CN103529843B - Lambda path planning algorithm - Google Patents
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- 238000013439 planning Methods 0.000 title claims abstract description 36
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- 230000004888 barrier function Effects 0.000 claims description 29
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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 to the Path Planning Technique field of mobile apparatus people.
[background technology]
Along with the further raising that industrial robot application requires, 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 apply to three-dimensional fast path planning technology.
Planing method based on free space structure is the important paths planning method of a class.This kind of method first passes through method of geometry and the continuous environment with barrier is expressed as figure, then utilizes graph search method to search for a nothing from starting point to impact point and touches shortest path.
Continuous print environment grid map (Gridgraphs), Visual Graph (Visibilitygraphs), navigation grid (Navigationmeshs), probability route map (Probabilisticroadmap, PRMs) and rapid discovery random tree (Rapidlyexploringrandomtrees) etc. are usually represented by the scholar in robot research field.Wherein, the node in Visual Graph includes starting point pstartWith terminal pgoal, and the summit of barrier in space.When the line that and if only if between two nodes does not intersect with the barrier in space, two node straight lines are coupled together and just constitutes Visual Graph.Owing to not having grid to limit, it is allowed to carry out route searching in any direction, the path searching for acquisition in Visual Graph is short compared with the path obtained in grid map.
Conventional graph search method includes non-heuritic approach and heuritic approach.Heuristic search is broadly divided into local preferentially searching method and best preferential search method.Local preferentially searching method gives up other the brotgher of node, father's node after have chosen " optimal node " in the process of search.Owing to having given up other node, it is possible to also best node is all given up, " optimal node " solved is simply in the best in this stage, not necessarily overall the best.And preferably preferential search method is when search, it does not have give 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 extensions node and before the assessment values of node compare and obtain one " best node ".A* algorithm is exactly a kind of preferably preferential search method, and A* algorithm utilizes heuristic information, and the node that current non-expanding node is chosen from target is nearest according to the evaluation function value set is extended, thus reducing search volume；Choose suitable heuristic function, then A* algorithm can be made to have admissibility.But node that A* algorithm is expanded is many, A* algorithm is adopted to carry out path planning it cannot be guaranteed that optimum at three dimensions, and consuming time more.
[summary of the invention]
The present invention makes improvements on the basis of the algorithm of analysis A*.For node many problems many, consuming time contained in open table in A* algorithm, it is proposed to one can apply to robot fast Route Planning Algorithm Lambda* path planning algorithm two-dimentional, three-dimensional.
Technical scheme is as follows:
A kind of Lambda* path planning algorithm, it is characterised in that comprise the following steps:
(1) environment of Visual Graph build path planning is adopted: adopt barrier enveloping solid envelope barrier, by the starting point p of path planningstart, terminal pgoal, and the summit of barrier, configuration node set P；
(2) creating two tables: open table and closed table, wherein record the node propagated through in closed table, open table only preserves the subsequent node of current extensions node, does not preserve other subsequent node of expanding node；But, in the subsequent node of current extensions node, have part to be probably the subsequent node of expanding node, once entered open list；
(3) data structure of node is created: α (p) represents in Visual Graph from pstartTo the shortest path length of node p, β (p) represents from p to terminal pgoalActual shortest path length；Each node p data structure comprises father node pre, g value gval and f value fval, the p.gval of node represent from starting point pstartTo 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 p to terminal pgoalThe estimated value of beeline, the evaluation function value p.fval of node represents through this node p, from starting point pstartTo terminal pgoalAn estimated value of shortest path；If hval (p)≤β (p), namely heuristic function value is less than or equal to node p to terminal pgoalActual shortest path length, then can find from starting point pstartTo terminal pgoalShortest path；
(4) searching route: extension present node pclosedTime first empty open table, only by pclosedThe not subsequent node in closed add open, lose the father node of current extensions node, the brotgher of node；Owing to these nodes lost are likely to and pclosedVisually, rejoined in open, thus at path pstart,p1,p2...px, on p, p is as pxSubsequent node add closed, but p with from pstartSet out pxPaths traversed point is visual；
(5) add Smooth process path to be smoothed: the node p checking on path from front to backiWith node p belowjWhether visual, wherein, 1≤i≤z-1, i+1 < j≤z, wherein z is the nodes on path；If visual, then the node between them is all deleted, and adjust pre, gval, the fval of smooth rear each node.
