CN108919818B - Spacecraft attitude orbit collaborative planning method based on chaotic population variation PIO - Google Patents
Spacecraft attitude orbit collaborative planning method based on chaotic population variation PIO Download PDFInfo
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Abstract
The invention discloses a collaborative planning method for spacecraft attitude orbits based on chaotic population variation PIO, and belongs to the technical field of satellite attitude orbit control. The invention adopts the dynamic optimization strategies of pigeon groups of 'exploration', 'search', 'variation' and 'homing' in the evolution stage of the algorithm. Adding a chaotic operator to perform initialization operation aiming at the initialization problem of the population at the map compass stage, adding an adaptive operator after the population is initialized to realize that the population can adaptively evolve according to the current population evolution state, and simultaneously adding a mutation operator to solve the problem that the population falls into a local optimal solution; a shrinkage operator is added in a landmark operator stage aiming at the population shrinkage problem, so that the problems of too fast loss of excellent individuals and population degradation are solved, the planning result is smoother, the population evolution is deeper, the problem of local optimal solution and the problem of algorithm divergence are solved, and the calculation amount of the algorithm is further reduced.
Description
Technical Field
The invention discloses a collaborative planning method for spacecraft attitude orbits based on chaotic population variation PIO, and belongs to the technical field of satellite attitude orbit control.
Background
The PIO (Pigeon-Inspired Optimization) algorithm is developed by inspiring the navigation process of a Pigeon group in the homing process, the Pigeon group mainly depends on the sun and the geomagnetism for navigation when being far away from the destination, and the landmark is used for navigation when being close to the destination, and individuals in the group who are not familiar with the landmark can fly along with the group familiar with the landmark.
The existing PIO algorithm can realize obstacle avoidance, path planning and image edge identification of unmanned aerial vehicles and robots, but the problem of coordinated planning of spacecraft attitude orbits under complex constraint conditions and strong coupling relations is not solved. The existing PIO algorithm has the following four defects: (1) researches show that the initialization of the population state can directly influence the population evolution result in the previous stage, and the current PIO algorithm cannot self-adaptively adjust the later evolution according to the current evolution state of the population during the population evolution, so that the algorithm has the problems of easy falling into the local optimal solution, stagnation of the evolution, early convergence, not deep evolution and the like; (2) the problem that the population quantity is reduced too fast in the landmark algorithm stage of the conventional PIO algorithm is solved, so that excellent individuals are eliminated when the population is not fully evolved in the final stage, and the algorithm has the possibility of divergence and even degradation; (3) in the aspect of fitness function, the current PIO algorithm cannot screen the smoothness of the planning result. (4) Researches find that the variance of the results of the conventional PIO algorithm is large, so that a control mechanism of the spacecraft is frequently started, and the mechanical structure is also abraded to a certain extent while precious energy of the spacecraft is consumed.
However, the attitude and the orbit are generally planned separately by the current planning algorithm for the attitude orbit of the spacecraft, but the attitude orbit of the spacecraft actually has a direct coupling relationship, and the attitude is planned on the basis of the planning result of the orbit of the spacecraft by considering the position of the spacecraft when guidance is performed. At present, aiming at the problem of spacecraft attitude planning, McInness constructs a model of an attitude limiting region through a potential function and obtains input of a control quantity by using a Lyapunov second law, although the method has low calculated quantity, the resource occupation of an on-board computer can be effectively reduced, the time and energy consumption of spacecraft attitude maneuver are not taken into consideration, and meanwhile, the Euler angle used in the calculation process generates singularities in kinematic description; melton uses a numerical solution from the perspective of optimal control, but it is computationally expensive and may not be suitable for barrier-free motion; suzhong et al plan the attitude of the satellite from the perspective of the low RCS characteristics of the satellite, but it does not plan the roll angle, and the pitch angle can only be planned within [0-180 ° ]; kjellberg et al adopt an icosahedron discretization technique and use an A-algorithm to realize the planning of an optimal path, but boundary constraint and dynamic constraint are not considered in the algorithm; kim Y et al transforms the path planning problem into a semi-definite planning problem, but the complexity of the method increases dramatically with increasing constraints.
The invention aims to deeply improve the core iterative algorithm and the fitness function of the conventional PIO algorithm so as to realize the attitude orbit collaborative planning of a spacecraft cluster.
