Dynamically-based target asteroid and impactor orbit simulation method

Abstract

This invention relates to a dynamics-based simulation method for the orbits of target asteroids and impactors, belonging to the technical field of aerospace technology and its applications. The invention aims to address the problems of poor accuracy and stability in existing asteroid impact simulation processes. This invention establishes the asteroid orbital dynamics equations, substituting the position vector into these equations to recursively obtain the asteroid's orbital model; it also establishes the impactor orbital dynamics equations, substituting the impactor's initial three-dimensional position, velocity, and acceleration into these equations, and combining them with the target asteroid's orbital model to recursively obtain the initial orbital model from the impactor's initial position to a distance of S km from the target asteroid; using this initial model, it establishes the full dynamics equations for the final segment of the impactor's orbit, obtaining the orbital model from the impactor's position S km from the target asteroid to the point of impact. This method is primarily used for impactor orbit simulation.

Description

Technical Field

[0001] This invention belongs to the technical field of aerospace technology and its applications. Background Technology

[0002] In the field of asteroid defense research, many schemes have been proposed, among which one of the most mature is the direct impact method using an impactor. This method can effectively change the asteroid's orbit. However, the economic and human costs of developing and launching deep-space impact probes are extremely high. Therefore, testing deep-space impact probes through actual deep-space experiments is impractical and costly. Currently, asteroid defense is an area of ​​research and discussion, and no impactor interception system or other systems have been actually deployed. Internationally, some simulations and experiments are being conducted to evaluate the effectiveness of these methods. Based on the above, impactor orbit simulation has significant research and application value for constructing asteroid defense systems.

[0003] Simulation of the entire flight process of a spacecraft is a complex and crucial computational technique. It simulates all key stages from launch to mission completion, ensuring the success of space missions. This simulation covers not only orbit design, gravitational interactions, rocket propulsion, attitude control, and celestial navigation, but also multiple key factors such as sensor performance, communication links, and the impact of the space environment. By accurately simulating these stages, it is possible to predict the spacecraft's operational status, resolve potential problems, and minimize mission risks. This helps optimize mission design, improve spacecraft performance, and ensure objectives are achieved. Therefore, simulation of the entire flight process of a spacecraft plays an indispensable and crucial role in the planning, execution, and data analysis of space missions.

[0004] Deep space impactors are small spacecraft with highly miniaturized and integrated internal electrical components. Before and after conducting equivalent ground-based tests, their comprehensive performance indicators need to be tested and verified. Therefore, a comprehensive ground-based testing system for the impactor needs to be established, combined with some visualization equipment, to facilitate testing and demonstration of the entire flight process. For impact mission scenarios, the spacecraft and impactor will face complex mechanical environments in deep space. During simulation, the dynamic deflection of the spacecraft by celestial gravity and the gravitational tug effect caused by continuous but small gravitational forces need to be considered to simulate the spacecraft's dynamic characteristics. To accurately simulate the impactor's on-orbit trajectory and orbit in the complex cosmic environment, it is necessary to study a series of dynamic factors, including: simulating the gravitational force applied to the spacecraft, solar perturbation force, thruster thrust and stress torque, and simulating the corresponding torques during the operation of the reaction wheel / torque gyroscope based on its mechanism. The spacecraft dynamic equations to be established for simulation need to include: rigid body dynamics equations, flexible appendage rotation equations, and flexible appendage elastic deformation vibration equations. Furthermore, fuel sloshing within the spacecraft's main body affects its attitude, which is also a factor that needs to be considered during the simulation. Based on the above, the impactor orbit simulation suffers from poor accuracy and stability in both the dynamic model establishment and orbit simulation calculations. Summary of the Invention

[0005] This invention aims to address the issues of poor accuracy and stability in existing asteroid impact simulation processes by providing a dynamic-based method for simulating the impact trajectory of a target asteroid and its impactor.

[0006] The dynamic-based target asteroid and impactor impact trajectory simulation method of the present invention includes:

[0007] Step 1: Calculate the asteroid's ephemeris using an ephemeris calculation algorithm to obtain the asteroid's position vector in the solar ecliptic inertial frame, establish the asteroid's orbital dynamics equation, substitute the position vector into the asteroid's orbital dynamics equation, and recursively obtain the asteroid's motion orbital model.

[0008] Step 2: Set the initial three-dimensional position and velocity of the impactor, and calculate the acceleration caused by gravity at the location of the impactor based on the initial three-dimensional position of the impactor;

[0009] Step 3: Establish the impactor orbital dynamics equations. Substitute the initial three-dimensional position, velocity, and acceleration of the impactor into the impactor orbital dynamics equations. Combine this with the target asteroid's motion orbital model to recursively obtain the first segment orbital model from the initial position of the impactor to a distance of Skm from the target asteroid.

[0010] Step 4: Using the first segment orbital model, obtain the three-dimensional position and velocity of the impactor when it is Skm away from the target asteroid. Combine the acceleration generated by the force on the impactor when it is Skm away from the target asteroid and the dynamic equation of the impactor attitude, establish the full dynamic equation of the final segment of the impactor, and obtain the orbital model from the position of the impactor Skm away from the target asteroid to the point of impact between the impactor and the target asteroid, where S is a positive number, preferably S is 30000.

