A composite planning method for three-dimensional reentry trajectory of spacecraft

Abstract

This invention proposes a composite planning method for a three-dimensional reentry trajectory of a spacecraft, comprising: analyzing the three-degree-of-freedom model of the reentering spacecraft to obtain models of the longitudinal and transverse planes; optimizing the trajectory of the longitudinal plane; evenly dividing the entire flight time domain and calculating the change in horizontal distance within each period; planning the trajectory of the transverse plane; smoothing the junctions of the transverse trajectories between adjacent time periods; inversely calculating the temporal variation of the trajectory deflection angle using the longitude and latitude relationships of the transverse trajectories; and planning the three-dimensional reentry trajectory of the spacecraft based on all state variables and control variables. This method can effectively improve the reliability of spacecraft reentry and address the poor convergence and low terminal accuracy of traditional gradient algorithms for solving complex nonlinear problems. It also avoids the reliance on initial values ​​and high computational complexity of dynamic programming methods.

Description

Technical Field

[0001] The present invention relates to a spacecraft re-entry trajectory compounding method, in particular to a compound planning method for a spacecraft three-dimensional re-entry trajectory. Background Art

[0002] For spacecraft reentry, the multi-scenario mission and rapidly changing flight speeds inevitably create a more complex aerodynamic environment. Throughout the reentry process, the spacecraft experiences rapid speed changes, strong maneuverability, and a wide range of landing points. This complex flight environment and unique flight conditions place significant challenges on the spacecraft's structural strength, aerodynamic layout, and material properties, while also presenting significant difficulties and challenges to control system design.

[0003] The key points of the reentry mission include constraining the spacecraft's thermal flux, dynamic pressure, and overload during high-speed reentry flight, while ensuring a safe landing that meets no-fly zone avoidance requirements. Given the numerous variables in flight, quickly and accurately planning a reentry trajectory that meets multiple objective constraints is a complex task. Trajectory planning methods are generally divided into direct and indirect methods. Traditional gradient algorithms are indirect methods and have poor convergence in solving complex nonlinear, multi-constrained problems such as spacecraft reentry trajectories, making it difficult to obtain an accurate analytical solution. Dynamic programming algorithms often rely on reliable initial values ​​when planning trajectories. When faced with multiple obstacle avoidance, they need to comprehensively compare all path costs, which requires a large amount of computation and is not suitable for online fast planning. Summary of the Invention

[0004] Purpose of the invention: The technical problem to be solved by the present invention is to provide a composite planning method for the three-dimensional re-entry trajectory of a spacecraft in response to the shortcomings of the existing technology.

[0005] In order to solve the above technical problems, the present invention discloses a composite planning method for a three-dimensional reentry trajectory of a spacecraft, comprising the following steps:

[0006] Step 1: Analyze the three-degree-of-freedom model of the reentry spacecraft and obtain the longitudinal and transverse plane models by decoupling.

[0007] Step 2: Set the initial angle of attack, combine the aerodynamic constraints, and use the conjugate gradient method to optimize the trajectory in the longitudinal plane to obtain the relationship between speed, altitude, and horizontal distance over time;

[0008] Step 3: Based on the data of the spacecraft's longitudinal trajectory, the entire flight time domain is evenly divided into N time periods ΔT, and the change in horizontal distance ΔS within each period is calculated;

[0009] Step 4: Dynamic programming is used to plan the trajectory in the transverse plane. The planning time interval is ΔT, the range of each planned trajectory is ΔS, the trajectory direction is constrained by the pre-set no-fly zone range, and the roll angle constraint is set.

[0010] Step 5: Smoothing the connections between the horizontal trajectories of adjacent time periods;

[0011] Step 6: Reversely calculate the change pattern of trajectory deflection over time through the longitude and latitude relationship of the horizontal trajectory;

[0012] Step 7: Plan the three-dimensional re-entry trajectory of the spacecraft based on all the state quantities and control quantities calculated in steps 2, 4, and 6.

