condition that the tangent line is perpendicular to the first line. The x-coordinate of a point parallel to the upper boundary line of an obstacle. And satisfy ; The boundary function for the internal obstacle is:

[0188] ;

[0189] ;

[0190] In the formula, , , and These are parameters to be determined, and are obtained from the coordinates of the lower and upper boundary endpoints of the obstacle.

[0191] S5 includes S5.7, establishing and solving the optimization problem under the constraints of path continuity, path smoothness, and obstacle avoidance, to obtain the minimum optimization objective function:

[0192] ;

[0193] ;

[0194] ;

[0195] ;

[0196] ;

[0197] ;

[0198] ;

[0199] Obstacle avoidance constraints ;

[0200] Obstacle avoidance constraints ;

[0201] ;

[0202] In the formula, for Euclidean space of dimensions;

[0203] based on ,get The optimal value of the independent variable, combined with Find the shortest smooth path from the starting point to the ending point that avoids all obstacles. .

[0204] The following description, in conjunction with the accompanying drawings, further illustrates the points, such as... Figure 1 As shown, select the environment area, establish a Cartesian coordinate system for the environment area, and determine the start and end points of the path planning based on this coordinate system. There are 4 obstacles in the environment area. By projecting the start point, end point, and the vertices of each obstacle onto the horizontal axis, the environment area is divided into 10 sub-regions based on the projection points. The projection points are recorded as follows: Sub-region records are .

[0205] Construct a first-order polynomial path function within each subregion, and build upon the path functions of all subregions. Use line integrals to establish the objective function for the total length; to make For a path to be continuous and avoid all obstacles, it must have a common endpoint between adjacent sub-regions, and each sub-region's path must avoid all obstacles. Therefore, the objective function is established as an optimization problem under the constraints of path continuity and obstacle avoidance:

[0206] ;

[0207] Solving for the shortest polyline path yields the following results: Figure 2 As shown, the reddest circle indicates the location of the apex.

[0208] according to middle The slope of the straight path in each sub-region Seek ,set up , The selection is based on the sensitivity of the intelligent unmanned system to deviations in its forward direction during movement, in order to reduce the computational load; judgment and The size relationship, if If so, the path does not need optimization; if If the intersection of the two straight paths is determined to be a cusp, the path needs to be smoothed.

[0209] A smoothing region is defined with the cusp as its midpoint. A cubic polynomial curve is used to smooth the paths within all smoothing regions to obtain the desired result. To make It must be a continuous, smooth path that can avoid obstacles, which requires and Paths within a region share a common endpoint and a common tangent at that endpoint. Furthermore, paths within the region can avoid all obstacles within that sub-region. Treat For tangent, in Treat The objective function is tangent; therefore, an optimization problem is established under the constraints of path continuity, path smoothness, and obstacle avoidance to achieve path obstacle avoidance and path smoothness, such as... Figure 3 As shown, all sharp points are smoothed, and the smoothing effect of the first sharp point is as follows. Figure 4 As shown, the smoothing effect of the second apex is as follows: Figure 5 As shown, the smoothing effect of the third apex is as follows: Figure 6 As shown, the smoothing effect of the fourth apex is as follows: Figure 7 As shown, the smoothed path can avoid obstacles and avoid sharp turns.

[0210] The derivation process of obstacle constraint conditions is as follows For example: Judgment If internal obstacles are present, If there are no obstacles inside, then no constraints are needed, and the corresponding set of obstacle avoidance constraints is empty; if If there are obstacles within the path, the obstacle avoidance constraint must be satisfied for the path curve to avoid the obstacles:

[0211] (1) The two endpoints of the curve are on the same side of the upper and lower boundary lines of all obstacles;

[0212] (2) If there are points on the curve that satisfy the condition that the tangent is parallel to the boundary line of the obstacle, they are all on the same side of the upper and lower boundary lines of the obstacle as the two endpoints of the curve.

[0213] Assumption Initially, it is an empty set. Let it be... The number of obstacles is To ensure that the path satisfies the obstacle avoidance constraint (1), assume that the first... The lower and upper boundary functions of the obstacle are:

[0214] ;

[0215] ;

[0216] In the formula, These are parameters to be determined, and are obtained using the coordinates of the obstacle vertices. Must meet:

[0217] ;

[0218] ;

[0219] ;

[0220] Add the above constraints to the set .

