CN114995391B - 4-order B spline curve path planning method for improving A-algorithm - Google Patents
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Abstract
The invention relates to a 4-order B spline curve path planning method for improving an A-algorithm, which comprises the following steps: s1, creating a robot work environment map by adopting a grid method, and defining a starting point and a target point; s2, searching an environment shortest path by adopting an A-algorithm, S3, performing B spline curve processing on the obtained path, and adopting a quasi-uniform B spline curve: the two end nodes have a repetition degree k+1, the middle node is not a decreasing sequence, such as u= {0,0,0,1,2,3,4,5,5,5}, and the quasi-uniform B-spline curve retains the properties of the bezier curve at the two end points: the tangent line of the spline curve at the end point is the connecting line of the two end points of the reciprocal, and a new path is obtained through a B spline curve method. The method has the advantages that the method is improved based on the A-algorithm, and the method can obtain the global optimal solution and simultaneously obtain the local optimal solution by combining the B-spline curve method, so that the path distance is shortened, and the smoothness of the path is improved.
Description
Technical Field
The invention relates to the technical field of path planning, in particular to a 4-order B spline path planning method for improving an A-algorithm.
Background
The path planning technology is an important component in the field of mobile robot research, and is mainly aimed at searching an optimal or suboptimal safe collision-free path from a starting position node to a target position node according to a certain criterion (such as shortest path, least position inflection point, shortest time, etc.) in an environment with obstacles.
The development of the path planning technology marks the intelligent level of the robot to a certain extent, and the advantages and disadvantages of the path planning method directly influence the path planning effect.
At present, many expert scholars at home and abroad are devoted to the research of path planning algorithms, and common optimization algorithms mainly comprise an artificial potential field method, an immune algorithm, an ant colony algorithm, a neural network, a particle swarm algorithm, a genetic algorithm and the like. The algorithm A combines a greedy algorithm and a Dijkstra algorithm, and is a heuristic search algorithm. The algorithm A is a direct searching method which is most effective in solving the shortest path in a static road network, is also the most effective algorithm for solving a plurality of searching problems, and is widely applied to indoor robot path searching, game animation path searching and the like.
Disclosure of Invention
The invention aims to provide a 4-order B spline curve path planning method for improving an A-algorithm, which is used for obtaining a path by combining the A-algorithm of a global path planning algorithm and the B-spline curve method of a local path planning algorithm, so that the path smoothing effect is improved, and the distance value obtained by the traditional A-algorithm is reduced.
The technical scheme adopted for solving the technical problems is as follows:
a4-order B spline curve path planning method for improving an A-algorithm comprises the following steps:
s1, creating a robot work environment map by adopting a grid method, and defining a starting point and a target point;
s2, searching an environment shortest path by adopting an A-algorithm, wherein the A-algorithm comprises the following steps of:
s21, adding a starting point into an open list;
s22, repeating the following steps:
s221, traversing open list, searching a node with the minimum F value, taking the node as a node to be processed currently, and then moving the node to close list, wherein F=G+H, G represents the moving overhead from an initial position A to a specified grid to be detected along a generated path, and H specifies the estimated moving overhead from the grid to be detected to a target node B;
s222, checking 8 adjacent squares of the current square one by one, if the current square is unreachable or is in a close list, ignoring the current square, otherwise, performing the following operation:
s2221, if it is not in the open list, add it to the open list and set the current pane as its parent;
s2222, if it is already in open list, checking if this path (i.e. it arrives there via the current square) is more recent, if so, setting its parent as the current square, and recalculating its G and F values;
s223, stopping searching when the following conditions are met:
s2231, adding the endpoint to the open list, where the path has been found, or,
s2232, searching for the end point fails, and the open list is empty, at which time there is no path;
s23, starting from the end point, each square moves along the father node until reaching the start point to form a path;
s3, performing B spline curve processing on the obtained path:
s31, setting a path coordinate point obtained by an A-algorithm as P 0 ,P 1 ,P 2 ,…,P n A total of n+1 control points, which are used for defining the trend and the limit range of the spline curve, and the definition of the k-order B spline curve is as follows:
wherein B is i,k (u) is the ith k-th order B-spline basis function, and the control point P i Correspondingly, k is more than or equal to 1; u is an argument;
s32, the basis function has the following Deboolean-Cox recursion formula:
s33, adopting a quasi-uniform B spline curve: the two end nodes have a repetition degree k+1, the middle node is not a decreasing sequence, such as u= {0,0,0,1,2,3,4,5,5,5}, and the quasi-uniform B-spline curve retains the properties of the bezier curve at the two end points: the tangent line of the spline curve at the end points is the connecting line of the two end points of the reciprocal;
s34, obtaining a new path through a B spline curve method.
