CN104635488B - A kind of martian atmosphere approach section Robust Prediction method of guidance - Google Patents

Abstract

A kind of martian atmosphere approach section Robust Prediction method of guidance disclosed by the invention, is related to suitable for the method for guidance under model condition of uncertainty, belongs to the guidance field that spacecraft enters process in martian atmosphere.The present invention Predictor-corrector guidance method is divided into week during the Predictor-corrector guidance adaptive generation and the adaptive generation guidanceed command of cycle interior prediction that instruct, by week during the adaptive generation correction model guidanceed command of the adaptive generation that instructs of Predictor-corrector guidance and cycle interior prediction it is uncertain caused by parachute-opening position deviation s_f, robustness of the parachute-opening position deviation to model uncertainty is improved, so that reduce existing martian atmosphere approach section Predictor-corrector guidance algorithm does not know susceptibility to model, the parachute-opening precision under compared with large-sized model condition of uncertainty is improved.In addition, the present invention is during carrying out guidanceing command adaptive correction, not convergent situation caused by can overcoming or using numerical value root finding method institute possible when suppressing to guidance command generation during week.

Description

A kind of martian atmosphere approach section Robust Prediction method of guidance

Technical field

The present invention relates to a kind of martian atmosphere approach section Predictor-corrector guidance method being applied under model condition of uncertainty, belong to Spacecraft enters the guidance field of process in martian atmosphere.

Background technology

Following martian surface landing detection mission proposes higher to the precision, security and reliability of Mars landing It is required that.Successfully realize that martian surface is soft using closed loop guidance method in martian atmosphere approach section from " curious number " Marsokhod in 2011 Since landing, using method of guidance realize that the high-precision safe landing of Mars landing task turns into following Mars landing task must So selection.

Current Mars can be divided mainly into two classes into method of guidance：Nominal trajectory method and Predictor-corrector guidance method.Predictor-corrector guidance side Method due to that with higher parachute-opening location prediction precision, can be forecast to the path constraint parameter such as overload during entrance, And it is insensitive to initial reentry condition, receive extensive concern into method of guidance research field in Mars.Predictor-corrector guidance side Method be within each guidance cycle, by online numerical integration is carried out to vehicle dynamics model until meet parachute-opening condition come Forecast parachute-opening position deviation, so produce that corresponding angle of heel guidances command using parachute-opening position deviation will to meet landing precision Ask.It can be seen that, the guidance precision of Predictor-corrector guidance method is heavily dependent on the precision of on-time model.Due to working as in actual task In, the disturbance of martian atmosphere is with being uncertain of, and the factor such as detector aerodynamic parameter change, all causes caused by the reason such as Aerodynamic Ablation Predictor-corrector guidance model has differences with full-scale condition, and then has influence on the guidance precision of Predictor-corrector guidance method.For this problem, Correlative study analyzes the uncertain influence brought to Predictor-corrector guidance method of model, and model bias pair during Mars landing Into the influence of track and landing precision.

In order to during the entrance of following martian atmosphere, enable lander to realize high accuracy under model condition of uncertainty Land.It is necessary to ask model bias and uncertain more sensitive this for martian atmosphere approach section Predictor-corrector guidance algorithm Topic, designs a kind of Predictor-corrector guidance rule with robustness uncertain to model.

The content of the invention

Technical problem solved by the invention is to overcome existing martian atmosphere approach section Predictor-corrector guidance algorithm not true to model A kind of this fixed more sensitive not enough, disclosed martian atmosphere approach section Predictor-corrector guidance side being applied under model condition of uncertainty Method, can suppress parachute-opening accuracy error of the detector under compared with large-sized model condition of uncertainty.

The present invention is achieved through the following technical solutions：

A kind of martian atmosphere approach section Robust Prediction method of guidance disclosed by the invention, by the way that Predictor-corrector guidance method is divided into The adaptive generation that the adaptive generation and cycle interior prediction that Predictor-corrector guidance is instructed during week are guidanceed command, guidances command finger and flies The angle of heel σ of row device, improves parachute-opening accuracy error to compared with the robustness under large-sized model condition of uncertainty, and then improve parachute-opening essence Degree.Specifically comprise the steps of：

Step one：Guidanceed command during week is generated under conditions of there is model bias

