CN107323691B - Multi-constraint Mars atmosphere entry prediction guidance method - Google Patents

Multi-constraint Mars atmosphere entry prediction guidance method Download PDF

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CN107323691B
CN107323691B CN201710536797.0A CN201710536797A CN107323691B CN 107323691 B CN107323691 B CN 107323691B CN 201710536797 A CN201710536797 A CN 201710536797A CN 107323691 B CN107323691 B CN 107323691B
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崔平远
龙嘉腾
高艾
刘阳
于正湜
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Beijing University of Technology
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Abstract

The invention discloses a multi-constraint mars atmospheric entry prediction guidance method, and belongs to the technical field of deep space exploration. According to the method, the peak value overload in the Mars atmosphere entering process is used as a performance index, so that the prediction guidance method which enables the peak value overload to be minimum is obtained, the peak value overload in the Mars atmosphere entering process is restrained to the maximum extent, and the overload safety margin is provided for the detector to fly in uncertain Mars atmosphere. And taking the deviation of the predicted tail end voyage and the target tail end voyage as a nonlinear equation of the switching time, solving the nonlinear equation to obtain the switching time, and improving the tail end position precision. The invention also takes the deviation of the actual terminal position and the expected terminal position as the performance index, and takes the minimum value of the deviation performance index to determine the switching time, thereby avoiding the situation of no solution which possibly occurs when a nonlinear equation is solved and improving the stability of the prediction guidance method.

Description

Multi-constraint Mars atmosphere entry prediction guidance method
Technical Field
The invention relates to a multi-constraint mars atmospheric entry prediction guidance method, and belongs to the technical field of deep space exploration.
Background
In the design of the Mars atmospheric entry section prediction guidance law, factors such as the end position precision, the parachute opening condition, the flight overload and the like need to be considered. Among other things, overloading of an aircraft has a significant impact on aircraft flight safety.
Mars atmospheric admission section guidance methods can be divided into two categories: a nominal trajectory method and a predictive guidance method. Aiming at the overload suppression problem in the guidance design process of the Mars atmosphere entering section, the two types of guidance methods adopt different guidance strategies. The nominal track method takes the peak overload which can be borne by the aircraft into consideration when designing the nominal track, so that the aircraft can meet the overload requirement when tracking the nominal track in actual flight; the prediction guidance method is characterized in that overload is predicted in the flight process, and when the overload exceeds an allowable range, an entering track is adjusted by controlling a roll angle, so that the overload requirement is met.
In the process of entering the Mars atmosphere, the safety of a detector in the process of entering the Mars atmosphere is considered, and the overload in the process of entering the atmosphere is required to be fully inhibited under the condition of meeting the precision of a terminal voyage, so that a sufficient safety margin is provided for an aircraft.
Disclosure of Invention
The invention discloses a multi-constraint mars atmosphere entry prediction guidance method, which aims to solve the technical problem that peak overload in the mars atmosphere entry process can be furthest inhibited while the end position precision is ensured, so that a sufficient safety margin is provided for an aircraft. The multiple constraints are peak overload constraints and end position constraints.
The purpose of the invention is realized by the following technical scheme:
the invention discloses a multi-constraint mars atmosphere entry prediction guidance method, which is used for obtaining a prediction guidance method for minimizing peak value overload by taking peak value overload in a mars atmosphere entry process as a performance index, so that the peak value overload in the mars atmosphere entry process is maximally inhibited at a mars atmosphere entry section, and a sufficient overload safety margin is provided for a detector flying in uncertain mars atmosphere. And the predicted deviation between the tail end voyage and the target tail end voyage is used as a nonlinear equation of the switching time, and the nonlinear equation is solved to obtain the switching time, so that the tail end position precision is improved.
The switching time is determined by taking the deviation between the actual terminal position and the expected terminal position as a performance index and taking the minimum value of the deviation performance index, so that the situation that no solution is possible when a nonlinear equation is solved by an online numerical value is avoided, and the stability of the Martian atmosphere entering the prediction guidance method is improved.