[0013] Furthermore, the model of the longitudinal plane and the transverse plane is obtained by decoupling as described in step 1, and the specific method includes:

[0014] Step 1-1: Analyze the three-degree-of-freedom model of the spacecraft on the reentry trajectory as follows:

[0015] The reentry motion of the spacecraft is considered as a non-rotating center-of-mass motion, and the flight process is an unpowered glide, with attitude changes affected by aerodynamic forces. At the same time, the earth is considered as a homogeneous sphere with a curved surface and rotation. The three-degree-of-freedom model of the spacecraft, that is, the reentry dynamics equation, is as follows:

[0016]

[0017] Where m is the mass of the spacecraft; V is the spacecraft velocity; γ is the trajectory inclination; ψ is the trajectory deflection; r is the distance from the center of mass of the spacecraft to the center of the earth; θ, are the longitude and latitude of the spacecraft's projection point on the surface; σ is the roll angle; ω d is the angular velocity of the Earth's rotation; μ is the Earth's gravitational constant; g is the acceleration of gravity; ρ is the atmospheric density; L and D are the aerodynamic lift and drag, respectively. represents the rate of change of the distance from the center of the Earth, represents the rate of change of longitude, represents the rate of change of latitude, represents the rate of change of speed, represents the rate of change of trajectory inclination, Indicates the rate of change of trajectory deflection angle;

[0018] Steps 1-2, obtain the longitudinal plane model, as follows:

[0019] Assume that the roll angle is zero and the trajectory deflection angle remains unchanged, that is: σ=0, The longitudinal plane model of the spacecraft, that is, the dynamic equation in the longitudinal plane is as follows:

[0020]

[0021] Steps 1-3, obtain the transverse plane model, as follows:

[0022] Assume that the angle of attack is zero and the trajectory inclination angle is fixed, that is: α=0, The lateral plane model of the spacecraft, that is, the dynamic equation in the lateral plane is as follows:

[0023]

[0024] Furthermore, the optimization of the longitudinal plane trajectory described in step 2 specifically includes:

[0025] Step 2-1, constructing a longitudinal plane trajectory optimization model;

[0026] In step 2-2, the conjugate gradient method is used to optimize the trajectory, and the penalty function method is used to deal with the constraint problem.

[0027] Furthermore, the longitudinal plane trajectory optimization model described in step 2-1 is constructed as follows:

[0028] min J=-S

[0029]

[0030] x(t0)=x0

[0031]

[0032]

[0033]

[0034] α min ≤α≤α max

[0035] Where J represents the performance index, x = [V, γ, ψ, r, θ] represents the state of the spacecraft, and the state at time t is represented by the function x(t); x0 is the initial state, that is, the state at time t0, represents the rate of change of state quantity, subject to represents the constraint condition, f(x, α, t) represents the differential equation of state quantity; S is the horizontal distance; represents the heat flow rate, k m is a constant related to the spacecraft material; R s is the equivalent radius of the spacecraft nose cone stagnation point, which is a constant value; n represents the overload, G is the gravity acting on the spacecraft at the current moment; q represents the dynamic pressure; n maxand q max are the maximum permissible stagnation aerodynamic heating rate, maximum normal overload and maximum dynamic pressure respectively; α min represents the minimum allowable angle of attack, α represents the angle of attack, α max Indicates the maximum allowable angle of attack.

[0036] Furthermore, the conjugate gradient method described in step 2-2 is used to optimize the trajectory, and the penalty function method is used to deal with the constraint problem, as follows:

[0037]

[0038] Where H represents the Hamiltonian function, λ T represents the transpose of the Lagrange multiplier, represents the co-state equation, arg sup represents the upper bound of the parameter, Ω represents the range of attack angle, λ(t f ) represents the transversality condition, x(t f ) represents the state quantity at the terminal moment, The symbol represents a partial derivative.

[0039] Furthermore, the dynamic programming method described in step 4 is used to plan the trajectory of the transverse plane, specifically including:

[0040] Step 4-1, constructing a transverse plane trajectory planning model;

[0041] In step 4-2, dynamic programming is used to plan the trajectory within each time period.

[0042] Furthermore, the lateral plane trajectory planning model described in step 4-1 is constructed as follows:

[0043]

[0044] subject to x(k)=f[x(k-1),σ(k-1),k-1]

[0045] x(t f )=x f

[0046] x(t0)=x0

[0047]

[0048]

[0049] σ min ≤σ(k)≤σ max

[0050] k=1,2,…,N

[0051] Among them, J[x(N), N] represents the performance index; x f is the terminal state quantity; θ z , are the longitude and latitude of the no-fly zone calibration location; R e is the average radius of the Earth; R z is the no-fly zone radius; is the terminal performance index; L[x(k), σ(k), k] is the integrand; x(N) represents the terminal state quantity, x(k) represents the state quantity at time k, σ(k) represents the roll angle at time k, k represents the kth time period, N represents the terminal time, θ(k) represents the longitude at time k, represents the latitude at time k, σ min represents the minimum allowable roll angle, σ max Indicates the maximum allowable roll angle.

