CN108919818A - Spacecraft attitude track collaborative planning method based on chaos Population Variation PIO - Google Patents
Spacecraft attitude track collaborative planning method based on chaos Population Variation PIO Download PDFInfo
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Abstract
The invention discloses the spacecraft attitude track collaborative planning methods based on chaos Population Variation PIO, belong to the technical field of satellite attitude orbit control.The present invention takes " exploration " in the evolutionary phase of algorithm, " search ", " variation ", dove group's dynamic optimization strategy of " going back to the nest ".Chaos operator is added for the initialization matter of population in the mapped directions needle stage to initialize, it joined adaptive operator after population completes initialization and realize population and can develop according to current Population Evolution state self-adaption, while joined mutation operator to solve the problems, such as that population falls into locally optimal solution；Problem is shunk for population in the terrestrial reference operator stage, and contraction operator is added, solve the problems, such as that excellent individual is lost too fast, population deterioration, keep program results more smooth, Population Evolution is more deep, locally optimal solution problem and algorithm divergence problem are resolved, and further reduce the calculation amount of algorithm.
Description
Technical field
The invention discloses the spacecraft attitude track collaborative planning methods based on chaos Population Variation PIO, belong to satellite
The technical field of posture orbits controlling.
Background technique
PIO (Pigeon-Inspired Optimization, dove group inspire optimization) algorithm is by dove group in the process of going back to the nest
In navigation procedure develop, dove group relies primarily on the sun when far from destination and earth magnetism led
Boat, and the individual that then will use terrestrial reference after approaching destination and navigate, and be unfamiliar with terrestrial reference in group will follow it is ripe
Know group's flight of terrestrial reference.
Existing PIO algorithm can be realized the avoidance and path planning, image border identification of unmanned plane and robot, but
It is the coordinated planning for not yet solving the problems, such as spacecraft attitude track under Complex Constraints condition and close coupling relationship.Existing PIO
There are following four classes defects for algorithm：(1) research discovery Population status initialization will have a direct impact on early period Population Evolution as a result,
And current PIO algorithm in Population Evolution can not according to the current Evolution States of population adaptively to it is subsequent develop into
Row adjustment, there is algorithm easily to fall into locally optimal solution, develop and stagnate, restrain, developing the problems such as not going deep into this in advance；(2)
It is too fast that existing PIO algorithm in the terrestrial reference algorithm stage has that population quantity declines, this fills population not in final stage
Divide to develop and just eliminates excellent individual, the possibility that algorithm has diverging even to degenerate；(3) in terms of fitness function, current PIO is calculated
Method can not be screened for the smoothness of program results.(4) research finds that the variance of the result of existing PIO algorithm is larger,
This makes the control mechanism frequent starting of spacecraft, also has certain mill to mechanical structure while consuming the spacecraft preciousness energy
Damage.
And be generally currently separately to plan posture and track for the planning algorithm of the posture track of spacecraft,
But the posture track of spacecraft there are in fact the relationship of being directly coupled, and should be taken into account the position of spacecraft when being guided
It sets, posture is planned on the basis of spacecraft orbit program results.Currently, it is directed to spacecraft attitude planning problem,
McInness constructs the model of posture restricted area by potential function and Liapunov's direct method has been used then to obtain
The input of control amount can effectively reduce the resource occupation of spaceborne computer although this method calculation amount is lower, will not
The time of Spacecraft During Attitude Maneuver and energy consumption are taken into account, meanwhile, the Eulerian angles used in calculating process are retouched in kinematics
State middle generation singular point；Melton uses numerical solution from the angle of optimum control, but its calculation amount is larger and possibly can not
Suitable for accessible motion；Soviet Union is anti-et al. to plan the posture of satellite from the angle of the low RCS characteristic of satellite, but its
Roll angle is not planned, and pitch angle only can the planning in [0-180 °]；Kjellberg et al. using icosahedron from
Dispersion technology and the planning that optimal path is realized using A* algorithm, but boundary constraint and dynamic constrained are not considered in algorithm；
Path planning problem is converted into Semidefinite Programming by Kim Y et al., but the complexity of this method can with the increase of constraint and
It increased dramatically.
The present invention is directed to existing PIO algorithm core iterative algorithm and fitness function carry out depth improve to realize
The posture track collaborative planning of spacecraft cluster.