Disclosure of Invention
The invention aims to provide a collaborative planning method of a spacecraft attitude orbit based on chaotic population variation PIO (particle image input) aiming at the defects of the background technology, the collaborative planning of the spacecraft attitude orbit under the strong coupling relation is realized by adopting an improved PIO algorithm, and the technical problems that the collaborative planning of the attitude and the orbit is not realized by the existing spacecraft attitude orbit planning scheme, and the overall dynamic constraint conditions and all factors influencing the planning result are not considered by the existing attitude planning scheme or orbit planning scheme and the complexity is large are solved.
The invention adopts the following technical scheme for realizing the aim of the invention:
a spacecraft attitude orbit collaborative planning method based on chaotic population variation PIO adopts a self-adaptive pigeon swarm algorithm based on chaotic population variation to plan a spacecraft path, establishes an attitude planning model according to the relative relation between a path node and attitude mandatory constraint and restrictive constraint of a spacecraft, maps the attitude planning model to an R parameter space, and plans a spacecraft attitude by adopting the self-adaptive pigeon swarm algorithm based on chaotic population variation to obtain a coupled attitude orbit planning result.
As a further optimization scheme of the spacecraft attitude orbit collaborative planning method based on the chaotic population variation PIO, the adaptive pigeon population algorithm based on the chaotic population variation comprises the following two stages:
a compass operator iterative evolution stage: respectively selecting a local optimal position in the current iteration process and a global optimal position generated by all individuals in the current iteration process in each iteration process, introducing a global updating operator for showing the fact that the individuals learn the elite individuals generated by the whole pigeon group in the previous iteration, an adaptive operator for showing the evolution trend of the previous two iterations and a mutation operator for carrying out mutation operation on the pigeon group, iteratively updating the position and the speed of the individuals, starting the mutation operator only when the population adaptation degree change rate reaches a judgment threshold value, generating a random number which takes the current position of the individual as a mean value and takes the reciprocal of the current population adaptation degree change rate as a variance after the mutation operator is started, and entering a landmark operator iterative evolution stage when the current iteration number reaches a set value;
and (3) a landmark operator iterative evolution stage: and screening the population according to the population fitness so as to iteratively update the local optimal individual and the global optimal individual.
As a further optimization scheme of the spacecraft attitude orbit collaborative planning method based on the chaotic population variation PIO, a compass operator is described as follows:
Vi(t +1) is the speed of the ith individual in the t-th iteration and the t +1 th iteration, respectively, Xi(t)、Xi(t +1) is the position of the ith individual in the t-th iteration and the t + 1-th iteration respectively, w is an inertia factor,
wmaxand wminMaximum and minimum values of the inertia factor, TmaxIn order to be the maximum number of iterations,
for the local optimum position of the ith individual in the t-th iteration, CpIn order to adapt the operator, the operator is,
the fitness (t-3), the fitness (t-2) and the fitness (t-1) are fitness values of the population in the t-3 th iteration, the t-2 th iteration and the t-1 th iteration respectively, and X isgFor the global optimal position of all individuals in the t-th iteration, CgIn order to update the operator globally,
Crin order to activate the factor(s),
Rd(t +1) is the random number generated by the mutation operator in the t +1 th iteration,
fitness (t) is the fitness value of the population in the tth iteration.
As a further optimization scheme of the spacecraft attitude orbit collaborative planning method based on the chaos population variation PIO, the population fitness is determined by the fitness of each individual, and the fitness (fitness) of the ith individual is (i) expressed as:
threat_inj(i)、w1threat _ out is the threat level and weight of the ith individual entering the threat zone jj(i)、w2The threat degree and the weight of the ith individual outside the threat zone j, distance (i), w3The influence degree of the overall distance consumption of the ith individually planned path on the overall planned distance and the weight thereof, angle (i), w4Maneuver angles and weights, w, for the ith individual to plan a path1+w2+w1+w4＝1。
As a further optimization scheme of a spacecraft attitude orbit collaborative planning method based on chaotic population variation PIO, the threat degree threat _ in of the ith individual entering a threat area jj(i) Comprises the following steps:
Li,klength, t, of kth segment of path planned for ith individualjThe threat level of the threat zone j, K is the number of segments of the planned path of the ith individual, d0.1,k、d0.3,k、d0.5,k、d0.7,k、d0.9,kOne tenth and one tenth of the kth segment of the path planned by the ith individual respectivelyDistance between three, five, seven, nine and the center of the threat zone j, TjIs the central position of the threat zone j, RjRadius of threat zone j, Xi(t) is the three-dimensional coordinates of the ith individual position in t iterations.
