CN108549388A - A kind of method for planning path for mobile robot based on improvement A star strategies - Google Patents

A kind of method for planning path for mobile robot based on improvement A star strategies Download PDF

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CN108549388A
CN108549388A CN201810506586.7A CN201810506586A CN108549388A CN 108549388 A CN108549388 A CN 108549388A CN 201810506586 A CN201810506586 A CN 201810506586A CN 108549388 A CN108549388 A CN 108549388A
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node
mobile robot
path
map
star
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翟冬灵
葛凯
张二阳
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SUZHOU XUNJI ZHIXING ROBOT TECHNOLOGY Co.,Ltd.
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Suzhou Zhi Vedad Robot Technology Co Ltd
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    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05DSYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02Control of position or course in two dimensions
    • G05D1/021Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0231Control of position or course in two dimensions specially adapted to land vehicles using optical position detecting means
    • G05D1/0234Control of position or course in two dimensions specially adapted to land vehicles using optical position detecting means using optical markers or beacons
    • G05D1/0236Control of position or course in two dimensions specially adapted to land vehicles using optical position detecting means using optical markers or beacons in combination with a laser
    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05DSYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02Control of position or course in two dimensions
    • G05D1/021Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0214Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory in accordance with safety or protection criteria, e.g. avoiding hazardous areas
    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05DSYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02Control of position or course in two dimensions
    • G05D1/021Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0221Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving a learning process
    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05DSYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02Control of position or course in two dimensions
    • G05D1/021Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0223Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving speed control of the vehicle
    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05DSYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02Control of position or course in two dimensions
    • G05D1/021Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0231Control of position or course in two dimensions specially adapted to land vehicles using optical position detecting means
    • G05D1/0238Control of position or course in two dimensions specially adapted to land vehicles using optical position detecting means using obstacle or wall sensors
    • G05D1/024Control of position or course in two dimensions specially adapted to land vehicles using optical position detecting means using obstacle or wall sensors in combination with a laser
    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05DSYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02Control of position or course in two dimensions
    • G05D1/021Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0231Control of position or course in two dimensions specially adapted to land vehicles using optical position detecting means
    • G05D1/0246Control of position or course in two dimensions specially adapted to land vehicles using optical position detecting means using a video camera in combination with image processing means
    • G05D1/0253Control of position or course in two dimensions specially adapted to land vehicles using optical position detecting means using a video camera in combination with image processing means extracting relative motion information from a plurality of images taken successively, e.g. visual odometry, optical flow
    • GPHYSICS
    • G05CONTROLLING; REGULATING
    • G05DSYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02Control of position or course in two dimensions
    • G05D1/021Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0276Control of position or course in two dimensions specially adapted to land vehicles using signals provided by a source external to the vehicle

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  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Electromagnetism (AREA)
  • Optics & Photonics (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Multimedia (AREA)
  • Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)

Abstract

The present invention relates to a kind of based on the method for planning path for mobile robot for improving A star strategies, it includes the following steps:(a)Laser data and mileage that mobile robot obtains are handled with slam algorithms;(b)The grating map of binaryzation is built into Voronoi diagram using dynamic dimension promise picture library;(c)According to the node coordinate on the Voronoi diagram, and build corresponding Voronoi costs map;(d)The beginning and end position of the mobile robot is transformed into map reference from its own coordinate system to fasten, checks whether the coordinated indexing of beginning and end is legal;(e)Initialize the g cost values of all nodes;(f)Discrete whole path is smoothed using smoother.Memory and computing resource is greatly saved, accelerates convergence speed of the algorithm;Voronoi diagram has also been incorporated, has made path far from barrier, has finally obtained an optimal path using smoother.

