CN103116356A - Method of search in mazes - Google Patents

Abstract

The invention relates to a method of search in mazes. The method includes the steps of firstly, generating a non-directional probabilistic distance map; secondly, generating a directional probabilistic distance map; and thirdly, applying the probabilistic distance maps. After the directional probabilistic distance map in the step 2 is generated, a robot starts from a starting maze cell to search a maze. When encountering an intersection, the robot judges to which one of the maze cells in certain directions the minimum probabilistic distance belongs so as to determine an advancing path by means of the probabilistic distance maps according to the current direction, and reaches a target area G. 'Probabilistic distance' is provided by organically combining probability in the science of probability and distance in kinematics. Based on the probabilistic distance, search in mazes is rational and rules-based. The method of search in mazes based on 'probabilistic distance' is realized.

Description

The method of a kind of labyrinth search

Technical field

The present invention relates to the method for a kind of labyrinth search, belong to the technical field of artificial intelligence and robot.

Technical background

Along with the development in epoch, artificial intelligence and Robotics are more and more very powerful and exceedingly arrogant, and the tide of study and research just have swepts the globe.It is also in the ascendant that the associated machine people walks the research in labyrinth, and various algorithms emerge in an endless stream, and have greatly promoted the development of artificial intelligence and Robotics.

How keeping away during barrier walks out the process in labyrinth smoothly in the research robot, adopt which kind of method search, traverse maze directly to affect the solution efficient of maze problem, is the marrow place of finding the solution maze problem.Current searching method commonly used is divided into two classes, and a class is non-Graph-theoretical Approach, as left hand, right hand method; Another kind of is Graph-theoretical Approach, as depth-first method, centripetal method etc.The general efficient of these methods is not high, can not make robot pass through fast the labyrinth and reach the destination.

In sum, how to search for for the labyrinth, propose a kind of high efficiency searching method, fast and effeciently solve the problem that the labyrinth arrives the destination of passing through.The present invention can be widely used in the search of various types of labyrinths, also can be used for reference by the application of other field.

Summary of the invention

For the deficiencies in the prior art, the invention discloses the method for a kind of labyrinth search.

Technical scheme of the present invention is as follows:

The method of a kind of labyrinth search comprises that step is as follows:

1) generate directionless probability metrics figure:

In the labyrinth, target area G is four maze lattices that communicate at center, labyrinth, and what the same external world, this target area was adjacent is eight maze lattices, and the target area must communicate with the external world, the wall that dotted line expresses possibility and exists, and the grid that dotted line surrounds is maze lattice;

Suppose that other walls all do not exist when initial, between maze lattice, distance is designated as 1, and each 90 degree turning spent time also equivalence be distance, are designated as a, each turn through 180 degree spent time equivalent be distance b (a ≈ of robot 1 that uses in test, b ≈ 10).

The residing position of robot is maze lattice A, and the computing method of the distance of maze lattice A and target area G are: the non-existent probability of the wall nearest apart from maze lattice A is p ₁=2 ⁷/ (2 ⁸-1), this moment, maze lattice A was s to the bee-line of target area G ₁, namely maze lattice A has p to target area G ₁Potential range be s ₁In the situation that described nearest wall existence, the non-existent Probability p of the wall near apart from maze lattice A second ₂=(1-p ₁) 2 ⁶/ (2 ⁷-1), this moment, maze lattice A was s to the bee-line of target area G ₂, namely maze lattice A has p to target area G ₂Possible bee-line be s ₂The rest may be inferred, p _n, s _nAs shown in table 1:

Table 1:

Finally can obtain maze lattice A to the distance of target area G as (1) formula:

S _A＝p ₁s ₁+p ₂s ₂+p ₃s ₃+p ₄s ₄+p ₅s ₅+p ₆s ₆+p ₇s ₇+p ₈s ₈ （1）

The product of a probability and distance due to the above results, the distance on the expression probability meaning, the S in formula (1) _ABe called probability metrics;

2) generation has the Direction Probability distance map:

At the described probability metrics S of step 1) _AComputation process in, do not consider the direction of the current motion of robot, this is obviously irrational, because each turning or tune, the capital affects the probability metrics between robot and target area G, so the current direction of robot is also one of factor that affects probability metrics.

