CN106341825A - Directional charger arranging method - Google Patents

Abstract

The invention discloses a highly efficient directional charger arranging method, which comprises the following steps: 1) arranging N chargeable sensors in a two-dimensional area, whose positions are known and M directional wireless chargers are about to be arranged; 2) conducting discretization to the entire two-dimensional area for multiple sub-areas so that the number of the candidate points for the multiple wireless chargers is made finite and the purpose of doing so is to ensure that the interface power of each sub-area after discretization can be close to a constant value; 3) for each sub-area, obtaining all possible sets of sensors that can be covered by the chargers in the sub-area; 4) obtaining the locations of all chargers and their direction combinations by discretizing the planar areas and after the covered dominating set extraction of each sub-area. and 5) continuing to select, combine and arrange the chargers from all positions and direction combinations so as to maximize the overall charging effect of a network.

Description

A kind of method for arranging of oriented charger

First, technical field

The present invention relates to the method for arranging of the wireless efficiently oriented charger of one of chargeable Sensor Network, in wireless sensing In device network, it can arrange position and the direction of charger effectively, makes the entirety charging maximization of utility of sensor network.

2nd, background technology

Traditional sensor node is generally powered using battery, and the limited energy content of battery limits sensor network entirety Life-span.Energy can wirelessly be sent to sensor by wireless energy transmission technology from charger, solves such that it is able to thorough This problem.That is, how effectively, wirelessly one of chargeable Sensor Network major issue is the Layout Problem of wireless charger, Arrangement charger makes the entirety charging maximization of utility of sensor network.Existing work primary concern is that omnidirectional's charger Layout Problem, and limited by the position that can arrange of charger, such as can only be arranged at the lattice point in triangular apex or grid, because This has suitable limitation.

The present invention considers the general Layout Problem of oriented charger first, and that is, charger charged area is sector, and Charger may be arranged at any position in region, and its direction can arbitrarily be adjusted.For: the charge power of (1) each sensor There is the receiving power at more complicated mathematical relationship, and certain point in space to exist for each charger with the distance to charger The superposition of this charge power；(2) because the position and orientation of oriented charger can be with continuous transformation, optional solution is empty in theory Between be infinitely great.The present invention proposes a series of innovative approach and this problem is processed, and devises one kind on this basis Efficient approximate data cdg (charger deployment-greedy) algorithm.

3rd, content of the invention

The purpose of the present invention is: a kind of method for arranging of the efficiently oriented charger in wirelessly chargeable Sensor Network is proposed, It can arrange position and the direction of charger effectively, makes the entirety charging maximization of utility of sensor network.

For achieving the above object, the technical scheme is that a kind of oriented charger method for arranging, walk including following Rapid:

(1) n chargeable transducer arrangements are in a 2 dimensional region, and the position of sensor is it is known that m oriented wireless charging Device needs to be disposed；

(2) multiple subregions are turned to by discrete for whole 2 dimensional region, thus multiple wireless charger candidate points have been reduced to Limit, the target of 2 dimensional region discretization be to ensure that discretization after each sub-regions in receiving power can be approximately constant Value；

(3) to every sub-regions, obtain all possible set of sensors that charger in this subregion can cover.

(4) all wireless chargings are obtained by discretization plane domain with after each sub-regions are carried out covering dominant set extraction Arrester location and direction combination.

(5) in the combination of all position and orientation, continue to select m oriented wireless charger of combination arrangement, thus reaching Maximization network integrally charges effectiveness

Arrange m oriented charger without restriction in given area, determine the position of m charger by method for arranging Put and towards so that the charging maximization of utility of region inner sensor network.

The core procedure that the present invention proposes an approximate data is divided into three steps.Turn to multiple sons by discrete for plane domain first Region, the charge power being approximately considered wireless charger in subregion is a certain constant value；Secondly by each sub-regions Internal point is analyzed, and finds out covering dominant set (dominant coverage set, dcs)；The submodule of last Utilizing question Property, design the greedy algorithm that can reach above-mentioned approximation ratio, that is, the arrangement that charges greedy algorithm cdg (charger deployment-greedy).

