CN106679667B - Towards the movable body paths planning method of more guidance station relays navigation - Google Patents

Abstract

The invention discloses a kind of movable body paths planning method towards more guidance station relays navigation, this method is on the premise of base station efficient navigation range constraint, navigation handing-over constraint and movable body curvature limitation is considered, a horizontal two-dimension space path that various can meet various constraintss and terminal is quickly arrived at from starting point is cooked up for movable body；First, it is determined that meet the complexity of navigation handing-over constraint, then, when constraint is easier to meet, using the paths planning method based on Dubins paths, when constraining more difficult meet, using the Dubins paths planning methods based on longest path pattern in handover region；Movable body paths planning method provided by the invention towards more base station relays navigation has broken the small limitation of single base station scope of heading, the controllable moving range of movable body is effectively extended, can solve under the different situations multi-constraint condition of sea, land and sky movable body from the path planning problem of origin-to-destination.

Description

Towards the movable body paths planning method of more 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 more guidance station relays navigation Kinetoplast paths planning method, for realizing under the different situations multi-constraint condition of sea, land and sky movable body from the path of origin-to-destination Planning.

Background technology

More guidance station relays navigation of movable body is by interspersing among different spatial and navigation function scope can be covered Multiple guidance stations of lid larger space are followed successively by movable body and continued the joint air navigation aid of navigation.This navigation mode is not only reliable Property is strong, and can effectively extend the controllable flight scope of movable body.Towards the movable body path rule of more guidance station relays navigation The problem of drawing is to realize the key issue solved needed for this advanced navigation mode with frontier nature, it is necessary 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 represents that scope of heading constraint and navigation handing-over constrain the path planning problem caused in the present invention with movable body curvature limitation Be different from general path planning problem, and in the present invention path planning problem Major Difficulties.

Movable body has a variety of 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 Cost is high, and guidance station navigation mode is highly reliable, and can be remote for movable body execution by way of multistation joint relay navigation 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 The movable body paths planning method to be navigated to more guidance station relays.This method is to consider guidance station scope of heading constraint, navigation Handing-over constraint and movable body curvature limitation on the premise of, for movable body cook up one various can meet various constraintss and The horizontal two-dimension space path of terminal is quickly arrived at from starting point.

Realize that technical scheme is as follows：

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

Step 0, input route planning information, are specifically included：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 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 in navigation circle；The navigation circle represents guidance station effective range, radius r；The guidance station navigation, which joins constraint, is Referring to ensures that navigation joins shortest path length D of the movable body successfully set in handover region；The navigation handing-over refers 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 for judging navigation handing-over constraint, and with difficulty or ease coefficient gamma_jRepresent complexity；γ_jFor jth Navigation handing-over constraint D in individual handover region_jWith the most long Dubins path lengths l of handover region that navigates_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 determined towards common；The middle waypoint refers to the waypoint in addition to beginning and end；

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

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 is generated at random on affiliated border arc, and middle waypoint is determined towards scope by its position, specifically Generated at random in the range of towards at it；

Step 3, evaluation path；Evaluation index includes path total length and constraint violation degree；The path total length is Refer to the whole road section length sums for being sequentially connected starting point, middle waypoint, terminal according to navigation order and being formed；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 length in region and being more than or equal to constraint value, constraint violation degree is 0, and otherwise, constraint violation degree is for both Absolute difference；

Step 4, the optimal path for recording initial population；If the path that constraint violation degree is 0 in initial population be present, Optimal path of that the most short paths of path selection total length as initial population in the path that constraint violation degree is 0, 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；New route is produced by variation, crossover operation first, 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, leave 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, that less paths of constraint violation degree are left；The path that selection operation is left and the kind recorded before Group's optimal path is compared, and comparative approach is identical with the principle of selection operation, using preferably one in both as currently planting The optimal path of group；When Evolution of Population algebraically reaches given maximum evolutionary generation, cyclic process is terminated, exports current population Optimal path, complete path planning；

Step 6, using the Dubins path plannings based on longest path pattern in handover region, specifically include following step Suddenly：

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

S402, calculate movable body min. turning radius r_tcWith the ratio for the radius of circle r that navigates