The adaptive generation that Predictor-corrector guidance is instructed during martian atmosphere approach section week is under conditions of there is model bias, first Nominally guidanceed command first with the generation of online flight dynamics modelThen according to online flight dynamics model and reality The deviation of flying condition is to nominally guidanceing commandAdaptively correcting is carried out, generation is accordingly guidanceed commandAnd will It is used as the initial parameter that generation is guidanceed command in subsequent cycle.Specially step 1,2,3：

Step 1, carrying out using detector kinetic model numerical integration, (and parachute-opening dynamic pressure is interval to parachute-opening condition is met [q_min,q_max] and parachute-opening Mach number interval [Ma_min,Ma_max]), calculate parachute-opening residue vertical journey and the target location at parachute-opening moment Parachute-opening accuracy error s_f, concrete methods of realizing is：

Consider the detector of Mars rotation influence to nondimensional timeThree Degree Of Freedom dimensionless enter Kinetic model is：

Wherein, s is remaining vertical journey, martian surface orthodrome of the sign from detector current location to target parachute-opening position Distance, r is distance of the Mars barycenter to detector barycenter, and dimensionless group is Mars radius R₀, v detectors are relative to Mars Speed, dimensionless group isWherein g₀For martian surface acceleration of gravity, γ is flight-path angle, and σ is angle of heel, G is local gravitational acceleration, and its dimensionless group is g₀.D and L difference drag accelerations and lift acceleration：

Its dimensionless group is g₀, C_DAnd C_LRespectively resistance coefficient and lift coefficient, S are detector area of reference, m For detector quality, ρ is martian atmosphere density, q=ρ v²/ 2 be dynamic pressure, β=m/SC_DFor detector ballistic coefficient, L/D is detection Device lift-drag ratio.

In the longitudinal dynamics equation of detector, parachute-opening position deviation is to be asked by detector kinetic model numerical integration Residue when obtaining parachute-opening indulges journey

s_f=s (t_f) (3)

Wherein, t_fFor the parachute-opening moment.

Step 2, the parachute-opening position deviation obtained using step 1 calculating, when each cycle starts, are generated using secant method Nominally guidance command

When j-th of guidance cycle starts, current with detector navigation system is output as integrating state initial value, according to step Rapid 1 obtains with current angle of heel initial valueCorresponding parachute-opening accuracy errorUsing secant method

It is iterated to meeting convergence criterionSolve and cause parachute-opening position deviation s_f=0 angle of heel InstructionNominally guidanceed command during the week in j-th of cycle as under nominal condition.

Step 3, consider model condition of uncertainty, to the week under the nominal condition that is produced in step 2 during guidance commandOnline adaptive amendment is carried out, so as to tentatively improve parachute-opening precision.The resistance that the uncertainty of model is exported with on-time model Power acceleration D_mThe drag acceleration D exported with navigation system ratio is characterized：

Introduce deviation

e_y=k (D_m-D) (6)

Nominally guidanceed command for what correction number prediction algorithm was generatedOpen caused by on-time model deviation with being corrected Umbrella position deviation.Guidance command and be modified during herein using PI corrections to week, method is as follows：

Wherein,Guidanceed command during week for j-th of cycle after correction, e_y(t) it is model bias, order For gain vector, and it is broken down into ratio adjustment gain Vector differential correction gain vector

K (t)=K_P(t)+K_I(t) (8)

Wherein

K_P(t)=e_y(t)r^T(t)T_P (9)

Corrected, nominally guidanceed command by amendment by above-mentioned PIObtain corresponding corrective guidance commandCome Amendment is due to parachute-opening position deviation s caused by model uncertainty_f。

Step 2：Adaptive generation is guidanceed command in the cycle, further improves parachute-opening positional precision.

Martian atmosphere approach section week during guidance command generation j-th of cycle start when guidance commandBasis On, when guidanceing command generation within the martian atmosphere approach section cycle, nominal week is produced by the tilt angle sections of parametrization first Guidanceed command in phase, then nominal instruction is corrected according to model bias, parachute-opening positional precision is further improved.It is specific real Applying method is divided into step 4,5：

Step 4, inside j-th of guidance cycle, using the nominal system of linear tilt angle sections generation of following parametrization Lead instruction

Wherein,WithRepresent energy corresponding when j-th of guidance cycle starts respectively and by week during method of guidance The nominal angle of heel (nominally guidanceing command) of generation；WithRepresent respectively in j-th of guidance cycle, the cycle of ith generation Energy and generation when inside guidanceing command are guidanceed command；e_fAnd σ_fThe energy and angle of heel at difference parachute-opening moment.σ_fSet to be variable Count constant.

