A method, device, medium and product for calculating modeled achievable track elements and making decisions on degraded tracks

Abstract

The present invention discloses a method, device, medium, and product for calculating patterned achievable orbital elements and making decisions about degraded orbits, relating to the field of rocket achievable orbital element calculation. The method comprises obtaining the rocket's initial flight state parameters, target orbital elements, and safety altitude constraints under non-lethal thrust descent, establishing a patterned optimal control problem model based on the rocket's dynamics differential equations and operational constraints, and convexifying it to obtain a convex optimal control subproblem. The convex optimal control subproblem is discretized and slack variables are introduced to obtain a convex optimization subproblem. The method further comprises setting the rocket's mode coefficients in different modes, iteratively solving the convex optimization subproblem using a convex optimization algorithm, obtaining achievable orbital elements for different modes, making decisions on rocket orbit degradation, obtaining the final rocket achievable orbital elements, and determining a reference trajectory for the rocket's operation. The present invention can improve the calculation efficiency of achievable orbital elements and enhance mission adaptability.

Description

Technical Field

[0001] The present invention relates to the field of rocket achievable orbit determination, and in particular to a method, device, medium and product for modeling achievable orbit element calculation and degraded orbit decision-making. Background Art

[0002] With the development of aerospace technology and the increasing demand for on-orbit services and other missions, the requirements for rocket autonomy and reliability have been further improved. In particular, when an engine fails during flight, it is necessary to evaluate the remaining capabilities of the rocket, calculate its achievable orbital elements and make decisions on its degraded orbit.

[0003] Existing technologies for calculating achievable orbital elements fall into two main categories. One is based on spacecraft orbital dynamics and solves for the reachable set of single-pulse spacecraft orbits. This type of technology is suitable for spacecraft with single-pulse thrust, while rockets use continuous thrust. In the event of a power loss caused by an engine failure, it cannot be approximated as single-pulse thrust, and existing technologies cannot be used to solve for the orbital reachable set. Another method uses optimal control theory to solve for the reachable set of spacecraft. While it can adapt to continuous thrust, it only provides the reachable domain of the spacecraft's terminal position rather than the reachable orbital elements, and typically requires a large amount of computing resources, making it difficult to meet requirements in terms of computational efficiency and adaptability. Existing degraded orbit decision-making technologies mainly pre-set a few fixed degraded orbits and then determine the degraded orbit based on the rocket's remaining energy after a failure, rather than determining the degraded orbit in real time based on the rocket's remaining capacity.

[0004] Therefore, there is an urgent need for a method for calculating achievable orbit elements and making degraded orbit decisions, which can improve the calculation efficiency of achievable orbit elements and enhance mission adaptability. Summary of the Invention

[0005] The purpose of the present invention is to provide a method, device, medium and product for modeling achievable orbit element calculation and degraded orbit decision-making, which can improve the calculation efficiency of achievable orbit elements and improve mission adaptability.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] A method for calculating modeled achievable orbit elements and making decisions on degraded orbits, the method comprising:

[0008] Obtaining initial flight state parameters of the rocket under a non-lethal thrust reduction condition; the initial flight state parameters include the rocket's initial position, initial velocity, initial total mass, initial engine total thrust, initial engine average effective exhaust velocity, initial fuel mass, and initial fault thrust coefficient;

[0009] Obtaining target orbit elements and a safety altitude constraint of the rocket's target orbit; the target orbit elements include the target orbit semi-major axis, the target orbit eccentricity, the target orbit inclination, the target ascending node right ascension, and the target perigee argument; the safety altitude constraint represents the minimum orbit altitude at which the rocket can operate stably;

[0010] Based on the initial flight state parameters, the target orbit elements and the safety altitude constraint, combined with the rocket dynamics differential equation and the rocket operation process constraint conditions, a patterned optimal control problem model is established;

[0011] The patterned optimal control problem model is convexified to obtain a convex optimal control subproblem;

[0012] Discretizing the convex optimal control subproblem and introducing slack variables to obtain a convex optimization subproblem;

[0013] Setting the mode coefficients of the rocket in different modes, and using a convex optimization algorithm to iteratively optimize and solve the convex optimization subproblem, to obtain the achievable orbit elements of the rocket in different modes;

[0014] Based on the achievable orbital elements of the rocket in different modes, decisions are made on the rocket orbit degradation to obtain the final achievable orbital elements of the rocket and determine the reference trajectory of the rocket operation.

[0015] Optionally, the expression of the patterned optimal control problem model is:

[0016]

[0017] Where r represents the coordinate position of the rocket's center of mass in the Earth's equatorial inertial coordinate system; represents the derivative of the rocket's coordinate position; V represents the velocity of the rocket's center of mass in the Earth's equatorial inertial coordinate system; 1 T represents the direction of rocket thrust; μ represents the earth's gravitational constant; k T represents the fault thrust coefficient; T represents the total thrust value; m is the total mass of the rocket; V ex Indicates the effective exhaust velocity; represents the derivative of the rocket's velocity; represents the derivative of the total mass of the rocket; t0 represents the initial time; r0 represents the initial position of the rocket under non-lethal thrust descent; V0 represents the initial velocity of the rocket under non-lethal thrust descent; m0 represents the initial total mass of the rocket under non-lethal thrust descent; t f Indicates the rocket flight terminal moment; R E represents the average radius of the Earth; k1, k2, k3, k4 and k5 are all model coefficients; H represents the momentum vector of the rocket; L represents the Laplace vector; d1, d2 and d3 are all coefficient vectors; m fuelrepresents the initial fuel mass; i(t f ) represents the orbital inclination at the terminal moment of the rocket flight; i ref represents the target orbit inclination; r p (t f ) represents the distance from the center of the earth corresponding to the orbital perigee at the terminal moment of the rocket flight; H(t f ) represents the moment of momentum vector at the terminal moment of the rocket flight; L(t f ) represents the Laplace vector at the terminal moment of the rocket flight; h safe represents the safety height constraint; ω ref represents the target perigee argument; Ω ref Indicates the right ascension of the target ascending node.