S403, basisWithPath mode of the movable body in each handover region is determined 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 cross-connecting area respectively 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 Dubins CLC paths, shaped like " S ", wherein first C represents the arc section of access point auxiliary circle, second C represents an auxiliary Round arc section, L are represented and the tangent straightway of two circular arcs；The access point auxiliary circle refers to using 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 for point of contact, with r_tcTwo auxiliary circles made for radius, 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 handover region is left from upper summit；

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, shaped like " 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 are represented and the tangent straightway of two circular arcs；Access point auxiliary circle is with going out the center that an auxiliary circle is tangential on handover region, directly The length of line segment is 0；Movable body enters arc from upper semisection and enters handover region, and going out arc from lower semisection leaves handover region, Huo Zhecong Lower semisection enters arc and enters handover region, and going out arc from upper semisection leaves handover region；

Pattern 3：Single tangent S types in summit；Under the pattern, movable body is located in the in and out point of handover region for one to be handed over The summit in region is connect, if access point is located at the summit of handover region, it is round tangent towards being navigated with first, if going out a little positioned at friendship The summit in region is connect, then it is round tangent towards being navigated with second；Longest path of the movable body in handover region is Dubins CLC paths, shaped like " 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 are represented and the tangent straightway of two circular arcs；Movable body enters arc from upper semisection and enters handover region, goes out arc from lower semisection Handover region is left, or enters arc from lower semisection and enters handover region, going out arc from upper semisection leaves handover region；

Pattern 4：The tangent c-type of Double Tops point；Under the pattern, movable body is cross-connecting area respectively 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 is Dubins CLC paths, shaped like " C ", wherein first C The arc section of access point auxiliary circle is represented, second C represents the arc section of an auxiliary circle, and L is represented and tangent straight of two circular arcs Line segment；Movable body enters handover region from upper summit, leaves handover region from lower summit, or enter cross-connecting area from lower summit Domain, handover region is left from upper summit；

Pattern 5：Spoon type；Under the pattern, movable body only has one to be located at handover region in the in and out point of handover region Summit, longest path of the movable body in handover region be Dubins CLC paths, shaped like " 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 is represented and the tangent straight line of two circular arcs Section；Movable body enters arc from upper semisection and enters handover region, and going out arc from lower semisection leaves handover region, or enters arc from lower semisection and enter Enter handover region, going out arc from upper semisection leaves handover region；

Pattern 6：Single tangent c-type in summit；Under the pattern, movable body only has one to be located in the in and out point 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 being navigated with second, if going out a position In the summit of handover region, then go out a direction and first navigation circle is tangent；Longest path of the movable body in handover region be Dubins CLC paths, shaped like " C ", wherein first C represents the arc section of access point auxiliary circle, second C represents an auxiliary Round arc section, L are represented and the tangent straightway of two circular arcs；Movable body enters arc from upper semisection and enters handover region, from lower half Section goes out arc and leaves handover region, or enters arc from lower semisection and enter handover region, and going out arc from upper semisection leaves handover region；

Mode 7：Circulation is turn-taked round；Movable body circulates movement of turn-taking in handover region；

S404, the path mode where movable body in former and later two adjacent handover regions of non-handover region determine fortune Path mode of the kinetoplast in non-handover region；

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

The representation of access point position is as follows：Using 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, establishes local polar coordinate system, the position of access point is represented with polar angle；The handover region Navigation circle refers to the navigation circle that movable body will enter afterwards；

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

Thus, the position of all middle waypoints of a paths 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 of middle waypoint is represented, when i is odd number, is expressed as the polar angle of access point, 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] section, i.e., by 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 of 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 NP-NP × γ is generated at random_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 is pattern 2, if in pattern 2 most long Dubins paths access point Position is σ₁Or σ₂, it is σ equally to go out a position₂Or σ₁；Middle waypoint position initialization of population method is as follows：For j-th of navigation Handover region, NP × γ is generated at random_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 of 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 NP-NP × γ is generated at random_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 using the center of circle of two navigation circles corresponding to handover region_tcConcentric circles, the public area of the two concentric circles As circulate the home position scope for turn-taking round in domain；For j-th of navigation handover region, turn-taked round heart position range in circulation Interior NP position vector (x of generation at random_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 refers to Whole road section length sums that starting point, middle waypoint, terminal 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 joining When path length 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, calculating is per paths Path total length and constraint violation degree, and select the path of wherein optimal path as movable body；

S408, the optimal path for recording initial population；If the path that constraint violation degree is 0 in initial population be present, Optimal path of that the most short paths of path selection total length as initial population in the path that constraint violation degree is 0, 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 carried out to S406 initial path population using the method for step 5, finally export current population Optimal path, complete path planning.