As the robot initial working direction upwards, maze lattice B has p to target area G ₁Possible bee-line be s _1dirP is arranged ₂Possible bee-line be s _2dirThe like can obtain p _n, s _NdirAs following table: as shown in the of 2:

Table 2:

Can obtain maze lattice B to the oriented probability metrics of target area G, as the formula (2):

$S_{\mathrm{Bdir}}=p_1{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA00002888486500021.png"\; state="\{\{state\}\}">s</figure-callout>}}_{1\mathrm{dir}}+p_2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA00002888486500021.png"\; state="\{\{state\}\}">s</figure-callout>}}_{2\mathrm{dir}}+p_3{\mathrm{<figure-callout\; id="3"\; label="s"\; filenames="HDA00002888486500021.png"\; state="\{\{state\}\}">s</figure-callout>}}_{3\mathrm{dir}}+p_4{\mathrm{<figure-callout\; id="4"\; label="s"\; filenames="HDA00002888486500021.png"\; state="\{\{state\}\}">s</figure-callout>}}_{4\mathrm{dir}}+p_5{\mathrm{<figure-callout\; id="5"\; label="s"\; filenames="HDA00002888486500021.png"\; state="\{\{state\}\}">s</figure-callout>}}_{5\mathrm{dir}}+p_6{\mathrm{<figure-callout\; id="6"\; label="s"\; filenames="HDA00002888486500021.png"\; state="\{\{state\}\}">s</figure-callout>}}_{6\mathrm{dir}}{+p}_7{\mathrm{<figure-callout\; id="7"\; label="s"\; filenames="HDA00002888486500021.png"\; state="\{\{state\}\}">s</figure-callout>}}_{7\mathrm{dir}}+p_8{\mathrm{<figure-callout\; id="8"\; label="s"\; filenames="HDA00002888486500021.png"\; state="\{\{state\}\}">s</figure-callout>}}_{8\mathrm{dir}}$

$=2\frac{209}{255}+2\frac{134}{255}a---\left(2\right)$

$\&ap;5\frac{88}{255}$

Be numbered according to the coordinate of labyrinth cell, and calculate according to above-mentioned algorithm, draw in the labyrinth each cell to the probability metrics of target area:

When being upper, obtain the probability metrics figure in the labyrinth of " upward direction " when the robot initial direction according to above-mentioned calculating and statistical statistics;

In like manner, when the robot initial direction is right, the probability metrics figure in the labyrinth of " upward direction " is turned clockwise 90 ° (keeping coordinate constant, only numerical value change);

The robot initial direction is lower time, and the probability metrics figure in the labyrinth of " upward direction " is turned clockwise 180 ° identical (keeping coordinate constant, only numerical value change);

When the robot direction is left, the probability metrics figure in the labyrinth of " upward direction " is rotated counterclockwise 90 ° identical (keeping coordinate constant, only numerical value change).

3) application of probability metrics figure

Establishment step 2) described the Direction Probability distance map is arranged after, robot is from starting point maze lattice search labyrinth, run into the crossing in advancing, direction current according to robot, utilize probability metrics figure, judge the probability metrics value minimum of the maze lattice distance objective of which direction, decide course with this, until robot arrives at target area G.

Advantage of the present invention and good effect are:

1, the present invention is applicable to the search in various labyrinths, for the robot path choice provides theoretical foundation, has filled up blank in this regard.

2, the present invention has improved the efficient of labyrinth search, has shortened labyrinth search time, and has been very easy to dispose, implement.

3, the present invention is novel unique, for thinking has been opened up in the further research of artificial intelligence and Robotics.

4, the present invention organically combines the probability in Probability and the distance in kinematics, has proposed " probability metrics " this parameter, take this parameter as benchmark, make labyrinth search reasonable can according to, have regulations to abide by.The present invention has realized the labyrinth searching method based on " probability metrics ".

Description of drawings

Fig. 1 is the labyrinth example of embodiment, and middle four cells are target area G;

Fig. 2 is robot initial direction corresponding probability metrics figure when making progress.

Embodiment

Below in conjunction with embodiment and Figure of description, the present invention is described in detail, but is not limited to this.

Embodiment

1) generate directionless probability metrics figure

In the labyrinth, target area G is four maze lattices that communicate at center, labyrinth, what G same external world in this target area was adjacent is eight maze lattices, target area G must communicate with the external world, be also that seven wall walls are arranged around the G of target area at the most, as shown in fig. 1, the wall that dotted line expresses possibility and exists, the grid that dotted line surrounds is maze lattice.