As a further optimization scheme of a collaborative planning method of spacecraft attitude orbits based on chaotic population variation PIO, the threat degree threat _ out of the ith individual out of a threat area jj(i) Comprises the following steps:
tjthe threat level of the threat zone j, K is the number of segments of the planned path of the ith individual, d0.1,k、d0.3,k、d0.5,k、d0.7,k、d0.9,kThe distances T from one tenth, three tenth, five tenth, seven tenth and nine tenth of the kth subsection of the path planned by the ith individual to the center of the threat area jjIs the central position of the threat zone j, RjRadius of threat zone j, Xi(t) is the three-dimensional coordinates of the ith individual position in t iterations.
Still further, in the collaborative planning method for spacecraft attitude orbits based on the PIO (particle swarm optimization) of the chaotic population variation, the threat level t of the threat area jjComprises the following steps:
representing a vector pointing from the center position of threat zone j to the (i-1) th individual position,
representing a vector pointing from the ith-1 individual position to the ith individual position.
Further optimization of spacecraft attitude orbit collaborative planning method based on chaotic population variation PIOIn the scheme, the maneuvering angle (i) of the ith individual planning path is:
m is the number of the individuals,
representing a vector pointing from the i-2 nd individual position to the i-1 st individual position,
representing a vector pointing from the ith-1 individual position to the ith individual position.
As a further optimization scheme of the collaborative planning method of the spacecraft attitude orbit based on the chaotic population variation PIO, the iterative evolution stage of the landmark operator is according to an expression:
update population number, NP(T) is the population number of the T-th iteration, N is the population number, TmaxIs the maximum number of iterations.
As a further optimization scheme of the spacecraft attitude orbit collaborative planning method based on the chaotic population variation PIO, a Tent Map is adopted to Map chaotic initialization populations before the compass operator iterative evolution stage begins.
By adopting the technical scheme, the invention has the following beneficial effects:
(1) aiming at the problem of attitude orbit collaborative planning of a spacecraft under complex constraint, a self-adaptive pigeon swarm improved algorithm based on chaotic population variation is designed, and a spacecraft attitude planning space is mapped into a Rodrigues parameter space for planning so as to meet the problem of Euler angle planning decoupling, so that each position of a satellite in the space corresponds to an attitude, and an attitude-limiting planning result is obtained;
(2) the introduced adaptive operator dynamically adjusts the range of population search according to the current state of the population, the search range is enlarged when the population evolves slowly, the search range is reduced when the population speed is too fast, the evolution depth can be improved, the local optimal solution is avoided to a certain extent, the introduced mutation operator enables the population to be separated from the local optimal solution when the population falls into the local optimal solution and keeps the global optimal solution when the population obtains the global optimal solution, in the landmark operator stage, a contraction operator is added aiming at the population contraction problem to update the population quantity, so that the problems of over-high loss of excellent individuals and population degradation are solved, the planning result is smoother, the population evolution is deeper, the problem of local optimal solution and the problem of algorithm divergence are solved, the algorithm has higher convergence speed, the calculated amount is greatly reduced, and the optimal planning of the spacecraft attitude orbit is realized;
(3) the fitness function introduces a smoothness evaluation factor to screen the smoothness of the population evolution result, so that the optimized result is as smooth as possible, the jitter is reduced, the improvement of the threat level is performed according to the distance between the formation of the spacecraft and the threat area, the threat level is very high after the spacecraft enters the threat area, the ascending trend is accelerated along with the approach of the distance, the solution entering the collision range can be avoided being selected during screening, the threat level is slowly reduced after the spacecraft leaves the threat area, the solution leaving the collision range can be screened, and the requirement on the position of the spacecraft is relatively loose.
Drawings
Fig. 1 is a diagram illustrating population initialization using Tent Map mapping.
Fig. 2 is a schematic diagram of the population number trend with the number of iterations.
Fig. 3 is a schematic diagram of attitude trajectory co-planning.
Fig. 4 is a flowchart for planning a spacecraft attitude orbit by using a chaos population variation-based adaptive pigeon swarm algorithm according to the present application.
FIG. 5 is a simulation diagram of a classical PIO algorithm orbit planning.
Fig. 6 is a simulation diagram of a particle swarm algorithm orbit planning.
