Space continuous path planning method based on curve integration

Abstract

The invention discloses a spatial continuous path planning method based on curve integration, which belongs to the technical field of path planning, is used for path planning of an intelligent unmanned system, and comprises the following steps: establishing a plane rectangular coordinate system of an environment region, dividing environment sub-regions, constructing a linear polynomial path function, and establishing a total path length objective function by utilizing the curve integration. Establishing an optimization problem of the target function under double constraint conditions to obtain a shortest broken line path; and smoothing the paths in the areas near all the sharp points by adopting a cubic polynomial curve to obtain a final planned path. According to the path planning method based on the piecewise polynomial function, errors generated by environment rasterization are avoided, the number of sharp points is reduced to the maximum extent, the total length of the path is shortened, and the situation that the intelligent unmanned system makes a sharp turn in the driving process is avoided.

Description

Technical Field

[0001] The invention discloses a space continuous path planning method based on curve integration, belonging to the technical field of path planning. Background Art

[0002] With the rapid development of intelligent unmanned systems such as drones, unmanned ships, robots and unmanned vehicles, efficient and smooth path planning technology has become a key core issue in current research. Traditional path planning algorithms such as Dijkstra algorithm, Although algorithms can realize basic path search functions in static environments, they have obvious limitations. For example, Dijkstra's algorithm has low computational efficiency due to its global traversal characteristics. Although the algorithm improves efficiency through heuristic search, it still cannot solve the problem of too many redundant points and uneven path. The algorithm has improved its defects of too many redundant points and non-smooth paths, but the algorithm still needs to discretize the environment and cannot avoid discrete errors.

[0003] Existing implementation solutions are mostly based on grid or sampling methods, which require the discretization of the continuous environment, resulting in the planned path being essentially approximately the shortest rather than the true shortest path; secondly, the computational complexity of these path planning methods increases significantly with the improvement of environmental resolution, and their application in high-precision scenarios has great limitations. Summary of the Invention

[0004] The purpose of the present invention is to provide a spatial continuous path planning method based on curve integrals to solve the problem in the prior art that the continuous environment needs to be discretized, resulting in the planned path being essentially approximately the shortest rather than the actual shortest, and the higher the environmental resolution, the higher the computational complexity.

[0005] A spatial continuous path planning method based on curve integration, comprising: S1. Establish a plane rectangular 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; S2, project the starting point, end point and vertices of each obstacle onto the horizontal axis of the plane rectangular coordinate system to obtain a set of projection points, and divide the environment area into A continuous sub-region, recording the coordinates of the intersection of the obstacle in the sub-region and the sub-region boundary; S3. Construct a linear polynomial path function in each sub-area, construct a path from the start point to the end point based on the path functions of all sub-areas, and establish a total path length objective function using curve integrals; S4. Establish an optimization problem for the objective function under dual constraints, including a path continuity constraint and an obstacle avoidance constraint. Solve the problem to obtain the minimum value and optimal independent variable value of the objective function under the dual constraints. Based on the optimal independent variable value of the objective function, obtain the shortest broken line path from the starting point to the end point that avoids all obstacles. S5. Based on the shortest broken line path, a smoothing area is set with the cusp as the midpoint. A cubic polynomial curve is used to smooth all paths within the smoothing area to obtain the optimization objective function. The optimization problem of the optimization objective function under triple constraints is established. The triple constraints include 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.

[0006] S1 includes establishing a plane rectangular coordinate system of the environment area, and determining the starting point, end point and obstacle set of the path planning based on the plane rectangular coordinate system of the environment area. The coordinates of each obstacle vertex in , , the starting point coordinates are , the end point coordinates are , the environmental areas are: ; Where, For the environmental area, for In the coordinate range of the horizontal axis, , for At the maximum value on the horizontal axis, for In the coordinate range of the vertical axis, , for At the maximum value on the vertical axis, and are all non-negative real numbers, is the Cartesian product.

