Method for designing multi-satellite rendezvous orbit of Walker constellation without maneuvering of single satellite under rendezvous constraint

Abstract

The invention discloses a method for designing a multi-satellite rendezvous orbit of a Walker constellation without maneuvering of a single satellite under rendezvous constraint, which is characterized in that service satellites are respectively configured for each orbit surface of the Walker constellation, the orbit period difference between the service satellites and constellation satellites is designed, and the traversal rendezvous of the service satellites with all satellites in a target orbit surface without maneuvering is realized. Designing and modeling other orbit parameters into an optimization problem with intersection condition constraints, fusing the intersection condition constraints into an optimization target in a penalty function form, and performing parameter optimization by adopting a genetic algorithm, so as to generate an orbit design scheme meeting the requirement of sequential continuous intersection. The method is suitable for task planning such as periodic patrol reconnaissance and on-orbit service of Walker constellation orbit plane satellites, an efficient and feasible intersection orbit preliminary scheme can be quickly generated in the initial stage of a task, and a good foundation is provided for subsequent task orbit design considering complex factors such as perturbation.

Description

Technical Field

[0001] This invention belongs to the field of satellite orbit design, specifically relating to a rendezvous constraint method for designing rendezvous orbits of a single satellite to multiple satellites in the Walker constellation without maneuvering. Background Technology

[0002] The Walker constellation, with its strong global coverage, high temporal resolution, and good system redundancy, has been widely used in remote sensing, communication, and navigation. To achieve tasks such as status monitoring, on-orbit servicing, and fault detection of the constellation's satellites, a servicing satellite typically needs to be able to sequentially rendezvous with multiple satellites in the constellation without significant orbital maneuvers, while satisfying specific rendezvous geometry and dynamic constraints. Therefore, rationally designing the servicing satellite's mission orbit is crucial for improving mission efficiency and conserving propellant consumption.

[0003] Orbit design based on a two-body orbit model can effectively reflect the basic laws of satellite orbital motion, avoid interference from complex perturbation factors, and is suitable for rapid scheme generation in the early stages of a mission. Currently, existing methods for orbit design of single-satellite rendezvous with multiple stars in a constellation without maneuvering do not systematically consider the constraints of rendezvous distance, velocity, and angle required in actual missions, and lack a complete and universal orbit design process. Therefore, there is an urgent need to develop a rendezvous-constrained single-satellite rendezvous orbit design method for multiple stars in the Walker constellation without maneuvering. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for designing rendezvous orbits of a single star to multiple stars in the Walker constellation without maneuvering, in order to overcome the defects of the prior art.

