CN106708049A - Path planning method of moving body under multi-station relay navigation - Google Patents
Path planning method of moving body under multi-station relay navigation Download PDFInfo
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
- G05D1/02—Control of position or course in two dimensions
- G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
- G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
- G05D1/0217—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory in accordance with energy consumption, time reduction or distance reduction criteria
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Abstract
The invention discloses a path planning method of a moving body under multi-station relay navigation. The method comprises the steps of inputting path planning information; modeling a navigation station environment to form a topologic network diagram and an adjacent relation matrix; listing all possible navigation station combinations; according to each navigation station combination, adopting differential evolution algorithms including problem special knowledges for carrying out path planning, and adopting paths outputted by the algorithms finally as candidate paths; comparing all of the candidate paths, adopting the best path as a final planning path, and adopting a navigation station combination corresponding to the final planning path as a finally selected navigation station combination. According to the path planning method of the moving body under multi-station relay navigation provided by the invention, a manner of relay navigation of multiple navigation stations is adopted, the path meeting various constraints and quickly arriving a target point is planned for the moving body to execute a remote task, the limitation of a small single-station navigation range is broken, a controlled moving range of the moving body is effectively extended, and the problem of path planning from a starting point to an end point for the moving body with different air-sea-land situations under multi-constrained conditions can be solved.
Description
Technical field
The invention belongs to movable body path planning research field, and in particular to a kind of road of the lower movable body of multistation relay navigation
Footpath planing method.
Background technology
Multistation relay navigation is a kind of by interspersing among different spatial and scope of heading can cover larger space
Multiple stations are followed successively by movable body and continue the joint air navigation aid of navigation.This navigation mode is not only highly reliable, and can have
Effect extends the controllable moving range of movable body.The path planning problem of the lower movable body of multistation relay navigation be realize it is this with preceding
Along the key issue solved needed for the advanced navigation mode of property, it is related to three basic constraintss：Multistation scope of heading
Constraint, multistation navigation handing-over constraint and the constraint of movable body maneuverability.Wherein, movable body maneuverability constraint maximum turning angle
Constrained approximation represents that the constraint of multistation scope of heading and multistation navigation handing-over constraint cause that the path planning problem in the present invention is different
It is also the Major Difficulties of path planning problem in the present invention in general path planning problem.
Movable body has various navigation modes, including itself navigation and external navigation, and external navigation includes satellite navigation, base station
Navigation etc..Wherein, movable body itself navigation and is easily disturbed mode limited precision, satellite navigation mode is easy go to pot and cost into
This height, and base station navigation mode is highly reliable, and can be by way of the relay of multistation joint is navigated for movable body performs long-range appointing
Business provides route guidance.
The content of the invention
The path planning problem of the lower movable body of multistation relay navigation mainly considers to be led in multiple station joint relay in the present invention
On the premise of boat, how for movable body cook up one disclosure satisfy that multistation scope of heading constraint, multistation navigation handing-over constraint and
Movable body maximum turning angle constraint and the quick path for arriving at impact point.
The paths planning method of the lower movable body of multistation relay navigation, comprises the following steps：
Step 1：Input route planning information, specifically includes：Movable body beginning and end positional information, guidance station navigation model
Enclose constraint information, guidance station navigation handing-over constraint information and movable body maximum turning angle constraint information；The guidance station navigation model
Enclose the whole piece path palpus of coordinate and effective range that constraint information refers to guidance station center, i.e. movable body from origin-to-destination
It is entirely located in navigation circle；The navigation circle represents guidance station effective range, and radius is r；The guidance station navigation handing-over
Constraint information refers to ensure that navigation joins shortest path length L of the movable body for successfully setting in handover region, movable body
Path length in handover region must be more than or equal to L；The navigation handing-over refers to transfer movable body between multiple guidance stations
Navigation power；The handover region refers to the overlapping region between two navigation circles；The movable body maximum turning angle constraint letter
Breath refers to the maximum turning angle that movable body can be performed by the limitation of itself maneuverabilityMovable body turns each waypoint
Bent angle must be less than or equal to
Step 2, to multistation environmental modeling, form topological network diagramming, specially：
By guidance station environmental modeling into a non-directed graph G=(V, E), wherein, V={ v1,v2,...,vpBe node collection
Close, represent all guidance stations, p represents the quantity of guidance station；E={ e1,e2,...,eqBe side set, represent it is all to adjoining
Guidance station；When the length of longest path in Liang Ge guidance stations handover region is more than or equal to navigation handing-over constraint L, this two stations
It is considered as adjacent, its corresponding two nodes connection；Longest path is two companies on summit of handover region in the handover region
Line；The handover region summit is two intersection points of navigation circle；
Step 3, first guidance station that movable body is determined by the start position and final position of movable body and last
Guidance station, first guidance station is start node, and last guidance station is destination node；According to the nothing that step 2 is obtained
To figure G and the syntople of guidance station, all feasible paths of the movable body from start node to destination node, as institute are determined
Possible guidance station combination, wherein requiring that each node is at most accessed once, i.e., each guidance station is at most only used once；
Step 4, each the possible guidance station combination obtained to step 3 using differential evolution algorithm carry out path rule
Draw, specifically include following steps：
