Predictive-correction guidance method for mars atmospheric braking under uncertain environment

Abstract

This invention relates to a predictive correction guidance method for Mars atmospheric braking energy reach control set under uncertain conditions, belonging to the field of deep space exploration technology. The method involves establishing dynamic models of the probe's flight outside and inside the atmosphere during the atmospheric braking process. Considering the impact of environmental parameter uncertainties on the probe's reach set, the reach set under different parameter uncertainties is calculated, and the reach union is solved. The corresponding near-Mars heat flux density set is obtained from the reach union, and the relationship between the near-Mars heat flux density set and the atmospheric braking corridor determines whether the far-Mars needs maneuvering. Considering the impact of environmental parameter uncertainties on the probe's control set, the control set under different parameter uncertainties is calculated, and the control intersection is solved. The control intersection is used to solve for the set of far-Mars velocity increments used to correct the near-Mars state. Based on the selected far-Mars maneuvering velocity increment, predictive correction guidance for Mars atmospheric braking energy reach control set under uncertain conditions is achieved.

Description

Technical Field

[0001] This invention relates to a guidance method, and more particularly to a method for predicting and correcting Martian atmospheric braking energy control set under uncertain conditions, belonging to the field of deep space exploration technology. Background Technology

[0002] Atmospheric braking utilizes the drag of the Martian atmosphere to alter the velocity of a probe, thereby guiding it to its predetermined orbit. This significantly reduces fuel requirements, launch costs, and increases the probe's payload capacity. During atmospheric braking, the probe traverses the Martian atmosphere multiple times, gradually lowering its apogee altitude using atmospheric drag until the target orbital altitude constraints are met. Atmospheric braking guidance consists of two phases: prediction and correction. After each atmospheric traverse, the state of the next perigee is predicted, and a decision is made based on the predicted perigee state to determine whether an apogee thrust maneuver is necessary. The apogee maneuver aims to correct the state of the next perigee, placing it within the atmospheric braking corridor defined by heat flux density. This generates appropriate dynamic pressure for deceleration while ensuring that the heat flux density does not exceed its upper limit.

[0003] The Martian atmosphere is complex, changeable, and highly uncertain. When a probe decelerates through the Martian atmosphere, these uncertainties alter its motion characteristics, causing its actual state to deviate from the predicted state. Therefore, the impact of environmental parameter uncertainties must be considered when making decisions regarding maneuvers to Mars and calculating the velocity increment at Mars. Otherwise, it may lead to decision-making errors or insufficient maneuver correction accuracy, causing the probe's perihelion state to fail to meet atmospheric braking corridor constraints. This would affect atmospheric braking deceleration efficiency, potentially damaging the probe's structure or causing it to impact the Martian surface, ultimately resulting in mission failure. Summary of the Invention

[0004] To address the problems of poor maneuvering decision-making and correction accuracy at the far-Mars apex due to environmental uncertainties during Martian atmospheric braking, which can lead to reduced braking efficiency, structural damage to the probe, or increased risk of Martian impact, this invention provides a guidance method for atmospheric braking under uncertain environments, based on the prediction and correction of the reachable and controllable set. This method improves the accuracy of far-Mars maneuvering decisions by introducing the reachable union during the guidance prediction stage and applying it to the far-Mars maneuvering decision-making. In the guidance correction stage, it introduces the controllable intersection and applies it to the calculation of the far-Mars maneuvering velocity increment, ultimately generating guidance commands. By executing guidance commands at the far-Mars apex, the probe's perihelion state satisfies the braking corridor constraint, thus achieving safe and efficient atmospheric braking under uncertain conditions until reaching the target orbit.

[0005] The objective of this invention is achieved through the following technical solution.

[0006] This invention discloses a predictive correction guidance method for Mars atmospheric braking energy reach set under uncertain conditions. It establishes dynamic models of the probe's flight outside and inside the atmosphere during the atmospheric braking process. Considering the impact of environmental parameter uncertainties on the probe's energy reach set, the energy reach set under different parameter uncertainties is calculated, and the energy reach union is solved. Further, the corresponding near-Mars heat flux density set is solved from the energy reach union, and the relationship between the near-Mars heat flux density set and the atmospheric braking corridor is used to determine whether the far-Mars needs maneuvering. Considering the impact of environmental parameter uncertainties on the probe's energy reach set, the energy reach set under different parameter uncertainties is calculated, and the energy reach intersection is solved. Further, the energy reach intersection is used to solve for the set of far-Mars velocity increments that can be used to correct the near-Mars state, and the far-Mars maneuvering velocity increment is selected from this set. Based on the selected far-Mars maneuvering velocity increment, predictive correction guidance for Mars atmospheric braking energy reach set under uncertain conditions is achieved.

[0007] The present invention discloses a method for predicting and correcting Martian atmospheric braking energy reach control set prediction guidance under uncertain conditions, comprising the following steps:

[0008] Step 1: Establish dynamic models of the detector flying outside the atmosphere and inside the atmosphere respectively.

[0009] The dynamic model of the detector flying outside the atmosphere during atmospheric braking is expressed as follows:

[0010]

[0011] Where μ is the gravitational constant of the central body, and r is the position vector of the spacecraft relative to the central body. r = ||r|| represents the distance of the probe from the center of Mars.

