CN103529843A - Lambda path planning algorithm - Google Patents
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- 230000004888 barrier function Effects 0.000 claims description 25
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Abstract
The invention discloses a Lambda path planning algorithm, which is improved aiming at the problems of more nodes and more time consumption in an open table in the existing A algorithm. The algorithm comprises the following steps: the method comprises the steps of constructing a path planning environment by adopting a visual graph, creating an open table and a closed table, creating a data structure of a node, searching a path, and adding a Smooth process to the path. The method is mainly applied to rapid path planning of two-dimensional and three-dimensional spaces of the robot.
Description
[technical field]
The present invention relates to field of intelligent control, particularly mobile robot's Path Planning Technique field.
[background technology]
Along with the further raising of industrial robot application requirements, existing 2D path planning technology can not meet industrial robot demand in a lot of fields, people in the urgent need to a set of maturation, can be applied to three-dimensional fast path planning technology.
Planing method based on free space structure is the important paths planning method of a class.These class methods are first expressed as figure by method of geometry by the continuous environment with barrier, then utilize one of graph search method search from starting point to impact point without touching shortest path.
The scholar in robot research field is usually by expressions such as continuous grid map for environment (Grid graphs), Visual Graph (Visibility graphs), navigation grid (Navigation meshs), probability route map (Probabilistic road map, PRMs) and quick exploration random trees (Rapidly exploring random trees).Wherein, the node in Visual Graph comprises starting point p
startwith terminal p
goal, and the summit of barrier in space.The line that and if only if between two nodes not with space in barrier while intersecting, two nodes are coupled together and have just formed Visual Graph with straight line.Owing to there is no grid restriction, allow to carry out in any direction route searching, the path that the path that search obtains in Visual Graph obtains in grid map is short.
Conventional graph search method comprises non-heuritic approach and heuritic approach.Heuristic search is broadly divided into part preferentially searching method and best first search method.Local preferentially searching method has been chosen after " optimal node " in the process of search, gives up other the brotgher of node, father's node.Owing to having given up other node, may also best node all have been given up, " optimal node " solving, in the best in this stage, might not be just overall the best.And preferably first search method, when search, is not given up node (unless this node is to die for the sake of honour a little), in the appraisal of each step all the subsequent node of current expanding node and before the assessment values of node relatively obtain one " best node ".A* algorithm is exactly a kind of best first search method, and A* algorithm utilizes heuristic information, current not expanding node is chosen from the nearest node of target and is expanded according to the evaluation function value of setting, thereby dwindle search volume; Choose suitable heuristic function, can make A* algorithm there is admissibility.Yet the node that A* algorithm is expanded is many, adopt A* algorithm to carry out path planning at three dimensions and can not guarantee optimum, and consuming time more.
[summary of the invention]
The present invention makes improvements on the basis of algorithm of analyzing A*.Problems more than many, consuming time for contained node in open table in A* algorithm, propose a kind ofly can be applied to robot two dimension, three-dimensional fast Route Planning Algorithm Lambda* path planning algorithm.
Technical scheme of the present invention is as follows:
A path planning algorithm, is characterized in that, comprises the following steps:
(1) adopt the environment of Visual Graph build path planning: adopt barrier enveloping solid envelope barrier, by the starting point p of path planning
start, terminal p
goal, and the summit of barrier, configuration node set P;
(2) create two table: open tables and closed table, the node that wherein in closed table, record had been expanded, the subsequent node that open table is only preserved current expanding node, does not preserve other subsequent node of expanding node; But in the subsequent node of current expanding node, having part may be the subsequent node of expanding node, once enters open list;
(3) creating the data structure of node: α (p) represents in Visual Graph from p
startto the shortest path length of node p, β (p) represents from p to terminal p
goalshortest path length; The g value gval that each node p data structure comprises father node pre, node and f value fval, p.gval represents from starting point p
startarrive the length of the existing shortest path of node p, p.gval>=α (p); Evaluation function value is p.fval=p.gval+hval (p), and heuristic function hval (p) is for p is to terminal p
goalthe estimated value of bee-line, the evaluation function value p.fval representative of node is through this node p, from starting point p
startto terminal p
goalan estimated value of shortest path; If hval (p)≤β (p), heuristic function value is less than node p to terminal p
goalactual shortest path length, can find shortest path;
(4) searching route: expansion present node p
closedtime first empty open table, only by p
closedthe not subsequent node in closed add open, lose father node, the brotgher of node of current expanding node; Due to these nodes of losing may with p
closedvisual, rejoined in open, thus at path p
start, p
1, p
2... px, p is upper, and p adds closed as the subsequent node of px, but the older generation of p and px is visual;
(5) add Smooth process to carry out smoothing processing to path: to check from front to back the node p on path<sub TranNum="93">i</sub>(1≤i≤z-1) and below node p<sub TranNum="94">j</sub>whether (i+1<j≤z) be visual; If visual, the node between them all deleted, and adjusted the pre of level and smooth rear each node, gval, fval.