S401, random generation initial path population：One paths are by the waypoint including starting point, multiple middle waypoints and terminal
It is connected in sequence, middle waypoint is arranged on the arc of handover region border；Handover region border arc includes into arc and going out arc, institute
It is border arc that movable body enters handover region to state into arc, it is described go out arc the border arc of handover region is left for movable body；Definition
Access point is that, positioned at the middle waypoint entered on arc, it is a little middle waypoint positioned at going out on arc to go out, wherein, the position of in and out point exists
Generated at random on border arc where each, connected using line segment between waypoint；
S402, initial path population is evaluated：
Evaluation index includes general objective functional value and total constraint violation degree；The general objective Function Synthesis consider that path is total
Length and average turning angle, i.e. catalogue scalar functions are path total length object function and average turning angle object function sum；Institute
State path total length refer to according to navigation order be sequentially connected whole road section lengths that starting point, middle waypoint, terminal formed it
With；The section refers to the path between two adjacent waypoints；The average turning angle refers to movable body turning in all waypoints
The average value of bent angle；Total constraint violation degree considers navigation handing-over constraint violation degree and maximum turning angle constraint is disobeyed
Return degree, i.e., total constraint violation degree is navigation handing-over constraint violation degree and maximum turning angle constraint violation degree sum；When
When path length of the movable body in handover region is more than or equal to navigation handing-over constraint L, navigation handing-over constraint violation degree is
0, otherwise it is both absolute differences；When movable body is less than or equal to maximum turning angle constraint in the turning angle of middle waypointWhen,
Maximum turning angle constraint violation degree is 0, is otherwise both absolute differences；
S403, the optimal path for recording current population；
If there is the path that total constraint violation degree is 0 in initial population, in being 0 path in total constraint violation degree
Choose optimal path of that the minimum paths of general objective functional value as initial population；If all paths of initial population it is total about
Beam violates degree and is all higher than 0, then choose optimal path of that the minimum paths of total constraint violation degree as initial population；
S404, the initial path population obtained based on S401, produce new route by variation, crossover operation first；
S405, left compared with the superior in new route and old path by selection operation；The principle of selection operation is：When two
When total constraint violation degree in path is equal, less that paths of general objective functional value are left, when total constraint of two paths
When violation degree is unequal, less that paths of total constraint violation degree are left；
S406, the optimal path for updating current population；The path that selection operation is left is optimal with the population for recording before
Path is compared, and comparative approach is identical with the principle of selection operation, using preferably one in both as current population most
Shortest path；
S407, based on current path population, continue to enter row variation according to the method for S404-S406, intersect and selection operation,
And the optimal path of current population is updated, until reaching given maximum evolutionary generation, complete path planning；
The possible guidance station combination of S408, each obtained based on step 3, according to the method for S401-S407 obtain compared with
Shortest path is used as path candidate；
Step 5：Compare all path candidates that S408 is obtained, a wherein best conduct is selected according to the method for S403
Final path planning, its corresponding guidance station combination is final selected guidance station combination.
Preferably, before S401, to access point position and go out a position and encode, specific method is as follows：
Used as limit, horizontal direction is to the right pole axis, is counterclockwise positive direction in the center of circle that the rear navigation of handover region is justified,
Local polar coordinate system is set up, the position of access point is represented with polar angle；The rear navigation circle of the handover region refers to that movable body will enter
The navigation circle for entering；It is a little middle waypoint positioned at going out on arc to define, and the method for expressing for going out a position is as follows：By handover region
Used as limit, horizontal direction is to the right pole axis, is counterclockwise positive direction in the center of circle of preceding navigation circle, sets up local polar coordinate system, is gone out
The position of point is also represented with polar angle；The preceding navigation circle of the handover region refers to the navigation circle that movable body will leave；Thus, one
Paths are by access point polar angle and go out a polar angle association list and be shown as θ=[θ1,θ2,...,θn], θiRepresent i-th position of middle waypoint
Put, when i is odd number, be expressed as the polar angle of access point, when i is even number, be expressed as out polar angle a little；Limit θiSpan be
[θi,min,θi,max], wherein θi,minAnd θi,maxPolar angle corresponding to handover region summit；The mode of relative coding is taken, by
Between waypoint position solution scope be mapped to [0,1] it is interval, will θ=[θ1,θ2,...,θn], θi∈[θi,min,θi,max] it is converted into x
=[x1,x2,...,xn], xi∈[0,1]；
In S401, the relative coding position x of middle waypointiThe random generation in [0,1] is interval；In S404, middle waypoint
Relative coding position xiBy variation, crossover operation generation in [0,1] is interval.
Preferably, in the S401 and S404, before generating waypoint on the arc of border, first limiting access point position range
Fixed, method is：
If navigation circle O1With navigation circle O2Intersect at summit A and summit B, circle center line connecting O1O2Point C is met at arc is entered；To push up
Point B is the center of circle, guidance station handing-over constraint L is that radius is made to justify, and it is point F with the intersection point for entering arc1；With summit A as the center of circle, L be half
Footpath is made to justify, and it is point F with the intersection point for entering arc2；According to following condition judgment access point position θiScope：
If 1. navigation joins constraint satisfaction L≤| | AC | |, access point position θi∈[θi,min,θi,max], θi,minIt is summit
The corresponding polar angles of A, θi,maxIt is the corresponding polar angles of summit B；
If 2. navigation joins constraint satisfaction | | AC | | ＜ L≤| | AB | |, access point position θi∈[θi,min,θi,1]∪
[θi,2,θi,max], θi,1It is point F1Corresponding polar angle, θi,2It is point F2Corresponding polar angle；
In S401 and S404, the relative coding position x of waypoint in the middle of generationiAfterwards and before path evaluation, to entering
The relative coding position of point is decoded, will xiChange into specific polar angle θi, xi∈ [0,1], i are odd number；Wherein：For