[0012] The dynamic model of the detector flying in the atmosphere during atmospheric braking is expressed as follows:

[0013]

[0014] Where v is the magnitude of the detector velocity and γ is the trajectory angle, g(r)=-μ / r 2 Let be the local gravitational acceleration. The aerodynamic drag acceleration D and lift acceleration L are calculated using the following formula:

[0015]

[0016] Where ρ is the actual atmospheric density, S is the reference area, m is the detector mass, and C... D and C L These are the drag coefficient and lift coefficient, respectively.

[0017] Considering the impact of atmospheric density uncertainty on atmospheric ingress dynamics, the true atmospheric density of a planet at any given time is expressed by the following equation.

[0018] ρ=ρ * (1+△ ρ (4)

[0019] Among them, △ ρ The atmospheric density uncertainty represents the percentage deviation between the model's nominal value and the actual value, and follows a uniform distribution, i.e., Δ. ρ ~U(△) ρ,min ,△ ρ,max ), △ ρ,min ,△ ρ,max These represent the minimum and maximum percentage deviations, respectively. Nominal value ρ * Calculated using equation (5):

[0020]

[0021] Where ρ0 is the reference atmospheric density, h is the current altitude of the detector, h0 is the reference altitude, and h s This refers to the proportional height.

[0022] Step 2: Given the position vector r of the detector when it exits the atmosphere. exit and velocity vector v exit The state x of the forecast probe when it reaches the far-field fire point a =[r a ,v a ,γ a ] T Based on the dynamic model in step one, define the mapping relationship from the far-fire point state to the near-fire point state.

[0023] The specific angular momentum H = r × v is conserved when the probe is flying outside the atmosphere. Multiplying both sides of equation (1) by H simultaneously yields...

[0024]

[0025] Considering H conservation, vector operation rules, and Equation (6) can be rewritten as

[0026]

[0027] Integrating both sides of equation (7) yields

[0028]

[0029] Where B is the constant vector of integration, the scalar equation is obtained by multiplying r by equation (8).

[0030]

[0031] From equation (9) we get

[0032] H2 =μr+rBcosθ (10)

[0033] Where H = ||H|| is the magnitude of the specific angular momentum, B = ||B|| is the magnitude of the integral constant vector B, and θ is the angle between the constant vector B and the position vector r. Solving for r yields the geometric equation of the probe's orbit outside the atmosphere.

[0034]

[0035] Let p = H 2 / μ, e=B / μ, then equation (11) can be rewritten as

[0036]

[0037] The geometric equation of the track (12) is the polar coordinate equation of a conic section, where the constant p is the semi-blind diameter and the constant e is the eccentricity.

[0038] Given that the position and velocity vector of the probe when it exits the atmosphere are r exit and v exit Based on the principle of energy conservation, the semi-major axis a0 of the orbit is calculated as follows:

[0039]

[0040] Where, r exit =||r exit ||and v exit =||v exit ||。 E0 is the specific mechanical energy.

[0041] From equations (11) and (12), we know that the semi-major diameter of the track, p0, is...

[0042]

[0043] Where e0 is the orbital eccentricity, H0=||r exit ×v exit || represents the magnitude of the specific angular momentum. Combining equations (13) and (14), we can obtain...

[0044]

[0045] The state of the detector when it reaches the far-field point is x a =[r a ,v a ,γ a ] T The position vector and velocity vector at the far-fetched firing point are perpendicular, and the trajectory angle γ a =0, the radius vector r of the detector at the far-field point a and speed magnitude v a From equation (16) we get

[0046]

[0047] The probe's state x when it enters the atmosphere entry =[r entry ,v entry ,γ entry ] T for

[0048]

[0049] Among them, the intermediate variable r atm =R m +h atm h atm R is the altitude of the atmospheric boundary. m The radius of Mars. Track angle γ. entry <0. Proximity to fire state x p =[r p ,v p ,γ p ] T Represented as

[0050]

[0051] Where f(·) represents the right-hand function of the dynamic equation (2), and the control quantity u = [C D C L ] T , t entry t is the time when the probe enters the atmosphere. p This refers to the moment the detector reaches the vicinity of the fire. When the detector reaches the near point of fire, x(t) p ) for t p The state of the time detector, set Defined as

[0052]

[0053] By combining equations (17) and (18), we obtain the mapping Φ that links the states of the far-fire point and the near-fire point. For ease of description, this mapping is expressed as...

[0054] x p =Φ(x a ,u,△ ρ (20)

[0055] Step 3: Solve for the reachable union under the influence of environmental uncertainties based on the mapping relationship in Step 2. According to the union of Nanda Calculate all possible near-fire point heat flux densities under the influence of environmental uncertainties. set The decision on whether to perform a thrust maneuver at the far fire point is based on the relationship between the heat flux density set at the near fire point and the atmospheric braking corridor.

[0056] For the problem of maneuvering decision-making at distant fire points, the reachable set is defined as: the set of all near fire point states that the detector can reach from its initial state under the influence of environmental uncertainties.

