CN113485379A - Mobile robot path planning method for improving A-Star algorithm - Google Patents
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Abstract
The invention discloses a mobile robot path planning method for improving an A-S t ar algorithm. Aiming at a two-dimensional grid map, how to more efficiently find out an optimal path by a mobile robot is a problem. The invention provides an improved algorithm based on A-S t ar, mainly aiming at the problem that the efficiency of a mobile robot is lower when the mobile robot uses the A-S t ar algorithm to plan a path under a two-dimensional grid map. The algorithm adopts an intermediate point searched between the starting point and the target point as a third node, so that the algorithm can simultaneously expand four search trees from the starting point, the intermediate point and the target point and simultaneously search for an optimal path, thereby improving the efficiency of the algorithm in path planning. In addition, an obstacle avoidance rule is added to the algorithm, so that the algorithm can more quickly deal with path planning in a complex space. Finally, the mobile robot finds the optimal path more quickly under complex conditions.
Description
Technical Field
The invention relates to the field of robot control, in particular to a mobile robot path planning method for improving an A-Star algorithm.
Background
The final purpose of path planning of the mobile robot is to find a path from a starting point to a target point, but the precondition is that the mobile robot can not collide with an obstacle when moving to the target point. In addition, on the premise of meeting the goal, how to find the optimal path with the shortest distance in the shortest time and the lowest cost needs to be solved.
Algorithms for planning shortest paths of common two-dimensional grid maps include Dijkstra algorithm, optimal priority search algorithm, A-Star algorithm, Floyd algorithm and the like. The Dijkstra algorithm is proposed by dickstra, a netherlands computer scientist, in 1959, and is a shortest path algorithm from one vertex to the rest of the vertices, and the problem of the shortest path in the weighted graph is solved. The Dijkstra algorithm is mainly characterized in that the Dijkstra algorithm expands outwards layer by taking a starting point as a center until the Dijkstra algorithm expands to a terminal point. Although Dijsktra's algorithm can eventually find a shortest path in any complex situation. Since Dijkstra's algorithm uses a divergent search, the spatial and temporal complexity of the algorithm is high. In order to solve the problem of Dijkstra algorithm, Nils John Nilsson, Peter E.Hart and Bertram Raphael jointly invented an A-Star search algorithm in 1968, and bring important influence to the field of artificial intelligence.
The A-Star algorithm integrates the advantages of BFS (breadth-first search) and Dijkstra algorithm, heuristic search is carried out to improve the efficiency of the algorithm, and an optimal path (based on an evaluation function) can be guaranteed to be found. The heuristic search is that when the next node is selected from the current search node, the selection can be performed through a heuristic function, and the node with the minimum cost is selected as the next search node. The A-Star algorithm is simple and fast, while Dijkstra's search depth may easily become inapplicable in some situations. The a-Star algorithm arises for these situations and can be considered an improvement over Dijkstra's algorithm and DFS. When the method is applied to the field of mobile robots, the A-StarA-Star algorithm calculates a heuristic function value on each node of a working area by using a heuristic function to obtain an optimal solution. If the starting point is far away from the target point and the environment is complex, the A-Star algorithm needs to detect each extended node from the starting point until the extended node reaches the target point. And thus, a huge amount of calculation is generated, resulting in a long path planning time. In addition, under the conditions of complex environment and excessive obstacles, due to the characteristics of the A-Star algorithm, only the node with the minimum cost is searched each time, so that a large number of nodes to be expanded need to be stored, and the memory is overlarge.
And for the two-dimensional grid map, how to make the mobile robot find out the optimal path more efficiently is a problem that needs to be solved by the technicians in the field.
Disclosure of Invention
In order to solve the above problems, the present invention provides a mobile robot path planning method with an improved a-Star algorithm, so as to solve the problem of low efficiency in path planning using the a-Star algorithm.
Aiming at the problem that the A-Star algorithm only expands nodes to a target point singly in the running process of the A-Star algorithm, the invention provides a method for optimizing the A-Star algorithm by combining the A-Star algorithm based on heuristic information expansion nodes and a divide-and-conquer strategy. And selecting a third node between the starting point and the target point to generate four exploration tree expansion nodes, and specifying an obstacle avoidance rule in the expansion process so as to improve the efficiency of the expansion nodes and further improve the path searching speed.