1. plant situation, θi∈[θi,min,θi,max], access point position decoding mode is θi=θi,min+xi·(θi,max-θi,min)；
Situation is 2. planted for, θi∈[θI, min, θI, 1]∪[θI, 2, θI, max], define coefficient ki=(θI, 1-θI, min)/
((θI, 1-θI, min)+(θI, max-θI, 2))；If xi≤ki, then the decoding process of the relative coding position of access point be：θi=θi,min+
(xi/ki)·(θi,1-θi,min), otherwise for：θi=θi,2+(xi-ki)/(1-ki)·(θi,max-θi,2)。
Preferably, after the position of access point determines, being defined to going out a position range, method is：
If 1. navigation joins constraint satisfaction L≤lmin, lminIt is with access point PinIt is circle phase of being navigated before the center of circle and handover region
The radius of the circle of inscribe, then go out a position θi∈[θi,min,θi,max], θi,minIt is the corresponding polar angles of summit B, θi,maxFor A pairs, summit
The polar angle answered；
If 2. navigation joins constraint satisfaction lmin＜ L≤min | | PinA||,||PinB | | }, with access point PinIt is the center of circle, L
For radius is made to justify, intersect at 2 points with arc is gone out, near summit A is point E1, near summit B is point E2, then a position θ is gone outi∈
[θi,min,θi,3]∪[θi,4,θi,max], θi,3It is point E2Corresponding polar angle；θi,4It is point E1Corresponding polar angle；PinA | | represent PinA
Line segment length；||PinB | | represent PinThe line segment length of B；
If the handing-over constraint satisfaction min that 3. navigates | | PinA | |, | | PinB | | } ＜ L≤max | | PinA | |, | | Pin| |,
If access point PinEnter on arc positioned at upper semisection, with access point PinFor the center of circle, L are that radius is made to justify, point E is met at arc is gone out2, then a position is gone out
θi∈[θi,min,θi,3], θi,3It is point E2Corresponding polar angle；If access point PinEnter on arc positioned at lower semisection, with access point PinIt is the center of circle, L
For radius is made to justify, point E is met at arc is gone out1, then a position θ is gone outi∈[θi,4,θi,max], θi,4It is point E2Corresponding polar angle；
In S401 and S404, the relative coding position x of waypoint in the middle of generationiAfterwards and before path evaluation, to going out
The relative coding position of point is decoded, will xiChange into specific polar angle θi, xi∈ [0,1], i are even number, wherein：For
1. plant situation, θi∈[θI, min, θI, max], go out a position decoding mode for θi=θi,min+xi·(θi,max-θi,min)；
Situation is 2. planted for, θi∈[θi,min,θi,3]∪[θi,4,θi,max], define coefficient ki=(θi,3-θi,min)/
((θi,3-θi,min)+(θi,max-θi,4)), if xi≤ki, then a position decoding mode is gone out for θi=θi,min+(xi/ki)·(θi,3-
θi,min), otherwise it is θi=θi,4+(xi-ki)/(1-ki)·(θi,max-θi,4)；
Situation is 3. planted for, if θi∈[θi,min,θi,3], then go out a position decoding mode for θi=θi,min+xi·
(θi,3-θi,min)；If θi∈[θI, 4, θI, maX], then go out a position decoding mode for θi=θi,4+xi·(θi,max-θi,4)。
Preferably, the step 3 is concretely comprised the following steps：
A, the neighbor node of each node is found out, and record the number of neighbor node；
B, since start node, select a side associated with the node, then and from another node on this side
Start, this process is repeated always until arriving at destination node；
C, repetition B are until all feasible paths from start node to destination node are found.
The beneficial effects of the invention are as follows：
Firstth, the present invention is considered the constraint of multistation scope of heading, multistation navigation and is handed over by the way of multistation relay navigation
Connect constraint and movable body maximum turning angle constraint, be movable body perform remote task cooked up meet it is various constraint and quickly support
Up to the path of impact point, break the small limitation of single 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, solution space is both have compressed, is easy to path representation and constraint to process again；
3rd, the present invention is using exterior guiding by the way of movable body itself navigation is combined, and high precision is highly reliable,
Even if in the case where base station range reduces, it is possible to for movable body cooks up a feasible path；
4th, the movable body in the present invention can select optimal guidance station to combine by multistation collaborative navigation in multistation, improve
The flexibility of path planning；
5th, in the paths planning method that the present invention is provided, guidance station can in the sky, ground, on the water surface or under water,
Movable body can be nobody or someone's manipulation, it is adaptable to be asked from the path planning of origin-to-destination under aeroamphibious different situations
Topic, has a wide range of applications in military and civilian field.
Brief description of the drawings
Fig. 1 is multistation surrounding three-dimensional exemplary plot；
Fig. 2 is multistation environment two-dimensional example figure；
Fig. 3 is handover region longest path section schematic diagram；
Fig. 4 is non-directed graph exemplary plot；
Fig. 5 is the differential evolution algorithm flow chart comprising problem specific knowledge；
Fig. 6 is in and out point schematic diagram；
Fig. 7 is the method for expressing of access point position；
Fig. 8 is the method for expressing for a position；
Fig. 9 is into point range second case schematic diagram；
Figure 10 is interval suture schematic diagram；
Figure 11 is lminSchematic diagram；
Figure 12 is point range second case schematic diagram；
Figure 13 is point range the third situation schematic diagram；
Figure 14 is final path planning and final selected guidance station combined result figure.
Specific embodiment
The present invention is elaborated with reference to the accompanying drawings and examples.
The present invention is achieved by the following technical solutions, comprises the following steps：
Step 1, input route planning information, specifically include：Movable body beginning and end positional information, base station navigation scope
Constraint information, base station navigation handing-over constraint information and movable body maximum turning angle constraint information；The base station navigation range constraint
Information refers to that the coordinate and effective range of base station center, i.e. movable body must be entirely located in from the whole piece path of origin-to-destination
In navigation circle；The navigation circle represents base station effective range, and radius is r；The base station navigation joins constraint information
Ensure that navigation joins shortest path length L of the movable body for successfully setting in handover region, movable body is in handover region
Path length must be more than or equal to L；The navigation handing-over refers to the navigation power of transfer movable body between multiple base stations；The friendship
It refers to the overlapping region between two navigation circles to connect region；Movable body maximum turning angle constraint information refer to movable body due to
The maximum turning angle that the limitation of itself maneuverability can be performedMovable body must be less than or equal in the turning angle of each waypoint
Step 2：To guidance station environmental modeling, non-directed graph and adjacent relation matrix are formed；
Regard movable body as particle, it is assumed that it is moved on sustained height all the time, and velocity magnitude v keeps invariable.