[0018] Optionally, the patterned optimal control problem model is convexified to obtain a convex optimal control subproblem, specifically including:

[0019] The rocket dynamics differential equation and the rocket operation process constraint conditions are convexified respectively to obtain the convexified rocket dynamics differential equation and the convexified rocket operation process constraint conditions;

[0020] Linearizing the constraints in the patterned optimal control problem model to obtain linearized constraints;

[0021] Linearizing the performance index function in the patterned optimal control problem model to obtain a linearized performance index function;

[0022] Determining the convex optimal control subproblem based on the convex rocket dynamics differential equation, the convex rocket operation process constraints, the linearized constraints, and the linearized performance index function;

[0023] The expression of the convex optimal control subproblem is:

[0024]

[0025] Where i represents the orbital inclination; κ represents the magnitude of the momentum vector; represents the derivative of the state quantity; A represents the coefficient matrix corresponding to the state quantity; x represents the state quantity; B represents the coefficient matrix corresponding to the control quantity; g k represents the gravitational acceleration sequence of the kth iteration; r k represents the position reference trajectory of the kth iteration; r T represents the transpose of the position vector; i k represents the kth iteration orbit inclination reference trajectory; r f Represents the terminal position vector; H k represents the k-th iteration momentum vector reference trajectory; L krepresents the k-th iteration Laplace vector reference trajectory; r p Indicates the distance from the center of the earth to the perigee of the orbit corresponding to the rocket's flight state; V f represents the terminal velocity vector; V k represents the k-th iteration velocity vector reference trajectory; ω k represents the reference trajectory of the argument of perigee at the kth iteration; represents the unit vector corresponding to the momentum vector; λ represents the amplitude corresponding to the Laplace vector; represents the unit vector corresponding to the Laplace vector; Ω k represents the reference trajectory of the right ascension of the ascending node at the kth iteration; represents the linearized momentum vector; represents the linearized Laplace vector.

[0026] Optionally, the expression of the convex optimization subproblem is:

[0027]

[0028] Where J represents the performance index function of the convex optimal control subproblem; ξ1 and ξ2 are both slack variables; k ξ,1 and k ξ,2 represents the penalty coefficient of the slack variable; φ1 and φ2 represent the terminal constraints of the convex optimal control subproblem; x k represents the reference trajectory of the k-th iteration state; x f Represents the terminal state quantity; x N Represents the Nth discrete point of state quantity; x j+1 Represents the state quantity of the j+1th discrete point; x j Represents the state quantity of the jth discrete point; x j Represents the state quantity of the jth discrete point; and represents the state transfer matrix; j represents the discrete point number; m j represents the mass of the rocket at the jth discrete point; g k j+1 Represents the gravitational acceleration vector of the j+1th discrete point.

[0029] Optionally, setting mode coefficients of the rocket in different modes, using a convex optimization algorithm to iteratively optimize and solve the convex optimization subproblem, and obtaining the reachable orbit elements of the rocket in different modes; making a decision on rocket orbit degradation based on the reachable orbit elements of the rocket in different modes, obtaining the final reachable orbit elements of the rocket, and determining the reference trajectory of the rocket operation, specifically including:

[0030] Set the values ​​of the mode coefficients for the rocket operation in the first mode. The values ​​of the mode coefficients are: k1 = 1, k2 = 0, k3 = 0, k4 = 0, k5 = 0; k1, k2, k3, k4 and k5 are all mode coefficients;

[0031] Based on the assigned mode coefficients of the rocket operation in the first mode, using a convex optimization algorithm to iteratively optimize and solve the convex optimization subproblem to obtain a first optimization result, and according to the first optimization result, obtaining the reachable orbit elements in the first mode;

[0032] Determining whether the rocket can form a safe and stable orbit based on the reachable orbit elements in the first mode; if not, using the reachable orbit elements in the first mode as the final reachable orbit elements for the rocket;

[0033] If yes, then set the value of the mode coefficient of the rocket operation in the second mode, and the value of each mode coefficient is: k1 = 0, k2 = 1, k3 = 0, k4 = 0, k5 = 0;

[0034] Based on the assigned mode coefficients of the rocket operation in the second mode, using a convex optimization algorithm to iteratively optimize and solve the convex optimization subproblem to obtain a second optimization result, and according to the second optimization result, obtaining the reachable orbit elements in the second mode;

[0035] Determining whether the rocket can reach the set orbital inclination according to the achievable orbital element in the second mode; if not, using the achievable orbital element in the first mode as the final rocket achievable orbital element;

[0036] If yes, then set the value of the mode coefficient of the rocket operation in the third mode, and assign the value of each mode coefficient to: k1 = 0, k2 = 0, k3 = 1, k4 = 0, k5 = 0;

[0037] Based on the assigned mode coefficients of the rocket operation in the third mode, an iterative optimization solution is performed on the convex optimization subproblem using a convex optimization algorithm to obtain a third optimization result, and according to the third optimization result, an element of the achievable orbit in the third mode is obtained;

[0038] Determining whether the rocket can reach the set right ascension of the ascending node based on the achievable orbit elements in the third mode; if not, using the achievable orbit elements in the first mode as the final achievable orbit elements for the rocket;

[0039] If so, the values ​​of the mode coefficients of the rocket operation in the fourth mode and the mode coefficients of the rocket operation in the fifth mode are set respectively; wherein the mode coefficients of the rocket operation in the fourth mode are assigned as follows: k1=0, k2=0, k3=0, k4=1, k5=0, and the mode coefficients of the rocket operation in the fifth mode are assigned as follows: k1=0, k2=0, k3=0, k4=0, k5=1;

[0040] Based on the mode coefficient of the rocket operation in the fourth mode, using a convex optimization algorithm to iteratively optimize and solve the convex optimization subproblem to obtain a fourth optimization result, and according to the fourth optimization result, obtaining the reachable orbit element in the fourth mode;

[0041] Based on the mode coefficients of the rocket operation in the fifth mode, using a convex optimization algorithm to iteratively optimize and solve the convex optimization subproblem to obtain a fifth optimization result, and according to the fifth optimization result, obtaining the achievable orbit elements in the fifth mode;

[0042] Determine whether the reachable orbit element in the fifth mode satisfies the reachable orbit element in the fourth mode. mod5 ≥a mod4 +800×10 3 ; Among them, a mod4 represents the semi-major axis of the fourth mode; a mod5 represents the semi-major axis of the fifth mode;

[0043] If so, the achievable orbital element in the fifth mode is used as the final rocket achievable orbital element; if not, the achievable orbital element in the fourth mode is used as the final rocket achievable orbital element.