Description

A kind of method for planning path for mobile robot based on improvement A star strategies
Technical field
The invention belongs to industrial robot fields, are related to a kind of method for planning path for mobile robot, and in particular to a kind of Based on the method for planning path for mobile robot for improving A star strategies.
Background technology
The main function of global path planning is to find one from the optimal of origin-to-destination on known static map Or approximate optimal path, the path is generally continuous, smoothly, clear, and the global path for being suitble to robot directly to execute. Path planning algorithm is the basis in entire navigation system, its result provides path letter for the planning of subsequent local path Breath.
Currently used path planning algorithm has very much, can be divided mainly into three categories:Method based on graph search, such as Dijkstra, A* (i.e. A stars), D*, Theta* etc.;Based on the method used at random, such as random walk figure method (PRM) is quickly searched Suo Shufa (RRT) etc.;It is more also based on didactic algorithm, classical has ant group algorithm, genetic algorithm, particle cluster algorithm Deng.Dijkstra is the founder of graph search method, guarantees to find a globally optimal solution, but it can traverse the institute of entire map There is grid, therefore calculation amount is very big, especially under big map.A* introduces heuristic search solution on the basis of Dijkstra The above problem, substantially increases the efficiency of search under the premise of ensure that optimal solution, is contained due to it is simple and is easily achieved Row is so far.It is required for based on didactic algorithm to determining that the barrier in space models, ordinary convergence speed is slower, nothing Method meets the requirement of robot real-time.The method of stochastical sampling avoids the modeling to space, passes through the random of state space Sampled point finds a complete and not optimal path of probability;But such method is insensitive to environment, when there is relatively narrow channel When, it often restrains very slowly, or even can be besieged in barrier;In addition, safety be always industrial robot consider before It carries, the path that existing algorithmic rule goes out all close to barrier, can not ensure the safety during robot ambulation.Industrially, The situation of the large scales map such as factory floor is often faced, therefore, how to accelerate convergence speed of the algorithm, improves robot Real-time becomes the focus being primarily upon.
Invention content
It is provided the invention aims to overcome the deficiencies in the prior art a kind of based on the mobile machine for improving A star strategies People's paths planning method.
In order to achieve the above objectives, the technical solution adopted by the present invention is:A kind of mobile robot based on improvement A star strategies Paths planning method, it includes the following steps:
(a) laser data and mileage that mobile robot obtains are subjected to processing with slam algorithms and obtain .pgm formats Grating map, the grating map binaryzation is made by two-dimensional array;
(b) grating map of binaryzation is built into Voronoi diagram using dynamic dimension promise picture library;
(c) according to the node coordinate on the Voronoi diagram, the potential energy for obtaining corresponding node is calculated by formula (I), and Build corresponding Voronoi costs map;
In formula, α is the fall off rate of potential energy,For the control range of potential energy;
(d) the beginning and end position of the mobile robot map reference is transformed into from its own coordinate system to fasten, Inspection is played with whether the coordinated indexing of terminal is legal;The map coordinates system is the laser number that the mobile robot obtains According to mileage coordinate system;
(e) initializing the g cost values of all nodes makes g (ni)=∞, wherein n be node, i=1 ..., mapsize;Newly-built one is drawn up table, calculates total cost value f (s)=g (s)+α of the starting point1× h (s), wherein s are starting point, α1For weight coefficient, then table will be drawn up described in starting point loading;When the g costs for drawing up table not and be the empty and described terminal Value enters cycle when being infinite, until finding target point, then recalls whole path;
(f) smoother is used to carry out discrete whole path smooth.
Optimally, in step (a), traverse the pixel of the grating map, when its value be 0, then assignment 0;Otherwise Value > 0, assignment 1.
Optimally, in step (c), control α andParameter value make potential energy value equably from barrier to Voronoi diagram Side on it is continuously distributed.
Optimally, in step (d), also judge whether the grid of the beginning and end is occupied by barrier.
Optimally, enter cycle when the g cost values for drawing up table not and be the empty and described terminal are infinite, including following Step:
(e1) it is present node to define node minimum in f cost values, labeled as being accessed, and by the node from institute It states to draw up in table and delete;
(e2) it is chosen at adjacent node of the node on map and there is no barrier as the present node;
When the adjacent node g cost values be it is infinite, calculate the g cost values of the present node:When the adjacent segments When point is located on straight line, g cost values are g (vi)=g (vi-1)+1×(1+w×p(vi));When the adjacent node is located at diagonal member When on line, g cost values areWherein, viIndicate that i-th of node, w are the power of potential energy Value coefficient, p (vi) indicate the point potential energy value;Calculate the total cost value f (v of the present nodei)=g (vi)+α1×h (vi), h (vi) it is heuristic function cost value h (vi)=| x1-x2|+|y1-y2|, and table is drawn up in present node loading;