Preferably, determine the most long Dubins path lengths l of navigation handover region_j,maxConcretely comprise the following steps：

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

S502, calculate movable body min. turning radius r_tcWith the ratio for the radius of circle r that navigates

S503, basisWithDrawn by looking into the most long Dubins path lengths table of handover region corresponding to this group of parameter Navigate the most long Dubins path lengths l of handover region_max；For the parameter combination situation do not listed in form, using two-dimensional line Property interpolation calculation l_max；

Preferably, the specific representation of waypoint position is among 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； Define be a little positioned at middle the waypoint gone out on arc, 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：Using 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, establishes local polar coordinate system, the position of access point is represented with polar angle；The handover region Navigation circle refers to the navigation circle that movable body will enter afterwards；

Thus, the position of all middle waypoints of a paths 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 of middle waypoint is represented, when i is odd number, is expressed as the polar angle of access point, 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] section, i.e., by 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 more guidance station relays navigation as claimed in claim 1 or 2, its It is characterized in, the circular of middle waypoint towards scope is 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, take 180 ° of angular ranges close to terminal as access point towards scope；Cross out the preceding navigation circle for a little making handover region Tangent line, tangent line by centered on going out a little 360 ° of angular ranges segmentation into two, takes close to terminal 180 ° of angular ranges make For go out a little towards scope.

Preferably, in S404, if the path mode of preceding handover region and rear handover region is pattern 1~6, non-friendship Connect region and use Dubins paths connection mode, otherwise, non-handover region uses 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 guarantor that the circulation justified and left of being turn-taked into circulation is turn-taked round 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, be respectively among waypoint turn left circle With circulating turn-take round outer tangent line, internal tangent, and middle waypoint turns right circle with circulating turn-take 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 Enclose the two outer tangent lines and two internal tangents of circle；

" circulation the turn-take circle-middle waypoint " pattern co-exists in 4 alternative paths, respectively circulation turn-take circle with it is middle Outer tangent line, the internal tangent of waypoint left-hand bend circle, and circulate outer tangent line, the internal tangent of turn-take circle and middle waypoint right-hand bend circle； The middle waypoint is turned left round and turned right round refer to using middle waypoint as point of contact, with r_tcThe left and right auxiliary circle made for radius；

" 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 length as finally Dubins paths.

Preferably, the coding 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 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 of generation is beyond the public affairs of two auxiliary circles Region altogether, then keep its ordinate constant, the border of two auxiliary circle public domains be pulled to by changing its abscissa.

Preferably, for pattern 1~6, after the position of middle waypoint determines, that is, calculate among 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, take 180 ° of angular ranges close to terminal as access point towards scope；Cross out the preceding 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 close to terminal Enclose as go out a little towards scope；The direction of middle waypoint generates at random in the range of it.

The beneficial effects of the invention are as follows：

Firstth, the invention provides a kind of movable body paths planning method towards more guidance station relays navigation, using more This advanced navigation mode with frontier nature of guidance station relay navigation, has broken the small 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) instead of coordinate (two variables) come The position of waypoint is represented, both have compressed solution space, is easy to path representation and constraint to handle again；

3rd, the present invention uses code segment scheme, only code optimization is carried out to the position of waypoint, towards in the range of it Random generation；This scheme has two major advantages：One is easy for the operation of differential evolution algorithm, reduces the dimension of operation Number, if second, towards also optimizing because the position of waypoint determine waypoint towards scope, when the position of waypoint determines Afterwards, it is also necessary to which substantial amounts of iterations goes to optimize the direction of waypoint, so as to cause the iterations of overall path planning to be position Iterations and the product towards iterations, amount of calculation is excessive, and time cost is too high, and is shown using this code segment scheme Work reduces calculation cost, is advantageous to improve the efficiency of path planning；

4th, for the present invention using exterior guiding by the way of movable body itself navigation is combined, precision is high, highly reliable, 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 Can be unmanned plane, unmanned vehicle, UAV navigation etc. Deng, movable body, available for realizing sea, land and sky different situations more about Path planning of the movable body from origin-to-destination under the conditions of beam.