[0044] Optionally, based on the mode coefficient of the rocket operation in the first mode, a convex optimization algorithm is used to iteratively optimize and solve the convex optimization subproblem to obtain a first optimization result, and according to the first optimization result, the reachable orbit elements in the first mode are obtained, specifically including:

[0045] Characterizing a first initial reference trajectory of the rocket according to the initial flight state parameters and the orbital elements of the target orbit of the rocket to obtain a characterized first initial reference trajectory of the rocket; the characterized first initial reference trajectory of the rocket includes a first initial reference position, a first initial reference velocity, and a first initial reference gravitational acceleration;

[0046] Setting a first allowable error, and iteratively optimizing and solving the convex optimization subproblem using a convex optimization algorithm based on the characterized first initial reference trajectory of the rocket, the mode coefficient of the rocket operation in the first mode, and the first allowable error, to obtain a first optimization result;

[0047] Calculating a first deviation based on the first optimization result and a characterized first initial reference trajectory of the rocket, and determining whether the first deviation is less than a first allowable error;

[0048] If not, updating the characterized first initial reference trajectory of the rocket, and re-performing iterative optimization on the convex optimization subproblem until the calculated first deviation is less than the first allowable error;

[0049] If so, the reachable trajectory elements in the first mode are obtained according to the first optimization result.

[0050] Optionally, judging whether the rocket can form a safe and stable orbit based on the achievable orbit elements in the first mode specifically includes:

[0051] Calculating, based on the reachable orbit elements in the first mode, the perigee geocenter distance and the apogee geocenter distance corresponding to the reachable orbit elements in the first mode;

[0052] Determine whether the perigee distance to the center of the earth and the apogee distance to the center of the earth both exceed the perigee height; if so, it is determined that the rocket can form a safe and stable orbit; if not, it is determined that the rocket cannot form a safe and stable orbit.

[0053] To achieve the above-mentioned purpose, the present invention also provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-mentioned method for calculating patterned achievable orbit elements and making degraded orbit decisions.

[0054] To achieve the above-mentioned objectives, the present invention also provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, it implements the above-mentioned method for calculating patterned achievable orbit elements and making degraded orbit decisions.

[0055] To achieve the above-mentioned objectives, the present invention also provides a computer program product, including a computer program, which, when executed by a processor, implements the above-mentioned method for calculating patterned achievable orbit elements and making degraded orbit decisions.

[0056] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0057] The present invention proposes a modeled method for calculating achievable orbital elements and making decisions about degraded orbits. In the event of a non-fatal thrust-descent failure on a rocket, a modeled approach is used to improve the calculation of achievable orbital elements and to make decisions about degraded orbits. Compared to the prior art, the present invention improves the computational efficiency of achievable orbital element calculations and degraded orbit decisions by combining modeled improvements with numerical methods. Furthermore, the rocket's orbital insertion capability is determined in the solution obtained under each model, and decisions about the rocket's degraded orbit are made based on this, improving adaptability. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0059] Figure 1 A flowchart of a method for calculating modeled achievable orbit elements and making degraded orbit decisions provided in Example 1 of the present invention. DETAILED DESCRIPTION

[0060] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0061] The purpose of the present invention is to provide a method, device, medium and product for modeling achievable orbit element calculation and degraded orbit decision-making, which can improve the calculation efficiency of achievable orbit elements and improve mission adaptability.

[0062] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0063] Example 1

[0064] like Figure 1 As shown, a method for calculating achievable track elements and determining degraded tracks in this embodiment includes the following steps:

[0065] Step S1: Obtain the initial flight state parameters of the rocket under non-lethal thrust reduction conditions; the initial flight state parameters include the rocket's initial position, initial velocity, initial total mass, initial engine total thrust, initial engine average effective exhaust velocity, initial fuel mass, and initial fault thrust coefficient; specifically, the initial flight state parameters are all obtained from the rocket's navigation system. The initial position r0 and initial velocity V0 are both three-dimensional vectors, the initial total mass m0, initial engine total thrust T, initial engine average effective exhaust velocity V ex , initial fuel mass m fuel and initial failure thrust coefficient k T All are scalars. Among them, the initial position r0 in the case of non-lethal thrust descent is the coordinate of the rocket's center of mass in the geocentric equatorial inertial coordinate system; the initial velocity V0 is the derivative of the position r0 with respect to time; the magnitude of the initial total engine thrust T represents the total thrust of all rocket engines; the initial effective exhaust velocity V ex represents the average effective exhaust velocity of all rocket engines; initial fuel mass m fuel represents the mass of the initial rocket fuel; the initial failure thrust coefficient k T The coefficient that represents the initial existing thrust of the rocket as a percentage of the thrust magnitude in the case of non-lethal thrust reduction.

[0066] Step S2: Obtain the target orbit elements and safety altitude constraints of the target orbit of the rocket; the target orbit elements include the target orbit semi-major axis a ref , target orbit eccentricity e ref , target orbit inclination i ref 、Right ascension of target ascending node Ω ref and the target perigee argument ω ref , the safety height constraint h safe It represents the minimum orbital altitude at which the rocket can operate stably; specifically, the target orbit elements and safety altitude constraints of the rocket's target orbit are loaded from the rocket's onboard computer.

[0067] Step S3: Based on the initial flight state parameters, the target orbit elements and the safety altitude constraints, combined with the rocket dynamics differential equations and the rocket operation process constraints, a patterned optimal control problem model is established.