The invention relates to a mobile robot path planning method for improving an A-Star algorithm, which adopts the following technical scheme: finding an intermediate point between the starting point and the target point as a third node, thereby generating four search trees and simultaneously expanding the nodes, and enabling the mobile robot path planning method to simultaneously expand the four search trees from the starting point, the intermediate point and the target point and simultaneously search for an optimal path so as to improve the efficiency of the algorithm in path planning.
Furthermore, the method is also provided with an obstacle avoidance rule, and a response scheme can be quickly made when an obstacle is encountered during expansion.
Further, the step of implementing the obstacle avoidance rule may be:
(1) after the third node is solved, obstacle detection is carried out on the third node before the third node is expanded, whether the third node exists in an obstacle or not is judged, if yes, the step (2) is carried out, and if not, the step (3) is carried out;
(2) if the third node exists in the obstacle, the third node is directly abandoned, the starting point and the target point are respectively used as the target point of the target point and the starting point, the nodes are expanded to the respective target points according to the principle of the A-Star algorithm, namely expanded trees T1 and T2, and the expanded nodes T2 are expanded until meeting with T1 or meeting with the target point of the node, and the whole algorithm stops;
(3) if the third node exists outside the barrier, the nodes are expanded towards four directions, the starting point is expanded towards the third node to form an expanded tree T1, the third node is expanded towards the starting point to form an expanded tree T2, the third node is expanded towards the target point to form an expanded tree T3, and the target point is expanded towards the third node to form an expanded tree T4; the expansion tree T2 stops when the expansion node meets T1 or meets its own target point, and the expansion tree T4 meets T3 or meets its own target point.
Preferably, in the estimation function of the present invention, the h (n) cost value can be calculated using a manhattan distance, a chebyshev distance or a euclidean distance.
The method has the beneficial effects that the method mainly aims at the problem that the efficiency of the mobile robot is low when the A-Star algorithm is used for path planning under a two-dimensional grid map, and the A-Star-based improved algorithm is provided. The algorithm adopts an intermediate point searched between the starting point and the target point as a third node, so that the algorithm can simultaneously expand four search trees from the starting point, the intermediate point and the target point and simultaneously search for an optimal path, thereby improving the efficiency of the algorithm in path planning. In addition, an obstacle avoidance rule is added to the algorithm, so that the algorithm can more quickly deal with path planning in a complex space. Finally, the mobile robot finds the optimal path more quickly under complex conditions.
Drawings
FIG. 1 is a schematic diagram of an A-Star algorithm obstacle avoidance search for mobile robot path planning;
FIG. 2 is a schematic diagram of the searching step when the current point selects the next point during path planning of the mobile robot;
FIG. 3 is a third node diagram of a mobile robot path planning method for improving the A-Star algorithm according to the present invention;
FIG. 4 is a schematic diagram of the algorithm of the present invention when the third node of the mobile robot path planning method for improving the A-Star algorithm is present in an obstacle;
FIG. 5 is a schematic diagram of the algorithm of the mobile robot path planning method for improving the A-Star algorithm according to the present invention when the third node is not in the obstacle;
fig. 6 is an algorithm flowchart of a mobile robot path planning method for improving the a-Star algorithm according to the present invention.
Detailed Description
The technical solution of the present invention is further described in detail by a specific embodiment and with reference to the accompanying drawings.
In order to fully understand the technical scheme of the invention, the A-Star algorithm is briefly introduced as follows:
when the A-Star algorithm is applied to path planning of a mobile robot, the A-Star algorithm is used for global path planning, overall path planning is carried out according to a given target position and a global map, and an optimal path from the robot to the target position is calculated by using the A-Star algorithm in navigation and is used as a global path of the robot.
The application of the A-Star algorithm mainly comprises the steps of virtualizing a map, dividing the map into a plurality of small blocks, representing the map by using a two-dimensional array, and finally planning a path according to a minimum cost principle. The specific process is that nodes are continuously expanded to a target point from a starting point according to an expansion principle, the cost value of each probed grid node is calculated, the state of the node is updated until the target point is searched, the node is stopped when the target point is searched, the minimum cost node is recorded during expansion, and finally the optimal path is obtained according to the recorded node. In the process, the A-Star algorithm, the Dijkstra algorithm and the BFS algorithm have basically the same flow, and the main difference is that the cost function is different. The A-Star algorithm is one of the most popular choices in the graph search algorithm, integrates the advantages of the Dijkstra algorithm and the BFS algorithm, utilizes a unique heuristic function of the A-Star algorithm, and adopts the formula I as the heuristic function of the A-Star algorithm, so that the A-Star algorithm is relatively flexible and can be used in various situations.
f(n)＝g(n)+h(n)
(formula one)
Wherein n is a grid node in the path; g (n) is the shortest path cost function to the current point, and h (n) is the shortest straight path cost function to the target point.