[0052] Furthermore, the dynamic programming method described in step 4-2 is used to plan the trajectory within each time period, specifically including:

[0053] Step 4-2-1, when k=1, the planning is as follows:

[0054]

[0055] x * (1) = f[x(0), σ(0), 0]

[0056]

[0057] in, represents the minimum performance index when k=1, x * (1) represents the state quantity when k=1, x * (0) represents the initial state, σ * (1) represents the roll angle when k = 1;

[0058] Substituting the initial state x0 into the above equation, we can obtain the solution:

[0059]

[0060] That is, the state quantity x when k=1 is obtained * (1) and minimum performance indicators

[0061] Step 4-2-2, when k=k+1, the planning is as follows:

[0062]

[0063] x * (k) = f[x *(k-1), σ * (k-1), k-1]

[0064]

[0065] in, represents the minimum performance index at time k, x * (k) represents the state quantity at time k, σ * (k) represents the roll angle at time k;

[0066] According to the above equation, we can solve it:

[0067]

[0068] That is, the state quantity x at time k is obtained * (k) and minimum performance indicators

[0069] Step 4-2-3, when k=N, the planning is as follows:

[0070]

[0071] x * (N) = f[x * (N-1), σ * (N-1), N-1]

[0072]

[0073] Terminal performance indicators Substituting into the above equation, we can get:

[0074]

[0075] That is, the state quantity x at the terminal moment is obtained * (N) and minimum performance indicators

[0076] Furthermore, the connection between the horizontal trajectories of adjacent time periods described in step 5 is smoothed, that is, the connection between the trajectories of adjacent time periods is smoothed using a second-order Bezier curve, as follows:

[0077] B(i)=(1-i) 2 P0+2i(1-i)P1+i 2 P2

[0078] Among them, B(i) represents the curve equation, P1 is the coordinate of the connection point; P0 and P2 are the coordinates of two adjacent points of P1; i is the scale parameter, i∈[0,1].

[0079] Furthermore, the reverse calculation of the change pattern of the trajectory deflection angle over time by using the longitude and latitude relationship of the horizontal trajectory described in step 6 specifically includes:

[0080] Through the reentry dynamics equation, the expressions for longitude and latitude are as follows:

[0081]

[0082]

[0083] The relationship between trajectory declination, longitude and latitude is further obtained as follows:

[0084]

[0085] Among them, S θ and are the distances in the longitude and latitude directions respectively.

[0086] Beneficial effects:

[0087] The method proposed in the present invention decouples three-dimensional trajectory planning into longitudinal trajectory planning and lateral trajectory planning, reducing the computational complexity of the planning process. Longitudinal plane: The conjugate gradient method is used to optimize the angle of attack parameters to obtain the largest possible horizontal range; only aerodynamic constraints are considered to avoid the problem of poor convergence. Transverse plane: Based on the longitudinal trajectory time period and horizontal range, the dynamic programming method is used to plan the lateral trajectory, which can meet the terminal constraints; segmented planning effectively improves the real-time performance and terminal accuracy of the process, and can simultaneously design the size and direction of the roll angle. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, and the above and / or other advantages of the present invention will become more apparent.

[0089] Figure 1 It is an overall flow chart of the method of the present invention.

[0090] Figure 2 It is the flowchart of longitudinal trajectory planning.

[0091] Figure 3 It is a flow chart of lateral trajectory planning.

[0092] Figure 4 It is a three-dimensional reentry trajectory planning map. DETAILED DESCRIPTION

[0093] The present invention provides a composite planning method for a three-dimensional re-entry trajectory of a spacecraft. In view of the complex re-entry flight process, the three-dimensional re-entry trajectory planning problem is divided into longitudinal trajectory planning and lateral trajectory planning. Aerodynamic constraints are considered in the longitudinal plane, and the re-entry horizontal range is used as a performance indicator. Under the condition that the roll angle is zero and the trajectory deflection angle remains unchanged, the conjugate gradient algorithm is used to optimize the control amount of the angle of attack to increase the horizontal range of the spacecraft. In the lateral plane, based on the flight time and horizontal range of the longitudinal trajectory, a dynamic programming algorithm is used to solve the optimal path to the target point. At the same time, the path constraints of multiple no-fly zones are introduced, and the constraints are converted into the control of the roll angle. Based on the planned lateral path, the change law of the trajectory deflection angle is reversely solved. All state quantities obtained by longitudinal planning and lateral planning are used to simulate the three-dimensional re-entry trajectory. This method can meet the aerodynamic constraints during the re-entry flight process, avoid multiple pre-set no-fly zones, and effectively improve the reliability of spacecraft re-entry. This method can effectively solve the problems of poor convergence and low terminal accuracy in solving complex nonlinear problems in traditional gradient algorithms, while avoiding the problems of dynamic programming methods' dependence on initial values ​​and large amount of calculation. The technical solutions adopted by the present invention are:

[0094] Step 1: Analyze the three-degree-of-freedom model of the reentry spacecraft and obtain the longitudinal and transverse plane models by decoupling;

[0095] Step 2: Given a large initial angle of attack and combined with aerodynamic constraints, the conjugate gradient method is used to optimize the trajectory in the longitudinal plane to obtain the relationship between speed, altitude, and horizontal distance over time;

[0096] Step 3: Based on the longitudinal trajectory data, the entire flight time domain is evenly divided into N time periods ΔT, and the change in horizontal distance ΔS within each period is calculated;

[0097] Step 4: Use dynamic programming to plan the trajectory in the transverse plane. The planning time interval is ΔT, the range of each planned trajectory is ΔS, the trajectory direction is constrained by the pre-set no-fly zone range, and the roll angle meets the constraint.

[0098] Step 5: Smoothing the connections between the horizontal trajectories of adjacent time periods;

[0099] Step 6: Reversely calculate the change pattern of trajectory deflection over time through the longitude and latitude relationship of the horizontal trajectory;

[0100] Step 7: Simulate the three-dimensional re-entry trajectory of the spacecraft based on all the state quantities and control quantities obtained in steps 2, 4, and 6.

[0101] The above step 1 is specifically as follows:

[0102] The spacecraft reentry motion is considered as the center of mass motion, and the rotation around the center of mass is not considered. The flight process is all unpowered gliding, and the thrust of the engine is not considered. The attitude change is affected by aerodynamic forces. At the same time, the earth is regarded as a homogeneous sphere, and the arc surface and rotation of the earth are taken into account. The spacecraft reentry dynamic equation is given as follows:

[0103]

[0104] Where: m is the mass of the spacecraft; V is the spacecraft velocity; γ is the trajectory inclination; ψ is the trajectory deflection; r is the distance from the center of mass of the spacecraft to the center of the earth; θ, are the longitude and latitude of the spacecraft's projection point on the surface; σ is the roll angle; ω d is the angular velocity of the Earth's rotation; μ is the Earth's gravitational constant; g is the acceleration of gravity; ρ is the atmospheric density; L and D are the aerodynamic lift and drag, respectively.

[0105] In the process of flight trajectory planning in the longitudinal plane, it is assumed that the bank angle is zero and the trajectory deviation angle remains unchanged, that is, σ=0. The dynamic model of the spacecraft in the longitudinal plane is given as:

[0106]

[0107] In the trajectory planning of the transverse plane, the change in the height direction is not considered, so the angle of attack is zero and the trajectory inclination angle is fixed, that is, α = 0. The dynamic equations for the transverse plane are given as:

[0108]

[0109] The above step 2 is specifically as follows:

[0110] Step 1: Construct a longitudinal plane trajectory optimization model:

[0111] min J=-S

[0112]

[0113] x(t0)=x0

[0114]

[0115]

[0116]

[0117] α min ≤α≤α max

[0118] Where: x = [V, γ, ψ, r, θ]; x0 is the initial state; S is the horizontal distance; k m is a constant related to the spacecraft material; R s is the equivalent radius of the spacecraft nose cone stagnation point, which is related to constants such as the angle of attack. To simplify the calculation, it is considered a constant here; G is the gravity acting on the spacecraft at the current moment; n max and q max are the maximum allowable stagnation aerodynamic heating rate, maximum normal overload, and maximum dynamic pressure, respectively.

[0119] Step 2: Use the conjugate gradient method to optimize the trajectory and use the penalty function method to deal with the constraint problem:

[0120]

[0121] The above step 4 is specifically as follows:

[0122] Step 1: Construct a transverse plane trajectory planning model:

[0123]

[0124] subject to x(k)=f[x(k-1),σ(k-1),k-1]

[0125] x(t f )=x f

[0126] x(t0)=x0

[0127]

[0128]

[0129] σ min ≤σ(k)≤σ max

[0130] k=1,2,…,N

[0131] Where: x f is the terminal state quantity; θ z , are the longitude and latitude of the no-fly zone calibration location; R e is the average radius of the Earth; R z is the no-fly zone radius; is the terminal performance index; L[x(k), σ(k), k] is the integrand.