Suppose that other walls all do not exist when initial, between maze lattice, distance is designated as 1, and each 90 degree turning spent time also equivalence be distance, are designated as a, each turn through 180 degree spent time equivalent be distance b (a ≈ of robot 1 that uses in test, b ≈ 10).

In Fig. 1, the distance of maze lattice A and target area G should be calculated like this: the non-existent probability of the wall nearest apart from maze lattice A is p ₁=2 ⁷/ (2 ⁸-1), this moment, maze lattice A was s to the bee-line of target area G ₁, namely maze lattice A has p to target area G ₁Potential range be s ₁In the situation that this wall existence, the non-existent Probability p of the wall near apart from maze lattice A second ₂=(1-p ₁) 2 ⁶/ (2 ⁷-1), this moment, maze lattice A was s to the bee-line of target area G ₂, namely maze lattice A has p to target area G ₂Possible bee-line be s ₂The rest may be inferred, p _n, s _nAs shown in table 1 below:

Table 1:

Finally can obtain maze lattice A to the distance of target area G as shown in the formula (1):

S _A=p ₁s ₁+p ₂s ₂+p ₃s ₃+p ₄s ₄+p ₅s ₅+p ₆s ₆+p ₇s ₇+p ₈s ₈ （1）

The product of a probability and distance due to the above results, the distance on the expression probability meaning, the S in formula (1) _ABe probability metrics;

2) generation has the Direction Probability distance map

Take Fig. 1 as example, suppose the robot initial working direction upwards, maze lattice B has p to target area G ₁Possible bee-line be s _1dirP is arranged ₂Possible bee-line be s _2dirThe like can obtain p _n, s _NdirAs shown in table 2 below:

Table 2:

Can obtain maze lattice B to the oriented probability metrics of target area G suc as formula (2):

$S_{\mathrm{Bdir}}=p_1{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA00002888486500021.png"\; state="\{\{state\}\}">s</figure-callout>}}_{1\mathrm{dir}}+p_2{\mathrm{<figure-callout\; id="2"\; label="s"\; filenames="HDA00002888486500021.png"\; state="\{\{state\}\}">s</figure-callout>}}_{2\mathrm{dir}}+p_3{\mathrm{<figure-callout\; id="3"\; label="s"\; filenames="HDA00002888486500021.png"\; state="\{\{state\}\}">s</figure-callout>}}_{3\mathrm{dir}}+p_4{\mathrm{<figure-callout\; id="4"\; label="s"\; filenames="HDA00002888486500021.png"\; state="\{\{state\}\}">s</figure-callout>}}_{4\mathrm{dir}}+p_5{\mathrm{<figure-callout\; id="5"\; label="s"\; filenames="HDA00002888486500021.png"\; state="\{\{state\}\}">s</figure-callout>}}_{5\mathrm{dir}}+p_6{\mathrm{<figure-callout\; id="6"\; label="s"\; filenames="HDA00002888486500021.png"\; state="\{\{state\}\}">s</figure-callout>}}_{6\mathrm{dir}}{+p}_7{\mathrm{<figure-callout\; id="7"\; label="s"\; filenames="HDA00002888486500021.png"\; state="\{\{state\}\}">s</figure-callout>}}_{7\mathrm{dir}}+p_8{\mathrm{<figure-callout\; id="8"\; label="s"\; filenames="HDA00002888486500021.png"\; state="\{\{state\}\}">s</figure-callout>}}_{8\mathrm{dir}}$

$=2\frac{209}{255}+2\frac{134}{255}a---\left(2\right)$

$\&ap;5\frac{88}{255}$

Take IEEE computer mouse contest standard used labyrinth as example, be numbered according to the coordinate of labyrinth cell.When being upper, obtain the probability metrics figure in the labyrinth of " upward direction " according to above-mentioned calculating and statistical statistics, as shown in Figure 2 when the robot initial direction;

In like manner, when the robot initial direction is right, the probability metrics figure in the labyrinth of " upward direction " is turned clockwise 90 ° (keeping coordinate constant, only numerical value change);

The robot initial direction is lower time, and the probability metrics figure in the labyrinth of " upward direction " is turned clockwise 180 ° identical (keeping coordinate constant, only numerical value change);

When the robot direction is left, the probability metrics figure in the labyrinth of " upward direction " is rotated counterclockwise 90 ° identical (keeping coordinate constant, only numerical value change).

