Multi-target grazing method based on water drop type relative motion characteristic parameters under illumination constraint

Abstract

The invention discloses a multi-target grazing method based on water drop type relative motion characteristic parameters under illumination constraint. The method comprises the following steps: establishing a mathematical model containing observation distance constraint and sunlight angle constraint; dividing the grazing flight process of each target satellite into a close-range grazing flight section and a long-range guide section, designing a close-range grazing flight section track based on water drop configuration characteristic parameters of a C-W equation, and realizing orbit transfer of the long-range guide section by adopting double-pulse Lambert transfer; and designing an objective function composed of the speed increment, the effective observation time and a penalty term, and optimizing the grazing trajectory parameters of multiple targets in a short-distance grazing section and a long-distance guide section by adopting a particle swarm algorithm to obtain a one-to-many grazing trajectory in which the speed increment meets the requirement and the effective observation time exists for each target. According to the invention, by optimizing the long-distance guide section and the short-distance sweep flight section, rapid sweep flight observation of a single spacecraft on a plurality of targets is realized.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft orbit design and control technology, specifically relating to a multi-target flyby method based on teardrop-shaped relative motion characteristic parameters under illumination constraints. Background Technology

[0002] Fly-by-fly observation is a close-range spacecraft reconnaissance technique. It refers to a method where an observation spacecraft flies at relatively high speeds within a certain area around a target spacecraft, observing and collecting data on the target spacecraft within a short period of time. Unlike other close-range observation methods such as fly-around and escort, fly-by-fly observation typically does not maintain a close distance to the target spacecraft for an extended period. Instead, it quickly passes over the target, utilizing the brief opportunity of approach to obtain characteristic information about the target. Considering the launch cost of spacecraft, using a single spacecraft to fly-by-fly over multiple targets can minimize fuel consumption and significantly reduce the research, development, manufacturing, launch, and maintenance costs of spacecraft.

[0003] However, existing technologies still have the following shortcomings in the design of multi-target flyby trajectories and the coordinated optimization of illumination constraints: (1) Insufficient consideration of illumination constraints. Existing research mainly focuses on long-distance guidance and mission timing planning, but ignores the illumination conditions required for optical imaging (such as sunlight angle and observation distance), which makes it difficult to guarantee the quality of actual observation data. (2) Limitations of single-target optimization. Some scholars have achieved single-target flyby by optimizing pulse maneuvers, but it is sensitive to initial values ​​and has not been extended to multi-target scenarios; or they have designed non-maneuver flyby trajectories based on binary star theory, but its applicability is limited by the distribution of targets and cannot actively meet observation constraints. (3) Mismatch between trajectory configuration and mission requirements. Some studies have used the revisit characteristics of teardrop-shaped trajectories to achieve natural flyby, but fixing the teardrop vertex to the coordinate axis will cause the target to be located inside the teardrop, requiring frequent adjustments to the spacecraft attitude, which is not conducive to stable communication and covert observation.

[0004] Therefore, current methods are unable to simultaneously meet the requirements of mission efficiency (optimal fuel, time allocation), optical imaging constraints (illumination angle, distance), and trajectory controllability (collision avoidance, attitude stability) for multi-target flyby observation. There is an urgent need for an optimization method that integrates illumination constraints and droplet-shaped trajectory parameterization design to achieve efficient and reliable multi-target flyby observation. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a multi-target flyby method based on droplet-shaped relative motion characteristic parameters under illumination constraints. Based on the typical trajectory characteristics of the linearized relative motion equation, it enables the observation of multiple targets under any given flyby sequence.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A multi-target flyby method based on droplet-shaped relative motion characteristic parameters under illumination constraints includes:

[0008] Step 1: Establish a mathematical model that includes observation distance constraints and sunlight angle constraints;

[0009] Step 2: Divide the flyby process of each target star into a close flyby segment and a long-range guidance segment. Based on the droplet configuration feature parameters of the CW equation, extract the trajectory design parameters for the close flyby segment. Use double-pulse Lambert transfer to realize the orbit transfer for the long-range guidance segment, and give the trajectory design parameters for the long-range guidance segment.

[0010] Step 3: Design an objective function consisting of velocity increment, effective observation time, and penalty term. Use particle swarm optimization to optimize the grazing trajectory parameters of multiple targets in the close-range grazing phase and the long-range guidance phase, and obtain a one-to-many grazing trajectory with velocity increment less than the maximum value and effective observation time for each target.

[0011] Furthermore, in step 1, the observation distance constraint is the relative distance between the target star and the tracking star. The upper and lower bounds are defined as 20km-80km, and the sunlight angle constraint is the angle between the relative position vector of the tracking star and the target star and the illumination vector. Limited to 0 to 60°.