[0132] Step 2: Use dynamic programming to plan the trajectory within each time period.

[0133] When k=1,

[0134]

[0135] x * (1) = f[x(0), σ(0), 0]

[0136]

[0137] Combined with the initial state x0, we can get

[0138]

[0139] When k=k+1,

[0140]

[0141]

[0142]

[0143] Obtain

[0144]

[0145] When k=N,

[0146]

[0147] x * (N) = f[x * (N-1), σ * (N-1), N-1]

[0148]

[0149] Joint terminal performance indicators Obtain

[0150]

[0151] The above step 5 is specifically as follows:

[0152] At the connection points of the trajectories of adjacent time periods, a second-order Bezier curve is used for smoothing:

[0153] B(i)=(1-i) 2 P0+2i(1-i)P1+i 2 P2

[0154] Where: P1 is the coordinate of the connection point; P0, P2 are the coordinates of two adjacent points of P1; i is the scale parameter, i∈[0,1].

[0155] The above step 6 is specifically as follows:

[0156] Through the reentry dynamics equation, the following expressions for longitude and latitude are obtained:

[0157]

[0158]

[0159] Combining the above formula and eliminating the interference of other factors, we can get the relationship between trajectory declination and longitude and latitude:

[0160]

[0161] Where: x, z are the distances in the longitude and latitude directions respectively.

[0162] The above step 7 is specifically as follows:

[0163] Constructing the three-dimensional flight trajectory of the aircraft requires the relationship between the state quantity and the control quantity over time. The state quantity [V, γ, h] and the angle of attack α are obtained in step 2; the state quantity The roll angle σ is obtained from step 4, and the trajectory deflection angle ψ is obtained from step 6. By simulating the obtained state variables and control variables, the three-dimensional reentry flight trajectory can be obtained.

[0164] Example:

[0165] Combine Figure 1 The present invention provides a composite planning method for a three-dimensional reentry trajectory of a spacecraft, comprising:

[0166] Step 1: Analyze the three-degree-of-freedom model of the reentry spacecraft and obtain the longitudinal and transverse plane models by decoupling;

[0167] The spacecraft reentry motion is considered as the center of mass motion, and the rotation around the center of mass is not considered. The flight process is all unpowered gliding, and the thrust of the engine is not considered. The attitude change is affected by aerodynamic forces. At the same time, the earth is regarded as a homogeneous sphere, and the arc surface and rotation of the earth are taken into account. The spacecraft reentry dynamic equation is given as follows:

[0168]

[0169] Where: m is the mass of the spacecraft; V is the spacecraft velocity; γ is the trajectory inclination; ψ is the trajectory deflection; r is the distance from the center of mass of the spacecraft to the center of the earth; θ, are the longitude and latitude of the spacecraft's projection point on the surface; σ is the roll angle; ω d is the angular velocity of the Earth's rotation; μ is the Earth's gravitational constant; g is the acceleration of gravity; ρ is the atmospheric density; L and D are the aerodynamic lift and drag, respectively.

[0170] In the process of flight trajectory planning in the longitudinal plane, it is assumed that the bank angle is zero and the trajectory deviation angle remains unchanged, that is, σ=0. The dynamic model of the spacecraft in the longitudinal plane is given as:

[0171]

[0172] In the trajectory planning of the transverse plane, the change in the height direction is not considered, so the angle of attack is zero and the trajectory inclination angle is fixed, that is, α = 0. The dynamic equations for the transverse plane are given as:

[0173]

[0174] Step 2, combine Figure 2 , given a large initial angle of attack, combined with aerodynamic constraints, the conjugate gradient method is used to optimize the trajectory in the longitudinal plane to obtain the relationship between speed, altitude and horizontal distance over time;

[0175] Step 1: Construct a longitudinal plane trajectory optimization model:

[0176] min J=-S

[0177]

[0178] x(t0)=x0

[0179]

[0180]

[0181]

[0182] αmax min

[0183] Where: x = [V, γ, ψ, r, θ]; x0 is the initial state; S is the horizontal distance; k m is a constant related to the spacecraft material; R s is the equivalent radius of the spacecraft nose cone stagnation point, which is related to constants such as the angle of attack. To simplify the calculation, it is considered a constant here; G is the gravity acting on the spacecraft at the current moment; are the maximum allowable stagnation aerodynamic heating rate, maximum normal overload, and maximum dynamic pressure, respectively.