[0005] The present invention provides a single-satellite rendezvous orbit design method for multiple satellites in the Walker constellation without maneuvering, which involves configuring service satellites for each orbital plane of the Walker constellation. Utilizing the characteristic of satellites in the same orbital plane of the constellation being distributed with equal phase intervals, the semi-major axis of the service satellite's orbit is designed so that the service satellite can naturally traverse and rendezvous with all satellites in the orbital plane. The design of the remaining orbital parameters is then modeled as an optimization problem with rendezvous constraints. The rendezvous constraints are transformed into penalty functions and incorporated into the optimization objective function. Finally, a genetic algorithm is used to optimize the orbital parameters. The design method includes the following steps: S1. Determine the input parameters for the track design task; Obtain the orbital parameters of the target Walker constellation satellites, including their semi-major axes. Track inclination Right ascension of ascending node Phase difference with adjacent satellites in the orbital plane ; Define the rendezvous task constraints, including: Intersection distance constraints: , Meeting speed constraints: , Intersection angle constraints: ; in, For the meeting distance, , These are the lower and upper limits of the permissible meeting distance, respectively. The rendezvous speed value. , These are the lower and upper limits of the permissible meeting speed, respectively. For the angle of intersection, , These are the lower and upper limits of the permissible angle of intersection, respectively. S2. Determine the design variables and parameter space for the service satellite's orbital parameters; Based on the orbital period requirement of the service satellite for traversing the intersection line between the service satellite and the target orbital satellite, the orbital period of the service satellite is calculated. : ; in, It is the gravitational constant; The semi-major axis of the target orbital plane satellite, The phase difference between satellites in adjacent target orbital planes. Then calculate the semi-major axis of the service satellite's orbit. : ; Determine the design variables of the orbital parameters to be optimized. ,in, For eccentricity, For the track inclination angle, Right ascension of the ascending node, The perigee argument; and the orbital parameter space is set as follows: ; in, For the Earth's radius, The minimum perigee altitude allowed for the service satellite, , These are the lower and upper limits of the permissible orbital inclination angle, respectively. , These are the lower and upper limits of the permissible right ascension of the ascending node, respectively. , These are the lower and upper limits of the permissible perigee angle, respectively; S3. Establish intersection constraint equations; S31. Establish the intersection distance constraint equation; Calculate the geocentric distance of the service satellites at the rendezvous point. : ; in, The true anterior angle of the service star at the intersection point; ; Calculate the intersection distance : ; Establish constraint equations: ; S32. Establish the intersection velocity constraint equations; Calculate the velocity vector of the service satellite at the intersection point. : ; in, , These are the unit vectors of the pericenter and the semi-circle of the service satellite in the orbital coordinate system, respectively. Calculate the velocity vectors of the constellation satellites at the rendezvous point. : ; in, , These are the unit vectors of the pericenter and the semi-circle of the constellation satellites in the orbital coordinate system, respectively. The ascending intersection distance of the constellation satellites at the rendezvous point; Calculate the rendezvous velocity values ​​between the service satellite and the constellation satellites. : ; The intersection velocity constraint equations are obtained as follows: ; S33. Establish the intersection angle constraint equations; The intersection angle is calculated using the following formula. : ; in, For the orbital angular momentum vector of the constellation satellites; Establish constraint equations: ; S4. Optimize the construction and solution of the objective function; Construct an optimization objective function that includes intersection constraints: ; in, , , , These are the weighting factors for the corresponding terms of the objective function; A genetic algorithm is used to optimize the objective function and obtain the optimal orbital parameters. S5. Track design verification; Based on the optimized service satellite orbit parameters, a simulation scenario for the two-body orbit evolution and rendezvous between the service satellite and the target orbital plane satellite is established, and rendezvous simulation verification is performed.

[0006] Furthermore, in formulas (8) and (9), the true anomaly angle of the serving satellite at the intersection point is... Ascending distance of the satellites in the constellation at the rendezvous point It is obtained through the following process: Calculate the angular momentum vector of the service satellite : ; Calculate the angular momentum vector of constellation satellites : ; in, For the orbital inclination of the constellation satellites, Right ascension of the ascending nodes of the constellation satellites; Find the unit vector of the intersection line of the orbital planes. : ; Calculate the unit position vector of the service satellite at perigee. : ; Furthermore, we can obtain: ; Ascending distance of constellation satellites at the rendezvous point Calculate using the following formula: ; in, .

[0007] Furthermore, in formulas (8) and (9), the unit vector of the pericenter of the service satellite in the orbital coordinate system... and semi-pipe unit vector Calculated using the following two formulas: .

[0008] Furthermore, the optimization solution of the genetic algorithm includes the following steps: S41. Population Initialization: Designing variables in orbital parameters Randomly generated within the parameter space of size N The initial population; S42. Fitness assessment: Calculate the objective function value for each individual as its fitness; S43. Selection operation: Sort by fitness from lowest to highest, and select the top 5% of individuals to be directly retained to the next generation; S44. Crossover operation: Perform crossover with a probability of 0.7 to generate new individuals. and : ; in, and 'c' represents the parent individuals to be crossed, and 'c' represents the randomly selected crossover point position. S45. Mutation operation: Mutate with a probability of 0.3: ; in, Design variables for orbital parameters The i One element, for The value after performing the mutation operation. and for The lower and upper limits of the allowed values. The result is a Gaussian random number with a mean of 0 and a standard deviation of 1. Values ​​exceeding the boundary after the mutation operation are handled using the reflection method: ; S46. Population Update: Replace the original population with all individuals obtained through selection, crossover, and mutation operations to form a new generation of population; S47. Termination condition judgment: Output the optimal solution when the maximum number of iterations is reached.