[0007] S2 includes, S2.1, projecting the starting point, the end point and the vertices of each obstacle onto the horizontal axis of the plane rectangular coordinate system to obtain the corresponding projection point set , ,based on Will Divided into contiguous subregions: ; ; Where, for No. sub-regions, for width.

[0008] S2 includes, S2.2, records Internal obstacles and The intersection coordinates of the boundaries, The coordinates of the lower intersection 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 , and the coordinates of the lower intersection point with the right boundary of the region are , and the coordinates of the upper intersection point with the right boundary of the region are .

[0009] S3 includes, Construct a linear polynomial path function internally: ; Where, is the path function, is the horizontal axis, for The path function, for The slope of for The intercept of and is the coefficient to be determined; based on Construct a path function from the start point to the end point: ; The total path length objective function is established using curve integration: ; Where, is the objective function, To seek guidance, is the differential.

[0010] S4 includes, S4.1, path continuity constraints, and Need to meet: ; ; ; S4 includes, S4.2, obstacle avoidance constraints, When there is an obstacle inside, To avoid obstacles, the path endpoint must be on the same side of the upper and lower boundary lines of the obstacle. Inside obstacles, Need to meet: ; ; ; Where, is the index, ; S4 includes, S4.3, establishing the optimization problem of the objective function under the path continuity constraint and obstacle avoidance constraint and solving it to obtain the minimum objective function , , for -dimensional Euclidean space; S4 includes, S4.4, based on the minimum objective function, obtaining the optimal independent variable value, combined with Get the shortest broken line path from the start point to the end point avoiding all obstacles .

[0011] S5 includes, S5.1, calculation and The slope difference : ; Where, is the slope difference, for the slope of the inner straight path; S5 includes, S5.2, is the threshold value of sudden change in driving direction, when When , the intersection of the two straight line paths is judged to be a sharp point, and the path needs to be smoothed; S5 includes, S5.3, if There are sharp points at the location, set the smooth distance parameter : ; by To smooth the starting point, To smoothly process the end point, plan the shortest curve path.

[0012] S5 includes, S5.4, setting up smoothing area for: ; Smooth the area Divided into and : ; ; Where, express area, express area; the path function after smoothing is: ; ; Where, is the path function after smoothing, for The cubic coefficient of Overall bending direction and end behavior, for The quadratic coefficient of Symmetry and inflection points, for The linear coefficient of The slope and extreme point location of is a constant term, determining The intersection with the vertical axis, is the unknown coefficient; the optimal path from the smoothing starting point to the smoothing end point is: ; Calculation using curve integral The total length of the path after smoothing is the optimization objective function: ; Where, To optimize the objective function.

[0013] S5 includes, S5.5, establishing path continuity constraints: ; ; ; Establish path smoothness constraints: ; ; ; S5 includes, S5.6, establishing obstacle avoidance constraints, setting obstacle avoidance constraints for The set of internal obstacle avoidance constraints, let The number of obstacles is ; Set obstacle avoidance constraints for The set of internal obstacle avoidance constraints, let The number of obstacles is The obstacle avoidance constraints are: the endpoints of the curve must be on the same side of the upper and lower boundary lines of all obstacles; the points on the curve whose tangents are parallel to the obstacle boundary lines must be on the same side of the upper and lower boundary lines of the obstacles as the endpoints of the curve. Obstacle avoidance constraints for: ; ; ; ; ; Where, is the obstacle boundary function, is the index, , for Neidi The lower boundary function of the obstacle, for Neidi The upper boundary function of the obstacle, is the index, , for The path curve satisfies the tangent line and the The horizontal coordinate of the point parallel to the boundary line under the obstacle, and satisfy ; for The path curve satisfies the tangent line and the The horizontal coordinate of the point on the obstacle parallel to the boundary line, and satisfy ; The inner obstacle boundary function is: ; ; Where, 、 、 and is an undetermined parameter, which is obtained from the coordinates of the lower and upper boundary endpoints of the obstacle; Obstacle avoidance constraints for: ; ; ; ; ; Where, is the index, ; for Neidi The lower boundary function of the obstacle, for Neidi The upper boundary function of the obstacle, for The path curve satisfies the tangent line and the The horizontal coordinate of the point parallel to the boundary line under the obstacle, and satisfy ; for The path curve satisfies the tangent line and the The horizontal coordinate of the point on the obstacle parallel to the boundary line, and satisfy ; The inner obstacle boundary function is: ; ; Where, 、 、 and It is an undetermined parameter, which is obtained from the coordinates of the lower and upper boundary endpoints of the obstacle.