The invention discloses a multi-constraint mars atmospheric entry prediction guidance method, which comprises the following steps:
step 1, determining the form of a roll angle section of longitudinal motion under the condition of minimum peak overload.
Performing numerical integration by using a detector dynamic model until the tail end condition of a Mars atmosphere entry section is met, wherein the tail end condition of the Mars atmosphere entry section is an parachute opening condition, and obtaining parachute opening precision deviation s of the remaining longitudinal distance of parachute opening and the target position at the moment of parachute openingf. The parachute opening condition means that the dynamic pressure of the detector is in an interval qmin,qmax]Mach number of internal sum detector in interval [ Mamin,Mamax]And (4) the following steps.
Detector pair dimensionless time considering Mars rotation influence
Figure BDA0001340804900000021
The three-degree-of-freedom dimensionless entry dynamics model is
Figure BDA0001340804900000022
Wherein s is the residual longitudinal range, the distance of the surface orthodrome of the mars from the current position of the detector to the nominal tail end position is represented, R is the distance from the centroid of the mars to the centroid of the detector, and the dimensionless parameter is the radius R of the mars0V is the velocity of the probe relative to the Mars, and the dimensionless parameter is
Figure BDA0001340804900000023
Wherein g is0The method is characterized in that the Mars surface gravity acceleration is adopted, gamma is a track angle, sigma is an inclination angle, longitudinal dynamics only determines the size | sigma | of the inclination angle sigma, the sign of the inclination angle sigma has corresponding lateral logic determination, g is the local gravity acceleration, and the dimensionless parameter is g0. D and L are respectively resistance acceleration and lift acceleration
Figure BDA0001340804900000031
Dimensionless parameters of the resistance acceleration D and the lift acceleration L are both g0，CDAnd CLRespectively as drag coefficient and lift coefficient, S as reference area of detector, m as mass of detector, q ═ ρ v2Dynamic pressure,. beta.m/SCDThe coefficient of the trajectory of the detector is, and the L/D is the lift-drag ratio of the detector. The Mars atmospheric density adopts an exponential model shown as a formula (3)
Figure BDA0001340804900000032
Where ρ is0For reference density, h0For reference height, hsIs the atmospheric density elevation. The specific energy of the aircraft at the inlet section is given by the formula (4)
Figure BDA0001340804900000033
Defining overload as shown in equation (5)
Figure BDA0001340804900000034
Wherein, gE＝9.81m/s2Is the earth surface gravitational acceleration. The derivative of the overload M with respect to time is expressed by equation (6)
Figure BDA0001340804900000035
According to the principle of minimums, the performance index is
Figure BDA0001340804900000036
In the form of peak overload minimum condition
Figure BDA0001340804900000037
Wherein, phi [ x (t)f),tf]＝0,
Figure BDA0001340804900000038
tfFor the end time, the subscript "f" indicates each physical quantity, x (t), corresponding to the end timef) Is an end time pairCorresponding state vector u (t)f) Is the control variable at the end time, i.e. the magnitude of the roll angle σ. Since the overload is usually a unimodal function of time and increases first and then decreases with time, in equation (8)
Figure BDA0001340804900000041
Wherein t isMTo make it possible to
Figure BDA0001340804900000042
At the moment of time, i.e.
Figure BDA0001340804900000043
The subscript "M" denotes tMThe time corresponds to each physical quantity. Predictive guidance algorithm in interval [ t0,tM]Inter alia, overload suppression problems. Then the Hamiltonian H is, according to equation (1) of the dynamics
Figure BDA0001340804900000044
Wherein is λ ═ λr,λv,λγ,λs]TCovariate, satisfy
Figure BDA0001340804900000045
When t is less than or equal to tMTime of flight
Figure BDA0001340804900000046
The boundary condition is
x(t0)＝x0＝[r0 v0 γ0 s0]T (11)
The cross-sectional condition is
Figure BDA0001340804900000048
Wherein the content of the first and second substances,
Figure BDA0001340804900000051
Figure BDA0001340804900000052
according to the principle of minimums, there are
Figure BDA0001340804900000053
Namely, it is
Figure BDA0001340804900000054
Equation (18) obtains a section of the roll angle | σ | for minimizing the peak overload during the Mars atmosphere entry section as a switching curve. The switching curve is in the form of a roll angle profile of the longitudinal movement under the condition of minimal peak overload.
