Anti-saturation trajectory optimization method for Mars entry

Abstract

The present invention discloses a method for optimizing an anti-saturation trajectory for Mars entry, which belongs to the field of aircraft guidance and control. The implementation method of the present invention is as follows: the roll angle obtained by tracking the drag acceleration curve is defined as the calculated roll angle; a three-level orthogonal table is used to select a combination of aerodynamic parameter disturbances, and then a sensitivity formula for the calculated roll angle to the disturbance combination is constructed, and the influence of aerodynamic parameter disturbances on the calculated roll angle is quantified by the sensitivity formula; in order to meet the terminal constraint requirements and anti-saturation capability requirements of the lander under aerodynamic disturbances, a terminal constraint optimization index and an anti-saturation optimization index based on the sensitivity formula are designed respectively, and the two optimization indicators of the altitude and range constraint index and the anti-saturation index are linearly weighted to obtain a comprehensive entry trajectory optimization index that improves the anti-saturation capability. The above comprehensive index is optimized using an optimization method to obtain an optimized roll angle-energy profile, and the anti-saturation entry trajectory is obtained after tracking the profile.

Description

Technical Field

[0001] The present invention relates to an entry trajectory optimization method, in particular to an anti-saturation trajectory optimization method for a Mars entry phase, and belongs to the field of aircraft guidance and control. Background Art

[0002] Mars landing exploration is a key area of ​​deep space exploration today. The Mars landing process is generally divided into atmospheric entry, parachute deceleration, and landing. The atmospheric entry phase, characterized by a large airspace span and a harsh aerodynamic environment, is a critical stage for Mars landing. This phase requires the use of aerodynamic forces to reduce the velocity from 5,000 to 7,000 m / s to approximately 400 m / s, posing significant technical challenges. Although the United States and my country have both successfully landed on the Martian surface, the maximum payload of these missions has not exceeded 900 kg. Future Mars return missions are expected to achieve landing payloads exceeding 2 tons, but due to the diameter of the launch vehicle's fairing, the effective area of ​​the lander cannot be significantly increased, which means that the lander's ballistic coefficient will increase. This increased ballistic coefficient results in a lower trajectory during the atmospheric entry phase, increasing the impact of aerodynamic disturbances and easily leading to trajectory tracker control saturation, ultimately affecting parachute deployment accuracy. Therefore, the design of Mars entry guidance methods must address the issue of trajectory tracking control saturation under parameter perturbations. For Mars entry missions with smaller payload masses, trajectory tracking laws are typically designed to mitigate the effects of parameter perturbations. However, as the payload mass increases, the aerodynamic control capability weakens, making it difficult to accurately track the nominal trajectory using the tracking law alone, and control saturation is very likely to occur. Therefore, it is necessary to consider the trackability of the trajectory under parameter perturbations in advance during the nominal trajectory design phase, that is, to design an entry trajectory with saturation resistance. This trajectory must not only meet traditional terminal constraints such as altitude, speed, and range, but also be less sensitive to aerodynamic disturbances. Summary of the Invention

[0003] Aiming at the problem that the entry trajectory tracking of future large-mass Mars landers is prone to saturation, the main purpose of the present invention is to provide an anti-saturation trajectory optimization method for the Mars entry phase, which defines the roll angle during trajectory tracking as the calculated roll angle, adopts a three-level orthogonal table to select the aerodynamic parameter perturbation combination, and then constructs a sensitivity formula for the calculated roll angle to the perturbation combination. The influence of the aerodynamic parameter perturbation on the calculated roll angle is quantified by the sensitivity formula. In order to meet the terminal constraint requirements and anti-saturation capability requirements of the lander under aerodynamic perturbations, a terminal constraint optimization index and an anti-saturation optimization index based on the sensitivity formula are designed respectively. The two optimization indexes are combined to obtain a comprehensive optimization index. The optimization method is used to obtain the anti-saturation trajectory of the Mars entry phase, that is, the anti-saturation trajectory optimization of the Mars entry phase is realized.

[0004] The present invention is achieved through the following technical solutions.