Stage 1: plane domain discretization

In view of charger candidate point in plane number be unlimited number of it is impossible to be effectively treated, carry in the present invention The method going out turns to limited sub-regions by discrete for plane domain, thus unlimited number of candidate point is reduced to limited multiple, convenient Subsequent treatment.

The target of plane domain discretization be to ensure that discretization after each sub-regions in receiving power can be approximated to be Constant value, and error of approximation is not more than given constant ε.

Firstly the need of discretization that the receiving power in charge model is adjusted the distance.Specifically, certain power any given Error constant ε, by the different radii l (1) of concentric circular, l (2) ..., l (k) divide distance, and receiving power is approximated as follows

$p_r\left(d\right)=\left\{\begin{array}{cc}{p}_r\left(l\right(1\left)\right),& 0\≤d\≤l\left(1\right)\\ p_r\left(l\right(k\left)\right),& l(k-1)\≤d\≤l\left(k\right)(k=2,...,k)\\ 0,& d>d\end{array}\right.$

And

$\frac{p_r\left(l\right(k-1\left)\right)}{p_r\left(l\right(k\left)\right)}\≤1+\mathrm{\ϵ},\frac{p_r\left(l\right(k-1\left)\right)}{p_r\left(l\right(k\left)\right)}=1+\mathrm{\ϵ},(k=2,...,k)$

Wherein k is charged area number；D is wireless charger charging maximum distance；In every sub-regions, receiving power is equal It is considered constant value；

Therefore have

$\frac{p_r\left(d\right)}{p_r\left(d\right)}\≤1+\mathrm{\ϵ},(d\≤d)$

Approximate power is by the power in [l (k-1), l (k)] interval all similar to for p_r(l (k)) is (to interval [0, l (1)], power is approximately p_r(l(1)))；In each interval, maximum error of approximation is all without more than ε；In every sub-regions, connect Receive power and be regarded as constant value；It is clear that the charged area number dividing in such a way is

Centered on each sensor, with l (1), l (2) ..., l (k) divide concentric circular l for radius⁽ⁱ⁾(k) labelling The radius of sensor i is the concentric circular of l (k).The foundation so dividing concentric circular is: in each neighboring concentric circle, such as l⁽ⁱ⁾ And l (k-1)⁽ⁱ⁾K (), at any point in the annulus of composition, if the anglec of rotation of certain charger setting just covers sensing Device i, then the power of this charger receiving of sensor i is approximately considered is constant p_r(l(k))；

Stage 2: cover dominant set and extract

Obtain limited many sub-regions after plane sliding-model control, in each sub-regions, owned further The set of sensors that possible charger covers；

Definition 3.1: set of sensors o that given charger covers_iAnd o_jIf,Then claim set o_jDomination (dominate) set o_i；

Define 3.2: give set of sensors o that certain sub-regions and its interior charger cover_iIf, in this subregion There is not any other covering set of sensors domination o_i, then claim set o_jFor covering dominant set (coverage dominant Set, cds)；

Obtain all of covering dominant set in the demand in certain sub-regions that gives；

Algorithm 1. |input paramete by charger and its is possible to set of sensors o covering_iPosition；Output parameter is All covering dominant set cds；

Step 1. selectes a certain reference angle, calculates the angle theta that all the sensors are with respect to charger_j(0°≤θ≤ 360°)；

All the sensors are sorted from small to large by step 2. by angle；For convenience, angle might as well be set after sequence as θ₁ ≤θ₂≤…≤θ_p, its respective sensor is o₁,o₂,…,o_p；

Step 3. makes o_cRecord is current to cover set, θ_min, θ_maxRecord current covering set o respectively_cMiddle sensor with respect to The minimum and maximum angle of charger；Initialization makes θ_min=θ_max=θ₁；o_c={ o₁}；