[0011] Furthermore, in this invention, in step one, the asteroid orbital dynamics equation is:

[0012]

[0013]

[0014] In the formula, r1 is the position vector of the asteroid in the solar ecliptic inertial frame, v1 is the velocity vector of the asteroid, a1 is the acceleration vector of the asteroid, and u is the acceleration caused by the force exerted on the asteroid by the impactor after impact. Let r1 be the derivative of the reciprocal of the position vector r1 in the asteroid's ecliptic inertial frame of reference. Let v1 be the derivative of the asteroid's velocity vector.

[0015] in,

[0016] a1=a sun +a planet +a moon +a asteroid +a J2 +a PN

[0017] In the formula, a sun a is the acceleration of an asteroid due to the Sun's gravity; planet The acceleration of an asteroid due to the gravitational pull of the eight planets; a asteroid a is the acceleration of the asteroid caused by the gravitational pull of Pluto and the four largest asteroids. J2 a is the acceleration caused by the oblateness perturbation of the asteroid by the Sun. PN This is the acceleration of the asteroid caused by the gravitational pull of the nebula.

[0018] Furthermore, in this invention, in step three, the acceleration generated by the force on the first segment of the orbital model includes: the acceleration generated by the perturbation of the central celestial body, the acceleration generated by the perturbation of solar radiation pressure, and the acceleration generated by the perturbation of a third body;

[0019] In step four, the acceleration generated by the forces acting on the final orbital model includes: the acceleration generated by the perturbation of the central celestial body, the acceleration generated by the perturbation of solar radiation pressure, the acceleration generated by the perturbation of the third body, and the acceleration generated by the jet ejection from the impactor's nozzle.

[0020] Furthermore, in this invention, the impactor experiences an acceleration α generated by the perturbation of the central celestial body. center for:

[0021]

[0022] In the formula: μ is the solar gravitational constant; r2 is the radius vector of the impactor relative to the central celestial body, which is the Sun.

[0023] The acceleration a generated by the impactor under solar radiation pressure perturbation SR for:

[0024]

[0025] In the formula: C R r is the solar radiation pressure coefficient; r2 is the radius vector of the impactor relative to the central celestial reference frame; r s The radius vector of the central object relative to the central object's reference frame; AU is 1 astronomical unit; P SR A is the solar constant; SR is the effective cross-sectional area of ​​the impactor that withstands the light pressure; m is the mass of the impactor.

[0026] The acceleration of the impactor caused by the perturbation of a third body is a 3B The acceleration produced by the d-th third-body perturbation is:

[0027]

[0028] Where: μ d r is the gravitational constant of the third body; d The radius vector of the third body relative to the central celestial body's reference frame;

[0029] The acceleration generated by the impactor nozzle is:

[0030] In the formula: u i is the on / off state of nozzle i; A is the transformation matrix from the impactor's own system to the central celestial body's inertial frame; Let be the acceleration generated by the i-th nozzle in the impactor system; n is the number of impactor nozzles.

[0031] Furthermore, in this invention, the transformation matrix A from the impactor's own system to the central celestial body's inertial frame is:

[0032] A = A1A2A3

[0033]

[0034]

[0035]

[0036] In the formula: ψ is the z-axis rotation angle; A1 is the transformation matrix relative to the z-axis; θ is the y-axis rotation angle; A2 is the transformation matrix relative to the y-axis; A3 is the x-axis rotation angle; A4 is the transformation matrix relative to the x-axis.

[0037] Acceleration generated by nozzles on each axis in the impactor system for:

[0038] In the formula: Let be the thrust generated by the i-th nozzle; m be the current mass of the impactor.

[0039] Furthermore, in this invention, in step three, the initial orbital model from the initial position of the impactor to the target asteroid at a distance of Skm is as follows:

[0040]

[0041] in, Let r be the derivative of the reciprocal of the radius vector r² of the impactor relative to the central celestial body. Let v be the derivative of the velocity vector v2 of the impactor.

[0042] Furthermore, in this invention, in step three, the first segment of the orbital model from the initial position of the impactor to the target asteroid Skm is obtained by recursion using the eighth-order Runge-Kutta formula.

[0043] Furthermore, in this invention, the method for determining the distance Skm from the target asteroid in step three is as follows:

[0044] The current coordinates of the impactor are transformed using the transformation matrix A from the impactor's own frame to the central celestial body's inertial frame, and then the three-dimensional distance calculation formula is used:

[0045] The distance between the impactor and the target asteroid in the same coordinate system is calculated during the recursive process of the orbit. In the formula, d is the relative distance between the impactor and the asteroid, x1 and y1 are the positions of the impactor in the two-dimensional coordinate system, and x2 and y2 are the positions of the asteroid in the two-dimensional coordinate system.

[0046] Furthermore, in this invention, in step four, the attitude dynamics model of the impactor is as follows:

[0047]

[0048] The impactor includes two sails. This represents the acceleration along the Y-axis of the impactor. Indicates the velocity of the impactor along the Y-axis. Let ω be the angular acceleration of the impactor, ω be the angular velocity of the impactor, and q be the position vector of the impactor. f1 q f2 Λf represents the modal coordinates of the solar panel in the +Y and -Y directions, respectively, retaining the modes up to order 5 (5×1); Λf is the diagonal matrix of the solar panel's modal frequencies (5×5); ζf is the modal damping coefficient of the solar panel, with a reference value set to 0.05; C af1 C af2 The coupling coefficient matrix (3×5) is the coupling coefficient matrix of solar panel vibration in the +Y and -Y directions to the rotation of the satellite's central body.