[0068] Specifically, first, consider the rocket dynamics differential equation:

[0069]

[0070] Where r represents the coordinate position of the rocket's center of mass in the Earth's equatorial inertial coordinate system; V represents the velocity of the rocket's center of mass in the Earth's equatorial inertial coordinate system; 1 T Indicates the direction of rocket thrust; μ represents the earth's gravitational constant; r, V, 1T is a three-dimensional vector, μ is a scalar; k T represents the fault thrust coefficient; T represents the total thrust value; m is the total mass of the rocket; V ex Indicates the effective exhaust velocity; represents the derivative of the rocket's coordinate position; represents the derivative of the rocket's velocity; represents the derivative of the total mass of the rocket.

[0071] Secondly, consider the rocket operation process constraints, including initial state constraints, process constraints, and terminal constraints. The expression of the initial state constraint is:

[0072]

[0073] Among them, t0 represents the initial time; r0 represents the initial position of the rocket under non-lethal thrust descent; V0 represents the initial velocity of the rocket under non-lethal thrust descent; m0 represents the initial total mass of the rocket under non-lethal thrust descent.

[0074] The expression of the process constraint condition is:

[0075] ||1 T ||=1 (3)

[0076] The expression of the terminal constraint condition is:

[0077]

[0078] Among them, t0 represents the initial time; t f Indicates the rocket flight terminal moment; R E represents the average radius of the Earth; k1, k2, k3, k4 and k5 are all model coefficients; t0, t f 、R E , k1, k2, k3, k4 and k5 are all scalars; H represents the momentum vector of the rocket; L represents the Laplace vector; d1, d2 and d3 are all coefficient vectors, which are all three-dimensional vectors; m fuel represents the initial fuel mass; i(t f ) represents the orbital inclination at the terminal moment of the rocket flight; i ref represents the target orbit inclination; r p (t f ) represents the distance from the center of the earth corresponding to the orbital perigee at the terminal moment of the rocket flight; H(t f ) represents the moment of momentum vector at the terminal moment of the rocket flight; L(t f ) represents the Laplace vector at the terminal moment of the rocket flight; h safe represents the safety height constraint; ω refrepresents the target perigee argument; Ω ref represents the right ascension of the target ascending node. Then, the performance index function of the optimal control problem is considered, and its expression is:

[0079] max(k1+k5)r a (t f )-k2 cos[i(t f )]+k3 tan[Ω(t f )]+k4||r(t f )|| (5)

[0080] Among them, r a represents the distance from the Earth's center to the rocket's apogee; Ω represents the right ascension of the rocket's ascending node; Ω(t f ) represents the right ascension of the rocket's ascending node at the terminal moment of the rocket's flight.

[0081] Finally, the model of the patterned optimal control problem is obtained, and its expression is:

[0082]

[0083] Step S4: Convexify the patterned optimal control problem model to obtain a convex optimal control subproblem.

[0084] Specifically, step S41: convexifying the rocket dynamics differential equation and the process constraints respectively, and obtaining the convexified rocket dynamics differential equation and the convexified rocket operation process constraints as follows:

[0085]

[0086] Among them, x represents the rocket flight state, which is a six-dimensional vector composed of the rocket's position and velocity; A represents the coefficient matrix corresponding to the state quantity; B represents the coefficient matrix corresponding to the control quantity; g represents the gravitational acceleration, which is a three-dimensional vector; k represents the kth iteration; Represents the derivative of the state quantity.

[0087] Step S42: Linearize the constraints in the modeled optimal control problem model to obtain linearized constraints, which are expressed as follows:

[0088]

[0089] in, represents the unit vector corresponding to the momentum vector; represents the unit vector corresponding to the Laplace vector, which are all three-dimensional vectors; κ represents the amplitude corresponding to the momentum vector, and λ is the amplitude corresponding to the Laplace vector, which are scalars respectively.

[0090] Step S43: Linearize the performance index function in the modeled optimal control problem model to obtain a linearized performance index function, which is expressed as follows:

[0091] max k1||H||+k2 cosi+k3 tanΩ+(k4+k5)κ (9)

[0092] Step S44: Determine the convex optimal control subproblem based on the convexified rocket dynamics differential equation, the convexified rocket operation process constraints, the linearized constraints, and the linearized performance index function; the expression of the convex optimal control subproblem is obtained as follows:

[0093]

[0094] Where i represents the orbital inclination; κ represents the magnitude of the momentum vector; represents the derivative of the state quantity; A represents the coefficient matrix corresponding to the state quantity; x represents the state quantity, which is a six-dimensional vector composed of the rocket position and velocity; B represents the coefficient matrix corresponding to the control quantity; g k represents the gravitational acceleration sequence of the kth iteration; r k represents the position reference trajectory of the kth iteration; r T represents the transpose of the position vector; i k represents the kth iteration orbit inclination reference trajectory; r f Represents the terminal position vector; H k represents the k-th iteration momentum vector reference trajectory; L k represents the k-th iteration Laplace vector reference trajectory; r p Indicates the distance from the center of the earth to the perigee of the orbit corresponding to the rocket's flight state; V f represents the terminal velocity vector; V k represents the k-th iteration velocity vector reference trajectory; ω k represents the reference trajectory of the argument of perigee at the kth iteration; represents the unit vector corresponding to the momentum vector; λ represents the amplitude corresponding to the Laplace vector; represents the unit vector corresponding to the Laplace vector; Ω k represents the reference trajectory of the right ascension of the ascending node at the kth iteration; represents the linearized momentum vector; represents the linearized Laplace vector.

[0095] Step S5: Discretize the convex optimal control subproblem and introduce slack variables to obtain a convex optimization subproblem. The convex optimization subproblem is established based on discretization and lossless convexification.

[0096] First, the convex optimal control subproblem is discretized, and the time series is discretized at equal intervals. The number of discrete points is N, and the discrete time interval is Δt=(t f -t0) / N, then the rocket dynamics differential equation is expressed as:

[0097]

[0098] in, and is the state transfer matrix, which is calculated as follows:

[0099]

[0100] Among them, the coefficient matrices A and B corresponding to the state quantity and control quantity are:

[0101]

[0102] Among them, I 3×3 Represents the 3 by 3 identity matrix.