Summary of the invention
Goal of the invention of the invention is the deficiency for above-mentioned background technique, is provided based on chaos Population Variation PIO's
Spacecraft attitude track collaborative planning method, the spacecraft attitude rail under close coupling relationship is realized using modified PIO algorithm
The collaborative planning in road, solve existing spacecraft attitude metro planning scheme not yet realize posture and track collaborative planning and
Existing posture programme or metro planning scheme do not consider whole dynamic constrained conditions and influence whole factors of program results
And the technical problem that complexity is big.
The present invention adopts the following technical scheme that for achieving the above object：
Spacecraft attitude track collaborative planning method based on chaos Population Variation PIO, using based on chaos Population Variation
Adaptive dove group algorithmic rule spacecraft path, the posture according to path node and spacecraft obligates and restricted
The relativeness of constraint establishes posture plan model, and posture plan model is mapped to R parameter space, using based on chaos population
The posture metro planning result that adaptive dove group's algorithmic rule spacecraft attitude of variation is coupled.
Scheme is advanced optimized as the spacecraft attitude track collaborative planning method based on chaos Population Variation PIO,
Adaptive dove group's algorithm based on chaos Population Variation includes the following two stage：
The compass operator iteration evolutionary phase：Part during selecting current iteration respectively in each iterative process is most
The global optimum position that excellent position and all individuals generate during current iteration, and it is whole to dove group to introduce expression individual
The global update operator and indicate the adaptive of preceding iteration evolution trend twice that generated elite individual learns in iteration before
It answers operator and carries out the mutation operator of mutation operation, the position and speed of iteration more new individual to population, mutation operator only exists
Population's fitness change rate starts when reaching decision gate limit value, generates one after the mutation operator starting and is with individual current location
Mean value and with current population's fitness change rate it is reciprocal be variance random number, when current iteration number reaches setting value into
Enter the terrestrial reference operator iteration evolutionary phase；
The terrestrial reference operator iteration evolutionary phase：Population screen according to population's fitness and then iteration updates local optimum
Individual and global optimum's individual.
Scheme is advanced optimized as the spacecraft attitude track collaborative planning method based on chaos Population Variation PIO,
Compass operator is described as：
ViIt (t+1) is respectively speed of i-th individual in the t times iteration, the t+1 times iteration, Xi(t)、Xi(t+1) it is respectively
Position of i-th individual in the t times iteration, the t+1 times iteration, w is inertial factor,
wmaxAnd wminFor inertial factor maximum value and minimum value, TmaxFor maximum number of iterations,It is i-th individual in the t times iteration
Local optimum position, CpFor adaptive operator,fitness(t-3)、fitness(t-2)、
Fitness (t-1) is respectively fitness value of the population in the t-3 times, the t-2 times, the t-1 times iteration, XgFor all individuals
Global optimum position in the t times iteration, CgFor global update operator,CrFor activity factor,Rd(t+1) random number generated in the t+1 times iteration for mutation operator,Fitness (t) is fitness value of the population in the t times iteration.
Scheme is advanced optimized as the spacecraft attitude track collaborative planning method based on chaos Population Variation PIO,
The population's fitness is determined that the expression formula of i-th individual fitness fitness (i) is by the fitness of each individual：
threat_inj(i)、w1Enter the Threat and its weight when threatening area j, threat_out for i-th individualj
(i)、w2Threat and its weight when for i-th individual outside threatening area j, distance (i), w3For i-th individual planning
Influence degree and its weight of the overall distance consumption in path to integrated planning distance, angle (i), w4For i-th individual planning
The motor-driven angle and its weight in path, w1+w2+w1+w4=1.
Further optimization side as the spacecraft attitude track collaborative planning method based on chaos Population Variation PIO
Case, i-th individual enter Threat threat_in when threatening area jj(i) it is：Li,kFor i-th individual
The length of k-th of planning path segmentation of institute, tjFor the threat level of threatening area j, K for i-th individual institute planning path point
Number of segment mesh, d0.1,k、d0.3,k、d0.5,k、d0.7,k、d0.9,k/ 10th of respectively i-th individual k-th of planning path segmentation of institute
Place, at 3/10ths, at 5/10ths, at 7/10ths, at 9/10ths at a distance from the center threatening area j, TjTo threaten
The center of region j, RjFor the radius of threatening area j, XiIt (t) is the three-dimensional coordinate of i-th body position in t iteration.