Fig. 7 is a simulation diagram of the improved chaotic population variation adaptive pigeon population algorithm orbit planning of the present application.
Fig. 8 is a comparison graph of the calculation costs of the cpvoapio algorithm, the PIO algorithm, and the PSO algorithm proposed in the present application.
Fig. 9 is a posture-limiting planning result obtained by using the cpvenio algorithm of the present application.
Fig. 10 is a spacecraft attitude angle planning result obtained by using the cpvoapio algorithm of the present application.
Detailed Description
The technical scheme of the invention is explained in detail in the following with reference to the attached drawings.
The method mainly researches three aspects of population initialization, population iterative evolution and fitness function of a pigeon group algorithm, and provides a pigeon group dynamic optimization strategy based on 'exploration', 'searching', 'mutation' and 'homing' aiming at the defects of the existing genetic algorithm so as to solve the problems of the existing algorithm in the aspects of convergence speed, local optimization and evolution depth.
(1) Exploring:
in the exploration stage, population is initialized as a typical phenomenon in a nonlinear system, namely a chaos phenomenon, and the population has the characteristics of randomness, ergodicity, regularity and the like. In the stage, the initialized population can be distributed in the whole space to be explored as dispersedly as possible by utilizing the ergodicity of the chaos phenomenon, meanwhile, individuals in the population have higher probability to be close to the global optimal solution in the search space, and the defect that iteration gradually falls into the local optimal solution caused by over-concentrated population initialization is improved to a certain extent.
Then, the population is chaotically initialized using Tent Map mapping in the initialization of the population:
Sn+1＝ξ*(1-2*|Sn-0.5|),n＝0,1,2...,N (1)，
wherein 0 < S0If the random number ξ is 1, the system is in a complete chaotic state, SnFor the chaotic individual in the ith individual position in the corresponding planning space in the chaotic space, Sn+1For chaotic individual corresponding to the (i +1) th individual position in the planning space, and the range of the space required to be initialized is [ X ]min,Xmax]The dimension of the plan is D, so the individual initialization positions are:
as shown in FIG. 1, the Tent Map may cover the space of 0-1 well.
(2) Searching:
the method comprises the steps that iteration is started to search and optimize the whole space after population initialization is completed, the core iterative operator of a classical PIO algorithm is researched, the population is updated mainly by referring to position information of a globally optimal individual in the evolution process, population evolution at the initial stage of iteration is not deep, the globally optimal individual does not have obvious advantages relative to a common individual, and therefore the reference value of the whole population is not high, and meanwhile, when the classical PIO algorithm is at the updating speed, the weight of the globally optimal solution is a random number. Thus, the global update operator C is added to the document for the globally optimal individualgTherefore, the global optimal individual has a higher weight only when the advantage is obvious, and the weight at the initial stage of iteration is smaller.
Research shows that in the initial stage of iteration, the evolution experience of a single individual in the existing iteration has higher reference value than that of the initial globally optimal individual, the convergence assisting purpose can be achieved, the information is not utilized by the classical PIO algorithm, and therefore the self-adaptive operator C is innovatively introduced into the methodpThe adaptive adjustment can be carried out according to the current iteration state of the individual in the population and the evolution trend of the previous two iterations, and the searching range is enlarged when the pigeon population evolves slowly, so that the aim of dynamically searching the optimal individual is fulfilled.
The optimization operator updating formula of the self-adaptive improved map compass is as follows:
Xi(t+1)＝Xi(t)+Vi(t+1) (4)，
wherein, Vi(t)、Vi(t +1) is the speed of the ith individual in the t-th iteration and the t +1 th iteration, respectively, Xi(t) is the position of the ith individual in the tth iteration,
for the local optimum position of the ith individual in t iterations, XgFor global optimal positions of all individuals in the t iteration, fitness (t-3), fitness (t-2) and fitness (t-1) are fitness values of the ith individual in the t-3 th iteration, the t-2 th iteration and the t-1 th iteration respectively, w is an inertia factor, w is the global optimal position of the ith individual in the t iterationmaxIs the maximum value of the inertia factor, and is 0.9, wminMinimum value of inertia factor, here taken to be 0.4, TmaxAnd t is the current iteration time.