[0103] Then, by introducing slack variables, the convex optimization subproblem is obtained as:

[0104]

[0105] Where J represents the performance index function of the convex optimal control subproblem; ξ1 and ξ2 are both slack variables; k ξ,1 and k ξ,2 represents the penalty coefficient of the slack variable; φ1 and φ2 represent the terminal constraints of the convex optimal control subproblem; x k represents the reference trajectory of the k-th iteration state; x f Represents the terminal state quantity; x N Represents the Nth state quantity discrete point, which is related to x f Equivalence; x j+1 Represents the state quantity of the j+1th discrete point; x j Represents the state quantity of the jth discrete point, and Represents the state transfer matrix; subscript j represents the discrete point number; m j represents the mass of the rocket at the jth discrete point; g k j+1 Represents the gravitational acceleration vector of the j+1th discrete point.

[0106] Step S6: setting the mode coefficients of the rocket in different modes, and using a convex optimization algorithm to iteratively optimize and solve the convex optimization subproblem to obtain the achievable orbit elements of the rocket in different modes.

[0107] Step S7: Based on the achievable orbital elements of the rocket in different modes, a decision is made on the rocket orbit degradation to obtain the final achievable orbital elements of the rocket and determine the reference trajectory of the rocket operation.

[0108] Furthermore, step S6 and step S7 specifically include:

[0109] Set the values ​​of the mode coefficients of the rocket operation in the first mode. The values ​​of the mode coefficients are: k1=1, k2=0, k3=0, k4=0, k5=0; k1, k2, k3, k4 and k5 are all mode coefficients.

[0110] Based on the assigned mode coefficients of the rocket operation in the first mode, a convex optimization algorithm is used to iteratively optimize and solve the convex optimization subproblem to obtain a first optimization result, and based on the first optimization result, the reachable orbit elements in the first mode are obtained.

[0111] A first allowable error is set, and a convex optimization algorithm is used to iteratively optimize and solve the convex optimization subproblem based on the characterized first initial reference trajectory of the rocket, the mode coefficient of the rocket operation in the first mode, and the first allowable error to obtain a first optimization result.

[0112] Calculating a first deviation based on the first optimization result and a characterized first initial reference trajectory of the rocket, and determining whether the first deviation is less than a first allowable error;

[0113] If not, updating the characterized first initial reference trajectory of the rocket, and re-performing iterative optimization on the convex optimization subproblem until the calculated first deviation is less than the first allowable error;

[0114] If so, the reachable trajectory elements in the first mode are obtained according to the first optimization result.

[0115] Based on the achievable orbital elements in the first mode, determine whether the rocket can form a safe and stable orbit; if not, use the achievable orbital elements in the first mode as the final achievable orbital elements of the rocket.

[0116] If so, then set the value of the mode coefficient of the rocket operation in the second mode, and the value of each mode coefficient is: k1=0, k2=1, k3=0, k4=0, k5=0.

[0117] Based on the assigned mode coefficient of the rocket operation in the second mode, the convex optimization algorithm is used to iteratively optimize and solve the convex optimization subproblem to obtain a second optimization result, and according to the second optimization result, the reachable orbit element in the second mode is obtained: a mod2 ,e mod2 ,i mod2 ,Ωmod2 ,ω mod2 .

[0118] According to the reachable orbit elements in the second mode, it is determined whether the rocket can reach the set orbital inclination, i.e. mod2 ≥i ref ; If not, the achievable orbital elements under the first mode will be used as the final achievable orbital elements of the rocket.

[0119] If so, then set the value of the mode coefficient of the rocket operation in the third mode, and the value of each mode coefficient is: k1=0, k2=0, k3=1, k4=0, k5=0.

[0120] Based on the assigned mode coefficients of the rocket operation in the third mode, the convex optimization algorithm is used to iteratively optimize and solve the convex optimization subproblem to obtain a third optimization result, and according to the third optimization result, the reachable orbit element in the third mode is obtained: a mod3 ,e mod3 ,i mod3 ,Ω mod3 ,ω mod3 .

[0121] According to the reachable orbit elements in the third mode, it is judged whether the rocket can reach the set ascending node right ascension, that is, Ω mod3 ≥Ω ref ; If not, the achievable orbital element under the first mode will be used as the final rocket achievable orbital element.

[0122] If so, the values ​​of the mode coefficients of the rocket operation in the fourth mode and the mode coefficients of the rocket operation in the fifth mode are set respectively; among which, the mode coefficients of the rocket operation in the fourth mode are assigned as follows: k1=0, k2=0, k3=0, k4=1, k5=0, and the mode coefficients of the rocket operation in the fifth mode are assigned as follows: k1=0, k2=0, k3=0, k4=0, k5=1.

[0123] Based on the mode coefficient of the rocket operation in the fourth mode, the convex optimization algorithm is used to iteratively optimize and solve the convex optimization subproblem to obtain a fourth optimization result, and according to the fourth optimization result, the reachable orbit element in the fourth mode is obtained, that is, a mod4 ,e mod4 ,i mod4 ,Ω mod4 ,ω mod4 .

[0124] Based on the mode coefficient of the rocket operation in the fifth mode, the convex optimization algorithm is used to iteratively optimize and solve the convex optimization subproblem to obtain the fifth optimization result, and according to the fifth optimization result, the reachable orbit element in the fifth mode is obtained, that is, a mod5,e mod5 ,i mod5 ,Ω mod5 ,ω mod5 .

[0125] Determine whether the reachable orbit element in the fifth mode satisfies the reachable orbit element in the fourth mode. mod5 ≥a mod4 +800×10 3 ; Among them, a mod4 represents the semi-major axis of the fourth mode; a mod5 represents the semi-major axis of the fifth mode.

[0126] If so, the achievable orbital element in the fifth mode is used as the final rocket achievable orbital element; if not, the achievable orbital element in the fourth mode is used as the final rocket achievable orbital element.