[0005] The present invention discloses a method for optimizing the anti-saturation trajectory of the Mars entry phase. A roll angle-energy profile is established, and a reference drag acceleration curve is obtained through the profile. The roll angle obtained by tracking the drag acceleration curve is defined as the calculated roll angle. A three-level orthogonal table is used to select a perturbation combination for the atmospheric density, lift coefficient, drag coefficient, and lander mass of the Mars entry phase. Based on the partial derivative of the roll angle with respect to a certain perturbation, a sensitivity formula for the calculated roll angle to the perturbation combination is established. The quantitative impact of the perturbation on the lander's control capability is obtained based on the sensitivity formula. Under the premise of a given terminal velocity, an altitude and range constraint index is designed. Based on the sensitivity formula of the lander's calculated roll angle to a typical perturbation combination, an anti-saturation index is designed. The two optimization indicators, the altitude and range constraint index and the anti-saturation index, are linearly weighted to obtain a comprehensive entry trajectory optimization index that improves the anti-saturation capability. The above comprehensive index is optimized using an optimization method to obtain an optimized roll angle-energy profile. After tracking the profile, the anti-saturation entry trajectory is obtained, thereby achieving the anti-saturation trajectory optimization of the Mars entry phase.

[0006] The Mars entry phase anti-saturation trajectory optimization method disclosed in the present invention includes the following steps:

[0007] Step 1: Design a sequence of energy segmentation points based on the initial and terminal energies to establish a piecewise linear roll angle-energy profile. Using this profile as the control variable, integrate the Mars entry dynamics equation to obtain a reference drag acceleration curve. This curve is tracked using the tracking law, and the resulting roll angle is defined as the calculated roll angle.

[0008] The specific implementation method of step one is:

[0009] The energy e is defined as follows:

[0010]

[0011] Where μ is the Martian gravitational constant, r is the distance from the center of mass of Mars to the center of mass of the lander, and v is the flight speed of the lander. The normalized energy E is defined as follows:

[0012]

[0013] Among them, e0 and e f are the energies determined according to the initial and terminal states, respectively.

[0014] Given a normalized energy segmentation point sequence, such that 0 = E0 <E1<E2<…<E n =1, n is the number of segments. According to the energy segmentation point sequence, a piecewise linear roll angle profile σ(E) with normalized energy as the independent variable is designed. For E j <E≤E j+1 , the corresponding roll angle is:

[0015]

[0016] The roll angle-energy profile is used as the amplitude of the control quantity, and the sign of the control quantity is determined by the roll angle inversion logic. By integrating the dynamic model of the Mars entry phase, the state at each time point can be solved, and then the corresponding reference resistance acceleration D can be obtained by the formula r , forming the reference resistance acceleration curve.

[0017]

[0018] Where ρ is the air density, S is the lander surface area, m is the lander mass, and C D is the drag coefficient. The following tracking law is used to track the curve:

[0019]

[0020] Where D is the actual drag acceleration, which is equal to D when there is no disturbance. r ; σ c is the roll angle value calculated by the tracking law, which is defined as the calculated roll angle; k d 、k p is the gain value; the formulas for a and b are as follows:

[0021]

[0022]

[0023]

[0024] Among them, h s is the altitude coefficient in the atmospheric density formula, g is the gravitational acceleration on the Martian surface, L is the lift acceleration, γ is the ballistic inclination angle, φ is the latitude of the lander, ψ is the heading angle, and ω is the angular velocity of Mars' rotation. The calculated roll angle value for each state is determined using the tracking law of the formula.

[0025] Step 2: Using a three-level orthogonal table to select perturbation combinations for the atmospheric density, lift coefficient, drag coefficient, and lander mass during Mars entry, a sensitivity formula for the roll angle to these perturbation combinations was established based on the partial derivative of the roll angle with respect to each perturbation. This sensitivity formula then quantitatively determined the impact of each perturbation on the lander's controllability.

[0026] The specific implementation method of step 2 is:

[0027] Since the increase of the lander's ballistic coefficient will cause the entry trajectory to be lower, the aerodynamic disturbance will become larger, and the control ability of the lander will be affected, it is necessary to consider the impact of the uncertainty of aerodynamic parameters on the control ability, that is, to establish a mapping relationship between aerodynamic parameter disturbance and roll angle. Aerodynamic parameter disturbances include atmospheric density, lift coefficient, drag coefficient and lander mass disturbance. In order to effectively analyze the impact of the four disturbances on control, L9(3 4 ) The three-level orthogonal table selects disturbance combinations as typical representatives of various disturbance situations to form a combined disturbance table. L9(3 4 ) where 9 represents 9 combined disturbances, which are arranged in sequence to form a disturbance sequence; 3 represents the number of levels, with positive disturbance, negative disturbance, and zero disturbance selected at the three levels, represented by Arabic numerals 1, -1, and 0, respectively; 4 represents the number of factors, with the four factors representing atmospheric density disturbance Δρ, lift coefficient disturbance ΔC, and so on. L , Drag coefficient disturbance ΔC D and the lander mass perturbation Δm. The set perturbation combinations are shown in Table 1.