[0012] Furthermore, in step 2, the close-range flyby segment is calculated in the local vertical-horizontal rectangular coordinate system LVLH, and the long-range guidance segment is calculated in the geocentric equatorial inertial coordinate system ECI.

[0013] Furthermore, the close-range flyby segment is used to observe the target star under the constraints of a mathematical model based on a droplet configuration, without any maneuvers throughout the entire process. The long-range guidance segment is used to shorten the relative distance between the tracking star and the target star. The tracking star is transferred from its original orbit to the droplet flyby orbit of the close-range flyby segment by applying two pulses.

[0014] Furthermore, in step 2, the droplet configuration description relative motion trajectory characteristic parameters based on the CW equation include the polar coordinates of the droplet vertex and the droplet vertex revisit time interval. The polar coordinates of the droplet vertex satisfy the observation distance constraint and the sunlight angle constraint (1), and the droplet vertex revisit time interval is less than the orbital period of the target star.

[0015] Furthermore, the optimization variable for the long-range guidance segment is selected as the waiting time before the Lambert transfer. Lambert transfer time The waiting time for the Lambert trajectory terminal to fly to the upper bound of the observation distance constraint .

[0016] Furthermore, after obtaining the polar coordinates of the droplet vertex and the revisit time interval of the droplet vertex, the relative motion state of the tracking star when entering the upper bound of the observation distance constraint is obtained based on the solution of the CW equation. The time it takes to fly from the upper bound of the observation distance constraint to the tip of the droplet. Based on the absolute state of the target star The relative motion state of the tracking star Find the absolute state of the tracking star under ECI at this time. ;

[0017] The absolute state of the tracking star under ECI Inverse numerical integration using the exact two-body dynamics equation (11) Determine the absolute state of the tracking star after the second pulse. , This represents the terminal position of Lambert's transfer trajectory. This indicates the velocity after the second pulse; it represents the initial absolute motion state of the tracked star under ECI. Using the exact two-body dynamics equation (11) for forward integration Find the initial state of the Lambert transition. , This is the initial position of Lambert's transfer trajectory. Indicates the velocity before the first pulse. Indicates the initial absolute position. Indicates the initial absolute velocity;

[0018] Initial position based on Lambert transfer trajectory Terminal location and Lambert transfer time The velocity at the initial position on Lambert's transfer trajectory is obtained using the Gooding method. and the speed of the terminal position , representing the velocity after the first pulse and the velocity before the second pulse, respectively, therefore, the total velocity increment required for long-distance transfer. ,in This represents the 2-norm of a vector.

[0019] Furthermore, in step 3, the overall objective function is the sum of the objective functions of the tracking satellite flying over individual target satellites; the effective observation time evaluation is performed under LVLH, and only the time period that simultaneously satisfies the observation distance constraint and the sunlight angle constraint is recorded as the effective observation time; the penalty term is used to prevent the tracking satellite from entering the target's no-fly zone and guide the tracking satellite to complete the flying over n targets, so that the effective observation time for each target is greater than the shortest time required for imaging. .

[0020] In a second aspect, the present invention provides an electronic device, comprising: one or more processors; and a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned multi-target flyby method based on droplet-shaped relative motion characteristic parameters under illumination constraints.

[0021] Thirdly, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enable the processor to implement the aforementioned multi-target fly-by method based on droplet-shaped relative motion characteristic parameters under illumination constraints.

[0022] The beneficial effects of this invention are as follows:

[0023] Highly efficient multi-target observation: By optimizing the trajectory design of the long-range guidance phase and the close-range flyby phase, a single spacecraft can quickly flyby observe multiple targets, significantly reducing fuel consumption and mission costs;

[0024] Precise fulfillment of illumination constraints: A mathematical model combining observation distance and sunlight angle constraints ensures that the optical camera acquires high-quality imaging data under optimal illumination conditions, thereby improving the effectiveness of observations;

[0025] Flexible and controllable trajectory optimization: Based on the droplet-shaped relative motion characteristic parameters and particle swarm algorithm, the nonlinear optimization problem of multi-target flyby is solved, taking into account both the minimization of fuel consumption and the maximization of effective observation time;

[0026] The project is highly practical: by setting up no-fly zones and implementing penalty mechanisms, it effectively avoids collision risks and optimizes mission time allocation, providing reliable technical support for actual space missions. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of the relative motion trajectory of a water droplet in the xOy plane;

[0028] Figure 2 A schematic diagram illustrating the time division of the single-target flyby phase;

[0029] Figure 3 Flowchart for calculating the objective function for a single particle;

[0030] Figure 4 The close-range flyby curve is the target of the embodiments of the present invention;

[0031] Figure 5 The observed trajectory curve of the flyby target in the embodiment of the present invention. Detailed Implementation