3) application of probability metrics figure

Establishment step 2) described the Direction Probability distance map is arranged after, robot is from starting point maze lattice search labyrinth, run into the crossing in advancing, direction current according to robot, utilize probability metrics figure, judge the probability metrics value minimum of the maze lattice distance objective of which direction, decide course with this, until robot arrives at target area G.

Claims (1)

1. the method for a labyrinth search, is characterized in that, it is as follows that the method comprising the steps of:

1) generate directionless probability metrics figure:

In the labyrinth, target area G is four maze lattices that communicate at center, labyrinth, and what G same external world in this target area was adjacent is eight maze lattices, and target area G must communicate with the external world, the wall that dotted line expresses possibility and exists, and the grid that dotted line surrounds is maze lattice;

Suppose that other walls all do not exist when initial, between maze lattice, distance is designated as 1, and each 90 degree turning spent time also equivalence be distance, are designated as a, each turn through 180 degree spent time equivalent be distance b (a ≈ of robot 1 that uses in test, b ≈ 10);

The residing position of robot is maze lattice A, and the computing method of the distance of maze lattice A and target area G are: the non-existent probability of the wall nearest apart from maze lattice A is p ₁=2 ⁷/ (2 ⁸-1), this moment, maze lattice A was s to the bee-line of target area G ₁, namely maze lattice A has p to target area G ₁Potential range be s ₁In the situation that described nearest wall existence, the non-existent Probability p of the wall near apart from maze lattice A second ₂=(1-p ₁) 2 ⁶/ (2 ⁷-1), this moment, maze lattice A was s to the bee-line of target area G ₂, namely maze lattice A has p to target area G ₂Possible bee-line be s ₂The rest may be inferred, p _n, s _nAs shown in table 1:

Table 1:

Finally can obtain maze lattice A to the distance of target area G as (1) formula:

S _A=p ₁s ₁+p ₂s ₂+p ₃s ₃+p ₄s ₄+p ₅s ₅+p ₆s ₆+p ₇s ₇+p ₈s ₈ （1）

The product of a probability and distance due to the above results, the distance on the expression probability meaning, the S in formula (1) _ABe probability metrics;

2) generation has the Direction Probability distance map:

As the robot initial working direction upwards, maze lattice B has p to target area G ₁Possible bee-line be s _1dirP is arranged ₂Possible bee-line be s _2dirThe like can obtain p _n, s _NdirAs following table: as shown in the of 2:

Table 2:

Can obtain maze lattice B to the oriented probability metrics of target area G, as the formula (2):

$S_{\mathrm{Bdir}}=p_1{s}_{1\mathrm{dir}}+p_2{s}_{2\mathrm{dir}}+p_3{s}_{3\mathrm{dir}}+p_4{s}_{4\mathrm{dir}}+p_5{s}_{5\mathrm{dir}}+p_6{s}_{6\mathrm{dir}}{+p}_7{s}_{7\mathrm{dir}}+p_8{s}_{8\mathrm{dir}}$

$=2\frac{209}{255}+2\frac{134}{255}a---\left(2\right)$

$\&ap;5\frac{88}{255}$

Be numbered according to the coordinate of labyrinth cell, and calculate according to above-mentioned algorithm, draw in the labyrinth each cell to the probability metrics of target area:

When the robot initial direction when being upper, add up to get the probability metrics figure in labyrinth of " upward direction " according to above-mentioned calculating and statistical;

In like manner, when the robot initial direction is right, the probability metrics figure in the labyrinth of " upward direction " is turned clockwise 90 ° (keeping coordinate constant, only numerical value change);

The robot initial direction is lower time, and the probability metrics figure in the labyrinth of " upward direction " is turned clockwise 180 ° identical (keeping coordinate constant, only numerical value change);

When the robot direction is left, the probability metrics figure in the labyrinth of " upward direction " is rotated counterclockwise 90 ° identical (keeping coordinate constant, only numerical value change);

3) application of probability metrics figure

Establishment step 2) described the Direction Probability distance map is arranged after, robot is from starting point maze lattice search labyrinth, run into the crossing in advancing, direction current according to robot, utilize probability metrics figure, the probability metrics value that judges which direction maze lattice is minimum, decides course with this, until robot arrives at target area G.

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