[0028] Table 1 Combined perturbation table

[0029]

[0030] The formula for calculating the sensitivity of the roll angle to typical disturbance combinations is established as follows:

[0031]

[0032] Among them, f i is the value of the sensitivity formula corresponding to the i-th combined disturbance, and Δ is the dimensionless disturbance constant. For a single disturbance, the formula reflecting the sensitivity of the roll angle to that disturbance is the partial derivative of the roll angle with respect to that disturbance. However, for combined disturbances, the dividend cannot be determined by using the partial derivative method. Therefore, the dimensionless disturbance constant Δ is used as the dividend in calculating the sensitivity of the roll angle to the combined disturbance.

[0033] According to the above combined perturbation table 1, the no-perturbation case and the eight perturbations together constitute nine perturbation combinations. Taking the no-perturbation case as the benchmark, the eight perturbations are respectively brought into the above sensitivity formula for corresponding sensitivity calculations, and the quantitative effects of the four perturbations on the lander's control capability are obtained.

[0034] Step 3: Given a given terminal velocity, design an altitude and range constraint. Design an anti-saturation index based on a formula that calculates the sensitivity of the lander's roll angle to typical perturbation combinations. Linearly weight the altitude and range constraint and the anti-saturation index to achieve a comprehensive entry trajectory optimization index that improves anti-saturation capability. This comprehensive index is optimized using an optimization method to obtain an optimized roll angle-energy profile. This profile is then tracked to obtain an anti-saturation entry trajectory, achieving anti-saturation trajectory optimization for the Mars entry phase.

[0035] The specific implementation method of step three is:

[0036] First, under the premise of a given terminal speed, the terminal constraint index J1 that meets the terminal altitude and range constraints is designed. The index is as follows:

[0037] J1=-h f +k|s togo | (9)

[0038] Among them, h f is the terminal height, k is the weighting constant, s togo Terminal range, its formula is as follows:

[0039] s togo =R0arccos[cosφcosφ T cos(θ-θ T )+sinφsinφ T ] (10)

[0040] Where R0 is the radius of Mars, θ is the longitude of the lander, and θ T With φ T are the longitude and latitude of the target point respectively.

[0041] Next, set the sequence of time t so that 0 = t0 <t1<t2<...<t z =t f , z is the length of the sequence. The sensitivity of the roll angle to the combined disturbance is calculated at each time series point, and the following anti-saturation index J2 is designed based on the obtained sensitivity:

[0042]

[0043]

[0044] Among them, σ max is the upper limit of the roll angle, σ minis the lower limit of the roll angle. C is a function of the time series, and J2 is obtained by summing C. ρ0 is the constant density of the Martian atmosphere. The first terminal constraint index J1 ensures that the trajectory meets the terminal constraint, and the second anti-saturation index J2 ensures that the trajectory's anti-saturation ability is improved. Therefore, after weighting these two indicators, the comprehensive optimization index J is obtained, which not only meets the terminal constraint but also improves the anti-saturation ability:

[0045] J=k1J1+k2J2 (13)

[0046] Among them, k1 and k2 are weight coefficients.

[0047] Taking the trajectory optimization comprehensive index as the optimization target, an optimization method is used to optimize the comprehensive index to obtain an anti-saturation entry trajectory, that is, to achieve the anti-saturation trajectory optimization for the Mars entry phase. Preferably, the optimization method uses a quadratic programming method.

[0048] Beneficial effects:

[0049] 1. The disclosed Mars entry lander anti-saturation trajectory optimization method, while satisfying conventional entry terminal velocity, altitude, and range constraints, integrates the roll angle-energy profile of the Mars entry dynamics model to obtain a reference drag acceleration curve. The curve is then tracked to define the calculated roll angle. A three-level orthogonal table is used to select perturbation combinations of aerodynamic parameters, and a sensitivity formula for the calculated roll angle to these combined perturbations is established. This sensitivity formula characterizes the quantitative impact of these perturbations on the lander's controllability, quantifying the impact of the combination of multi-parameter perturbations on the lander's controllability and facilitating the construction of an anti-saturation optimization index.