Step 5, to being guidanceed command in nominal periodCarry out adaptive correction, generation

It is to correct on-time model deviation to being guidanceed command in the cycleInfluence, the model bias in introduction-type (6) uses To correct σ_f。

Then by formula (12) and formula (13), guidanceed command in the cycle after correctionFor

So as to parachute-opening position deviation s caused by not known by corrective guidance command come correction model_f, improve parachute-opening position Deviation is not known to the robustness of model uncertainty so as to reduce existing martian atmosphere approach section Predictor-corrector guidance algorithm to model Susceptibility, improves the parachute-opening precision under compared with large-sized model condition of uncertainty.

By the adaptive correction guidanceed command and guidanceed command in the cycle during to week, overcome or suppress to guide during week During instruction generation, using not convergent situation caused by numerical value root finding method institute possibility.

Beneficial effect

1st, a kind of martian atmosphere approach section Robust Prediction method of guidance disclosed by the invention first introduces adaptive approach Guidanceed command during to week and the amendment guidanceed command in the cycle in, with the uncertain shadow to Predictor-corrector guidance precision of calibration model Ring, so as to improve Predictor-corrector guidance precision for the uncertain robustness of model, reduce existing martian atmosphere approach section prediction Guidance algorithm does not know susceptibility to model, improves the parachute-opening precision under compared with large-sized model condition of uncertainty.

2nd, during carrying out guidanceing command adaptive correction, when overcoming or suppressing to guidance command generation during week, adopt With not convergent situation caused by numerical value root finding method institute possibility.

Brief description of the drawings

Fig. 1 is martian atmosphere approach section Predictor-corrector guidance method flow diagram；

Fig. 2 guidances command PI adaptively correcting structure charts during being week.

Embodiment

By the guidance process of whole martian atmosphere approach section, △ t=1s are divided into some guidance weeks at regular intervals Phase.Online numerical integration is carried out using online kinetic model when each guidance cycle starts, parachute-opening position deviation is forecast, and Numerical value root finding method is used according to parachute-opening position deviation, solves and guidances command accordingly, i.e., is guidanceed command during week；In guidance Inside cycle, guidance command to parameterize section generation accordingly, i.e., guidanceed command in the cycle.This Predictor-corrector guidance method is divided into week The adaptive generation that the adaptive generation and cycle interior prediction of period Predictor-corrector guidance instruction are guidanceed command, is comprised the steps of First, two：

Step one：Guidanceed command during week is generated under conditions of there is model bias

The adaptive generation that Predictor-corrector guidance is instructed during martian atmosphere approach section week is under conditions of there is model bias, first Nominally guidanceed command first with the generation of online flight dynamics modelThen according to online flight dynamics model and reality The deviation of flying condition is to nominally guidanceing commandAdaptively correcting is carried out, generation is accordingly guidanceed commandAnd will It is used as the initial parameter that generation is guidanceed command in subsequent cycle.Specially step 1,2,3：

Step 1, carrying out using detector kinetic model numerical integration, (and parachute-opening dynamic pressure is interval to parachute-opening condition is met [q_min,q_max] and parachute-opening Mach number interval [Ma_min,Ma_max]), calculate parachute-opening residue vertical journey and the target location at parachute-opening moment Parachute-opening accuracy error s_f, concrete methods of realizing is：

Consider the detector of Mars rotation influence to nondimensional timeThree Degree Of Freedom dimensionless enter Kinetic model is：

Wherein, s is remaining vertical journey, martian surface orthodrome of the sign from detector current location to target parachute-opening position Distance, r is distance of the Mars barycenter to detector barycenter, and dimensionless group is Mars radius R₀, v detectors are relative to Mars Speed, dimensionless group isWherein g₀=3.71m/s²For martian surface acceleration of gravity, γ is flight-path angle, σ For angle of heel, g is local gravitational acceleration, and its dimensionless group is g₀.D and L difference drag accelerations and lift acceleration

Its dimensionless group is g₀, C_DAnd C_LRespectively resistance coefficient and lift coefficient, S are detector area of reference, m For detector quality, ρ is martian atmosphere density, q=ρ v²/ 2 be dynamic pressure, β=m/SC_DFor detector ballistic coefficient, L/D is detection Device lift-drag ratio.Martian atmosphere density uses the models of Mars-GRAM 2001.

