CN106679667A - Method for planning paths of moving bodies for relay navigation of multiple navigation stations - Google Patents

Abstract

The invention discloses a method for planning paths of moving bodies for relay navigation of multiple navigation stations. A horizontal two-dimensional spatial path which meets various constraint conditions is planned for each moving body on the premise that effective navigation range constraints of base stations, navigation connection constraints and curvature constraints of the moving bodies are considered, and each moving body can reach an end point from a starting point via the corresponding horizontal two-dimensional spatial path. The method includes judging the difficulty level of meeting the navigation connection constraints; planning the paths by the aid of processes for planning the paths on the basis of Dubins paths if the constraints are easy to meet; planning the paths by the aid of processes for planning the Dubins paths on the basis of modes of the longest paths in connection regions if the constraints are difficult to meet. The method for planning the paths of the moving bodies for relay navigation of the multiple base stations has the advantages that limitation of narrow navigation ranges of single base stations can be broken through, controllable moving ranges of the moving bodies can be effectively expanded, the paths can be planned under multi-constrained conditions in different sea, land and air circumstances, and the moving bodies can reach end points from starting points via the paths.

Description

Towards the movable body paths planning method of many guidance station relays navigation

Technical field

The invention belongs to movable body path planning research field, and in particular to a kind of fortune towards many guidance station relays navigation Kinetoplast paths planning method, for realizing sea, land and sky different situations multi-constraint condition under movable body from the path of origin-to-destination Planning.

Background technology

Many guidance station relays navigation of movable body can be covered by interspersing among different spatial and navigation function scope Multiple guidance stations of lid larger space are followed successively by movable body and continue the joint air navigation aid of navigation.This navigation mode is not only reliable Property it is strong, and can effectively extend the controllable flight scope of movable body.Towards the movable body path rule of many guidance station relays navigation The problem of drawing is a key issue for realizing being solved needed for this advanced navigation mode with frontier nature, needs to consider three bases The constraint of this constraints, i.e. scope of heading, navigation handing-over constraint, the constraint of movable body maneuverability.Wherein, movable body maneuverability Constraint movable body curvature limitation represents that scope of heading constraint and handing-over constraint of navigating are so that the path planning problem in the present invention General path planning problem is different from, is also the Major Difficulties of path planning problem in the present invention.

Movable body has various navigation modes, including itself navigation and external navigation, and external navigation includes satellite navigation, navigation Stand navigation etc..Wherein, movable body itself navigation and is easily disturbed mode limited precision, and satellite navigation mode easily goes to pot and cost High cost, and guidance station navigation mode is highly reliable, and can perform far for movable body by way of the relay of multistation joint is navigated Journey task provides route guidance.

The content of the invention

In order to effectively extend the controllable moving range of movable body, the reliability of navigation is improved, the invention provides a kind of face To the movable body paths planning method of many guidance station relays navigation.The method is to consider guidance station scope of heading constraint, navigation Handing-over constraint and movable body curvature limitation on the premise of, be movable body cook up one various can meet various constraintss and The quick horizontal two-dimension space path that terminal is arrived at from starting point.

Realize that technical scheme is as follows：

A kind of movable body paths planning method towards many guidance station relays navigation, step is：

Step 0, input route planning information, specifically include：Movable body beginning and end positional information, guidance station navigation model Enclose constraint information, guidance station navigation handing-over constraint information and movable body curvature limitation information；The guidance station scope of heading constraint Information refers to that the coordinate and effective range at guidance station center, i.e. movable body must whole positions from the whole piece path of origin-to-destination In navigation circle；The navigation circle represents guidance station effective range, and radius is r；The guidance station navigation joins constraint is Finger guarantees to navigate and joins successfully and shortest path length D of the movable body of setting in handover region；The navigation handing-over is referred to The navigation power of movable body is transferred between multiple guidance stations；The handover region refers to the overlapping region between two navigation circles；Institute State movable body curvature limitation information and refer to movable body min. turning radius r_tc, using the Dubins paths for limiting curvature between waypoint Connection；

Step 1, the complexity of judgement navigation handing-over constraint, and use difficulty or ease coefficient gamma_jRepresent complexity；γ_jFor jth Navigation handing-over constraint D in individual handover region_jWith most long Dubins paths l of navigation handover region_maxRatio；If γ_j＜ 0.7, using the paths planning method based on Dubins paths, i.e., final path is obtained using the method for step 2 to 5；If γ_j≥ 0.7, using the Dubins paths planning methods based on longest path pattern in handover region, i.e., final road is obtained using step 6 Footpath；

Step 2, random generation initial path population；One paths by start position, final position and middle waypoint position Put and towards common determination；The middle waypoint refers to the waypoint in addition to beginning and end；

Wherein, " CLC " path between middle waypoint and middle waypoint using Dubins connects；

Middle waypoint is arranged on the arc of handover region border, it is random to generate mulitpath composition initial path population, its In, the position of middle waypoint generates at random on affiliated border arc, and middle waypoint is determined towards scope by its position, specifically Direction is generated at random at it towards in the range of；

Step 3, evaluation path；Evaluation index includes path total length and constraint violation degree；The path total length is Refer to and be sequentially connected whole road section length sums that starting point, middle waypoint, terminal are formed according to navigation order；The section refers to Path between two adjacent waypoints；The constraint violation degree refers to navigation handing-over constraint violation degree, when movable body is being handed over When connecing the path in region more than or equal to constraint value, constraint violation degree is 0, and otherwise, constraint violation degree is for both Absolute difference；

The optimal path of step 4, record initial population；If there is the path that constraint violation degree is 0 in initial population, In the path that constraint violation degree is 0 that most short paths of path selection total length as initial population optimal path, If the constraint violation degree in all paths of initial population is all higher than 0, that minimum paths conduct of constraint violation degree is chosen The optimal path of initial population；

Step 5, using differential evolution algorithm path optimizing；First new route is produced by variation, crossover operation, wherein, Variation and crossover operation act only on the position of waypoint, and waypoint changes towards scope with the change of its position, towards at it In the range of generate at random；

Then selected in new route and old path, left preferably path；The principle of selection operation is：When two When the constraint violation degree in path is equal, that shorter paths of path total length are left, when the constraint violation journey of two paths When spending unequal, less that paths of constraint violation degree are left；The path that selection operation is stayed and the kind for recording before Group's optimal path is compared, and comparative approach is identical with the principle of selection operation, by preferably one in both as current kind The optimal path of group；When Evolution of Population algebraically reaches given maximum evolutionary generation, terminate cyclic process, export current population Optimal path, complete path planning；

The Dubins path plannings of step 6, employing based on longest path pattern in handover region, specifically include following step Suddenly：

S401, the width rd for calculating each handover region, and the ratio of handover region width rd and navigation radius of circle rThe width of the handover region refers to that handover region enters arc midpoint and goes out the distance between arc midpoint；

S402, calculating movable body min. turning radius r_tcWith the ratio of navigation radius of circle r

S403, basisWithDetermine path mode of the movable body in each handover region by looking into following table：

Path mode in the handover region includes 7 kinds, is defined respectively as：

Pattern 1：The tangent S types of Double Tops point；Under the pattern, movable body is respectively cross-connecting area in the in and out point of handover region Two summits in domain, movable body is tangent in direction first navigation circle corresponding with this juncture area of access point, and movable body is going out Direction second navigation circle corresponding with this juncture area of point is tangent；Longest path of the movable body in handover region be The CLC paths of Dubins, shape is such as " S ", wherein first C represents the arc section of access point auxiliary circle, second C represents an auxiliary Round arc section, L represents the straightway tangent with two circular arcs；The access point auxiliary circle is referred to access point as point of contact, with r_tcFor Two auxiliary circles that radius is made, referred to as turn left circle and circle of turning right；It is described go out an auxiliary circle refer to go out a little as point of contact, with r_tcFor two auxiliary circles that radius is made, referred to as turn left circle and circle of turning right；Movable body enters handover region from upper summit, from Handover region is left on lower summit, or enters handover region from lower summit, and from upper summit handover region is left；

Pattern 2：The tangent S types in center；Under the pattern, the center of the handover region is the summit line of handover region two and friendship Connect the intersection point of two navigation circle circle center line connectings belonging to region；Longest path of the movable body in handover region is Dubins's CLC paths, shape is such as " S ", wherein first C represents the arc section of access point auxiliary circle, second C represents the circular arc of an auxiliary circle Section, L represents the straightway tangent with two circular arcs；Access point auxiliary circle is tangential on the center of handover region with an auxiliary circle is gone out, directly The length of line segment is 0；Movable body enters arc and enters handover region from upper semisection, goes out arc from lower semisection and leaves handover region, Huo Zhecong Lower semisection enters arc and enters handover region, goes out arc from upper semisection and leaves handover region；