[0184] Step 2: Use the conjugate gradient method to optimize the trajectory and use the penalty function method to deal with the constraint problem:

[0185]

[0186] Step 3: Based on the longitudinal trajectory data, the entire flight time domain is evenly divided into N time periods ΔT, and the change in horizontal distance ΔS within each period is calculated;

[0187] Step 4, combine Figure 3 , dynamic programming is used to plan the trajectory in the transverse plane. The planning time interval is ΔT, the range of each planned trajectory is ΔS, the trajectory direction is constrained by the pre-set no-fly zone range, and the roll angle meets the constraint;

[0188] Step 1: Construct a transverse plane trajectory planning model:

[0189]

[0190] subject to x(k)=f[x(k-1),σ(k-1),k-1]

[0191] x(t f )=x f

[0192] x(t0)=x0

[0193]

[0194]

[0195] σ min ≤σ(k)≤σ max

[0196] k=1,2,…,N

[0197] Where: x f is the terminal state quantity; θ z , are the longitude and latitude of the no-fly zone calibration location; R e is the average radius of the Earth; R z is the no-fly zone radius; is the terminal performance index; L[x(k), σ(k), k] is the integrand.

[0198] Step 2: Use dynamic programming to plan the trajectory within each time period.

[0199] When k=1,

[0200]

[0201] x * (1) = f[x(0), σ(0), 0]

[0202]

[0203] Combined with the initial state x0, we can get

[0204]

[0205] When k=k+1,

[0206]

[0207] x * (k) = f[x * (k-1), σ * (k-1), k-1]

[0208]

[0209] Obtain

[0210]

[0211] When k=N,

[0212]

[0213] x * (N) = f[x * (N-1), σ * (N-1), N-1]

[0214]

[0215] Joint terminal performance indicators Obtain

[0216]

[0217] Step 5: Smoothing the connections between the horizontal trajectories of adjacent time periods;

[0218] At the connection points of the trajectories of adjacent time periods, a second-order Bezier curve is used for smoothing:

[0219] B(i)=(1-i) 2 P0+2i(1-i)P1+i 2 P2

[0220] Where: P1 is the coordinate of the connection point; P0, P2 are the coordinates of two adjacent points of P1; i is the scale parameter, i∈[0,1].

[0221] Step 6: Reversely calculate the change pattern of trajectory deflection over time through the longitude and latitude relationship of the horizontal trajectory;

[0222] Through the reentry dynamics equation, the following expressions for longitude and latitude are obtained:

[0223]

[0224]

[0225] Combining the above formula and eliminating the interference of other factors, we can get the relationship between trajectory declination and longitude and latitude:

[0226]

[0227] Where: x, z are the distances in the longitude and latitude directions respectively.

[0228] Step 7: Simulate the three-dimensional re-entry trajectory of the spacecraft based on all the state quantities and control quantities obtained in steps 2, 4, and 6.

[0229] like Figure 4 As shown, it is a three-dimensional reentry trajectory planning diagram, where:

[0230] Select three different initial reentry states and calibrate multiple no-fly zones. Simulate the flight process according to the above steps to obtain the time-dependent relationships of all state and control variables. Plot the relationships between the longitude, latitude, and altitude of the three trajectories based on the longitude, latitude, and altitude values ​​at the same time.

[0231] In a specific implementation, the present application provides a computer storage medium and a corresponding data processing unit, wherein the computer storage medium is capable of storing a computer program that, when executed by the data processing unit, executes the invention content of the composite planning method for a three-dimensional reentry trajectory of a spacecraft provided by the present invention and some or all of the steps in each embodiment. The storage medium may be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM).

[0232] Those skilled in the art will clearly understand that the technical solutions in the embodiments of the present invention can be implemented by means of computer programs and their corresponding general hardware platforms. Based on this understanding, the technical solutions in the embodiments of the present invention, in essence or in other words, the part that contributes to the prior art, can be embodied in the form of a computer program, i.e., a software product. The computer program software product can be stored in a storage medium and includes a number of instructions for enabling a device including a data processing unit (which can be a personal computer, server, single-chip microcomputer, MCU, or network device, etc.) to execute the methods described in various embodiments of the present invention or certain parts of the embodiments.