[0221] To ensure the path curve satisfies obstacle avoidance constraint (2), calculate... The x-coordinate of the point where the tangent to the inner path curve is parallel to the lower boundary line of the obstacle is used to solve the equation. The solution is obtained. and ,judge and Whether it is a real number; if it is not a real number, no constraints are needed; if it is... and It is a real number, determine Does it belong to If it does not belong to the category, then no constraints are needed; if it belongs to the category, then the function... Must meet:

[0222] ;

[0223] calculate The x-coordinate of the point where the tangent to the inner path curve is parallel to the upper boundary line of the obstacle is used to solve the equation. The solution is obtained. and ,judge and Whether it is a real number; if it is not a real number, no constraints are needed; if it is... and It is a real number, determine Does it belong to If it does not belong to the category, then no constraints are needed; if it belongs to the category, then the function... Must meet:

[0224] ;

[0225] Add the above constraints to the set ,right The above operation is performed on the upper and lower boundaries of all obstacles within the area.

[0226] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A spatial continuous path planning method based on curve integration, characterized in that, Comprise: S1, establish the planar rectangular coordinate system of the environmental area, determine the start point and end point of path planning, determine the vertex coordinates of the obstacles in the obstacle set; S2, project the start point, the end point and the vertexes of each obstacle to the horizontal axis of the plane rectangular coordinate system to obtain a set of projection points, divide the environment region into a plurality of continuous sub-regions based on the set of projection points, and record the intersection coordinates of the obstacles and the sub-region boundaries in the sub-regions; S3, construct a polynomial path function in each sub-region, construct the path from the start point to the end point based on the path functions of all sub-regions, and establish the total path length objective function by curve integration; S4, establish the optimization problem of the objective function under the double constraint conditions, the double constraint conditions include the path continuity constraint condition and the obstacle avoidance constraint condition, solve to get the minimum value and the optimal independent variable value of the objective function under the double constraint conditions, based on the optimal independent variable value of the objective function, get the shortest broken line path from the start point to the end point which avoids all obstacles; S5, based on the shortest broken line path, set the smoothing processing area with the cusp as the midpoint, smooth the path in all smoothing processing areas by using cubic polynomial curve, get the optimization objective function, establish the optimization problem of the optimization objective function under the triple constraint conditions, the triple constraint conditions include the path continuity constraint condition, the path smoothness constraint condition and the obstacle avoidance constraint condition, solve to get the minimum value and the optimal independent variable value of the optimization objective function under the triple constraint conditions, based on the optimal independent variable value of the optimization objective function, get the final planning path.

2. The spatial continuous path planning method based on curve integral according to claim 1, characterized in that, S1 comprises establishing a planar rectangular coordinate system of the environment area, determining a start point, an end point and an obstacle set of path planning based on the planar rectangular coordinate system of the environment area each obstacle vertex coordinate, the start point coordinate is the end point coordinate is the environment area is ； wherein is the environmental region, is is the coordinate range of the horizontal axis, , is is the maximum of the horizontal axis, is is the coordinate range of the vertical axis, , is is the maximum of the vertical axis, and are non-negative real numbers, is the Cartesian product.

3. The spatially continuous path planning method based on curve integration according to claim 2, characterized in that, S2 comprises, S2.1, projecting the start point, the end point and the vertexes of each obstacle to the horizontal axis of the plane rectangular coordinate system to obtain a corresponding set of projection points , , based on the is divided into continuous sub-regions: ； ； wherein is the first sub-region, is the width.

4. The spatially continuous path planning method based on curve integration according to claim 3, characterized in that, S2 includes, S2.2, recording The inner obstacle and The intersection coordinates of the boundary, the The lower intersection coordinates of the first obstacle and the left boundary of the region are The upper intersection coordinates of the first obstacle and the left boundary of the region are The lower intersection coordinates of the first obstacle and the right boundary of the region are The upper intersection coordinates of the first obstacle and the right boundary of the region are .

5. The spatially continuous path planning method based on curve integration according to claim 4, characterized in that, S3 comprises, in constructing an inner polynomial path function: ； wherein is a path function, is an abscissa, is is a path function, is is a slope of is is an intercept of and are undetermined coefficients; based on constructing a path function from the start point to the end point: ； The total path length objective function is established by curve integration: ； In the formula, is the objective function, is the derivative, is the differential.