[0014] S5 includes, S5.7, establishing and solving the optimization problem of the optimization objective function under the path continuity constraint, the path smoothness constraint, and the obstacle avoidance constraint, and obtaining the minimum optimization objective function: ; ; ; ; ; ; ; Obstacle avoidance constraints ; Obstacle avoidance constraints ; ; Where, for -dimensional Euclidean space; based on ,get The optimal value of the independent variable, combined with Get the shortest smooth path from the start point to the end point avoiding all obstacles .

[0015] Compared with the existing technology, the present invention has the following beneficial effects: the present invention uses a path planning method based on a piecewise polynomial function to avoid the errors caused by environmental rasterization, minimize the number of cusps, fundamentally shorten the total length of the path, and uses a piecewise cubic polynomial to achieve path smoothness at cusps, which can avoid sharp turns in the intelligent unmanned system during driving. Through local area optimization processing, the present invention effectively solves the discrete error problem caused by traditional methods when smoothing at path cusps. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a schematic diagram of regional division; Figure 2 This is a diagram of the shortest broken line path; Figure 3 Schematic diagram of the final planned smooth path; Figure 4 This is the smoothing effect diagram of the path around the first cusp; Figure 5 This is the smoothing effect diagram of the path around the second cusp; Figure 6 This is the smoothing effect diagram of the path around the third cusp; Figure 7 This is the smoothing effect of the path around the fourth sharp point. DETAILED DESCRIPTION

[0017] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention are described clearly and completely below. Obviously, the embodiments described are only some of the embodiments of the present invention, not all of them. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0018] A spatial continuous path planning method based on curve integration, comprising: S1. Establish a plane rectangular 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; S2, project the starting point, end point and vertices of each obstacle onto the horizontal axis of the plane rectangular coordinate system to obtain a set of projection points, and divide the environment area into A continuous sub-region, recording the coordinates of the intersection of the obstacle in the sub-region and the sub-region boundary; S3. Construct a linear polynomial path function in each sub-area, construct a path from the start point to the end point based on the path functions of all sub-areas, and establish a total path length objective function using curve integrals; S4. Establish an optimization problem for the objective function under dual constraints, including a path continuity constraint and an obstacle avoidance constraint. Solve the problem to obtain the minimum value and optimal independent variable value of the objective function under the dual constraints. Based on the optimal independent variable value of the objective function, obtain the shortest broken line path from the starting point to the end point that avoids all obstacles. S5. Based on the shortest broken line path, a smoothing area is set with the cusp as the midpoint. A cubic polynomial curve is used to smooth all paths within the smoothing area to obtain the optimization objective function. The optimization problem of the optimization objective function under triple constraints is established. The triple constraints include 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.

[0019] S1 includes establishing a plane rectangular coordinate system of the environment area, and determining the starting point, end point and obstacle set of the path planning based on the plane rectangular coordinate system of the environment area. The coordinates of each obstacle vertex in , , the starting point coordinates are , the end point coordinates are , the environmental areas are: ; Where, For the environmental area, for In the coordinate range of the horizontal axis, , for At the maximum value on the horizontal axis, for In the coordinate range of the vertical axis, , for At the maximum value on the vertical axis, and are all non-negative real numbers, is the Cartesian product.

[0020] S2 includes, S2.1, projecting the starting point, the end point and the vertices of each obstacle onto the horizontal axis of the plane rectangular coordinate system to obtain the corresponding projection point set , ,based on Will Divided into contiguous subregions: ; ; Where, for No. sub-regions, for width.