In the estimation function of the A-Star algorithm, the h (n) cost value can be calculated using Manhattan distance, Chebyshev distance, or Euclidean distance. One embodiment of the present invention uses manhattan distance as the band value.
Setting the coordinates of the current node as (Xi, Yi), the target node as (Xn, Yn), the formula two as the distance between the current node and the horizontal line of the target node, the formula three as the distance between the current node and the column of the target node, and the formula four as h (n) as the cost distance between the starting point and the ending point, wherein zxdj is the linear distance.
Xh＝|(Xn-Xi)|
(formula two)
YhEither | Yn-Yi | (equation three)
H(n)＝ZXDJ*(Xh+Yh) (formula four)
As shown in fig. 1, the search area is shown, in which the node wall is an obstacle node and the blank node is a walkable node. Fig. 2 shows the searching step when the current point selects the next point, assuming that the straight line cost (zxdj) is 10 and the oblique line cost (xxdj) is 14, as shown in fig. 2, the cost function of the lower right corner is the minimum, so the next node coordinate is (3, 4), and so on, if touching the wall, according to the obstacle-encountering rule set before, the obstacle is not considered to be within the considered range; and stopping until the final destination point is reached, and obtaining the shortest path, wherein the path connected by the broken line represents the found shortest path, as shown in fig. 1.
The invention discloses a mobile robot path planning method for improving an A-Star algorithm. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
Although the speed of the A-Star algorithm expanded node is greatly improved compared with the Dijkstra algorithm and the BFS algorithm, the problem of slightly low planning efficiency still exists in some fields needing high sensitivity, such as unmanned aerial vehicle obstacle avoidance, unmanned driving and the like. In view of the above reasons, the invention proposes a four-way a-Star algorithm, and the main design concept is to trade space for time, wherein some division strategies are fused, and nodes are extended under the heuristic function rule of the traditional a-Star algorithm.
The improvement proposed to the a-Star algorithm is mainly:
1. firstly, the coordinates of a third node are calculated through a formula, and the algorithm realizes that four expansion trees are simultaneously carried out based on the expansion principle of the A-Star algorithm, so that the effect of doubling the expansion of the A-Star algorithm is achieved.
2. And secondly, an obstacle avoidance rule is added into the algorithm, so that the decision is quickly made under the condition of judging the state of the third node, the efficiency of the algorithm is improved, and the speed of finding the optimal path is increased.
In order to realize the simultaneous expansion of the algorithm of the invention to four target points, a third node needs to be selected in advance. Therefore, the third point of the 1 st and the first points is selected as follows:
and calculating coordinates of a third node by using the preset starting point and the preset target point according to a formula five and a formula six, wherein the coordinates of the starting point are assumed to be (X1, Y1), the coordinates of the target point are assumed to be (X2, Y2), and the coordinates of the third node are assumed to be (X3, Y3).
As shown in fig. 3, the middle one of the filled squares is the third node 31, and the calculation formulas are formula five and formula six:
X3＝(X1+X2) /2 (formula five)
Y3＝(Y1+Y2) /2 (formula six)
Additionally, after calculating the third node: in view of the fact that sometimes complex environments are encountered, and obstacles are encountered in the operation process of the algorithm, the invention further sets an obstacle avoidance principle, and the encountered obstacle states mainly include the following two conditions: 1) two cases when the third node is among the obstacle nodes and 2) the third node is not among the obstacle nodes.