Assuming that multistation is centrally located at sustained height, scope of heading is 0~360 degree of azimuth, 0~90 degree of the angle of pitch, therefore, it is single to lead
Navigate station scope of heading can be represented with a hemisphere, referred to as " navigation ball ".For example, as shown in figure 1, five hemisphere are represented respectively
Five sphere of actions of guidance station, its center is respectively O1、O2、O3、O4And O5, starting point Start is positioned at first navigation model at station
In enclosing, terminal End is located in the 5th scope of heading at station.Because movable body is moved on sustained height all the time, i.e. position all the time
In in S planes, " navigation ball " can be reduced to " navigation circle ", and three-dimensional path planning problem changes into the path rule in two dimensional surface
The problem of drawing, as shown in Figure 2；
By guidance station environmental modeling into a non-directed graph G=(V, E), V={ v1,v2,...,vpBe node set, table
Show all guidance stations, p represents the quantity of guidance station；E={ e1,e2,...,eqBe side set, represent and all adjacent led
Boat station；When longest path length constrains L more than or equal to navigation handing-over in two adjacent guidance station handover regions, the two station quilts
It is considered as adjoining, its corresponding two nodes connection；Longest path length is two summits of handover region in the handover region
Line, the handover region summit is two intersection points of navigation circle, as shown in figure 3, navigation circle O1With navigation circle O2Intersect at point A
With point B, point A and point B is the summit of the handover region, and line segment AB is the longest path in the handover region；
The p for characterizing the syntople between guidance station two-by-two that the adjacent relation matrix A (G) of non-directed graph is made up of 0 and 1
× p symmetrical matrixes, 0 two nodes of expression are not connected, and Ji Liangge guidance stations are to separate, and 1 represents two node connections, i.e., two
Guidance station is adjacent；
For example, by the guidance station environmental modeling in Fig. 2 into a non-directed graph G=(V, E), as shown in figure 4, wherein V=
{v1,v2,.v3,v4,v5Represent a total of five guidance stations, E={ v1v2,v1v3,v2v3,v2v4,v2v5,v3v4,v4v5Represent total
Have seven pairs of adjacent guidance stations.The sign that the adjacent relation matrix A (G) of non-directed graph is made up of 0 and 1 is two-by-two between guidance station
Syntople p × p symmetrical matrixes, 0 expression two nodes do not connect, Ji Liangge guidance stations be separate, 1 represent two section
Point connection, Ji Liangge guidance stations are adjacent, therefore, the element in matrix meets：
Step 3：By exhaustion, all possible guidance station combination is listed；
First guidance station and last guidance station of movable body are determined by the beginning and end of movable body, first is led
Boat station is start node, and last guidance station is destination node；The non-directed graph and syntople square obtained according to step 2
Battle array, obtains all feasible paths from start node to destination node, it is desirable to which each node is at most accessed once, and as owns
Possible guidance station combination, comprises the following steps that：
S301, the neighbor node of each node is found out, and record the number of neighbor node；
S302, since start node, select a side associated with the node, then and from this side
Another node starts, and this process is repeated always until arriving at destination node；
S303, repetition S302 are until all feasible paths from start node to destination node are found；
Step 4：Combined according to each possible guidance station, entered using the differential evolution algorithm comprising problem specific knowledge
Row path planning, searching meet multistation scope of heading constraint, multistation navigation handing-over constraint, movable body maximum turning angle constraint compared with
Shortest path is as path candidate, flow chart as shown in figure 5, comprising the following steps that：
S401, random generation initial path population；
Waypoint is W in the middle of definitioni(i=1,2 ..., n), starting point W0With terminal Wn+1Position, it is known that a paths are by
Point, multiple middle waypoints, terminal are connected in sequence；In order to meet scope of heading constraint and be easy to calculate in handover region
Path length, middle waypoint is arranged on the arc of handover region border；Handover region border arc includes into arc and goes out arc, it is described enter
Arc is the border arc that movable body enters handover region, it is described go out arc the border arc of handover region is left for movable body；Such as Fig. 6 institutes
Show, middle waypoint is divided into access point PinWith go out point Pout, the access point be positioned at the middle waypoint entered on arc, it is described go out be a little positioned at
The middle waypoint gone out on arc；Access point positional representation method is as shown in fig. 7, the center of circle that the rear navigation of handover region is justified is used as pole
Point, horizontal direction is to the right pole axis, is counterclockwise positive direction, sets up local polar coordinate system, position polar angle θ and the polar diameter of access point
ρ represents, the radius justified due to the rear navigation of handover region, it is known that and navigate on round circumference after access point is located at handover region, because
This, the position of access point can be represented with mono- variable of θ；Go out a positional representation method as shown in figure 8, by the preceding navigation of handover region
Used as limit, horizontal direction is to the right pole axis, is counterclockwise positive direction in the round center of circle, sets up local polar coordinate system, goes out position a little
Put and represented with polar angle θ and polar diameter ρ, the radius justified due to the preceding navigation of handover region is, it is known that and go out a little before the handover region
Navigate on the circumference of circle, therefore, the position for going out a little is represented with mono- variable of θ；Thus, the position of all middle waypoints of a paths