The switching curve described by the formula (18) can maximally inhibit peak overload in the process of entering the Mars atmosphere, so that a sufficient overload safety margin is provided for the detector flying in the uncertain Mars atmosphere.
And 2, determining the terminal condition which needs to be met by the longitudinal motion switch curve.
From the cross-sectional condition (13)
Figure BDA0001340804900000055
Bringing formula (12) into formula (19) as upsilonM(tM) 0. Therefore, the cross-sectional conditional expression (13) is converted to
λ(tM)＝B＝[-paM qbM 0 0]T (20)
As is known from the formula (20),
Figure BDA0001340804900000061
from the cross-sectional conditional expression (20), λM,γ(tM) 0. In the formula (21), when t is tMIn a left neighborhood of (A), there are
λM,γ<0 (22)
Then, according to equation (18), when t is tMIn a left neighborhood of (A), there are
|σ|*＝|σ|min (23)
As shown in the formula (23), the tilt angle | σ | of the longitudinal movement switch curve after the last switch to the end of the entering segment needs to satisfy the minimum value | σ |minThe terminal conditions of (1).
And 3, determining the switching time of the switching curve so as to ensure the end position precision.
The switching time is
Figure BDA00013408049000000614
The time t corresponding to the condition that the physical quantity zeta of the Mars atmosphere entering section track satisfies the formula (24)s
Figure BDA0001340804900000062
The physical quantity zeta is selected as an entering speed v or a specific energy e according to actual needs, and the corresponding switch time vs，esRespectively, switching speed, switching energy. By determining switching timing
Figure BDA00013408049000000616
The moment when the switching curve performs a switching operation is determined.
The passing determines the switching time
Figure BDA00013408049000000615
Determining switch curvesThe time searching method of the row switch operation comprises the following steps: the predicted end course s is taken throughout the entry processfVoyage with target end
Figure BDA0001340804900000063
Deviation of (2)Considering switching timing
Figure BDA0001340804900000065
By solving a non-linear equation (25) to obtain the switching timing
Figure BDA0001340804900000066
In order to increase the solving switching speed
Figure BDA0001340804900000068
Robustness of (2), will actual end position
Figure BDA0001340804900000069
And desired end position
Figure BDA00013408049000000610
Taking the deviation of (a) as a performance index, solving the value of (a) to a non-linear equation (25) to determine the switching speedIn a method of (1), the improvement is that the switching time is determined by searching for the mode of making the performance index described by the formula (26) obtain the minimum value
Figure BDA00013408049000000612
By adopting the performance index described by the formula (26), the situation that no solution is possible when the nonlinear equation (25) is solved by an online numerical value can be avoided, so that the stability of the Mars atmosphere entering the prediction guidance method is improved. Performance index as described for equation (26)
Figure BDA0001340804900000071
Optimizing so that the actual end position
Figure BDA0001340804900000072
And desired end position
Figure BDA0001340804900000073
The deviation of (a) is a minimum value, that is, the end position accuracy can be improved.
Has the advantages that:
1. the invention discloses a multi-constraint Mars atmosphere entry prediction guidance method, which takes peak value overload in a Mars atmosphere entry process as a performance index to obtain a prediction guidance method for minimizing the peak value overload, realizes the purpose of maximally inhibiting the peak value overload in the Mars atmosphere entry process at the Mars atmosphere entry stage, and thus provides a sufficient safety margin for a detector.
2. The invention discloses a multi-constraint mars atmosphere entry prediction guidance method, which is characterized in that the predicted deviation between a tail end voyage and a target tail end voyage is used as a nonlinear equation of switching time, and the nonlinear equation is solved to obtain the switching time, so that the tail end position precision is improved.