Described a kind of Lambda* path planning algorithm, it is characterised in that visually refer between node, for spatial obstacle thing, straightway between node, not by the inside of spatial obstacle thing, also not by the common sides of spatial obstacle thing, but allows the common wire by spatial obstacle thing；For impediment in plane thing, refer to that the line segment between node is not by the inside of impediment in plane thing, also not by the common wire of impediment in plane thing, but allow the common point by impediment in plane thing, visually whether judged by the position relationship of internodal line section Yu each of barrier enveloping solid, can apparent time lineofsight (p between node, p') it is true, wherein, function lineofsight (p, p') it is used for judging that whether p and p' is visual, specifically judges p and p' and barrier OjThe position relationship of each summit line；It is the node set visual with node p.
Described a kind of Lambda* path planning algorithm, it is characterised in that choose node p to terminal pgoalEuclidean distance as heuristic function hval (p).
The beneficial effects of the present invention is, only preserve the subsequent node of current extensions node due to open, do not preserve other subsequent node of expanding node, greatly reduce amount of calculation, preferably path can be obtained within the less time.This algorithm increases to cost with less path, decreases the consuming time of path planning significantly.
[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 flow chart of the embodiment of the present invention 2
[detailed description of the invention]
In order to make the purpose of the embodiment of the present invention, technical scheme, advantage become apparent from, clearly, below in conjunction with embodiment and accompanying drawing, the present invention is described in further details.
Embodiment 1: the invention process algorithm when panel path is planned
It it is the invention process algorithm false code when panel path is planned shown in Fig. 2.As in figure 2 it is shown, the path planning algorithm of the embodiment of the present invention 1 includes:
1. generating enveloping solid according to the position of barrier and shape, generate path intermediate point set V, adopt rectangular envelope in the embodiment of the present invention 1, path intermediate point is the summit of barrier enveloping solid；
2. build the data structure of centre, create open and closed table；
3. by pstartInsert closed table；
4. p is worked asgoalNot in closed table, then expanding node, turn to 5.；Otherwise smooth paths (algorithm false code is as shown in Figure 3), and outgoing route information；
5. using node minimum for fval in closed as pclosedIt is extended, searches in node set V not in closed and lineofsight (p, pclosed) for really to put p, as pclosedSubsequent node insert open table, update node data, including the father node of more new node, node gval and fval；
If 6. open table is empty, then output " could not find path "；Otherwise, from open table, node city closed minimum for fval is selected；Proceed to 4..
In embodiment 1, lineofsight (p, pclosed) judge p and pclosedWhether visual, specifically judge p and pclosedWith barrier OjThe position relationship of each summit line, lineofsight (p, pclosed) it is false when meeting situations below:
There is barrier Oj, p and pclosedLine and OjFour summits in any two summit q1,q2Line is crossed over mutually, and namely p is at q1,q2One side, pclosedAt q1,q2Another side, q1At p and pclosedLine side, q2At p and pclosedThe opposite side of line；
There is barrier Oj, p is at OjFour summits in any two summit q1,q2On line, and at q1,q2In line segment；
There is barrier Oj, pclosedAt OjFour summits in any two summit q1,q2On line, and at q1,q2In line segment；
The path smooth algorithm false code that the embodiment of the present invention 1 adopts is as shown in Figure 3.Check the node p on path from front to backi(1≤i≤z-1) and node p belowjWhether (i+1 < j≤z) be visual.If visual, then the node between them is all deleted, and adjust pre, gval, the fval of smooth rear each node.Although adding Smooth () process, time consumption also increase accordingly, but owing to the node on path is only smoothed by Smooth (), the node of process is few compared with the number of nodes in open table, under thus like applied environment, Lambda* algorithm is consuming time fewer than A* algorithm.