Put and be expressed as θ=[θ1,θ2,...,θn], limit θiSpan be [θi,min,θi,max], wherein θi,minAnd θi,maxIt is handing-over
Polar angle corresponding to the summit of region；The handover region summit is into arc and the intersection point for going out arc；The present invention takes relative coding
Mode, [0,1] interval is mapped to by the solution scope of middle waypoint position, will θ=[θ1,θ2,...,θn](θi∈[θi,min,
θi,max]) it is converted into x=[x1,x2,...,xn](xi∈[0,1])；
Random generation mulitpath composition initial path population, wherein, xiThe random generation in [0,1] is interval；
S402, calculating access point position range are simultaneously decoded；
The present invention makes full use of the specific knowledge of the path planning problem of the lower movable body of multistation relay navigation, by geometry point
Analysis, calculates the access point position for meeting navigation handing-over constraint and the scope for going out a position in advance, solution space is have compressed, so as to reach
Accelerate the purpose of algorithm the convergence speed；
Access point PinThe scope of position is determined by multistation environment and navigation handing-over constraint L；If navigation circle O1With navigation circle O2Phase
Meet at summit A and summit B, circle center line connecting O1O2Point C is met at arc is entered；With summit B as the center of circle, L be radius make justify, its with enter arc
Intersection point be point F1；With summit A as the center of circle, L be radius make justify, its with enter arc intersection point be point F2；It is assumed that going out point PoutIt is summit
B, for positioned at arcOn access point Pin, at least going out point (summit B) in the presence of one makes | | PinPout| | >=L, that is, meet navigation
Handing-over constraint；It is assumed that it is a little summit A to go out, for positioned at arcOn access point Pin, at least going out point (summit A) in the presence of one makes
||PinPout| | >=L, that is, meet navigation handing-over constraint；Therefore, the scope of access point isI.e. two sections arcs and
Collection；
Access point P is determined according to following conditioninThe scope of position：
(1) if navigation handing-over constraint satisfaction L≤| | AC | |,WithPartly overlap, i.e. the scope of access point
Enter arc, access point position θ for whole sectioni∈[θi,min,θi,max], θi,minIt is the corresponding polar angles of summit A, θi,maxIt is the corresponding poles of summit B
Angle；
(2) if navigation handing-over constraint satisfaction | | AC | | ＜ L≤| | AB | |,WithWithout overlap, access point
Position θi∈[θi,min,θi,1]∪[θi,2,θi,max], as shown in figure 9, red thickened portion represents the scope of access point position, θi,1
It is point F1Corresponding polar angle, θi,2It is point F2Corresponding polar angle；
(3) if navigation handing-over constraint satisfaction L ＞ | | AB | | (| | AB | | is the longest path length in handover region),
Access point positionI.e. in the absence of the access point for meeting navigation handing-over constraint, this kind of situation will not occur, and calculate syntople
Avoided during matrix；
Situation is planted for (1st), access point position decoding mode is：
θi=θi,min+xi·(θi,max-θi,min) (2)
Situation is planted for (2nd) because differential evolution algorithm can only act on one section of continuum, therefore need first by this two
The interval that section is separate is stitched into one section of continuum, and is mapped to [0,1] interval, as shown in Figure 10, then carries out again follow-up
Differential evolution operator, access point position decoding mode is：
Wherein,
S403, calculate a position range and decode；
The scope for going out a little is determined by the position of multistation environment, navigation handing-over constraint and access point；Determine in the position of access point
Afterwards, point P is determined according to following conditionoutThe scope of position：
(1) if navigation handing-over constraint satisfaction L≤lmin(lminIt is with access point PinIt is circle phase of being navigated before the center of circle and handover region
The radius of the circle of inscribe, as shown in figure 11), then the whole section of point gone out on arc can make | | PinPout| | >=L, that is, meet navigation handing-over
Constraint, therefore, go out a position θi∈[θi,min,θi,max],θi,minIt is the corresponding polar angles of summit B, θi,maxIt is the corresponding poles of summit A
Angle；
(2) if navigation handing-over constraint satisfaction lmin＜ L≤min | PinA||,||PinB | | }, with access point PinIt is the center of circle, L
For radius is made to justify, intersect at 2 points with arc is gone out, near summit A is point E1, near summit B is point E2, onlyOn point can make | | PinPout| | >=L, that is, meet navigation handing-over constraint, therefore, go out a position θi∈
[θi,min,θi,3]∪[θi,4,θi,max], as shown in figure 12, red thickened portion represents the scope of a position, θi,3It is point E2It is right
The polar angle answered；θi,4It is point E1Corresponding polar angle；
(3) if navigation handing-over constraint satisfaction min | | PinA||,||PinB | | } ＜ L≤max | | PinA||,||PinB|
|, if access point PinEnter on arc positioned at upper semisection, with access point PinFor the center of circle, L are that radius is made to justify, point E is met at arc is gone out2, onlyOn point can make | | PinPout| | >=L, that is, meet navigation handing-over constraint, therefore, go out a position θi∈[θi,min,θi,3],
As shown in figure 13, red thickened portion represents point range, θi,3It is point E2Corresponding polar angle；If access point PinEnter positioned at lower semisection
On arc, with access point PinFor the center of circle, L are that radius is made to justify, point E is met at arc is gone out1, onlyOn point can make | | PinPout||
>=L, that is, meet navigation handing-over constraint, therefore, go out a position θi∈[θi,4,θi,max], θi,4It is point E2Corresponding polar angle；
(4) if navigation handing-over constraint satisfaction L ＞ max | | PinA||,||PinB | | }, then go out a positionI.e. not
In the presence of going out a little for navigation handing-over constraint is met, this kind of situation will not occur, and avoided when point range is compressed into；
Situation is planted for (1st), (3), goes out the first decoding process of a position decoding mode with access point position；For