Brief description of the drawings

Fig. 1 is the movable body path planning schematic diagram towards more 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 diagrames；

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

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.

Embodiment

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

For meeting that navigation joins the difference of constraint complexity, summary draws towards more guidance station relays and navigated the present invention 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 constraining more difficult meet, 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 the paths planning method based on intelligent optimization algorithm；Path planning in the present invention For continuous domain constrained optimization problem, there is the intelligent optimization algorithm of stronger ability of searching optimum to be applied to the solving problem for some, Optimization Solution algorithm of the present invention using differential evolution algorithm as the movable body path planning to be navigated towards more guidance station relays；

The movable body paths planning method towards more guidance station relays navigation comprises the following steps that：

Step 1, input route planning information, are specifically included：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 ceases the two-dimensional coordinate for referring to beginning and end；The guidance station scope of heading constraint information refers to the coordinate at guidance station center And effective range, movable body must be entirely located in navigation circle from the whole piece path of origin-to-destination；The navigation circle represents Guidance station effective range, radius r；The guidance station navigation handing-over constraint information refers to ensure that navigation joins successfully and set Shortest path length D of the fixed movable body in handover region；The navigation handing-over refers to transfer motion between multiple guidance stations 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, 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 1~section of section 5 that each waypoint is formed and formed according to this, and wherein section 2 and section 4 are that movable body is joining Path in region；l_2j(j=1,2) represents movable body path length in j-th of 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 the path, which meets to navigate, joins constraint；

As shown in Fig. 2 A and B represents waypoint, arrow represents movable body direction, and the movable body curvature limitation refers to move 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, judge to meet the complexity that navigation handing-over constrains, when constraint is easier to meet, using based on Dubins The paths planning method in path, when constraining more difficult meet, using the Dubins roads based on longest path pattern in handover region Footpath planing method, is specifically included：

S201, calculate handover region width rd, and handover region width rd and navigation radius of circle r ratioIt 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 round radius that navigates is r, then

S202, calculate movable body min. turning radius r_tcWith the ratio for the radius of circle r that navigates

S203, basisWithDrawn by looking into the most long Dubins path lengths table of handover region corresponding to this group of parameter Navigate the most long Dubins path lengths l of 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 path lengths table is drawn by a large amount of the simulation experiment results statistics in domain；Entering arc respectively first and going out on arc uniformly Waypoint among 51 is chosen, then is uniformly choosing 91 directions corresponding to each waypoint in the range of 180 ° of directions, then judges this 51 × 51 × 91 × 91 whether Dubins paths exceed handover region, and calculate path length；By comparing, will both without departing from Handover region scope and the length records in the most long Dubins paths of the path length most long Dubins path lengths in handover region Spend in table；

S204, define γ_jFor navigation handing-over constraint D in j-th of 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 the boundary value using two methods, is 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, initial path population is evaluated, and record the optimal path of current population, specifically include：

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；Define be a little positioned at middle the waypoint gone out on arc, it is described go out arc to move 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 pole axis to the right, is counterclockwise positive direction, establishes local polar coordinate system, the position of access point with polar angle θ and Polar diameter ρ represent, due to handover region rear navigation justify radius, it is known that and access point be 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 The center of circle of preceding navigation circle is pole axis to the right as limit, horizontal direction, is counterclockwise positive direction, establishes local polar coordinate system, go out Point position represented with polar angle θ and polar diameter ρ, due to handover region preceding navigation justify radius, it is known that and going out a little to be located at cross-connecting area On the circumference of the preceding navigation circle in domain, therefore, the position gone 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 For the 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, the solution scope of middle waypoint position is mapped to [0,1] section, i.e., by 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 the paths planning method based on Dubins paths, a paths by start position, final position and The position of middle waypoint and determined towards common；