Described a kind of Lambda* path planning algorithm, is characterized in that, visual referring between node, for spatial obstacle thing, straight-line segment between node, not by the inside of spatial obstacle thing, also not by the common sides of spatial obstacle thing, but allows by the concentric line of spatial obstacle thing; For impediment in plane thing, line segment between dactylus point is not by the inside of impediment in plane thing, also not by the concentric line of impediment in plane thing, but allow by the common point of impediment in plane thing, the whether visual position relationship by internodal line section and each face of barrier enveloping solid judges, between node, can apparent time lineofsight (p, p') be true;
the node set visual with node p.
Described a kind of Lambda* path planning algorithm, is characterized in that, evaluation function value is p.fval=p.gval+hval (p).
Described a kind of Lambda* path planning algorithm, is characterized in that, chooses node p to terminal p
goaleuclidean distance as heuristic function hval (p).
Beneficial effect of the present invention is, due to the subsequent node that open only preserves current expanding node, does not preserve other subsequent node of expanding node, has greatly reduced calculated amount, can within the less time, obtain preferably path.This algorithm increases to cost with less path, has reduced significantly the consuming time of path planning.
[accompanying drawing explanation]
Fig. 1 is A* algorithm false code
Fig. 2 is the path planning algorithm false code of the embodiment of the present invention 1
Fig. 3 is the path smooth algorithm false code that the embodiment of the present invention 1 adopts
Fig. 4 is the path planning algorithm process flow diagram of the embodiment of the present invention 2
[embodiment]
In order to make object, technical scheme, the advantage of the embodiment of the present invention more clear, clear and definite, below in conjunction with embodiment and accompanying drawing, the present invention is described in further details.
Embodiment 1: the algorithm of the invention process when panel path is planned
Shown in Fig. 2, be the algorithm false code of the invention process when panel path is planned.As shown in Figure 2, the path planning algorithm of the embodiment of the present invention 1 comprises:
1. according to the position of barrier and shape, generate enveloping solid, generation pass intermediate point set V, adopts rectangle envelope in the embodiment of the present invention 1, and path intermediate point is the summit of barrier enveloping solid;
2. the data structure in the middle of building, creates open and closed table;
3. by p
startinsert closed table;
4. work as p
goal, in closed table, 5. expanding node, do not turn to; Otherwise smooth paths (algorithm false code as shown in Figure 3), and outgoing route information;
5. using the node of fval minimum in closed as p
closedexpand, in node set V, search not in closed and lineofsight (p, p
closed) for really putting p, as p
closedsubsequent node insert open table, upgrade node data, comprise more father node, node gval and the fval of new node;
If 6. open table is for empty, output " could not find path "; Otherwise the node of selecting fval minimum from open table inserts closed; Proceed to 4..
In embodiment 1, lineofsight (p, p
closed) judgement p and p
closedwhether visual, specifically judge p and p
closedwith barrier O
jthe position relationship of each summit line, lineofsight (p, p
closed) be false while meeting following situation:
◆ there is barrier O
j, p and p
closedline and O
jfour summits in any two summit q
1, q
2line is crossed over mutually, and p is at q
1, q
2one side, p
closedat q
1, q
2another side, q
1at p and p
closedline one side, q
2at p and p
closedthe opposite side of line;
◆ there is barrier O
j, p is at O
jfour summits in any two summit q
1, q
2on line, and at q
1, q
2in line segment;
◆ there is barrier O
j, p
closedat O
jfour summits in any two summit q
1, q
2on line, and at q
1, q
2in line segment;
The path smooth algorithm false code that the embodiment of the present invention 1 adopts as shown in Figure 3.Check from front to back the node p on path<sub TranNum="158">i</sub>(1≤i≤z-1) and below node p<sub TranNum="159">j</sub>whether (i+1<j≤z) be visual.If visual, the node between them all deleted, and adjusted the pre of level and smooth rear each node, gval, fval.Although increased Smooth () process, the also corresponding increase of time consumption, but because Smooth () only carries out smoothing processing to the node on path, the node of processing is few compared with the number of nodes in open table, therefore under same application environment, Lambda* algorithm is consuming time fewer than A* algorithm.
