A launch vehicle orbital trajectory planning method based on orbit prediction

Abstract

This invention provides a method for planning a launch vehicle's orbital insertion trajectory based on orbital prediction. The method comprises the following steps: 1. Establishing a model for the launch vehicle's orbital insertion flight problem based on the orbital prediction; 2. Establishing a convex optimization subproblem for the launch vehicle's orbital insertion; and 3. Iteratively solving the convex optimization subproblem for the launch vehicle's orbital insertion, given an initial guess. Through these steps, the invention can implement launch vehicle orbital insertion trajectory planning. This method can be applied online, achieving good stability and universality. It is scientific, manufacturable, and has broad application value.

Description

Technical Field

[0001] The present invention provides a method for planning a launch vehicle's trajectory for orbital entry based on orbit prediction. The method is a trajectory planning method for a launch vehicle that needs to be pushed into orbit in a vacuum, and belongs to the fields of aerospace; guidance, navigation and control technology; and trajectory planning. Background Art

[0002] In recent years, humanity's increasing demand for space resources has led to an increasing number of launch vehicle missions. Launch vehicles may face numerous uncertainties while flying in space, requiring them to have trajectory planning capabilities to ensure normal entry into the intended orbit, or to enter a degraded orbit in the event of a failure.

[0003] In actual flight, launch vehicles typically enter their intended orbits via a push-glide approach. Current methods for this push-glide approach primarily focus on solving the optimal push-glide-push sequence offline, and then planning a single, full-thrust sequence online based on real-time conditions. This approach requires extensive offline mission design and struggles to cope with large deviations and failures during flight. Therefore, developing launch vehicle trajectory planning methods that can adapt to push-glide approaches has become a key and challenging research topic in the aerospace field.

[0004] In summary, the present invention aims to solve the existing difficulty in orbital trajectory planning for launch vehicles. It mathematically describes the glide phase flight based on orbit prediction and designs a trajectory planning method for push-glide-push flight. This method is widely applicable to push-glide-push orbital missions and has a certain degree of originality. Summary of the Invention

[0005] (1) Purpose of the present invention

[0006] The present invention proposes a method for planning the orbital insertion trajectory of a launch vehicle based on orbit prediction. For orbital insertion missions in a vacuum environment, the push-glide-push orbit insertion flight mode makes it difficult to optimize the glide phase flight. Therefore, based on the orbit prediction description of the glide phase flight of the launch vehicle, a trajectory planning method is studied to solve the problems of poor versatility and difficulty in online operation in the existing technology.

[0007] (2) Technical solution

[0008] The present invention provides a method for planning a launch vehicle's orbital trajectory based on orbit prediction, and the specific steps are as follows:

[0009] Step 1: Establish a model for the cargo rack's orbital insertion problem based on orbit prediction;

[0010] According to the mission requirements, the push-glide-push flight mode of the launch vehicle into orbit is determined, the orbit prediction formula is used to describe the glide phase flight, and the optimal control problem model of the launch vehicle into orbit is established;

[0011] Step 2: Establish the convex optimization sub-problem of launch vehicle orbit insertion;

[0012] Based on the launch vehicle orbit insertion optimal control problem model established in step 1, it is transformed into a launch vehicle orbit insertion convex optimization subproblem through linearization method;

[0013] Step 3: Given an initial guess, iteratively solve the convex optimization subproblem of launching the launch vehicle into orbit;

[0014] The "push-glide-push flight mode" mentioned in step 1 is the flight time of two full-push phases and the glide phase during the launch vehicle's orbital entry flight.