[0233] This invention provides a concept and method for a complex planning method for three-dimensional spacecraft reentry trajectories. There are numerous methods and approaches for implementing this technical solution. The foregoing description is merely a preferred embodiment of the invention. It should be noted that those skilled in the art may make improvements and modifications without departing from the principles of the invention, and such improvements and modifications are also within the scope of protection of the invention. Any components not specified in this embodiment may be implemented using existing technologies.

Claims

1. A composite planning method for three-dimensional reentry trajectories of spacecraft, characterized by: The following steps are involved: Step 1: Analyze the three-degree-of-freedom model of the reentry spacecraft and obtain the longitudinal and transverse plane models by decoupling. Step 2: Set the initial angle of attack, combine the aerodynamic constraints, and use the conjugate gradient method to optimize the trajectory in the longitudinal plane to obtain the relationship between speed, altitude, and horizontal distance over time; Step 3: Based on the data of the spacecraft's longitudinal trajectory, the entire flight time domain is evenly divided into N time periods ΔT, and the change in horizontal distance ΔS within each period is calculated; Step 4: Dynamic programming is used to plan the trajectory in the transverse plane. The planning time interval is ΔT, the range of each planned trajectory is ΔS, the trajectory direction is constrained by the pre-set no-fly zone range, and the roll angle constraint is set. Step 5: Smoothing the connections between the horizontal trajectories of adjacent time periods; Step 6: Reversely calculate the change pattern of trajectory deflection over time through the longitude and latitude relationship of the horizontal trajectory; Step 7, planning the three-dimensional reentry trajectory of the spacecraft based on all state quantities and control quantities calculated in steps 2, 4, and 6; The model of the longitudinal plane and the transverse plane is obtained by decoupling in step 1, and the specific method includes: Step 1-1: Analyze the three-degree-of-freedom model of the spacecraft on the reentry trajectory as follows: The reentry motion of the spacecraft is considered as a non-rotating center-of-mass motion, and the flight process is an unpowered glide, with attitude changes affected by aerodynamic forces. At the same time, the earth is considered as a homogeneous sphere with a curved surface and rotation. The three-degree-of-freedom model of the spacecraft, that is, the reentry dynamics equation, is as follows: Where m is the mass of the spacecraft; V is the spacecraft velocity; γ is the trajectory inclination; ψ is the trajectory deflection; r is the distance from the center of mass of the spacecraft to the center of the earth; θ, are the longitude and latitude of the spacecraft's projection point on the surface; σ is the roll angle; ω d is the angular velocity of the Earth's rotation; μ is the Earth's gravitational constant; g is the acceleration of gravity; ρ is the atmospheric density; L and D are the aerodynamic lift and drag, respectively. represents the rate of change of the distance from the center of the Earth, represents the rate of change of longitude, represents the rate of change of latitude, represents the rate of change of speed, represents the rate of change of trajectory inclination, Indicates the rate of change of trajectory deflection angle; Steps 1-2, obtain the longitudinal plane model, as follows: Assume that the roll angle is zero and the trajectory deflection angle remains unchanged, that is: σ=0, The longitudinal plane model of the spacecraft, that is, the dynamic equation in the longitudinal plane is as follows: Steps 1-3, obtain the transverse plane model, as follows: Assume that the angle of attack is zero and the trajectory inclination angle is fixed, that is: α=0, The lateral plane model of the spacecraft, that is, the dynamic equation in the lateral plane is as follows:

2. A composite planning method for a three-dimensional reentry trajectory of a spacecraft according to claim 1, characterized in that: The optimization of the longitudinal plane trajectory described in step 2 specifically includes: Step 2-1, constructing a longitudinal plane trajectory optimization model; In step 2-2, the conjugate gradient method is used to optimize the trajectory, and the penalty function method is used to deal with the constraint problem.

3. The composite planning method for a three-dimensional reentry trajectory of a spacecraft according to claim 2, characterized in that: The longitudinal plane trajectory optimization model described in step 2-1 is constructed as follows: minJ=-S x(t0)=x0 α min ≤α≤α max Where J represents the performance index, x = [V, γ, ψ, r, θ] represents the state of the spacecraft, and the state at time t is represented by the function x(t); x0 is the initial state, that is, the state at time t0, represents the rate of change of state quantity, subjectto represents the constraint condition, f(x,α,t) represents the differential equation of state quantity; S is the horizontal distance; represents the heat flow rate, k m is a constant related to the spacecraft material; R s is the equivalent radius of the spacecraft nose cone stagnation point, which is a constant value; n represents the overload, G is the gravity acting on the spacecraft at the current moment; q represents the dynamic pressure; n max and q max are the maximum permissible stagnation aerodynamic heating rate, maximum normal overload and maximum dynamic pressure respectively; α min represents the minimum allowable angle of attack, α represents the angle of attack, α max Indicates the maximum allowable angle of attack.