[0021] S2 includes, S2.2, records Internal obstacles and The intersection coordinates of the boundaries, The coordinates of the lower intersection 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 , and the coordinates of the lower intersection point with the right boundary of the region are , and the coordinates of the upper intersection point with the right boundary of the region are .

[0022] S3 includes, Construct a linear polynomial path function internally: ; Where, is the path function, is the horizontal axis, for The path function, for The slope of for The intercept of and is the coefficient to be determined; based on Construct a path function from the start point to the end point: ; The total path length objective function is established using curve integration: ; Where, is the objective function, To seek guidance, is the differential.

[0023] S4 includes, S4.1, path continuity constraints, and Need to meet: ; ; ; S4 includes, S4.2, obstacle avoidance constraints, When there is an obstacle inside, To avoid obstacles, the path endpoint must be on the same side of the upper and lower boundary lines of the obstacle. Inside obstacles, Need to meet: ; ; ; Where, is the index, ; S4 includes, S4.3, establishing the optimization problem of the objective function under the path continuity constraint and obstacle avoidance constraint and solving it to obtain the minimum objective function , , for -dimensional Euclidean space; S4 includes, S4.4, based on the minimum objective function, obtaining the optimal independent variable value, combined with Get the shortest broken line path from the start point to the end point avoiding all obstacles .

[0024] S5 includes, S5.1, calculation and The slope difference : ; Where, is the slope difference, for the slope of the inner straight path; S5 includes, S5.2, is the threshold value of sudden change in driving direction, when When , the intersection of the two straight line paths is judged to be a sharp point, and the path needs to be smoothed; S5 includes, S5.3, if There are sharp points at the location, set the smooth distance parameter : ; by To smooth the starting point, To smoothly process the end point, plan the shortest curve path.

[0025] S5 includes, S5.4, setting up smoothing area for: ; Smooth the area Divided into and : ; ; Where, express area, express area; the path function after smoothing is: ; ; Where, is the path function after smoothing, for The cubic coefficient of Overall bending direction and end behavior, for The quadratic coefficient of Symmetry and inflection points, for The linear coefficient of The slope and extreme point location of is a constant term, determining The intersection with the vertical axis, is the unknown coefficient; the optimal path from the smoothing starting point to the smoothing end point is: ; Calculation using curve integral The total length of the path after smoothing is the optimization objective function: ; Where, To optimize the objective function.

[0026] S5 includes, S5.5, establishing path continuity constraints: ; ; ; Establish path smoothness constraints: ; ; ; S5 includes, S5.6, establishing obstacle avoidance constraints, setting obstacle avoidance constraints for The set of internal obstacle avoidance constraints, let The number of obstacles is ; Set obstacle avoidance constraints for The set of internal obstacle avoidance constraints, let The number of obstacles is The obstacle avoidance constraints are: the endpoints of the curve must be on the same side of the upper and lower boundary lines of all obstacles; the points on the curve whose tangents are parallel to the obstacle boundary lines must be on the same side of the upper and lower boundary lines of the obstacles as the endpoints of the curve. Obstacle avoidance constraints for: ; ; ; ; ; Where, is the obstacle boundary function, is the index, , for Neidi The lower boundary function of the obstacle, for Neidi The upper boundary function of the obstacle, is the index, , for The path curve satisfies the tangent line and the The horizontal coordinate of the point parallel to the boundary line under the obstacle, and satisfy ; for The path curve satisfies the tangent line and the The horizontal coordinate of the point on the obstacle parallel to the boundary line, and satisfy ; The inner obstacle boundary function is: ; ; Where, 、 、 and is an undetermined parameter, which is obtained from the coordinates of the lower and upper boundary endpoints of the obstacle; Obstacle avoidance constraints for: ; ; ; ; ; Where, is the index, ; for Neidi The lower boundary function of the obstacle, for Neidi The upper boundary function of the obstacle, for The path curve satisfies the tangent line and the The horizontal coordinate of the point parallel to the boundary line under the obstacle, and satisfy ; for The path curve satisfies the tangent line and the The horizontal coordinate of the point on the obstacle parallel to the boundary line, and satisfy ; The inner obstacle boundary function is: ; ; Where, 、 、 and It is an undetermined parameter, which is obtained from the coordinates of the lower and upper boundary endpoints of the obstacle.