Get fire star radius R₀=3396km, detector lift-drag ratio L/D=0.24, ballistic coefficient β=146kg/m², entering The initial state vector of the nondimensionalization of interface is x₀=[0.2356,1.0368,1.5488, -0.0269].

In the longitudinal dynamics equation of detector, parachute-opening position deviation is to be asked by detector kinetic model numerical integration Residue when obtaining parachute-opening indulges journey

s_f=s (t_f) (17)

Wherein, t_fFor the parachute-opening moment.

Step 2, the parachute-opening position deviation obtained using step 1 calculating, when each cycle starts, are generated using secant method Nominally guidance command

When j-th of guidance cycle starts, current with detector navigation system is output as integrating state initial value, according to step Rapid 1 obtains with current angle of heel initial valueCorresponding parachute-opening accuracy errorUsing secant method

It is iterated to meeting convergence criterionSolve and cause parachute-opening position deviation s_f=0 angle of heel InstructionNominally guidanceed command during the week in j-th of cycle as under nominal condition.

Step 3, consider model condition of uncertainty, to the week under the nominal condition that is produced in step 2 during guidance commandOnline adaptive amendment is carried out, so as to tentatively improve parachute-opening precision.The resistance that the uncertainty of model is exported with on-time model Power acceleration D_mThe drag acceleration D exported with navigation system ratio is characterized：

△_model=D_m-D (19)

Introduce deviation

e_y=k △_model (20)

Nominally guidanceed command for what correction number prediction algorithm was generatedOpen caused by on-time model deviation with being corrected Umbrella position deviation.Guidance command and be modified during herein using PI corrections to week, method is as follows：

Wherein,Guidanceed command during week for j-th of cycle after correction, e_y(t) it is model bias, order For gain vector, and it is broken down into ratio adjustment gain Vector differential correction gain vector

K (t)=K_P(t)+K_I(t) (22)

Wherein

K_P(t)=e_y(t)r^T(t)T_P (23)

K_I,0=[0,0.798],

Corrected, nominally guidanceed command by amendment by above-mentioned PIObtain corresponding corrective guidance commandCome Amendment is due to parachute-opening position deviation s caused by model uncertainty_f。

Step 2：Adaptive generation is guidanceed command in the cycle, further improves parachute-opening positional precision.

Martian atmosphere approach section week during guidance command generation j-th of cycle start when guidance commandBasis On, when guidanceing command generation within the martian atmosphere approach section cycle, nominal week is produced by the tilt angle sections of parametrization first Guidanceed command in phase, then nominal instruction is corrected according to model bias, parachute-opening positional precision is further improved.It is specific real Applying method is divided into step 4,5：

Step 4, inside j-th of guidance cycle, using the nominal system of linear tilt angle sections generation of following parametrization Lead instruction

Wherein,WithRepresent energy corresponding when j-th of guidance cycle starts respectively and by week during guidance side The nominal angle of heel (nominally guidanceing command) of method generation；WithRepresent respectively in j-th of guidance cycle, the week of ith generation Energy and generation when being guidanceed command in the phase are guidanceed command；e_fAnd σ_fThe energy and angle of heel at difference parachute-opening moment.σ_fTo be variable Design constant.

Step 5, to being guidanceed command in nominal periodCarry out adaptive correction, generation

It is to correct on-time model deviation to being guidanceed command in the cycleInfluence, the model bias in introduction-type (6) uses To correct σ_f。

Then by formula (12) and formula (13), guidanceed command in the cycle after correctionFor

Wherein, chooseε=80.Table 1 is given under 5 kinds of model bias level conditions, in correction model Parachute-opening positional precision before and after deviation.

Parachute-opening positional precision before and after the correction model deviation of table 1

△model	1.0	1.1	1.2	1.3	1.5
						The parachute-opening positional precision (km) of non-correction model deviation	0.76	1.71	3.46	5.85	18.1
Using the parachute-opening positional precision (km) of context of methods correction model deviation	-0.007	1.39	3.06	4.58	7.21

Guidanceed command as it can be seen from table 1 introducing model bias to correct under model condition of uncertainty to parachute-opening position Deviation has stronger capability for correcting.So as to parachute-opening position deviation caused by not known by corrective guidance command come correction model s_f, robustness of the parachute-opening position deviation to model uncertainty is improved, so as to reduce existing martian atmosphere approach section Predictor-corrector guidance Algorithm does not know susceptibility to model, improves the parachute-opening precision under compared with large-sized model condition of uncertainty.