Connected between middle waypoint and middle waypoint using Dubins paths；The Dubins paths refer to for same There are any two points of direction in plane, in the case where limiting curvature, calculated using method of geometry another by some arrival A little and with direction shortest path；" CLC " path of the invention for mainly using Dubins paths, first C are represented Circular arc in the starting point auxiliary circle of Dubins paths, second C represent 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 refers to using Dubins paths starting point as point of contact, with r_tcMake for radius 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 using Dubins path terminations as point of contact, with r_tcTwo auxiliary circles made for radius, referred to as Dubins path terminations are turned left Curved circle and circle of turning right；" CLC " path in the Dubins paths shares 4 kinds of situations, is respectively that " 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；

Dubins paths connection between starting point and middle waypoint using head end towards relaxation；The head end is towards relaxation The footpath head end direction that shows the way can be any direction；The head end shares 2 kinds of situations towards the Dubins paths of relaxation, is 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 Loose Dubins routing algorithms select that most short paths of length as final Dubins paths in this 2 kinds of situations；

Dubins paths connection between middle waypoint and terminal using terminal towards relaxation；The terminal is towards relaxation It can be any direction to refer to Trail termination direction；The terminal shares 2 kinds of situations towards the Dubins paths of relaxation, is 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 Loose 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 is generated at random on affiliated border arc, and middle waypoint is determined towards scope by its position, specifically Generated at random in the range of towards at it；

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 segmentation centered on access point into two, takes 180 ° of angular ranges close to terminal as access point towards model Enclose；The tangent line for the preceding 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 close to 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 generation path, are specifically included：

S30301, basisWithDetermine movable body 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 is obtained most long by a large amount of emulation experiments of summary and induction 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, as shown in Fig. 7 (a)；Under the pattern, movable body handover region access point and go out Point is two summits of handover region respectively, and movable body is tangent in the direction of access point and first navigation circle, and movable body is going out a little Direction and second navigation circle it is tangent；Longest path of the movable body in handover region is Dubins CLC paths, shaped like " 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 refers to using access point as point of contact, with r_tcTwo auxiliary circles made for radius, claim For turn left circle and turn right circle；It is described go out an auxiliary circle refer to go out a little for point of contact, with r_tcTwo auxiliary made for radius Circle, referred to as turn left circle and circle of turning right；Movable body enters handover region from upper summit, and handover region is left from lower summit, Or enter handover region from lower summit, leave handover region from upper summit；

Pattern 2：The tangent S types in center, as shown in Fig. 7 (b)；Under the pattern, the center of the handover region is handover region The intersection point of two summit lines and two navigation circle circle center line connectings belonging to handover region；Longest path of the movable body in handover region Footpath is Dubins CLC paths, and shaped like " 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 are represented and the tangent straightway of two circular arcs；Access point auxiliary circle is tangential on cross-connecting area with going out an auxiliary circle The center in domain, the length of straightway is 0；Movable body enters arc from upper semisection and enters handover region, and going out arc from lower semisection leaves handing-over Region, or enter arc from lower semisection and enter handover region, going out arc from upper semisection leaves handover region；

Pattern 3：Single tangent S types in summit, as shown in 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, it is round tangent towards being navigated with first, if going out Point is round tangent towards being navigated with second positioned at the summit of handover region, then its；Longest path of the movable body in handover region For Dubins CLC paths, shaped like " S ", wherein first C represents the arc section of access point auxiliary circle, second C represents a little auxiliary Round arc section is helped, L is represented and the tangent straightway of two circular arcs；Movable body enters arc from upper semisection and enters handover region, under Half section goes out arc and leaves handover region, or enter arc from lower semisection and enter handover region, and going out arc from upper semisection leaves handover region；

Pattern 4：The tangent c-type of Double Tops point, as shown in Fig. 7 (d)；Under the pattern, movable body handover region access point and go out Point is two summits of handover region respectively, otherwise movable body is tangent all 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 Dubins CLC paths, shaped like " 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 handover region is left from lower summit, or from Xia Ding Point enters handover region, and handover region is left from upper summit；

Pattern 5：Spoon type, as shown in Fig. 7 (e)；Under the pattern, movable body only has one in the in and out point of handover region Positioned at the summit of handover region, longest path of the movable body in handover region is Dubins CLC paths, shaped like " 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 from upper semisection and enters handover region, and going out arc from lower semisection leaves handover region, Huo Zhecong Lower semisection enters arc and enters handover region, and going out arc from upper semisection leaves handover region；