[0032] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0033] This invention provides a multi-target flyby method based on teardrop-shaped relative motion characteristic parameters under illumination constraints. The method first provides mathematical models for observation distance constraints and illumination angle constraints as engineering constraints in trajectory design. Then, the flyby of a single target is divided into two stages: a long-range guidance stage and a short-range flyby stage. The long-range guidance stage is implemented using a double-pulse Lambert transfer. Based on the characteristic parameters of the teardrop-shaped relative motion trajectory described by the CW equation, the trajectory design for the short-range flyby stage of a single target is transformed into a constrained parameter optimization problem. Finally, the particle swarm optimization algorithm is used to optimize 6n optimization variables of the flyby trajectories of n targets. The objective function is set as a linear combination of effective observation time, velocity increment, and penalty term. By assigning different magnitudes of penalty term values ​​to different cases, a reasonable distribution of effective observation time is achieved, enabling multi-target flyby observation. The implementation process of this invention is described in detail below:

[0034] First, the basic design premise is given. In this invention, the executor of the observation mission is called the tracking star, and the object being observed is called the target star (or target spacecraft). Two reference coordinate systems are used to describe the motion of the spacecraft:

[0035] (1) The Earth-centered Inertial (ECI) coordinate system is denoted as The coordinate system is a right-handed rectangular coordinate system in space. The origin is the Earth's center of mass. The axis is perpendicular to the Earth's equatorial plane and points towards the Earth's North Pole; The axis lies within the equatorial plane, pointing from the Earth's center to the vernal equinox; The axis also lies within the equatorial plane, and... axis, The axes form a right-handed coordinate system. The ECI coordinate system is often used when describing the motion of spacecraft near Earth in inertial space. In this invention, the long-range guidance segment is calculated in the ECI inertial frame.

[0036] (2) The spacecraft's local vertical-horizontal (LVLH) spatial rectangular coordinate system is denoted as With the spacecraft's center of mass O as the origin and its orbital plane as the reference plane, The axis points from the Earth's center to the spacecraft's center of mass, which is related to the spacecraft's position vector. Same direction; The axis is perpendicular to the orbital plane and is in the same direction as the spacecraft's orbital angular momentum relative to the Earth's center; The axis is located in the orbital plane, and axis, The axes together form a right-handed coordinate system. Spacecraft close approach missions are mostly conducted in the LVLH system, with the origin of the coordinate system being the target spacecraft's center of mass. In this invention, the close-range flyby segment is calculated in the LVLH system of the flyby target.

[0037] Step 1: Establish a mathematical model that includes observation distance constraints and sunlight angle constraints; good lighting conditions are the basis for effective imaging of optical cameras, which are mainly reflected in the orbital state constraints, namely the two parameters of apparent angle and relative distance.

[0038] The relative distance between the target and tracking stars, i.e., the object distance, is a crucial factor in determining the sharpness of a camera's image. A camera can only achieve a normal image when the object distance is greater than twice the focal length; beyond that, the smaller the object distance, the larger the image size. Therefore, if the target spacecraft is too close to the camera, the camera will be unable to capture a normal image or the image size will exceed the CCD panel; conversely, if the target spacecraft is too far from the camera, the image of the target will shrink to a single point, making it impossible to discern information about the object itself. Therefore, the relative distance between the target and tracking stars is crucial. It should be within a reasonable range, such as 20km-80km:

[0039] (1)

[0040] In the formula, , These are the lower and upper bounds of the relative distance constraint, respectively. The lower bound typically depends on the camera's focal length and the size of the CCD panel used for imaging, while the upper bound typically depends on the size of the target star and the camera's resolution. To ensure accuracy, during the observation feasibility assessment, the relative distance is obtained by subtracting the position vectors of the tracking star and the target star in the ECI inertial frame, i.e. ,in, To track the absolute position of the star under ECI, This represents the absolute position of the target star at the same time under ECI.

[0041] In the high-orbit space environment, there is a lack of atmospheric diffuse reflection. When an optical camera images a target, its line of sight needs to follow the sunlight so that the sunlight reflected from the target can enter the tracker's camera lens. In reality, due to the influence of the target spacecraft's shape and material on reflection, as well as the onboard camera's own resistance to backlighting, it is only necessary to ensure the angle between the line of sight and the light, i.e., the sunlight angle. As long as it's within the permissible range. Sunny Corner The solution can be found by the vector product of the relative distance vector and the ray, i.e.:

[0042] (2)

[0043] Since we only need to focus on the size of the angle between the line of sight and the light, Then, using the sunlight angle constraint, it can be expressed by the inequality:

[0044] (3)

[0045] In the formula, This is the lower limit of the sunlight angle. If it is set to 0°, it means that the camera's overexposure is ignored. This is the upper limit of the sunlight angle. Beyond this range, the intensity of sunlight directly hitting the tracker camera is much greater than the intensity of sunlight reflected from the target, resulting in a blurred target outline.