In embodiment 1, adopt respectively algorithm of the present invention and A* algorithm to carry out path planning.Setting 2D environment size is 100*100, and starting point is (0,0), and terminal is (100,100); Random dyspoiesis thing, barrier ratio is made as respectively 0%, 5%, 10%, 20%, 30%, 40%.Two kinds of algorithms are all realized on Matlab2012a, and experiment is Intel (R) Core (TM) 2Duo T6500 by computer CPU model, and dominant frequency is 2.1GHz, and RAM is 1.86Gbyte.Add up in every kind of situation and carry out respectively with two kinds of algorithms the node sum holding in the average path length of 100 path plannings, consuming time, total nodes, expanding node number and open, result is as shown in table 1 below.
Table 1
Result shown in table 1 shows, random moving obstacle ratio is larger, and total nodes increases, and path planning also becomes increasingly complex, and the nodes in gained path and consuming time, expanding node number and open table is all increase trend.
By two kinds of algorithms institute's way to acquire length and consuming time comparing in various barrier ratio situations, result is as shown in table 2 below.
Table 2
In general, under same case, in the nodes that Lambda* need expand and open table, node sum is all significantly less than the respective value of A*, consuming time less.Along with barrier ratio increases, Lambda* path quality that algorithm obtains is a little less than A* algorithm, 1.0030 times of the length average out to A* path that algorithm obtains in Lambda* path that algorithm obtains, be that path has increased by 0.3%, meanwhile, Lambda* algorithm is consuming time has reduced 48.76% with respect to A* algorithm.
Algorithm flow chart while shown in Fig. 4 being the path planning of the invention process under 3D environment.As shown in Figure 4, the path planning algorithm of the embodiment of the present invention 2 comprises:
1. according to the position of barrier and shape, generate enveloping solid, generation pass intermediate point set V, adopts rectangular parallelepiped envelope in the embodiment of the present invention 2, and path intermediate point is the summit of barrier enveloping solid;
2. the data structure in the middle of building, creates open and closed table;
3. by p
startinsert closed table;
4. work as p
goal, in closed table, 5. expanding node, do not turn to; Otherwise smooth paths (algorithm false code as shown in Figure 3), and outgoing route information.
5. using the node of fval minimum in closed as p
closedexpand, in node set V, search not in closed, and lineofsight (p, p
closed) for really putting p as p
closedsubsequent node insert open table.Upgrade node data, comprise more father node, node gval and the fval of new node.
If 6. open table is exported " could not find path " for sky; Otherwise the node of selecting fval minimum from open table inserts closed; Proceed to 4..
The path smooth algorithm flow that embodiment 2 adopts is identical with the path smooth algorithm in embodiment 1, repeats no more.
In embodiment 2, lineofsight (p, p
closed) judgement p and p
closedwhether visual, specifically judge p and p
closedline and rectangular parallelepiped barrier envelope O
jthe relation of 6 square surface positions.Only when having a square surface, p and p
closedline and this face have a common point, and common point is at p and p
closedline segment on time, lineofsight (p, p
closed) be false.
In embodiment 2, adopt respectively algorithm of the present invention and A* algorithm to carry out path planning.Setting 3D environment size is 100*100*100, and starting point is (0,0,0), and terminal is (100,100,100), random dyspoiesis thing, and barrier ratio is made as respectively 0%, 5%, 10%, 20%, 30%, 40%.Two kinds of algorithms are all realized on Matlab2012a, and computer CPU model is Intel (R) Core (TM) 2DuoT6500, and dominant frequency is 2.1GHz, and RAM is 1.86Gbyte.Add up in every kind of situation and carry out respectively the average path length of 100 path plannings with two kinds of algorithms, consuming time, total nodes, the node holding in expanding node number and open sum, result is as shown in table 3 below.