Step 4.j=2；

Step 5.while charger can cover θ_minTo angle, θ_jScope, i.e. θ_j-θ_min≤a；

Step 6. θ_max=θ_j；

Step 7. adds o₁Arrive；

Step 8.j=(j+1) mod p；

Step 9.end while

Step 10. adds current covering set o_cTo covering dominant set record；

Step 11. θ_max=θ_j, add o_jCover set o to current_c；

Step 12.while charger can not cover θ_minTo angle, θ_maxScope, i.e. θ_max-θ_min>a；

Step 13. is from o_cRemove the minimum sensor of angle, and update θ_minFor o_cThe minimum folder that in set, sensor has Angle；

If step 14. θ_min=θ₁, algorithm termination；

Step 15.end while

Step 16.goto step 5.

Algorithm 1 is substantially a greedy algorithm, and the implementation procedure of algorithm is understood to as the continuous court rotating charger Always investigate the situation of change covering set of sensors；The step 5 of algorithm～step 9 is to add as much as possible in rotary course New sensor, till the sensor until there are covering can not be capped；Covering set of sensors when recording critical For covering dominant set；Step 12～step 15 is to remove the current sensor covering minimum angle in set successively, until current Till set can be capped again；Algorithm terminates when the minimum angle running into record is equal to initialized minimum angle, now Mean that charger just has been rotated through one week.

When the optional position of charger is a subregion, how to extract covering dominant set；One important observation is to the greatest extent The pipe optional position of charger and combination of direction in given area have infinitely multiple, but its all possible covering sensor Combination be limited it means that multiple combination is equivalent；During all position and orientation of equal value are combined, only Need to be selected one of them analyze；If the set of sensors of certain position and orientation combined covering arrange existing position and Towards the set of sensors of combined covering, then only need to consider the former；

Algorithm 2. |input paramete is charger place subzone boundaries, is possible to set of sensors o covering_iPosition； Output parameter is all covering dominant set cds；

Step 1.for all set of sensors o_iIn sensor pair, such as o₁And o₂；

Step 2. connects o₁And o₂And extend and intersect at several intersection points with zone boundary；Take each intersection point successively as filling Arrester location；o₁And o₂Line direction radius border clockwise as overlay area, so that it is determined that charger direction, meter Calculate current location and the set of sensors towards combined covering, be added to candidate and cover in dominant set；

Step 3. calculates and o₁, o₂Angle is all intersection points with zone boundary for the track of point of fixed value a；Successively with every Individual intersection point is current location, o₁, o₂With current location line as current coverage area radius border so that it is determined that charger court To, the set of sensors that calculating can cover, it is added to candidate and cover in dominant set；

Step 4.end for

Step 5. times takes 1 point of p on zone boundary_refAs fixing point position, execute algorithm 1 and obtain p_refPlace is possible to Covering dominant set, be added to candidate cover dominant set in；

To an optional point p_refEnter the analysis in line algorithm 1, you can acquisition meets all possible of situation (c) and covers Lid dominant set.Finally obtain all of covering dominant set and its corresponding charger position and orientation composite set, be designated as γ.

Stage 3: approximate data solves charger position and direction

Carry out by discretization plane domain with to each sub-regions cover dominant set extract after obtain all positions and Towards in combination, continue to select combination to arrange charger, integrally charged effectiveness with maximization network.

The present invention proposes the details of a greedy algorithm；Each step in algorithm all can add one for current collection x Make the maximum element e of increment size^*, until | x |=m, till that is, m charger all arranges.

Algorithm 3. |input paramete be charger quantity m, candidate's charger position with towards composite set г, optimization aim letter Number f (x)；The set x that output parameter combines for position and orientation.

Step 1.

Step 2.while | x |≤m

Step 3.e^*=arg max_e∈γ\xf(x{e}-f(x))

Step 4.x=x { e^*}

Step 5.end while

Finally the algorithm solving charger position and direction is summarized as follows.

Algorithm 4. |input paramete is charger quantity m, set of sensors o position, charge model and utility models parameter alpha, β,a,d,c_p,p_w；Output parameter is the position and orientation of each charger.