Further optimization side as the spacecraft attitude track collaborative planning method based on chaos Population Variation PIO
Case, Threat threat_out when i-th individual is outside threatening area jj(i) it is：
tjFor the threat level of threatening area j, division number of the K for i-th individual institute planning path, d0.1,k、d0.3,k、
d0.5,k、d0.7,k、d0.9,kAt 1/10th of k-th of planning path segmentation of respectively i-th individual institute, at 3/10ths, very
Five at, at 7/10ths, at 9/10ths at a distance from the center threatening area j, TjFor the center of threatening area j, RjFor
The radius of threatening area j, XiIt (t) is the three-dimensional coordinate of i-th body position in t iteration.
Further, in the spacecraft attitude track collaborative planning method based on chaos Population Variation PIO, threatening area
The threat level t of jjFor： It indicates to be directed toward from the center of threatening area j
The vector of (i-1)-th body position,Indicate the vector that i-th body position is directed toward from (i-1)-th body position.
Further optimization side as the spacecraft attitude track collaborative planning method based on chaos Population Variation PIO
The motor-driven angle angle (i) of case, i-th individual planning path is：M is
Individual amount,Indicate the vector that (i-1)-th body position is directed toward from the i-th -2 body positions,It indicates from the
It is directed toward the vector of i-th body position in i-1 body positions.
Scheme is advanced optimized as the spacecraft attitude track collaborative planning method based on chaos Population Variation PIO,
The terrestrial reference operator iteration evolutionary phase is according to expression formula：Population Regeneration quantity, NP(t) repeatedly for the t times
The population quantity in generation, N are population quantity, TmaxFor maximum number of iterations.
Further optimization side as the spacecraft attitude track collaborative planning method based on chaos Population Variation PIO
Case maps chaos intialization population using Tent Map before the compass operator iteration evolutionary phase starts.
The present invention by adopting the above technical scheme, has the advantages that：
(1) the posture track collaborative planning problem herein for spacecraft under Complex Constraints devises a kind of based on chaos
Adaptive dove group's improved algorithm of Population Variation, and spacecraft attitude planning space is mapped to Rodrigues parameter sky
Between in planned, the problem of to meet Eulerian angles planning decoupling, so that satellite each position in space is one corresponding
Posture has obtained the restrictive program results of posture；
(2) adaptive operator introduced carrys out dynamic according to population current state and adjusts the range of kind of group hunting, population into
Search range is increased when changing slow, is reduced in population excessive velocities and is searched range, can promote evolution depth and to a certain degree
On avoid locally optimal solution, the mutation operator of introducing make when population falls into locally optimal solution population be detached from locally optimal solution and
Population obtains retaining globally optimal solution when globally optimal solution, shrinks problem for population in the terrestrial reference operator stage and contraction operator is added
With Population Regeneration quantity, solves the problems, such as that excellent individual is lost too fast, population deterioration, keep program results more smooth, population is drilled
Change is more deep, and locally optimal solution problem and algorithm divergence problem are resolved, and algorithm has faster convergence rate, greatly
Calculation amount is reduced greatly, realizes the optimum programming of spacecraft attitude track；
(3) fitness function is introduced smoothness evaluation points and is screened with the smoothness to Population Evolution result,
Keep optimum results smooth as far as possible, reduce shake, to the improvement of threat level for Spacecraft formation and threatening area distance
It carries out, spacecraft enters that threat level after threatening area is very high and ascendant trend is accelerated with the close of distance, can sieve
Selection is avoided to enter the solution of collision range when selecting, and threat level declines gently after spacecraft leaves threatening area, can screen
The solution for leaving collision range, mutually requires relative loose to the position of spacecraft.
Detailed description of the invention
Fig. 1 is the schematic diagram that initialization of population is mapped using Tent Map.
Fig. 2 is schematic diagram of the population quantity with the number of iterations variation tendency.
Fig. 3 is the schematic diagram of posture track collaborative planning.
Fig. 4 is stream of the application using adaptive dove group's algorithmic rule spacecraft attitude track based on chaos Population Variation
Cheng Tu.
Fig. 5 is the analogous diagram of classical money PIO algorithm metro planning.
Fig. 6 is the analogous diagram of particle swarm algorithm metro planning.
Fig. 7 is the analogous diagram of the adaptive dove group algorithm metro planning of the application modified chaos Population Variation.