In embodiment 1, it is respectively adopted inventive algorithm and A* algorithm carries out path planning.Setting 2D environment and be sized to 100*100, starting point is (0,0), and terminal is (100,100)；Stochastic generation barrier, barrier ratio is set to 0%, and 5%, 10%, 20%, 30%, 40%.Two kinds of algorithms all realize on Matlab2012a, and experiment computer CPU model is Intel (R) Core (TM) 2DuoT6500, and it is 1.86Gbyte that dominant frequency is 2.1GHz, RAM.Adding up and carry out the node total number of accommodation in the average path length of 100 path plannings, nodes consuming time, total, expanding node number and open respectively with two kinds of algorithms in every kind of situation, result is as shown in table 1 below.
Table 1
Result shown in table 1 shows, random moving obstacle ratio is more big, and total nodes increases, and path planning also becomes increasingly complex, and gained path and consuming time, expanding node number and the nodes in open table are all increase trend.
By two kinds of algorithms obtained path and consuming time compare in various barrier ratio situations, result is as shown in table 2 below.
Table 2
In general, in the same circumstances, nodes that Lambda* need to extend and open table interior joint sum are all significantly smaller than the respective value of A*, consuming time less.Along with barrier ratio increases, the obtained path quality of Lambda* algorithm is slightly below A* algorithm, 1.0030 times of length average out to the obtained path of A* algorithm in the obtained path of Lambda* algorithm, namely path adds 0.3%, meanwhile, Lambda* algorithm is consuming time decreases 48.76% relative to A* algorithm.
Embodiment 2, algorithm during the invention process path planning under 3D environment
It it is algorithm flow chart during the invention process path planning under 3D environment shown in Fig. 4.As shown in Figure 4, the path planning algorithm of the embodiment of the present invention 2 includes:
1. generating enveloping solid according to the position of barrier and shape, generate path intermediate point set V, adopt cuboid envelope in the embodiment of the present invention 2, path intermediate point is the summit of barrier enveloping solid；
2. build the data structure of centre, create open and closed table；
3. by pstartInsert closed table；
4. p is worked asgoalNot in closed table, then expanding node, turn to 5.；Otherwise smooth paths (algorithm false code is as shown in Figure 3), and outgoing route information.
5. using node minimum for fval in closed as pclosedIt is extended, searches not in closed in node set V, and lineofsight (p, pclosed) it is really put p as pclosedSubsequent node insert open table.Update node data, including the father node of more new node, node gval and fval.
If 6. open table is sky, export " path could not be found "；Otherwise, from open table, node city closed minimum for fval is selected；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, pclosed) judge p and pclosedWhether visual, specifically judge p and pclosedLine and cuboid barrier envelope OjThe relation of 6 square surface positions.Only when there is a square surface, p and pclosedLine and this face have a common point, and common point is at p and pclosedLine segment on time, lineofsight (p, pclosed) it is false.
In embodiment 2, it is respectively adopted inventive algorithm and A* algorithm carries out path planning.Setting 3D environment and be sized to 100*100*100, starting point is (0,0,0), and terminal is (100,100,100), stochastic generation barrier, and barrier ratio is set to 0%, 5%, 10%, 20%, 30%, 40%.Two kinds of algorithms all realize on Matlab2012a, and computer CPU model is Intel (R) Core (TM) 2DuoT6500, and it is 1.86Gbyte that dominant frequency is 2.1GHz, RAM.Adding up the average path length carrying out 100 path plannings in every kind of situation with two kinds of algorithms respectively, consuming time, total nodes, the node total number held in expanding node number and open, result is as shown in table 3 below.
