CN112193437A - Spacecraft out-of-plane orbital transfer trajectory planning method - Google Patents

Abstract

The invention provides a spacecraft out-of-plane orbital transfer trajectory planning method, which comprises the following steps: step 1: obtaining corresponding parameters of a trajectory planning method according to actual parameters and task conditions of the rocket; step 2: establishing a convex optimization problem under the condition of rocket failure; and step 3: and (4) giving an initial guess, and iteratively solving a convex optimization problem under the condition of rocket faults by adopting a model compensation method. Through the steps, the near-circular orbit planning method based on convex optimization under the condition of rocket failure can effectively solve the problem of rocket entry under the condition of failure, and quickly generates the circular orbit with the largest radius and the corresponding track which can be entered by the rocket within a certain time; the method of the invention is scientific, has good manufacturability and has wide popularization and application value.

Description

Spacecraft out-of-plane orbital transfer trajectory planning method

Technical Field

The invention provides a spacecraft out-of-plane orbital transfer trajectory planning method, and belongs to the technical field of trajectory planning in aerospace technology.

Background

In recent years, with the development of scientific technology, the demand for satellite transmission resources is increasing. Therefore, the spacecraft is required to have the online autonomous trajectory planning capability, so that the task design workload before launching of the spacecraft is reduced, the launching period is shortened, and the success rate of tasks is improved. For the traditional launching mode, a great deal of pre-task design work is needed, and flight path deviation and some emergencies are difficult to deal with after launching. For the traditional spacecraft out-of-plane orbital transfer control method, the spacecraft trajectory cannot be planned, and when the spacecraft trajectory and the nominal task trajectory have large deviation, the traditional method is difficult to work. In this context, a spacecraft out-of-plane orbital transfer trajectory planning method becomes particularly important. The convex optimization method has the characteristics of global optimality, high calculation speed, stable convergence and the like, so that the convex optimization method can be applied to the spacecraft different-plane orbital transfer trajectory planning method.

Disclosure of Invention

The purpose of the invention is as follows: the invention aims to provide a spacecraft different-surface orbital transfer trajectory planning method to solve the problem of spacecraft different-surface orbital transfer trajectory planning, so that a spacecraft can enter a circular orbit with the largest orbit radius under the fault condition.

Technical scheme

The invention provides a spacecraft out-of-plane orbital transfer trajectory planning method, namely an online trajectory planning method based on convex optimization, which comprises the following steps:

(1) step 1: obtaining corresponding parameters of a trajectory planning method according to actual parameters and task conditions of the spacecraft;

the "actual parameters and task conditions of the spacecraft" in step 1 are:

engine parameters under the condition of spacecraft failure and current state parameters of the spacecraft;

the "corresponding parameters of the trajectory planning method" in step 1 are as follows:

at discrete time points t_kK is 0,1, …, N, the logarithm of mass z at each discrete time point₀(t_k)；

According to experience, taking the number N of discrete points as 10-100;

(2) step 2: establishing a convex optimization problem of spacecraft out-of-plane orbital transfer;

the convex optimization problem of spacecraft out-of-plane orbital transfer in the step 2 is as follows:

wherein, x (t)_k) Representing the spacecraft at a discrete point in time t_kThe state variable of (b), X represents the optimization variable, u (t)_k)∈IR³Representing the spacecraft at a discrete point in time t_kThe control variable of (d), g (t)_k)∈IR³Representing the spacecraft at a discrete point in time t_kSubject to gravitational acceleration, A, B₁,B₂For the state transition matrix, F ∈ IR¹For the virtual control variable, T represents the thrust magnitude of the spacecraft, z (T)_k) Representing the logarithmic mass sequence of the spacecraft,. kappa.epsilon.IR¹For relaxation variables, γ ∈ IR¹As a penalty factor, x₀Is an initial state quantity, H, R, S_j,v_j,c_j,d_jIs a terminal matrix parameter;

according to experience, the value of the penalty factor gamma is more than or equal to 100;

(3) and step 3: giving an initial guess, and iteratively solving a convex optimization problem of spacecraft out-of-plane orbital transfer by adopting a model compensation method;

the "initial guess" in step 3 is: log-of-mass sequence z₀(t_k)；

The "model compensation method" described in step 3 is: for the (i + 1) th iteration, the result of the ith iteration solution is used as the initial guess of the current iteration;

the "iterative solution" described in step 3 means that: solving the convex optimization problem of spacecraft out-of-plane orbital transfer by adopting CVX software, and stopping solving when the solution result meets the convergence precision; empirically, the convergence accuracy was 0.01-0.0001.