Method discretization plane domain is introduced in step 1. operational phase 1；

Step 2., to the subregion execution algorithm 2 obtaining after each discretization, obtains candidate's charger position and towards group Intersection closes г；

Step 3. execution algorithm 3 obtains m position and orientation combination, and this is and solves.

Beneficial effect: based on actual measurement data, the charge model of oriented wireless charger is modeled first, and grinds Study carefully the general Layout Problem on two dimensional surface, and how effectively to have arranged charger and it is set towards so that network is overall Charging maximization of utility.Propose a series of analysis method of innovations, extract including plane domain discretization and covering dominant set, Significantly reduce the complex nature of the problem, finally obtain efficient approximate data cdg that approximation ratio is (1-1/e)/(1+ ε) and calculate Method.A kind of method for arranging of the efficiently oriented charger in wirelessly chargeable Sensor Network is proposed, it can arrange charging effectively The position of device and direction；Acquisition after being carried out by discretization plane domain with to each sub-regions covering dominant set extraction is owned In position and orientation combination, continue to select combination to arrange charger, the algorithm of employing is also referred to as cdg (charger Deployment-greedy) algorithm.The scheme of the arrangement charger being obtained by cdg algorithm can cover all of sensor, Reach the purpose of the entirety charging effectiveness of maximization network.

Brief description

Fig. 1 is the model example figure of power approximation；

Fig. 2 is the extraction exemplary plot covering dominant set during fixing point of the present invention；The step illustrating algorithm 1 execution, wherein Fig. 2 (a) algorithm is from sensor o₁Start, add o successively₂And o₃；Fig. 2 (b) algorithm removes { o from current covering set₁,o₂With So that the sensor o compared with mitre₄Can be capped, Fig. 2 (c) -2 (d) adds o₅When there is situation about can not cover, record again {o₃,o₄For covering dominant set；Terminator after rotating a circle.The final all covering dominant sets extracting are { o₁,o₂,o₃, {o₃,o₄, { o₄,o₅And { o₆,o₁}.

Fig. 3 is the extraction exemplary plot covering dominant set in subregion of the present invention.Fig. 3 (a) determines charger direction；Fig. 3 (b) Angle is the track of the point of fixed value a, and Fig. 3 (c) obtains p_refLocate all possible covering dominant set.

Specific embodiment

The invention will be further described with embodiment referring to the drawings.

As shown in figure 1, centered on each sensor, with l (1), l (2) ..., l (k) divide concentric circular for radius.For For the sake of convenient, use l⁽ⁱ⁾K the radius of () mark sensor i is the concentric circular of l (k).The foundation so dividing concentric circular is: Each neighboring concentric is justified, such as l⁽ⁱ⁾And l (k-1)⁽ⁱ⁾K (), at any point in the annulus of composition, if the setting of certain charger The anglec of rotation just cover sensor i, then the power of this charger receiving of sensor i can be approximately considered is constant p_r (l(k)).

Stage 2: cover dominant set and extract

Obtain limited many sub-regions after plane sliding-model control, in each sub-regions, it is contemplated that how to enter One step obtains the set of sensors that all possible charger covers.

It is defined as follows two concepts first.

Definition 3.1: set of sensors o that given charger covers_iAnd o_jIf,Then claim set o_jDomination (dominate) set o_i.

Define 3.2: give set of sensors o that certain sub-regions and its interior charger cover_iIf, in this subregion There is not any other covering set of sensors domination o_i, then claim set o_jFor covering dominant set (coverage dominant Set, cds).

Obtain all of covering dominant set in the demand in certain sub-regions that gives, and all possible covering need not be calculated Lid set.This be according to plane discretization after result, sensor covered by the optional position charger in certain sub-regions When its receiving power all identical, so select cover dominant set necessarily be better than select its domination any may set.

Algorithm 1. |input paramete by charger and its is possible to set of sensors o covering_iPosition；Output parameter is All covering dominant set cds.