Table 3
Result shown in table 3 shows, random moving obstacle ratio is more big, and total nodes increases, and path planning also becomes increasingly complex, and gained path and consuming time, expanding node number and the nodes in open table are all increase trend.By two kinds of algorithms obtained path and consuming time compare in various barrier ratio situations, result is as shown in table 4 below.
Table 4
In general, in the same circumstances, nodes that Lambda* need to extend and open table interior joint sum are all significantly smaller than the respective value of A*, consuming time less.In example 2,1.0025 times of length average out to the obtained path of A* algorithm in the obtained path of Lambda* algorithm, namely path adds 0.25%, and meanwhile, Lambda* algorithm is consuming time decreases 30.11% relative to A* algorithm.
The purpose of the present invention, technical scheme and beneficial effect have been carried out further instruction by the above specific embodiment.Being it should be understood that the above protection domain being not intended to limit the present invention, all any amendments of making in the spirit and principles in the present invention, equivalent replacement, improvement etc. should be included within protection scope of the present invention.
The beneficial effects of the present invention is, by reducing the nodes kept in open table, decrease amount of calculation.Although this can have impact on path quality to a certain extent, but can obtain preferably path in the less time, it is possible to meet the application demand of robot fast path planning two-dimentional, three-dimensional.
Claims (3)
1. a Lambda* path planning algorithm, it is characterised in that comprise the following steps:
(1) environment of Visual Graph build path planning is adopted: adopt barrier enveloping solid envelope barrier, by the starting point p of path planningstart, terminal pgoal, and the summit of barrier, configuration node set P；
(2) creating two tables: open table and closed table, wherein record the node propagated through in closed table, open table only preserves the subsequent node of current extensions node, does not preserve other subsequent node of expanding node；But, in the subsequent node of current extensions node, have part to be probably the subsequent node of expanding node, once entered open table；
(3) data structure of node is created: α (p) represents in Visual Graph from pstartTo the shortest path length of node p, β (p) represents from p to terminal pgoalActual shortest path length；Each node p data structure comprises father node pre, g value gval and f value fval, the p.gval of node represent from starting point pstartTo 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 p to terminal pgoalThe estimated value of beeline, the evaluation function value p.fval of node represents through this node p, from starting point pstartTo terminal pgoalAn estimated value of shortest path；If hval (p)≤β (p), namely heuristic function value is less than or equal to node p to terminal pgoalActual shortest path length, then can find from starting point pstartTo terminal pgoalShortest path；
(4) searching route: extension present node pclosedTime first empty open table, only by pclosedThe not subsequent node in closed table add open table, lose the father node of current extensions node, the brotgher of node；Owing to these nodes lost are likely to and pclosedVisually, rejoined in open table, thus at path pstart,p1,p2...px, on p, p is as pxSubsequent node add closed table, but p with from pstartSet out pxPaths traversed point is visual；
(5) add Smooth process path is smoothed: the node p checking on path from front to backiWith node p belowjWhether visual, wherein, 1≤i≤z-1, i+1 < j≤z, wherein z is the nodes on path；If visual, then the node between them is all deleted, and adjust pre, gval, the fval of smooth rear each node.
2. a kind of Lambda* path planning algorithm according to claim 1, it is characterized in that, visually refer between node, for spatial obstacle thing, straightway between node is not by the inside of spatial obstacle thing, also not by the common sides of spatial obstacle thing, but the common wire by spatial obstacle thing is allowed；For impediment in plane thing, refer to that the line segment between node is not by the inside of impediment in plane thing, also not by the common wire of impediment in plane thing, but allow the common point by impediment in plane thing, visually whether judged by the position relationship of internodal line section Yu each of barrier enveloping solid, can apparent time lineofsight (p between node, p') it is true, wherein, function lineofsight (p, p') it is used for judging that whether p and p' is visual, specifically judges p and p' and barrier OjThe position relationship of each summit line；It is the node set visual with node p.
3. a kind of Lambda* path planning algorithm according to any claim in claim 1 or 2, it is characterised in that choose node p to terminal pgoalEuclidean distance as heuristic function hval (p).
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