[0050] 2. The anti-saturation trajectory optimization method for the Mars entry phase lander disclosed in the present invention designs an altitude-range optimization index based on the constraints of the lander entry phase. At the same time, on the basis of achieving beneficial effect 1, the terminal velocity is given and an altitude-range constraint index is designed; based on the sensitivity formula of the lander's roll angle to the disturbance combination, an anti-saturation index is designed. The two optimization indicators of the altitude-range constraint index and the anti-saturation index are linearly weighted to obtain a comprehensive entry trajectory optimization index that improves the anti-saturation capability. Taking the trajectory optimization comprehensive index as the optimization target, the optimization method is used to optimize the above comprehensive index to obtain the optimized roll angle-energy profile. After tracking the profile, the anti-saturation entry trajectory is obtained, that is, the anti-saturation trajectory optimization of the Mars entry phase is achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 Flowchart of the anti-saturation trajectory optimization method for the Mars entry phase lander;

[0052] Figure 2 is a schematic diagram of the tilt angle-energy profile;

[0053] Figure 3 is the heel angle-energy profile solved under the comprehensive optimization index;

[0054] Figure 4 is the reference resistance acceleration curve solved under the comprehensive optimization index;

[0055] Figure 5 Comparison of terminal range percentages using Monte Carlo simulations using different methods. DETAILED DESCRIPTION

[0056] In order to better illustrate the purpose and advantages of the present invention, the invention is described below with reference to an example and corresponding drawings.

[0057] In order to verify the feasibility and advantages of the trajectory optimization method, a large-mass Mars lander is selected for simulation. The lander mass m = 4000 kg, and the lander surface area S = 15.9043 m 2 Initial conditions for entry: altitude h0 = 123 km, speed v0 = 5505 m / s, longitude θ0 = -90.072°, latitude φ0 = -43.898°, heading angle ψ0 = 85.01°, trajectory inclination angle γ0 = -14.15°. Terminal conditions for entry: speed v f =460m / s, longitude θ T =-73.26°, latitude φ T =-41.45°. Upper limit of the tilt angle σ max =90°, lower limit of the tilt angle σ min =10°.

[0058] like Figure 1 As shown, the anti-saturation trajectory optimization method for the Mars entry phase disclosed in this example has the following specific implementation steps:

[0059] Step 1: Design the energy segmentation point sequence according to the initial and terminal energies, and establish Figure 2 The piecewise linear roll angle-energy profile is shown. Using this profile as the control variable, the reference drag acceleration curve is integrated through the Mars entry dynamics equation. This curve is tracked using the tracking law, and the resulting roll angle is defined as the calculated roll angle.

[0060] The specific implementation method of step one is:

[0061] Energy e is defined as follows

[0062]

[0063] Where μ = 4.284 × 10 13 is the Martian gravitational constant, r is the distance from the center of mass of Mars to the center of mass of the lander, and v is the flight speed of the lander. The normalized energy E is defined as follows:

[0064]

[0065] where, e0 and e f are energies determined according to the initial and terminal states respectively.

[0066] Given a sequence of normalized energy segmentation points, the normalized energy is divided into 7 segments from 0 to 1, such that 0 = E0 < E1 < E2 < … < E7 = 1. A piecewise linear bank angle profile σ(E) with the normalized energy as the independent variable is designed according to the energy segmentation point sequence. For E j < E ≤ E j+1 , the corresponding bank angle is:

[0067]

[0068] Taking the bank angle - energy profile as the amplitude of the control quantity, the sign of the control quantity is determined by the bank angle reversal logic. The state at each time point can be obtained by integrating the dynamic model of the Mars entry segment, and then the corresponding reference drag acceleration D r is obtained, and a reference drag acceleration curve is formed.