(3) Mutation:
the local optimal solution is a problem existing in both a classical PIO algorithm and a similar genetic algorithm, and a key for solving the problems is to inhibit the algorithm from falling into the local optimal solution and to activate the population to be separated from the local optimal solution after the algorithm falls into the local optimal solution, so that a population variation operator is further added on the basis of the optimization operator. When the variation rate of the population fitness value is continuously lower than 0.01 for 30 times, the population is likely to fall into the local optimal solution, at this time, the half (namely the second half of individuals sorted according to the fitness value) of the pigeon population farther from the current local optimal solution is mutated, and the mutation operator takes a random number which takes the current position of the individual as the mean value and the reciprocal of the current fitness change rate as the variance. The second half of the population can be activated in the next iteration, so that large-range search is realized, and the population is brought out of a local optimal solution. Meanwhile, only the second half of the population is subjected to variation, and if the algorithm finds the global optimal solution, the result of the large-range search is not superior to the currently found global optimal solution, so that the algorithm is not diverged.
The final map compass optimization operator is as follows:
wherein, Cr(Rd(t+1)-Xi(t)) is a mutation operator, CrAs an activating factor, Rd(t +1) is represented by Xi(t) is a mean value and is based on
Is a gaussian random variable of variance.
(4) Homing:
after the iterative evolution stage of the map compass operator is finished, the algorithm enters the iterative evolution stage of the landmark operator, and the landmark operator rapidly reduces the population number at the stage so as to keep the global optimal solution and inhibit the population divergence. However, in the classical PIO algorithm, the population descending speed at this stage is reduced by half at each time, and the reduction speed is too high to exceed the convergence speed of the population, thereby causing the degradation of the population. Therefore, the population reduction strategy is improved, so that the population number is rapidly reduced in the early stage to screen dominant individuals, and is slowly reduced in the later stage to keep the dominant individuals.
Number of groups NP(t) updating as follows:
wherein N is the population number, where N is 30, T max50, the variation trend of the population quantity along with the iteration number is shown in figure 2As shown.
In a fitness function of a classical PIO algorithm, only the length of a planned path and the distance from a barrier region are defined, and in an actual problem, path planning of a non-threat region still has an important influence on the overall maneuvering optimization degree of a spacecraft.
In the classical PIO algorithm, t is used for defining the threat degree of the barrier areakDifferent threat levels can be set for different threat areas as a variable, the obstacle avoidance of the spacecraft is different from the situation that the aircraft passes through the radar area, any contact with the threat areas can cause collision, and the collision is a problem to be avoided in path planning of the spacecraft. Thus, the present application will now turn tkThe improvement is a function related to the distance of the spacecraft from the obstacle spacecraft, with closer distances representing higher threat levels and with the spacecraft away from the obstacle, the threat levels are rapidly reduced to avoid unnecessary maneuvering of the spacecraft.
Meanwhile, for the problem of spacecraft maneuvering, the optimized track should be as smooth as possible to reduce large-angle large-range maneuvering and further prolong the service life of the spacecraft, and then a maneuvering angle factor should be added into the fitness function.
Then, the following formula is improved on the basis of the original fitness function:
wherein, the fitness (i) is the fitness of the ith individual, threat _ inj(i)、w1Threat _ out is the threat level and weight of the ith individual entering the threat zone jj(i)、w2The threat degree and the weight of the ith individual outside the threat zone j, distance (i), w3The influence degree of the overall distance consumption of the ith individually planned path on the overall planned distance and the weight thereof, angle (i), w4Maneuver angles and weights, w, for the ith individual to plan a path1+w2+w1+w 41. The fitness function is established in the planning space for the situation where the path enters the threat zone and is outside the threat zoneDifferent fitness functions and add an angle (i) that evaluates the degree of smoothness of the path.
When the planned path enters the threat zone, the fitness function is:
wherein, Li,kLength, t, of kth segment of path planned for ith individualjThe threat level of the threat zone j, K is the number of segments of the planned path of the ith individual, d0.1,k、d0.3,k、d0.5,k、d0.7,k、d0.9,kThe distances T from one tenth, three tenth, five tenth, seven tenth and nine tenth of the kth subsection of the path planned by the ith individual to the center of the threat area jjIs the central position of the threat zone j, RjRadius of threat zone j, in practice, RjIs the outer contour radius, X, of the jth obstacle spacecrafti(t) is the three-dimensional coordinates of the ith individual position in the tth iteration.
When the planned path does not enter the threat zone, the fitness function is as follows:
in the above two formulae, tjCharacterizing the current threat level:
wherein the content of the first and second substances,
representing a vector pointing from the center position of threat zone j to the (i-1) th individual position,
representing a vector pointing from the ith-1 individual position to the ith individual position.