3. According to the multi-constraint mars atmosphere entry prediction guidance method disclosed by the invention, the on-off time is determined by taking the deviation between the actual terminal position and the expected terminal position as a performance index and obtaining a minimum value, so that the situation that no solution is possible when a nonlinear equation is solved by an online numerical value is avoided, and the stability of the mars atmosphere entry prediction guidance method is improved.
Drawings
FIG. 1 is a flowchart of Mars atmospheric ingress segment overload suppression instruction generation;
FIG. 2 is a plot of roll angle versus entry speed solved by the overload suppression method;
fig. 3 is a comparison of overload curves with and without the overload suppression method.
Detailed Description
For a better understanding of the objects and advantages of the invention, reference is made to the following description, taken in conjunction with the accompanying drawings, which illustrate, by way of example, the principles of the invention.
Example 1
According to the multi-constraint mars atmosphere entry prediction guidance method disclosed by the embodiment, an optimal control method is introduced into the prediction guidance law design under the multi-constraint condition of the mars atmosphere entry section for the first time, and the peak overload in the mars atmosphere entry process can be furthest suppressed while the accuracy of the tail-end parachute opening position is met by determining the section form under the minimum peak overload condition and the switching time of a switching curve, so that a sufficient overload safety margin is provided for a detector. The method comprises the following steps:
step 1, determining the form of a roll angle section of longitudinal motion under the condition of minimum peak overload.
Performing numerical integration by using a detector dynamic model until the tail end condition of a Mars atmosphere entry section is met, wherein the tail end condition of the Mars atmosphere entry section is an parachute opening condition, and obtaining parachute opening precision deviation s of the remaining longitudinal distance of parachute opening and the target position at the moment of parachute openingf. The parachute opening condition means that the dynamic pressure of the detector is in an interval qmin,qmax]Mach number of internal sum detector in interval [ Mamin,Mamax]And (4) the following steps. The specific implementation method for carrying out numerical integration by utilizing the detector dynamic model until the condition that the Mars atmosphere enters the tail end of the section comprises the following steps:
detector pair dimensionless time considering Mars rotation influenceThe three-degree-of-freedom dimensionless entry dynamics model is
Figure BDA0001340804900000082
Wherein s is the residual longitudinal range, the distance of the surface orthodrome of the mars from the current position of the detector to the nominal tail end position is represented, R is the distance from the centroid of the mars to the centroid of the detector, and the dimensionless parameter is the radius R of the mars0V is the velocity of the probe relative to the Mars, and the dimensionless parameter isWherein g is0The method is characterized in that the Mars surface gravity acceleration is adopted, gamma is a track angle, sigma is an inclination angle, longitudinal dynamics only determines the size | sigma | of the inclination angle sigma, the sign of the inclination angle sigma has corresponding lateral logic determination, g is the local gravity acceleration, and the dimensionless parameter is g0. D and L are respectively resistance acceleration and lift acceleration
Figure BDA0001340804900000084
The dimensionless parameters are all g0，CDAnd CLRespectively as drag coefficient and lift coefficient, S as reference area of detector, m as mass of detector, q ═ ρ v2Dynamic pressure,. beta.m/SCDTaking 146kg/m as the ballistic coefficient of the detector2And L/D is the lift-drag ratio of the detector and is 0.24. Mars atmospheric density adopts formula (29) exponential model
Figure BDA0001340804900000091
Where ρ is0＝2×10-4kg/m3For reference density, h040000m as reference height, hs7500m is the atmospheric density elevation. The specific energy of the aircraft at the inlet section is given by the formula (30)
Defining overload as shown in equation (31)
Figure BDA0001340804900000093
Wherein, gE＝9.81m/s2Is the earth surface gravitational acceleration. The derivative of the overload with respect to time is expressed by equation (32)
Figure BDA0001340804900000094
According to the principle of minimums, performance indexes
Figure BDA0001340804900000095
In the form of peak overload minimum condition
Wherein, phi [ x (t)f),tf]＝0,tfFor the end time, the subscript "f" indicates each physical quantity, x (t), corresponding to the end timef) For the state vector corresponding to the end time, u (t)f) Is the control variable at the end time, i.e. the magnitude of the roll angle σ. Since the overload is usually a unimodal function of time and increases first and then decreases with time, in equation (34)
Figure BDA0001340804900000098
Wherein t isMTo make it possible to
Figure BDA0001340804900000099
At the moment of time, i.e.