The invention has the advantages and effects that:

through the steps, the method for planning the different-surface orbital transfer track of the spacecraft can effectively solve the problem of different-surface orbital transfer of the spacecraft, and quickly generate the different-surface orbital transfer track and control quantity of the spacecraft in a certain time; the method of the invention is scientific, has good manufacturability and has wide popularization and application value.

Drawings

FIG. 1 is a block diagram of the process of the present invention.

FIG. 2 is a graph of trace results obtained in an embodiment of the present invention.

FIG. 3 is a diagram of control results obtained in an embodiment of the present invention.

Detailed Description

The invention is described in detail below with reference to the figures and specific embodiments.

Examples

As shown in fig. 1, the method for planning the trajectory of the spacecraft orbital transfer in the different planes comprises the following steps:

(1) step 1: obtaining corresponding parameters of a trajectory planning method according to actual parameters and task conditions of the spacecraft;

(2) step 2: establishing a convex optimization problem of spacecraft out-of-plane orbital transfer;

(3) and step 3: giving an initial guess, and iteratively solving a convex optimization problem of spacecraft out-of-plane orbital transfer by adopting a model compensation method;

the "actual parameters and task conditions of the spacecraft" in step 1 are specifically:

maximum thrust T of the spacecraft, initial mass m of the spacecraft₀Second consumption Δ m of spacecraft, time of flight t of spacecraft_f。

The "corresponding parameters of the trajectory planning method" in step 1 are as follows:

at discrete time points t_kK is 0,1, …, N, which is obtained by:

t_k＝k·t_f/N，k＝0,1,…,N

thrust acceleration z at discrete time points₀(t_k) It is obtained by the following way:

z₀(t_k)＝ln(m₀-Δm·t_k)，k＝0,1,…,N

the "spacecraft different-plane orbital transfer trajectory planning problem" in the step 2 specifically is as follows:

wherein, x (t)_k) Representing the spacecraft at a discrete point in time t_kThe state variable of (b), X represents the optimization variable, u (t)_k)∈IR³Representing the spacecraft at a discrete point in time t_kThe control variable of (d), g (t)_k)∈IR³Representing the spacecraft at a discrete point in time t_kSubject to gravitational acceleration, A, B₁,B₂For the state transition matrix, F ∈ IR¹For the virtual control variable, T represents the thrust magnitude of the spacecraft, z (T)_k) Representing the logarithmic mass sequence of the spacecraft,. kappa.epsilon.IR¹For relaxation variables, γ ∈ IR¹As a penalty factor, x₀Is an initial state quantity, H, R, S_j,v_j,c_j,d_jIs a terminal matrix parameter;

the calculation mode of the state transition matrix is as follows:

the "initial guess" in step 3 is: log-of-mass sequence z₀(t_k)；

The "model compensation method" described in step 3 is: for the (i + 1) th iteration, the result z of the solution of the ith iteration is adoptedⁱ⁺¹As an initial guess z for the current iteration₀(t_k)；

The "iterative solution" described in step 3 means: solving the convex optimization problem of the spacecraft different-plane orbital transfer trajectory planning method by adopting ECOS software, and when the solution result meets the convergence condition | | zⁱ-z^i-1Stopping solving when | | is less than or equal to epsilon; in this embodiment, ε is taken to be 0.01.