When the g cost values of the adjacent node are non-infinite, skip the adjacent node and do not visit again;
(e3) it repeats step (e1) and (e2) to continually look for, until finding terminal, recalls whole path.
Optimally, step (f) includes the following steps:
(f1) by whole path according to formulaIt is divided into k sections;WhereinTo round up, Length is path length;Step is step-length and step=λ/resolution, λ are can to set step parameter, and resolution is Map resolution ratio;
Coordinate points are then averaging as follows to every section of path:ave_xi=sum_xi/stepi、ave_yi=sum_ yi/stepi, wherein i ∈ [1, k) it is integer, sum_xi=sum_xi-1+xi, sum_yi=sum_yi-1+yi;It collects described average Coordinate points are as sampled point;
(f2) use cubic spline interpolation algorithm to the sampled point into row interpolation.
Since above-mentioned technical proposal is used, the present invention has following advantages compared with prior art:The present invention is based on improve A The method for planning path for mobile robot of star strategy, it is only necessary to which one is drawn up table, judges whether the node is accessed with g cost values Come over substitution pass list, also only needs to calculate once to the g cost values of each node, memory and computing resource is greatly saved, Accelerate convergence speed of the algorithm;Voronoi diagram has also been incorporated, has made path far from barrier, finally obtains one using smoother Optimal path.
Description of the drawings
Attached drawing 1 is that the present invention is based on the flow charts for the method for planning path for mobile robot for improving A star strategies;
Attached drawing 2 is our company's floor maps that mobile robot obtains;
Attached drawing 3 is the Voronoi diagram of our company's floor maps;
Attached drawing 4 is the Voronoi cost maps of our company's floor maps;
Attached drawing 5 is that the present invention is based on the path profiles that the method for planning path for mobile robot for improving A star strategies obtains;
Attached drawing 6 is the schematic diagram of point spread of the present invention.
Specific implementation mode
The present invention is based on the method for planning path for mobile robot for improving A star strategies, as shown in Figure 1, it includes following step Suddenly:
(a) laser data and mileage that mobile robot obtains are subjected to processing with slam algorithms and obtain .pgm formats Grating map (each pixel be 0~255 gray value);The grating map binaryzation is stored in a two-dimensional array In (as create Voronoi diagram input, specially traverse the pixel of entire map, if value=0, assignment 0 is no Then 0 assignment 1 of value >);Fig. 2 is our company's floor maps that mobile robot obtains, and is obtained by slam algorithms;It generally comprises .pgm with two files of .yaml;.pgm it is the gray level image for including 256 grades of gray values .yaml is corresponding configuration file (packet The information such as filename, resolution ratio and origin containing image);Wherein, there are three types of gray value, white area 0, tables in map Show robot wheeled region;Gray area is zone of ignorance, indicates that robot cannot enter;Black region is barrier, table Show that robot cannot collide;
(b) (international conference on intelligent are specifically referred to using dynamic dimension promise picture library robots and systems,2010:The grating map of binaryzation 281-286) is built into Voronoi diagram;Physical interface ten Divide simply, calling initializeMap () and update (), principle is only updated to ring using a dynamic variable The influential barrier in border has very high update efficiency.The expression barrier of black in Fig. 3, grey lines are that Tyson is polygon The side of shape;The figure has following feature:1, discrete points data there are one being contained only in each Thiessen polygon;2, in Thiessen polygon Point to corresponding discrete point distance it is nearest;3, distance phase of the point on Thiessen polygon side to the discrete point on its both sides Deng.As seen from Figure 3, Voronoi maps can be in the intermediate path for generating a near linear on road.
(c) Voronoi maps provide any one position to the position of barrier near the point and range information;It can be with According to the node coordinate on Voronoi diagram, the potential energy for obtaining corresponding node is calculated by formula (I), and build corresponding Voronoi cost maps;
In formula, α is the fall off rate (α ∈ [0, ∞) of potential energy, and α values are smaller, potential energy decline it is faster),For potential energy Control rangeAs α andWhen being arranged to suitable parameter, potential energy value will equably from barrier to It is continuously distributed on Voronoi diagram side.Fig. 4 is the Voronoi cost maps created, as seen from the figure, the both sides (obstacle on road Object) potential energy is maximum, toward road among potential energy slowly reduce, to the side of most intermediate Thiessen polygon on potential energy minimum be 0;That is traversal ground Each node on figure, if the node on barrier, assignment 1;If on Thiessen polygon side, assignment 0;If two Between person, the node is calculated to the distance of neighbouring barrier, substitutes into potential energy formula.Voronoi cost maps are made one Table provides look-up table for subsequent searching algorithm.
The cost map has following feature:1, potential energy P ∈ [0,1] are continuously distributed on 0 to 1;2, when on map point (x, Y) on barrier or when interior, potential energy is up to 1;3, when the point (x, y) on map is on Thiessen polygon side, potential energy minimum It is 0.