[0069]

[0070] where, ρ is the local air density of Mars, and C D is the drag coefficient. The following tracking law is used to track this curve:

[0071]

[0072] where, D is the actual drag acceleration, which is equal to D r without disturbance; σ c is the bank angle value calculated using the tracking law, defined as the calculated bank angle; k d , k p are gain values; the formulas for a and b are as follows:

[0073]

[0074]

[0075]

[0076] where, h s = 9354.5 m is the height coefficient in the atmospheric density formula, g is the gravitational acceleration on the Mars surface, L is the lift acceleration, γ is the ballistic inclination angle, ω = 7.0948×10 -5 rad / s is the angular velocity of Mars' rotation, φ is the latitude of the lander, and ψ is the heading angle. The calculated bank angle value at each state can be determined by the tracking law of the formula.

[0077] Step 2: Using a three-level orthogonal table to select perturbation combinations for the atmospheric density, lift coefficient, drag coefficient, and lander mass during Mars entry, a sensitivity formula for the roll angle to these perturbation combinations was established based on the partial derivative of the roll angle with respect to each perturbation. This sensitivity formula then quantitatively determined the impact of each perturbation on the lander's controllability.

[0078] The specific implementation method of step 2 is:

[0079] Since the increase of the lander's ballistic coefficient will cause the entry trajectory to be lower, the aerodynamic disturbance will become larger, and the control ability of the lander will be affected, it is necessary to consider the impact of the uncertainty of aerodynamic parameters on the control ability, that is, to establish a mapping relationship between aerodynamic parameter disturbance and roll angle. Aerodynamic parameter disturbances generally include atmospheric density, lift coefficient, drag coefficient and lander mass disturbance. In order to effectively analyze the impact of the four disturbances on control, L9(3 4 ) The three-level orthogonal table selects disturbance combinations as typical representatives of various disturbance situations to form a combined disturbance table. L9(3 4 ) where 9 represents 9 combined perturbations, which are arranged in sequence to form a perturbation sequence; 4 represents the number of factors, which represent atmospheric density perturbation, lift coefficient perturbation, drag coefficient perturbation, and lander mass perturbation; 3 represents the number of levels, which are positive perturbation, negative perturbation, and zero perturbation, represented by the Arabic numerals 1, -1, and 0, respectively, as shown in Table 2.

[0080] Table 2 Combined perturbation table

[0081]

[0082] Among them, the amplitude of atmospheric density perturbation Δρ is 5%; the lift coefficient perturbation ΔC L and the drag coefficient disturbance ΔC D The amplitude of the lander mass perturbation Δm is 3.33%, and the amplitude of the lander mass perturbation Δm is 1%. The formula for calculating the sensitivity of the roll angle to the combined perturbation is established as follows:

[0083]

[0084] Among them, f i is the value of the sensitivity formula corresponding to the i-th combined disturbance, Δ = 100, and is the dimensionless disturbance constant. For a single disturbance, the formula reflecting the sensitivity of the roll angle to that disturbance is the partial derivative of the roll angle with respect to that disturbance. However, for combined disturbances, the dividend cannot be determined by using the partial derivative method. Therefore, the dimensionless disturbance constant Δ is used as the dividend for calculating the sensitivity of the roll angle to the combined disturbance.

[0085] According to the above table, the undisturbed case and the eight disturbances together constitute nine typical disturbance combinations. Taking the undisturbed case as the benchmark, the eight disturbances are respectively brought into the above sensitivity formula for corresponding sensitivity calculations, and the quantitative impact of aerodynamic parameter disturbances on the lander's control capability can be obtained.

[0086] Step 3: Given a given terminal velocity, design an altitude and range constraint. Design an anti-saturation index based on a formula that calculates the sensitivity of the lander's roll angle to typical perturbation combinations. Linearly weight the altitude and range constraint and the anti-saturation index to achieve a comprehensive entry trajectory optimization index that improves anti-saturation capability. This comprehensive index is optimized using an optimization method to obtain an optimized roll angle-energy profile. This profile is then tracked to obtain an anti-saturation entry trajectory, achieving anti-saturation trajectory optimization for the Mars entry phase.

[0087] The specific implementation method of step three is:

[0088] First, under the premise of a given terminal speed, the terminal constraint index J1 that meets the terminal altitude and range constraints is designed. The index is as follows:

[0089] J1=-h f +k|s togo | (22)

[0090] Among them, h f is the terminal height, k=2 is the weighting constant, s togo is the terminal range, and its formula is as follows:

[0091] s togo =R0arccos[cosφcosφ T cos(θ-θ T )+sinφsinφ T ] (twenty three)

[0092] Among them, R0=3397km is the radius of Mars, and θ is the longitude of the lander.