[0009] The rendezvous constraint-based single-star rendezvous orbit design method for multiple stars in the Walker constellation, which does not require maneuvering, embeds constraints such as rendezvous distance, velocity, and angle during the orbit design stage, effectively improving the mission applicability and engineering application value of the design results. By employing a genetic algorithm for global optimization, it avoids the problem of traditional gradient-based methods easily getting trapped in local optima, and can obtain a near-globally optimal orbit scheme that satisfies complex rendezvous constraints. At the same time, it rapidly generates high-quality initial orbit schemes under a two-body orbit model, and achieves natural ergodic rendezvous by accurately matching orbital periods and phases. This lays a good foundation for subsequent orbit design of single-star rendezvous missions for multiple stars in the constellation that do not require large orbital maneuvers, taking perturbation factors into account.

[0010] The rendezvous constraint single-satellite rendezvous orbit design method for multiple satellites in the Walker constellation without maneuvering, utilizes a genetic algorithm to optimize satellite orbital parameters. This method enables a single serving satellite to sequentially traverse and rendezvous with all satellites in a specified orbital plane within the Walker constellation without maneuvering, while satisfying preset rendezvous constraints.

[0011] The rendezvous constraint single-satellite rendezvous orbit design method for multiple satellites in the Walker constellation without maneuvering, as described in this invention, is applicable to mission planning for periodic reconnaissance and on-orbit servicing of satellites in the Walker constellation orbital plane. It can quickly generate efficient and feasible preliminary rendezvous orbit schemes in the early stages of a mission and provide a good foundation for subsequent mission orbit design that takes into account complex factors such as perturbations. Attached Figure Description

[0012] The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. Furthermore, the same reference numerals denote the same parts throughout the drawings.

[0013] Figure 1 A flowchart illustrating the rendezvous constraint single-star rendezvous orbit design method for multiple stars in the Walker constellation without maneuvering, as described in this invention. Figure 2 This is a schematic diagram illustrating the change in fitness function value with the number of population iterations when using a genetic algorithm to optimize orbital parameters in Example 1. Detailed Implementation