Figure BDA00013408049000000910
The subscript "M" denotes tMThe time corresponds to each physical quantity. Predictive guidance algorithm in interval [ t0,tM]Inter alia, overload suppression problems. Then the Hamiltonian is calculated according to equation of dynamics (27)H is
Figure BDA0001340804900000101
Wherein is λ ═ λr,λv,λγ,λs]TCovariate, satisfy
Figure BDA0001340804900000102
When t is less than or equal to tMTime of flight
The boundary condition is
x(t0)＝x0＝[r0 v0 γ0 s0]T (37)
The cross-sectional condition is
Figure BDA0001340804900000105
Figure BDA0001340804900000106
Wherein the content of the first and second substances,
Figure BDA0001340804900000111
Figure BDA0001340804900000112
according to the principle of minimums, there are
Figure BDA0001340804900000113
Namely, it is
Figure BDA0001340804900000114
Equation (44) shows that the roll angle | σ | profile that minimizes peak overload during the Mars atmosphere entry segment is a switching curve. The switching curve is in the form of a roll angle profile of the longitudinal movement under the condition of minimal peak overload.
The switching curve described by the formula (44) can maximally inhibit peak overload in the process of entering the Mars atmosphere, so that a sufficient overload safety margin is provided for the detector flying in the uncertain Mars atmosphere.
And 2, determining the terminal condition which needs to be met by the longitudinal motion switch curve.
From the cross-sectional condition (40)
Figure BDA0001340804900000115
Bringing formula (38) into formula (45) as upsilonM(tM) 0. Therefore, the cross-sectional conditional expression (39) is written
λ(tM)＝B＝[-paM qbM 0 0]T (46)
As can be seen from the formula (46),
Figure BDA0001340804900000121
from the cross-sectional conditional expression (46), λM,γ(tM) 0. In the formula (47), when t is tMIn a left neighborhood of (A), there are
λM,γ<0 (48)
Then, according to the formula (48), when t is t ═ tMIn a left neighborhood of (A), there are
|σ|*＝|σ|min (49)
As shown in equation (49), the tilt angle | σ | of the longitudinal movement switch curve is full after the last switch to the end of the entrance segmentTaking minimum value | sigma-minThe terminal conditions of (1).
And 3, determining the switching time of the switching curve so as to ensure the end position precision.
The switching time is
Figure BDA0001340804900000122
The time t corresponding to the condition that the physical quantity zeta of the Mars atmosphere entering section track satisfies the formula (50)s
Figure BDA0001340804900000123
The physical quantity zeta is selected as an entering speed v or a specific energy e according to actual needs. Corresponding switching time vs，esRespectively, switching speed, switching energy. By determining switching timing
Figure BDA0001340804900000129
To determine the moment at which the switching curve performs a switching operation. The passing determines the switching time
Figure BDA00013408049000001210
The time searching method for determining the switching curve to execute the switching operation comprises the following steps: the predicted end course s is taken throughout the entry processfVoyage with target end
Figure BDA0001340804900000124
The deviation of (A) is regarded as the switching timing
Figure BDA00013408049000001215
By solving a non-linear equation (51) to obtain the switching timing
Figure BDA00013408049000001211
Figure BDA0001340804900000125
To improve the solutionOff speed
Figure BDA00013408049000001212
Robustness of (2), will actual end positionAnd desired end position
Figure BDA0001340804900000126
Taking the deviation of (2) as a performance index, solving the value of the deviation with a non-linear equation (51) to determine the switching speed
Figure BDA00013408049000001213
In a method of (1), the improvement is that the switching time is determined by searching for a mode which enables the performance index described by the formula (52) to obtain a minimum value
Figure BDA0001340804900000127
By adopting the performance index of the formula (52), the situation that no solution exists when the nonlinear equation (51) is solved by an online numerical value can be avoided, so that the stability of the Mars atmosphere entering the prediction guidance method is improved. Performance index described for equation (52)
Figure BDA00013408049000001217
Optimizing so that the actual end positionAnd desired end position
Figure BDA0001340804900000128
The deviation of (a) is a minimum value, that is, the end position accuracy can be improved.