[0027] S5 includes, S5.7, establishing and solving the optimization problem of the optimization objective function under the path continuity constraint, the path smoothness constraint, and the obstacle avoidance constraint, and obtaining the minimum optimization objective function: ; ; ; ; ; ; ; Obstacle avoidance constraints ; Obstacle avoidance constraints ; ; Where, for -dimensional Euclidean space; based on ,get The optimal value of the independent variable, combined with Get the shortest smooth path from the start point to the end point avoiding all obstacles .

[0028] The following further describes the following with reference to the accompanying drawings. Figure 1 As shown, the environment area is selected, a rectangular coordinate system of the environment area is established, and the starting point and end point of the path planning are determined based on the coordinate system. There are 4 obstacles in the environment area. By projecting the starting point, end point and the vertices of each obstacle onto the horizontal axis, the environment area is divided into 10 sub-areas based on the projection points. The projection points are recorded as , the sub-region record is .

[0029] Construct a polynomial path function in the subregion and build a polynomial path function based on the path functions of all subregions. , use curve integral to establish the total length objective function; to make In order to have a continuous path and avoid all obstacles, the paths in two adjacent sub-areas must have a common endpoint, and the path in each sub-area must avoid all obstacles. Therefore, the optimization problem of the objective function under the path continuity constraint and obstacle avoidance constraint is established: ; Solve to get the shortest broken line path, such as Figure 2 As shown, the reddest circle indicates where the cusp is located.

[0030] according to middle The slope of the straight line path of each sub-region Obtain ,set up , Select according to the sensitivity of the intelligent unmanned system to the deflection of the forward direction during movement to reduce the amount of calculation; judge and The size relationship of , then the path does not need to be optimized; if , then the intersection of the two straight line paths is determined to be a sharp point, and the path needs to be smoothed.

[0031] The smoothing area is set with the cusp as the midpoint, and the paths within the smoothing area are smoothed using a cubic polynomial curve. , to make It is a continuous smooth path and can avoid obstacles, so it is necessary to and The paths within the region have a common endpoint and a common tangent at the common endpoint. At the same time, the paths within the region can avoid all obstacles in the sub-region. In addition, Punish is a tangent line, Punish is a tangent line; 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 the sharp points are smoothed, and the smoothing effect of the first sharp point is as follows Figure 4 As shown, the second point smoothing effect is as follows Figure 5 As shown, the smoothing effect of the third cusp is as follows Figure 6 As shown, the fourth point smoothing effect is as follows Figure 7 As shown in the figure, the smoothed path can avoid obstacles and sharp turns.

[0032] The process of derivation of obstacle constraints is as follows For example: judge If there are obstacles inside, If there is no obstacle inside, no constraints are required, and the corresponding obstacle avoidance constraint set is an empty set; if If there are obstacles inside, in order to make the path curve avoid the obstacles, the obstacle avoidance constraints need to be met: (1) The two end points of the curve are on the same side of the upper and lower boundary lines of all obstacles; (2) If there are points on the curve where the tangent line is parallel to the obstacle boundary line, they are all on the same side of the upper and lower boundary lines of the obstacle as the two end points of the curve; Assumptions Initially, it is an empty set. The number of obstacles is , in order to make the path satisfy the obstacle avoidance constraint (1), assuming that The lower and upper boundary functions of the obstacle are: ; ; Where, is an undetermined parameter, which is obtained by the coordinates of the obstacle vertex. Therefore, Need to meet: ; ; ; Add the above constraints to the set .