[0127] Among them, based on the mode coefficient of the rocket operation in the first mode after assignment, the convex optimization algorithm is used to iteratively optimize and solve the convex optimization subproblem to obtain a first optimization result, and based on the first optimization result, the achievable orbit element in the first mode is obtained, specifically: according to the initial flight state parameters and the orbital elements of the rocket's target orbit, the first initial reference trajectory of the rocket is characterized to obtain the characterized first initial reference trajectory of the rocket; the characterized first initial reference trajectory of the rocket includes a first initial reference position, a first initial reference velocity and a first initial reference gravitational acceleration; a first allowable error is set, and according to the characterized first initial reference trajectory of the rocket, the mode coefficient of the rocket operation in the first mode and the first allowable error, the convex optimization algorithm is used to iteratively optimize and solve the convex optimization subproblem to obtain a first optimization result; based on the first optimization result and the characterized first initial reference trajectory of the rocket, a first deviation is calculated, and it is determined whether the first deviation is less than the first allowable error; if not, the characterized first initial reference trajectory of the rocket is updated, and the convex optimization subproblem is iteratively optimized and solved again until the calculated first deviation is less than the first allowable error; if so, the achievable orbit element in the first mode is obtained according to the first optimization result.

[0128] Specifically, first set the values ​​of the mode coefficients k1, k2, k3, k4, k5, k1 = 1, k2 = 0, k3 = 0, k4 = 0, k5 = 0, and then, according to the initial flight state parameters r0, V0 and the orbital element a of the target orbit of the rocket ref 、e ref ,Ω ref 、ω ref , characterize the first initial reference trajectory of the rocket, and obtain the first initial reference trajectory r of the rocket after characterization 0,V 0 and g 0 The first initial reference trajectory of the rocket after the characterization includes a first initial reference position r 0 The first initial reference speed V 0 and the first initial reference gravitational acceleration g 0 That is, the flight state parameters r0 and V0 are converted into the corresponding orbital elements a0, e0, i0, Ω0, ω0, and the first reference orbital element a is set. 0 ,e 0 ,i 0 ,Ω 0 ,ω 0 For: a 0 =a ref ,e 0 =e ref ,i 0 =i0,Ω 0 =Ω ref ,ω 0 =ω ref .

[0129] The first reference orbit inclination is represented by the orbit element i0 corresponding to the flight state parameter, i.e., i0=i0, and then the first reference orbit element a 0 ,e 0 ,i 0 ,Ω 0 ,ω 0 Transformed into the first initial reference trajectory r 0 ,V 0 .

[0130] Furthermore, set the initial reference trajectory g 0 for:

[0131] Finally, the convex optimization algorithm is used to solve the convex optimization subproblem, and the optimization result is recorded as r * ,V * , set the first allowable error ε, and calculate the first deviation ΔE:

[0132]

[0133] If ΔE≤ε, then the optimization result r * ,V * As the first optimization result, it is converted into the track element under the first mode, recorded as a mod1 ,e mod1 ,i mod1 ,Ω mod1 ,ω mod1 .

[0134] Otherwise, update the first initial reference trajectory to

[0135]

[0136] And re-solve the convex optimization subproblem until ΔE≤ε, where r k+1 represents the reference trajectory of the k+1th iteration position vector; Represents the position vector of the Nth discrete point solved in the current iteration; V k+1 represents the reference trajectory of the velocity vector at the k+1th iteration; Represents the velocity vector of the Nth discrete point solved in the current iteration; represents the reference trajectory of the gravitational acceleration of the jth discrete point in the k+1th iteration; Represents the position vector of the jth discrete point solved in the current iteration.

[0137] Furthermore, judging whether the rocket can form a safe and stable orbit based on the achievable orbit elements in the first mode includes:

[0138] According to the reachable track element a in the first mode mod1 ,e mod1 ,i mod1 ,Ω mod1 ,ω mod1 , calculate the perigee and apogee distances corresponding to the reachable orbit elements in the first mode: r p,mod1 =a mod1 (1-e mod1 ),r a,mod1 =a mod1 (1+e mod1 ), where r p,mod1 Indicates the perigee distance corresponding to the orbital element in the first mode, r a,mod1 is the distance from the apogee to the center of the earth corresponding to the orbital element in the first mode.

[0139] Determine whether the perigee and apogee distances are both greater than the perigee height: If so, that is, r p,mod1 ≥R E +h safe ,r a,mod1 ≥R E +h safe , then it is determined that the rocket can form a safe and stable orbit; if not, then it is determined that the rocket cannot form a safe and stable orbit.

[0140] Furthermore, in the second mode, the third mode, the fourth mode and the fifth mode, the convex optimization algorithm is used to iteratively optimize and solve the convex optimization subproblem. The steps for obtaining the achievable trajectory elements corresponding to each mode are the same as the iterative optimization solution process of the convex optimization subproblem in the first mode, and will not be repeated here.

[0141] Technical effects of the present invention:

[0142] 1) This invention utilizes a modeling approach to improve the calculation of achievable orbital elements in the event of a non-fatal thrust-descent failure. This allows for real-time calculation of achievable orbital elements in the event of a rocket propulsion system failure, and uses this information to inform decisions about downgraded orbits. Compared to existing technologies, this invention improves the computational efficiency of both achievable orbital element calculations and downgraded orbit decisions by combining modeling improvements with numerical methods.

[0143] 2) The modeled achievable orbit element calculation method proposed in the present invention solves a series of optimal control problems through numerical methods instead of the complex analytical or numerical methods used in existing methods. It can calculate the achievable orbit elements in real time and use them to make downgraded orbit decisions instead of the preset downgraded orbit. The rocket's orbit insertion capability is judged in the solution results in each mode, and decisions on the downgraded orbit are made based on this, which has stronger real-time performance and mission adaptability.

[0144] Example 2

[0145] A computer device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement a method for calculating patterned achievable orbit elements and determining degraded orbits in Example 1.

[0146] Example 3

[0147] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements a method for calculating patterned achievable orbit elements and making degraded orbit decisions in Example 1.