Pattern 3：The tangent S types in single summit；Under the pattern, movable body is one and is located at friendship in the in and out point of handover region The summit in region is connect, if access point is located at the summit of handover region, it is handed over towards tangent with first navigation circle if going out and being a little located at The summit in region is connect, then it is round tangent towards navigating with second；Longest path of the movable body in handover region is Dubins CLC paths, shape is such as " S ", wherein first C represents the arc section of access point auxiliary circle, second C represents the circle of an auxiliary circle Segmental arc, L represents the straightway tangent with two circular arcs；Movable body enters arc and enters handover region from upper semisection, and from lower semisection arc is gone out Handover region is left, or enters arc from lower semisection and enter handover region, gone out arc from upper semisection and leave handover region；

Pattern 4：The tangent c-type of Double Tops point；Under the pattern, movable body is respectively cross-connecting area in the in and out point of handover region Two summits in domain, otherwise movable body in and out point direction all with first navigation circle it is tangent, or all with second Navigation circle is tangent；Longest path of the movable body in handover region for Dubins CLC paths, shape such as " C ", wherein first C The arc section of access point auxiliary circle is represented, second C represents the arc section of an auxiliary circle, L represents tangent with two circular arcs straight Line segment；Movable body enters handover region from upper summit, and from lower summit handover region is left, or enters cross-connecting area from lower summit Domain, from upper summit handover region is left；

Pattern 5：Spoon type；Under the pattern, movable body is located at handover region in the in and out point only one of which of handover region Summit, longest path of the movable body in handover region for Dubins CLC paths, shape such as " spoon ", wherein first C table The arc section of an auxiliary circle is shown into, second C represents the arc section of an auxiliary circle, and L represents the straight line tangent with two circular arcs Section；Movable body enters arc and enters handover region from upper semisection, goes out arc from lower semisection and leave handover region, or enter arc from lower semisection Enter handover region, go out arc from upper semisection and leave handover region；

Pattern 6：The tangent c-type in single summit；Under the pattern, movable body is located in the in and out point only one of which of handover region The summit of handover region, if access point is located at the summit of handover region, access point is round tangent towards navigating with second, if going out a position In the summit of handover region, then go out a direction tangent with first navigation circle；Longest path of the movable body in handover region be The CLC paths of Dubins, shape is such as " C ", wherein first C represents the arc section of access point auxiliary circle, second C represents an auxiliary Round arc section, L represents the straightway tangent with two circular arcs；Movable body enters arc and enters handover region from upper semisection, from lower half Section goes out arc and leaves handover region, or enters arc from lower semisection and enter handover region, goes out arc from upper semisection and leaves handover region；

Mode 7：Circulation is turn-taked round；Movable body is turn-taked movement in handover region interior circulation；

Path mode in S404, former and later two the adjacent handover regions for the non-handover region that is located by movable body determines fortune Path mode of the kinetoplast in non-handover region；

S405, middle waypoint position is encoded, specially：Middle waypoint includes two kinds of in and out point, and access point is The middle waypoint being located on arc, enters the border arc that arc is that movable body enters handover region；It is a little centre positioned at going out on arc to go out Waypoint, it is described go out arc the border arc of handover region is left for movable body；

The representation of access point position is as follows：The center of circle that the rear navigation of handover region is justified as limit, horizontal direction to The right side is pole axis, is counterclockwise positive direction, sets up local polar coordinate system, and the position of access point is represented with polar angle；The handover region The circle that navigates afterwards refers to the navigation circle that movable body will be entered；

The method for expressing for going out a position is as follows：The center of circle that the front navigation of handover region is justified as limit, horizontal direction to The right side is pole axis, is counterclockwise positive direction, sets up local polar coordinate system, and the position polar angle θ for going out a little is represented；The handover region Front navigation circle refers to the navigation circle that movable body will leave；

Thus, the position of all middle waypoints of a paths is by access point polar angle and goes out a polar angle association list and is shown as θ=[θ₁, θ₂,...,θ_n], θ_iThe position of i-th middle waypoint is represented, when i is odd number, the polar angle of access point is expressed as, when i is even number, is represented To go out polar angle a little；Limit θ_iSpan be [θ_i,min,θ_i,max], wherein θ_i,minAnd θ_i,maxIt is right for handover region summit The polar angle answered；The handover region summit is into arc and the intersection point for going out arc；The mode of relative coding is taken, first by middle waypoint position The solution scope put is mapped to [0,1] interval, will 6=[θ₁, θ₂..., θ_n], θ_i∈[θ_{I, min}, θ_{I, max}] it is converted into x=[x₁, x₂..., x_n], x_i∈ [0,1]

S406, random generation initial path population；

When path mode of the movable body in handover region is pattern 1, middle waypoint position initialization of population method is such as Under：For j-th navigation handover region, NP × γ is generated at random_jIndividual middle waypoint position vector (x_2j-1,x_2j), access point position x_2j-1With go out a position x_2jMeet x_2j-1∈ [0,1- γ_j]&x_2j∈ [0,1- γ_j] or x_2j-1∈[γ_j,1]&x_2j∈[γ_j, 1], And at random generate NP-NP × γ_jThe individual middle waypoint position vector for being unsatisfactory for conditions above；The NP represents population scale；

When path mode of the movable body in handover region be pattern 2 when, if in pattern 2 most long Dubins paths access point Position is σ₁Or σ₂, equally go out a position for σ₂Or σ₁；Middle waypoint position initialization of population method is as follows：For j-th navigation Handover region, generates at random NP × γ_jIndividual middle waypoint position vector, access point position x_2j-1With go out a position x_2jMeet x_2j-1∈ [σ₁-σ₁(1-γ_j), σ₁+(0.5-σ₁)(1-γ_j)] and x_2j∈[σ₁-σ₁(1-γ_j),σ₁+(0.5-σ₁)(1-γ_j)] or x_2j-1 ∈[σ₂-(σ₂-0.5)(1-γ_j),σ₂+(1-σ₂)(1-γ_j)] and x_2j∈[σ₂-(σ₂-0.5)(1-γ_j),σ₂+(1-σ₂)(1- γ_j)], and NP-NP × γ is generated at random_jThe individual middle waypoint position vector for being unsatisfactory for conditions above；

When path mode of the movable body in handover region is 3~pattern 6 of pattern, middle waypoint position initialization of population Method is as follows：For j-th navigation handover region, NP × γ is generated at random_jIndividual waypoint position vector (x_2j-1,x_2j), access point position Put x_2j-1With go out a position x_2jMeet x_2j-1∈ [0,1- γ_j]&x_2j∈ 0,0.5] or x_2j-1∈[γ_j,1]&x_2j∈ [0.5,1], with And at random generate NP-NP × γ_jThe individual waypoint position vector for being unsatisfactory for conditions above；

When path mode of the movable body in handover region is mode 7, middle waypoint position initialization of population method is such as Under：Radius is made as r-r with the center of circle of the corresponding two navigation circle of handover region_tcConcentric circular, the public area of the two concentric circulars As circulate the home position scope for turn-taking round in domain；For j-th navigation handover region, turn-take round heart position range in circulation NP position vector (x of interior random generation_2j-1,x_2j), wherein (x_2j-1,x_2j) represent that circulation is turn-taked round relative coding central coordinate of circle；

S407, evaluation path；Evaluation index includes path total length and constraint violation degree；The path total length is referred to Whole road section length sums that starting point, middle waypoint, terminal are formed are sequentially connected according to navigation order；The section refers to two Path between individual adjacent waypoint；The constraint violation degree refers to navigation handing-over constraint violation degree, when movable body is in handing-over When path in region is more than or equal to constraint value, constraint violation degree is 0, and otherwise, constraint violation degree is both Absolute difference；Wherein, when the path mode in handover region is mode 7, when the path of movable body has a plurality of, calculate per paths Path total length and constraint violation degree, and select wherein optimum path as the path of movable body；

The optimal path of S408, record initial population；If there is the path that constraint violation degree is 0 in initial population, In the path that constraint violation degree is 0 that most short paths of path selection total length as initial population optimal path, If the constraint violation degree in all paths of initial population is all higher than 0, that minimum paths conduct of constraint violation degree is chosen The optimal path of initial population；

S409, path optimization is carried out to the initial path population of S406 using the method for step 5, finally export current population Optimal path, complete path planning.