6. The spatially continuous path planning method based on curve integration according to claim 5, characterized in that, S4 comprises, S4.1, a path continuity constraint condition, and must be fulfilled: ； ； ； S4 comprises, S4.2, an obstacle avoidance constraint condition, when there are obstacles inside, The obstacle avoidance needs to satisfy that the path endpoints are located on the same side of the upper and lower boundary lines of the obstacle, set when there are obstacles inside, one obstacle, The following needs to be satisfied: ； ； ； In the formulae, is an index, ; S4 comprises, S4.3, establishing an optimization problem of the objective function under the path continuity constraint condition and the obstacle avoidance constraint condition and solving to obtain the minimum objective function , , For dimensional Euclidean space; S4 includes, S4.4, based on the minimum objective function, get the optimal independent variable value, combined with get the shortest broken line path from the starting point to the end point avoiding all obstacles .

7. The spatially continuous path planning method based on curve integration according to claim 6, characterized in that, S5 comprises, S5.1, calculating and the slope difference of ； wherein is the slope difference, is is the slope of the inner straight path; S5 includes, S5.2, setting a threshold value for the mutation of the driving direction, when the intersection point of the two straight line paths is judged as a cusp point, and the path needs to be smoothed. S5 comprises, S5.3, if A position exists with a sharp point, set a smoothing distance parameter : ； Start point for smoothing, End point for smoothing, Plan shortest curve path.

8. The spatially continuous path planning method based on curve integration according to claim 7, characterized in that, S5 comprises, S5.4, setting a smoothing processing area is: ； Smooth the treated area Divide into And : ； ； wherein represents region, represents region; the path function after smoothing is: ； ； wherein, is the smoothed path function, is the is the coefficient of the cubic term of the overall curvature direction and the end behavior, is the is the coefficient of the quadratic term of the symmetry and the inflection point, is the is the coefficient of the linear term of the slope and the position of the extreme point, is the constant term determining the intersection with the longitudinal axis, is the undetermined coefficient; the optimized path from the start of smoothing to the end of smoothing is: ； The total length of the smoothed path is calculated using the integral of the curve The total length of the smoothed path is calculated using the integral of the curve ； In the formula, is to optimize the objective function.

9. The spatially continuous path planning method based on curve integration according to claim 8, characterized in that, S5 includes S5.5, the path continuity constraint condition is established: ； ； ； The path smoothness constraint condition is established: ； ； ； S5 comprises, S5.6, establishing an obstacle avoidance constraint condition, set obstacle avoidance constraint condition For The set of obstacle avoidance constraint conditions is set to The number of obstacles in the set is ; Set obstacle avoidance constraint condition For The set of obstacle avoidance constraint conditions is set to The number of obstacles in the set is The obstacle avoidance constraint condition is that the two endpoints of the curve are on the same side of the upper and lower boundary lines of all obstacles; the points on the curve that satisfy the tangent parallel to the obstacle boundary line are on the same side of the two endpoints of the curve on the upper and lower boundary lines of the obstacle. Obstacle avoidance constraints are: ； ； ； ； ； In the formula, For obstacle boundary functions, For indexing, , for Inner The lower boundary function of an obstacle for Inner The upper boundary function of the obstacle, For indexing, , for The path curve satisfies the condition that the tangent line is perpendicular to the first line. The x-coordinate of a point parallel to the lower boundary line of an obstacle. And satisfy ; for The path curve satisfies the condition that the tangent line is perpendicular to the first line. The x-coordinate of a point parallel to the upper boundary line of an obstacle. And satisfy ; The boundary function for the internal obstacle is: ； ； where , , and are to be determined parameters, calculated from the obstacle lower and upper boundary end points coordinates; Obstacle avoidance constraints are: ； ； ； ； ； wherein is an index, ; is the lower boundary function of the th obstacle, is the upper boundary function of the th obstacle, is the horizontal coordinate of the point on the path curve where the tangent is parallel to the lower boundary line of the th obstacle, and satisfies ; is the horizontal coordinate of the point on the path curve where the tangent is parallel to the upper boundary line of the th obstacle, and satisfies ; the obstacle boundary function in the interval ； ； where , , and are to be determined parameters, calculated from the obstacle lower and upper boundary end points coordinates.

10. The spatially continuous path planning method based on curve integration according to claim 9, characterized in that, S5 includes S5.7, the optimization problem of the optimization objective function under the path continuity constraint condition, the path smoothness constraint condition and the obstacle avoidance constraint condition is established and solved, and the minimum optimization objective function is obtained: ； ； ； ； ； ； ； Obstacle avoidance constraints ; Obstacle avoidance constraints ; ； In the formula, is Euclidean space; based on ,get The optimal value of the independent variable, combined with Find the shortest smooth path from the starting point to the ending point that avoids all obstacles. .

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