[0046] Step 2: Divide the flyby process of each target star into a close flyby segment and a long-range guidance segment. The relative motion trajectory characteristic parameters are described by the teardrop shape based on the CW equation. The trajectory design of the close flyby segment is transformed into a parameter optimization problem that meets the constraints of the mathematical model. The orbit transfer of the long-range guidance segment is realized by using a double-pulse Lambert transfer.

[0047] For ease of design, the basic form and state transition matrix of the linearized relative motion model of the spacecraft, the CW equations, are first given. It is assumed that the target operates in a circular or near-circular orbit, environmental disturbances are ignored, and the initial position error of the tracking spacecraft relative to the target is a small first-order quantity. Projecting the vector equations describing the relative motion into an LVLH frame with the target spacecraft's center of mass as the origin, and performing a Taylor expansion of the nonlinear terms of the resulting nonlinear equations while retaining the first-order terms, we obtain the Clohessy–Wiltshire equations, which only consider the control acceleration of the tracking spacecraft, and are simply referred to as the CW equations:

[0048] (4)

[0049] in, This is the component array of the control angular velocity vector acting on the tracking spacecraft in the LVLH frame. The superscript · denotes the first derivative, and the superscript ·· denotes the second derivative. Let be the angular velocity of the target spacecraft orbiting in the reference orbit, and its angular velocity relative to the semi-major axis of the reference orbit. satisfy:

[0050] (5)

[0051] In the formula, The gravitational constant of Earth is generally taken as... .

[0052] Choose the relative motion state of the tracker star in the target LVLH system. As state variables, equation (4) can be written in the form of a state equation:

[0053] (6)

[0054] In the formula, coefficient matrix and The expansion is as follows:

[0055] ,

[0056] Let the initial time Without control input, the CW equations become a system of first-order homogeneous differential equations with constant coefficients. The solution to the equations is:

[0057] (7)

[0058] In this context, the subscript 0 represents the initial time. The corresponding physical quantities, such as represent The relative motion state at any given moment; Let be the state transition matrix. To simplify the expression, let the intermediate parameters be... t represents the time it takes to track the star's flight from the initial moment. Let be the angular velocity of the target spacecraft orbiting in the reference orbit. Then, the component expansion of the state transition matrix is:

[0059] ,

[0060] ,

[0061] Planar relative motion trajectories based on the CW equations have four basic types: rugby ball maneuver, oscillating maneuver, teardrop maneuver, and straight-line maneuver. Among them, the teardrop maneuver is more general and has been widely used in actual rendezvous and docking and spacecraft hovering missions. The teardrop configuration has four characteristic parameters, including the teardrop revisit period. Vertex position parameters , , ,like Figure 1 As shown, only two of the first three feature parameters are independent. Adjustment It can change the geometry of the water droplet configuration and adjust it. and It can only scale the configuration up or down proportionally. If only the relative motion of the xOy plane in LVLH is considered, and Two parameters can determine the position of the droplet's vertex H. To ensure that the orbital time is controllable, only the droplet's revisit period needs to be determined. This allows for the unique determination of the relative motion trajectory of the water droplet.

[0062] The essence of the droplet configuration is the existence of self-intersections at positions. Assume that when the tracking star first passes through the droplet vertex H, its relative motion state is as follows: ,in, To track the star's first pass through point H, which is also the coordinate of the droplet's vertex under LVLH, The relative velocity at the first crossing of point H. Given the vertex position parameters. and Waterdrop revisit cycle Based on the solution (7) of the CW equation, the state of the droplet vertex after the first pass can be obtained accordingly:

[0063] (8)

[0064] in, To and identity diagonal matrices of the same order Let z be the z-axis component of the vertex position. Since z is decoupled from x and y and the solution changes sinusoidally with time, the z-axis motion can be designed separately.

[0065] Equation (8) has a solution if it is a square matrix. It can be inverted, meaning the determinant of the matrix is ​​non-zero. Let the intermediate parameter... Considering the rapid flyby scenario, it is assumed that the revisit period of the droplet apex is less than the orbital period of the target spacecraft. ,Right now ,therefore The determinants were calculated using numerical methods. From the numerator and denominator, we know that the numerator is always greater than zero. Therefore, only when hour It cannot be reversed. When hour, We can use its second-order submatrix to solve for the velocities of the x and y directions when they first pass through the vertex of the water droplet.