[0148] Example 4

[0149] A computer program product includes a computer program, which, when executed by a processor, implements a method for calculating patterned achievable orbit elements and making degraded orbit decisions in Example 1.

[0150] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0151] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. A method for calculating achievable orbit elements and making decisions on degraded orbits based on a model, characterized in that: The method comprises: Obtaining initial flight state parameters of the rocket under a non-lethal thrust reduction condition; the initial flight state parameters include the rocket's initial position, initial velocity, initial total mass, initial engine total thrust, initial engine average effective exhaust velocity, initial fuel mass, and initial fault thrust coefficient; Obtaining target orbit elements and a safety altitude constraint of the rocket's target orbit; the target orbit elements include the target orbit semi-major axis, the target orbit eccentricity, the target orbit inclination, the target ascending node right ascension, and the target perigee argument; the safety altitude constraint represents the minimum orbit altitude at which the rocket can operate stably; Based on the initial flight state parameters, the target orbit elements and the safety altitude constraint, combined with the rocket dynamics differential equation and the rocket operation process constraint conditions, a patterned optimal control problem model is established; The patterned optimal control problem model is convexified to obtain a convex optimal control subproblem; Discretizing the convex optimal control subproblem and introducing slack variables to obtain a convex optimization subproblem; Setting the mode coefficients of the rocket in different modes, and using a convex optimization algorithm to iteratively optimize and solve the convex optimization subproblem, to obtain the achievable orbit elements of the rocket in different modes; According to the achievable orbit elements of the rocket in different modes, the rocket orbit degradation decision is made to obtain the final achievable orbit elements of the rocket and determine the reference trajectory of the rocket operation; The expression of the modeled optimal control problem model is: Where r represents the coordinate position of the rocket's center of mass in the Earth's equatorial inertial coordinate system; represents the derivative of the rocket's coordinate position; V represents the velocity of the rocket's center of mass in the Earth's equatorial inertial coordinate system; 1 T represents the direction of rocket thrust; μ represents the earth's gravitational constant; k T represents the fault thrust coefficient; T represents the total thrust value; m is the total mass of the rocket; V ex Indicates the effective exhaust velocity; represents the derivative of the rocket's velocity; represents the derivative of the total mass of the rocket; t0 represents the initial time; r0 represents the initial position of the rocket under non-lethal thrust descent; V0 represents the initial velocity of the rocket under non-lethal thrust descent; m0 represents the initial total mass of the rocket under non-lethal thrust descent; t f Indicates the rocket flight terminal moment; R E represents the average radius of the earth; k1, k2, k3, k4 and k5 are all model coefficients; H represents the momentum vector of the rocket; L represents the Laplace vector; d1, d2, and d3 are all coefficient vectors; m fuel represents the initial fuel mass; i(t f ) represents the orbital inclination at the terminal moment of the rocket flight; i ref represents the target orbit inclination; r p (t f ) represents the distance from the center of the earth corresponding to the orbital perigee at the terminal moment of the rocket flight; H(t f ) represents the moment of momentum vector at the terminal moment of the rocket flight; L(t f ) represents the Laplace vector at the terminal moment of the rocket flight; h safe represents the safety height constraint; ω ref represents the target perigee argument; Ω ref Indicates the right ascension of the target ascending node.

2. The method for calculating achievable orbit elements and making degraded orbit decisions based on modeling according to claim 1, characterized in that: The patterned optimal control problem model is convexified to obtain the convex optimal control subproblem, which includes: The rocket dynamics differential equation and the rocket operation process constraint conditions are convexified respectively to obtain the convexified rocket dynamics differential equation and the convexified rocket operation process constraint conditions; Linearizing the constraints in the patterned optimal control problem model to obtain linearized constraints; Linearizing the performance index function in the patterned optimal control problem model to obtain a linearized performance index function; Determining the convex optimal control subproblem based on the convex rocket dynamics differential equation, the convex rocket operation process constraints, the linearized constraints, and the linearized performance index function; The expression of the convex optimal control subproblem is: Where i represents the orbital inclination; κ represents the magnitude of the momentum vector; represents the derivative of the state quantity; A represents the coefficient matrix corresponding to the state quantity; x represents the state quantity, which is a six-dimensional vector composed of the rocket position and velocity; B represents the coefficient matrix corresponding to the control quantity; g k represents the gravitational acceleration sequence of the kth iteration; r k represents the position reference trajectory of the kth iteration; r T represents the transpose of the position vector; i k represents the kth iteration orbit inclination reference trajectory; r f Represents the terminal position vector; H k represents the k-th iteration momentum vector reference trajectory; L k represents the k-th iteration Laplace vector reference trajectory; r p Indicates the distance from the center of the earth to the perigee of the orbit corresponding to the rocket's flight state; V f represents the terminal velocity vector; V k represents the k-th iteration velocity vector reference trajectory; ω k represents the reference trajectory of the argument of perigee at the kth iteration; represents the unit vector corresponding to the momentum vector; λ represents the amplitude corresponding to the Laplace vector; represents the unit vector corresponding to the Laplace vector; Ω k represents the reference trajectory of the right ascension of the ascending node at the kth iteration; represents the linearized momentum vector; represents the linearized Laplace vector.

3. The method for calculating achievable orbit elements and making degraded orbit decisions based on modeling according to claim 1, characterized in that: The expression of the convex optimization subproblem is: Where J represents the performance index function of the convex optimal control subproblem; ξ1 and ξ2 are both slack variables; k ξ,1 and k ξ,2 represents the penalty coefficient of the slack variable; φ1 and φ2 represent the terminal constraints of the convex optimal control subproblem; x k represents the reference trajectory of the k-th iteration state; x f Represents the terminal state quantity; x N Represents the Nth discrete point of state quantity; x j+1 Represents the state quantity of the j+1th discrete point; x j Represents the state quantity of the jth discrete point; and represents the state transfer matrix; j represents the discrete point number; m j represents the mass of the rocket at the jth discrete point; g k j+1 Represents the gravitational acceleration vector of the j+1th discrete point in the kth iteration.