Pattern 6：Single tangent c-type in summit, as shown in Fig. 7 (f)；Under the pattern, movable body handover region access point and go out A point only summit for being located at handover region, if access point is located at the summit of handover region, access point is navigated towards with second Circle is tangent, if going out a little to be located at the summit of handover region, goes out a direction and first navigation circle is tangent；Movable body is in handover region Interior longest path is Dubins CLC paths, shaped like " 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 is represented and the tangent straightway of two circular arcs；Movable body enters arc from upper semisection and entered Handover region, go out arc from lower semisection and leave handover region, or enter arc from lower semisection and enter handover region, from upper semisection go out arc from Open handover region；

Mode 7：Circulation turn-take it is round, as shown in Fig. 7 (g)；Movable body circulates movement of turn-taking in handover region；

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 --- circular pattern of turn-taking is circulated, therefore the path mode in non-handover region adds 5 kinds of Dubins paths Connection mode, be 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, pay attention to turn-taking circle and that leaves follow into circulation 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 Bar tangent line, as shown in Fig. 8 (a)；

" middle waypoint-circulation the turn-take circle " pattern co-exists in 4 alternative paths, be respectively among waypoint turn left circle Turn-taked round outer tangent line, internal tangent with circulation, as shown in Fig. 8 (b), and middle waypoint turn right circle and circulation turn-take it is round outside Tangent line, internal tangent, as shown in 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, as shown in 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 turn left circle outer tangent line, internal tangent, as shown in Fig. 8 (e), and circulation turn-take circle with middle waypoint turn right circle outside Tangent line, internal tangent, as shown in Fig. 8 (f)；The middle waypoint is turned left, and round and right-hand bend is round to be referred to using middle waypoint as point of contact, With r_tcThe left and right auxiliary circle made for radius；

" 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, as shown in Fig. 8 (g)；

Keep circulation turn-take circular direction it is consistent on the premise of, select most short that paths of path length as finally 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 of 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 NP-NP × γ is generated at random_jThe individual waypoint position vector for being unsatisfactory for conditions above；The NP represents population rule Mould；

When path mode of the movable body in handover region is pattern 2, if in pattern 2 most long Dubins paths access point Position is σ₁(movable body enters access point position when arc enters handover region from upper semisection) or σ₂(movable body enters arc from lower semisection and entered 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 goes 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 of 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 NP-NP × γ is generated at random_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 of 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 NP-NP × γ is generated at random_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 using the center of circle of two navigation circles_tcConcentric circles, the public domain of the two concentric circles is To circulate the home position scope for turn-taking round；For j-th of navigation handover region, circulation turn-take in round heart position range 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 refers to the minimum enclosed rectangle for making two auxiliary circle public domains, 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 ordinate constant, by changing its abscissa beyond the public domain of two auxiliary circles It is pulled to the border of two auxiliary circle public domains；

For pattern 1~6, after the position of middle waypoint determines, you can waypoint towards scope among calculating；Middle road The direction of point generates 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 the whole road section length sums for being sequentially connected starting point, middle waypoint, terminal according to navigation order and being formed；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 length in region and being more than or equal to constraint value, constraint violation degree is 0, and otherwise, constraint violation degree is for both Absolute difference；

Step 5, the optimal path for recording initial population；If the path that constraint violation degree is 0 in initial population be present, Optimal path of that the most short paths of path selection total length as initial population in the path that constraint violation degree is 0, 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 of path planning problem as schemed Shown in 12, it is first randomly generated initial path population and evaluates, record the optimal path of current population；Then into algorithm Major cycle, evolutional operation is performed repeatedly, until reaching algorithm end condition, finally export 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 optimal of current population Path；New route is produced by variation, crossover operation first, wherein, variation and crossover operation act only on the position of waypoint, road Point changes towards scope with the change of its position, and direction generates 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 That less paths；By the path that selection operation leaves compared with the population optimal path recorded before, comparative approach It is identical with the principle of selection operation, using a preferably optimal path as current population in both；When Evolution of Population algebraically When reaching given maximum evolutionary generation, cyclic process is terminated, exports the optimal path of current population, completes path planning.