[0066] To facilitate determining the range of parameter values, polar coordinates are used to represent the position of the water droplet's vertex in the xOy plane, that is, let the coordinates of the water droplet's vertex be:

[0067] (9)

[0068] in, This represents the distance from the tip of the droplet to the origin of the LVLH system, i.e., the relative distance between the tracking star and the target star. Let be the polar angle of the vertex in the xOy plane. Using equation (8), the velocity of the first passage through the vertex of the water droplet can be obtained, thus uniquely determining the relative motion trajectory of the skimming segment.

[0069] Single-target flyby observation is divided into a long-range guidance segment and a short-range flyby segment. The purpose of the long-range guidance segment is to shorten the relative distance between the tracker and the target. The tracker transfers from its original orbit to the droplet flyby trajectory by applying two pulses. The short-range flyby segment is non-maneuverable and achieves target observation under illumination constraints based on the droplet configuration.

[0070] First, the design parameters for the close-range flyby observation segment are given. Equation (1) shows that, considering the illumination distance constraint, the feasible region for flyby in the xOy plane of the LVLH system is a torus centered on the target. Since the z-axis motion is relatively independent, without loss of generality, the z-axis position of the vertex is taken. .

[0071] For single-target flyby observations, the close-range flyby segment is designed in the LVLH coordinate system, and the optimization variable is selected as the polar coordinates of the droplet vertex. Water droplet vertex revisit time interval ,in, Satisfying the illumination distance constraint (1), .

[0072] The long-distance transfer segment was designed based on the Lambert problem. The Lambert problem refers to determining a transfer trajectory that passes through two points in space relative to the center of gravity and satisfies the transfer time requirement, given the position vectors of these two points and the transfer time. For an elliptical transfer trajectory, the flight time between the two points... Dependent only on the semi-major axis of the track The sum of the radii from the two endpoints to the center of gravity and the length of the chord connecting the two points That is, Lambert's theorem:

[0073] (10)

[0074] There are already well-established solutions to the Lambert problem, which will not be elaborated upon here. This invention adopts Gooding's solution, which, given the transition time (i.e., the initial and final states of the transition trajectory), allows us to solve for the Lambert transition trajectory and thus calculate the magnitude of the velocity increment required for the transition.

[0075] Based on this, the long-distance transfer segment is designed in a geocentric inertial frame (ECI), and the optimization variable is the waiting time before the Lambert transfer. Lambert transfer time The waiting time for the Lambert trajectory terminal to fly to the upper bound of the observation distance constraint Setting waiting times before and after the Lambert transfer helps optimize fuel consumption and adjust observation lighting conditions. To limit the total mission time for flyby observations, an upper bound is set for the waiting time. The upper bound of the Lambert transition time is Based on the two-body dynamics equations:

[0076] (11)

[0077] Initial absolute motion state of the tracking star under ECI Numerical integration The initial state of the Lambert transition can then be obtained. In equation (11) This represents the absolute position of the spacecraft in the ECI inertial frame. The perturbation force experienced by the spacecraft.

[0078] Since the close-range flyby phase is uncontrolled, the state of the tracking star when it first reaches the tip of the droplet is obtained according to equation (9). Then, based on the solution (7) of the CW equation, the relative motion state of the tracking star under LVLH when entering the upper bound of the observation range constraint can be obtained. The time it takes to fly from the upper bound of the observation distance constraint to the tip of the droplet. Initial absolute motion state of the target star under ECI. Numerical integration based on equation (11) Determine the absolute state of the target star when the relative distance between the tracking star and the target star enters the upper bound of the observation constraint. .in accordance with and The absolute state of the tracking star under ECI at this time can be obtained. Further Using (11) inverse numerical integration The terminal state of the Lambert transition can then be obtained. . This represents the terminal position of Lambert's transfer trajectory. This indicates the velocity after the second pulse; it represents the initial absolute motion state of the tracked star under ECI. Using the exact two-body dynamics equation (11) for forward integration Find the initial state of the Lambert transition. , This is the initial position of Lambert's transfer trajectory. Indicates the velocity before the first pulse. Indicates the initial absolute position. Indicates the initial absolute velocity;

[0079] Initial position based on Lambert transfer trajectory Terminal location and Lambert transfer time The velocity at the initial position on Lambert's transfer trajectory is obtained using the Gooding method. and the speed of the terminal position Let represent the velocity after the first pulse and the velocity before the second pulse, respectively, and then calculate the velocity increments for the two pulses. Among them, the magnitude of the first pulse velocity increment during Lambert transfer. The magnitude of the second pulse velocity increment Therefore, the total speed increment required for long-distance transfer is... ,in, The 2-norm of a vector is used to represent the time division of a single target's flyby. Figure 2 .

[0080] Step 3: The particle swarm optimization algorithm is used to optimize the parameters of the multi-target flyby trajectory. The objective function integrates the effective observation time, velocity increment and penalty term to achieve multi-target flyby observation.