By the adaptive correction guidanceed command and guidanceed command in the cycle during to week, overcome or suppress to guide during week During instruction generation, using not convergent situation caused by numerical value root finding method institute possibility.

The scope of the present invention is not only limited to embodiment, and embodiment is used to explaining the present invention, it is all with of the invention identical Change or modification under the conditions of principle and design is within protection domain disclosed by the invention.

Claims (2)

1. a kind of martian atmosphere approach section Robust Prediction method of guidance, it is characterised in that：Implement step as follows,

Step one：Guidanceed command during week is generated under conditions of there is model bias

The adaptive generation that Predictor-corrector guidance is instructed during martian atmosphere approach section week is under conditions of there is model bias, sharp first Nominally guidanceed command with the generation of online flight dynamics modelThen according to online flight dynamics model and practical flight The deviation of condition is to nominally guidanceing commandAdaptively correcting is carried out, generation is accordingly guidanceed commandAnd willAs rear The initial parameter of generation is guidanceed command in the continuous cycle；

Step 2：Adaptive generation is guidanceed command in the cycle, further improves parachute-opening positional precision；

Martian atmosphere approach section week during guidance command generation j-th of cycle start when guidance commandOn the basis of, When martian atmosphere guidances command generation in the approach section cycle, produced in nominal period make by the tilt angle sections of parametrization first Instruction is led, then nominal instruction is corrected according to model bias, parachute-opening positional precision is further improved；

Step one：Guidanceed command during week is generated under conditions of there is model biasImplement step for step 1,2, 3：

Step 1, using detector kinetic model numerical integration is carried out to meeting parachute-opening condition, i.e. parachute-opening dynamic pressure interval [q_min, q_max] and parachute-opening Mach number interval [Ma_min,Ma_max], calculate the vertical journey of parachute-opening residue and the parachute-opening position of target location at parachute-opening moment Put deviation s_f, concrete methods of realizing is：

Consider the detector of Mars rotation influence to nondimensional timeThree Degree Of Freedom dimensionless enter power Learning model is：

$\left\{\begin{array}{c}\stackrel{\·}{s}=-\frac{v\cos \mathrm{\γ}}{r}\\ \stackrel{\·}{r}=v\sin \mathrm{\γ}\\ \stackrel{\·}{v}=-D-\left(\frac{sin\mathrm{\γ}}{r^2}\right)\\ \stackrel{\·}{\mathrm{\γ}}=\frac{1}{v}\[L\cos \mathrm{\σ}+(v^2-\frac{1}{r})\left(\frac{\cos \mathrm{\γ}}{r^2}\right)\]\end{array}\right.$

Wherein, s is remaining vertical journey, characterize martian surface orthodrome from detector current location to target parachute-opening position away from From r is distance of the Mars barycenter to detector barycenter, and dimensionless group is Mars radius R₀, speed of the v detectors relative to Mars Spend, dimensionless group isWherein g₀For martian surface acceleration of gravity, γ is flight-path angle, and σ is angle of heel, and g is Local gravitational acceleration, its dimensionless group is g₀；D and L difference drag accelerations and lift acceleration：

$D=\frac{1}{2}{\mathrm{\ρv}}^2\frac{S}{m}{C}_D=q/\mathrm{\β},L=\frac{1}{2}{\mathrm{\ρv}}^2\frac{S}{m}{C}_L=D\·(L/D)$

Its dimensionless group is g₀, C_DAnd C_LRespectively resistance coefficient and lift coefficient, S is detector area of reference, and m is visits Device quality is surveyed, ρ is martian atmosphere density, q=ρ v²/ 2 be dynamic pressure, β=m/SC_DFor detector ballistic coefficient, L/D is detector liter Resistance ratio；

In the longitudinal dynamics equation of detector, parachute-opening position deviation is to be tried to achieve out by detector kinetic model numerical integration Residue during umbrella indulges journey

s_f=s (t_f)

Wherein, t_fFor the parachute-opening moment；

Step 2, the parachute-opening position deviation obtained using step 1 calculating, when each cycle starts, are generated nominal using secant method Guidance command

When j-th of guidance cycle starts, current with detector navigation system is output as integrating state initial value, according to step 1 Obtain with current angle of heel initial valueCorresponding parachute-opening position deviationUsing secant method