[0014] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0015] The present invention provides a single-satellite rendezvous orbit design method for multiple satellites in the Walker constellation without maneuvering, which involves configuring service satellites for each orbital plane of the Walker constellation. Utilizing the characteristic of satellites in the same orbital plane of the constellation being distributed with equal phase intervals, the semi-major axis of the service satellite's orbit is designed so that the service satellite can naturally traverse and rendezvous with all satellites in the orbital plane. The design of the remaining orbital parameters is then modeled as an optimization problem with rendezvous constraints. The rendezvous constraints are transformed into penalty functions and incorporated into the optimization objective function. Finally, a genetic algorithm is used to optimize the orbital parameters. like Figure 1 As shown, the design method includes the following steps: S1. Determine the input parameters for the track design task; Obtain the orbital parameters of the target Walker constellation satellites, including their semi-major axes. Track inclination Right ascension of ascending node Phase difference with adjacent satellites in the orbital plane ; Define the rendezvous task constraints, including: Intersection distance constraints: , Meeting speed constraints: , Intersection angle constraints: ; in, For the meeting distance, , These are the lower and upper limits of the permissible meeting distance, respectively. The rendezvous speed value. , These are the lower and upper limits of the permissible meeting speed, respectively. For the angle of intersection, , These are the lower and upper limits of the permissible angle of intersection, respectively. S2. Determine the design variables and parameter space for the service satellite's orbital parameters; Based on the orbital period requirement of the service satellite for traversing the intersection line between the service satellite and the target orbital satellite, the orbital period of the service satellite is calculated. : ; in, It is the gravitational constant; The semi-major axis of the target orbital plane satellite, The phase difference between satellites in adjacent target orbital planes. Then calculate the semi-major axis of the service satellite's orbit. : ; Determine the design variables of the orbital parameters to be optimized. ,in, For eccentricity, For the track inclination angle, Right ascension of the ascending node, The perigee argument; and the orbital parameter space is set as follows: ; in, For the Earth's radius, The minimum perigee altitude allowed for the service satellite, , These are the lower and upper limits of the permissible orbital inclination angle, respectively. , These are the lower and upper limits of the permissible right ascension of the ascending node, respectively. , These are the lower and upper limits of the permissible perigee angle, respectively; S3. Establish intersection constraint equations; S31. Establish the intersection distance constraint equation; Calculate the geocentric distance of the service satellites at the rendezvous point. : ; in, The true anterior angle of the service star at the intersection point; ; Calculate the intersection distance : ; Establish constraint equations: ; S32. Establish the intersection velocity constraint equations; Calculate the velocity vector of the service satellite at the intersection point. : ; in, , These are the unit vectors of the pericenter and the semi-circle of the service satellite in the orbital coordinate system, respectively. Calculate the velocity vectors of the constellation satellites at the rendezvous point. : ; in, , These are the unit vectors of the pericenter and the semi-circle of the constellation satellites in the orbital coordinate system, respectively. The ascending intersection distance of the constellation satellites at the rendezvous point; Calculate the rendezvous velocity values ​​between the service satellite and the constellation satellites. : ; The intersection velocity constraint equations are obtained as follows: ; S33. Establish the intersection angle constraint equations; The intersection angle is calculated using the following formula. : ; in, For the orbital angular momentum vector of the constellation satellites; Establish constraint equations: ; S4. Optimize the construction and solution of the objective function; Construct an optimization objective function that includes intersection constraints: ; in, , , , These are the weighting factors for the corresponding terms of the objective function; A genetic algorithm is used to optimize the objective function and obtain the optimal orbital parameters. S5. Track design verification; Based on the optimized service satellite orbit parameters, a simulation scenario for the two-body orbit evolution and rendezvous between the service satellite and the target orbital plane satellite is established, and rendezvous simulation verification is performed.

[0016] Furthermore, in formulas (8) and (9), the true anomaly angle of the serving satellite at the intersection point is... Ascending distance of the satellites in the constellation at the rendezvous point It is obtained through the following process: Calculate the angular momentum vector of the service satellite : ; Calculate the angular momentum vector of constellation satellites : ; in, For the orbital inclination of the constellation satellites, Right ascension of the ascending nodes of the constellation satellites; Find the unit vector of the intersection line of the orbital planes. : ; Calculate the unit position vector of the service satellite at perigee. : ; Furthermore, we can obtain: ; Ascending distance of constellation satellites at the rendezvous point Calculate using the following formula: ; in, ; Furthermore, in formulas (8) and (9), the unit vector of the pericenter of the service satellite in the orbital coordinate system... and semi-pipe unit vector Calculated using the following two formulas: .

[0017] Furthermore, the optimization solution of the genetic algorithm includes the following steps: S41. Population Initialization: Designing variables in orbital parameters Randomly generated within the parameter space of size N The initial population; S42. Fitness assessment: Calculate the objective function value for each individual as its fitness; S43. Selection operation: Sort by fitness from lowest to highest, and select the top 5% of individuals to be directly retained to the next generation; S44. Crossover operation: Perform crossover with a probability of 0.7 to generate new individuals. and : ; in, and 'c' represents the parent individuals to be crossed, and 'c' represents the randomly selected crossover point position. S45. Mutation operation: Mutate with a probability of 0.3: ; in, Design variables for orbital parameters The i One element, for The value after performing the mutation operation. and for The lower and upper limits of the allowed values. The result is a Gaussian random number with a mean of 0 and a standard deviation of 1. Values ​​exceeding the boundary after the mutation operation are handled using the reflection method: ; S46. Population Update: Replace the original population with all individuals obtained through selection, crossover, and mutation operations to form a new generation of population; S47. Termination condition judgment: Output the optimal solution when the maximum number of iterations is reached.