[0081] Given the initial UTC time of the mission, the Earth-Sun position vector can be calculated based on the ephemeris. Considering that the flyby observation time is small relative to the Earth's orbital period, it is assumed that... The direction is kept constant throughout the observation period and is taken as the direction at the moment the tracker first reaches the teardrop-shaped apex. The ray vector is derived from the Earth-Sun position vector. and the position vector of the target spacecraft relative to Earth Find:

[0082] (12)

[0083] Because the target spacecraft rotates relative to the Earth, although during the observation period It is considered constant, but the direction of the ray vector still changes over time in the LVLH system.

[0084] The observation period is based on the relative distance between the tracker and the target spacecraft. The observation period begins when the upper bound of the observation distance constraint is reached, and ends when the droplet passes the vertex for the second time and then flies out of the upper bound of the observation distance constraint. The effective observation duration that satisfies the illumination constraint can then be obtained by integration:

[0085] (13)

[0086] in, The logical judgment result for lighting constraints:

[0087] (14)

[0088] In actual simulation, the observation period is discretized into Time points If the first If the lighting constraint is satisfied at all times, then it is considered that... The time period is considered the valid observation period and is recorded in [the relevant data]. ,Right now:

[0089] (15)

[0090] To prevent the tracker from colliding with the target spacecraft, a sphere with the target as its center and a radius of [missing information] will be used. The ball is set as a no-fly zone, which requires a relative distance. satisfy:

[0091] (16)

[0092] In summary, the design of a single-target flyby observation trajectory considering illumination constraints is transformed into a constrained optimization problem, with the optimization variables being: The objective function is set as a function of the observation duration and the magnitude of the total velocity increment:

[0093] (17)

[0094] Therefore, for the first Based on the single-target flyby design concept, there are three long-range optimization parameters and three short-range optimization parameters: the long-range transfer optimization parameter is the waiting time before the Lambert transfer. Lambert transfer time The waiting time for the Lambert trajectory terminal to fly into the observation range constraint The optimization parameters for close-range flyby are the distance between the droplet revisit position and the target. and polar angle Water droplet vertex revisit time interval When flying When there are multiple objectives, the total optimization variable is: The solution space is large, and the illumination constraint is a nonlinear constraint, which cannot be used to directly narrow down the solution space. Since Particle Swarm Optimization (PSO) has less dependence on initial values ​​and better global search capabilities, especially when the solution space is large, it can avoid getting trapped in local optima. Furthermore, it inherently supports parallel computing; when global variables are not called in the code, PSO can simultaneously process the calculation of multiple particle objective functions, making it suitable for use on multi-core processors. Therefore, choosing PSO for parameter optimization is beneficial for obtaining a feasible solution for trajectory design.

[0095] This invention sets the objective function as a linear combination of effective observation time and total velocity increment, and introduces a penalty term. For the ... The objective function for the flyby target is:

[0096] (18)

[0097] in, , That is, the smaller the total velocity increment and the longer the observation time, the smaller the objective function and the smaller the penalty term. When flying into a no-fly zone, the search efficiency for feasible solutions is improved. Furthermore, an upper limit is set on the sum of two Lambert velocity increments for a single target. For the portion exceeding this upper limit, multiply by a weighting factor and then add it to the total. This increases the objective function, guiding the particle to find the optimal fuel solution that satisfies the constraints.

[0098] The flowchart for calculating the objective function of a single particle in the particle swarm optimization algorithm is shown below. Figure 3 For a given set of optimization parameters, before flying over the k-th target, the parameters are first initialized based on the terminal states of the (k-1) targets flown over. and Based on the aforementioned method, the maneuvering scheme of the tracking satellite is obtained. Under ECI, the initial state of the tracking satellite at the moment of starting flyby of the current target is determined. and the initial state of the target star The states of the tracking and target stars at any moment during the close flyby period can be obtained by numerical integration of the exact two-body dynamics equation (11), thus determining the closest distance between the tracking and target stars. If the closest distance is less than the radius of the target no-fly zone... That is, when a tracking star enters the no-fly zone during its flyby, and a collision occurs due to the current flyby trajectory of the particle, it will... Assign a large positive number and terminate the target function calculation for the current particle early; if the tracking star does not enter the target star's no-fly zone during the entire process, record the target function and penalty term for the k-th target's flyby. After all n targets have flown past, calculate the total target function, which is the cumulative sum of the single-target flyby target functions:

[0099] (19)

[0100] in, For the first Additional penalty for failing to fly over a target. The closer The smaller the penalty, the more successfully the particles can fly past as many targets as possible.

[0101] Example

[0102] The effectiveness of the proposed method is illustrated using three target stars flying past different orbital planes as an example. The initial time is set to November 1, 2024. The projection of the Sun-Earth relative position vector in the geocentric inertial frame can be obtained through ephemeris analysis. The initial orbital elements of the tracking stars and targets are shown in Table 1. .