The path smoothness fitness function is:
wherein, M is the number of individuals,
representing a vector pointing from the i-2 nd individual position to the i-1 st individual position.
Spacecraft attitude orbit collaborative planning scheme
The problem of attitude and orbit planning of a spacecraft is a hotspot problem in the field of spaceflight, but currently existing researches mainly independently research attitude and orbit, and in practice, due to the change of the orbit of the spacecraft, the relative positions of an observation task target and other celestial bodies are also changed. Therefore, the planning problem of the track and the planning problem of the attitude are coupled, and the two problems are considered cooperatively.
Therefore, a model of a path planning space is established according to obstacles to be avoided when the spacecraft is in maneuvering orbit change, an obstacle area, the current position and the target position of the spacecraft are initialized, and the path planning of the spacecraft is carried out by using the algorithm. Then, on the basis of the completed path planning, an attitude planning model is established according to the relative relation between the path point and the attitude mandatory constraint and the restrictive constraint of the spacecraft, and the model is mapped into an R parameter space, so that the collaborative planning of the attitude orbit is completed by planning by using the self-adaptive pigeon group optimization method based on the chaotic population variation (hereinafter, referred to as CPAPIO algorithm) provided by the text, the coupled attitude orbit planning result is output, and the flow of the collaborative planning is shown in FIG. 3.
The method adopts the adaptive pigeon swarm algorithm of chaotic population variation to realize the collaborative planning of the attitude orbit of the spacecraft, and is shown in figure 4.
(1) Initializing pigeon flock positions and algorithm parameters
The Tent Map chaos theory is applied to the position initialization of the pigeon flock, so that the initialization positions of the pigeon flock are as uniform as possibleEvenly and irregularly dispersed throughout the planning space. And setting the number Q of the pigeon groups, the searching dimension D and the initialization position of the pigeon groups as X0＝[x0y0z0]The target position of the pigeon group is XD＝[xDyDzD]Number of iterations T of compass operator of map1Maximum number of iterations TMAXCenter coordinate T of jth threat zonej＝[xTyTzT]TRadius R of jth threat zonej。
(2) Starting map compass operator to perform population evolution
In order to increase the evolution depth of the population and avoid falling into the local optimal solution in the population evolution process as much as possible, compared with the traditional algorithm in which the global optimal solution is singly referenced, the population should determine the reference to the global optimal solution in the next iterative evolution according to the current evolution state. Therefore, the optimization operator of the adaptive improved map compass is innovatively designed as shown in the formulas (3) to (7).
(3) Local optimal solution separation
One problem common to the current same-type algorithms is that the population may fall into a locally optimal solution. However, the problem of how to make the population separate from the local optimal solution after the local optimal solution falls into the local optimal solution, and meanwhile, the problem that the population is not too active to make the algorithm diverge, and the problem that the algorithm separates from the global optimal solution after the global optimal solution is misjudged as the local optimal solution is a difficult problem. To solve the problem, mutation operators are designed in the algorithm. When the change rate of the population fitness value is continuously lower than 0.01 for 30 times, the population is likely to fall into a local optimal solution, at the moment, the half (namely the second half of individuals sorted according to the fitness value) of the pigeon population farther away from the current local optimal solution is mutated, a mutation operator generates a random number which takes the current value as the mean value and the reciprocal of the current fitness value change rate as the variance, and the random number is taken as a reference for subsequent evolution, so that the current solution is reserved. If the current solution is the local optimal solution, the second half of the population farther away from the solution can be separated from the solution after variation; if the current solution is already the global optimal solution, the evolution of the second half population will not produce a result superior to this solution, thus preserving the global optimal solution. And finally obtaining the optimization operator of the map compass as shown in the formulas (8) to (10).
(4) Starting a landmark operator for population evolution
In the landmark operator part of the original algorithm, the population reduction rate is too fast and even exceeds the population convergence rate, so the population reduction rate is designed, the population quantity is rapidly reduced in the early stage to screen dominant individuals, the dominant individuals are slowly reduced in the later stage to keep the dominant individuals, and the population quantity is updated according to the formula (11).
(5) Fitness function
And in the evolution process, the population is screened and sequenced according to the fitness function, and a local optimal solution and a global optimal solution are generated.