Preferably, determining most long Dubins paths l of navigation handover region_j,maxConcretely comprise the following steps：

S501, calculating handover region width rd, and the ratio of handover region width rd and navigation radius of circle r

S502, calculating movable body min. turning radius r_tcWith the ratio of navigation radius of circle r

S503, basisWithShow that this group of parameter is corresponding by looking into the most long Dubins paths table of handover region Most long Dubins paths l of navigation handover region_max；For the parameter combination situation do not listed in form, using two-dimensional line Property interpolation calculation l_max；

Preferably, the concrete representation of waypoint position is in the middle of in the step 2：

Define access point be positioned at middle the waypoint entered on arc, it is described enter arc be border arc of the movable body into handover region； It is a little middle waypoint positioned at going out on arc to define, it is described go out arc the border arc of handover region is left for movable body；

The representation of access point position is as follows：The center of circle that the rear navigation of handover region is justified as limit, horizontal direction to The right side is pole axis, is counterclockwise positive direction, sets up local polar coordinate system, and the position of access point is represented with polar angle；The handover region The circle that navigates afterwards refers to the navigation circle that movable body will be entered；

Thus, the position of all middle waypoints of a paths is by access point polar angle and goes out a polar angle association list and is shown as θ=[θ₁, θ₂..., θ_n], θ_iThe position of i-th middle waypoint is represented, when i is odd number, the polar angle of access point is expressed as, when i is even number, is represented To go out polar angle a little；Limit θ_iSpan be [θ_{I, min}, θ_{I, max}], wherein θ_{I, min}And θ_{I, max}It is right for handover region summit The polar angle answered；The handover region summit is into arc and the intersection point for going out arc；The mode of relative coding is taken, first by middle waypoint position The solution scope put is mapped to [0,1] interval, will θ=[θ₁, θ₂..., θ_n], θ_i∈[θ_{I, min}, θ_{I, max}] it is converted into x=[x₁, x₂..., x_n], x_i∈ [0,1].

4th, a kind of movable body paths planning method towards many guidance station relays navigation as claimed in claim 1 or 2, its It is characterized in that, middle waypoint is towards the circular of scope in the step 2：

The tangent line that access point makees the rear navigation circle of handover region is crossed, tangent line splits 360 ° of angular ranges centered on access point Into two, 180 ° of angular ranges near terminal are taken as access point towards scope；Cross out the front navigation circle for a little making handover region Tangent line, tangent line by centered on going out a little 360 ° of angular ranges split into two, take near terminal 180 ° of angular ranges make For go out a little towards scope.

Preferably, in S404, if the path mode of front handover region and rear handover region is pattern 1~6, non-friendship Region is connect using Dubins paths connection mode, otherwise, non-handover region adopts following 5 kinds of Dubins paths connection mode, point Not Wei " starting point-circulation turn-take circle ", " middle waypoint-circulation turn-take circle ", " circulation turn-take circle-circulation turn-take circle ", " circulation is turn-taked Circle-middle waypoint ", " circulation turn-take circle-terminal "；Wherein, the direction that the circulation justified and leave of turn-taking into circulation is turn-taked round is protected Hold consistent, be all clockwise or be all counterclockwise；

" starting point-circulation the turn-take circle " pattern co-exists in 2 alternative paths, and respectively starting point and circulation is turn-taked round two Bar tangent line；

" middle waypoint-circulation the turn-take circle " pattern co-exists in 4 alternative paths, respectively in the middle of waypoint turn left circle Turn-take round outer tangent line, internal tangent with circulation, and turn right circle and the circulation of middle waypoint is turn-taked round outer tangent line, internal tangent；

" circulation turn-take circle-circulation the turn-take circle " pattern co-exists in 4 alternative paths, and respectively two circulations turn Two outer tangent lines and two internal tangents of circle circle；

" circulation the turn-take circle-middle waypoint " pattern co-exists in 4 alternative paths, respectively circulation turn-take circle with it is middle Waypoint left-hand bend round outer tangent line, internal tangent, and circulate circle of turn-taking outer tangent line, the internal tangent round with centre waypoint right-hand bend； The middle waypoint is turned left, and round and right-hand bend is round to be referred to middle waypoint as point of contact, with r_tcFor the left and right auxiliary circle that radius is made；

" circulation the turn-take circle-terminal " pattern co-exists in 2 alternative paths, and respectively circulation is turn-taked circle and the two of terminal Bar tangent line；

Keep circulation turn-take circular direction it is consistent on the premise of, select most short that paths of path as final Dubins paths.

Preferably, the coded method for mode 7 is：The relative coding central coordinate of circle refers to that two auxiliary circles of work are public The minimum enclosed rectangle in region, then this boundary rectangle scope is mapped to into the square scope that the length of side is 1, central coordinate of circle is used (x_2j-1,x_2j) represent, wherein x_2j-1∈[0,1],x_2j∈[0,1]；If the central coordinate of circle for generating is beyond the public affairs of two auxiliary circles Altogether region, then keep its vertical coordinate constant, and the border of two auxiliary circle public territorys is pulled to by changing its abscissa.

Preferably, for pattern 1~6, after the position of middle waypoint determines, that is, calculate in the middle of waypoint towards scope, Specially：The tangent line that access point makees the rear navigation circle of handover region is crossed, tangent line splits 360 ° of angular ranges centered on access point Into two halves, 180 ° of angular ranges near terminal are taken as access point towards scope；Cross out the front navigation for a little making handover region 360 ° of angular ranges centered on going out a little have been divided into two halves by round tangent line, tangent line, take 180 ° of angle models near terminal Enclose as go out a little towards scope；The direction of middle waypoint is generated at random in the range of it.

The invention has the beneficial effects as follows：

Firstth, the invention provides a kind of movable body paths planning method towards many guidance station relays navigation, adopts many This advanced navigation mode with frontier nature of guidance station relay navigation, has broken the little limitation of single guidance station scope of heading, Effectively extend the controllable moving range of movable body；

Secondth, the present invention using angular coding by the way of, by angle (variable) replacement coordinate (two variables) come The position of waypoint is represented, solution space had both been have compressed, is easy to path representation and constraint to process again；

3rd, the present invention adopts code segment scheme, and code optimization is only carried out to the position of waypoint, towards in the range of it It is random to generate；This scheme has two major advantages：One operation for being easy for differential evolution algorithm, reduces the dimension of operation Number, two be if towards being also carried out optimization because the position of waypoint determine waypoint towards scope, when the position of waypoint determines Afterwards, in addition it is also necessary to which substantial amounts of iterationses go the direction for optimizing waypoint, so as to the iterationses for causing overall path planning are position Iterationses and the product towards iterationses, amount of calculation is excessive, and time cost is too high, and adopts this code segment scheme to show Work reduces calculation cost, is conducive to improving the efficiency of path planning；

4th, the present invention is by the way of exterior guiding is in combination with movable body itself navigation, and high precision is highly reliable, Even if in the case of guidance station range shorter, it is possible to cooking up a feasible path for movable body；

5th, the paths planning method in the present invention is applied widely, and guidance station can be space-based, ground, airborne, carrier-borne Deng movable body can be unmanned plane, unmanned vehicle, UAV navigation etc., can be used to realizing more than the different situations of sea, land and sky about Path planning of the movable body from origin-to-destination under the conditions of beam.

Description of the drawings

Fig. 1 is the movable body path planning schematic diagram towards many guidance station relays navigation；

Fig. 2 is curvature limitation schematic diagram；

Fig. 3 is handover region width indication figure；

Fig. 4 is access point positional representation method schematic diagram；

Fig. 5 is a positional representation method schematic diagram；

Fig. 6 is waypoint towards scope schematic diagram；

Fig. 7 is handover region path mode schematic diagram；Wherein (a)-(g) is respectively pattern 1- mode 7 schematic diagram；

Fig. 8 is non-handover region path mode schematic diagram；Wherein (a)-(g) is respectively pattern 1- mode 7 schematic diagram；

Fig. 9 is the waypoint position scope schematic diagram of pattern 1 and pattern 2；

Figure 10 is the waypoint position scope schematic diagram of 3~pattern of pattern 6；

Figure 11 follows winged round heart position range schematic diagram for mode 7；

Figure 12 is that differential evolution algorithm solves optimum path planning problem flow chart；

Figure 13 is the result figure of emulation experiment one；

Figure 14 is the result figure of emulation experiment two.

Specific embodiment

The present invention is elaborated with reference to the accompanying drawings and examples.