[0103] Table 1

[0104]

[0105] Upper limit of single target fly-by speed increment The speed is set to 80 m / s, the upper and lower bounds of the illumination distance constraint are set to 80 km and 20 km respectively, the no-fly zone radius is set to 10 km, and the upper and lower bounds of the apparent angle are set to 0 degrees and 60 degrees respectively. The particle swarm size is set to 1000, and the maximum number of iterations is set to 100. The penalty terms are selected as follows:

[0106] The initial penalty term is set to zero.

[0107] To ensure a reasonable allocation of global observation time, the distance from the water droplet vertex to the maximum observation distance is set. The maximum transfer time is one orbital period. When the transfer time is too long, penalties will be imposed. Increase by 10;

[0108] The closest approach between the tracking and target satellites occurs during the flyby phase. The shortest distance between them during the flyby phase is calculated based on an accurate two-body model. When the tracking satellite enters the target satellite's no-fly zone, a collision is considered to have occurred, the penalty is increased, and the calculation of the current flyby trajectory for the target satellite is terminated. The closer the tracking satellite is to the target, the greater the penalty. ,in The radius of the no-fly ball, This is the closest distance between the two stars;

[0109] To ensure a reasonable distribution of pulses, an upper limit is set for the expected consumption of the total velocity increment during single-target flyby. If the total speed increase from two Lambert maneuvers targeting a specific target exceeds the upper limit, an additional penalty will be applied. ,in It is the sum of two velocity increments during the flyby of the current target.

[0110] The above describes the penalty increases for a single target flyby process. Furthermore, whenever a target no-fly zone is entered, the penalty is increased accordingly based on the number of completed flyby targets, and trajectory calculations for this set of parameters are terminated early to improve the particle swarm iteration rate. For a three-target flyby, if the first target flyby results in entering the no-fly zone, then... If the second target is flown over and the no-fly zone is entered, then... If the flyby phase of a third target enters the no-fly zone, then .

[0111] The final optimization results are shown in Table 2. All times in the table are in hours, and distances are in kilometers. The total flight time of the tracker was 7.63 days, the total effective observation time for the three targets was 37.07 hours, the total velocity increment consumed was 113.41 m / s, and the objective function was -36.95.

[0112] Table 2

[0113]

[0114] Using the LVLH system of target 1 as the projected coordinate system, the close-range flyby phase of the tracking star of target 1 is as follows: Figure 4 The purple square marks the start of the flyby phase, where the tracking satellite first enters the feasible observation area of ​​target 1, and the orange rhombus marks the end of the flyby phase. During the flyby phase, the droplet is positioned to one side of the target, allowing for controllable camera attitude adjustments and facilitating the observation mission. The flyby trajectory of target 1 is shown below. Figure 5 The tracking satellite first shifts its orbital plane through two pulse maneuvers, and then conducts flyby observations of the target within the orbital plane.

[0115] Therefore, the design method provided by this invention can achieve multi-target flyby observation with comprehensive fuel consumption and effective observation time.

[0116] In summary, this invention addresses the background of spacecraft flyby observation by transforming the multi-target rapid flyby problem considering illumination conditions into a constrained parameter optimization problem. Based on the basic parameters of the droplet configuration derived from the CW equations, the flyby trajectory of a single target is divided into a long-range guidance segment based on the Lambert problem and a short-range flyby segment based on the droplet configuration. Six optimization parameters can uniquely determine a single-target flyby trajectory. Taking into account observation distance constraints and sunlight angle constraints, the invention uses two-body dynamics equations with perturbations as dynamic constraints, with the mission objectives of maximizing effective observation time and minimizing fuel consumption. A penalty term is introduced to improve search efficiency. The multi-target flyby observation trajectory is optimized based on the particle swarm optimization algorithm, forming a method for designing multi-target rapid flyby trajectories under illumination constraints.

[0117] In a second aspect, the present invention provides an electronic device, comprising: one or more processors; and a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned multi-target flyby method based on droplet-shaped relative motion characteristic parameters under illumination constraints.

[0118] Thirdly, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enable the processor to implement the aforementioned multi-target fly-by method based on droplet-shaped relative motion characteristic parameters under illumination constraints.

[0119] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multi-target flyby method based on teardrop-shaped relative motion characteristic parameters under illumination constraints, characterized in that, include: Step 1: Establish a mathematical model that includes observation distance constraints and sunlight angle constraints; Step 2: Divide the flyby process of each target star into a close flyby segment and a long-range guidance segment. Based on the droplet configuration feature parameters of the CW equation, extract the trajectory design parameters for the close flyby segment. Use double-pulse Lambert transfer to realize the orbit transfer for the long-range guidance segment, and give the trajectory design parameters for the long-range guidance segment. Step 3: Design an objective function consisting of velocity increment, effective observation time, and penalty term. Use particle swarm optimization to optimize the grazing trajectory parameters of multiple targets in the close-range grazing phase and the long-range guidance phase, and obtain a one-to-many grazing trajectory with velocity increment less than the maximum value and effective observation time for each target.