[0057] The far-field firing point status x obtained from step two prediction a =[r a ,v a ,γ a ] T Given the initial state and the k-th atmospheric density uncertainty. Corresponding Nengda set Represented as

[0058]

[0059] By the definition of the Nydus set, r p,k v p,k γ p,k The atmospheric density uncertainty is Δ ρ,k At that time, the probe's distance from the center of Mars, its speed, and its trajectory angle when it reaches the perihelion. (Nengda Collection) element x in p,k It is by changing the state of the far-fire point x a Control quantity u = [C D C L ] T and △ ρ,k Substituting into equations (17) and (18) yields the result.

[0060] The uncertainty of the kth atmospheric density Δ ρ,k Represented as:

[0061]

[0062] Where N is the selected △ ρ,k The total number.

[0063] N N reachable sets are obtained through equations (21) and (22). Then the union can be achieved for

[0064]

[0065] According to the union of Nanda Calculate all possible near-fire point heat flux densities under the influence of environmental uncertainties. set

[0066]

[0067] Heat flux density for

[0068]

[0069] in, Let x be the constant for calculating heat flux density, where x = [r, v, γ]. T This is a state variable.

[0070] During the aerodynamic deceleration phase, when the detector is near the fire point, the atmospheric braking heat flux density reaches its peak as velocity and atmospheric density reach their peak values. Therefore, the atmospheric braking heat flux density corridor constraint is expressed as:

[0071]

[0072] in, This represents the peak heat flux density near the ignition point. and These are the lower and upper boundaries of the heat flux density corridor, respectively. Upper boundary Used to ensure the flight safety of the probe, lower boundary Used to ensure the deceleration efficiency of atmospheric braking.

[0073] when If the detector reaches the far-fire point, no far-fire point maneuver is required; that is, the guidance command executed when the detector reaches the far-fire point is no maneuver. Otherwise, a far-fire point maneuver is required to correct the near-fire point status, and the far-fire point maneuver speed increment is calculated in step four.

[0074] Step 4: Solve for the energy-controllable intersection under the influence of environmental uncertainties Furthermore, the set of far-fire velocity increments that can be used to correct the near-fire state is solved by the controllable intersection. The incremental maneuvering speed of the distant Mars flank is selected, and the atmospheric braking energy reach control set prediction and correction guidance under uncertain conditions is realized based on the selected incremental maneuvering speed of the distant Mars flank.

[0075] The speed increment provided by the long-range firing point maneuver is Δv. When Δv > 0, the speed increment is along the positive speed direction. When Δv < 0, the speed increment is along the negative speed direction. The state of the long-range firing point before the maneuver is x. a Then, after the maneuver is executed, the state at the far-field firing point... for

[0076]

[0077] Where vector C = [0, 1, 0] T If it is known Then the velocity increment Δv can be solved using equation (28).

[0078]

[0079] For the problem of solving the incremental maneuvering velocity at the far-fire point, the controllable set is defined as: under the influence of environmental uncertainties, the set of far-fire point states that enable the detector to satisfy the atmospheric braking corridor constraint at the next near-fire point in terms of heat flux density. Given the i-th atmospheric density uncertainty... Corresponding control set Represented as

[0080]

[0081] According to the definition of a controllable set, The atmospheric density uncertainty is Δ ρ At time i, after performing the maneuver, the distance, speed, and trajectory angle of the probe from the farthest point of Mars to the center of Mars are recorded.

[0082] Given the atmospheric exit conditions, the distance from the farthest point of Mars to the center of Mars and the trajectory angle can be determined, i.e. Therefore, solving for the energy control set is essentially solving for the velocity of the far-fire point. The range. Let. and They are respectively The upper and lower bounds are defined in equation (30) for the iterative function.

[0083]

[0084] in, The Gauss-Newton iteration method is used to iterate over these two functions until the function value is less than the given precision ε, at which point the solution can be obtained. and At this point, the controllable set is represented as

[0085]

[0086] The i-th atmospheric density uncertainty is expressed as:

[0087]

[0088] Where M is the selected △ ρ,i The total number.

[0089] M Nydae sets are obtained through equations (31) and (32). Then the intersection can be controlled for

[0090]

[0091] Right now

[0092]

[0093] According to equation (28), the state x of the far-field firing point can be obtained by solving. a Change to The set of required far-fire point maneuver speed increments Right now

[0094]

[0095] Ultimately, the increase in the maneuver speed of the long-range fire points originates from the set. Selected from, i.e. When the probe reaches the far fire point, it executes the guidance command, which involves applying a maneuver to provide a velocity increment Δv, thereby adjusting the state of the far fire point and correcting the state of the near fire point to meet the braking corridor constraints, ensuring braking efficiency and probe flight safety until it reaches the target orbit.

[0096] Beneficial effects:

[0097] 1. This invention discloses a guidance method for predicting and correcting the reachable set of Mars atmospheric braking under uncertain conditions. It establishes dynamic models of the probe's flight outside and inside the atmosphere during the atmospheric braking process. Considering the impact of environmental parameter uncertainties on the probe's reachable set, the reachable set under different parameter uncertainties is calculated. By introducing the reachable union during the guidance prediction stage and using it to determine the maneuver requirements at the far-horizon point, the accuracy of maneuver decisions is improved, and the safety of atmospheric braking is enhanced.