The method has the advantages that the method is improved based on the A-algorithm, and the method can obtain the global optimal solution and simultaneously obtain the local optimal solution by combining the B-spline curve method, so that the path distance is shortened, and the smoothness of the path is improved.
Drawings
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
FIG. 1 is a schematic flow chart of the present invention;
FIG. 2 is a schematic view of the direction of movement of the robot of the present invention;
fig. 3 is a conventional a-algorithm optimizing path diagram;
FIG. 4 is a modified A-algorithm optimizing path diagram;
FIG. 5 is a graph of path comparisons derived from two algorithms;
FIG. 6 is a schematic diagram of a search route of others improving the algorithm A in another grid environment;
FIG. 7 is a schematic view of the optimizing route of the method of the present invention in another grid environment.
Detailed Description
As shown in fig. 1, the method for planning a 4-order B spline curve path for improving an a-algorithm provided by the invention comprises the following steps:
s1, creating a robot work environment map by adopting a grid method, and defining a starting point and a target point;
s2, searching an environment shortest path by adopting an A-algorithm, wherein the A-algorithm comprises the following steps of:
s21, dividing the area to be searched into square lattices. This is the first step in finding the path, simplifying the search area. This particular approach simplifies our search area into a 2-dimensional array. Each entry of the array represents a trellis whose state is walkable or non-walkable. The shortest path from a to B is found by using the algorithm a, and the side length of each square is 10, i.e. the moving overhead in the vertical and horizontal directions is 10. The diagonal movement overhead is therefore approximately equal to 14.
S22, starting from a starting point A, adding the starting point A into an open list (open list) formed by squares, wherein the open list is like a shopping list. The lattice in the Open list may or may not be along the way. It can be seen as a list to be checked. Looking at the 8 tiles adjacent to A, add the walkable or reachable tiles to the open list. And set the starting point a as the parent node of these squares. A is then removed from the Open List and added to the Close List, each square in the Close List is not of interest.
S23, next, selecting a square adjacent to the starting point A from the open list. F values of nodes in the Open List are compared, where f=g+h. G represents the movement overhead from the initial position a along the generated path to the designated grid to be detected. H is a heuristic function and is also known as a heuristic, since it is uncertain what obstacles will appear in front before finding the unique path, an algorithm for calculating H is used, specifically determined according to the actual scenario. In the simplified model, H is the conventional Manhattan distance (Manhattan Distance), i.e., the sum of the distances taken in the transverse and longitudinal directions. And finding that the F value of one node on the side A is minimum after comparison. Select it as the current processing node and delete this point from the Open List, move to the Close List.
S24, judging 8 grids around the node, and if the 8 grids cannot pass through (such as a wall, water or other illegal terrains) or are already in a Close List, neglecting. Otherwise, the following steps are executed:
s241, if the neighboring grid of the current processing node is already in the Open List, it is checked whether this path is better, i.e. it is calculated whether the grid reached via the current processing node has a smaller G value. If not, do nothing. Conversely, if the G value is smaller, the parent node of that box is set as the current processing node (the box we selected), and then the F and G values of that box are recalculated.
S242, if the neighboring lattice of the current processing node is not in the Open List, it is added, and its parent node is set as the node.
S24, repeating the process until the end point is added to the open list.
S25, starting from the end point, moving along the arrow toward the parent node until returning to the start point, which is the path obtained by the a-algorithm.
S3, performing B spline curve processing on the obtained path:
s31, setting a path coordinate point obtained by an A-algorithm as P 0 ,P 1 ,P 2 ,…,P n A total of n+1 control points, which are used for defining the trend and the limit range of the spline curve, and the definition of the k-order B spline curve is as follows:
wherein B is i,k (u) is the ith k-th order B-spline basis function, and the control point P i Correspondingly, k is more than or equal to 1; u is an argument.
S32, the basis function has the following Deboolean-Cox recursion formula:
s33, adopting a quasi-uniform B spline curve: the order k is chosen to be 4, the two end nodes have a repetition degree k+1, and the middle node has a non-decreasing sequence, such as U= {0,0,0,1,2,3,4,5,5,5}. The quasi-uniform B-spline retains the properties of the bezier curve at both endpoints: the tangent line of the spline curve at the end point is the connecting line of the two end points of the reciprocal.