In this embodiment, after setting the specific parameters, the method for planning the near-circular orbit is specifically implemented as follows:

the corresponding parameter of the specific track planning method is set as t_f＝1,N＝10,m ₀1, T2, and the initial state quantity is set to x₀＝[1 0 0 0 1 0]^TBy the invention, a track result graph shown in fig. 2 and a control result graph shown in fig. 3 can be obtained; the details of the specific implementation are as follows:

step 1: obtaining corresponding parameters of a trajectory planning method according to actual parameters and task conditions of the spacecraft; wherein the maximum thrust of the spacecraft is set to gamma 2, and the initial mass m of the spacecraft ₀1, the second consumption Δ m of the spacecraft is 0.5, and the flight time t of the spacecraft is 0_f1, the terminal state of the task is determined

x_f＝[1 0 0.5 0 1 0],z_f＝ln0.5；

The corresponding parameters of the trajectory planning method are set as follows: at discrete time points t_k＝k·0.1，k＝0,1,…,10，z₀(t_k)＝ln(1-0.05·k)，k＝0,1,…,10。

Step 2: the method comprises the following steps of establishing a convex optimization problem of a spacecraft out-of-plane orbital transfer trajectory planning problem, wherein the convex optimization problem specifically comprises the following steps:

wherein the state transition matrix is as follows:

and step 3: giving an initial guess, and iteratively solving a convex optimization problem of spacecraft out-of-plane orbital transfer trajectory planning by adopting a model compensation method:

for the (i + 1) th iteration, the result z of the solution of the ith iteration is adoptedⁱ⁺¹As the initial guess z of the current iteration, when the solution result meets the convergence condition | | zⁱ-z^i-1And the solution is stopped, and the | | | is less than or equal to 0.01.

Claims (1)

1. A spacecraft out-of-plane orbital transfer trajectory planning method comprises the following steps:

step 1: obtaining corresponding parameters of a trajectory planning method according to actual parameters and task conditions of the spacecraft;

the "actual parameters and task conditions of the spacecraft" in step 1 are: engine parameters under the condition of spacecraft failure and current state parameters of the spacecraft; the "corresponding parameters of the trajectory planning method" in step 1 are as follows: at discrete time points t_kK is 0,1, …, N, the logarithm of mass z at each discrete time point₀(t_k) (ii) a According to experience, taking the number N of discrete points as 10-100;

step 2: establishing a convex optimization problem of spacecraft out-of-plane orbital transfer;

the convex optimization problem of spacecraft out-of-plane orbital transfer in the step 2 is as follows:

subjectto x(t_k+1)＝Ax(t_k)+B₁[u(t_k)+g(t_k)]+B₂[u(t_k+1)+g(t_k+1)],k＝0,1,…,N

Hx(t_f)＝R,||S_jX+v_j||≤c_jX+d_j,j＝1,2

x(t₀)＝x₀

wherein, x (t)_k) Representing the spacecraft at a discrete point in time t_kThe state variable of (b), X represents the optimization variable, u (t)_k)∈IR³Representing the spacecraft at a discrete point in time t_kThe control variable of (d), g (t)_k)∈IR³Representing the spacecraft at a discrete point in time t_kSubject to gravitational acceleration, A, B₁,B₂For the state transition matrix, F ∈ IR¹For the virtual control variable, T represents the thrust magnitude of the spacecraft, z (T)_k) Representing the logarithmic mass sequence of the spacecraft,. kappa.epsilon.IR¹For relaxation variables, γ ∈ IR¹As a penalty factor, x₀Is an initial state quantity, H, R, S_j,v_j,c_j,d_jIs a terminal matrix parameter; the value of the penalty factor gamma is more than or equal to 100;

and step 3: giving an initial guess, and iteratively solving a convex optimization problem of spacecraft out-of-plane orbital transfer by adopting a model compensation method;

the "initial guess" in step 3 is: log-of-mass sequence z₀(t_k)；

The "model compensation method" described in step 3 is: for the (i + 1) th iteration, the result of the ith iteration solution is used as the initial guess of the current iteration;

the "iterative solution" described in step 3 means that: solving the convex optimization problem of spacecraft out-of-plane orbital transfer by adopting CVX software, and stopping solving when the solution result meets the convergence precision; the convergence accuracy is 0.01-0.0001.

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