[0015] The “orbit prediction formula” described in step 1 is:

[0016]

[0017] Where r0 and v0 are the position and velocity at the start of the sliding segment, r c With v c are the position and velocity at the start of the glide segment, μ is the earth's gravitational constant, and β is the normalized glide segment flight time;

[0018] The "optimal control model for launch vehicle orbit insertion" described in step 1 is:

[0019] min-γκ2

[0020]

[0021]

[0022]

[0023]

[0024]

[0025] r1(t 1,f )=r0,v1(t 1,f )=v0,r2(t 2,0 )=r c ,v2(t 2,0 )=v c

[0026]

[0027]

[0028] Where r l With v lare the position and velocity of the launch vehicle in the full propulsion phase, u l is the thrust acceleration of the launch vehicle in the full thrust phase, a l is the maximum thrust acceleration allowed by the rocket in the full thrust phase, g l is the gravitational acceleration of the rocket during the full thrust phase, t 1,0 With t 2,0 are the starting flight moments of the two full thrust segments, t 1,f With t 2,f are the flight times of the two full push sections, h 1,f With h 2,f are the normal vectors of the orbital planes of the two terminal launch vehicles, h 1,set With h 2,set are the orbital plane normal vectors corresponding to the two full-thrust stage terminals given by the mission, κ1 and κ2 are the momentum vector moduli of the launch vehicles at the two full-thrust stage terminals, and L 1,f With L 2,f are the Laplace vectors of the two full-thrust terminal launch vehicles, L 1,set With L 2,set are the Laplace vectors corresponding to the two full push segment terminals given by the task, r p is the perigee height of the orbit corresponding to the current state of the launch vehicle, r p,set is the terminal perigee height given for the mission, r 1,0 With v 1,0 is the initial position and velocity of the launch vehicle, γ is the penalty factor;

[0029] Among them, the "linearization method" described in step 2 is a classic method in launch vehicle trajectory planning;

[0030] The “convex optimization subproblem of launch vehicle orbit insertion” described in step 2 is:

[0031]

[0032] Where N l is the number of discrete points corresponding to the two full push segments, x l,k ,l=1,2,k=1,…,N l +1 is the state of the two full-thrust stage launch vehicles, x c with x c They are the status of the launch vehicle in the glide phase, is the initial guess, F is the virtual control variable, γ1, γ2, γ3 are penalty factors, η is the neighboring operator, C, D, H x,1 、H x,2 、L x,1 、L x,2 、H1、H2、L1、L2、R x,2, R is the linearization parameter generated by the linearization method, A l 、B l,1 、B l,2 is the state transfer matrix;

[0033] Among them, the "initial guess" mentioned in step 3 is the guess of the terminal state of the two full thrust phases and the glide phase of the launch vehicle. l 0 , l = 0, 1, 2, and the gravitational acceleration sequence g l ;

[0034] The iterative solution mentioned in step 3 means: solving the convex optimization subproblem of the launch vehicle orbit insertion based on the initial guess, and using the solution result as the initial guess for the next solution. When the deviation between the solution result and the initial guess is less than the allowable error, the solution is stopped. According to experience, the allowable error is 0.0001-0.00001.

[0035] Through the above steps, the present invention can realize the trajectory planning of the launch vehicle into orbit. The method can be applied online, achieving good stability and universality. The method is scientific, has good processability, and has broad promotion and application value.

[0036] (3) Advantages and effects of the present invention

[0037] (1) The present invention is based on an orbit prediction formula that can describe the glide phase flight of a launch vehicle, can satisfy the terminal orbit constraints given by the mission, and can be used online;

[0038] (2) The method of the present invention is scientific, has good processability, and has broad promotion and application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a flow chart of the method of the present invention.

[0040] Figure 2 Schematic diagram of the flight trajectory of a carrier rocket in an embodiment of the present invention.

[0041] Figure 3 2 is a schematic diagram of the control result of the carrier rocket in an embodiment of the present invention. DETAILED DESCRIPTION

[0042] The present invention will be further described in detail below with reference to the accompanying drawings and implementation examples.