(2) situation is planted, goes out second decoding process of a position decoding mode with access point position；
S404, initial path population is evaluated；
Evaluation index includes target function value f and constraint violation degree fcv；The object function f considers path overall length
Degree f1With average turning angle f2；The path total length refers to be sequentially connected starting point, middle waypoint, terminal institute according to navigation order
Whole road section length sums of formation；The section refers to the path between two adjacent waypoints；The average turning angle refers to
Average value of the movable body in the turning angle of all waypoints；Path length is short to be conducive to save energy, and average turning angle is small to be conducive to
Movable body Execution plan path；
Optimum path planning problem in the present invention considers three constraintss：The constraint of multistation scope of heading, multistation navigation
Handing-over constraint and movable body maximum turning angle are constrained, and the constrained optimization problem model is：
Wherein, θ represents the position of middle waypoint, and d is the Euclidean distance from origin-to-destination, liRepresent i-th section
Length, ψiRepresent movable body in i-th turning angle of middle waypoint, LjJ-th navigation handing-over binding occurrence of handover region is represented,
ψmaxRepresent movable body maximum turning angle binding occurrence；
The constraint violation degree fcvConsider navigation handing-over constraint violation degree fcv1With maximum turning angle constraint violation
Degree fcv2；Constraint violation degree fcvComputational methods are as follows：
fcv=fcv1+fcv2
δj=max { 0, Lj-l2j, j=1,2 ..., n/2 (6)
φi=max { 0, ψi-ψres, i=1,2 ..., n
Wherein, δjRepresent j-th navigation handing-over constraint violation degree of handover region, φiRepresent movable body on i-th tunnel
The maximum turning angle constraint violation degree of point；
S405, the optimal path for recording current population；
If there is f in initial populationcv=0 path, then in fcvThat of target function value f minimums is chosen in=0 path
Paths as initial population optimal path；If the constraint violation degree f in all paths of initial populationcv0 is all higher than, is then chosen
Constraint violation degree fcvThat minimum paths as initial population optimal path；
S406, judge whether Evolution of Population algebraically reaches given maximum evolutionary generation, if not up to turning S407, otherwise turn
S412；
S407, variation, crossover operation generation new route；
S408, access point position decoding, the same S402 of specific method；
S409, according to new access point position, recalculate the scope of a position and decode, the same S403 of specific method；
S410, new route is evaluated, the same S404 of specific method；
S411, selection operation are left compared with the superior in new route and old path；The principle of selection operation is：When two paths
Constraint violation degree fcvWhen equal, less that paths of target function value f are left, when the constraint violation degree of two paths
fcvWhen unequal, constraint violation degree f is leftcvLess that paths；
S412, the optimal path for updating current population；The path that selection operation is left is optimal with the population for recording before
Path is compared, and comparative approach is identical with the principle of selection operation, using preferably one in both as current population most
Shortest path；
S413, the optimal path for exporting current population, complete path planning；
S414, combined according to each possible guidance station, the relatively shortest path that will be obtained according to the method for S401-S413 is made
It is path candidate；
Step 5：Compare all path candidates that S414 is obtained, select wherein best one as final planning road
Footpath, the same S405 of system of selection, its corresponding guidance station combination is final selected guidance station combination.
Embodiment：
The paths planning method of the lower movable body of multistation relay navigation is illustrated with reference to example；According to actual ginseng
Number, the effective range of guidance station is 50km, and the rapidly degree that patrols of certain fixed wing aircraft is 120km/h, and two neighbor stations are complete
It is 6 minutes into the shortest time needed for navigation handing-over, then handing-over of navigating is constrained to L=12km, the maximum turning of the fixed wing aircraft
Angle is constrained to ψres=30 °；If a total of seven guidance stations, the coordinate at its center is respectively O1(0,0)、O2(60,50)、O3
(80,-30)、O4(130,80)、O5(160,-20)、O6And O (210,50)7(240, -30), starting point Start coordinates for (30,
30), terminal End coordinates are (250,0), and unit is km；Starting point is located at " navigation circle " O1" navigation circle " O2Public domain,
I.e. first guidance station both can be that station 1 can also be station 2；Terminal is located at " navigation circle " O7In the range of, i.e., last is led
Boat station is station 7；
Table 1, all possible guidance station are combined and its compared with shortest path information table
As shown in table 1, co-exist in 14 kinds of possible guidance stations combinations under this multistation environment, respectively ' 1-2-3-5-6-7 ',
‘1-2-3-5-7’、‘1-2-4-6-5-7’、‘1-2-4-6-7’、‘1-3-2-4-6-5-7’、‘1-3-2-4-6-7’、‘1-3-5-6-
7 ', ' 1-3-5-7 ', ' 2-1-3-5-6-7 ', ' 2-1-3-5-7 ', ' 2-3-5-6-7 ', ' 2-3-5-7 ', ' 2-4-6-5-7 ' and ' 2-
4-6-7 ', numeral represents the numbering of guidance station；Based on the combination of every kind of guidance station, using the differential evolution comprising problem specific knowledge
Algorithm is found out compared with shortest path as path candidate；It can be seen that only wherein 6 path candidates are feasible (fcv=
0), respectively based on guidance station combination ' 1-3-5-6-7 ', ' 1-3-5-7 ', ' 2-3-5-6-7 ', ' 2-3-5-7 ', ' 2-4-6-5-
7 ' and ' 2-4-6-7 ' relatively shortest path；In this 6 feasible path candidates, based on the more excellent of guidance station combination ' 2-3-5-7 '
The target function value in path is minimum, therefore, the path candidate is final path planning, as shown in figure 14, guidance station combination
' 2-3-5-7 ' is final selected guidance station combination.