The present invention joins the difference of constraint complexity for meeting navigation, and summary is drawn towards many guidance station relays navigation Movable body path planning integrated approach.The complexity for meeting navigation handing-over constraint is first determined whether, when constraint is easier to meet When, using the paths planning method based on Dubins paths, when constraint is more difficult to be met, using based on longest path in handover region The Dubins paths planning methods of footpath pattern；Paths planning method based on Dubins paths and based on longest path in handover region The Dubins paths planning methods of footpath pattern are based on the paths planning method of intelligent optimization algorithm；Path planning in the present invention For continuous domain constrained optimization problems, some have the intelligent optimization algorithm of stronger ability of searching optimum suitable for solving the problem, The present invention is using differential evolution algorithm as the Optimization Solution algorithm of the movable body path planning navigated towards many guidance station relays；

The movable body paths planning method towards many guidance station relays navigation is comprised the following steps that：

Step 1, input route planning information, specifically include：Movable body beginning and end positional information, guidance station navigation model Enclose constraint information, guidance station navigation handing-over constraint information and movable body curvature limitation information；The movable body beginning and end position Confidence breath refers to the two-dimensional coordinate of beginning and end；The guidance station scope of heading constraint information refers to the coordinate at guidance station center And effective range, it is interior that movable body must be entirely located in navigation circle from the whole piece path of origin-to-destination；The navigation circle is represented Guidance station effective range, radius is r；The guidance station navigation handing-over constraint information is referred to and guarantees that navigation joins successfully and sets Shortest path length D of the fixed movable body in handover region；The navigation handing-over is referred to and transfer between multiple guidance stations motion The navigation power of body；The handover region refers to the overlapping region between two navigation circles；The movable body curvature limitation information is Refer to movable body min. turning radius r_tc, using the Dubins paths connection for limiting curvature between waypoint；

As shown in figure 1, the starting point of movable body is located in the navigation circle of first guidance station, terminal is located at the 3rd guidance station Navigation circle in, therefore, movable body need to carry out relay navigation by three guidance stations；The path of movable body is by from origin-to-destination Multiple waypoints simultaneously connect according to this 1~section of section 5 that each waypoint formed and constitute, and wherein section 2 and section 4 are movable body in handing-over Path in region；l_2j(2) j=1 represents movable body path in j-th handover region, if l_2j>=D (j=1,2) and friendship The path of movable body in region is connect without departing from handover region scope, then path satisfaction navigation handing-over constraint；

As shown in Fig. 2 A and B represent waypoint, arrow represents movable body direction, and the movable body curvature limitation refers to motion Body realizes the change of direction and position in its horizontal two-dimension space using the Dubins paths for limiting curvature, i.e., section is by straightway It is movable body min. turning radius r with radius_tcCircle on arc composition；

Step 2, the complexity for judging satisfaction navigation handing-over constraint, when constraint is easier to meet, using based on Dubins The paths planning method in path, when constraint is more difficult to be met, using the Dubins roads based on longest path pattern in handover region Footpath planing method, specifically includes：

S201, calculating handover region width rd, and the ratio of handover region width rd and navigation radius of circle rIt is described Handover region width refers to that handover region enters arc midpoint and goes out the distance between arc midpoint, as shown in Figure 3；If navigation circle O₁And O₂ Central coordinate of circle be respectively (x₁,y₁) and (x₂,y₂), the radius of the circle that navigates is r, then

S202, calculating movable body min. turning radius r_tcWith the ratio of navigation radius of circle r

S203, basisWithShow that this group of parameter is corresponding by looking into the most long Dubins paths table of handover region Most long Dubins paths l of navigation handover region_max, it is as shown in the table；

For the parameter combination situation do not listed in form, using two-dimensional linear interpolation calculation l_max；The cross-connecting area Most long Dubins paths table is drawn by a large amount of the simulation experiment results statistics in domain；Entering arc and going out uniform on arc respectively first Waypoint in the middle of 51 is chosen, then 91 directions are uniformly chosen in the range of the corresponding 180 ° of directions of each waypoint, then judge this 51 × 51 × 91 × 91 whether Dubins paths exceed handover region, and calculate path；By comparing, will both without departing from The length records in the most long Dubins paths of handover region scope and path most long Dubins path lengths in handover region In degree table；

S204, definition γ_jFor navigation handing-over constraint D in j-th handover region_jWith the most long Dubins roads of navigation handover region Electrical path length l_j,maxRatio, characterize navigation handing-over constraint complexity, i.e.,

If γ_j＜ 0.7, then it is assumed that navigation handing-over constraint is easier to meet；If γ_j>=0.7, then it is assumed that navigation handing-over constraint compared with Hardly possible meets；Threshold value 0.7 is, using the boundary value of two methods, to be drawn by the experiment of multigroup contrast simulation.

Step 3, according to two methods respective coordinates measurement rule, generate initial road at random in the range of its respective solution Footpath population, evaluates initial path population, and records the optimal path of current population, specifically includes：

S301, the coded system for determining middle waypoint position；Define access point be positioned at the middle waypoint entered on arc, it is described enter Arc is the border arc that movable body enters handover region；It is a little middle waypoint positioned at going out on arc to define, it is described go out arc be motion Body leaves the border arc of handover region；Access point positional representation method is as shown in figure 4, the center of circle that the rear navigation of handover region is justified is made For limit, horizontal direction is to the right pole axis, is counterclockwise positive direction, sets up local polar coordinate system, the position of access point with polar angle θ and Polar diameter ρ represents that the radius justified due to the rear navigation of handover region is, it is known that and access point is located at after handover region the round circumference that navigates On, therefore, the position of access point can be represented with mono- variable of θ；Go out a positional representation method as shown in figure 5, by handover region Used as limit, horizontal direction is to the right pole axis, is counterclockwise positive direction, sets up local polar coordinate system, is gone out in the center of circle of front navigation circle The position polar angle θ and polar diameter ρ of point represents that the radius justified due to the front navigation of handover region is, it is known that and to go out a little be located at cross-connecting area On the circumference of the front navigation circle in domain, therefore, the position for going out a little is represented with mono- variable of θ；Thus, all middle roads of a paths The positional representation of point is θ=[θ₁,θ₂,...,θ_n], limit θ_iSpan be [θ_i,min,θ_i,max], wherein θ_i,minAnd θ_i,max Polar angle corresponding to handover region summit；The handover region summit is into arc and the intersection point for going out arc；The present invention takes relatively The mode of coding, by the solution scope of middle waypoint position [0,1] interval is mapped to, will θ=[θ₁,θ₂,...,θ_n](θ_i∈ [θ_i,min,θ_i,max]) it is converted into x=[x₁,x₂,...,x_n](x_i∈ [0,1]),

S302, according to based on Dubins paths paths planning method, a paths by start position, final position and The position of middle waypoint and the common determination of direction；

Connected using Dubins paths between middle waypoint and middle waypoint；The Dubins paths are referred to for same Any two points with direction in plane, in the case where curvature is limited, reach another using what method of geometry was calculated by a bit A little and the shortest path with direction；Main " CLC " path using Dubins paths of the invention, first C is represented Circular arc in the starting point auxiliary circle of Dubins paths, second C represents the circular arc in Dubins path termination auxiliary circles, and L represents two The tangent line of bar circular arc；The Dubins paths starting point auxiliary circle is referred to Dubins paths starting point as point of contact, with r_tcFor radius work Two auxiliary circles, referred to as Dubins paths starting point turn left circle and turn right circle；The Dubins path terminations auxiliary circle Refer to Dubins path terminations as point of contact, with r_tcFor two auxiliary circles that radius is made, referred to as Dubins path terminations left-hand rotation Curved circle and circle of turning right；" CLC " path in the Dubins paths has 4 kinds of situations, and respectively " Dubins paths starting point is turned left The curved round arc-round arc of tangent section-Dubins path terminations left-hand bend ", " round arc-tangent line of Dubins paths starting point left-hand bend The round arc of section-Dubins path termination right-hand bends ", " round arc-tangent section-Dubins paths of Dubins paths starting point right-hand bend The round arc of terminal left-hand bend " and " the round arc of Dubins paths starting point right-hand bend-tangent section-Dubins path terminations right-hand bend circle Circular arc ", Dubins routing algorithms select that most short paths of length as final Dubins paths in this 4 kinds of situations；

Using head end towards lax Dubins paths connection between starting point and middle waypoint；The head end direction is lax to be The footpath head end direction that shows the way can be any direction；The head end has 2 kinds of situations towards lax Dubins paths, respectively " the round arc of tangent line-Dubins path terminations left-hand bend " and " the round arc of tangent line-Dubins path terminations right-hand bend "；Head end direction Lax Dubins routing algorithms select that most short paths of length as final Dubins paths in this 2 kinds of situations；

Using terminal towards lax Dubins paths connection between middle waypoint and terminal；The terminal direction is lax to be Refer to that Trail termination direction can be any direction；The terminal has 2 kinds of situations towards lax Dubins paths, respectively " the round arc-tangent line of Dubins paths starting point left-hand bend " and " the round arc-tangent line of Dubins paths starting point right-hand bend "；Terminal direction Lax Dubins routing algorithms select that most short paths of length as final Dubins paths in this 2 kinds of situations；

Middle waypoint is arranged on the arc of handover region border, it is random to generate mulitpath composition initial path population, its In, the position of middle waypoint generates at random on affiliated border arc, and middle waypoint is determined towards scope by its position, specifically Direction is generated at random at it towards in the range of；

Middle waypoint towards scope as shown in fig. 6, crossing the tangent line that access point makees the rear navigation circle of handover region, tangent line will be with 360 ° of angular ranges centered on access point are split into two, take 180 ° of angular ranges near terminal as access point towards model Enclose；The tangent line of the front navigation circle for a little making handover region is crossed out, 360 ° of angular ranges centered on going out a little are divided into two by tangent line Half, take 180 ° of angular ranges near terminal as go out a little towards scope；