Fig. 8 is the comparison diagram that the CPVAPIO algorithm that the application proposes and PIO algorithm and PSO algorithm calculate cost.
Fig. 9 is the restricted program results of posture obtained using the application CPVAPIO algorithm.
Figure 10 is the spacecraft attitude angle program results obtained using the application CPVAPIO algorithm.
Specific embodiment
The technical solution of invention is described in detail with reference to the accompanying drawing.
Herein for the initialization of population of dove group's algorithm, population iteration develops and three aspects of fitness function carry out
Primary study, and needle proposes based on " exploration ", " search ", " variation " deficiency of existing genetic algorithm, " going back to the nest "
Dove group's dynamic optimization strategy is to solve existing algorithm in convergence rate, local optimum, in terms of evolution depth there are the problem of.
(1) it explores：
In " exploration " stage, population is initialized, as typical case a kind of in nonlinear system phenomenon --- chaos is existing
As having the characteristics that randomness, ergodic and regularity.It can make initialization kind using the ergodic of chaos phenomenon at this stage
Group is dispersedly distributed in as far as possible in the space for entirely needing to explore, meanwhile, the individual in population has higher probability close to search
Globally optimal solution in space, to a certain extent improve initialization of population excessively collect resulted in iteration gradually fall into part
The defect of optimal solution.
Then, chaos intialization population is mapped using Tent Map in the initialization of population：
Sn+1=ξ * (1-2* | Sn- 0.5 |), n=0,1,2..., N (1),
Wherein, 0 < S0Then system is in Complete Chaos state, S when < 1, random number ξ take 1nFor rule corresponding in chaotic space
Draw the chaos individual of i-th body position in space, Sn+1Chaos for i+1 body position in corresponding planning space is individual,
The range in the space initialized required for simultaneously is [Xmin,Xmax], the dimension of planning is D, and then, individual initialization bit is set to：
As shown in Figure 1, Tent Map mapping can be very good the space of covering 0-1.
(2) it searches：
Start iteration after population completes initialization and optimizing is scanned for entire space, this part is calculated for classics PIO
The core iteration operator of method is studied, and the location information of population Primary Reference global optimum individual during evolution comes
It updates, and the Evolution of Population at iteration initial stage does not go deep into, global optimum's individual is with respect to average individual and does not have fairly obvious
Advantage, thus not high to the reference value of entire population, at the same time, classical PIO algorithm is in renewal speed, global optimum
The weight of solution is a random number.Then, it joined global update operator C herein for global optimum's individualg, make global optimum
Individual only just has higher weight when with the obvious advantage, and the weight at iteration initial stage is smaller.
The study found that evolution experience of the single individual in existing iteration compares the global optimum at initial stage at iteration initial stage
Individual has higher reference value, can achieve and helps convergent purpose, and there is no be subject to the information to classics PIO algorithm
It utilizes, then, innovatively introduces adaptive operator C hereinp, make it possible to according to current iteration state individual in population with
The evolution trend of preceding iteration twice is adaptively adjusted, and increases the range of search when dove group evolves slow, to reach dynamic
Search for the purpose of optimum individual.
The Optimizing operator more new formula of adaptive impovement type mapped directions needle is as follows：
Xi(t+1)=Xi(t)+Vi(t+1) (4),
Wherein, Vi(t)、ViIt (t+1) is respectively speed of i-th individual in the t times iteration, the t+1 times iteration, Xi(t)
For position of i-th individual in the t times iteration,For local optimum position of i-th individual in t iteration, XgFor institute
There is global optimum position of the individual in the t times iteration, fitness (t-3), fitness (t-2), fitness (t-1) are respectively
For fitness value of i-th individual in the t-3 times, the t-2 times, the t-1 times iteration, w is inertial factor, wmaxFor inertia because
Sub- maximum value, takes 0.9, w hereinminInertial factor minimum value, takes 0.4, T hereinmaxFor maximum number of iterations, t is current iteration
Number.