Claims (5)
1. the paths planning method of movable body under multistation relay is navigated, it is characterised in that comprise the following steps：
Step 1：Input route planning information, specifically includes：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 maximum turning angle constraint information；The guidance station scope of heading is about
Beam information refers to that the coordinate and effective range at guidance station center, i.e. movable body must be all 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 handing-over constraint
Information refers to ensure that navigation joins shortest path length L of the movable body for successfully setting in handover region, and movable body is being handed over
Connecing the path length in region must be more than or equal to L；The navigation handing-over refers to that leading for movable body is transferred between multiple guidance stations
Boat power；The handover region refers to the overlapping region between two navigation circles；Movable body maximum turning angle constraint information is
Refer to the maximum turning angle that movable body can be performed by the limitation of itself maneuverabilityTurning angle of the movable body in each waypoint
Must be less than or equal to
Step 2, to multistation environmental modeling, form topological network diagramming, specially：
By guidance station environmental modeling into a non-directed graph G=(V, E), wherein, V={ v1,v2,...,vpBe node set, table
Show all guidance stations, p represents the quantity of guidance station；E={ e1,e2,...,eqBe side set, represent and all adjacent led
Boat station；When the length of longest path in Liang Ge guidance stations handover region is more than or equal to navigation handing-over constraint L, this two stations are regarded
It is adjoining, its corresponding two nodes connection；Longest path is two lines on summit of handover region in the handover region；Institute
It is two intersection points of navigation circle to state handover region summit；
Step 3, first guidance station that movable body is determined by the start position and final position of movable body and last navigation
Stand, first guidance station is start node, and last guidance station is destination node；According to the non-directed graph G that step 2 is obtained
And the syntople of guidance station, determine all feasible paths of the movable body from start node to destination node, it is as all can
The guidance station combination of energy, wherein requiring that each node is at most accessed once, i.e., each guidance station is at most only used once；
Step 4, each the possible guidance station combination obtained to step 3 using differential evolution algorithm carry out path planning, have
Body comprises the following steps：
S401, random generation initial path population：One paths by including starting point, it is multiple in the middle of waypoint and terminal waypoint successively
It is formed by connecting, middle waypoint is arranged on the arc of handover region border；Handover region border arc includes into arc and goes out arc, it is described enter
Arc is the border arc that movable body enters handover region, it is described go out arc the border arc of handover region is left for movable body；Define access point
It is that, positioned at the middle waypoint entered on arc, it is a little middle waypoint positioned at going out on arc to go out, wherein, the position of in and out point is respective
Generated at random on the arc of place border, connected using line segment between waypoint；
S402, initial path population is evaluated：
Evaluation index includes general objective functional value and total constraint violation degree；The general objective Function Synthesis consider path total length
It is path total length object function and average turning angle object function sum with average turning angle, i.e. catalogue scalar functions；The road
Footpath total length refers to be sequentially connected whole road section length sums that starting point, middle waypoint, terminal are formed according to navigation order；Institute
It refers to the path between two adjacent waypoints to state section；The average turning angle refers to turning angle of the movable body in all waypoints
Average value；Total constraint violation degree considers navigation handing-over constraint violation degree and maximum turning angle constraint violation journey
Degree, i.e., total constraint violation degree is navigation handing-over constraint violation degree and maximum turning angle constraint violation degree sum；Work as motion
When path length of the body in handover region is more than or equal to navigation handing-over constraint L, navigation handing-over constraint violation degree is 0, no
It is then both absolute differences；When movable body is less than or equal to maximum turning angle constraint in the turning angle of middle waypointWhen, it is maximum
Turning angle constraint violation degree is 0, is otherwise both absolute differences；
S403, the optimal path for recording current population；
If there is the path that total constraint violation degree is 0 in initial population, chosen in the path that total constraint violation degree is 0
That minimum paths of general objective functional value as initial population optimal path；If total constraint in all paths of initial population is disobeyed
Return degree is all higher than 0, then choose optimal path of that the minimum paths of total constraint violation degree as initial population；
S404, the initial path population obtained based on S401, produce new route by variation, crossover operation first；
S405, left compared with the superior in new route and old path by selection operation；The principle of selection operation is：When two paths
Total constraint violation degree it is equal when, less that paths of general objective functional value are left, when total constraint violation of two paths
When degree is unequal, less that paths of total constraint violation degree are left；
S406, the optimal path for updating current population；The path that selection operation is left and the population optimal path for recording before
It is compared, comparative approach is identical with the principle of selection operation, using the preferably one optimal road as current population in both
Footpath；
S407, based on current path population, continue to enter row variation according to the method for S404-S406, intersect and selection operation, and more
The optimal path of new current population, until reaching given maximum evolutionary generation, completes path planning；
S408, each the possible guidance station combination obtained based on step 3, more excellent road is obtained according to the method for S401-S407
Footpath is used as path candidate；
Step 5：Compare all path candidates that S408 is obtained, wherein best one is selected as final according to the method for S403
Path planning, its corresponding guidance station combination is final selected guidance station combination.
2. the paths planning method of the lower movable body of multistation relay as claimed in claim 1 navigation, it is characterised in that S401 it
Before, to access point position and going out a position and encode, specific method is as follows：
Used as limit, horizontal direction is to the right pole axis, is counterclockwise positive direction, is set up in the center of circle that the rear navigation of handover region is justified
Local polar coordinate system, the position of access point is represented with polar angle；The rear navigation circle of the handover region refers to that movable body will enter
Navigation circle；It is a little middle waypoint positioned at going out on arc to define, and the method for expressing for going out a position is as follows：By the leading of handover region
The round center of circle navigate as limit, horizontal direction is to the right pole axis, is counterclockwise positive direction, local polar coordinate system is set up, goes out a little
Position is also represented with polar angle；The preceding navigation circle of the handover region refers to the navigation circle that movable body will leave；Thus, Yi Tiaolu
Footpath is by access point polar angle and goes out a polar angle association list and is shown as θ=[θ1,θ2,...,θn], θiRepresent i-th position of middle waypoint, i
During for odd number, the polar angle of access point is expressed as, when i is even number, is expressed as out polar angle a little；Limit θiSpan be [θi,min,
θi,max], wherein θi,minAnd θi,maxPolar angle corresponding to handover region summit；The mode of relative coding is taken, by middle waypoint
The solution scope of position is mapped to [0,1] interval, will θ=[θ1,θ2,...,θn], θi∈[θi,min,θi,max] it is converted into x=[x1,
x2,...,xn], xi∈[0,1]；
In S401, the relative coding position x of middle waypointiThe random generation in [0,1] is interval；In S404, middle waypoint it is relative
Coding site xiBy variation, crossover operation generation in [0,1] is interval.