[0018] Example: The semi-major axis of the Walker constellation reference satellite in this example. 950km, orbital inclination 81°, right ascension of the ascending node 82.6°, ascending angle distance The constellation has 12 orbital planes, with 7 satellites deployed in each plane, for a total of 84 satellites. The phase difference between adjacent satellites within each orbital plane is... In the orbit design mission, the rendezvous targets of the service satellites are all satellites in the orbital plane of the Walker constellation's reference satellites. The rendezvous mission constraints are set as follows: , , The relevant parameters in formula (3) are set as follows: , , , , , , The relevant parameters in formula (14) are set as follows: , , , When using a genetic algorithm to optimize orbital parameters, the initial population size is set to N=500 and the maximum number of iterations is set to 500. During the optimization process, the optimal fitness function value changes with the number of population iterations as follows: Figure 2 As shown. The final service satellite orbit design result is: semi-major axis eccentricity Track inclination Right ascension of ascending node Perimeter argument When the service satellite rendezvous with all satellites in the target orbital plane of the Walker constellation, the rendezvous distance is... Meeting speed Intersection angle The above results demonstrate that the rendezvous constraint single-star maneuver-free rendezvous orbit design method for multiple stars in the Walker constellation of the present invention can provide orbit design schemes that meet mission design requirements.

[0019] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. For those skilled in the art, all features disclosed in the present invention, or all steps in all methods or processes disclosed, except for mutually exclusive features and / or steps, can be combined in any way without departing from the principles of the present invention. The present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A method for designing a multi-satellite encounter orbit of Walker constellation without single satellite maneuver, characterized in that, The service satellite is configured for each orbit plane of Walker constellation, and the orbit semi-major axis of the service satellite is designed according to the equal phase interval distribution characteristics of the satellites in the same orbit plane of the constellation, so that the service satellite can naturally traverse and meet all the satellites in the orbit plane; and the design of the remaining orbit parameters is modeled as an optimization problem with a meeting condition constraint, the meeting constraint is converted into a penalty function form and incorporated into the optimization objective function, and the genetic algorithm is used to optimize the design of the orbit parameters; The design method comprises the following steps: S1. determining the input parameters of the orbit design task; Obtain the orbital parameters of the Walker constellation target orbit plane satellite to be accessed, including the orbital semi-major axis of the target orbit plane satellite , the orbital inclination , the ascending node right ascension , and the phase difference of the adjacent satellite in the orbit plane ; The meeting task constraint conditions are set, including: Intersection distance constraint: , Intersection velocity constraint: , Intersecting angle constraints: ; wherein, is the intersection distance, , are, respectively, a lower limit of tolerance and an upper limit of tolerance of the intersection distance; is the intersection speed value, , are, respectively, a lower limit of tolerance and an upper limit of tolerance of the intersection speed value; is the intersection angle, , are, respectively, a lower limit of tolerance and an upper limit of tolerance of the intersection angle; S2. determining the design variables and their parameter space of the orbit parameters of the service satellite; Based on the orbit period requirement of the service satellite for traversing the intersection with the target satellite at the intersection line of the orbit planes, the orbit period of the service satellite is calculated : ； wherein is the gravitational constant; is the semi-major axis of the target orbit plane satellite, is the phase difference between adjacent target orbit plane satellites, Further, the orbit semi-major axis of the service satellite is calculated : ； determining the orbit parameter design variables to be optimized wherein is the eccentricity, is the inclination, is the longitude of the ascending node, is the argument of the perigee; and setting the orbit parameter space as: ； wherein, is the Earth radius, is the minimum perigee altitude allowed for the service star, , are the lower limit of the allowed range of the orbit inclination value, the upper limit of the allowed range of the orbit inclination value, respectively; , are the lower limit of the allowed range of the ascending node right ascension, the upper limit of the allowed range of the ascending node right ascension, respectively; , are the lower limit of the allowed range of the perigee argument, the upper limit of the allowed range of the perigee argument, respectively; S3. establishing a meeting constraint equation; S31. establishing a meeting distance constraint equation; Computing the geocentric distance of a service satellite at an encounter point : ； wherein, is the true anomaly of the service star at the point of intersection; ； Computing the intersection distance : ； The constraint equation is established: ； S32. establishing a meeting speed constraint equation; Computing the velocity vector of a service satellite at the point of intersection : ； wherein, , are the pericenter unit vector and the semi-major axis unit vector of the service satellite in the orbital coordinate system, respectively. Computing the velocity vector of a constellation satellite at an intersection point : ； in, , These are the unit vectors of the pericenter and the semi-circle of the constellation satellites in the orbital coordinate system, respectively. The ascending intersection distance of the constellation satellites at the rendezvous point; Computing the value of the velocity of the intersection of a service star with a constellation of satellites : ； The meeting speed constraint equation is obtained: ； S33. establishing a meeting angle constraint equation; The intersection angle is calculated according to the following formula : ； wherein is the orbital momentum vector of the constellation satellite; The constraint equation is established: ； S4. optimization objective function construction and solution; The optimization objective function containing the meeting constraint is constructed: ； wherein , , , is a weight factor for the corresponding term of the objective function; The genetic algorithm is used to optimize and solve the objective function, and the optimal orbit parameters are obtained; S5. orbit design verification; Based on the optimized orbit parameters of the service satellite, a two-body orbit evolution and meeting simulation scene of the service satellite and the satellites in the reference orbit plane is established, and the meeting simulation verification is performed.