[0043] The present invention provides a method for planning the trajectory of a launch vehicle into orbit based on orbit prediction, the flow chart of which is as follows: Figure 1 As shown, it includes the following steps:

[0044] Step 1: Establish a model for the cargo rack's orbital insertion problem based on orbit prediction;

[0045] According to the mission requirements, determine the flight time t of the first full thrust phase of the launch vehicle 1,set , the flight time of the second full push segment t 2,set , the normalized flight time β of the glide segment set , the trajectory prediction formula is used to describe the glide segment flight:

[0046]

[0047] Where r0 and v0 are the position and velocity at the start of the sliding segment, r c With v c are the position and velocity at the start of the glide phase, and μ is the Earth's gravitational constant. Based on the orbit prediction formula, the optimal control model for the launch vehicle into orbit is established:

[0048] min-γκ2

[0049]

[0050]

[0051]

[0052]

[0053]

[0054] r1(t 1,set )=r0,v1(t 1,set )=v0,r2(t 2,0 )=r c ,v2(t 2,0 )=v c

[0055]

[0056]

[0057] Where r l With v l are the position and velocity of the launch vehicle in the full propulsion phase, u l is the thrust acceleration of the launch vehicle in the full thrust phase, a l is the maximum thrust acceleration allowed by the rocket in the full thrust phase, g l is the gravitational acceleration of the rocket during the full thrust phase, t 1,0 With t 2,0 are the starting flight moments of the two full-thrust segments, h 1,f With h 2,fare the normal vectors of the orbital planes of the two terminal launch vehicles, h 1,set With h 2,set are the orbital plane normal vectors corresponding to the two full-thrust stage terminals given by the mission, κ1 and κ2 are the momentum vector moduli of the launch vehicles at the two full-thrust stage terminals, and L 1,f With L 2,f are the Laplace vectors of the two full-thrust terminal launch vehicles, L 1,set With L 2,set are the Laplace vectors corresponding to the two full push segment terminals given by the task, r p is the perigee height of the orbit corresponding to the current state of the launch vehicle, r p,set is the terminal perigee height given for the mission, r 1,0 With v 1,0 is the initial position and velocity of the launch vehicle, γ is the penalty factor;

[0058] Step 2: Establish the convex optimization sub-problem of launch vehicle orbit insertion;

[0059] According to the launch vehicle orbit insertion optimal control problem model established in step 1, it is transformed into the launch vehicle orbit insertion convex optimization subproblem through the linearization method:

[0060]

[0061] Where N l is the number of discrete points corresponding to the two full push segments, x l,k ,l=1,2,k=1,…,N l +1 is the state of the two full-thrust stage launch vehicles, x c with x c They are the status of the launch vehicle in the glide phase, is the initial guess, F is the virtual control variable, γ1, γ2, γ3 are penalty factors, η is the neighboring operator, C, D, H x,1 、H x,2 、L x,1 、L x,2 、H1、H2、L1、L2、R x,2 , R is the linearization parameter generated by the linearization method, A l 、B l,1 、B l,2 is the state transfer matrix, which is calculated as follows:

[0062]

[0063] Step 3: Given an initial guess, iteratively solve the convex optimization subproblem of launching the launch vehicle into orbit;

[0064] Given an initial guess, the terminal states x of the launch vehicle in the two full thrust phases and the glide phase arel 0, l = 0, 1, 2 and the gravitational acceleration sequence g l Make a guess; the gravitational acceleration sequence is calculated as follows when it is solved for the first time:

[0065]

[0066] The gravitational acceleration sequence is calculated in the following way in the second and subsequent solutions:

[0067]

[0068] Where r l,j j = 1, ..., N + 1 is the position state of the launch vehicle obtained by solving the launch vehicle orbit insertion convex optimization subproblem last time; definition:

[0069]

[0070] According to the initial guess, the convex optimization subproblem of the launch vehicle into orbit is solved and the solution result X * As the initial guess X for the next solution 0 , when ||X * -X 0 When ||≤ε, stop solving;

[0071] Simulation case:

[0072] This section will use a numerical simulation case as a demonstration of the method, not an actual flight mission;

[0073] The dimensionless initial state of the launch vehicle is x 1,0 =[-0.7528,0.6346,0.3070,-0.6431,-0.6920,-0.1483] T , the dimensionless flight time of the first full push segment is t 1,set = 0.0872, the dimensionless flight time of the second full push segment is t 1,set =0.8394, the normalized flight time of the glide segment is β set =0.491, the number of discrete points is N1=50, N2=100, and the thrust acceleration sequence is:

[0074] a 1,j =0.327 / (1-0.327 / 0.556×0.0017×(j-1)),j=1,…,51

[0075] a 2,j =0.327 / (0.9488-0.327 / 0.556×0.0084×(j-1)),j=1,…,101

[0076] The first iteration solves the given dimensionless initial guess as:

[0077]

[0078] According to the implementation process of this method, the schematic diagram of the launch vehicle flight trajectory is obtained as follows: Figure 2 The control result diagram of the launch vehicle is shown in Figure 3 As shown, this method can enable the launch vehicle to enter orbit by push-glide method.