Step 1. selectes a certain reference angle, calculates the angle theta that all the sensors are with respect to charger_j(0°≤θ≤ 360°)；

All the sensors are sorted from small to large by step 2. by angle.For convenience, angle might as well be set after sequence as θ₁ ≤θ₂≤…≤θ_p, its respective sensor is o₁,o₂,…,o_p.

Step 3. makes o_cRecord is current to cover set, θ_min, θ_maxRecord current covering set o respectively_cMiddle sensor with respect to The minimum and maximum angle of charger；Initialization makes θ_min=θ_max=θ₁；o_c={ o₁}；

Step 4.j=2；

Step 5.while charger can cover θ_minTo angle, θ_jScope, i.e. θ_j-θ_min≤a；

Step 6. θ_max=θ_j；

Step 7. adds o₁Arrive；

Step 8.j=(j+1) mod p；

Step 9.end while

Step 10. adds current covering set o_cTo covering dominant set record；

Step 11. θ_max=θ_j, add o_jCover set o to current_c；

Step 12.while charger can not cover θ_minTo angle, θ_maxScope, i.e. θ_max-θ_min>a；

Step 13. is from o_cRemove the minimum sensor of angle, and update θ_minFor o_cThe minimum folder that in set, sensor has Angle；

If step 14. θ_min=θ₁, algorithm termination；

Step 15.end while

Step 16.goto step 5

Algorithm 1 is substantially a greedy algorithm, and the implementation procedure of algorithm is appreciated that to become continuous rotation charger Direction covers the situation of change of set of sensors to investigate.The step 5 of algorithm～step 9 is to add as much as possible in rotary course Plus new sensor, till the sensor until there are covering can not be capped.Covering sensor collection when recording critical It is combined into covering dominant set.Step 12～step 15 is to remove the current sensor covering minimum angle in set successively, until working as Till front set can be capped again.Algorithm terminates when the minimum angle running into record is equal to initialized minimum angle, this When mean that charger just has been rotated through one week.

Fig. 2 illustrates an example of algorithm 1 execution.As shown in Fig. 2 (a), algorithm is from sensor o₁Start, add successively o₂And o₃；As interpolation o₄Shi Faxian exceeds coverage, then records current covering and gathers { o₁,o₂,o₃For covering dominant set.It Algorithm removes { o from current covering set afterwards₁,o₂So that the sensor o of relatively mitre₄Can be capped, as Fig. 2 (b) institute Show.Next add o₅When there is situation about can not cover again, record { o₃,o₄For covering dominant set；Add o₅Remove sensing afterwards Device o₃.Fig. 2 (c) -2 (d) by that analogy, algorithm determines set { o in succession₄,o₅, { o₆,o₁Also it is to cover dominant set.In rotation one Terminator after week.The final all covering dominant sets extracting are { o₁,o₂,o₃, { o₃,o₄, { o₄,o₅And { o₆,o₁}.

Investigate below when the optional position of charger is a subregion, how to extract covering dominant set (Fig. 2 can be found in). It is infinitely multiple that one important observation is that while that in given area the optional position of charger and the combination of direction have, but its institute The possible combination covering sensor is limited it means that multiple combination is equivalent.For all equivalences In position and orientation combination, only need to select one of them and analyze.Further, if certain position and orientation combined covering Set of sensors arrange existing position and orientation combined covering set of sensors, then only need to consider the former.Therefore Ensuing task is how to choose these combinations.

Algorithm 2. |input paramete is charger place subzone boundaries, is possible to set of sensors o covering_iPosition； Output parameter is all covering dominant set cds.