Therefore, the various obstacle avoidance principles in point 2 of the present invention are respectively explained as follows:
(1) after the third node is solved, the third node is subjected to obstacle detection before the third node is expanded, whether the third node exists in an obstacle or not is judged, if the third node exists in the obstacle, the step (2) is carried out, and if the third node does not exist in the obstacle, the step (3) is carried out;
(2) if the third node exists in the barrier nodes, the third node is directly abandoned, the starting point and the target point are respectively used as the target point of the target point and the target point of the starting point, the nodes are expanded to the respective target points according to the principle of the A-Star algorithm, namely an expanded tree T1 and an expanded tree T2, and the expanded tree T2 expands the nodes until meeting the target point of the nodes or meeting the expanded tree T1, and the whole algorithm stops;
(3) if the third node does not exist in the barrier nodes, the nodes are alternately expanded to four directions, the starting point is expanded to the third node to be T1, the third node is expanded to the starting point to be T2, the third node is expanded to the target point to be T3, and the target point is expanded to the third node to be T4; the T2 expansion node stops expanding until meeting with the self node or meeting with the T1 expansion node, and the T4 also stops expanding until meeting with the self node or meeting with the T3 expansion node;
2.3 when the third node fails
When it is detected that the third node exists in the obstacle, the start point is set to be expanded to the target point by T1, and the target point is expanded to the start point by T2. Based on the A-Star algorithm heuristic function, T1 and T2 alternately expand, and stop expanding when T2 expands to the starting point until meeting T1 or the starting point, and simultaneously stop expanding when T3 expands to the target point until meeting T4 or the target point. As shown in fig. 4, where T1 expands nodes to a third node, T2 expands the path, eventually meeting at coordinate (6, 5); until the convergence with the expansion point of the T2 expansion path stops.
2.4 third node not failed
Let the start point expand to a third node as T1, the third node expand to a start point as T2, the third node expand to a target point as T3, and the target point expand to a third node as T4. If the third node is not in the obstacle, T2 extends towards the starting point and T1 extends towards the third node. If the T2 meets the T1 expansion node in the expansion process or meets the starting point, stopping; if T1 meets T2 expansion node or meets a third node in the expansion process, stopping; and if the T3 expands towards the end point, the T4 expands towards the third node if meeting with the T4 expansion node midway or the end point, and the T4 expands towards the third node if meeting with the T3 expansion node midway or the third node, and finally the optimal path is obtained, as shown in FIG. 5.
The following detailed description of a specific embodiment is provided:
the invention discloses a mobile robot path planning method using an improved A-Star algorithm in a robot navigation device, which utilizes the improved A-Star algorithm to calculate the optimal path from a robot to a target position as the global path of the robot.
In this embodiment, as in the prior art, the map is virtualized and divided into many small blocks, the map is represented by a two-dimensional array, and then the improved a-Star algorithm of the present invention is adopted to perform path planning following the principle of minimum cost.
Fig. 6 is a flowchart of an algorithm of the mobile robot path planning method for improving the a-Star algorithm according to the present invention.
The steps of the improved A-Star algorithm are as follows:
first, start → select third node → determine if the third node is in obstacle:
the algorithm searches for an intermediate point between the starting point and the target point as a third node, so that four search trees are generated and nodes are expanded simultaneously, the mobile robot path planning method expands four search trees from the starting point, the intermediate point and the target point simultaneously and simultaneously searches for an optimal path to improve the efficiency of the algorithm in path planning, and the coordinate calculation of the third node can adopt a formula five and a formula six.
Secondly, if the judgment result is yes, the step (1) is carried out, otherwise, the step (2) is skipped
Step (1): discarding the third node → building T1, T2 expanded tree → alternating steps (1.1) and (1.2);
step (1.1): t1 expands to the target point → judges that the T2 meets the T1 expansion point → turns to step (1.3);
step (1.2): t2 expands to the target point → judges that the T1 meets the T2 expansion point → turns to step (1.3);
step (1.3): t1 meeting T2 → transfer step (5);
step (2): third node is reserved → T1, T2, T3, T4 tree is built → steps (2.1), (2.2), (2.3) and (2.4) are run alternately:
step (2.1): t1 expands toward the third node → judge T2 meets with T1 expansion point → step (2.5);
step (2.2): expanding the T2 to the starting point → judging that the T1 meets the T2 expansion point → step (2.5);
step (2.3): t3 expands to the target point → judges that the T3 meets the T4 expansion point → step (2.5);
step (2.4): t4 expanding toward the end point → judging that the T4 meets the T3 expansion point → step (2.5);
step (2.5): t1 meeting T2, T3 meeting T4 → transfer step (5);
and (5): and (5) finishing the algorithm.