(3) it makes a variation：
Locally optimal solution is classical PIO algorithm and the problem of similar genetic algorithm exists jointly, and how restrainable algorithms are fallen into
Entering locally optimal solution and population how to be activated to be detached from locally optimal solution after algorithm falls into locally optimal solution is to solve such ask
The key of topic then further joined Population Variation operator on the basis of above-mentioned Optimizing operator herein.Work as population's fitness
The change rate of value continuous 30 times be lower than 0.01 when, then population is possible to fall into locally optimal solution, at this point, to dove group in distance work as
The preceding farther away half of locally optimal solution (i.e. by the later half individual of fitness value sequence) makes a variation, mutation operator take one with
Individual current location is mean value and the random number reciprocal for variance with current variety rate of fitness.It can make later half population under
It is activated in secondary iteration, and then realizes extensive search, take population out of locally optimal solution.Simultaneously as only to latter semispecies
Group makes a variation, if algorithm has found globally optimal solution, the result of extensive search will not be better than the overall situation currently found
Optimal solution, therefore algorithm will not be made to dissipate.
The Optimizing operator of final map compass is as follows：
Wherein, Cr(Rd(t+1)-XiIt (t)) is mutation operator, CrFor activity factor, Rd(t+1) for Xi(t) for mean value and
WithFor the Gaussian random variable of variance.
(4) it goes back to the nest：
After terminating the mapped directions needle operator iteration evolutionary phase, algorithm enters terrestrial reference operator iteration evolutionary phase, terrestrial reference
Operator reduces population quantity quickly at this stage to retain globally optimal solution, inhibit population diverging.But in classical PIO algorithm,
The stage population decrease speed is to reduce half every time, reduces excessive velocities so that being more than the speed of convergence in population, thus
Lead to population deterioration.Then, the application reduces strategy to population and is improved, and screens population quantity in rapid decrease early period
Advantage is individual and slowly declines reservation advantage individual in the later period.
Population quantity NP(t) it is updated as the following formula：
Wherein, N is population quantity, herein, takes N=30, Tmax=50, population quantity with the number of iterations variation tendency such as
Shown in Fig. 2.
In the fitness function of classical PIO algorithm, only done to the length of planning path and at a distance from barrier zone
Definition, and in practical problem, the path planning in non-threat region still has the motor-driven optimization degree of the entirety of spacecraft
Important influence.
In classical PIO algorithm, for defining the t of barrier zone threat degreekIt, can be for threatening area for a variable
The different threat level of different set, and spacecraft avoidance and aircraft pass through that radar volume is different, any connecing with threatening area
Touching can cause to collide, and collision is that spacecraft path planning needs the problem of evading.Then, the application is by tkIt is improved to and space flight
For device with obstacle spacecraft apart from relevant function, the nearlyr expression threat degree of distance is higher, and when spacecraft is far from obstacle, prestige
Side of body degree reduces rapidly, unnecessary motor-driven to avoid spacecraft.
Meanwhile for spacecraft maneuver problem, it is motor-driven on a large scale that the track of optimization smoothly should reduce wide-angle as far as possible
And then extend the service life of spacecraft, motor-driven angular factors should then be added in fitness function.
Then, it improves on the basis of former fitness function such as following formula：
Wherein, fitness (i) is i-th individual fitness, threat_inj(i)、w1Enter for i-th individual and threatens
Threat and its weight when the j of region, threat_outj(i)、w2Threat when for i-th individual outside threatening area j and
Its weight, distance (i), w3The influence journey to integrated planning distance is consumed for the overall distance of i-th individual planning path
Degree and its weight, angle (i), w4For the motor-driven angle and its weight of i-th individual planning path, w1+w2+w1+w4=1.This is suitable
Response function enters in threatening area for path in planning space and establishes different adaptations from the situation outside threatening area
Function is spent, and the angle (i) of evaluation path smooth degree is added.
When planning path enters threatening area, fitness function is：
Wherein, Li,kFor the length of i-th individual k-th of planning path segmentation of institute, tjFor the threat level of threatening area j,
Division number of the K for i-th individual institute planning path, d0.1,k、d0.3,k、d0.5,k、d0.7,k、d0.9,kRespectively i-th individual institute
At 1/10th of k-th of planning path segmentation, at 3/10ths, at 5/10ths, at 7/10ths, at 9/10ths and prestige
Coerce the distance at the center region j, TjFor the center of threatening area j, RjFor the radius of threatening area j, in practice, RjIt is j-th
The outer profile radius of obstacle spacecraft, XiIt (t) is the three-dimensional coordinate of i-th body position in the t times iteration.