The paths planning method of movable body illustrates under being navigated with reference to the simulation experiment result to more guidance station relays；

As shown in figure 13, guidance station centre coordinate is (0,0), (1.5,0), (3,0), and the round radius that navigates is r=1, fortune Kinetoplast starting point coordinate is (- 1,0), and terminal point coordinate is (3,0), and movable body min. turning radius is 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 (1.2229) in handover region section 2 and the length in section 4 (1.2285) close to navigation handing-over binding occurrence, total path length is smaller, has obtained preferably route programming result；

As shown in figure 14, in the case of navigation handing-over binding occurrence is excessive, as guidance station is interfered or sent out in handing-over When giving birth to failure and needing the handover time of overlength, guidance station centre coordinate is set to (0,0), (1,0), (2,0), and navigate round radius For r=1, movable body starting point coordinate is (- 1,0), and terminal point coordinate is (3,0), and movable body min. turning radius is 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, Obtained route programming result 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 smaller, can Think that the Dubins path plannings based on handover region longest path pattern have obtained a preferably path.

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 described above, this hair 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 be more readily understood and use.All local changes done on the basis of technical scheme, it is equal Replacement, improvement etc. should be included in the scope of the protection.

Claims (6)

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

Step 0, input route planning information, are specifically included：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 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 and lead In boat circle；The navigation circle represents guidance station effective range, radius r；The guidance station navigation handing-over constraint refers to really Protect navigation and join shortest path length D of the movable body successfully set 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 for judging navigation handing-over constraint, and with difficulty or ease coefficient gamma_jRepresent complexity；γ_jFor j-th of friendship Meet navigation handing-over constraint D in region_jWith the most long Dubins path lengths l of handover region that navigates_maxRatio；If γ_j＜ 0.7, is adopted 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, final position and middle waypoint position and Determined towards common；The middle waypoint refers to the waypoint in addition to beginning and end；

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

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 generated at random on affiliated border arc, middle waypoint is determined towards scope by its position, specific direction Generated at random 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 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 length in domain is more than or equal to constraint value, constraint violation degree is 0, and otherwise, constraint violation degree is exhausted for both To difference；

Step 4, the optimal path for recording initial population；If the path that constraint violation degree is 0 in initial population be present, about Beam violates degree as optimal path of that the most short paths of path selection total length in 0 path as initial population, if just The constraint violation degree in all paths of beginning population is all higher than 0, then chooses that minimum paths of constraint violation degree as initial The optimal path of population；

Step 5, using differential evolution algorithm path optimizing；New route is produced by variation, crossover operation first, wherein, variation The position of waypoint is acted only on crossover operation, 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, leave 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, that less paths of constraint violation degree are left；Path that selection operation is left and the population that records before are 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, cyclic process is terminated, exports current population most Shortest path, complete path planning；

Step 6, using the Dubins path plannings based on longest path pattern in handover region, specifically comprise the following steps：

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

S402, calculate movable body min. turning radius r_tcWith the ratio for the radius of circle r that navigates

S403, basisWithPath mode of the movable body in each handover region is determined 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 handover region respectively 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, shaped like " 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 are represented and the tangent straightway of two circular arcs；The access point auxiliary circle refers to using 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 for 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 enters handover region from lower summit, handover region is left from upper summit；

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 Dubins CLC roads Footpath, shaped like " 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 with going out the center that an auxiliary circle is tangential on handover region, straightway Length be 0；Movable body enters arc from upper semisection and enters handover region, and going out arc from lower semisection leaves handover region, or from lower half Section enters arc and enters handover region, and going out arc from upper semisection leaves handover region；

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

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

Pattern 5：Spoon type；Under the pattern, movable body only has a top for being located at handover region in the in and out point of handover region Point, longest path of the movable body in handover region is Dubins CLC paths, shaped like " spoon ", wherein first C represent into The arc section of point auxiliary circle, second C represent the arc section of an auxiliary circle, and L is represented and the tangent straightway of two circular arcs；Fortune Kinetoplast enters arc from upper semisection and enters handover region, and going out arc from lower semisection leaves handover region, or enters arc from lower semisection and enter friendship Region is connect, going out arc from upper semisection leaves handover region；