(d) the beginning and end position of mobile robot is transformed into map reference from its own coordinate system to fasten, is checked It plays and whether the coordinated indexing of terminal is legal (specially judges whether beginning and end is the same point, judge 0 < mx < Mapwidth and 0 < my < mapheight judges whether beginning and end grid is occupied by barrier using look-up table);It is described Map coordinates system is using the lower left corner of map as the rectangular coordinate system of coordinate origin;
(e) the g cost values for initializing all nodes are infinite, i.e. g (ni)=∞, wherein n be node, i=1 ..., mapsize.Here it no longer needs to close list, only need to create one draws up table (i.e. OpenList), the total cost value f of zequin (s)=g (s)+α1× h (s), wherein s are starting point, α1For weight coefficient.Then starting point is packed into OpenList;
Enter cycle when the g cost values that OpenList is not the empty and described terminal are infinite, until finding target point, so After recall whole path, specially:
(e1) it is present node to define node minimum in f cost values, labeled as being accessed, and by the node from institute It states to draw up in table and delete;
(e2) it is chosen at adjacent node of the node as the present node on map and not in barrier;
Adjacent node as shown in fig. 6, generally around eight nodes of present node, i.e., on, under, left, right, upper left is right On, lower-left, bottom right.When the adjacent node g cost values be it is infinite, calculate the g cost values of the present node:When the phase When neighbors is located on straight line, g cost values are g (vi)=g (vi-1)+1×(1+w×p(vi));When the adjacent node be located at pair When on the oblique line of angle, g cost values areWherein, viIndicate that i-th of node, w are potential energy Weight coefficient, p (vi) indicate the point potential energy value;Calculate the total cost value f (v of the present nodei)=g (vi)+α1× h(vi), h (vi) it is heuristic function cost value h (vi)=| x1-x2|+|y1-y2|, and table is drawn up in present node loading;
(e3) it repeats step (e1) and (e2) to continually look for, until finding target point (i.e. terminal), then recalls whole road (backtracking path is to determine next node according to the g cost values of each node to diameter;Target point is traversed to starting point, reversed searching The consecutive points of node find out that node of g cost value minimums as next node every time, and iteration continues successively until rising Point can find whole path).
(f) it uses smoother to carry out discrete whole path smooth, specifically includes following steps:
(f1) original route is sampled:Since original route is discrete, it is understood that there may be singular point, therefore directly to original route Sampling may get singular point.It is segmented used here as to original route, it is sampled point then to take the average value of its every section coordinate, this Sample is it is possible to prevente effectively from the above problem.Specially:By whole path according to formulaIt is divided into k sections;Wherein To round up, length is path length;Step is step-length and step=λ/resolution, λ are can to set step parameter, Resolution is map resolution ratio;Coordinate points are then averaging as follows to every section of path:ave_xi=sum_xi/ stepi、ave_yi=sum_yi/stepi, wherein i ∈ [1, k) it is integer, sum_xi=sum_xi-1+xi, sum_yi=sum_ yi-1+yi;The average coordinates point is collected as sampled point;
(f2) use cubic spline interpolation algorithm to the sampled point into row interpolation.
After having sampled point, so that it may with interpolation.Interpolation algorithm has very much, since high order interpolation does not restrain and unstable, Low order interpolation slickness is inadequate, therefore used here as common cubic spline interpolation algorithm to sampling-point interpolation.It is defined on [a, b] On just like lower node a=x0< x1< ... < xn-1< xn=b is divided into n sections, cubic spline equation is full for this n+1 sampled point The following condition of foot:1, in every section of section [xi,xi+1], S (x)=Si(x);2, meet S (xi)=yi;3, the first derivative S ' of S (x) (x) and second dervative S " (x) is continuous on [a, b].Polynomial equation on every section is Si(x)=ai+bi(x-xi)+ci(x-xi )2+di(x-xi)3, wherein ai, bi, ci, diFor undetermined coefficient.As soon as section having 4 unknowm coefficients, n sections need 4n equation.Also Two equations are provided by endpoint, usually by three kinds of methods:1, natural boundary;2, fixed boundary;3, not a node boundary.According to Hermite interpolating functions,Whereinx∈[xi,xi+1], hi=xi+1-xi, i=0,1 ..., n-1;Side is added Behind boundary, a tri-diagonal system can be obtained, all undetermined coefficients are calculated, every section of S (x) can be acquired and (utilize equation The step-length for determining interpolation, generally is 0.05m), to path interpolation to obtain the path being made of smoothed curve, such as Fig. 5 institutes Show, the centre on the whole roads Dou;Clearly as can be seen that although this paths is not shortest, but comparatively safe (road Diameter about 38m, used time 0.065s or so).Entire method is simple, and it is convenient to realize, calculation amount is small, ensure that machine to a certain extent The safety of device people's global path.Experiments have shown that no matter the size in channel, algorithm can cook up always one it is complete, continuously, put down It is sliding, and ensure the executable global path among road.
The above embodiments merely illustrate the technical concept and features of the present invention, and its object is to allow person skilled in the art Scholar cans understand the content of the present invention and implement it accordingly, and it is not intended to limit the scope of the present invention, all according to the present invention Equivalent change or modification made by Spirit Essence, should be covered by the protection scope of the present invention.