Step 1.for all set of sensors o_iIn sensor pair, such as o₁And o₂；

Step 2. connects o₁And o₂And extend and intersect at several intersection points with zone boundary；Take each intersection point successively (as Fig. 3 A in (), intersection point p ' and p ") is as charger position；o₁And o₂Line direction radius border clockwise as overlay area, So that it is determined that charger is towards (as shown in Fig. 3 (a)), calculate current location and the set of sensors towards combined covering, add Cover in dominant set to candidate；

Step 3. calculates and o₁, o₂Angle is track (the two ends circular arc as shown in Fig. 3 (b)) and the area of the point of fixed value a All intersection points on domain border；Successively with each intersection point as current location, o₁, o₂With current location line as current coverage area Radius border so that it is determined that charger direction, calculate the set of sensors that can cover, be added in candidate's covering dominant set；

Step 4.end for

Step 5. times takes 1 point of p on zone boundary_refAs fixing point position, execute algorithm 1 and obtain p_refPlace is possible to Covering dominant set, be added to candidate cover dominant set in, Fig. 3 (c).

Below algorithm 2 is explained.The possible situation (a) encountered during step 2 corresponding charger adjustment in algorithm. It is also noted that and need the position and orientation analyzing all point of intersection to combine.Although intersection point p ' is corresponding in Fig. 3 (a)<p′,θ″>? Join corresponding closer to intersection point p '<p′,θ″>.But this situation is set up only when a≤180 °.Step 3 is corresponding may situation (b).Step 5 corresponding possible situations (c), noting at this time only need to be to an optional point p_refEnter the analysis in line algorithm 1, you can obtain Meet all possible covering dominant set of situation (c).Finally obtain all of covering dominant set and its corresponding charging Device position and orientation combine, and are designated as γ.

Stage 3: approximate data solves charger position and direction (referring to Fig. 3)

Carry out by discretization plane domain with to each sub-regions cover dominant set extract after obtain all positions and Towards in combination, continue to select combination to arrange charger, integrally charged effectiveness with maximization network.

The present invention propose a greedy algorithm come to choose charger position with towards combining.This calculation is given in algorithm 3 The details of method.Can see, each step in this algorithm all can make the maximum element of increment size for current collection x plus one e^*, until | x |=m, till that is, m charger all arranges.

Algorithm 3. |input paramete be charger quantity m, candidate's charger position with towards composite set г, optimization aim letter Number f (x)；The set x that output parameter combines for position and orientation.

Step 1.

Step 2.while | x |≤m

Step 3.e^*=arg max_e∈γ\xf(x{e}-f(x))

Step 4.x=x { e^*}

Step 5.end while

Finally the algorithm solving charger position and direction is summarized as follows.

Algorithm 4. |input paramete is charger quantity m, set of sensors o position, charge model and utility models parameter alpha, β,a,d,c_p,p_w；Output parameter is the position and orientation of each charger.

Method discretization plane domain is introduced in step 1. operational phase 1；

Step 2., to the subregion execution algorithm 2 obtaining after each discretization, obtains candidate's charger position and towards group Intersection closes г；

Step 3. execution algorithm 3 obtains m position and orientation combination, and this is and solves.

This algorithm is also referred to as cdg (charger deployment-greedy) algorithm.The cloth being obtained by cdg algorithm The scheme putting charger can cover all of sensor, reaches the purpose of the entirety charging effectiveness of maximization network.

Claims (2)

1. a kind of oriented charger method for arranging, is characterized in that comprising the following steps:

(1) in a 2 dimensional region, the position of sensor is it is known that m oriented wireless charger has n chargeable transducer arrangements Wait to dispose；

(2) multiple subregions are turned to by discrete for whole 2 dimensional region, thus multiple wireless charger candidate points are reduced to limited, The target of 2 dimensional region discretization be to ensure that discretization after each sub-regions in receiving power can be approximately constant value；

(3) to every sub-regions, obtain all possible set of sensors that charger in this subregion can cover；

(4) all wireless chargers are obtained by discretization plane domain with after each sub-regions are carried out covering dominant set extraction Position and orientation combine；

(5) in the combination of all position and orientation, continue to select m oriented wireless charger of combination arrangement, thus reaching maximum Change network integrally to charge effectiveness.