[0049] Furthermore, in this invention, in step four, the total dynamic equation of the impactor's final stage is:

[0050]

[0051] Where a0 represents the initial acceleration of the impactor, I represents the inertia matrix of the impactor in its own system; M j This represents the control torque of the impactor's principal axes at different moments of inertia. The derivative of the z-axis rotation angle ψ; The derivative of the y-axis rotation angle θ; x-axis rotation angle The derivative, These are the derivatives of the solar panel modal coordinates in the +Y and -Y directions, respectively; a 3B ω represents the acceleration produced by the gravitational pull of all third bodies on the accelerator. x Let ω be the component of the impactor's angular velocity ω in the X-axis direction. y Let u be the component of the impactor's angular velocity ω in the Y-axis direction. j For the on / off state of nozzle j, ω z Let ω be the component of the impactor's angular velocity ω in the Z-axis direction;

[0052]

[0053] a Tx a is the magnitude of the acceleration generated by the nozzle along the x-axis of this system; Ty a represents the magnitude of the acceleration generated by the nozzle along the y-axis of this system. Tz Let |a| represent the magnitude of the acceleration generated by the nozzle along the z-axis of this system. M | represents the absolute value of the jet acceleration generated by the attitude control torque.

[0054]

[0055] Where: M x M represents the magnitude of the control torque acting on the x-axis. y M represents the magnitude of the control torque acting on the y-axis. z r is the magnitude of the control torque acting on the z-axis.lx Let r be the length of the lever arm along the x-axis. ly Let r be the length of the lever arm along the y-axis. ls Let I be the length of the lever arm along the z-axis. x I represents the component of the impactor's inertia matrix I along the x-axis in the impactor's intrinsic system. y I represents the component of the impactor's inertia matrix I along the y-axis in the self-contained system of the impactor. z This represents the component of the impactor's inertia matrix I along the z-axis in the impactor's own system.

[0056] This method, through orbital simulation of asteroids and impactors, combines software algorithms with a physical model, and uses dynamic simulation with the eighth-order Runge-Kutta method to achieve a complete simulation of the entire process of controlling an impactor to collide with an asteroid that poses a threat to Earth. This simulation is accurate, real-time, and allows for some orbital modification to ensure successful impact. It provides a reliability verification method for using deep-space spacecraft to defend against asteroids and solves the problems of poor accuracy and stability in existing asteroid impact simulation processes. Attached Figure Description

[0057] Figure 1 This is a flowchart of the method described in this invention. Detailed Implementation

[0058] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0059] Specific implementation method one: Refer to Figure 1 This embodiment specifically describes the dynamics-based target asteroid and impactor trajectory simulation method, which includes:

[0060] Step 1: Calculate the asteroid's ephemeris using an ephemeris calculation algorithm to obtain the asteroid's position vector in the solar ecliptic inertial frame, establish the asteroid's orbital dynamics equation, substitute the position vector into the asteroid's orbital dynamics equation, and recursively obtain the asteroid's motion orbital model.

[0061] Step 2: Set the initial three-dimensional position and velocity of the impactor, and calculate the acceleration caused by gravity at the location of the impactor based on the initial three-dimensional position of the impactor;

[0062] Step 3: Establish the impactor orbital dynamics equations. Substitute the initial three-dimensional position, velocity, and acceleration of the impactor into the impactor orbital dynamics equations. Combine this with the target asteroid's motion orbital model to recursively obtain the first segment orbital model from the initial position of the impactor to a distance of Skm from the target asteroid.

[0063] Step 4: Using the first segment orbital model, obtain the three-dimensional position and velocity of the impactor when it is Skm away from the target asteroid. Combine the acceleration generated by the force on the impactor when it is Skm away from the target asteroid and the dynamic equation of the impactor attitude, establish the full dynamic equation of the final segment of the impactor, and obtain the orbital model from the position of the impactor Skm away from the target asteroid to the point of impact between the impactor and the target asteroid, where S is a positive number, preferably S is 30000.

[0064] Furthermore, in this invention, in step one, the asteroid orbital dynamics equation is:

[0065]

[0066]

[0067] In the formula, r1 is the position vector of the asteroid in the solar ecliptic inertial frame, v1 is the velocity vector of the asteroid, a1 is the acceleration vector of the asteroid, and u is the acceleration caused by the force exerted on the asteroid by the impactor after impact. Let r1 be the derivative of the reciprocal of the position vector r1 in the asteroid's ecliptic inertial frame of reference. Let v1 be the derivative of the asteroid's velocity vector.