Claims (6)

1. a kind of based on the method for planning path for mobile robot for improving A star strategies, which is characterized in that it includes the following steps:
(a) laser data and mileage that mobile robot obtains are subjected to the grid that processing obtains .pgm formats with slam algorithms The grating map binaryzation is stored in a two-dimensional array by lattice map;
(b) grating map of binaryzation is built into Voronoi diagram using dynamic dimension promise picture library;
(c) according to the node coordinate on the Voronoi diagram, the potential energy for obtaining corresponding node is calculated by formula (I), and build Corresponding Voronoi costs map;
In formula, α is the fall off rate of potential energy,For the control range of potential energy;
(d) the beginning and end position of the mobile robot is transformed into map reference from its own coordinate system to fasten, is checked It plays with whether the coordinated indexing of terminal is legal;The map coordinates system be the mobile robot obtain laser data and Mileage coordinate system;
(e) initializing the g cost values of all nodes makes g (ni)=∞, wherein n are node, i=1 ..., mapsize;It is newly-built One is drawn up table, calculates total cost value f (s)=g (s)+α of the starting point1× h (s), wherein s are starting point, α1For weight coefficient, Then it will draw up table described in starting point loading;When the g cost values for drawing up table not and be the empty and described terminal are infinite into Enter cycle, until finding target point, then recalls whole path;
(f) smoother is used to carry out discrete whole path smooth.
2. according to claim 1 based on the method for planning path for mobile robot for improving A star strategies, it is characterised in that:Step Suddenly in (a), traverse the pixel of the grating map, when its value be 0, then assignment 0;Otherwise value > 0, assignment 1.
3. according to claim 1 based on the method for planning path for mobile robot for improving A star strategies, it is characterised in that:Step Suddenly in (c), control α andParameter value keep potential energy value continuously distributed on the side equably from barrier to Voronoi diagram.
4. according to claim 1 based on the method for planning path for mobile robot for improving A star strategies, it is characterised in that:Step Suddenly in (d), also judge whether the grid of the beginning and end is occupied by barrier.
5. according to claim 1 based on the method for planning path for mobile robot for improving A star strategies, which is characterized in that when The g cost values for drawing up table not and be the empty and described terminal enter cycle when being infinite, include the following steps:
(e1) it is present node to define node minimum in f cost values, labeled as being accessed, and the node is opened from described It is deleted in list;
(e2) it is chosen at adjacent node of the node on map and there is no barrier as the present node;
When the adjacent node g cost values be it is infinite, calculate the g cost values of the present node:When the adjacent segments point When on straight line, g cost values are g (vi)=g (vi-1)+1×(1+w×p(vi));When the adjacent node is located on diagonal oblique line When, g cost values areWherein, viIndicate that i-th of node, w are the weights system of potential energy Number, p (vi) indicate the point potential energy value;Calculate the total cost value f (v of the present nodei)=g (vi)+α1×h(vi), h (vi) it is heuristic function cost value h (vi)=| x1-x2|+|y1-y2|, and table is drawn up in present node loading;
When the g cost values of the adjacent node are non-infinite, skip the adjacent node and do not visit again;
(e3) it repeats step (e1) and (e2) to continually look for, until finding terminal, recalls whole path.
6. according to claim 1 based on the method for planning path for mobile robot for improving A star strategies, which is characterized in that step Suddenly (f) includes the following steps:
(f1) by whole path according to formulaIt is divided into k sections;WhereinTo round up, length For path length;Step is step-length and step=λ/resolution, λ are can to set step parameter, and resolution is map point Resolution;
Coordinate points are then averaging as follows to every section of path:ave_xi=sum_xi/stepi、ave_yi=sum_yi/ stepi, wherein i ∈ [1, k) it is integer, sum_xi=sum_xi-1+xi, sum_yi=sum_yi-1+yi;Collect the average coordinates Point is used as sampled point;
(f2) use cubic spline interpolation algorithm to the sampled point into row interpolation.
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CN109947101A (en) * 2019-03-18 2019-06-28 北京智行者科技有限公司 Path smooth processing method and processing device
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