2. The method of claim 1, wherein the method is a method of rendezvous constrained single-impulsive maneuver for Walker constellation multi-spacecraft transfer orbit design. In the above formula (8) and formula (9), the true anomaly of the service satellite at the intersection point is and the elevation angle distance of the constellation satellite at the intersection point is obtained by the following process: Computing the momentum vector of a service star : ； Computing momentum vector of a constellation satellite : ； wherein, is the inclination of the constellation satellite orbit, is the right ascension of the ascending node of the constellation satellite. The unit vector of the intersection line of the orbital planes is obtained : ； Unit position vector of the computing service satellite at perigee : ； Further, the following is obtained: ； The ascending node argument of the constellation satellite at the point of intersection is calculated as follows: ； Wherein, 。 3. The method of claim 2, wherein the method is a method of rendezvous constrained single-impulsive maneuver to Walker constellation multi-spacecraft rendezvous orbit design. In the formula (8) and formula (9), the perigee unit vector of the service satellite in the orbit coordinate system And the semi-radial unit vector Is calculated by the following two formulas: 。 4. The method of claim 1, wherein the method is a method of rendezvous constrained single-impulsive maneuver-free orbit design for a multi-satellite rendezvous with Walker constellation, characterized in that, The optimization solution of the genetic algorithm comprises the following steps: S41. Initialize population: Randomly generate an initial population of size Npop within the parameter space of the orbital parameter design variables S42. Evaluate population: Evaluate the fitness of each individual in the initial population N S43. Select population: Select the best individuals from the initial population S42. fitness evaluation: calculate the objective function value of each individual as the fitness; S43. selection operation: sort the individuals according to the fitness from small to large, and select the first 5% of the individuals to be directly reserved to the next generation; S44. Crossover operation: crossover is performed with a crossover probability of 0.7 to generate new individuals and : ； wherein, and are parent individuals to be crossed, c is a randomly selected crossing point position; S45. mutation operation: mutation is performed according to a mutation probability of 0.3: ； wherein, is a design variable for the track parameter is the i element of the is is the value after performing the mutation operation, and is the is the lower limit of the allowable value, the upper limit of the allowable value, is a Gaussian random number with mean 0, standard deviation 1; The values exceeding the boundary after the mutation operation are processed by the reflection method: ； S46. update population: replace the original population with all the individuals obtained by the selection, crossover and mutation operations to form a new generation population; S47. termination condition judgment: when the maximum number of iterations is reached, the optimal solution is output.

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