[0033] To make the path curve satisfy the obstacle avoidance constraint (2), calculate The horizontal coordinate of the point where the tangent line on the inner path curve is parallel to the lower boundary line of the obstacle, that is, solving the equation , and get the solution and ,judge and Is it a real number? If it is not a real number, no constraints are required; if and Is a real number, judge Whether it belongs to If it does not belong to, then no constraints are required; if it belongs to, then the function Need to meet: ; calculate The horizontal coordinate of the point where the tangent line on the inner path curve is parallel to the upper boundary line of the obstacle, that is, solving the equation , and get the solution and ,judge and Is it a real number? If it is not a real number, no constraints are required; if and Is a real number, judge Whether it belongs to If it does not belong to, then no constraints are required; if it belongs to, then the function Need to meet: ; Add the above constraints to the set ,right The above operations are performed on the upper and lower boundaries of all obstacles.

[0034] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents, and these modifications or replacements 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: include: S1. Establish a plane rectangular 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; S2, project the starting point, end point and vertices of each obstacle onto the horizontal axis of the plane rectangular coordinate system to obtain a set of projection points, and divide the environment area into A continuous sub-region, recording the coordinates of the intersection of the obstacle in the sub-region and the sub-region boundary; S3. Construct a linear polynomial path function in each sub-area, construct a path from the start point to the end point based on the path functions of all sub-areas, and establish a total path length objective function using curve integrals; S4. Establish an optimization problem for the objective function under dual constraints, including a path continuity constraint and an obstacle avoidance constraint. Solve the problem to obtain the minimum value and optimal independent variable value of the objective function under the dual constraints. Based on the optimal independent variable value of the objective function, obtain the shortest broken line path from the starting point to the end point that avoids all obstacles. S5. Based on the shortest broken line path, a smoothing area is set with the cusp as the midpoint. A cubic polynomial curve is used to smooth all paths within the smoothing area to obtain the optimization objective function. The optimization problem of the optimization objective function under triple constraints is established. The triple constraints include 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.

2. The spatial continuous path planning method based on curve integration according to claim 1, characterized in that: S1 includes establishing a plane rectangular coordinate system of the environment area, and determining the starting point, end point and obstacle set of the path planning based on the plane rectangular coordinate system of the environment area. The coordinates of each obstacle vertex in , , the starting point coordinates are , the end point coordinates are , the environmental areas are: ； Where, For the environmental area, for In the coordinate range of the horizontal axis, , for At the maximum value on the horizontal axis, for In the coordinate range of the vertical axis, , for At the maximum value on the vertical axis, and are all non-negative real numbers, is the Cartesian product.

3. The spatial continuous path planning method based on curve integration according to claim 2, characterized in that: S2 includes, S2.1, projecting the starting point, the end point and the vertices of each obstacle onto the horizontal axis of the plane rectangular coordinate system to obtain the corresponding projection point set , ,based on Will Divided into contiguous subregions: ； ； Where, for No. sub-regions, for width.

4. The spatial continuous path planning method based on curve integration according to claim 3, characterized in that: S2 includes, S2.2, records Internal obstacles and The intersection coordinates of the boundaries, The coordinates of the lower intersection 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 , and the coordinates of the lower intersection point with the right boundary of the region are , and the coordinates of the upper intersection point with the right boundary of the region are .

5. The spatial continuous path planning method based on curve integration according to claim 4, characterized in that: S3 includes, Construct a linear polynomial path function internally: ； Where, is the path function, is the horizontal axis, for The path function, for The slope of for The intercept of and is the coefficient to be determined; based on Construct a path function from the start point to the end point: ； The total path length objective function is established using curve integration: ； Where, is the objective function, To seek guidance, is the differential.

6. The spatial continuous path planning method based on curve integration according to claim 5, characterized in that: S4 includes, S4.1, path continuity constraints, and Need to meet: ； ； ； S4 includes, S4.2, obstacle avoidance constraints, When there is an obstacle inside, To avoid obstacles, the path endpoint must be on the same side of the upper and lower boundary lines of the obstacle. Inside obstacles, Need to meet: ； ； ； Where, is the index, ; S4 includes, S4.3, establishing the optimization problem of the objective function under the path continuity constraint and obstacle avoidance constraint and solving it to obtain the minimum objective function , , for -dimensional Euclidean space; S4 includes, S4.4, based on the minimum objective function, obtaining the optimal independent variable value, combined with Get the shortest broken line path from the start point to the end point avoiding all obstacles .