Simulation experiment and result verification
The experiment sets that the current maneuvering spacecraft is located at the origin (0,0, 0) KM of a coordinate system when starting maneuvering under a moving coordinate system, the target position is (65,80,30) KM, the relative position of the obstacle spacecraft in front of the orbital transfer spacecraft is (45,50,5) KM, (8,25,15) KM, (40,68,7) KM, and the minimum safe distance of the spacecraft is 5 KM.
The simulation experiment conditions are that a main core is a four-core 2.8Hz memory, a 16GB memory and a 64-bit computer, and the internal parameters of the algorithm are set as follows:
● classic PIO algorithm and improved PIO algorithm: the number of individuals M is 30, the planning dimension D is 20, and the number of iterations is 200 (map compass operator 150 times, landmark operator 50 times).
● particle swarm optimization: the number of individuals M is 30, the planning dimension D is 20, and the number of iterations is 200.
● chaos population variation adaptive pigeon swarm algorithm (CPAPIO algorithm): the number of individuals M is 30, the planning dimension D is 20, and the number of iterations is 200.
1.1 spacecraft orbit planning experiment result and algorithm performance comparison
The classic PIO algorithm track planning result is shown in fig. 5, the Particle Swarm Optimization (PSO) algorithm track planning result is shown in fig. 6, the chaotic population variation adaptive pigeon swarm optimization (CPVPAPIO) based improved algorithm track planning result is shown in fig. 7, the CPVPAPIO algorithm, the PIO algorithm and the PSO algorithm are calculated with costs shown in fig. 8, and the CPVPAPIO algorithm, the PIO algorithm and the PSO algorithm are calculated with quantities shown in table 1.
TABLE 1CPVAPIO Algorithm and PIO Algorithm and PSO Algorithm calculated quantity comparison
The attitude restrictive planning result obtained by the cpvpapo algorithm of the present application is shown in fig. 9, and the spacecraft attitude angle planning result obtained by the cpvpapo algorithm of the present application is shown in fig. 10.
Therefore, a self-adaptive pigeon swarm improved algorithm based on chaotic population variation is designed for the attitude orbit collaborative planning problem of the spacecraft under complex constraint, and the attitude planning space of the spacecraft is mapped into the Rodrigues parameter space for planning so as to meet the problem of euler angle planning decoupling. Compared with the classical PIO algorithm and the PSO algorithm, the algorithm is smoother in planning result and can reduce unnecessary attitude and orbit adjustment; simulation results show that compared with PIO and PSO algorithms, the chaotic population variation adaptive pigeon population algorithm (CPAPIO algorithm) has deeper population evolution, the fitness reduction value is about 10, the other two algorithms are about 5, and meanwhile, the algorithm has higher convergence speed; and the improved algorithm greatly reduces the calculated amount and realizes the optimal planning of the spacecraft attitude orbit through comparison of the calculated amount.
Claims (10)
1. A spacecraft attitude orbit collaborative planning method based on chaotic population variation PIO is characterized in that a spacecraft path is planned by adopting an adaptive pigeon group algorithm based on chaotic population variation, an attitude planning model is established according to the relative relation of path nodes and attitude mandatory constraint and restrictive constraint of a spacecraft, the attitude planning model is mapped to an R parameter space, the spacecraft attitude is planned by adopting the adaptive pigeon group algorithm based on chaotic population variation and comprising a compass operator iterative evolution stage and a landmark operator iterative evolution stage to obtain a coupled attitude orbit planning result, wherein,
a compass operator iterative evolution stage: the method comprises the steps of selecting a local optimal position in the current iteration process and a global optimal position generated by all individuals in the current iteration process in each iteration process, introducing a global updating operator for showing the fact that the individuals learn about elite individuals generated by the whole pigeon group in the previous iteration, an adaptive operator for showing the evolution trend of the previous two iterations and a mutation operator for carrying out mutation operation on the pigeon group, iteratively updating the position and the speed of the individuals, starting the mutation operator only when the population adaptation degree change rate reaches a judgment threshold value, generating a random number which takes the current position of the individuals as a mean value and the inverse of the current population adaptation degree change rate as a variance after the mutation operator is started, and entering a landmark operator iterative evolution stage when the current iteration number reaches a set value.
2. The collaborative planning method for spacecraft attitude orbit based on the PIO (particle swarm optimization) based on the chaotic population variation of claim 1,
and (3) a landmark operator iterative evolution stage: and screening the population according to the population fitness so as to iteratively update the local optimal individual and the global optimal individual.