2. oriented charger method for arranging according to claim 1, it is characterized in that first by discrete for plane domain turn to many Sub-regions, the charge power being approximately considered wireless charger in subregion is a certain constant value；Secondly by each height Intra-zone point is analyzed, and finds out covering dominant set (dominant coverage set, dcs)；The son of last Utilizing question Mould, proposes to reach the greedy algorithm of above-mentioned approximation ratio；Concrete steps:

Stage 1: plane domain discretization

Any given certain power error constant ε, by the different radii l (1) of concentric circular, l (2) ..., l (k) divide distance, and Receiving power is approximated as follows

$p_r\left(d\right)=\left\{\begin{array}{cc}{p}_r\left(l\right(1\left)\right),& 0\&le;d\&le;l\left(1\right)\\ p_r\left(l\right(k\left)\right),& l(k-1)\&le;d\&le;l\left(k\right)(k=2,\mathrm{...},k)\\ 0,& d>l\left(k\right)\end{array}\right.$

And

$\begin{array}{cc}\frac{p_r\left(l\right(k-1))}{p_r\left(l\right(k))}\&le;1+\mathrm{\&epsiv;},\frac{p_r\left(l\right(k-1))}{p_r\left(l\right(k))}=1+\mathrm{\&epsiv;}& (k=2,\mathrm{...},k)\end{array}$

Wherein k is charged area number；D is wireless charger charging maximum distance；In every sub-regions, receiving power is all regarded For constant value；

Therefore have

$\begin{array}{cc}\frac{p_r\left(d\right)}{p_r\left(d\right)}\&le;1+\mathrm{\&epsiv;}& (d\&le;d)\end{array}$

Approximate power is by the power in [l (k-1), l (k)] interval all similar to for p_r(l (k)) is (to interval [0, l (1)], work( Rate is approximately p_r(l(1)))；In each interval, maximum error of approximation is all without more than ε；In every sub-regions, receiving power is equal It is considered constant value；It is clear that the charged area number dividing in such a way is:

Centered on each sensor, with l (1), l (2) ..., l (k) divide concentric circular for radius, use l⁽ⁱ⁾K () labelling senses The radius of device i is the concentric circular of l (k)；The foundation so dividing concentric circular is: in each neighboring concentric circle, such as l⁽ⁱ⁾(k- 1) and l⁽ⁱ⁾K (), at any point in the annulus of composition, if the anglec of rotation of certain charger setting just covers sensor I, then the power of this charger receiving of sensor i can be approximately considered is constant p_r(l(k))；

Stage 2: cover dominant set and extract

Obtain limited many sub-regions after plane sliding-model control, in each sub-regions, obtain further being possible to Charger cover set of sensors；

Definition 3.1: set of sensors o that given charger covers_iAnd o_jIf,Then claim set o_jDomination (dominate) set o_i；

Define 3.2: give set of sensors o that certain sub-regions and its interior charger cover_iIf do not deposited in this subregion In any other covering set of sensors domination o_i, then claim set o_jFor cover dominant set (coverage dominant set, cds)；

Obtain all of covering dominant set in the demand in certain sub-regions that gives；

Set of sensors o covering by charger and its is possible to using algorithm 1. |input paramete_iPosition；Output parameter is All covering dominant set cds；

Step 1. selectes a certain reference angle, calculates the angle theta that all the sensors are with respect to charger_j(0°≤θ≤360°)；

All the sensors are sorted from small to large by step 2. by angle；For convenience, angle might as well be set after sequence as θ₁≤θ₂ ≤…≤θ_p, its respective sensor is o₁,o₂,…,o_p；

Step 3. makes o_cRecord is current to cover set, θ_min, θ_maxRecord current covering set o respectively_cMiddle sensor is with respect to charging The minimum and maximum angle of device；Initialization makes θ_min=θ_max=θ₁；o_c={ o₁}；

Step 4.j=2；

Step 5.while charger can cover θ_minTo angle, θ_jScope, i.e. θ_j-θ_min≤a；

Step 6. θ_max=θ_j；

Step 7. adds o₁Arrive；

Step 8.j=(j+1) mod p；

Step 9.end while

Step 10. adds current covering set o_cTo covering dominant set record；

Step 11. θ_max=θ_j, add o_jCover set o to current_c；

Step 12.while charger can not cover θ_minTo angle, θ_maxScope, i.e. θ_max-θ_min>a；