[0098] 2. The present invention discloses a guidance method for predicting and correcting the energy control set of Mars atmospheric braking under uncertain conditions. It solves for the corresponding near-Mars heat flux density set by the union of energy reachable values, and determines whether the far-Mars needs maneuvering based on the relationship between the near-Mars heat flux density set and the atmospheric braking corridor. Considering the influence of environmental parameter uncertainties on the probe's energy control set, the method calculates the energy control set under different parameter uncertainties and solves for the energy control intersection. Considering the influence of parameter uncertainties on the probe's motion characteristics, the method introduces the energy control intersection during the guidance correction stage and applies it to calculate the far-Mars velocity increment, thereby improving maneuver correction accuracy and atmospheric braking safety. Attached Figure Description

[0099] Figure 1 Flowchart of a prediction and correction guidance method for Martian atmospheric braking energy under uncertain conditions;

[0100] Figure 2 Flowchart for solving the union of Martian atmospheric braking energy;

[0101] Figure 3 Flowchart for solving the intersection of Martian atmospheric braking energy control;

[0102] Figure 4 The figure shows the Monte Carlo simulation results for Example 1, where, Figure 4 (a) is a diagram showing the simulation results of the traditional Monte Carlo method. Figure 4 (b) is a Monte Carlo simulation result of the Mars atmospheric braking energy control-energy collection prediction correction guidance method under uncertain conditions.

[0103] Figure 5 The figure shows the Monte Carlo simulation results of Example 2, where, Figure 5 (a) is a diagram showing the simulation results of the traditional Monte Carlo method. Figure 5 (b) is a Monte Carlo simulation result of the Mars atmospheric braking energy control-energy collection prediction correction guidance method under uncertain conditions. Detailed Implementation

[0104] To better illustrate the purpose and advantages of the present invention, the following description, in conjunction with two embodiments and corresponding drawings, further explains the invention.

[0105] Example 1:

[0106] The parameters used are shown in Table 1. Atmospheric density uncertainty Δ ρ Follows a uniform distribution △ ρ ~U(-15%, 15%), lower boundary of the atmospheric braking corridor upper boundary The initial state of the detector is shown in Table 2. The number of calculations is N=500 and M=500.

[0107] Table 1 Simulation Parameters

[0108]

[0109] Table 2. Position and velocity vectors of the detector when it exits the atmosphere.

[0110]

[0111] like Figure 1 As shown in this embodiment, the specific implementation steps of the Martian atmospheric braking energy reach control set prediction and correction guidance method under uncertain conditions are as follows:

[0112] Step 1: Establish dynamic models of the detector's flight outside and inside the atmosphere during the atmospheric braking process;

[0113] When the probe is outside the Martian atmosphere, treating both the probe and the central celestial body as point masses, the dynamic model of the probe's flight outside the atmosphere during atmospheric braking is expressed as follows:

[0114]

[0115] Where μ is the gravitational constant of the central celestial body, r is the position vector of the spacecraft relative to the central celestial body; r = ||r|| represents the distance of the probe from the center of Mars;

[0116] During atmospheric braking, the longitudinal motion of the probe within the atmosphere is of greater concern; therefore, the influence of Mars' rotation is ignored, and the longitudinal and lateral motions of the probe within the atmosphere are decoupled, using x = [r, v, γ]. T The dynamic model of the detector flying in the atmosphere during the atmospheric braking process is obtained by using state variables, and is expressed as follows:

[0117]

[0118] Where v is the magnitude of the detector velocity and γ is the trajectory angle; g(r) = -μ / r 2 The local gravitational acceleration is given; the aerodynamic drag acceleration D and lift acceleration L are calculated by the following formula:

[0119]

[0120] Where ρ is the actual atmospheric density, S is the reference area, m is the detector mass, and C... D and C L These are the drag coefficient and lift coefficient, respectively.

[0121] Considering the impact of atmospheric density uncertainty on atmospheric ingress dynamics; at any given time, the true atmospheric density of a planet is expressed by the following formula.

[0122] ρ=ρ * (1+△ ρ (39)

[0123] Among them, △ ρ The atmospheric density uncertainty represents the percentage deviation between the model's nominal value and the actual value, and follows a uniform distribution, i.e., Δ. ρ ~U(△) ρ,min ,△ ρ,max ), △ ρ,min ,△ ρ,max These are the minimum and maximum percentage deviations, respectively; nominal value ρ * Calculated using equation (5):

[0124]

[0125] Where ρ0 is the reference atmospheric density, h is the current altitude of the detector, h0 is the reference altitude, and h s Proportional height;

[0126] Step 2: Given the position vector r of the detector when it exits the atmosphere. exit and velocity vector v exit The state x of the forecast probe when it reaches the far-field fire pointa =[r a ,v a ,γ a ] T Define the mapping relationship from the far-fire point state to the near-fire point state based on the dynamic model in step one;

[0127] The specific angular momentum H = r × v is conserved when the probe is flying outside the atmosphere. Multiplying both sides of equation (36) by H, we get...

[0128]

[0129] Considering H conservation, vector operation rules, and Equation (41) can be rewritten as

[0130]

[0131] Integrating both sides of equation (42) yields

[0132]

[0133] Where B is the constant vector of integration, the scalar equation is obtained by multiplying r by equation (8).