[0068] in,

[0069] a1=a sun +a planet +a moon +a asteroid +a J2 +a PN

[0070] In the formula, a sun a is the acceleration of an asteroid due to the Sun's gravity; asteroid a is the acceleration of the asteroid caused by the gravitational pull of Pluto and the four largest asteroids. J2 a is the acceleration caused by the oblateness perturbation of the asteroid by the Sun. PN represents the acceleration of the asteroid due to the gravitational pull of the nebula, where

[0071]

[0072] a planet The acceleration of the asteroid due to the gravitational pull of the eight planets; the acceleration a of the asteroid due to the gravitational pull of Mercury. mercury For example, the following is an explanation:

[0073]

[0074] Where, r mercury The radius vector of the asteroid relative to Mercury, μ mercury is the gravitational constant of Mercury.

[0075] In the actual implementation of the algorithm, the numerical methods used must be high-precision and stable. When calculating over long periods, it is essential not only to maintain the overall structure without distortion of the motion states of each celestial body, but also to ensure high positional accuracy, so that the given rendezvous state is reliable. Furthermore, compared to the motion of near-Earth asteroids, the positional quantity corresponding to the lunar motion is a fast variable. This requires that the orbital characteristics of the asteroid and the relatively fast motion of the moon be considered simultaneously when selecting the integration step size; otherwise, lunar orbital errors will affect the true state of the asteroid-Earth rendezvous. Therefore, during the orbital recursion process, an automatic variable-step Runge-Kutta 78 integrator (RKF78) is used to integrate the equations of motion to obtain the relative position of the asteroid in the solar system at a certain moment.

[0076] For the orbit simulation of the impactor, it is divided into the recursive physical model of the initial orbit and the recursive physical model of the final orbit control.

[0077] The first segment of the orbit recursion is responsible for the long-distance orbit recursion of the impactor from launch to a distance of 30,000 km from the target asteroid. The three-dimensional coordinates and three-dimensional velocities of the impactor recursion will be used as inputs to the kinematics module, and the output of the kinematics model will be used as inputs to the next module. The physical forces considered in the kinematics module recursion include three parts: perturbation of the central celestial body, perturbation of solar radiation pressure, and perturbation of the third body. Before the subsequent impact, the force generated by the impactor's nozzle ejection will also be added.

[0078] Furthermore, in this invention, in step three, the initial orbital model from the initial position of the impactor to the target asteroid at a distance of Skm is as follows:

[0079]

[0080] in, Let r be the derivative of the reciprocal of the radius vector r² of the impactor relative to the central celestial body. Let v be the derivative of the velocity vector v2 of the impactor.

[0081] Furthermore, in this invention, in step three, the acceleration generated by the force on the first segment of the orbital model includes: the acceleration generated by the perturbation of the central celestial body, the acceleration generated by the perturbation of solar radiation pressure, and the acceleration generated by the perturbation of a third body;

[0082] In step four, the acceleration generated by the forces acting on the final orbital model includes: the acceleration generated by the perturbation of the central celestial body, the acceleration generated by the perturbation of solar radiation pressure, the acceleration generated by the perturbation of the third body, and the acceleration generated by the jet ejection from the impactor's nozzle.

[0083] In the first phase of the trajectory, the impactor is accelerated by the celestial body to a position close to the target asteroid. In the final phase, to accurately impact the asteroid, it is necessary to inject acceleration to adjust the direction and speed.

[0084] Furthermore, in this invention, the impactor experiences an acceleration α generated by the perturbation of the central celestial body. center for:

[0085]

[0086] In the formula: μ is the solar gravitational constant; r2 is the radius vector of the impactor relative to the central celestial body, which is the Sun.

[0087] The acceleration a generated by the impactor under solar radiation pressure perturbation SR for:

[0088]

[0089] In the formula: C R r is the solar radiation pressure coefficient; r2 is the radius vector of the impactor relative to the central celestial reference frame; r s The radius vector of the central object relative to the central object's reference frame; AU is 1 astronomical unit; P SR A is the solar constant; SR is the effective cross-sectional area of ​​the impactor that withstands the light pressure; m is the mass of the impactor.

[0090] The acceleration of the impactor caused by the perturbation of a third body is a 3B The acceleration produced by the d-th third-body perturbation is:

[0091]

[0092] Where: μ d r is the gravitational constant of the third body; d The radius vector of the third body relative to the central celestial body's reference frame;

[0093] The acceleration generated by the impactor nozzle is:

[0094]

[0095] In the formula: u i is the on / off state of nozzle i; A is the transformation matrix from the impactor's own system to the central celestial body's inertial frame; Let be the acceleration generated by the i-th nozzle in the impactor system; n is the number of impactor nozzles.

[0096] Furthermore, in this invention, the transformation matrix A from the impactor's own system to the central celestial body's inertial frame is:

[0097] A = A1A2A3

[0098]

[0099]

[0100]

[0101] In the formula: ψ is the z-axis rotation angle; A1 is the transformation matrix relative to the z-axis; θ is the y-axis rotation angle; A2 is the transformation matrix relative to the y-axis; A3 is the x-axis rotation angle; A4 is the transformation matrix relative to the x-axis.

[0102] Acceleration generated by nozzles on each axis in the impactor system for:

[0103]

[0104] In the formula: Let m be the thrust generated by the i-th nozzle; m be the current mass of the impactor; ui be the on / off function for whether the acceleration of the i-th nozzle is applied. i = 0 or 1.