3. the paths planning method of movable body under multistation relay as claimed in claim 2 is navigated, it is characterised in that the S401
In S404, before generating waypoint on the arc of border, first access point position range is defined, method is：
If navigation circle O1With navigation circle O2Intersect at summit A and summit B, circle center line connecting O1O2Point C is met at arc is entered；It is with summit B
The center of circle, guidance station handing-over constraint L are that radius is made to justify, and it is point F with the intersection point for entering arc1；With summit A as the center of circle, L be radius make
Circle, it is point F with the intersection point for entering arc2；According to following condition judgment access point position θiScope：
If 1. navigation joins constraint satisfaction L≤| | AC | |, access point position θi∈[θi,min,θi,max], θi,minIt is summit A correspondences
Polar angle, θi,maxIt is the corresponding polar angles of summit B；
If 2. navigation joins constraint satisfaction | | AC | | ＜ L≤| | AB | |, access point position θi∈[θi,min,θi,1]∪[θi,2,
θi,max], θi,1It is point F1Corresponding polar angle, θi,2It is point F2Corresponding polar angle；
In S401 and S404, the relative coding position x of waypoint in the middle of generationiAfterwards and before path evaluation, to the phase of access point
Coding site is decoded, will xiChange into specific polar angle θi, xi∈ [0,1], i are odd number；Wherein：1. planted for
Situation, θi∈[θi,min,θi,max], access point position decoding mode is θi=θi,min+xi·(θi,max-θi,min)；
Situation is 2. planted for, θi∈[θI, min, θI, 1]∪[θI, 2, θI, max], define coefficient ki=(θI, 1-θI, min)/((θI, 1-
θI, min)+(θI, max-θI, 2))；If xi≤ki, then the decoding process of the relative coding position of access point be：θi=θi,min+(xi/ki)·
(θi,1-θi,min), otherwise for：θi=θi,2+(xi-ki)/(1-ki)·(θi,max-θi,2)。
4. the paths planning method of movable body under multistation relay as claimed in claim 2 or claim 3 is navigated, it is characterised in that entering
After the position of point determines, it is defined to going out a position range, method is：
If 1. navigation joins constraint satisfaction L≤lmin, lminIt is with access point PinIt is circle phase inscribe of being navigated before the center of circle and handover region
Circle radius, then go out a position θi∈[θi,min,θi,max], θi,minIt is the corresponding polar angles of summit B, θi,maxFor summit A is corresponding
Polar angle；
If 2. navigation joins constraint satisfaction lmin＜ L≤min { PinA,PinB }, with access point PinFor the center of circle, L are that radius is made to justify, with
Go out arc and intersect at 2 points, near summit A is point E1, near summit B is point E2, then a position θ is gone outi∈[θi,min,θi,3]∪
[θi,4,θi,max], θi,3It is point E2Corresponding polar angle；θi,4It is point E1Corresponding polar angle；||PinA | | represent PinThe line segment length of A；|
|PinB | | represent PinThe line segment length of B；
If the handing-over constraint satisfaction min that 3. navigates | | PinA | |, | | PinB | | } ＜ L≤max | | PinA | |, | | PinB | | }, if entering
Point PinEnter on arc positioned at upper semisection, with access point PinFor the center of circle, L are that radius is made to justify, point E is met at arc is gone out2, then a position θ is gone outi∈
[θi,min,θi,3], θi,3It is point E2Corresponding polar angle；If access point PinEnter on arc positioned at lower semisection, with access point PinFor the center of circle, L are half
Footpath is made to justify, and point E is met at arc is gone out1, then a position θ is gone outi∈[θi,4,θi,max], θi,4It is point E2Corresponding polar angle；
In S401 and S404, the relative coding position x of waypoint in the middle of generationiAfterwards and before path evaluation, to going out phase a little
Coding site is decoded, will xiChange into specific polar angle θi, xi∈ [0,1], i are even number, wherein：1. planted for
Situation, θi∈[θI, min, θI, max], go out a position decoding mode for θi=θi,min+xi·(θi,max-θi,min)；
Situation is 2. planted for, θi∈[θi,min,θi,3]∪[θi,4,θi,max], define coefficient ki=(θi,3-θi,min)/((θi,3-
θi,min)+(θi,max-θi,4)), if xi≤ki, then a position decoding mode is gone out for θi=θi,min+(xi/ki)·(θi,3-θi,min),
Otherwise it is θi=θi,4+(xi-ki)/(1-ki)·(θi,max-θi,4)；
Situation is 3. planted for, if θi∈[θI, min, θI, 3], then go out a position decoding mode for θi=θi,min+xi·(θi,3-
θi,min)；If θi∈[θI, 4, θI, max], then going out a position decoding mode is
5. the paths planning method of movable body under multistation relay as claimed in claim 1 is navigated, it is characterised in that the step
3 concretely comprise the following steps：
A, the neighbor node of each node is found out, and record the number of neighbor node；
B, since start node, select a side associated with the node, then and since another node on this side,
This process is repeated always until arriving at destination node；
C, repetition B are until all feasible paths from start node to destination node are found.
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| CN107478233B (en) * | 2017-08-25 | 2019-08-20 | 中国地质大学（武汉） | A kind of geological prospecting path planning method and system |
| CN109975748A (en) * | 2017-12-28 | 2019-07-05 | 腾讯科技（深圳）有限公司 | Paths planning method, device, computer equipment and storage medium |
| CN109084800A (en) * | 2018-10-10 | 2018-12-25 | 北京理工大学 | Movable body paths planning method under multistation relay based on space compression is navigated |
| CN109084800B (en) * | 2018-10-10 | 2020-10-09 | 北京理工大学 | Moving body path planning method under multi-station relay navigation based on space compression |
| CN109634304A (en) * | 2018-12-13 | 2019-04-16 | 中国科学院自动化研究所南京人工智能芯片创新研究院 | Unmanned plane during flying paths planning method, device and storage medium |
| CN109634304B (en) * | 2018-12-13 | 2022-07-15 | 中国科学院自动化研究所南京人工智能芯片创新研究院 | Unmanned aerial vehicle flight path planning method and device and storage medium |
| CN115824248A (en) * | 2023-02-15 | 2023-03-21 | 交通运输部规划研究院 | Navigation method and device of pure electric heavy truck |
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