The simulation initial conditions are
[r0,v0,γ0,s0]＝[3522.2km,6083.3m/s,-15.48°,0.2195rad] (53)
Under the initial condition of the simulation, taking the maximum value | sigma & lt & gtof the control of the roll angle bang-bangmaxAnd minimum value | σminRespectively being | sigma-max＝70°，|σ|max20 deg. is equal to. Respectively switch on and off
Figure BDA0001340804900000131
Fig. 2 is a curve of the change of the roll angle with the entering speed, and it can be seen from the graph that the change rule of the roll angle is a switch curve. Fig. 3 shows the variation of overload with respect to the entering speed obtained with and without the overload suppression method, and it can be seen that the overload suppression method according to the present invention can significantly reduce the peak overload compared to the guidance method without the overload suppression.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (2)

1. A multi-constraint Mars atmospheric entry prediction guidance method is characterized by comprising the following steps: comprises the following steps of (a) carrying out,
step 1, determining a form of a roll angle section of longitudinal movement under a condition of minimum peak overload;
performing numerical integration by using a detector dynamic model until the tail end condition of a Mars atmosphere entry section is met, wherein the tail end condition of the Mars atmosphere entry section is an parachute opening condition, and obtaining parachute opening precision deviation s of the remaining longitudinal distance of parachute opening and the target position at the moment of parachute openingf(ii) a The parachute opening condition means that the dynamic pressure of the detector is in an interval qmin,qmax]Mach number of internal sum detector in interval [ Mamin,Mamax]Internal;
detector pair dimensionless time considering Mars rotation influenceThe three-degree-of-freedom dimensionless entry dynamics model is
Figure FDA0002196111560000012
Wherein s is the residual longitudinal range, the distance of the surface orthodrome of the mars from the current position of the detector to the nominal tail end position is represented, R is the distance from the centroid of the mars to the centroid of the detector, and the dimensionless parameter is the radius R of the mars0V is the velocity of the probe relative to the Mars, and the dimensionless parameter is
Figure FDA0002196111560000013
Wherein g is0The Mars surface gravity acceleration is determined, gamma is a track angle, sigma is an inclination angle, longitudinal dynamics only determines the size of the inclination angle sigma, the sign of the inclination angle sigma is determined by corresponding lateral logic, g is the local gravity acceleration, and the dimensionless parameter is g0(ii) a D and L are respectively resistance acceleration and lift acceleration
Figure FDA0002196111560000014
Dimensionless parameters of the resistance acceleration D and the lift acceleration L are both g0，CDAnd CLRespectively as drag coefficient and lift coefficient, S as reference area of detector, m as mass of detector, q ═ ρ v2Dynamic pressure,. beta.m/SCDThe coefficient is the ballistic coefficient of the detector, and L/D is the lift-drag ratio of the detector; the Mars atmospheric density adopts an exponential model shown as a formula (3)
Figure FDA0002196111560000015
Where ρ is0For reference density, h0For reference height, hsThe atmospheric density elevation; the specific energy of the aircraft at the inlet section is given by the formula (4)
Figure FDA0002196111560000021
Defining overload as shown in equation (5)
Figure FDA0002196111560000022
Wherein, gE＝9.81m/s2Is the earth surface gravitational acceleration; the derivative of the overload M with respect to time is expressed by equation (6)
Figure FDA0002196111560000023
According to the principle of minimums, the performance index is
Figure FDA0002196111560000024
In the form of peak overload minimum condition
Figure FDA0002196111560000025
Wherein the content of the first and second substances,tffor the end time, the subscript "f" indicates each physical quantity, x (t), corresponding to the end timef) For the state vector corresponding to the end time, u (t)f) The control variable at the end moment, i.e. the size of the roll angle | σ |; since the overload is usually a unimodal function of time and increases first and then decreases with time, in equation (8)Wherein t isMTo make it possible to
Figure FDA0002196111560000027
At the moment of time, i.e.