Claims

1. A method for planning a launch vehicle's trajectory based on orbit prediction, characterized in that: The specific steps are as follows: Step 1: Establish a model for the cargo rack's orbital insertion problem based on orbit prediction; According to the mission requirements, the push-glide-push flight mode of the launch vehicle into orbit is determined, the orbit prediction formula is used to describe the glide phase flight, and the optimal control problem model of the launch vehicle into orbit is established; Step 2: Establish the convex optimization sub-problem of launch vehicle orbit insertion; Based on the launch vehicle orbit insertion optimal control problem model established in step 1, it is transformed into a launch vehicle orbit insertion convex optimization subproblem through linearization method; Step 3: Given an initial guess, iteratively solve the convex optimization subproblem of launching the launch vehicle into orbit; In step 1, the push-glide-push flight mode is the flight time of two full-thrust phases and the glide phase during the launch vehicle's orbital flight; In step 1, the orbit prediction formula is: Where r0 and v0 are the position and velocity at the start of the sliding segment, r c With v c are the position and velocity at the start of the glide segment, μ is the earth's gravitational constant, and β is the normalized glide segment flight time; In step 1, the optimal control model for the launch vehicle into orbit is: Where r l With v l are the position and velocity of the launch vehicle in the full propulsion phase, u l is the thrust acceleration of the launch vehicle in the full thrust phase, a l is the maximum thrust acceleration allowed by the rocket in the full thrust phase, g l is the gravitational acceleration of the rocket during the full thrust phase, t 1,0 With t 2,0 are the starting flight moments of the two full thrust segments, t 1,f With t 2,f are the flight times of the two full push sections, h 1,f With h 2,f are the normal vectors of the orbital planes of the two terminal launch vehicles, h 1,set With h 2,set are the orbital plane normal vectors corresponding to the two full-thrust stage terminals given by the mission, κ1 and κ2 are the momentum vector moduli of the launch vehicles at the two full-thrust stage terminals, and L 1,f With L 2,f are the Laplace vectors of the two full-thrust terminal launch vehicles, L 1,set With L 2,set are the Laplace vectors corresponding to the two full push segment terminals given by the task, r p is the perigee height of the orbit corresponding to the current state of the launch vehicle, r p,set is the terminal perigee height given for the mission, r 1,0 With v 1,0 is the initial position and velocity of the launch vehicle, γ is the penalty factor; In step 2, the convex optimization sub-problem of the launch vehicle into orbit is: Where N l is the number of discrete points corresponding to the two full push segments, x l,k ,l=1,2,k=1,…,N l +1 is the state of the two full-thrust stage launch vehicles, x c with x c They are the status of the launch vehicle in the glide phase, is the initial guess, F is the virtual control variable, γ1, γ2, γ3 are penalty factors, η is the neighboring operator, C, D, H x,1 、H x,2 、L x,1 、L x,2 、H1、H2、L1、L2、R x,2 , R is the linearization parameter generated by the linearization method, A l 、B l,1 、B l,2 is the state transfer matrix; In step 3, the initial guess is the terminal state of the two full thrust phases and the glide phase of the launch vehicle. and the gravitational acceleration series g l .

2. The method for planning a launch vehicle's trajectory for orbital entry based on orbit prediction according to claim 1, wherein: In step three, iterative solution means: according to the initial guess, the convex optimization subproblem of the launch vehicle into orbit is solved, and the solution result is used as the initial guess for the next solution. When the deviation between the solution result and the initial guess is less than the allowable error, the solution is stopped; the allowable error is 0.0001-0.00001.

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