Step 13. is from o_cRemove the minimum sensor of angle, and update θ_minFor o_cThe minimum angle that in set, sensor has；

If step 14. θ_min=θ₁, algorithm termination；

Step 15.end while

Step 16.goto step 5；

Algorithm 1 is substantially a greedy algorithm, and the direction that the implementation procedure of algorithm is understood to as continuous rotation charger is come Investigate the situation of change covering set of sensors；The step 5 of algorithm～step 9 be add as much as possible in rotary course new Sensor, till the sensor until there are covering can not be capped；Covering set of sensors when recording critical is to cover Lid dominant set；Step 12～step 15 is to remove the current sensor covering minimum angle in set successively, until current collection Till being capped again；Algorithm terminates when the minimum angle running into record is equal to initialized minimum angle, now means Charger and just have been rotated through one week；

When the optional position of charger is a subregion, how to extract covering dominant set；One important observation is that while In given area, the optional position of charger and the combination of direction have infinitely multiple, but its all possible group covering sensor Conjunction is limited it means that multiple combination is equivalent；For in all position and orientation combinations of equal value, only need to choose One of them is selected to analyze；If the set of sensors of certain position and orientation combined covering arranges existing position and orientation The set of sensors of combined covering, then only need to consider the former；

It is charger place subzone boundaries using algorithm 2. |input paramete, be possible to set of sensors o covering_iPosition；Defeated Going out parameter is all covering dominant set cds；

Step 1.for all set of sensors o_iIn sensor pair, such as o₁And o₂；

Step 2. connects o₁And o₂And extend and intersect at several intersection points with zone boundary；Take each intersection point successively as charger Position；o₁And o₂Line direction radius border clockwise as overlay area, so that it is determined that charger direction, calculates and works as Front position and the set of sensors towards combined covering, are added to candidate and cover in dominant set；

Step 3. calculates and o₁, o₂Angle is all intersection points with zone boundary for the track of point of fixed value a；Handed over each successively Point is current location, o₁, o₂With current location line as current coverage area radius border so that it is determined that charger direction, Calculate the set of sensors that can cover, be added to candidate and cover in dominant set；

Step 4.end for

Step 5. times takes 1 point of p on zone boundary_refAs fixing point position, execute algorithm 1 and obtain p_refPlace is all possible to be covered Lid dominant set, is added to candidate and covers in dominant set；

To an optional point p_refEnter the analysis in line algorithm 1, you can all possible covering that acquisition meets situation (c) is propped up Join collection；Finally obtain all of covering dominant set and its corresponding charger position and orientation composite set, be designated as γ；

Stage 3: approximate data solves charger position and direction

Carry out by discretization plane domain with to each sub-regions covering all position and orientation obtaining after dominant set extracts In combination, continue to select combination to arrange charger, integrally charged effectiveness with maximization network；

The present invention proposes the details of a greedy algorithm；For current collection x, each step in algorithm all can add that one makes The maximum element e of increment size^*, until | x |=m, till that is, m charger all arranges；

Algorithm 3. |input paramete is charger quantity m, candidate's charger position with towards composite set г, optimization object function f (x)；The set x that output parameter combines for position and orientation；

Step 1.

Step 2. works as | x |≤m

Step 3.e^*=arg max_e∈γ\xf(x{e}-f(x))

Step 4.x=x { e^*}

Step 5.end；

Finally the algorithm solving charger position and direction is summarized as follows；

Algorithm 4. |input paramete is charger quantity m, set of sensors o position, charge model and utility models parameter alpha, β, a, d,c_p,p_w；Output parameter is the position and orientation of each charger；

Method discretization plane domain is introduced in step 1. operational phase 1；

Step 2., to the subregion execution algorithm 2 obtaining after each discretization, obtains candidate's charger position and towards combination of sets Close г；

Step 3. execution algorithm 3 obtains m position and orientation combination, and this is and solves.