[0134]

[0135] From equation (44), we can obtain

[0136] H 2 =μr+rBcosθ (45)

[0137] Where H = ||H|| is the magnitude of the specific angular momentum, B = ||B|| is the magnitude of the integral constant vector B, and θ is the angle between the constant vector B and the position vector r. Solving for r yields the geometric equation of the probe's orbit outside the atmosphere.

[0138]

[0139] Let p = H 2 / μ, e=B / μ, then equation (46) can be rewritten as

[0140]

[0141] The geometric equation of the track (47) is the polar coordinate equation of a conic section, where the constant p is the semi-blind diameter and the constant e is the eccentricity.

[0142] Given that the position and velocity vector of the probe when it exits the atmosphere are r exit and v exit Based on the principle of energy conservation, the semi-major axis of the orbit is calculated to be a0 = 7780.300 km.

[0143]

[0144] Where, r exit =||r exit ||and v exit =||v exit ||;E0 is the specific mechanical energy;

[0145] From equations (46) and (47), it can be seen that the semi-major diameter p0 of the track is

[0146]

[0147] Where e0 is the orbital eccentricity, H0=||r exit ×v exit || represents the magnitude of the specific angular momentum; by combining equations (48) and (49), we can obtain

[0148]

[0149] From equation (50), the eccentricity is e0 = 0.5471;

[0150] The state of the detector when it reaches the far-field point is x a =[r a ,v a ,γ a ] T The position vector and velocity vector at the far-fetched firing point are perpendicular, and the trajectory angle γ a =0, the radius vector r of the detector at the far-field point a and speed magnitude v a From equation (51) we get

[0151]

[0152] From equation (51), the state of the far-field firing point can be obtained as x. a =[12036.554km,1269.514m / s,0] T ;

[0153] The probe's state x when it enters the atmosphere entry =[r entry ,v entry ,γ entry ] T for

[0154]

[0155] Among them, the intermediate variable r atm =R m +h atm h atm R is the altitude of the atmospheric boundary. mMars radius; track angle γ entry <0; x can be obtained through calculation. entry =[3547km,4.318km / s,-0.0677rad] T Near-fire state x p =[r p ,v p ,γ p ] T Represented as

[0156]

[0157] Where f(·) represents the right-hand function of the dynamic equation (37), and the control quantity u = [C D C L ] T , t entry t is the time when the probe enters the atmosphere. p The moment when the detector reaches the point of near-fire; when When the detector reaches the near point of fire, x(t) p ) for t p The state of the time detector, set Defined as

[0158]

[0159] By combining equations (52) and (53), we obtain the mapping Φ that links the states of the far-fire point and the near-fire point. For ease of description, this mapping is expressed as...

[0160] x p =Φ(x a ,u,△ ρ (55)

[0161] Step 3: Solve for the reachable union under the influence of environmental uncertainties based on the mapping relationship in Step 2. According to the union of Nanda Calculate all possible near-fire point heat flux densities under the influence of environmental uncertainties. set The decision on whether to perform thrust maneuvers at the far fire point is based on the relationship between the heat flux density set at the near fire point and the atmospheric braking corridor.

[0162] For the problem of maneuvering decision-making at distant fire points, the reachable set is defined as: the set of all near fire point states that the detector can reach from its initial state under the influence of environmental uncertainties;

[0163] The far-field firing point status x obtained from step two prediction a =[r a ,v a ,γ aT is the initial state, and the k-th atmospheric density uncertainty is given The corresponding reachable set is expressed as

[0164]

[0165] As can be known from the definition of the reachable set, r p,k , v p,k , γ p,k are respectively the distance from the detector to the center of Mars, the velocity and the flight path angle when the detector arrives at the periapsis of Mars under the atmospheric density uncertainty △ ρ, k; the elements x in the reachable set in the p,k are obtained by substituting the apoapsis of Mars state x a , the control quantity u=[C D ,C L T and △ ρ,k into Equation (52) and Equation (53);

[0166] The k-th atmospheric density uncertainty △ ρ,k is expressed as:

[0167]

[0168] where N is the total number of selected △ ρ,k .

[0169] N reachable sets are obtained through Equation (56) and Equation (57) Then the reachable union set is

[0170]

[0171] According to the reachable union set the set of all possible heat flux densities at the periapsis of Mars under the influence of environmental uncertainties is calculated

[0172]

[0173] The heat flux density is

[0174]

[0175] where, is a constant for heat flux density calculation;

[0176] In the aerodynamic deceleration phase, when the detector is at the periapsis of Mars, the heat flux density reaches its peak because the velocity and atmospheric density reach their peaks. Therefore, the aerobraking heat flux density corridor constraint is expressed as:​​​

[0177]

[0178] in, This represents the peak heat flux density near the ignition point. and These are the lower and upper boundaries of the heat flux density corridor, respectively; upper boundary Used to ensure the flight safety of the probe, lower boundary Used to ensure the deceleration efficiency of atmospheric braking;

[0179] when When the detector reaches the far point, no maneuver is required; otherwise, a far point maneuver is required to correct the near point status. The speed increment of the far point maneuver is calculated in step four.

[0180] Calculation yields because A long-range fire point maneuver is required to correct the near-fire point status. The speed increment of the long-range fire point maneuver is calculated in step four.