${\mathrm{\σ}}_j^{(k+1)}={\mathrm{\σ}}_j^{\left(k\right)}-\frac{{\mathrm{\σ}}_j^{\left(k\right)}-{\mathrm{\σ}}_j^{(k-1)}}{s_f\left({\mathrm{\σ}}_j^{\left(k\right)}\right)-s_f\left({\mathrm{\σ}}_j^{(k-1)}\right)}{s}_f\left({\mathrm{\σ}}_j^{\left(k\right)}\right)$

It is iterated to meeting convergence criterionSolve and cause parachute-opening position deviation s_f=0 angle of heel instructionNominally guidanceed command during the week in j-th of cycle as under nominal condition；

Step 3, consider model condition of uncertainty, to the week under the nominal condition that is produced in step 2 during guidance commandCarry out Online adaptive amendment, so as to tentatively improve parachute-opening precision；The drag acceleration that the uncertainty of model is exported with on-time model D_mThe drag acceleration D exported with navigation system ratio is characterized：

${\mathrm{\Δ}}_{\mathrm{mod}el}=\frac{D_m}{D}$

Introduce deviation

e_y=k (D_m-D)

Nominally guidanceed command for what correction number prediction algorithm was generatedTo correct parachute-opening position caused by on-time model deviation Put deviation；Guidance command and be modified during being corrected using PI to week, method is as follows：

$\left|{\widehat{\mathrm{\σ}}}_j^0\right|=K_{e_y}\left(t\right)e_y\left(t\right)+K_{u_m}\left(t\right)\left|{\mathrm{\σ}}_j^0\right|=K\left(t\right)r\left(t\right)$

Wherein,Guidanceed command during week for j-th of cycle after correction, e_y(t) it is model bias, orderFor gain vector, and it is broken down into ratio adjustment gain Vector differential correction gain vector

K (t)=K_P(t)+K_I(t)

Wherein

K_P(t)=e_y(t)r^T(t)T_P

$K_I\left(t\right)=K_{I,0}+{\∫}_0^t{\stackrel{\·}{K}}_I\left(t\right)dt$

${\stackrel{\·}{K}}_I\left(t\right)=e_y\left(t\right)r^T\left(t\right)T_I$

Corrected, nominally guidanceed command by amendment by above-mentioned PIObtain corresponding corrective guidance commandCome correct by The parachute-opening position deviation s caused by model uncertainty_f。

2. a kind of martian atmosphere approach section Robust Prediction method of guidance according to claim 1, it is characterised in that：Step Two：Adaptive generation is guidanceed command in the cycle, further improves parachute-opening positional precision, and specific implementation method is divided into step 4,5：

Step 4, inside j-th of guidance cycle, referred to using the nominal guidance of linear tilt angle sections generation of following parametrization Order

$\left|{\mathrm{\σ}}_j^i\right|={\mathrm{\σ}}_j^0+\frac{({\mathrm{\σ}}_f-{\mathrm{\σ}}_j^0)}{(e_f-e_j^0)}(e_j^i-e_j^0)$

Wherein,WithRepresent energy corresponding when j-th of guidance cycle starts respectively and by week during method of guidance generate Nominal angle of heel (nominally guidanceing command)；WithRepresent in j-th of guidance cycle, made in the cycle of ith generation respectively Energy and generation when leading instruction are guidanceed command；e_fAnd σ_fThe energy and angle of heel at difference parachute-opening moment；σ_fIt is normal for Variable Designing Of Number；

Step 5, to being guidanceed command in nominal periodCarry out adaptive correction, generation

It is to correct on-time model deviation to being guidanceed command in the cycleInfluence, the model bias in introduction-type is to correct σ_f；

${\widehat{\mathrm{\σ}}}_f={\mathrm{\σ}}_f+{\mathrm{\ϵe}}_y$

Then by formula and formula, guidanceed command in the cycle after correctionFor

$\left|{\widehat{\mathrm{\σ}}}_j^i\right|={\mathrm{\σ}}_j^0+\frac{({\widehat{\mathrm{\σ}}}_j-{\mathrm{\σ}}_j^0)}{(e_f-e_j^0)}(e_j^i-e_j^0)$

So as to parachute-opening position deviation s caused by not known by corrective guidance command come correction model_f, improve parachute-opening position deviation To the robustness of model uncertainty, so as to reduce existing martian atmosphere approach section Predictor-corrector guidance algorithm to the uncertain sensitivity of model Degree, improves the parachute-opening precision under compared with large-sized model condition of uncertainty.