[0105] The reference value amplitude of the acceleration can be set as follows: the impactor's y and z axes can generate a. y =a x = ±0.5m / s 2 and a y =a z = ±0.05m / s 2 Two levels of thrust acceleration, taking an 8-nozzle configuration as an example:

[0106] a1=[0,0.5,0], a2=[0,-0.5,0], a3=[0,0.05,0], a4=[0,-0.05,0]

[0107] a5=[0,0,0.5], a6=[0,0,-0.5], a7=[0,0,0.05], a8=[0,0,-0.05]

[0108] Considering the complex motion of a deep-space impactor in its environment, the dynamic model of the impactor is considered from both rigid and non-rigid perspectives. Assuming the impactor is a rigid body, its attitude dynamic equations are as follows:

[0109]

[0110] In the formula: I represents the inertia matrix of the impactor in this system; M j M represents the control torque of the j-th principal axis of inertia of the impactor. j M represents the control torque of the j-th principal axis of inertia of the impactor. j The magnitude can be calculated based on the jet thrust and its lever arm relative to the impactor's center of mass. Taking the x-axis torque as an example, it is:

[0111]

[0112] In the formula:

[0113] F i Indicates the magnitude of the nozzle thrust perpendicular to the axis; l i This represents the corresponding lever arm length. Based on the conditions required for the final impact target, the reference value can be set as follows: the lever arm is assumed to be 1m. For the x-axis, M... x = ±6 N·m for the y and z axes, M y = ±6 N·m and M y -±: 0.6 N·m and M z = ±0.6 N·m, arranged in sequence, that is:

[0114] M1=[6,0,0], M2=[-6,0,0], M3=[0.6,0,0], M4=[-0.6,0,0]

[0115] M5=[0,8,0], M6=[0,-8,0], M7=[0,0.8,0], M8=[0,-0.8,0]

[0116] M9 = [0, 0, 8], M 10 = [0, 0, -8], M 11 = [0, 0, 0.8], M 12 = [0, 0, -0.8]

[0117] The relationship between the impactor's attitude angle and angular velocity relative to the central celestial coordinate system is as follows:

[0118]

[0119] Furthermore, in this invention, in step three, the first segment of the orbital model from the initial position of the impactor to the target asteroid at a distance of skm is obtained by recursion using the eighth-order Runge-Kutta formula.

[0120] In this embodiment, the core idea of ​​the eighth-order Runge-Kutta method is to advance the numerical solution of the differential equation to the next time step based on the slope of the approximate differential equation. In each step, it calculates multiple intermediate slopes and then updates the numerical solution by combining these slopes. While calculating these intermediate slopes requires more computation, it also provides higher accuracy for the numerical solution. This method is used for recursive integration of the trajectory of a kinematic model, and with a defined step size, it can complete the recursive integration of the trajectory while meeting accuracy requirements.

[0121] Furthermore, in this invention, the method for determining the distance skm from the target asteroid in step three is as follows:

[0122] The current coordinates of the impactor are transformed using the transformation matrix A from the impactor's own frame to the central celestial body's inertial frame, and then the three-dimensional distance calculation formula is used:

[0123]

[0124] The distance between the impactor and the target asteroid in the same coordinate system is calculated during the recursive process of the orbit. In the formula, d is the relative distance between the impactor and the asteroid, x1 and y1 are the positions of the impactor in the two-dimensional coordinate system, and x2 and y2 are the positions of the asteroid in the two-dimensional coordinate system.

[0125] In this embodiment, after completing the initial trajectory recursion, the kinetic energy impact handling module transmits the parameter results of the initial trajectory recursion to the final trajectory control recursion. By introducing a control module, the current position and attitude of the impactor can be interfered with, causing it to fly along a preset trajectory. During the specific trajectory recursion process, the dynamics module is called in stages and steps to achieve the final trajectory handling result. The dynamics model mainly includes two parts: the trajectory dynamics model and the attitude dynamics model.

[0126] Furthermore, in this invention, in step four, the attitude dynamics model of the impactor is as follows:

[0127]

[0128] The impactor includes two sails. This represents the acceleration along the Y-axis of the impactor. Indicates the velocity of the impactor along the Y-axis. Let ω be the angular acceleration of the impactor, ω be the angular velocity of the impactor, and q be the position vector of the impactor. f1 q f2Λf represents the modal coordinates of the solar panel in the +Y and -Y directions, respectively, retaining the modes up to order 5 (5×1); Λf is the diagonal matrix of the solar panel's modal frequencies (5×5); ζf is the modal damping coefficient of the solar panel, with a reference value set to 0.05; C af1 C af2 The coupling coefficient matrix (3×5) is the coupling coefficient matrix of solar panel vibration in the +Y and -Y directions to the rotation of the satellite's central body.