When planning path does not enter threatening area, fitness function is：
In above two formula, tjCharacterize current threat level：
Wherein,Indicate the vector that (i-1)-th body position is directed toward from the center of threatening area j,It indicates
The vector of i-th body position is directed toward from (i-1)-th body position.
Path smooth fitness function is：
Wherein, M is individual amount,Indicate to be directed toward from the i-th -2 body positions (i-1)-th body position to
Amount.
Spacecraft attitude track collaborative planning scheme
The posture metro planning problem of spacecraft is the hot issue of space industry, but existing research mainly will at present
Posture is individually studied with track, and in practice due to the variation of spacecraft orbit, observation mission target and other days
The relative position of body is also changed.To which the planning problem of track and the planning problem of posture are there are coupled relation,
The two should be cooperateed with and be considered.
Then, it is first depending on the mould for needing the obstacle evaded to establish path planning space when spacecraft maneuver becomes rail herein
Type initializes the current location and target position of barrier zone and spacecraft, carries out spacecraft using algorithm herein
Path planning.Then on the basis of path planning is completed, the mandatory constraint of posture according to path point and spacecraft with
And the relativeness of restricted constraint establishes posture plan model, and model is mapped in R parameter space, to utilize again
Adaptive dove group optimizing method (hereinafter referred CPAVPIO algorithm) proposed in this paper based on chaos Population Variation planned
At the collaborative planning of posture track, the posture metro planning of output coupling is as a result, the process of collaborative planning is as shown in Figure 3.
The present invention realizes the posture track collaborative planning of spacecraft such as using adaptive dove group's algorithm of chaos Population Variation
Shown in Fig. 4.
(1) initialization dove group position and algorithm parameter
Dove group position initialization in apply Tent Map chaology, make dove group initialized location as far as possible uniformly and
It is irregular to be dispersed in entire planning space.And be arranged dove group quantity Q, search dimension D, dove group initialization bit be set to X0
=[x0 y0 z0], the target position of dove group is XD=[xD yD zD], mapped directions needle operator the number of iterations T1, greatest iteration time
Number TMAX, j-th threatening area centre coordinate Tj=[xT yT zT]T, j-th threatening area radius Rj。
(2) starting mapped directions needle operator carries out Population Evolution
In order to make to increase the evolution depth of population, avoids falling into locally optimal solution as far as possible during Population Evolution, compare
To the single reference of globally optimal solution in traditional algorithm, it should make population according to the state currently to develop to determine next iteration
To the reference of globally optimal solution in evolution.Then, the adaptive impovement type as shown in formula (3) to formula (7) is innovatively devised
The Optimizing operator of mapped directions needle.
(3) locally optimal solution is detached from
The current common existing problem of same type algorithm is that population is possible to that locally optimal solution can be fallen into.And it is falling into
Population how is set to be detached from locally optimal solution after entering locally optimal solution, meanwhile, so that population is unlikely to too active and dissipates algorithm,
And the problem of making algorithm be detached from globally optimal solution after globally optimal solution is mistaken for locally optimal solution is a difficulties.
To solve this problem, mutation operator is devised in the algorithm.When being lower than 0.01 the change rate of Population adaptation angle value continuous 30 times
Then population is possible to fall into locally optimal solution, at this point, to the farther away half of the current locally optimal solution of distance in dove group (i.e. by suitable
The later half individual for answering angle value to sort) it makes a variation, mutation operator will be generated using current value as mean value and with the change of current fitness
The inverse of rate is a random number of variance, using this random number as with reference to progress subsequent evolution, so that current
Solution is retained.If current solution is locally optimal solution, solving farther away later half population apart from this can be by population after variation
Take away this solution；If current solution has been globally optimal solution, evolutions of later half population will not generate better than this solve as a result, because
And remain globally optimal solution.Finally obtain the Optimizing operator of the mapped directions needle as shown in formula (8) to formula (10).
(4) starting terrestrial reference operator carries out Population Evolution
The terrestrial reference operator part of primal algorithm, population reduce the too fast speed for being even more than convergence in population of rate, then,
The application is designed the fall off rate of population, make population quantity early period rapid decrease with screen advantage individual and in the later period
Slowly decline reservation advantage individual, population quantity are updated by formula (11).
(5) fitness function
Screening and sequencing is carried out to population according to fitness function during evolution, generates locally optimal solution and the overall situation most
Excellent solution.