S303, according to the Dubins paths planning methods based on longest path pattern in handover region, according to cross-connecting area Domain path mode and non-handover region path mode generate path, specifically include：

S30301, basisWithDetermine movable body at each by looking into the most long Dubins path modes table of handover region Path mode in handover region, it is as shown in the table；

The most long Dubins path modes table of the handover region by a large amount of emulation experiments of summary and induction obtain it is most long The geometric properties in Dubins paths and draw；Path mode in the handover region includes 7 kinds, is defined respectively as：

Pattern 1：The tangent S types of Double Tops point, shown in such as Fig. 7 (a)；Under the pattern, movable body handover region access point and go out Point is respectively two summits of handover region, and movable body is tangent with first navigation circle in the direction of access point, and movable body is going out a little Direction with second navigation circle it is tangent；Longest path of the movable body in handover region is the CLC paths of Dubins, and shape is such as " S ", wherein first C represents the arc section of access point auxiliary circle, second C represents the arc section of an auxiliary circle, and L is represented and two The tangent straightway of bar circular arc；The access point auxiliary circle is referred to access point as point of contact, with r_tcFor two auxiliary circles that radius is made, claim For turn left circle and turn right circle；It is described go out an auxiliary circle refer to go out a little as point of contact, with r_tcFor two auxiliary that radius is made Circle, referred to as turn left circle and circle of turning right；Movable body enters handover region from upper summit, and from lower summit handover region is left, Or handover region is entered from lower summit, leave handover region from upper summit；

Pattern 2：The tangent S types in center, shown in such as Fig. 7 (b)；Under the pattern, the center of the handover region is handover region The intersection point of two navigation circle circle center line connectings belonging to two summit lines and handover region；Longest path of the movable body in handover region Footpath for Dubins CLC paths, shape is such as " S ", wherein first C represents the arc section of access point auxiliary circle, second C is represented a little The arc section of auxiliary circle, L represents the straightway tangent with two circular arcs；Access point auxiliary circle is tangential on cross-connecting area with an auxiliary circle is gone out The center in domain, the length of straightway is 0；Movable body enters arc and enters handover region from upper semisection, goes out arc from lower semisection and leaves handing-over Region, or enter arc from lower semisection and enter handover region, go out arc from upper semisection and leave handover region；

Pattern 3：The tangent S types in single summit, shown in such as Fig. 7 (c)；Under the pattern, movable body handover region access point or go out Point is positioned at the summit of handover region, if access point is located at the summit of handover region, its direction is tangent with first navigation circle, if going out Point is round tangent towards navigating with second positioned at the summit of handover region, then its；Longest path of the movable body in handover region For the CLC paths of Dubins, such as " S ", wherein first C represents the arc section of access point auxiliary circle, second C represents a little auxiliary shape Round arc section, L is helped to represent the straightway tangent with two circular arcs；Movable body enters arc and enters handover region from upper semisection, under Half section goes out arc and leaves handover region, or enters arc from lower semisection and enter handover region, goes out arc from upper semisection and leaves handover region；

Pattern 4：The tangent c-type of Double Tops point, shown in such as Fig. 7 (d)；Under the pattern, movable body handover region access point and go out Point is respectively two summits of handover region, or movable body is all tangent with first navigation circle in the direction of in and out point, It is all tangent with second navigation circle；Longest path of the movable body in handover region is the CLC paths of Dubins, and shape is such as " C ", wherein first C represents the arc section of access point auxiliary circle, second C represents the arc section of an auxiliary circle, and L is represented and two The tangent straightway of bar circular arc；Movable body enters handover region from upper summit, and from lower summit handover region is left, or from Xia Ding Point enters handover region, and from upper summit handover region is left；

Pattern 5：Shown in spoon type, such as Fig. 7 (e)；Under the pattern, in and out point only one of which of the movable body in handover region Positioned at the summit of handover region, longest path of the movable body in handover region for Dubins CLC paths, shape such as " spoon ", Wherein first C represents the arc section of access point auxiliary circle, and second C represents the arc section of an auxiliary circle, and L is represented and two circles The tangent straightway of arc；Movable body enters arc and enters handover region from upper semisection, goes out arc from lower semisection and leaves handover region, Huo Zhecong Lower semisection enters arc and enters handover region, goes out arc from upper semisection and leaves handover region；

Pattern 6：The tangent c-type in single summit, shown in such as Fig. 7 (f)；Under the pattern, movable body handover region access point and go out Point only one of which is located at the summit of handover region, if access point is located at the summit of handover region, access point direction and second navigation Circle is tangent, if going out a little positioned at the summit of handover region, goes out a direction tangent with first navigation circle；Movable body is in handover region Interior longest path for Dubins CLC paths, shape is such as " C ", wherein first C represents the arc section of access point auxiliary circle, second Individual C represents the arc section of an auxiliary circle, and L represents the straightway tangent with two circular arcs；Movable body enters arc and enters from upper semisection Handover region, goes out arc and leaves handover region, or enter arc from lower semisection to enter handover region from lower semisection, from upper semisection go out arc from Open handover region；

Mode 7：Circulation turn-take it is round, shown in such as Fig. 7 (g)；Movable body is turn-taked movement in handover region interior circulation；

S30302, determine path mode of the movable body in each non-handover region；Movable body is in non-handover region Path mode is determined by the path mode in handover region；

For the Dubins paths planning methods based on longest path pattern in handover region, due to proposing handover region Interior path mode 7 --- the path mode that circulation is turn-taked in circular pattern, therefore non-handover region increased 5 kinds of Dubins paths Connection mode, respectively " starting point-circulation turn-take circle ", " middle waypoint-circulation turn-take circle ", " circulation circle-circulation of turn-taking is turn-taked Circle ", " circulation turn-take circle-middle waypoint ", " circulation turn-take circle-terminal "；Wherein, note into circulation turn-taking circle and following of leaving Ring round direction of turn-taking must be consistent, and be all clockwise or be all counterclockwise；

" starting point-circulation the turn-take circle " pattern co-exists in 2 alternative paths, and respectively starting point and circulation is turn-taked round two Shown in bar tangent line, such as Fig. 8 (a)；

" middle waypoint-circulation the turn-take circle " pattern co-exists in 4 alternative paths, respectively in the middle of waypoint turn left circle Turn-take round outer tangent line, internal tangent with circulation, shown in such as Fig. 8 (b), and middle waypoint turn right circle and circulation turn-take it is round outer Shown in tangent line, internal tangent, such as Fig. 8 (c)；

" circulation turn-take circle-circulation the turn-take circle " pattern co-exists in 4 alternative paths, and respectively two round two are outer Tangent line and two internal tangents, shown in such as Fig. 8 (d)；

" circulation the turn-take circle-middle waypoint " pattern co-exists in 4 alternative paths, respectively circulation turn-take circle with it is middle Waypoint is turned left outer tangent line, the internal tangent of circle, and shown in such as Fig. 8 (e), and turn-take circle and middle waypoint of circulation is turned right the outer of circle Shown in tangent line, internal tangent, such as Fig. 8 (f)；The middle waypoint is turned left, and round and right-hand bend is round to be referred to middle waypoint as point of contact, With r_tcFor the left and right auxiliary circle that radius is made；

" circulation the turn-take circle-terminal " pattern co-exists in 2 alternative paths, and respectively circulation is turn-taked circle and the two of terminal Shown in bar tangent line, such as Fig. 8 (g)；

Keep circulation turn-take circular direction it is consistent on the premise of, select most short that paths of path as final Dubins paths；

S30303, random generation initial path population；

When path mode of the movable body in handover region is pattern 1, the scope of waypoint position is as shown in figure 9, centre Waypoint position initialization of population method is as follows：For j-th navigation handover region, NP × γ is generated at random_jIndividual middle waypoint position Put vector (x_2j-1,x_2j), access point position x_2j-1With go out a position x_2jMeet:

x_2j-1∈[0,1-γ_j]&x_2j∈[0,1-γ_j] (3)

Or

x_2j-1∈[γ_j,1]&x_2j∈[γ_j,1] (4)

And at random generate NP-NP × γ_jThe individual waypoint position vector for being unsatisfactory for conditions above；The NP represents that population is advised Mould；

When path mode of the movable body in handover region be pattern 2 when, if in pattern 2 most long Dubins paths access point Position is σ₁(movable body enters arc into access point position during handover region from upper semisection) or σ₂(movable body enters arc and enters from lower semisection Enter access point position during handover region), it is also σ equally to go out a position₁(movable body goes out when arc leaves handover region from lower semisection Go out a position) or σ₂(movable body goes out from upper semisection and go out a position when arc leaves handover region)；The scope of waypoint position such as Fig. 9 Shown, middle waypoint position initialization of population method is as follows：For j-th navigation handover region, NP × γ is generated at random_jIn individual Between waypoint position vector, access point position x_2j-1With go out a position x_2jMeet:

Or

And at random generate NP-NP × γ_jThe individual waypoint position vector for being unsatisfactory for conditions above；

When path mode of the movable body in handover region is pattern 3~6, the scope of waypoint position is as shown in Figure 10, Middle waypoint position initialization of population method is as follows：For j-th navigation handover region, NP × γ is generated at random_jIndividual waypoint position Put vector (x_2j-1,x_2j), access point position x_2j-1With go out a position x_2jMeet:

x_2j-1∈[0,1-γ_j]&x_2j∈[0,0.5] (7)

Or

x_2j-1∈[γ_j,1]&x_2j∈[0.5,1] (8)

And at random generate NP-NP × γ_jThe individual waypoint position vector for being unsatisfactory for conditions above；

When path mode of the movable body in handover region is mode 7, as shown in figure 11, at the beginning of middle waypoint position population Beginning method is as follows：Radius is made as r-r with the center of circle of two navigation circles_tcConcentric circular, the public territory of the two concentric circulars is To circulate the home position scope for turn-taking round；For j-th navigation handover region, in round heart position range is turn-taked in circulation with Machine generates NP position vector (x_2j-1,x_2j), wherein (x_2j-1,x_2j) represent that circulation is turn-taked round relative coding central coordinate of circle；It is described Relative coding central coordinate of circle is referred to makees the minimum enclosed rectangle of two auxiliary circle public territorys, then this boundary rectangle scope is reflected It is mapped to the square scope that the length of side is 1, central coordinate of circle (x_2j-1,x_2j) represent, wherein x_2j-1∈[0,1],x_2j∈[0,1]；If The central coordinate of circle of generation then keeps its vertical coordinate constant, by changing its abscissa beyond the public territory of two auxiliary circles It is pulled to the border of two auxiliary circle public territorys；

For pattern 1~6, after the position of middle waypoint determines, you can waypoint towards scope in the middle of calculating；Middle road The direction of point is generated at random in the range of it；

Step 4, evaluation path；Evaluation index includes path total length and constraint violation degree；The path total length is Refer to and be sequentially connected whole road section length sums that starting point, middle waypoint, terminal are formed according to navigation order；The section refers to Path between two adjacent waypoints；The constraint violation degree refers to navigation handing-over constraint violation degree, when movable body is being handed over When connecing the path in region more than or equal to constraint value, constraint violation degree is 0, and otherwise, constraint violation degree is for both Absolute difference；

The optimal path of step 5, record initial population；If there is the path that constraint violation degree is 0 in initial population, In the path that constraint violation degree is 0 that most short paths of path selection total length as initial population optimal path, If the constraint violation degree in all paths of initial population is all higher than 0, that minimum paths conduct of constraint violation degree is chosen The optimal path of initial population；

Step 6, using differential evolution algorithm path optimizing；Differential evolution algorithm solves the flow process of path planning problem as schemed Shown in 12, it is first randomly generated initial path population and evaluates, records the optimal path of current population；Then into algorithm Major cycle, performs evolutional operation repeatedly, until it reaches algorithm end condition, finally exports the optimal path of current population as road The more excellent solution of footpath planning problem；Once complete iterative process includes：Make a variation, intersect, select and update the optimum of current population Path；First new route is produced by variation, crossover operation, wherein, variation and crossover operation act only on the position of waypoint, road That what is put changes towards scope with the change of its position, and direction is generated at random in the range of it；Then in new route and old path In selected, leave preferably path；The principle of selection operation is：When the constraint violation degree of two paths is equal, stay That shorter paths of lower path total length, when the constraint violation degree of two paths is unequal, leave constraint violation degree Less that paths；The path that selection operation is stayed is compared with the population optimal path for recording before, comparative approach It is identical with the principle of selection operation, using preferably one optimal path as current population in both；When Evolution of Population algebraically When reaching given maximum evolutionary generation, terminate cyclic process, export the optimal path of current population, complete path planning.

The paths planning method of the lower movable body of many guidance station relays navigation is illustrated with reference to the simulation experiment result；

As shown in figure 13, guidance station centre coordinate is for (0,0), (1.5,0), (3,0), the radius of the circle that navigates is r=1, is transported Kinetoplast starting point coordinate is for (- 1,0), terminal point coordinate is for (3,0), movable body min. turning radius are r_tc=0.3, navigation handing-over constraint For D=[1.1849,1.1849], differential evolution algorithm population scale is NP=50, and maximum evolutionary generation is Gen=1400, is obtained To route programming result meet institute's Prescribed Properties, and the length in the length (1.2229) in handover region section 2 and section 4 (1.2285) navigation handing-over binding occurrence is close to, total path length is less, has obtained preferably route programming result；

As shown in figure 14, in the case of excessive for navigation handing-over binding occurrence, such as guidance station is interfered or sends out in handing-over Raw failure and when needing the handover time of overlength, guidance station centre coordinate be set to (0,0), (1,0), (2,0), the radius of the circle that navigates For r=1, movable body starting point coordinate is for (- 1,0), terminal point coordinate is for (3,0), movable body min. turning radius are r_tc=0.2, lead Boat handing-over is constrained to D=[0.1,20], and differential evolution algorithm population scale is NP=50, and maximum evolutionary generation is Gen=1000, The route programming result for obtaining meets institute's Prescribed Properties, and movable body has turned nearly 16 circle in second handover region, section 4 Length (20.1061) is sufficiently close to binding occurrence, and is connected with other sections and is similar to straight line, and total path length is less, can Think to have obtained a preferably path based on the Dubins path plannings of handover region longest path pattern.

Embodiments disclosed above is implemented under premised on technical solution of the present invention, gives detailed embodiment party Formula and specific operating process, but protection scope of the present invention is not limited to described embodiment.By the above, this Many contents in bright can make an amendment and replace, and the present embodiment secures some values and is intended merely to be better described the present invention's Principle and application, so as to being more readily understood and using.All local done on the basis of technical scheme are changed, equivalent Replacement, improvement etc. should be included within the scope of the present invention.

Claims (7)

1. it is a kind of towards many guidance station relays navigation movable body paths planning method, it is characterised in that comprise the steps：

Step 0, input route planning information, specifically include：Movable body beginning and end positional information, guidance station scope of heading are about Beam information, guidance station navigation handing-over constraint information and movable body curvature limitation information；The guidance station scope of heading constraint information Refer to that the coordinate and effective range at guidance station center, i.e. movable body must be entirely located in from the whole piece path of origin-to-destination to lead In boat circle；The navigation circle represents guidance station effective range, and radius is r；The guidance station navigation handing-over constraint is referred to really Protect navigation and join shortest path length D of the movable body for successfully setting in handover region；The navigation handing-over refers to multiple The navigation power of movable body is transferred between guidance station；The handover region refers to the overlapping region between two navigation circles；The fortune Kinetoplast curvature limitation information refers to movable body min. turning radius r_tc, connected using the Dubins paths for limiting curvature between waypoint Connect；

Step 1, the complexity of judgement navigation handing-over constraint, and use difficulty or ease coefficient gamma_jRepresent complexity；γ_jFor j-th friendship Meet navigation handing-over constraint D in region_jWith most long Dubins paths l of navigation handover region_maxRatio；If γ_j＜ 0.7, adopts With the paths planning method based on Dubins paths, i.e., final path is obtained using the method for step 2 to 5；If γ_j>=0.7, adopt With the Dubins paths planning methods based on longest path pattern in handover region, i.e., final path is obtained using step 6；

Step 2, random generation initial path population；One paths by start position, the position in final position and middle waypoint and Towards common determination；The middle waypoint refers to the waypoint in addition to beginning and end；

Wherein, " CLC " path between middle waypoint and middle waypoint using Dubins connects；

Middle waypoint is arranged on the arc of handover region border, it is random to generate mulitpath composition initial path population, wherein, in Between the position of waypoint generate at random on affiliated border arc, middle waypoint is determined towards scope by its position, concrete direction Generate at random towards in the range of at it；

Step 3, evaluation path；Evaluation index includes path total length and constraint violation degree；The path total length refer to by Whole road section length sums that starting point, middle waypoint, terminal are formed are sequentially connected according to navigation order；The section refers to two Path between adjacent waypoint；The constraint violation degree refers to navigation handing-over constraint violation degree, when movable body is in cross-connecting area When path in domain is more than or equal to constraint value, constraint violation degree is 0, and otherwise, constraint violation degree is both exhausted To difference；