Those skilled in the art will appreciate that: the invention discloses a mobile robot path planning method for improving an A-Star algorithm.
Although the present invention has been described in detail with reference to the above embodiments, it should be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the spirit and scope of the invention.
Claims (6)
1. A mobile robot path planning method for improving an A-Star algorithm is characterized in that the algorithm searches for an intermediate point between a starting point and a target point to serve as a third node, so that four search trees are generated and nodes are expanded simultaneously, the mobile robot path planning method expands the four search trees from the starting point, the intermediate point and the target point simultaneously and searches for an optimal path, and the efficiency of the algorithm in path planning is improved.
2. The method for planning the path of a mobile robot with an improved a-Star algorithm of claim 1, wherein the third point selecting step of the method is as follows:
the coordinates of the third node are calculated by using a formula five and a formula six, then the algorithm realizes that four expansion trees are simultaneously carried out based on the expansion principle of the A-Star algorithm so as to achieve the effect of doubling the expansion of the A-Star algorithm,
X3＝(X1+X2) /2 (formula five)
Y3＝(Y1+Y2) /2 (formula six)
Wherein, X1、Y1And X2、Y2Is the coordinates of the first node and the second node, X3、Y3Is the third node coordinate.
3. The method as claimed in claim 2, wherein the selected third node is added with a judgment rule that divides the obstacle condition into:
1) two cases when the third node is among the obstacle nodes and 2) the third node is not among the obstacle nodes.
4. The method for planning the path of the mobile robot with the improved A-Star algorithm of claim 3, wherein the obstacle avoidance rule is implemented by the following steps:
(1) after the third node is solved, obstacle detection is carried out on the third node before the third node is expanded, whether the third node exists in an obstacle or not is judged, if yes, the step (2) is carried out, and if not, the step (3) is carried out;
(2) if the third node exists in the obstacle, the third node is directly abandoned, the starting point and the target point are respectively used as the target point of the target point and the starting point, the expansion is carried out on the respective target points according to the principle of an A-Star algorithm, namely expansion trees T1 and T2, the T2 expansion node meets the T1 expansion node in the midway or one of the expansion trees finds the target point of the expansion node, and the whole algorithm is stopped;
(3) if the third node exists outside the barrier, the nodes are expanded to four directions simultaneously, the starting point is expanded to the third node to form an expanded tree T1, the third node is expanded to the starting point to form an expanded tree T2, the third node is expanded to the target point to form an expanded tree T3, and the target point is expanded to the third node to form an expanded tree T4; the expansion tree T2 expansion node meets the expansion tree T1 expansion node and the expansion tree T3 also stops until meeting the expansion tree T4.
5. The method for planning the path of the mobile robot with the improved A-Star algorithm of claim 1, comprising the following steps:
the map is virtualized and divided into a plurality of small blocks, the map is represented by a two-dimensional array, and then the optimal route from the robot to the target position is calculated by using the improved A-Star algorithm to be used as the global route of the robot.
6. The method for planning the path of the mobile robot with the improved A-Star algorithm according to claim 5, wherein the improved A-Star algorithm comprises the following specific steps:
first, start → select the third node → determine if the third node is in the obstacle,
secondly, if the judgment result is yes, the step (1) is carried out, otherwise, the step (2) is skipped
Step (1) abandoning the third node → building T1, T2 expanded tree → alternatively performing steps (1.1) and (1.2):
step (1.1): t1 expands to the target point → judges that the T2 meets the T1 expansion point → turns to step (1.3);
step (1.2): t2 expands to the target point → judges that the T1 meets the T2 expansion point → turns to step (1.3);
step (1.3): t1 meeting T2 → transfer step (5)
Step (2): third node is reserved → T1, T2, T3, T4 tree is built → steps (2.1), (2.2), (2.3) and (2.4) are run alternately:
step (2.1): t1 expands toward the third node → judge T2 meets with T1 expansion point → step (2.5);
step (2.2): expanding the T2 to the starting point → judging that the T1 meets the T2 expansion point → step (2.5);
step (2.3): t3 expands to the target point → judges that the T3 meets the T4 expansion point → step (2.5);
step (2.4): t4 expanding toward the end point → judging that the T4 meets the T3 expansion point → step (2.5);
step (2.5): t1 meeting T2, T3 meeting T4 → transfer step (5);
and (5) finishing the algorithm.
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