[0129] Furthermore, in this invention, in step four, the total dynamic equation of the impactor's final stage is:

[0130]

[0131] Where a0 represents the initial acceleration of the impactor, I represents the inertia matrix of the impactor in its own system; M j μ represents the control torque of the j-th principal axis of inertia of the impactor. i Indicates the on / off state of nozzle i. The derivative of the z-axis rotation angle ψ; The derivative of the y-axis rotation angle θ; x-axis rotation angle The derivative, These are the derivatives of the solar panel modal coordinates in the +Y and -Y directions, respectively; a 3B ω represents the acceleration produced by the gravitational pull of all third bodies on the accelerator. x Let ω be the component of the impactor's angular velocity ω in the X-axis direction. y Let ω be the component of the impactor's angular velocity ω in the Y-axis direction. z Let ω be the component of the impactor's angular velocity ω in the Z-axis direction;

[0132]

[0133] a Tx a is the magnitude of the acceleration generated by the nozzle along the x-axis of this system; Ty a represents the magnitude of the acceleration generated by the nozzle along the y-axis of this system. Tz Let |a| represent the magnitude of the acceleration generated by the nozzle along the z-axis of this system. M | represents the absolute value of the jet acceleration generated by the attitude control torque.

[0134]

[0135] Where: M x M represents the magnitude of the control torque acting on the x-axis. y M represents the magnitude of the control torque acting on the y-axis. z r is the magnitude of the control torque acting on the z-axis. lx Let r be the length of the lever arm along the x-axis. ly Let r be the length of the lever arm along the y-axis.ls Let I be the length of the lever arm along the z-axis. x I represents the component of the impactor's inertia matrix I along the x-axis in the impactor's intrinsic system. y I represents the component of the impactor's inertia matrix I along the y-axis in the self-contained system of the impactor. z This represents the component of the impactor's inertia matrix I along the z-axis in the impactor's own system.

[0136] This invention employs a software approach for trajectory acquisition. To ensure the accuracy and stability of the target asteroid's orbit simulation, based on the asteroid's dynamics model and calculated asteroid parameters, the Runge-Kutta 78 integrator (RKF78) performs orbit recursion. A self-developed ephemeris calculation algorithm is used to calculate the asteroid's ephemeris, obtaining its position vector in the solar ecliptic inertial frame. This vector is then substituted into the asteroid's orbital dynamics equations for orbit recursion. To prevent distortion of the motion states of various celestial bodies over a long calculated time period and to ensure high positional accuracy, guaranteeing that the asteroid-impactor orbital intersection states provided by the simulation system are accurate, an automatically variable step-size Runge-Kutta 78 integrator (RKF78) is used to integrate the motion equations during orbit recursion, thereby obtaining the asteroid's relative position in the solar system at a given moment.

[0137] This invention focuses on impactor trajectory simulation, enabling adjustments to the impactor's operating mode via command transmission. It features image display capabilities for received information, providing excellent visualization. It can display data processed by the flight control data processing terminal and the processing results from the image processing test terminal. Orbital control of the impactor is achieved by injecting specific commands into the deep-space impactor. Simulation data processing is performed using a simulation computer. By modeling and loading asteroid models, the observation perspective of the asteroid is controlled using simulation data. The trajectory and real-time attitude of the deep-space impactor are then generated based on the simulation data, and the results are displayed on the screen.

[0138] Regarding simulation data reception, this invention establishes a flight control data processing system to receive and process simulation data generated by the main control system, simulating the flight trajectory and attitude of a deep space impact probe during its impact mission. It communicates with the main control system via TCP and can refresh the display in real time. The flight control data processing system is implemented through secondary development of STK, integrating STKX components into the QT development environment using the header files and dynamic link library files provided by STK. In the program, elements in the sc file provided by STK are controlled using variables of type IAgStkObjectRootPtr (m_pRoot) and IAgSTKXApplicationPt (m_app). The network communication module receives data or commands from the main control system and inputs the data and commands into the STKX controls through variables m_pRoot and m_app, thereby simulating the flight trajectory and attitude of the deep space impact probe.

[0139] To visualize the impactor's trajectory through simulation, this invention utilizes STK (Satellite Tool Kit), a professional analysis software specifically designed for aerospace simulation, for secondary development. This software is used to analyze and calculate data, displaying the real-time attitude and trajectory of the deep space impactor during its flight. STK's powerful real-time 3D display capabilities make this easily achievable. Two entities are used for displaying the flight trajectory and attitude: the asteroid and the deep space impactor. To ensure system scalability, the asteroid uses STK's Facility object, and the deep space impactor uses STK's Aircraft object. By replacing the model files of these two entities with specified files, a realistic simulation effect is achieved.

[0140] To achieve dynamic image simulation, this invention establishes a dynamic image simulation system. This system receives simulation data from the main control system and simulates images of the asteroid target and the starry background captured by the navigation sensor of the impact probe. The dynamic image simulation system uses a combination of QT and OpenGL to simulate the starry background and the asteroid target. A class `SceneWindow` in the program publicly inherits from `QOpenGLWidget` and `QOpenGLFunctions_3_3_Core`, allowing this class to use OpenGL rendering and drawing functions to complete a series of simulation operations.

[0141] For the full-process simulation of the impactor, based on the aforementioned asteroid data collection and orbit simulation, eight parameters—the impactor's initial three-dimensional position, initial three-dimensional velocity, approximate time interval, and the number of days before impact—are used as inputs for the first segment of orbital grounding. The parameters for the final recursion setting—including the last pulse correction time, the pre-correction recursion interval, the post-correction recursion interval, and the number of seconds before impact—are used. After the first segment of orbital recursion, corresponding recursion parameters are provided for the second segment of dynamic control recursion. The last pulse correction time determines the end point of the impactor nozzle switching control quantity. After this control, the impactor will continue flying without control until impact. The pre-correction recursion time interval is mainly used by the dynamic control module for the recursion step size when it is far from the target asteroid; the time interval requirement is low, aiming to complete long-distance recursion. The post-correction recursion time interval considers the situation when it is closer to the target asteroid, thus placing higher demands on the real-time performance of the impactor position. The number of days before impact determines the final time node of the dynamic control module's recursion; after this node, the impactor will be out of control and continue flying under the influence of the external environment.