Figure FDA0002196111560000028
The subscript "M" denotes tMEach physical quantity corresponding to the moment; predictive guidance algorithm in interval [ t0,tM]Overload suppression issues are taken into account; then the Hamiltonian H is, according to equation (1) of the dynamics
Figure FDA0002196111560000029
Wherein the co-state variable λ ═ λr,λv,λγ,λs]TSatisfy the following requirementsWhen t is less than or equal to tMTime of flight
Figure FDA0002196111560000031
The boundary condition is
x(t0)＝x0＝[r0 v0 γ0 s0]T (11)
Figure FDA0002196111560000032
The cross-sectional condition is
Figure FDA0002196111560000033
Figure FDA0002196111560000034
Wherein the content of the first and second substances,
Figure FDA0002196111560000035
Figure FDA0002196111560000036
according to the principle of minimums, there are
Figure FDA0002196111560000037
Namely, it is
Figure FDA0002196111560000041
Obtaining a section of a roll angle sigma which enables peak overload to be minimum in the process of the Mars atmosphere entering section as a switch curve by the formula (18); the switching curve is in the form of a tilting angle section of longitudinal movement under the condition of minimum peak overload;
step 2, determining a terminal condition required to be met by a longitudinal motion switch curve;
from the cross-sectional condition (13)
Figure FDA0002196111560000042
Bringing formula (12) into formula (19) as upsilonM(tM) 0; therefore, the cross-sectional conditional expression (13) is converted to
λ(tM)＝B＝[-paM qbM 0 0]T (20)
As is known from the formula (20),
Figure FDA0002196111560000043
from the cross-sectional conditional expression (20), λM,γ(tM) 0; in the formula (21), when t is tMIn a left neighborhood of (A), there are
λM,γ＜0 (22)
Then, according to equation (18), when t is tMIn a left neighborhood of (A), there are
|σ|*＝|σ|min (23)
As shown in the formula (23), the tilt angle | σ | of the longitudinal movement switch curve after the last switch to the end of the entering segment needs to satisfy the minimum value | σ |minThe terminal conditions of (a);
and 3, determining the switching time of the switching curve so as to ensure the end position precision.
2. The multi-constraint mars atmospheric admission predictive guidance method of claim 1, wherein: the specific implementation method of the step 3 is that,
the switching time refers to the time t corresponding to the condition that the physical quantity zeta of the Mars atmosphere entering section track meets the formula (24)s
The physical quantity zeta is selected as the speed v or specific energy e of the detector relative to the spark and the switching time t according to actual requirementssThe corresponding speed is called the switching speed vsThe energy is called switching energy es(ii) a Determining the time of executing the switching operation of the switching curve by determining the switching time;
the time searching method for determining the switching curve to execute the switching operation by determining the switching time comprises the following steps: the predicted end course is processed during the whole entering process
Figure FDA0002196111560000051
Voyage with target end
Figure FDA0002196111560000052
Deviation of (2)The switching time is regarded as a nonlinear function of the switching time, and the switching time is obtained by solving a nonlinear equation (25);
Figure FDA0002196111560000054
in order to increase the solution switching speed vsRobustness of (1), the predicted end course
Figure FDA0002196111560000055
Voyage with target end
Figure FDA0002196111560000056
Taking the deviation of (a) as a performance index, solving the value of (a) a non-linear equation (26) to determine the switching speed vsIn the method of (1), the improvement is that the switching time is determined by searching the mode of enabling the performance index described by the formula (26) to obtain a minimum value;
Figure FDA0002196111560000057
by adopting the performance index of the formula (26), the situation that no solution is possible when the nonlinear equation (25) is solved by an online numerical value can be avoided, so that the stability of the Mars atmosphere entering the prediction guidance method is improved; performance index as described for equation (26)
Figure FDA0002196111560000058
Optimizing so that the predicted end voyageVoyage with target end
Figure FDA00021961115600000510
The deviation of (a) is a minimum value, that is, the end position accuracy can be improved.
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