4. The method for calculating achievable orbit elements and making degraded orbit decisions based on modeling according to claim 1, characterized in that: The mode coefficients of the rocket in different modes are set, and the convex optimization algorithm is used to iteratively optimize and solve the convex optimization sub-problem to obtain the achievable orbit elements of the rocket in different modes; based on the achievable orbit elements of the rocket in different modes, a decision is made on the rocket orbit degradation to obtain the final achievable orbit elements of the rocket and determine the reference trajectory of the rocket operation, which specifically includes: Set the values ​​of the mode coefficients for the rocket operation in the first mode. The values ​​of the mode coefficients are: k1 = 1, k2 = 0, k3 = 0, k4 = 0, k5 = 0; k1, k2, k3, k4 and k5 are all mode coefficients; Based on the assigned mode coefficients of the rocket operation in the first mode, using a convex optimization algorithm to iteratively optimize and solve the convex optimization subproblem to obtain a first optimization result, and according to the first optimization result, obtaining the reachable orbit elements in the first mode; Determining whether the rocket can form a safe and stable orbit based on the reachable orbit elements in the first mode; if not, using the reachable orbit elements in the first mode as the final reachable orbit elements for the rocket; If yes, then set the value of the mode coefficient of the rocket operation in the second mode, and the value of each mode coefficient is: k1 = 0, k2 = 1, k3 = 0, k4 = 0, k5 = 0; Based on the assigned mode coefficients of the rocket operation in the second mode, using a convex optimization algorithm to iteratively optimize and solve the convex optimization subproblem to obtain a second optimization result, and according to the second optimization result, obtaining the reachable orbit elements in the second mode; Determining whether the rocket can reach the set orbital inclination according to the achievable orbital element in the second mode; if not, using the achievable orbital element in the first mode as the final rocket achievable orbital element; If yes, then set the value of the mode coefficient of the rocket operation in the third mode, and assign the value of each mode coefficient to: k1 = 0, k2 = 0, k3 = 1, k4 = 0, k5 = 0; Based on the assigned mode coefficients of the rocket operation in the third mode, an iterative optimization solution is performed on the convex optimization subproblem using a convex optimization algorithm to obtain a third optimization result, and according to the third optimization result, an element of the achievable orbit in the third mode is obtained; Determining whether the rocket can reach the set right ascension of the ascending node based on the achievable orbit elements in the third mode; if not, using the achievable orbit elements in the first mode as the final achievable orbit elements for the rocket; If so, the values ​​of the mode coefficients of the rocket operation in the fourth mode and the mode coefficients of the rocket operation in the fifth mode are set respectively; wherein the mode coefficients of the rocket operation in the fourth mode are assigned as follows: k1=0, k2=0, k3=0, k4=1, k5=0, and the mode coefficients of the rocket operation in the fifth mode are assigned as follows: k1=0, k2=0, k3=0, k4=0, k5=1; Based on the mode coefficient of the rocket operation in the fourth mode, using a convex optimization algorithm to iteratively optimize and solve the convex optimization subproblem to obtain a fourth optimization result, and according to the fourth optimization result, obtaining the reachable orbit element in the fourth mode; Based on the mode coefficients of the rocket operation in the fifth mode, using a convex optimization algorithm to iteratively optimize and solve the convex optimization subproblem to obtain a fifth optimization result, and according to the fifth optimization result, obtaining the achievable orbit elements in the fifth mode; Determine whether the reachable orbit element in the fifth mode satisfies the reachable orbit element in the fourth mode. mod5 ≥a mod4 +800×10 3 ; Among them, a mod4 represents the semi-major axis of the fourth mode; a mod5 represents the semi-major axis of the fifth mode; If so, the achievable orbital element in the fifth mode is used as the final rocket achievable orbital element; if not, the achievable orbital element in the fourth mode is used as the final rocket achievable orbital element.

5. The method for calculating modeled achievable orbit elements and making decisions on degraded orbits according to claim 4, characterized in that: Based on the mode coefficient of the rocket operation in the first mode, the convex optimization algorithm is used to iteratively optimize and solve the convex optimization subproblem to obtain a first optimization result, and based on the first optimization result, the reachable orbit elements in the first mode are obtained, specifically including: Characterizing a first initial reference trajectory of the rocket according to the initial flight state parameters and the orbital elements of the target orbit of the rocket to obtain a characterized first initial reference trajectory of the rocket; the characterized first initial reference trajectory of the rocket includes a first initial reference position, a first initial reference velocity, and a first initial reference gravitational acceleration; Setting a first allowable error, and iteratively optimizing and solving the convex optimization subproblem using a convex optimization algorithm based on the characterized first initial reference trajectory of the rocket, the mode coefficient of the rocket operation in the first mode, and the first allowable error, to obtain a first optimization result; Calculating a first deviation based on the first optimization result and a characterized first initial reference trajectory of the rocket, and determining whether the first deviation is less than a first allowable error; If not, updating the characterized first initial reference trajectory of the rocket, and re-performing iterative optimization on the convex optimization subproblem until the calculated first deviation is less than the first allowable error; If so, the reachable trajectory elements in the first mode are obtained according to the first optimization result.

6. The method for calculating achievable orbit elements and making decisions on degraded orbits according to claim 4, characterized in that: Based on the achievable orbital elements in the first mode, it is determined that the rocket can form a safe and stable orbit, including: Calculating, based on the reachable orbit elements in the first mode, the perigee geocenter distance and the apogee geocenter distance corresponding to the reachable orbit elements in the first mode; Determine whether the perigee distance to the center of the earth and the apogee distance to the center of the earth both exceed the perigee height; if so, it is determined that the rocket can form a safe and stable orbit; if not, it is determined that the rocket cannot form a safe and stable orbit.

7. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement a method for calculating patterned achievable orbit elements and making degraded orbit decisions as described in any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, it implements a method for calculating patterned achievable orbit elements and making degraded orbit decisions as described in any one of claims 1 to 6.

9. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, it implements a method for calculating patterned achievable orbit elements and making degraded orbit decisions as described in any one of claims 1 to 6.

Images