Emulation experiment and result verification
Experiment setting current maneuver spacecraft is located at coordinate origin (0,0,0) when start of evolution under kinetic coordinate system
KM, target position are (65,80,30) KM, set the relative position for becoming rail spacecraft preceding object spacecraft as (45,50,5)
KM, (8,25,15) KM, (40,68,7) KM, the minimum safe distance of spacecraft are 5KM.
Emulation experiment condition is main four core 2.8Hz, 16GB memory of core, 64 bit machines, on this basis in set algorithm
Portion's parameter is respectively：
● classical money PIO algorithm and modified PIO algorithm：Individual amount M=30, plans dimension D=20, and the number of iterations is
200 times (mapped directions needle operator 150 times, terrestrial reference operator 50 times).
● particle swarm algorithm：Individual amount M=30, plans dimension D=20, and the number of iterations is 200 times.
● adaptive dove group's algorithm (CPAVPIO algorithm) of chaos Population Variation：Individual amount M=30 plans dimension D=
20, the number of iterations is 200 times.
1.1 spacecraft orbits plan experimental result and algorithm performance comparison
Classical money PIO algorithm metro planning result is as shown in figure 5, population (PSO) algorithm metro planning result such as Fig. 6 institute
Show, the application be based on the result of chaos Population Variation adaptive dove group's (CPVAPIO) innovatory algorithm metro planning as shown in fig. 7,
CPVAPIO algorithm and PIO algorithm and PSO algorithm calculate cost as shown in figure 8, CPVAPIO algorithm and PIO algorithm and PSO algorithm
Calculation amount comparison is as shown in table 1.
Table 1CPVAPIO algorithm and PIO algorithm and the comparison of PSO algorithm calculation amount
The restricted program results of posture obtained using the application CPVAPIO algorithm are as shown in figure 9, using the application
The spacecraft attitude angle program results that CPVAPIO algorithm obtains are as shown in Figure 10.
As it can be seen that being devised herein for posture track collaborative planning problem of the spacecraft under Complex Constraints a kind of based on mixed
Adaptive dove group's improved algorithm of ignorant Population Variation, and spacecraft attitude planning space is mapped to Rodrigues parameter
It is planned in space, to meet the problem of Eulerian angles planning decouples.By comparative experiments it can be seen that the algorithm of this paper is compared
It is more smooth on program results in classical PIO algorithm and PSO algorithm, unnecessary appearance rail adjustment can be reduced；Simulation result
Show adaptive dove group's algorithm (CPAVPIO algorithm) of chaos Population Variation compared to PIO and PSO algorithm, Evolution of Population is more
Deeply, fitness drop-out value is 10 or so, and remaining two kinds of algorithm is 5 or so, meanwhile, algorithm has convergence speed faster
Degree；And spacecraft is realized it can be seen that the improved algorithm of this paper greatly reduces calculation amount by the comparison of calculation amount
The optimum programming of posture track.
Claims (10)
1. the spacecraft attitude track collaborative planning method based on chaos Population Variation PIO, which is characterized in that using based on chaos
The adaptive dove group algorithmic rule spacecraft path of Population Variation, the posture according to path node and spacecraft obligate with
And the relativeness of restricted constraint establishes posture plan model, and posture plan model is mapped to R parameter space, using being based on
The posture metro planning result that adaptive dove group's algorithmic rule spacecraft attitude of chaos Population Variation is coupled.
2. the spacecraft attitude track collaborative planning method based on chaos Population Variation PIO according to claim 1, feature
It is, adaptive dove group's algorithm based on chaos Population Variation includes the following two stage：
The compass operator iteration evolutionary phase：Local optimum position during selecting current iteration respectively in each iterative process
It sets and global optimum position that all individuals generate during current iteration, and it is whole to dove group at it to introduce expression individual
The adaptive calculation of the global update operator of generated elite individual study and the preceding iteration evolution trend twice of expression in preceding iteration
Son and the mutation operator that mutation operation is carried out to population, the position and speed of iteration more new individual, mutation operator is only in population
Variety rate of fitness starts when reaching decision gate limit value, generates one using individual current location as mean value after the mutation operator starting
And with the random number reciprocal for variance of current population's fitness change rate, enter ground when current iteration number reaches setting value
Mark the operator iteration evolutionary phase；
The terrestrial reference operator iteration evolutionary phase：Population screen according to population's fitness and then iteration updates local optimum individual
With global optimum's individual.