[0181] Step 4: Solve for the energy-controllable intersection under the influence of environmental uncertainties Furthermore, the set of far-fire velocity increments that can be used to correct the near-fire state is solved by the controllable intersection. And select the speed increment of the long-range firing point from it;

[0182] The speed increment provided by the long-range firing point maneuver is Δv. When Δv > 0, the speed increment is along the positive speed direction; when Δv < 0, the speed increment is along the negative speed direction. The state of the long-range firing point before the maneuver is x. a Then, after the maneuver is executed, the state at the far-field firing point... for

[0183]

[0184] Where vector C = [0, 1, 0] T If it is known Then the velocity increment Δv can be solved using equation (63).

[0185]

[0186] For the problem of solving the incremental maneuvering velocity at the far-fire point, the controllable set is defined as: under the influence of environmental uncertainties, the set of far-fire point states that enable the detector to satisfy the atmospheric braking corridor constraint at the next near-fire point in terms of heat flux density; given the i-th atmospheric density uncertainty... Corresponding control set Represented as

[0187]

[0188] According to the definition of a controllable set, The atmospheric density uncertainty is Δ ρ,i At that time, after performing the maneuver, the distance, speed, and trajectory angle of the probe from the farthest point of Mars to the center of Mars;

[0189] Given the atmospheric exit conditions, the distance from the farthest point of Mars to the center of Mars and the trajectory angle can be determined, i.e. Therefore, solving for the energy control set is essentially solving for the velocity of the far-fire point. Scope; and They are respectively The upper and lower bounds are defined in equation (65) for the iterative function.

[0190]

[0191] in, The Gauss-Newton iteration method is used to iterate over these two functions until the function value is less than the given precision ε, at which point the solution can be obtained. and At this point, the controllable set is represented as

[0192]

[0193] The i-th atmospheric density uncertainty is expressed as:

[0194]

[0195] Where M is the selected △ ρ,i The total number.

[0196] M Nanda sets are obtained through equations (66) and (67). Then the intersection can be controlled for

[0197]

[0198] Right now

[0199]

[0200] The calculated controllable intersection is as follows

[0201] According to equation (63), the state x of the far-field firing point can be obtained by solving. a Change to The set of required far-fire point maneuver speed increments Right now

[0202]

[0203] The calculated set of maneuver speed increments is as follows Ultimately, the increase in the maneuver speed of the long-range fire points originates from the set. Selected from, i.e. When the probe reaches the far fire point, it executes the guidance command, which involves applying a maneuver to provide a velocity increment Δv, thereby adjusting the state of the far fire point and correcting the state of the near fire point to meet the braking corridor constraints, ensuring braking efficiency and probe flight safety.

[0204] Using traditional prediction methods, without considering the impact of parameter uncertainties, the nominal near-fire point heat flux density obtained from the initial state shown in Table 2 is: Satisfying the heat flux density constraint, the decision is that the far-end point does not need to maneuver. However, the conclusion drawn from the Mars atmospheric braking energy control energy collection prediction and correction guidance method under uncertain conditions proposed in this invention is that the far-end point needs to maneuver, and the maneuver velocity increment Δv ∈ [0.187, 0.283] m / s. To verify the effectiveness of the proposed method, 1000 Monte Carlo simulations were performed, with atmospheric density uncertainty randomly selected in each simulation. The near-end heat flux density constraint satisfaction of the traditional method and the method proposed in this invention were compared. The simulation results are as follows: Figure 4 As shown. Traditional methods determine that no maneuvering is required at the far-fire point. However, under the influence of atmospheric density uncertainty, the probability that the heat flux density at the near-fire point meets the constraint is 54.5%. In contrast, the method proposed in this invention has a 100% probability that the heat flux density at the near-fire point meets the constraint, making the judgment of the far-fire point maneuvering requirement more accurate. Furthermore, the calculated maneuvering speed increment ensures that the heat flux density constraint at the near-fire point can still be met even under conditions of parameter uncertainty.

[0205] Each time the detector leaves the atmosphere during atmospheric braking, the guidance method proposed in this invention is used to generate guidance commands, and the corresponding guidance commands are executed when it reaches the far-point of the fire, ensuring that the near-point of the fire is within the atmospheric braking corridor, thus achieving safe and efficient atmospheric braking, and finally reaching the target orbit to complete atmospheric braking.

[0206] Example 2:

[0207] To further verify the effectiveness of the method proposed in this invention, the initial conditions were changed as shown in Table 3, while the remaining simulation parameters were the same as in Example 1.

[0208] Table 3. Detector enters initial state

[0209]

[0210] The calculated state of the far-field firing point is x. a = [1084.021km, 1391.890m / s, 0]T The method proposed in this invention calculates the union of energy points and the set of heat flux densities near the firing point. If the heat flux density constraint is not met, the far-fetched firing point needs to maneuver. The controllable intersection is calculated using the method proposed in this invention, and the set of velocity increments of the far-fetched firing point is further calculated as follows:

[0211] Using traditional prediction methods, without considering the impact of parameter uncertainties, the nominal near-fire point heat flux density obtained from the initial states shown in Table 3 is: If the heat flux density constraint is not met, the far-field firing point needs to maneuver. Under nominal conditions, the calculated maneuvering energy control set of the far-field firing point is... Further calculations yielded the set of velocity increments at the far-field firing points as follows:

[0212] Both methods determine that the far-fire point needs to maneuver, but the range of the maneuvering velocity increment obtained is different. To verify the effectiveness of the proposed method, 1000 Monte Carlo simulations were performed. In each simulation, atmospheric density uncertainty was randomly selected, and the far-fire point maneuvering velocity increment was randomly selected from the set of far-fire point velocity increments. The near-fire point heat flux density constraint satisfaction of the traditional method and the proposed method were compared. The simulation results are as follows: Figure 5 As shown, the probability of the near-fire point heat flux density satisfying the constraint using the traditional method is 81.6%, while the probability of the near-fire point heat flux density satisfying the constraint using the method proposed in this invention is 100%. Simulation results show that the set of far-fire point velocity increments calculated using the method proposed in this invention... Selecting a velocity increment can increase the probability that the heat flux density near the fire point satisfies the constraints compared to traditional methods.

[0213] Each time the detector leaves the atmosphere during atmospheric braking, the guidance method proposed in this invention is used to generate guidance commands, and the corresponding guidance commands are executed when it reaches the far-point of the fire, ensuring that the near-point of the fire is within the atmospheric braking corridor, thus achieving safe and efficient atmospheric braking, and finally reaching the target orbit to complete atmospheric braking.

[0214] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for predicting and correcting guidance of Martian atmospheric braking energy reach control set under uncertain conditions, characterized by: Includes the following steps, Step 1: Establish dynamic models of the detector's flight outside the atmosphere and its flight inside the atmosphere during the atmospheric braking process, respectively. Step 2: Given the position vector of the detector when it exits the atmosphere. and velocity vector The state of the forecast probe when it reaches the far-field fire point. , The radius vector of the detector at the far-field point. For speed magnitude, The trajectory angle is defined; based on the dynamic model in step one, the mapping relationship from the far-fire point state to the near-fire point state is defined; Step 3: Solve for the reachable union under the influence of environmental uncertainties based on the mapping relationship in Step 2. According to the union of the two sets of energies Calculate all possible near-fire point heat flux densities under the influence of environmental uncertainties. set ; The decision on whether to perform thrust maneuvers at the far fire point is based on the relationship between the heat flux density set at the near fire point and the atmospheric braking corridor. Step 4: Solve for the energy-controllable intersection under the influence of environmental uncertainties Furthermore, the set of far-fire velocity increments that can be used to correct the near-fire state is solved by the controllable intersection. The system selects the maneuver speed increment of the far-end point and uses the selected far-end point maneuver speed increment to achieve predictive correction guidance for Mars atmospheric braking energy under uncertain conditions.

2. The method for predicting and correcting Martian atmospheric braking energy reach control set prediction guidance under uncertain conditions as described in claim 1, characterized in that: The dynamic model of the detector flying outside the atmosphere during the atmospheric braking process described in step one is expressed as follows: in, The gravitational constant of the central celestial body, This is the position vector of the spacecraft relative to the central celestial body; This indicates the distance of the probe from the center of Mars.

3. The method for predicting and correcting Martian atmospheric braking energy reach control set prediction guidance under uncertain conditions as described in claim 1, characterized in that: The dynamic model of the detector flying in the atmosphere during the atmospheric braking process described in step one is expressed as follows: in, For the detector speed magnitude, The track angle; Local gravitational acceleration; aerodynamic drag acceleration and lift acceleration Calculated by the following formula: in, This represents the actual atmospheric density. For reference area, For detector quality, and These are the drag coefficient and lift coefficient, respectively. Considering the impact of atmospheric density uncertainty on atmospheric ingress dynamics; at any given time, the true atmospheric density of a planet is expressed by the following formula. in, The atmospheric density uncertainty represents the percentage deviation between the model's nominal value and the actual value, and follows a uniform distribution, i.e. , These are the minimum and maximum percentage deviations, respectively; nominal value Through calculate: in, For reference atmospheric density, This is the current altitude of the probe. For reference height, This refers to the proportional height.