S34, obtaining a new path through a B spline curve method.
The effect of the invention can be further illustrated by the following simulation experiments:
to verify the correctness and rationality of the method, matlab language programming is used to simulate the algorithm under a 20×20 grid environment model and compare it with the conventional a-algorithm.
To further verify the superiority of the improved algorithm proposed by the present invention, the present invention was compared with another conventional a-algorithm, using random generation of obstacles on a 20 x 20 grid map, and comparing the calculated path lengths.
As can be seen from fig. 3, the conventional a-algorithm needs a path 15.31 to reach the end point, and as can be seen from fig. 4, the modified a-algorithm needs only a path 14.81 to reach the end point, which is different for different maps and different start-end position differences.
By contrast simulation it can be concluded that: the path planning using the improved a-algorithm of the present invention is significantly better than the conventional a-algorithm. And the A-algorithm provided by the invention is smoother in the aspect of path optimization than the traditional A-algorithm.
To further verify the stability of the improved algorithm proposed by the present invention, the present invention was compared with another improved algorithm a, which is an improved algorithm a described in journal "computer simulation", pages 313 to 317, p.38, p.313 to 317, p.38, robot movement path optimization simulation based on the improved algorithm a ", of the journal, and was simulated using the method of the present invention under the grid environment condition of 20×20 described in the article.
As can be seen from fig. 6, the algorithm a modified by others requires 20.06 to reach the endpoint; as can be seen from fig. 7, the method of the present invention only requires 18.06 to reach the endpoint.
By contrast simulation it can be concluded that: the path planning efficiency of the improved A-algorithm is obviously superior to that of the traditional A-algorithm. The improved A-algorithm provided by the invention has faster evolution than the traditional A-algorithm and the improved A-algorithm of other people, which shows that the improved A-algorithm provided by the invention has high stability in the aspect of path optimization.
The above description is only a partial example of the invention and is not intended to limit the invention in any way; any person skilled in the art can make many possible variations and modifications to the technical solution of the present invention or modifications to equivalent embodiments using the methods and technical contents disclosed above, without departing from the scope of the technical solution of the present invention. Therefore, any simple modification, equivalent substitution, equivalent variation and modification of the above embodiments according to the technical substance of the present invention, which do not depart from the technical solution of the present invention, still fall within the scope of the technical solution of the present invention.
Claims (1)
1. A4-order B spline curve path planning method for improving an A-algorithm comprises the following steps:
s1, creating a robot work environment map by adopting a grid method, and defining a starting point and a target point;
s2, searching an environment shortest path by adopting an A-algorithm, wherein the A-algorithm comprises the following steps of:
s21, adding a starting point into an open list;
s22, repeating the following steps:
s221, traversing open list, searching a node with the minimum F value, taking the node as a node to be processed currently, and then moving the node to close list, wherein F=G+H, G represents the moving overhead from an initial position A to a specified grid to be detected along a generated path, and H specifies the estimated moving overhead from the grid to be detected to a target node B;
s222, checking 8 adjacent squares of the current square one by one, if the current square is unreachable or is in a close list, ignoring the current square, otherwise, performing the following operation:
s2221, if it is not in the open list, add it to the open list and set the current pane as its parent;
s2222, if it is already in open list, checking if this path is closer, if so, setting its parent as the current pane, and recalculating its G and F values;
s223, stopping searching when the following conditions are met:
s2231, adding the endpoint to the open list, where the path has been found, or,
s2232, searching for the end point fails, and the open list is empty, at which time there is no path;
s23, starting from the end point, each square moves along the father node until reaching the start point to form a path;
s3, performing B spline curve processing on the obtained path:
s31, setting a path coordinate point obtained by an A-algorithm as P 0 ,P 1 ,P 2 ,…,P n A total of n+1 control points, which are used for defining the trend and the limit range of the spline curve, and the definition of the k-order B spline curve is as follows:
wherein B is i,k (u) is the ith k-th order B-spline basis function, and the control point P i Correspondingly, k is more than or equal to 1; u is an argument;
s32, the basis function has the following Deboolean-Cox recursion formula:
s33, adopting a quasi-uniform B spline curve: the two end nodes have a repetition degree k+1, the middle node is in a non-decreasing sequence, and the quasi-uniform B spline curve retains the properties of the Bezier curve at the two end points: the tangent line of the spline curve at the end points is the connecting line of the two end points of the reciprocal;
s34, obtaining a new path through a B spline curve method.
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