[0142] In the simulation of this invention, the initial orbit recursion physical model is responsible for the long-distance orbit recursion of the impactor from launch to a distance of 30,000 km from the target asteroid. The three-dimensional coordinates and three-dimensional velocities of the impactor are used as inputs to the kinematics module, and the output of the kinematics model is used as inputs to the next module. The kinematics module recursion is realized by utilizing the dynamic factors received by the impactor, including perturbations from the central celestial body, solar radiation pressure, and third-body perturbations. Using the eighth-order Runge-Kutta method, the orbits of the impactor and the target asteroid are recursively calculated given the initial input, and the position information and relative physical distance between the target asteroid and the impactor in the same coordinate system are calculated. After completing the initial orbit recursion, the kinetic energy impact disposal module transmits the parameter results of the initial orbit recursion to the final orbit control recursion. By introducing a control module, the current position and attitude of the impactor can be interfered with, causing it to fly according to a preset orbit. During the specific orbit recursion process, the dynamics module is called in stages and steps to achieve the final orbit disposal result. A dynamic simulation model is established using two main parts: the orbit dynamics model and the attitude dynamics model. Through end-point control ground propulsion, attitude dynamics model and sensitive period model were established, and the terminal trajectory control results were recursively derived, thus realizing the terminal correction and simulation of the guided trajectory.

[0143] This invention features the following technological innovations and design characteristics: The high-level software coupling of each data simulation unit facilitates the implementation of data models under different configuration requirements, resulting in high system flexibility and compatibility; precise modeling is achieved using dynamics, completing the simulation of the entire process of kinetic energy impact; a set of inter-module data interaction management methods is designed, enabling customizable and convenient data interaction between modules; a self-designed multi-threaded structure effectively adapts to different data reception conditions; and the software adopts a Windows standard design.

[0144] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A dynamic-based simulation method for the orbits of target asteroids and impactors, characterized in that, include: Step 1: Calculate the asteroid's ephemeris using an ephemeris algorithm to obtain the asteroid's position vector in the solar ecliptic inertial frame, establish the asteroid's orbital dynamics equation, substitute the position vector into the asteroid's orbital dynamics equation, and recursively obtain the asteroid's motion orbital model. Step 2: Set the initial three-dimensional position and velocity of the impactor, and calculate the acceleration caused by gravity at the location of the impactor based on the initial three-dimensional position of the impactor; Step 3: Establish the impactor orbital dynamics equations. Substitute the initial three-dimensional position, velocity, and acceleration of the impactor into the impactor orbital dynamics equations. Combine this with the target asteroid's motion orbital model to recursively obtain the first segment of the impactor's orbital model from its initial position to a distance of Skm from the target asteroid. Step 4: Using the first segment orbital model, obtain the three-dimensional position and velocity of the impactor when it is Skm away from the target asteroid. Combine the acceleration generated by the force on the impactor when it is Skm away from the target asteroid and the dynamic equation of the impactor attitude, establish the full dynamic equation of the final segment of the impactor, and obtain the orbital model from the position of the impactor Skm away from the target asteroid to the point of impact between the impactor and the target asteroid, where S is a positive number. The impactor is accelerated by the perturbation of the central celestial body. for: In the formula: r is the solar gravitational constant; r2 is the radius vector of the impactor relative to the central celestial body, which is the Sun. Acceleration of the impactor due to solar radiation pressure perturbation for: In the formula: The solar radiation pressure coefficient; The radius vector of the impactor relative to the central celestial body's reference frame; AU is the radius vector of the central object relative to the central object's reference frame; AU is 1 astronomical unit. It is the solar constant; is the effective cross-sectional area of ​​the impactor that withstands the light pressure; m is the mass of the impactor. The acceleration of the impactor caused by the perturbation of a third body is The acceleration produced by the d-th third-body perturbation is: In the formula: The gravitational constant of the third body; The radius vector of the third body relative to the central celestial body's reference frame; The acceleration generated by the impactor nozzle is: In the formula: u i is the on / off state of nozzle i; A is the transformation matrix from the impactor's own system to the central celestial body's inertial frame; Let be the acceleration generated by the i-th nozzle in the impactor system; n is the number of impactor nozzles.

2. The dynamics-based target asteroid and impactor orbit simulation method according to claim 1, characterized in that, In step one, the asteroid orbital dynamics equations are: In the formula, r1 is the position vector of the asteroid in the solar ecliptic inertial frame. Let be the velocity vector of the asteroid. Let be the acceleration vector of the asteroid. The acceleration caused by the force exerted on the asteroid by the impactor after it strikes the asteroid; Let r1 be the derivative of the position vector r1 in the asteroid's ecliptic inertial frame of reference. The velocity vector of the asteroid The derivative; in, In the formula, This is the acceleration of the asteroid due to the Sun's gravity. The acceleration of the asteroid due to the gravitational pull of the eight planets. This refers to the acceleration of the asteroid due to the gravitational pull of Pluto and the four largest asteroids. This is the acceleration caused by the asteroid's oblateness perturbation by the Sun. This is the acceleration of the asteroid caused by the gravitational pull of the nebula.