[0093] Secondly, at t0 and t f A time point is selected every 5 seconds as the time t sequence, so that 0 = t0 <t1<t2<...<t z =t f , z is the length of the sequence. The sensitivity of the roll angle to the combined disturbance is calculated at each time series point, and the following anti-saturation index J2 is designed based on the obtained sensitivity:

[0094]

[0095]

[0096] Where ρ0 = 0.0158 kg / m 2 is the Martian atmospheric density constant. C is a function of the time series, and the anti-saturation index J2 is obtained by summing C. The first index ensures that the trajectory meets the terminal constraint, and the second index ensures that the trajectory's anti-saturation ability is improved. Therefore, by weighting the above two indexes, we can obtain a comprehensive optimization index J that both meets the terminal constraint and improves the anti-saturation ability:

[0097] J=k1J1+k2J2 (26)

[0098] Among them, k1 and k2 are weight coefficients, with values ​​of 1 and 100 respectively.

[0099] The above comprehensive indicators are optimized by using the sequential quadratic programming method to obtain Figure 3 The tilt angle profile of the Mars entry dynamics model is integrated through the profile to obtain the state quantity at each time, and then obtain Figure 4 The reference resistance curve is shown in Figure 2. Monte Carlo simulation is used to compare this method with the traditional method without adding anti-saturation optimization indicators. Figure 5 The results show that, given the same number of drop points, the proposed method has a drop point deviation greater than 5 km in 15.6% of the cases, significantly lower than the 19% achieved by the traditional method. Furthermore, only 0.4% of the cases have a drop point deviation greater than 10 km, compared to 0.9% achieved by the traditional method. Therefore, given the same perturbation, the proposed method exhibits smaller drop point deviations and greater saturation resistance than the traditional method.

[0100] The above specific description further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. 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 in the scope of protection of the present invention.

Claims

1. Anti-saturation trajectory optimization method for Mars entry phase, characterized by: The following steps are included: Step 1: Design an energy segmentation point sequence based on the initial and terminal energies to establish a piecewise linear roll angle-energy profile. Using this profile as the control variable, integrate the Mars entry dynamics equation to obtain a reference drag acceleration curve. Track this curve using the tracking law, and the resulting roll angle is defined as the calculated roll angle. Step 2: For the perturbations of atmospheric density, lift coefficient, drag coefficient, and lander mass during the Mars entry phase, a three-level orthogonal table is used to select a perturbation combination. Based on the partial derivative of the roll angle with respect to a particular perturbation, a formula is established to calculate the sensitivity of the roll angle to the perturbation combination. Based on the sensitivity formula, the quantitative impact of the perturbation on the lander's controllability is obtained. The specific implementation method of step 2 is: Since the increase of the lander's ballistic coefficient will cause the entry trajectory to be lower and the aerodynamic disturbance to become larger, which will affect the control ability of the lander, it is necessary to consider the impact of the uncertainty of aerodynamic parameters on the control ability, that is, to establish a mapping relationship between aerodynamic parameter disturbance and roll angle; aerodynamic parameter disturbance includes atmospheric density, lift coefficient, drag coefficient and lander mass disturbance. In order to effectively analyze the impact of the four disturbances on the control, L9(3 4 ) The three-level orthogonal table selects disturbance combinations as typical representatives of various disturbance situations to form a combined disturbance table; L9(3 4 ) where 9 represents 9 combined disturbances, which are arranged in sequence to form a disturbance sequence; 3 represents the number of levels, with positive disturbance, negative disturbance, and zero disturbance selected at the three levels, represented by Arabic numerals 1, -1, and 0, respectively; 4 represents the number of factors, with the four factors representing atmospheric density disturbance Δρ, lift coefficient disturbance ΔC, and so on. L , Drag coefficient disturbance ΔC D and the lander mass perturbation Δm; the set perturbation combinations are shown in Table 1; Table 1 Combined perturbation table The formula for calculating the sensitivity of the roll angle to typical disturbance combinations is established as follows: Among them, f i is the value of the sensitivity formula corresponding to the i-th combined disturbance, and Δ is the dimensionless disturbance constant set. For a single disturbance, the formula reflecting the sensitivity of the roll angle to the disturbance is the partial derivative of the roll angle with respect to the disturbance. However, for combined disturbances, if the partial derivative method is used, the dividend cannot be given. Therefore, the dimensionless disturbance constant Δ is used as the dividend for calculating the sensitivity of the roll angle to the combined disturbance. According to the above combined perturbation table 1, the no-perturbation case and the eight perturbations together constitute nine perturbation combinations. Taking the no-perturbation case as the benchmark, the eight perturbations are respectively brought into the above sensitivity formula to perform corresponding sensitivity calculations, and the quantitative effects of the four perturbations on the lander's control capability are obtained. Step 3. Under the premise of a given terminal velocity, design an altitude and range constraint index; design an anti-saturation index based on the sensitivity formula of the lander's roll angle to typical disturbance combinations; linearly weight the two optimization indicators of altitude and range constraint index and anti-saturation index to obtain an entry trajectory optimization comprehensive index that improves anti-saturation capability, and use the optimization method to optimize the above comprehensive index to obtain the optimized roll angle-energy profile. After tracking this profile, the anti-saturation entry trajectory is obtained, thus realizing the anti-saturation trajectory optimization of the Mars entry segment.