The optimal path of step 4, record initial population；If there is the path that constraint violation degree is 0 in initial population, about Beam violates most short that paths of path selection total length in the path that degree is 0 as the optimal path of initial population, if just The constraint violation degree in all paths of beginning population is all higher than 0, then choose that minimum paths of constraint violation degree as initial The optimal path of population；

Step 5, using differential evolution algorithm path optimizing；First new route is produced by variation, crossover operation, wherein, variation With position that crossover operation acts only on waypoint, waypoint changes towards scope with the change of its position, towards in its scope Interior random generation；

Then selected in new route and old path, left preferably path；The principle of selection operation is：When two paths Constraint violation degree it is equal when, leave that shorter paths of path total length, when two paths constraint violation degree not When equal, less that paths of constraint violation degree are left；The path that selection operation is stayed is with the population for recording before most Shortest path is compared, and comparative approach is identical with the principle of selection operation, using preferably one in both as current population Optimal path；When Evolution of Population algebraically reaches given maximum evolutionary generation, terminate cyclic process, export current population most Shortest path, completes path planning；

The Dubins path plannings of step 6, employing based on longest path pattern in handover region, specifically include following steps：

S401, the width rd for calculating each handover region, and the ratio of handover region width rd and navigation radius of circle rInstitute The width for stating handover region refers to that handover region enters arc midpoint and goes out the distance between arc midpoint；

S402, calculating movable body min. turning radius r_tcWith the ratio of navigation radius of circle r

S403, basisWithDetermine path mode of the movable body in each handover region by looking into following table：

Path mode in the handover region includes 7 kinds, is defined respectively as：

Pattern 1：The tangent S types of Double Tops point；Under the pattern, movable body is respectively handover region in the in and out point of handover region Two summits, movable body is tangent in direction first navigation circle corresponding with this juncture area of access point, and movable body is going out a little It is tangent towards second corresponding with this juncture area navigation circle；Longest path of the movable body in handover region is Dubins's CLC paths, shape is such as " S ", wherein first C represents the arc section of access point auxiliary circle, second C represents the circular arc of an auxiliary circle Section, L represents the straightway tangent with two circular arcs；The access point auxiliary circle is referred to access point as point of contact, with r_tcMake for radius Two auxiliary circles, referred to as turn left circle and circle of turning right；It is described go out an auxiliary circle refer to go out a little as point of contact, with r_tcFor radius Two auxiliary circles made, referred to as turn left circle and circle of turning right；Movable body enters handover region from upper summit, from lower summit from Handover region is opened, or handover region is entered from lower summit, from upper summit handover region is left；

Pattern 2：The tangent S types in center；Under the pattern, the center of the handover region is the summit line of handover region two and cross-connecting area The intersection point of two navigation circle circle center line connectings belonging to domain；Longest path of the movable body in handover region is the CLC roads of Dubins Footpath, shape is such as " S ", wherein first C represents the arc section of access point auxiliary circle, second C represents the arc section of an auxiliary circle, L Represent and the tangent straightway of two circular arcs；Access point auxiliary circle is tangential on the center of handover region, straightway with an auxiliary circle is gone out Length be 0；Movable body enters arc and enters handover region from upper semisection, goes out arc from lower semisection and leaves handover region, or from lower half Section enters arc and enters handover region, goes out arc from upper semisection and leaves handover region；

Pattern 3：The tangent S types in single summit；Under the pattern, movable body is one and is located at cross-connecting area in the in and out point of handover region The summit in domain, if access point is located at the summit of handover region, it is round tangent towards navigating with first, if going out a little be located at cross-connecting area The summit in domain, then its direction is tangent with second navigation circle；Longest path of the movable body in handover region is the CLC of Dubins Path, shape is such as " S ", wherein first C represents the arc section of access point auxiliary circle, second C represents the arc section of an auxiliary circle, L represents the straightway tangent with two circular arcs；Movable body enters arc and enters handover region from upper semisection, goes out arc from lower semisection and leaves friendship Region is connect, or enters arc from lower semisection and enter handover region, gone out arc from upper semisection and leave handover region；

Pattern 4：The tangent c-type of Double Tops point；Under the pattern, movable body is respectively handover region in the in and out point of handover region Two summits, or movable body is all tangent with first navigation circle in the direction of in and out point, or all navigating with second Circle is tangent；Longest path of the movable body in handover region for Dubins CLC paths, shape such as " C ", wherein first C is represented The arc section of access point auxiliary circle, second C represents the arc section of an auxiliary circle, and L represents the straightway tangent with two circular arcs； Movable body enters handover region from upper summit, and from lower summit handover region is left, or enters handover region from lower summit, from upper Leave handover region in summit；

Pattern 5：Spoon type；Under the pattern, movable body is located at the top of handover region in the in and out point only one of which of handover region Point, longest path of the movable body in handover region for Dubins CLC paths, shape such as " spoon ", wherein first C represent into The arc section of point auxiliary circle, second C represents the arc section of an auxiliary circle, and L represents the straightway tangent with two circular arcs；Fortune Kinetoplast enters arc and enters handover region from upper semisection, goes out arc from lower semisection and leave handover region, or enter arc from lower semisection to enter friendship Region is connect, is gone out arc from upper semisection and is left handover region；

Pattern 6：The tangent c-type in single summit；Under the pattern, movable body is located at handing-over in the in and out point only one of which of handover region The summit in region, if access point is located at the summit of handover region, access point is handed over towards tangent with second navigation circle if going out and being a little located at The summit in region is connect, then goes out a direction tangent with first navigation circle；Longest path of the movable body in handover region be The CLC paths of Dubins, shape is such as " C ", wherein first C represents the arc section of access point auxiliary circle, second C represents an auxiliary Round arc section, L represents the straightway tangent with two circular arcs；Movable body enters arc and enters handover region from upper semisection, from lower half Section goes out arc and leaves handover region, or enters arc from lower semisection and enter handover region, goes out arc from upper semisection and leaves handover region；

Mode 7：Circulation is turn-taked round；Movable body is turn-taked movement in handover region interior circulation；

Path mode in S404, former and later two the adjacent handover regions for the non-handover region that is located by movable body determines movable body Path mode in non-handover region；

S405, middle waypoint position is encoded, specially：Middle waypoint include two kinds of in and out point, access point be positioned at Enter the middle waypoint on arc, enter the border arc that arc is that movable body enters handover region；It is a little middle waypoint positioned at going out on arc to go out, It is described go out arc the border arc of handover region is left for movable body；

The representation of access point position is as follows：Used as limit, horizontal direction is to the right in the center of circle that the rear navigation of handover region is justified Pole axis, is counterclockwise positive direction, sets up local polar coordinate system, and the position of access point is represented with polar angle；Lead after the handover region Boat circle refers to the navigation circle that movable body will be entered；

The method for expressing for going out a position is as follows：Used as limit, horizontal direction is to the right in the center of circle that the front navigation of handover region is justified Pole axis, is counterclockwise positive direction, sets up local polar coordinate system, and the position polar angle θ for going out a little is represented；The handover region it is leading Boat circle refers to the navigation circle that movable body will leave；

Thus, the position of all middle waypoints of a paths is by access point polar angle and goes out a polar angle association list and is shown as θ=[θ₁, θ₂,...,θ_n], θ_iThe position of i-th middle waypoint is represented, when i is odd number, the polar angle of access point is expressed as, when i is even number, is represented To go out polar angle a little；Limit θ_iSpan be [θ_i,min,θ_i,max], wherein θ_i,minAnd θ_i,maxIt is right for handover region summit The polar angle answered；The handover region summit is into arc and the intersection point for going out arc；The mode of relative coding is taken, first by middle waypoint position PutSolution scope[0,1] interval is mapped to, will θ=[θ₁, θ₂..., θ_n], θ_i∈[θ_{I, min}, θ_{I, max}] it is converted into x=[x₁, x₂..., x_n], x_i∈ [0,1]；

S406, random generation initial path population；

When path mode of the movable body in handover region is pattern 1, middle waypoint position initialization of population method is as follows：It is right Navigate handover region in j-th, and NP × γ is generated at random_jIndividual middle waypoint position vector (x_2j-1,x_2j), access point position x_2j-1With Go out a position x_2jMeet x_2j-1∈] 0,1- γ_j]&x_2j∈ [0,1- γ_j] or x_2j-1∈[γ_j,1]&x_2j∈[γ_j, 1], Yi Jisui Machine generates NP-NP × γ_jThe individual middle waypoint position vector for being unsatisfactory for conditions above；The NP represents population scale；