2. The multi-target flyby method based on teardrop-shaped relative motion characteristic parameters under illumination constraints according to claim 1, characterized in that, In step 1, the observation distance constraint is the relative distance between the target star and the tracking star. The upper and lower bounds are defined as 20km-80km, and the sunlight angle constraint is the angle between the relative position vector of the tracking star and the target star and the illumination vector. Limited to 0 to 60°.

3. The multi-target flyby method based on teardrop-shaped relative motion characteristic parameters under illumination constraints according to claim 1, characterized in that, In step 2, the close-range flyby segment is calculated in the local vertical-horizontal rectangular coordinate system LVLH, and the long-range guidance segment is calculated in the geocentric equatorial inertial coordinate system ECI.

4. The multi-target flyby method based on teardrop-shaped relative motion characteristic parameters under illumination constraints according to claim 3, characterized in that, The close-range flyby phase is used to observe the target star under the constraints of a mathematical model based on a droplet configuration, with no maneuvers throughout. The long-range guidance phase is used to shorten the relative distance between the tracking star and the target star. The tracking star is transferred from its original orbit to the droplet flyby orbit of the close-range flyby phase by applying two pulses.

5. A multi-target flyby method based on teardrop-shaped relative motion characteristic parameters under illumination constraints according to claim 3, characterized in that, In step 2, the droplet configuration description relative motion trajectory characteristic parameters based on the CW equation include the polar coordinates of the droplet vertex and the droplet vertex revisit time interval. The polar coordinates of the droplet vertex satisfy the observation distance constraint and the sunlight angle constraint (1), and the droplet vertex revisit time interval is less than the orbital period of the target star.

6. A multi-target flyby method based on teardrop-shaped relative motion characteristic parameters under illumination constraints according to claim 4, characterized in that, The optimization variable for the long-range guidance segment is the waiting time before the Lambert transfer. Lambert transfer time The waiting time for the Lambert trajectory terminal to fly to the upper bound of the observation distance constraint .

7. A multi-target flyby method based on teardrop-shaped relative motion characteristic parameters under illumination constraints according to claim 6, characterized in that, After obtaining the polar coordinates of the droplet vertex and the revisit time interval of the droplet vertex, the relative motion state of the tracking star when entering the upper bound of the observation distance constraint is obtained based on the solution of the CW equation. The time it takes to fly from the upper bound of the observation distance constraint to the tip of the droplet. Based on the absolute state of the target star The relative motion state of the tracking star Find the absolute state of the tracking star under ECI at this time. ; The absolute state of the tracking star under ECI Inverse numerical integration using the exact two-body dynamics equation (11) Determine the absolute state of the tracking star after the second pulse. , This represents the terminal position of Lambert's transfer trajectory. This indicates the velocity after the second pulse; it represents the initial absolute motion state of the tracked star under ECI. Using the exact two-body dynamics equation (11) for forward integration Find the initial state of the Lambert transition. , This is the initial position of Lambert's transfer trajectory. Indicates the velocity before the first pulse. Indicates the initial absolute position. Indicates the initial absolute velocity; Initial position based on Lambert transfer trajectory Terminal location and Lambert transfer time The velocity at the initial position on Lambert's transfer trajectory is obtained using the Gooding method. and the speed of the terminal position , representing the velocity after the first pulse and the velocity before the second pulse, respectively, therefore, the total velocity increment required for long-distance transfer. ,in, This represents the 2-norm of a vector.

8. A multi-target flyby method based on teardrop-shaped relative motion characteristic parameters under illumination constraints, as described in claim 5 or 6, characterized in that... In step 3, the overall objective function is the sum of the objective functions of the tracking satellite flying over individual target satellites; the effective observation time evaluation is performed under LVLH, and only the time period that simultaneously satisfies the observation distance constraint and the sunlight angle constraint is recorded as the effective observation time; the penalty term is used to prevent the tracking satellite from entering the target's no-fly zone and guide the tracking satellite to complete the fly-over mission of n targets, so that the effective observation time for each target is greater than the shortest time required for imaging. .

9. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs; When one or more programs are executed by the one or more processors, the one or more processors implement the multi-target flyby method based on droplet-shaped relative motion characteristic parameters under illumination constraints as described in any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed by a processor, enable the processor to implement the multi-target flyby method based on droplet-shaped relative motion characteristic parameters under illumination constraints as described in any one of claims 1-8.

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