3. The collaborative planning method for spacecraft attitude orbits based on chaotic population variation (PIO) according to claim 2, characterized in that the compass operator is described as:
Vi(t)、Vi(t +1) is the speed of the ith individual in the t-th iteration and the t +1 th iteration, respectively, Xi(t)、Xi(t +1) is the position of the ith individual in the t-th iteration and the t + 1-th iteration respectively, w is an inertia factor,
wmaxand wminMaximum and minimum values of the inertia factor, TmaxIn order to be the maximum number of iterations,
for the local optimum position of the ith individual in the t-th iteration, CpIn order to adapt the operator, the operator is,
the fitness (t-3), the fitness (t-2) and the fitness (t-1) are fitness values of the population in the t-3 th iteration, the t-2 th iteration and the t-1 th iteration respectively, and X isgFor the global optimal position of all individuals in the t-th iteration, CgIn order to update the operator globally,
Crin order to activate the factor(s),
Rd(t +1) is the random number generated by the mutation operator in the t +1 th iteration,
fitness (t) is the fitness value of the population in the tth iteration.
4. The collaborative planning method for spacecraft attitude orbits based on chaotic population variation PIO according to claim 2, characterized in that the population fitness is determined by the fitness of each individual, and the fitness (i) of the ith individual has the expression:
fit (i) is the fitness of the ith individual, threat _ inj(i)、w1Threat _ out is the threat level and weight of the ith individual entering the threat zone jj(i)、w2The threat degree and the weight of the ith individual outside the threat zone j, distance (i), w3Planning a path for the ith individualThe influence degree of the overall distance consumption on the overall planning distance and the weight thereof, angle (i), w4Maneuver angles and weights, w, for the ith individual to plan a path1+w2+w1+w4＝1。
5. The collaborative planning method for spacecraft attitude orbit based on PIO (particle swarm optimization) based on chaotic population variation according to claim 4, characterized in that the threat degree threat _ in of the ith individual entering a threat zone jj(i) Comprises the following steps:
Li,klength, t, of kth segment of path planned for ith individualjThe threat level of the threat zone j, K is the number of segments of the planned path of the ith individual, d0.1,k、d0.3,k、d0.5,k、d0.7,k、d0.9,kThe distances T from one tenth, three tenth, five tenth, seven tenth and nine tenth of the kth subsection of the path planned by the ith individual to the center of the threat area jjIs the central position of the threat zone j, RjRadius of threat zone j, Xi(t) is the three-dimensional coordinates of the ith individual position in t iterations.
6. The collaborative planning method for spacecraft attitude orbit based on PIO (particle image analysis) with chaotic population variation according to claim 4, characterized in that the threat degree threat _ out of the ith individual is outside a threat zone jj(i) Comprises the following steps:
tjthe threat level of the threat zone j, K is the number of segments of the planned path of the ith individual, d0.1,k、d0.3,k、d0.5,k、d0.7,k、d0.9,kThe distances T from one tenth, three tenth, five tenth, seven tenth and nine tenth of the kth subsection of the path planned by the ith individual to the center of the threat area jjIs the central position of the threat zone j, RjRadius of threat zone j, Xi(t) is the three-dimensional coordinates of the ith individual position in t iterations.
7. The collaborative planning method for spacecraft attitude orbits based on PIO (particle image analysis) based on chaotic population variation (5) or (6), characterized in that threat level t of threat zone jjComprises the following steps:
representing a vector pointing from the center position of threat zone j to the (i-1) th individual position,
representing a vector pointing from the ith-1 individual position to the ith individual position.
8. The collaborative planning method for spacecraft attitude orbits based on the PIO (chaotic population variation) as claimed in claim 4, wherein the maneuvering angle (i) of the ith individual planning path is:
m is the number of the individuals,
representing a vector pointing from the i-2 nd individual position to the i-1 st individual position,
representing a vector pointing from the ith-1 individual position to the ith individual position.
9. The collaborative planning method for spacecraft attitude orbit based on chaotic population variation (PIO) of claim 2, characterized in that landmark operator iterative evolution orderThe segment is according to the expression:
update population number, NP(T) is the population number of the T-th iteration, N is the population number, TmaxIs the maximum number of iterations.
10. The collaborative planning method for spacecraft attitude orbits based on the chaotic population variation PIO according to claim 2, characterized in that a Tent Map is adopted to Map the chaotic initialization population before the iterative evolution stage of compass operators begins.
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