3. the spacecraft attitude track collaborative planning method based on chaos Population Variation PIO, feature exist according to claim 2
In the compass operator is described as：
Vi(t)、ViIt (t+1) is respectively speed of i-th individual in the t times iteration, the t+1 times iteration, Xi(t)、XiIt (t+1) is respectively
Position of the i individuals in the t times iteration, the t+1 times iteration, w is inertial factor,wmax
And wminFor inertial factor maximum value and minimum value, TmaxFor maximum number of iterations,It is i-th individual in the t times iteration
Local optimum position, CpFor adaptive operator,fitness(t-3)、fitness(t-2)、
Fitness (t-1) is respectively fitness value of the population in the t-3 times, the t-2 times, the t-1 times iteration, XgFor all individuals
Global optimum position in the t times iteration, CgFor global update operator,CrFor activity factor,Rd(t+1) it is generated in the t+1 times iteration for mutation operator random
Number,Fitness (t) is fitness value of the population in the t times iteration.
4. the spacecraft attitude track collaborative planning method based on chaos Population Variation PIO according to claim 2, feature
It is, the population's fitness is determined by the fitness of each individual, the expression formula of i-th individual fitness fitness (i)
For：threat_inj
(i)、w1Enter the Threat and its weight when threatening area j, threat_out for i-th individualj(i)、w2For i-th individual
Threat and its weight when outside threatening area j, distance (i), w3Overall distance for i-th individual planning path disappears
Consume the influence degree and its weight to integrated planning distance, angle (i), w4For i-th individual planning path motor-driven angle and
Its weight, w1+w2+w1+w4=1.
5. the spacecraft attitude track collaborative planning method based on chaos Population Variation PIO according to claim 4, feature
It is, i-th individual enters Threat threat_in when threatening area jj(i) it is：Li,kFor i-th individual
The length of k-th of planning path segmentation of institute, tjFor the threat level of threatening area j, K for i-th individual institute planning path point
Number of segment mesh, d0.1,k、d0.3,k、d0.5,k、d0.7,k、d0.9,k/ 10th of respectively i-th individual k-th of planning path segmentation of institute
Place, at 3/10ths, at 5/10ths, at 7/10ths, at 9/10ths at a distance from the center threatening area j, TjTo threaten
The center of region j, RjFor the radius of threatening area j, XiIt (t) is the three-dimensional coordinate of i-th body position in t iteration.
6. the spacecraft attitude track collaborative planning method based on chaos Population Variation PIO according to claim 4, feature
It is, Threat threat_out when i-th individual is outside threatening area jj(i) it is：|Xi(t)-Tj| > Rj, tjFor
The threat level of threatening area j, division number of the K for i-th individual institute planning path, d0.1,k、d0.3,k、d0.5,k、d0.7,k、
d0.9,kAt 1/10th of k-th of planning path segmentation of respectively i-th individual institute, at 3/10ths, at 5/10ths, very
Seven at, at 9/10ths at a distance from the center threatening area j, TjFor the center of threatening area j, RjFor threatening area j's
Radius, XiIt (t) is the three-dimensional coordinate of i-th body position in t iteration.
7. the spacecraft attitude track collaborative planning method according to claim 5 or 6 based on chaos Population Variation PIO,
It is characterized in that, the threat level t of threatening area jjFor： It indicates from threat area
The vector of (i-1)-th body position is directed toward in the center of domain j,It indicates to be directed toward i-th from (i-1)-th body position
The vector of body position.
8. the spacecraft attitude track collaborative planning method based on chaos Population Variation PIO according to claim 4, feature
It is, the motor-driven angle angle (i) of i-th individual planning path is：M
For individual amount,Indicate the vector that (i-1)-th body position is directed toward from the i-th -2 body positions,Indicate from
It is directed toward the vector of i-th body position in (i-1)-th body position.
9. the spacecraft attitude track collaborative planning method based on chaos Population Variation PIO according to claim 2, feature
It is, the terrestrial reference operator iteration evolutionary phase is according to expression formula：Population Regeneration quantity, NPIt (t) is the
The population quantity of t iteration, N are population quantity, TmaxFor maximum number of iterations.
10. the spacecraft attitude track collaborative planning method based on chaos Population Variation PIO according to claim 2, special
Sign is, before the compass operator iteration evolutionary phase starts, maps chaos intialization population using Tent Map.
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