4. The composite planning method for a three-dimensional reentry trajectory of a spacecraft according to claim 3, characterized in that: The conjugate gradient method is used to optimize the trajectory as described in step 2-2, and the penalty function method is used to deal with the constraint problem, as follows: Where H represents the Hamiltonian function, λ T represents the transpose of the Lagrange multiplier, represents the co-state equation, argsup represents the upper bound of the parameter, Ω represents the range of the angle of attack, λ(t f ) represents the transversality condition, x(t f ) represents the state quantity at the terminal moment, The symbol represents a partial derivative.

5. The composite planning method for a three-dimensional reentry trajectory of a spacecraft according to claim 4, characterized in that: The dynamic programming method described in step 4 is used to plan the trajectory of the transverse plane, specifically including: Step 4-1, constructing a transverse plane trajectory planning model; In step 4-2, dynamic programming is used to plan the trajectory within each time period.

6. The composite planning method for a three-dimensional reentry trajectory of a spacecraft according to claim 5, characterized in that: The construction of the transverse plane trajectory planning model described in step 4-1 is as follows: subject to x(k)=f[x(k-1),σ(k-1),k-1] x(t f )=x f x(t0)=x0 s min ≤σ(k)≤σ max k=1,2,…,N Among them, J[x(N),N] represents the performance index; x f is the terminal state quantity; θ z , are the longitude and latitude of the no-fly zone calibration location; R e is the average radius of the Earth; R z is the no-fly zone radius; is the terminal performance index; L[x(k),σ(k),k] is the integrand; x(N) represents the terminal state quantity, x(k) represents the state quantity at time k, σ(k) represents the roll angle at time k, k represents the kth time period, N represents the terminal time, θ(k) represents the longitude at time k, represents the latitude at time k, σ min represents the minimum allowable roll angle, σ max Indicates the maximum allowable roll angle.

7. The composite planning method for a three-dimensional reentry trajectory of a spacecraft according to claim 6, characterized in that: The dynamic programming method described in step 4-2 is used to plan the trajectory within each time period, specifically including: Step 4-2-1, when k=1, the planning is as follows: x * (1)=f[x(0),σ(0),0] in, represents the minimum performance index when k=1, x * (1) represents the state quantity when k=1, x * (0) represents the initial state, σ * (1) represents the roll angle when k = 1; Substituting the initial state x0 into the above equation, we can obtain the solution: That is, the state quantity x when k=1 is obtained * (1) and minimum performance indicators Step 4-2-2, when k=k+1, the planning is as follows: x * (k)=f[x * (k-1),σ * (k-1),k-1] in, represents the minimum performance index at time k, x * (k) represents the state quantity at time k, σ * (k) represents the roll angle at time k; According to the above equation, we can solve it: That is, the state quantity x at time k is obtained * (k) and minimum performance indicators Step 4-2-3, when k=N, the planning is as follows: x * (N)=f[x * (N−1),σ * (N−1),N−1] Terminal performance indicators Substituting into the above equation, we can get: That is, the state quantity x at the terminal moment is obtained * (N) and minimum performance indicators 8. The composite planning method for a three-dimensional reentry trajectory of a spacecraft according to claim 7, characterized in that: The smoothing process for the connection of the horizontal trajectories of adjacent time periods described in step 5 is to use a second-order Bezier curve to smooth the connection of the trajectories of adjacent time periods, as follows: B(i)=(1-i) 2 P0+2i(1-i)P1+i 2 P2 Among them, B(i) represents the curve equation, P1 is the coordinate of the connection point; P0, P2 are the coordinates of two adjacent points of P1; i is the scale parameter, i∈[0,1].

9. The composite planning method for a three-dimensional reentry trajectory of a spacecraft according to claim 8, characterized in that: The reverse calculation of the change pattern of the trajectory deflection angle over time using the longitude and latitude relationship of the horizontal trajectory described in step 6 specifically includes: Through the reentry dynamics equation, the expressions for longitude and latitude are as follows: The relationship between trajectory declination, longitude and latitude is further obtained as follows: Among them, S θ and are the distances in the longitude and latitude directions respectively.

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