Table 3
Result shown in table 3 shows, random moving obstacle ratio is larger, and total nodes increases, and path planning also becomes increasingly complex, and the nodes in gained path and consuming time, expanding node number and open table is all increase trend.By two kinds of algorithms institute's way to acquire length and consuming time comparing in various barrier ratio situations, result is as shown in table 4 below.
Table 4
In general, under same case, in the nodes that Lambda* need expand and open table, node sum is all significantly less than the respective value of A*, consuming time less.In embodiment 2,1.0025 times of the length average out to A* path that algorithm obtains in Lambda* path that algorithm obtains, path has increased by 0.25%, and meanwhile, Lambda* algorithm is consuming time has reduced 30.11% with respect to A* algorithm.
The above specific embodiment has carried out further instruction to object of the present invention, technical scheme and beneficial effect.The protection domain that the above is not intended to limit the present invention that it should be understood that, all any modifications of making in the spirit and principles in the present invention, is equal within replacement, improvement etc. all should be included in protection scope of the present invention.
Beneficial effect of the present invention is, by reducing the nodes keeping in open table, has reduced calculated amount.Although this can affect path quality to a certain extent, can in the less time, obtain preferably path, can meet the application demand of robot two dimension, the planning of three-dimensional fast path.
Claims (4)
1. a Lambda* path planning algorithm, is characterized in that, comprises the following steps:
(1) adopt the environment of Visual Graph build path planning: adopt barrier enveloping solid envelope barrier, by the starting point p of path planning
start, terminal p
goal, and the summit of barrier, configuration node set P;
(2) create two table: open tables and closed table, the node that wherein in closed table, record had been expanded, the subsequent node that open table is only preserved current expanding node, does not preserve other subsequent node of expanding node; But in the subsequent node of current expanding node, having part may be the subsequent node of expanding node, once enters open list;
(3) creating the data structure of node: α (p) represents in Visual Graph from p
startto the shortest path length of node p, β (p) represents from p to terminal p
goalshortest path length; The g value gval that each node p data structure comprises father node pre, node and f value fval, p.gval represents from starting point p
startarrive the length of the existing shortest path of node p, p.gval>=α (p); Evaluation function value is p.fval=p.gval+hval (p), and heuristic function hval (p) is for p is to terminal p
goalthe estimated value of bee-line, the evaluation function value p.fval representative of node is through this node p, from starting point p
startto terminal p
goalan estimated value of shortest path; If hval (p)≤β (p), heuristic function value is less than node p to terminal p
goalactual shortest path length, can find shortest path;
(4) searching route: expansion present node p
closedtime first empty open table, only by p
closedthe not subsequent node in closed add open, lose father node, the brotgher of node of current expanding node; Due to these nodes of losing may with p
closedvisual, rejoined in open, thus at path p
start, p
1, p
2... px, p is upper, and p adds closed as the subsequent node of px, but the older generation of p and px is visual;
(5) add Smooth process to carry out smoothing processing to path: to check from front to back the node p on path<sub TranNum="230">i</sub>(1≤i≤z-1) and below node p<sub TranNum="231">j</sub>whether (i+1<j≤z) be visual; If visual, the node between them all deleted, and adjusted the pre of level and smooth rear each node, gval, fval.
2. a kind of Lambda* path planning algorithm according to claim 1, it is characterized in that, visual referring between node, for spatial obstacle thing, straight-line segment between node is not by the inside of spatial obstacle thing, do not pass through the common sides of spatial obstacle thing, but allow by the concentric line of spatial obstacle thing yet; For impediment in plane thing, line segment between dactylus point is not by the inside of impediment in plane thing, also not by the concentric line of impediment in plane thing, but allow by the common point of impediment in plane thing, the whether visual position relationship by internodal line section and each face of barrier enveloping solid judges, between node, can apparent time lineofsight (p, p') be true;
the node set visual with node p.
3. a kind of Lambda* path planning algorithm according to claim 1 and 2, is characterized in that, evaluation function value is p.fval=p.gval+hval (p).
4. a kind of Lambda* path planning algorithm according to claim 3, is characterized in that, chooses node p to terminal p
goaleuclidean distance as heuristic function hval (p).
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