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

Mode 7：Circulation is turn-taked round；Movable body circulates movement of turn-taking in handover region；

S404, the path mode where movable body in former and later two adjacent handover regions of non-handover region determine movable body Path mode in non-handover region；

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

The representation of access point position is as follows：It is to the right as limit, horizontal direction using the center of circle that the rear navigation of handover region is justified Pole axis, it is counterclockwise positive direction, establishes local polar coordinate system, the position of access point is represented with polar angle；Led after the handover region Boat circle refers to the navigation circle that movable body will enter；

The method for expressing for going out a position is as follows：It is to the right as limit, horizontal direction using the center of circle that the preceding navigation of handover region is justified Pole axis, it is counterclockwise positive direction, establishes local polar coordinate system, the position gone out a little is represented with polar angle θ；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 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 of middle waypoint is represented, when i is odd number, is expressed as the polar angle of access point, 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] section, i.e., by 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, generates NP × γ 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 NP-NP × γ is generated at random_jThe individual middle waypoint position vector for being unsatisfactory for conditions above；The NP represents population rule Mould；

When path mode of the movable body in handover region is pattern 2, if in pattern 2 most long Dubins paths access point position For σ₁Or σ₂, it is σ equally to go out a position₂Or σ₁；Middle waypoint position initialization of population method is as follows：For j-th of navigation handing-over Region, NP × γ is generated at random_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 It is as follows：For j-th of 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],

And NP-NP × γ is generated at random_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 It is r-r that radius is made in the center of circle of two navigation circles corresponding to handover region_tcConcentric circles, the public domain of the two concentric circles is Circulate the home position scope for turn-taking round；For j-th of navigation handover region, turn-taked in circulation random in round heart position range 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 length is more than or equal to constraint value, constraint violation degree is 0, and otherwise, constraint violation degree is absolute for both 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 select path of the wherein optimal path as movable body；

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

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

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

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

S502, calculate movable body min. turning radius r_tcWith the ratio for the radius of circle r that navigates

S503, basisWithNavigation corresponding to this group of parameter is drawn by looking into the most long Dubins path lengths table of handover region The most long Dubins path lengths 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 more guidance station relays navigation as claimed in claim 1 or 2, its feature It is, the circular of middle waypoint towards scope is in the step 2：

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, take 180 ° of angular ranges close to terminal as access point towards scope；Cross out a little make handover region preceding navigation circle cut 360 ° of angular ranges segmentation centered on going out a little into two, is taken 180 ° of angular ranges close to terminal to be used as by line, tangent line Point towards scope.

4. a kind of movable body paths planning method towards more guidance station relays navigation as claimed in claim 1, its feature exist In in S404, if the path mode of preceding handover region and rear handover region is pattern 1~6, non-handover region uses Dubins paths connection mode, otherwise, non-handover region use following 5 kinds of Dubins paths connection mode, be 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, into circulation turn-take circle and the circulation left round direction of turn-taking is consistent, together For 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 round two that turn-take cut Line；

" middle waypoint-circulation the turn-take circle " pattern co-exists in 4 alternative paths, be respectively among waypoint turn left circle with following 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 Outer tangent line, the internal tangent of left-hand bend circle, and circulate outer tangent line, the internal tangent of turn-take circle and middle waypoint right-hand bend circle；It is described Middle waypoint is turned left round and turned right round refer to using middle waypoint as point of contact, with r_tcThe left and right auxiliary circle made for radius；

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

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

5. a kind of movable body paths planning method towards more guidance station relays navigation as claimed in claim 1 or 2, its feature It is, the coding method for mode 7 is：The relative coding central coordinate of circle refers to the minimum for making two auxiliary circle public domains Boundary rectangle, then this boundary rectangle scope is mapped to 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 of generation is protected beyond the public domain of two auxiliary circles Hold that its ordinate is constant, the border of two auxiliary circle public domains is pulled to by changing its abscissa.

6. a kind of movable body paths planning method towards more 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 among waypoint towards scope, be 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, taken by tangent line Close to terminal 180 ° of angular ranges as access point towards scope；The tangent line for the preceding 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 close to terminal as going out a little Towards scope；The direction of middle waypoint generates at random in the range of it.