3. The dynamics-based target asteroid and impactor orbit simulation method according to claim 2, characterized in that, In step three, the acceleration generated by the forces acting on the first segment of the orbital model includes: the acceleration generated by the perturbation of the central celestial body, the acceleration generated by the perturbation of solar radiation pressure, and the acceleration generated by the perturbation of a third body; In step four, the acceleration generated by the forces acting on the final orbital model includes: the acceleration generated by the perturbation of the central celestial body, the acceleration generated by the perturbation of solar radiation pressure, the acceleration generated by the perturbation of the third body, and the acceleration generated by the jet ejection from the impactor's nozzle.

4. The dynamics-based target asteroid and impactor orbit simulation method according to claim 3, characterized in that, The transformation matrix A from the impactor's own frame to the central body's inertial frame: In the formula: Let A1 be the rotation angle along the z-axis; A1 is the transformation matrix relative to the z-axis. A1 is the y-axis rotation angle; A2 is the transformation matrix relative to the y-axis; A3 is the x-axis rotation angle; A4 is the transformation matrix relative to the x-axis. Acceleration generated by nozzles on each axis in the impactor system for: In the formula: The thrust generated by the i-th nozzle; m is the current mass of the impactor.

5. The dynamic-based target asteroid and impactor orbit simulation method according to claim 3, characterized in that, In step three, the initial orbital model from the impactor's initial position to the target asteroid at a distance of Skm is as follows: in, The radius vector of the impactor relative to the central celestial body The derivative of 2, The velocity vector of the impactor The derivative of .

6. The dynamics-based target asteroid and impactor orbit simulation method according to claim 5, characterized in that, In step three, the first segment of the orbit model from the initial position of the impactor to the target asteroid Skm is obtained by recursion using the eighth-order Runge-Kutta formula.

7. The dynamic-based target asteroid and impactor orbit simulation method according to claim 5, characterized in that, In step three, the method for determining the distance Skm from the target asteroid is as follows: The current coordinates of the impactor are transformed using the transformation matrix A from the impactor's own frame to the central celestial body's inertial frame, and then the three-dimensional distance calculation formula is used: The calculation involves determining the distance between the impactor and the target asteroid in the same coordinate system during the recursive orbit calculation. In the formula, d represents the relative distance between the impactor and the asteroid, and x1, y1, and z1 represent the impactor's position in the three-dimensional coordinate system. 2、 z2 represents the position of the asteroid in a three-dimensional coordinate system.

8. The dynamic-based target asteroid and impactor orbit simulation method according to claim 7, characterized in that, In step four, the attitude dynamics model of the impactor is as follows: The impactor includes two sails. This represents the acceleration along the Y-axis of the impactor. Indicates the velocity of the impactor along the Y-axis. Let ω be the angular acceleration of the impactor. Let ω be the angular velocity of the impactor, and q be the position vector of the impactor. , These are the modal coordinates of the solar panel in the +Y and -Y directions, respectively, preserving modes up to order 5; Λ f This is a diagonal array of modal frequencies for the solar panel; The modal damping coefficient for the solar panel is set to a reference value of 0.

05. , , respectively, are the coupling coefficient matrices of solar panel vibration in the +Y and -Y directions to the rotation of the satellite's central body, and I represents the inertia matrix of the impactor in its own system.

9. The dynamics-based target asteroid and impactor orbit simulation method according to claim 8, characterized in that, The full dynamic equations for the final stage of the impactor are: in, This represents the initial acceleration of the impactor. This represents the control torque of the impactor's principal axes at different moments of inertia. Z-axis rotation angle The derivative; y-axis rotation angle The derivative; x-axis rotation angle The derivative, , These are the derivatives of the solar panel modal coordinates in the +Y and -Y directions, respectively. This represents the acceleration produced by the gravitational pull of all third bodies on the accelerator. Angular velocity of the impactor The component in the X-axis direction, Angular velocity of the impactor The component in the Y-axis direction, u j This refers to the on / off state of nozzle j. Angular velocity of the impactor Component in the Z-axis direction; This represents the magnitude of the acceleration generated by the nozzle along the x-axis of this system. This represents the magnitude of the acceleration generated by the nozzle along the y-axis of this system. This represents the magnitude of the acceleration generated by the nozzle along the z-axis of this system. This represents the absolute value of the jet acceleration generated by the attitude control torque. In the formula: The magnitude of the control torque on the x-axis. The magnitude of the control torque acting on the y-axis. The magnitude of the control torque on the z-axis. Let x be the length of the lever arm along the x-axis. The length of the lever arm along the y-axis. Let z be the length of the lever arm. This represents the component of the impactor's inertia matrix I along the x-axis in the self-contained system of the impactor. This represents the component of the impactor's inertia matrix I along the y-axis in the self-contained system of the impactor. This represents the component of the impactor's inertia matrix I along the z-axis in the impactor's own system.

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