7. The spatial continuous path planning method based on curve integration according to claim 6, characterized in that: S5 includes, S5.1, calculation and The slope difference : ； Where, is the slope difference, for the slope of the inner straight path; S5 includes, S5.2, is the threshold value of sudden change in driving direction, when When , the intersection of the two straight line paths is judged to be a sharp point, and the path needs to be smoothed; S5 includes, S5.3, if There are sharp points at the location, set the smooth distance parameter : ； by To smooth the starting point, To smoothly process the end point, plan the shortest curve path.

8. The spatial continuous path planning method based on curve integration according to claim 7, characterized in that: S5 includes, S5.4, setting up smoothing area for: ； Smooth the area Divided into and : ； ； Where, express area, express area; the path function after smoothing is: ； ； Where, is the path function after smoothing, for The cubic coefficient of Overall bending direction and end behavior, for The quadratic coefficient of Symmetry and inflection points, for The linear coefficient of The slope and extreme point location of is a constant term, determining The intersection with the vertical axis, is the unknown coefficient; the optimal path from the smoothing starting point to the smoothing end point is: ； Calculation using curve integral The total length of the path after smoothing is the optimization objective function: ； Where, To optimize the objective function.

9. The spatial continuous path planning method based on curve integration according to claim 8, characterized in that: S5 includes, S5.5, establishing path continuity constraints: ； ； ； Establish path smoothness constraints: ； ； ； S5 includes, S5.6, establishing obstacle avoidance constraints, setting obstacle avoidance constraints for The set of internal obstacle avoidance constraints, let The number of obstacles is ; Set obstacle avoidance constraints for The set of internal obstacle avoidance constraints, let The number of obstacles is The obstacle avoidance constraints are: the endpoints of the curve must be on the same side of the upper and lower boundary lines of all obstacles; the points on the curve whose tangents are parallel to the obstacle boundary lines must be on the same side of the upper and lower boundary lines of the obstacles as the endpoints of the curve. Obstacle avoidance constraints for: ； ； ； ； ； Where, is the obstacle boundary function, is the index, , for Neidi The lower boundary function of the obstacle, for Neidi The upper boundary function of the obstacle, is the index, , for The path curve satisfies the tangent line and the The horizontal coordinate of the point parallel to the boundary line under the obstacle, and satisfy ; for The path curve satisfies the tangent line and the The horizontal coordinate of the point on the obstacle parallel to the boundary line, and satisfy ; The inner obstacle boundary function is: ； ； Where, 、 、 and is an undetermined parameter, which is obtained from the coordinates of the lower and upper boundary endpoints of the obstacle; Obstacle avoidance constraints for: ； ； ； ； ； Where, is the index, ; for Neidi The lower boundary function of the obstacle, for Neidi The upper boundary function of the obstacle, for The path curve satisfies the tangent line and the The horizontal coordinate of the point parallel to the boundary line under the obstacle, and satisfy ; for The path curve satisfies the tangent line and the The horizontal coordinate of the point on the obstacle parallel to the boundary line, and satisfy ; The inner obstacle boundary function is: ； ； Where, 、 、 and It is an undetermined parameter, which is obtained from the coordinates of the lower and upper boundary endpoints of the obstacle.

10. The spatial continuous path planning method based on curve integration according to claim 9, characterized in that: S5 includes, S5.7, establishing and solving the optimization problem of the optimization objective function under the path continuity constraint, the path smoothness constraint, and the obstacle avoidance constraint, and obtaining the minimum optimization objective function: ； ； ； ； ； ； ； Obstacle avoidance constraints ; Obstacle avoidance constraints ; ； Where, for -dimensional Euclidean space; based on ,get The optimal value of the independent variable, combined with Get the shortest smooth path from the start point to the end point avoiding all obstacles .

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