4. The method for predicting and correcting Martian atmospheric braking energy reach control set prediction guidance under uncertain conditions as described in claim 1, characterized in that: Specific angular momentum of the probe during its flight outside the atmosphere It is conserved; the formula Both sides simultaneously Cross product Considering Conservation, rules of vector operations, and , will Rewritten as Mode Integrating both sides yields in For a constant vector for integration, use dot product Scalar equations are obtained From the formula have to in, To compare the magnitude of angular momentum, For the integral constant vector Size, constant vector With position vector The angle between them, solve The geometric equations for the probe's orbit outside the atmosphere can be obtained as follows: make , , then the formula Rewritten as Geometric equations of the orbit It is the polar coordinate equation of a conic section, with constants. For semi-pipe diameter, constant Eccentricity; Given that the position and velocity vectors of the probe when it exits the atmosphere are respectively and Calculate the semi-major axis of the orbit based on the principle of energy conservation. for: in, and ; For mechanical energy; From the formula Japanese style Okay, the orbital semi-circular diameter for in, For orbital eccentricity, To compare the magnitudes of angular momentum; simultaneous equations and achievable The status of the detector when it reaches the far-field fire point is The position vector and velocity vector at the far-fetched point are perpendicular, and the trajectory angle is... The radius vector of the detector at the far-field point and speed magnitude From the formula get The state of the probe when it enters the atmosphere for Among them, intermediate variables , At atmospheric boundary height, Mars radius; track angle Near-fire state Represented as in, Representing the dynamic formula The right-hand function controls the variable. , This is the moment the probe enters the atmosphere. The moment when the detector reaches the vicinity of the fire; when When the detector reaches the vicinity of the fire, for The state of the time detector, set Defined as Through joint Japanese style A mapping is obtained that links the states of the far-fire points to the states of the near-fire points. The mapping is represented as 。 5. The method for predicting and correcting Martian atmospheric braking energy reach control set prediction guidance under uncertain conditions as described in claim 1, characterized in that: Step three involves solving for the reachable union under the influence of environmental uncertainties based on the mapping relationship described in step two. The method is, For the problem of maneuvering decision-making at distant fire points, the reachable set is defined as: the set of all near fire point states that the detector can reach from its initial state under the influence of environmental uncertainties; Based on the far-field fire point status predicted in step two Given the initial state and the k-th atmospheric density uncertainty. The corresponding Nengda set Represented as According to the definition of Nanda set, , , The atmospheric density uncertainty is respectively At that time, the distance, speed, and trajectory angle of the probe from the center of Mars when it reaches the perihelion; [the data is missing from the original text]. elements in It is by changing the state of the far-fire point Control quantity and Substitution Japanese style get; The k-th atmospheric density uncertainty Represented as: Where N is the selected value. The total number; Through Japanese style Obtain N N-sets Then the union can be achieved. for 。 6. The method for predicting and correcting Martian atmospheric braking energy reach control set prediction guidance under uncertain conditions as described in claim 1, characterized in that: Step 3 describes the method based on the union of reachable sets. Calculate all possible near-fire point heat flux densities under the influence of environmental uncertainties. set : Heat flux density for in, This is the constant for calculating heat flux density. It is a state variable.

7. The method for predicting and correcting Martian atmospheric braking energy reach control set prediction guidance under uncertain conditions as described in claim 1, characterized in that: Step three describes the use of near-fire point heat flux density sets. The method for determining whether a thrust maneuver needs to be performed at the far end of the firing range, based on the relationship with the atmospheric braking corridor, is as follows. During the aerodynamic deceleration phase, when the detector is near the fire point, the atmospheric braking heat flux density reaches its peak as velocity and atmospheric density reach their peak values. Therefore, the atmospheric braking heat flux density corridor constraint is expressed as: in, This represents the peak heat flux density near the ignition point. and These are the lower and upper boundaries of the heat flux density corridor, respectively; upper boundary Used to ensure the flight safety of the probe, lower boundary Used to ensure the deceleration efficiency of atmospheric braking; when When the detector reaches the far-fire point, no far-fire point maneuver is required; otherwise, a far-fire point maneuver is required to correct the near-fire point status. The speed increment of the far-fire point maneuver is calculated in step four.

8. The method for predicting and correcting Martian atmospheric braking energy reach control set prediction guidance under uncertain conditions as described in claim 1, characterized in that: Step 4: Solve for the energy-controllable intersection under the influence of environmental uncertainties Furthermore, the set of far-fire velocity increments that can be used to correct the near-fire state is solved by the controllable intersection. And select the speed increment of the long-range firing point from it; The speed increment provided by performing long-range fire maneuvers is ,when When, the velocity increment is along the positive velocity direction; when At that time, the speed increment is in the opposite direction of the speed; the state of the far-end fire point before the maneuver is... Then, after the maneuver is executed, the state at the far-field firing point... for Where, vector If it is known Then through the formula Solving for velocity increments , For the problem of solving the incremental maneuvering velocity at the far-fire point, the controllable set is defined as: under the influence of environmental uncertainties, the set of far-fire point states that enable the detector to satisfy the atmospheric braking corridor constraint at the next near-fire point in terms of heat flux density; given the i-th atmospheric density uncertainty... The corresponding controllable set Represented as According to the definition of a controllable set, , , The atmospheric density uncertainty is respectively At that time, after performing the maneuver, the distance, speed, and trajectory angle of the probe from the farthest point of Mars to the center of Mars; Given the atmospheric exit conditions, the distance from the farthest point of Mars to the center of Mars and the trajectory angle can be determined, that is... , Therefore, solving for the energy control set is actually solving for the velocity of the far-initiated firing point. Scope; and They are respectively The upper and lower bounds are as follows: Define iteration function in, , The Gauss-Newton iteration method is used to iterate over these two functions until the function value is less than the given precision. That is, to obtain the solution and At this point, the controllable set is represented as The i-th atmospheric density uncertainty is expressed as: Where M is the selected... The total number; Through Japanese style M control sets are obtained Then the intersection can be controlled. for Right now According to the formula Solving for the state of the far-field firing point Change to The set of required far-fire point maneuver speed increments ,Right now Ultimately, the increase in the maneuver speed of the long-range fire points originates from the set. Selected from, i.e. When the probe reaches the far-field point, it applies maneuvers to provide a speed increment. This adjusts the state of the far-point fire and corrects the state of the near-point fire, ensuring that it meets the braking corridor constraints and guaranteeing braking efficiency and probe flight safety.

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