When path mode of the movable body in handover region be pattern 2 when, if in pattern 2 most long Dubins paths access point position For σ₁Or σ₂, equally go out a position for σ₂Or σ₁；Middle waypoint position initialization of population method is as follows：For j-th navigation handing-over Region, generates at random NP × γ_jIndividual middle waypoint position vector, access point position x_2j-1With go out a position x_2jMeet x_2j-1∈[σ₁- σ₁(1-γ_j), σ₁+(0.5-σ₁)(1-γ_j)] and x_2j∈[σ₁-σ₁(1-γ_j),σ₁+(0.5-σ₁)(1-γ_j)] or x_2j-1∈ [σ₂-(σ₂-0.5)(1-γ_j),σ₂+(1-σ₂)(1-γ_j)] and x_2j∈[σ₂-(σ₂-0.5)(1-γ_j),σ₂+(1-σ₂)(1-γ_j)], And at random generate NP-NP × γ_jThe individual middle waypoint position vector for being unsatisfactory for conditions above；

When path mode of the movable body in handover region is 3~pattern 6 of pattern, middle waypoint position initialization of population method It is as follows：For j-th navigation handover region, NP × γ is generated at random_jIndividual waypoint position vector (x_2j-1,x_2j), access point position x_2j-1 With go out a position x_2jMeet x_2j-1∈ [0,1- γ_j]&x_2j∈ [0,0.5] or x_2j-1∈[γ_j,1]&x_2j∈ [0.5,1], Yi Jisui Machine generates NP-NP × γ_jThe individual waypoint position vector for being unsatisfactory for conditions above；

When path mode of the movable body in handover region is mode 7, middle waypoint position initialization of population method is as follows：With Make radius for r-r in the center of circle of the corresponding two navigation circle of handover region_tcConcentric circular, the public territory of the two concentric circulars is The home position scope that circulation is turn-taked round；It is random in round heart position range is turn-taked in circulation for j-th navigation handover region Generate NP position vector (x_2j-1,x_2j), wherein (x_2j-1,x_2j) represent that circulation is turn-taked round relative coding central coordinate of circle；

S407, evaluation path；Evaluation index includes path total length and constraint violation degree；The path total length refer to according to Navigation order is sequentially connected whole road section length sums that starting point, middle waypoint, terminal are formed；The section refers to two phases Path between adjacent waypoint；The constraint violation degree refers to navigation handing-over constraint violation degree, when movable body is in handover region When interior path is more than or equal to constraint value, constraint violation degree is 0, and otherwise, constraint violation degree is both absolute Difference；Wherein, when the path mode in handover region is mode 7, when the path of movable body has a plurality of, the road per paths is calculated Footpath total length and constraint violation degree, and wherein optimum path is selected as the path of movable body；

The optimal path of S408, record initial population；If there is the path that constraint violation degree is 0 in initial population, about Beam violates most short that paths of path selection total length in the path that degree is 0 as the optimal path of initial population, if just The constraint violation degree in all paths of beginning population is all higher than 0, then choose that minimum paths of constraint violation degree as initial The optimal path of population；

S409, path optimization is carried out to the initial path population of S406 using the method for step 5, finally export current population most Shortest path, completes path planning.

2. a kind of movable body paths planning method towards many guidance station relays navigation as claimed in claim 1, its feature exists In it is determined that most long Dubins paths l of navigation handover region_j,maxConcretely comprise the following steps：

S501, calculating handover region width rd, and the ratio of handover region width rd and navigation radius of circle r

S502, calculating movable body min. turning radius r_tcWith the ratio of navigation radius of circle r

S503, basisWithThe corresponding navigation of this group of parameter is drawn by looking into the most long Dubins paths table of handover region Most long Dubins paths l of handover region_max；For the parameter combination situation do not listed in form, inserted using two-dimensional linear Value method calculates l_max；

3. a kind of movable body paths planning method towards many guidance station relays navigation as claimed in claim 1 or 2, its feature It is that the concrete representation of middle waypoint position is in the step 2：

Define access point be positioned at middle the waypoint entered on arc, it is described enter arc be border arc of the movable body into handover region；Definition It is a little middle waypoint positioned at going out on arc to go out, it is described go out arc the border arc of handover region is left for movable body；

The representation of access point position is as follows：Used as limit, horizontal direction is to the right in the center of circle that the rear navigation of handover region is justified Pole axis, is counterclockwise positive direction, sets up local polar coordinate system, and the position of access point is represented with polar angle；Lead after the handover region Boat circle refers to the navigation circle that movable body will be entered；

Thus, the position of all middle waypoints of a paths is by access point polar angle and goes out a polar angle association list and is shown as θ=[θ₁, θ₂,...,θ_n], θ_iThe position of i-th middle waypoint is represented, when i is odd number, the polar angle of access point is expressed as, when i is even number, is represented To go out polar angle a little；Limit θ_iSpan be [θ_i,min,θ_i,max], wherein θ_i,minAnd θ_i,maxIt is right for handover region summit The polar angle answered；The handover region summit is into arc and the intersection point for going out arc；The mode of relative coding is taken, first by middle waypoint position PutSolution scope[0,1] interval is mapped to, will θ=[θ₁, θ₂..., θ_n], θ_i∈[θ_{I, min}, θ_{I, max}] it is converted into x=[x₁, x₂..., x_n], x_i∈ [0,1].

4. a kind of movable body paths planning method towards many guidance station relays navigation as claimed in claim 1 or 2, its feature It is that middle waypoint is in the step 2 towards the circular of scope：

The tangent line that access point makees the rear navigation circle of handover region is crossed, 360 ° of angular ranges centered on access point are divided into two by tangent line Half, 180 ° of angular ranges near terminal are taken as access point towards scope；Cross out a little make handover region front navigation circle cut Line, tangent line splits 360 ° of angular ranges centered on going out a little into two, takes 180 ° of angular ranges near terminal as going out Point towards scope.

5. a kind of movable body paths planning method towards many guidance station relays navigation as claimed in claim 1, its feature exists In in S404, if the path mode of front handover region and rear handover region is pattern 1~6, non-handover region is adopted Dubins paths connection mode, otherwise, non-handover region adopts following 5 kinds of Dubins paths connection mode, respectively " starting point- Circulation is turn-taked circle ", " middle waypoint-circulation turn-take circle ", " circulation turn-take circle-circulation turn-take circle ", " circulation is turn-taked circle-middle road Point ", " circulation turn-take circle-terminal "；Wherein, turn-take circle into circulation and the circulation left round direction of turn-taking is consistent, together Clockwise or to be all counterclockwise；

" starting point-circulation the turn-take circle " pattern co-exists in 2 alternative paths, and respectively starting point and circulation round two that turn-take cut Line；

" middle waypoint-circulation the turn-take circle " pattern co-exists in 4 alternative paths, respectively in the middle of waypoint turn left circle and to follow Ring is turn-taked round outer tangent line, internal tangent, and turn right circle and the circulation of middle waypoint is turn-taked round outer tangent line, internal tangent；

" circulation turn-take circle-circulation the turn-take circle " pattern co-exists in 4 alternative paths, and respectively two circulations are turn-taked circle Two outer tangent lines and two internal tangents；

" circulation the turn-take circle-middle waypoint " pattern co-exists in 4 alternative paths, and respectively circulation is turn-taked circle and middle waypoint Turn left round outer tangent line, internal tangent, and circulates circle of turn-taking outer tangent line, the internal tangent round with middle waypoint right-hand bend；It is described Middle waypoint is turned left, and round and right-hand bend is round to be referred to middle waypoint as point of contact, with r_tcFor the left and right auxiliary circle that radius is made；

" circulation the turn-take circle-terminal " pattern co-exists in 2 alternative paths, and respectively circulation circle of turn-taking is cut with two of terminal Line；

Keep circulation turn-take circular direction it is consistent on the premise of, select most short that paths of path as final Dubins paths.

6. a kind of movable body paths planning method towards many guidance station relays navigation as claimed in claim 1 or 2, its feature It is that the coded method for mode 7 is：The relative coding central coordinate of circle refers to the minimum for making two auxiliary circle public territorys Boundary rectangle, then this boundary rectangle scope is mapped to into the square scope that the length of side is 1, central coordinate of circle (x_2j-1,x_2j) table Show, wherein x_2j-1∈[0,1],x_2j∈[0,1]；If the central coordinate of circle for generating is protected beyond the public territory of two auxiliary circles Hold that its vertical coordinate is constant, the border of two auxiliary circle public territorys is pulled to by changing its abscissa.

7. a kind of movable body paths planning method towards many guidance station relays navigation as claimed in claim 1 or 2, its feature Be, for pattern 1~6, after the position of middle waypoint determines, that is, calculate in the middle of waypoint towards scope, specially：Cross into Point makees the tangent line of the rear navigation circle of handover region, and 360 ° of angular ranges centered on access point have been divided into two halves, have been taken by tangent line 180 ° of angular ranges of close terminal are as access point towards scope；The tangent line of the front navigation circle for a little making handover region is crossed out, is cut 360 ° of angular ranges centered on going out a little have been divided into two halves by line, take 180 ° of angular ranges near terminal as going out a little Towards scope；The direction of middle waypoint is generated at random in the range of it.