2. The Mars entry phase anti-saturation trajectory optimization method according to claim 1, characterized in that: The specific implementation method of step one is: The energy e is defined as follows: Where μ is the Martian gravitational constant, r is the distance from the center of mass of Mars to the center of mass of the lander, and v is the flight speed of the lander. The normalized energy E is defined as follows: Among them, e0 and e f are the energies determined according to the initial and terminal states, respectively; Given a normalized energy segmentation point sequence, such that 0 = E0 <E1<E2<…<E n =1, n is the number of segments; according to the energy segmentation point sequence, a piecewise linear roll angle profile σ(E) with normalized energy as the independent variable is designed. For E j <E≤E j+1 , the corresponding roll angle is: The roll angle-energy profile is used as the amplitude of the control variable, and the sign of the control variable is determined by the roll angle inversion logic. The state at each time point is obtained by integrating the dynamic model of the Mars entry phase, and then the corresponding reference resistance acceleration D is obtained by formula (4). r , forming the reference resistance acceleration curve; Where ρ is the air density, S is the lander surface area, m is the lander mass, and C D is the drag coefficient; the curve is tracked using the following tracking law: Where D is the actual drag acceleration, which is equal to D when there is no disturbance. r ; σ c is the roll angle value calculated by the tracking law, which is defined as the calculated roll angle; k d 、k p is the gain value; the formulas for a and b are as follows: Among them, h s is the height coefficient in the atmospheric density formula, g is the gravitational acceleration of the Martian surface, L is the lift acceleration, γ is the ballistic inclination angle, φ is the latitude of the lander, ψ is the heading angle, and ω is the angular velocity of Martian rotation. The calculated roll angle value in each state is determined by the tracking law of formula (5).

3. The Mars entry phase anti-saturation trajectory optimization method according to claim 2, characterized in that: The specific implementation method of step three is: First, under the premise of a given terminal speed, the terminal constraint index J1 that meets the terminal altitude and range constraints is designed. The index is as follows: J1=-h f +k|s togo | (9) Among them, h f is the terminal height, k is the weighting constant, s togo Terminal range, the formula is as follows: s togo =R0arccos[cosφcosφ T cos(θ-θ T )+sinφsinφ T ] (10) Where R0 is the radius of Mars, θ is the longitude of the lander, and θ T With φ T are the longitude and latitude of the target point respectively; Next, set the sequence of time t so that 0 = t0 <t1<t2<...<t z =t f , z is the length of the sequence; the sensitivity of the roll angle to the combined disturbance is calculated at each time series point, and the following anti-saturation index J2 is designed based on the obtained sensitivity: Among them, σ max is the upper limit of the roll angle, σ min is the lower limit of the roll angle; C is a function of the time series, and J2 is obtained by summing C; ρ0 is the Martian atmospheric density constant; the first terminal constraint index J1 ensures that the trajectory meets the terminal constraint, and the second anti-saturation index J2 ensures that the anti-saturation ability of the trajectory is improved. Therefore, after weighting the above two indicators, the comprehensive optimization index J that satisfies the terminal constraint and improves the anti-saturation ability is obtained: J=k1J1+k2J2 (13) Among them, k1 and k2 are weight coefficients.

4. The Mars entry phase anti-saturation trajectory optimization method according to claim 3, characterized in that: The optimization method adopts a quadratic programming method.

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